Actual source code: mpimatmatmult.c
petsc-3.7.1 2016-05-15
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      2: /*
      3:   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
      4:           C = A * B
      5: */
      6: #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
      7: #include <../src/mat/utils/freespace.h>
      8: #include <../src/mat/impls/aij/mpi/mpiaij.h>
      9: #include <petscbt.h>
     10: #include <../src/mat/impls/dense/mpi/mpidense.h>
     11: #include <petsc/private/vecimpl.h>

     15: PETSC_INTERN PetscErrorCode MatMatMult_MPIAIJ_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill, Mat *C)
     16: {
     18:   const char     *algTypes[2] = {"scalable","nonscalable"};
     19:   PetscInt       alg=1; /* set default algorithm */
     20:   MPI_Comm       comm;

     23:   if (scall == MAT_INITIAL_MATRIX) {
     24:     PetscObjectGetComm((PetscObject)A,&comm);
     25:     if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);

     27:     PetscObjectOptionsBegin((PetscObject)A);
     28:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,2,algTypes[1],&alg,NULL);
     29:     PetscOptionsEnd();

     31:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
     32:     switch (alg) {
     33:     case 1:
     34:       MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
     35:       break;
     36:     default:
     37:       MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
     38:       break;
     39:     }
     40:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
     41:   }
     42:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
     43:   (*(*C)->ops->matmultnumeric)(A,B,*C);
     44:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
     45:   return(0);
     46: }

     50: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
     51: {
     53:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
     54:   Mat_PtAPMPI    *ptap = a->ptap;

     57:   PetscFree2(ptap->startsj_s,ptap->startsj_r);
     58:   PetscFree(ptap->bufa);
     59:   MatDestroy(&ptap->P_loc);
     60:   MatDestroy(&ptap->P_oth);
     61:   MatDestroy(&ptap->Pt);
     62:   PetscFree(ptap->api);
     63:   PetscFree(ptap->apj);
     64:   PetscFree(ptap->apa);
     65:   ptap->destroy(A);
     66:   PetscFree(ptap);
     67:   return(0);
     68: }

     72: PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult(Mat A, MatDuplicateOption op, Mat *M)
     73: {
     75:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
     76:   Mat_PtAPMPI    *ptap = a->ptap;

     79:   (*ptap->duplicate)(A,op,M);

     81:   (*M)->ops->destroy   = ptap->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's special structure! */
     82:   (*M)->ops->duplicate = ptap->duplicate; /* = MatDuplicate_MPIAIJ */
     83:   return(0);
     84: }

     88: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
     89: {
     91:   Mat_MPIAIJ     *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
     92:   Mat_SeqAIJ     *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
     93:   Mat_SeqAIJ     *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
     94:   PetscScalar    *cda=cd->a,*coa=co->a;
     95:   Mat_SeqAIJ     *p_loc,*p_oth;
     96:   PetscScalar    *apa,*ca;
     97:   PetscInt       cm   =C->rmap->n;
     98:   Mat_PtAPMPI    *ptap=c->ptap;
     99:   PetscInt       *api,*apj,*apJ,i,k;
    100:   PetscInt       cstart=C->cmap->rstart;
    101:   PetscInt       cdnz,conz,k0,k1;
    102:   MPI_Comm       comm;
    103:   PetscMPIInt    size;

    106:   PetscObjectGetComm((PetscObject)A,&comm);
    107:   MPI_Comm_size(comm,&size);

    109:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    110:   /*-----------------------------------------------------*/
    111:   /* update numerical values of P_oth and P_loc */
    112:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    113:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    115:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    116:   /*----------------------------------------------------------*/
    117:   /* get data from symbolic products */
    118:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    119:   p_oth = NULL;
    120:   if (size >1) {
    121:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    122:   }

    124:   /* get apa for storing dense row A[i,:]*P */
    125:   apa = ptap->apa;

    127:   api = ptap->api;
    128:   apj = ptap->apj;
    129:   for (i=0; i<cm; i++) {
    130:     /* compute apa = A[i,:]*P */
    131:     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);

    133:     /* set values in C */
    134:     apJ  = apj + api[i];
    135:     cdnz = cd->i[i+1] - cd->i[i];
    136:     conz = co->i[i+1] - co->i[i];

    138:     /* 1st off-diagoanl part of C */
    139:     ca = coa + co->i[i];
    140:     k  = 0;
    141:     for (k0=0; k0<conz; k0++) {
    142:       if (apJ[k] >= cstart) break;
    143:       ca[k0]      = apa[apJ[k]];
    144:       apa[apJ[k]] = 0.0;
    145:       k++;
    146:     }

    148:     /* diagonal part of C */
    149:     ca = cda + cd->i[i];
    150:     for (k1=0; k1<cdnz; k1++) {
    151:       ca[k1]      = apa[apJ[k]];
    152:       apa[apJ[k]] = 0.0;
    153:       k++;
    154:     }

    156:     /* 2nd off-diagoanl part of C */
    157:     ca = coa + co->i[i];
    158:     for (; k0<conz; k0++) {
    159:       ca[k0]      = apa[apJ[k]];
    160:       apa[apJ[k]] = 0.0;
    161:       k++;
    162:     }
    163:   }
    164:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    165:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    166:   return(0);
    167: }

    171: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat *C)
    172: {
    173:   PetscErrorCode     ierr;
    174:   MPI_Comm           comm;
    175:   PetscMPIInt        size;
    176:   Mat                Cmpi;
    177:   Mat_PtAPMPI        *ptap;
    178:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
    179:   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data,*c;
    180:   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    181:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    182:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    183:   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
    184:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n,Crmax;
    185:   PetscBT            lnkbt;
    186:   PetscScalar        *apa;
    187:   PetscReal          afill;
    188:   PetscTable         ta;

    191:   PetscObjectGetComm((PetscObject)A,&comm);
    192:   MPI_Comm_size(comm,&size);

    194:   /* create struct Mat_PtAPMPI and attached it to C later */
    195:   PetscNew(&ptap);

    197:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    198:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

    200:   /* get P_loc by taking all local rows of P */
    201:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    203:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    204:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    205:   if (size > 1) {
    206:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    207:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    208:   } else {
    209:     p_oth = NULL;
    210:     pi_oth = NULL; pj_oth = NULL;
    211:   }

    213:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    214:   /*-------------------------------------------------------------------*/
    215:   PetscMalloc1(am+2,&api);
    216:   ptap->api = api;
    217:   api[0]    = 0;

    219:   /* create and initialize a linked list */
    220:   PetscTableCreate(pN,pN,&ta);
    221:   MatRowMergeMax_SeqAIJ(p_loc,ptap->P_loc->rmap->N,ta);
    222:   MatRowMergeMax_SeqAIJ(p_oth,ptap->P_oth->rmap->N,ta);
    223:   PetscTableGetCount(ta,&Crmax);
    224:   PetscTableDestroy(&ta);

    226:   PetscLLCondensedCreate(Crmax,pN,&lnk,&lnkbt);

    228:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    229:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
    230:   current_space = free_space;

    232:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    233:   for (i=0; i<am; i++) {
    234:     /* diagonal portion of A */
    235:     nzi = adi[i+1] - adi[i];
    236:     for (j=0; j<nzi; j++) {
    237:       row  = *adj++;
    238:       pnz  = pi_loc[row+1] - pi_loc[row];
    239:       Jptr = pj_loc + pi_loc[row];
    240:       /* add non-zero cols of P into the sorted linked list lnk */
    241:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    242:     }
    243:     /* off-diagonal portion of A */
    244:     nzi = aoi[i+1] - aoi[i];
    245:     for (j=0; j<nzi; j++) {
    246:       row  = *aoj++;
    247:       pnz  = pi_oth[row+1] - pi_oth[row];
    248:       Jptr = pj_oth + pi_oth[row];
    249:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    250:     }

    252:     apnz     = lnk[0];
    253:     api[i+1] = api[i] + apnz;

    255:     /* if free space is not available, double the total space in the list */
    256:     if (current_space->local_remaining<apnz) {
    257:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    258:       nspacedouble++;
    259:     }

    261:     /* Copy data into free space, then initialize lnk */
    262:     PetscLLCondensedClean(pN,apnz,current_space->array,lnk,lnkbt);
    263:     MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);

    265:     current_space->array           += apnz;
    266:     current_space->local_used      += apnz;
    267:     current_space->local_remaining -= apnz;
    268:   }

    270:   /* Allocate space for apj, initialize apj, and */
    271:   /* destroy list of free space and other temporary array(s) */
    272:   PetscMalloc1(api[am]+1,&ptap->apj);
    273:   apj  = ptap->apj;
    274:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    275:   PetscLLDestroy(lnk,lnkbt);

    277:   /* malloc apa to store dense row A[i,:]*P */
    278:   PetscCalloc1(pN,&apa);

    280:   ptap->apa = apa;

    282:   /* create and assemble symbolic parallel matrix Cmpi */
    283:   /*----------------------------------------------------*/
    284:   MatCreate(comm,&Cmpi);
    285:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    286:   MatSetBlockSizesFromMats(Cmpi,A,P);

    288:   MatSetType(Cmpi,MATMPIAIJ);
    289:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
    290:   MatPreallocateFinalize(dnz,onz);
    291:   for (i=0; i<am; i++) {
    292:     row  = i + rstart;
    293:     apnz = api[i+1] - api[i];
    294:     MatSetValues(Cmpi,1,&row,apnz,apj,apa,INSERT_VALUES);
    295:     apj += apnz;
    296:   }
    297:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
    298:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);

    300:   ptap->destroy        = Cmpi->ops->destroy;
    301:   ptap->duplicate      = Cmpi->ops->duplicate;
    302:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    303:   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
    304:   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatMatMult;

    306:   /* attach the supporting struct to Cmpi for reuse */
    307:   c       = (Mat_MPIAIJ*)Cmpi->data;
    308:   c->ptap = ptap;

    310:   *C = Cmpi;

    312:   /* set MatInfo */
    313:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    314:   if (afill < 1.0) afill = 1.0;
    315:   Cmpi->info.mallocs           = nspacedouble;
    316:   Cmpi->info.fill_ratio_given  = fill;
    317:   Cmpi->info.fill_ratio_needed = afill;

    319: #if defined(PETSC_USE_INFO)
    320:   if (api[am]) {
    321:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    322:     PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    323:   } else {
    324:     PetscInfo(Cmpi,"Empty matrix product\n");
    325:   }
    326: #endif
    327:   return(0);
    328: }

    332: PETSC_INTERN PetscErrorCode MatMatMult_MPIAIJ_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
    333: {

    337:   if (scall == MAT_INITIAL_MATRIX) {
    338:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
    339:     MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,fill,C);
    340:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
    341:   }
    342:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
    343:   MatMatMultNumeric_MPIAIJ_MPIDense(A,B,*C);
    344:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
    345:   return(0);
    346: }

    348: typedef struct {
    349:   Mat         workB;
    350:   PetscScalar *rvalues,*svalues;
    351:   MPI_Request *rwaits,*swaits;
    352: } MPIAIJ_MPIDense;

    356: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
    357: {
    358:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*) ctx;
    359:   PetscErrorCode  ierr;

    362:   MatDestroy(&contents->workB);
    363:   PetscFree4(contents->rvalues,contents->svalues,contents->rwaits,contents->swaits);
    364:   PetscFree(contents);
    365:   return(0);
    366: }

    370: /*
    371:     This is a "dummy function" that handles the case where matrix C was created as a dense matrix
    372:   directly by the user and passed to MatMatMult() with the MAT_REUSE_MATRIX option

    374:   It is the same as MatMatMultSymbolic_MPIAIJ_MPIDense() except does not create C
    375: */
    376: PetscErrorCode MatMatMultNumeric_MPIDense(Mat A,Mat B,Mat C)
    377: {
    378:   PetscErrorCode         ierr;
    379:   PetscBool              flg;
    380:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
    381:   PetscInt               nz   = aij->B->cmap->n;
    382:   PetscContainer         container;
    383:   MPIAIJ_MPIDense        *contents;
    384:   VecScatter             ctx   = aij->Mvctx;
    385:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
    386:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;

    389:   PetscObjectTypeCompare((PetscObject)B,MATMPIDENSE,&flg);
    390:   if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Second matrix must be mpidense");

    392:   /* Handle case where where user provided the final C matrix rather than calling MatMatMult() with MAT_INITIAL_MATRIX*/
    393:   PetscObjectTypeCompare((PetscObject)A,MATMPIAIJ,&flg);
    394:   if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"First matrix must be MPIAIJ");

    396:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;

    398:   PetscNew(&contents);
    399:   /* Create work matrix used to store off processor rows of B needed for local product */
    400:   MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);
    401:   /* Create work arrays needed */
    402:   PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues,
    403:                       B->cmap->N*to->starts[to->n],&contents->svalues,
    404:                       from->n,&contents->rwaits,
    405:                       to->n,&contents->swaits);

    407:   PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);
    408:   PetscContainerSetPointer(container,contents);
    409:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
    410:   PetscObjectCompose((PetscObject)C,"workB",(PetscObject)container);
    411:   PetscContainerDestroy(&container);

    413:   (*C->ops->matmultnumeric)(A,B,C);
    414:   return(0);
    415: }

    419: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
    420: {
    421:   PetscErrorCode         ierr;
    422:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
    423:   PetscInt               nz   = aij->B->cmap->n;
    424:   PetscContainer         container;
    425:   MPIAIJ_MPIDense        *contents;
    426:   VecScatter             ctx   = aij->Mvctx;
    427:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
    428:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;
    429:   PetscInt               m     = A->rmap->n,n=B->cmap->n;

    432:   MatCreate(PetscObjectComm((PetscObject)B),C);
    433:   MatSetSizes(*C,m,n,A->rmap->N,B->cmap->N);
    434:   MatSetBlockSizesFromMats(*C,A,B);
    435:   MatSetType(*C,MATMPIDENSE);
    436:   MatMPIDenseSetPreallocation(*C,NULL);
    437:   MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);
    438:   MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);

    440:   (*C)->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;

    442:   PetscNew(&contents);
    443:   /* Create work matrix used to store off processor rows of B needed for local product */
    444:   MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);
    445:   /* Create work arrays needed */
    446:   PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues,
    447:                       B->cmap->N*to->starts[to->n],&contents->svalues,
    448:                       from->n,&contents->rwaits,
    449:                       to->n,&contents->swaits);

    451:   PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);
    452:   PetscContainerSetPointer(container,contents);
    453:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
    454:   PetscObjectCompose((PetscObject)(*C),"workB",(PetscObject)container);
    455:   PetscContainerDestroy(&container);
    456:   return(0);
    457: }

    461: /*
    462:     Performs an efficient scatter on the rows of B needed by this process; this is
    463:     a modification of the VecScatterBegin_() routines.
    464: */
    465: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,Mat C,Mat *outworkB)
    466: {
    467:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)A->data;
    468:   PetscErrorCode         ierr;
    469:   PetscScalar            *b,*w,*svalues,*rvalues;
    470:   VecScatter             ctx   = aij->Mvctx;
    471:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
    472:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;
    473:   PetscInt               i,j,k;
    474:   PetscInt               *sindices,*sstarts,*rindices,*rstarts;
    475:   PetscMPIInt            *sprocs,*rprocs,nrecvs;
    476:   MPI_Request            *swaits,*rwaits;
    477:   MPI_Comm               comm;
    478:   PetscMPIInt            tag  = ((PetscObject)ctx)->tag,ncols = B->cmap->N, nrows = aij->B->cmap->n,imdex,nrowsB = B->rmap->n;
    479:   MPI_Status             status;
    480:   MPIAIJ_MPIDense        *contents;
    481:   PetscContainer         container;
    482:   Mat                    workB;

    485:   PetscObjectGetComm((PetscObject)A,&comm);
    486:   PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);
    487:   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
    488:   PetscContainerGetPointer(container,(void**)&contents);

    490:   workB = *outworkB = contents->workB;
    491:   if (nrows != workB->rmap->n) SETERRQ2(comm,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",nrows,workB->cmap->n);
    492:   sindices = to->indices;
    493:   sstarts  = to->starts;
    494:   sprocs   = to->procs;
    495:   swaits   = contents->swaits;
    496:   svalues  = contents->svalues;

    498:   rindices = from->indices;
    499:   rstarts  = from->starts;
    500:   rprocs   = from->procs;
    501:   rwaits   = contents->rwaits;
    502:   rvalues  = contents->rvalues;

    504:   MatDenseGetArray(B,&b);
    505:   MatDenseGetArray(workB,&w);

    507:   for (i=0; i<from->n; i++) {
    508:     MPI_Irecv(rvalues+ncols*rstarts[i],ncols*(rstarts[i+1]-rstarts[i]),MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);
    509:   }

    511:   for (i=0; i<to->n; i++) {
    512:     /* pack a message at a time */
    513:     for (j=0; j<sstarts[i+1]-sstarts[i]; j++) {
    514:       for (k=0; k<ncols; k++) {
    515:         svalues[ncols*(sstarts[i] + j) + k] = b[sindices[sstarts[i]+j] + nrowsB*k];
    516:       }
    517:     }
    518:     MPI_Isend(svalues+ncols*sstarts[i],ncols*(sstarts[i+1]-sstarts[i]),MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);
    519:   }

    521:   nrecvs = from->n;
    522:   while (nrecvs) {
    523:     MPI_Waitany(from->n,rwaits,&imdex,&status);
    524:     nrecvs--;
    525:     /* unpack a message at a time */
    526:     for (j=0; j<rstarts[imdex+1]-rstarts[imdex]; j++) {
    527:       for (k=0; k<ncols; k++) {
    528:         w[rindices[rstarts[imdex]+j] + nrows*k] = rvalues[ncols*(rstarts[imdex] + j) + k];
    529:       }
    530:     }
    531:   }
    532:   if (to->n) {MPI_Waitall(to->n,swaits,to->sstatus);}

    534:   MatDenseRestoreArray(B,&b);
    535:   MatDenseRestoreArray(workB,&w);
    536:   MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);
    537:   MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);
    538:   return(0);
    539: }
    540: extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);

    544: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
    545: {
    547:   Mat_MPIAIJ     *aij    = (Mat_MPIAIJ*)A->data;
    548:   Mat_MPIDense   *bdense = (Mat_MPIDense*)B->data;
    549:   Mat_MPIDense   *cdense = (Mat_MPIDense*)C->data;
    550:   Mat            workB;

    553:   /* diagonal block of A times all local rows of B*/
    554:   MatMatMultNumeric_SeqAIJ_SeqDense(aij->A,bdense->A,cdense->A);

    556:   /* get off processor parts of B needed to complete the product */
    557:   MatMPIDenseScatter(A,B,C,&workB);

    559:   /* off-diagonal block of A times nonlocal rows of B */
    560:   MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);
    561:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    562:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    563:   return(0);
    564: }

    568: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
    569: {
    571:   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
    572:   Mat_SeqAIJ     *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
    573:   Mat_SeqAIJ     *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
    574:   PetscInt       *adi = ad->i,*adj,*aoi=ao->i,*aoj;
    575:   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
    576:   Mat_SeqAIJ     *p_loc,*p_oth;
    577:   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
    578:   PetscScalar    *pa_loc,*pa_oth,*pa,valtmp,*ca;
    579:   PetscInt       cm          = C->rmap->n,anz,pnz;
    580:   Mat_PtAPMPI    *ptap       = c->ptap;
    581:   PetscScalar    *apa_sparse = ptap->apa;
    582:   PetscInt       *api,*apj,*apJ,i,j,k,row;
    583:   PetscInt       cstart = C->cmap->rstart;
    584:   PetscInt       cdnz,conz,k0,k1,nextp;
    585:   MPI_Comm       comm;
    586:   PetscMPIInt    size;

    589:   PetscObjectGetComm((PetscObject)A,&comm);
    590:   MPI_Comm_size(comm,&size);

    592:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    593:   /*-----------------------------------------------------*/
    594:   /* update numerical values of P_oth and P_loc */
    595:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    596:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    598:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    599:   /*----------------------------------------------------------*/
    600:   /* get data from symbolic products */
    601:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    602:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
    603:   if (size >1) {
    604:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    605:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
    606:   } else {
    607:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
    608:   }

    610:   api = ptap->api;
    611:   apj = ptap->apj;
    612:   for (i=0; i<cm; i++) {
    613:     apJ = apj + api[i];

    615:     /* diagonal portion of A */
    616:     anz = adi[i+1] - adi[i];
    617:     adj = ad->j + adi[i];
    618:     ada = ad->a + adi[i];
    619:     for (j=0; j<anz; j++) {
    620:       row = adj[j];
    621:       pnz = pi_loc[row+1] - pi_loc[row];
    622:       pj  = pj_loc + pi_loc[row];
    623:       pa  = pa_loc + pi_loc[row];
    624:       /* perform sparse axpy */
    625:       valtmp = ada[j];
    626:       nextp  = 0;
    627:       for (k=0; nextp<pnz; k++) {
    628:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    629:           apa_sparse[k] += valtmp*pa[nextp++];
    630:         }
    631:       }
    632:       PetscLogFlops(2.0*pnz);
    633:     }

    635:     /* off-diagonal portion of A */
    636:     anz = aoi[i+1] - aoi[i];
    637:     aoj = ao->j + aoi[i];
    638:     aoa = ao->a + aoi[i];
    639:     for (j=0; j<anz; j++) {
    640:       row = aoj[j];
    641:       pnz = pi_oth[row+1] - pi_oth[row];
    642:       pj  = pj_oth + pi_oth[row];
    643:       pa  = pa_oth + pi_oth[row];
    644:       /* perform sparse axpy */
    645:       valtmp = aoa[j];
    646:       nextp  = 0;
    647:       for (k=0; nextp<pnz; k++) {
    648:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    649:           apa_sparse[k] += valtmp*pa[nextp++];
    650:         }
    651:       }
    652:       PetscLogFlops(2.0*pnz);
    653:     }

    655:     /* set values in C */
    656:     cdnz = cd->i[i+1] - cd->i[i];
    657:     conz = co->i[i+1] - co->i[i];

    659:     /* 1st off-diagoanl part of C */
    660:     ca = coa + co->i[i];
    661:     k  = 0;
    662:     for (k0=0; k0<conz; k0++) {
    663:       if (apJ[k] >= cstart) break;
    664:       ca[k0]        = apa_sparse[k];
    665:       apa_sparse[k] = 0.0;
    666:       k++;
    667:     }

    669:     /* diagonal part of C */
    670:     ca = cda + cd->i[i];
    671:     for (k1=0; k1<cdnz; k1++) {
    672:       ca[k1]        = apa_sparse[k];
    673:       apa_sparse[k] = 0.0;
    674:       k++;
    675:     }

    677:     /* 2nd off-diagoanl part of C */
    678:     ca = coa + co->i[i];
    679:     for (; k0<conz; k0++) {
    680:       ca[k0]        = apa_sparse[k];
    681:       apa_sparse[k] = 0.0;
    682:       k++;
    683:     }
    684:   }
    685:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    686:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    687:   return(0);
    688: }

    690: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
    693: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
    694: {
    695:   PetscErrorCode     ierr;
    696:   MPI_Comm           comm;
    697:   PetscMPIInt        size;
    698:   Mat                Cmpi;
    699:   Mat_PtAPMPI        *ptap;
    700:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
    701:   Mat_MPIAIJ         *a         = (Mat_MPIAIJ*)A->data,*c;
    702:   Mat_SeqAIJ         *ad        = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    703:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    704:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    705:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max;
    706:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
    707:   PetscReal          afill;
    708:   PetscScalar        *apa;
    709:   PetscTable         ta;

    712:   PetscObjectGetComm((PetscObject)A,&comm);
    713:   MPI_Comm_size(comm,&size);

    715:   /* create struct Mat_PtAPMPI and attached it to C later */
    716:   PetscNew(&ptap);

    718:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    719:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    720:
    721:   /* get P_loc by taking all local rows of P */
    722:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    724:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    725:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    726:   if (size > 1) {
    727:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    728:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    729:   } else {
    730:     p_oth  = NULL;
    731:     pi_oth = NULL; pj_oth = NULL;
    732:   }

    734:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    735:   /*-------------------------------------------------------------------*/
    736:   PetscMalloc1(am+2,&api);
    737:   ptap->api = api;
    738:   api[0]    = 0;

    740:   /* create and initialize a linked list */
    741:   apnz_max = 6*(p_loc->rmax + (PetscInt)(1.e-2*pN)); /* expected apnz_max */
    742:   if (apnz_max > pN) apnz_max = pN;
    743:   PetscTableCreate(apnz_max,pN,&ta);

    745:   /* Calculate apnz_max */
    746:   apnz_max = 0;
    747:   for (i=0; i<am; i++) {
    748:     PetscTableRemoveAll(ta);
    749:     /* diagonal portion of A */
    750:     nzi  = adi[i+1] - adi[i];
    751:     Jptr = adj+adi[i];  /* cols of A_diag */
    752:     MatMergeRows_SeqAIJ(p_loc,nzi,Jptr,ta);
    753:     PetscTableGetCount(ta,&apnz);
    754:     if (apnz_max < apnz) apnz_max = apnz;

    756:     /*  off-diagonal portion of A */
    757:     nzi = aoi[i+1] - aoi[i];
    758:     Jptr = aoj+aoi[i];  /* cols of A_off */
    759:     MatMergeRows_SeqAIJ(p_oth,nzi,Jptr,ta);
    760:     PetscTableGetCount(ta,&apnz);
    761:     if (apnz_max < apnz) apnz_max = apnz;
    762:   }
    763:   PetscTableDestroy(&ta);
    764:
    765:   PetscLLCondensedCreate_Scalable(apnz_max,&lnk);

    767:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    768:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
    769:   current_space = free_space;
    770:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    771:   for (i=0; i<am; i++) {
    772:     /* diagonal portion of A */
    773:     nzi = adi[i+1] - adi[i];
    774:     for (j=0; j<nzi; j++) {
    775:       row  = *adj++;
    776:       pnz  = pi_loc[row+1] - pi_loc[row];
    777:       Jptr = pj_loc + pi_loc[row];
    778:       /* add non-zero cols of P into the sorted linked list lnk */
    779:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    780:     }
    781:     /* off-diagonal portion of A */
    782:     nzi = aoi[i+1] - aoi[i];
    783:     for (j=0; j<nzi; j++) {
    784:       row  = *aoj++;
    785:       pnz  = pi_oth[row+1] - pi_oth[row];
    786:       Jptr = pj_oth + pi_oth[row];
    787:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    788:     }

    790:     apnz     = *lnk;
    791:     api[i+1] = api[i] + apnz;

    793:     /* if free space is not available, double the total space in the list */
    794:     if (current_space->local_remaining<apnz) {
    795:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    796:       nspacedouble++;
    797:     }

    799:     /* Copy data into free space, then initialize lnk */
    800:     PetscLLCondensedClean_Scalable(apnz,current_space->array,lnk);
    801:     MatPreallocateSet(i+rstart,apnz,current_space->array,dnz,onz);

    803:     current_space->array           += apnz;
    804:     current_space->local_used      += apnz;
    805:     current_space->local_remaining -= apnz;
    806:   }

    808:   /* Allocate space for apj, initialize apj, and */
    809:   /* destroy list of free space and other temporary array(s) */
    810:   PetscMalloc1(api[am]+1,&ptap->apj);
    811:   apj  = ptap->apj;
    812:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    813:   PetscLLCondensedDestroy_Scalable(lnk);

    815:   /* create and assemble symbolic parallel matrix Cmpi */
    816:   /*----------------------------------------------------*/
    817:   MatCreate(comm,&Cmpi);
    818:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    819:   MatSetBlockSizesFromMats(Cmpi,A,P);
    820:   MatSetType(Cmpi,MATMPIAIJ);
    821:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
    822:   MatPreallocateFinalize(dnz,onz);

    824:   /* malloc apa for assembly Cmpi */
    825:   PetscCalloc1(apnz_max,&apa);

    827:   ptap->apa = apa;
    828:   for (i=0; i<am; i++) {
    829:     row  = i + rstart;
    830:     apnz = api[i+1] - api[i];
    831:     MatSetValues(Cmpi,1,&row,apnz,apj,apa,INSERT_VALUES);
    832:     apj += apnz;
    833:   }
    834:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
    835:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);

    837:   ptap->destroy             = Cmpi->ops->destroy;
    838:   ptap->duplicate           = Cmpi->ops->duplicate;
    839:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
    840:   Cmpi->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
    841:   Cmpi->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult;

    843:   /* attach the supporting struct to Cmpi for reuse */
    844:   c       = (Mat_MPIAIJ*)Cmpi->data;
    845:   c->ptap = ptap;

    847:   *C = Cmpi;

    849:   /* set MatInfo */
    850:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    851:   if (afill < 1.0) afill = 1.0;
    852:   Cmpi->info.mallocs           = nspacedouble;
    853:   Cmpi->info.fill_ratio_given  = fill;
    854:   Cmpi->info.fill_ratio_needed = afill;

    856: #if defined(PETSC_USE_INFO)
    857:   if (api[am]) {
    858:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    859:     PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    860:   } else {
    861:     PetscInfo(Cmpi,"Empty matrix product\n");
    862:   }
    863: #endif
    864:   return(0);
    865: }

    867: /*-------------------------------------------------------------------------*/
    870: PetscErrorCode MatTransposeMatMult_MPIAIJ_MPIAIJ(Mat P,Mat A,MatReuse scall,PetscReal fill,Mat *C)
    871: {
    873:   const char     *algTypes[3] = {"scalable","nonscalable","matmatmult"};
    874:   PetscInt       alg=0; /* set default algorithm */

    877:   if (scall == MAT_INITIAL_MATRIX) {
    878:     PetscObjectOptionsBegin((PetscObject)A);
    879:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,3,algTypes[0],&alg,NULL);
    880:     PetscOptionsEnd();

    882:     PetscLogEventBegin(MAT_TransposeMatMultSymbolic,P,A,0,0);
    883:     switch (alg) {
    884:     case 1:
    885:       MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(P,A,fill,C);
    886:       break;
    887:     case 2:
    888:     {
    889:       Mat         Pt;
    890:       Mat_PtAPMPI *ptap;
    891:       Mat_MPIAIJ  *c;
    892:       MatTranspose(P,MAT_INITIAL_MATRIX,&Pt);
    893:       MatMatMult(Pt,A,MAT_INITIAL_MATRIX,fill,C);
    894:       c        = (Mat_MPIAIJ*)(*C)->data;
    895:       ptap     = c->ptap;
    896:       ptap->Pt = Pt;
    897:       (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
    898:       return(0);
    899:     }
    900:       break;
    901:     default:
    902:       MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(P,A,fill,C);
    903:       break;
    904:     }
    905:     PetscLogEventEnd(MAT_TransposeMatMultSymbolic,P,A,0,0);
    906:   }
    907:   PetscLogEventBegin(MAT_TransposeMatMultNumeric,P,A,0,0);
    908:   (*(*C)->ops->mattransposemultnumeric)(P,A,*C);
    909:   PetscLogEventEnd(MAT_TransposeMatMultNumeric,P,A,0,0);
    910:   return(0);
    911: }

    913: /* This routine only works when scall=MAT_REUSE_MATRIX! */
    916: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
    917: {
    919:   Mat_MPIAIJ     *c=(Mat_MPIAIJ*)C->data;
    920:   Mat_PtAPMPI    *ptap= c->ptap;
    921:   Mat            Pt=ptap->Pt;

    924:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
    925:   MatMatMultNumeric(Pt,A,C);
    926:   return(0);
    927: }

    929: /* Non-scalable version, use dense axpy */
    932: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
    933: {
    934:   PetscErrorCode      ierr;
    935:   Mat_Merge_SeqsToMPI *merge;
    936:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
    937:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    938:   Mat_PtAPMPI         *ptap;
    939:   PetscInt            *adj,*aJ;
    940:   PetscInt            i,j,k,anz,pnz,row,*cj;
    941:   MatScalar           *ada,*aval,*ca,valtmp;
    942:   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    943:   MPI_Comm            comm;
    944:   PetscMPIInt         size,rank,taga,*len_s;
    945:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    946:   PetscInt            **buf_ri,**buf_rj;
    947:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    948:   MPI_Request         *s_waits,*r_waits;
    949:   MPI_Status          *status;
    950:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    951:   PetscInt            *ai,*aj,*coi,*coj;
    952:   PetscInt            *poJ,*pdJ;
    953:   Mat                 A_loc;
    954:   Mat_SeqAIJ          *a_loc;

    957:   PetscObjectGetComm((PetscObject)C,&comm);
    958:   MPI_Comm_size(comm,&size);
    959:   MPI_Comm_rank(comm,&rank);

    961:   ptap  = c->ptap;
    962:   merge = ptap->merge;

    964:   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
    965:   /*--------------------------------------------------------------*/
    966:   /* get data from symbolic products */
    967:   coi  = merge->coi; coj = merge->coj;
    968:   PetscCalloc1(coi[pon]+1,&coa);

    970:   bi     = merge->bi; bj = merge->bj;
    971:   owners = merge->rowmap->range;
    972:   PetscCalloc1(bi[cm]+1,&ba);

    974:   /* get A_loc by taking all local rows of A */
    975:   A_loc = ptap->A_loc;
    976:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    977:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    978:   ai    = a_loc->i;
    979:   aj    = a_loc->j;

    981:   PetscCalloc1(A->cmap->N,&aval); /* non-scalable!!! */

    983:   for (i=0; i<am; i++) {
    984:     /* 2-a) put A[i,:] to dense array aval */
    985:     anz = ai[i+1] - ai[i];
    986:     adj = aj + ai[i];
    987:     ada = a_loc->a + ai[i];
    988:     for (j=0; j<anz; j++) {
    989:       aval[adj[j]] = ada[j];
    990:     }

    992:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    993:     /*--------------------------------------------------------------*/
    994:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    995:     pnz = po->i[i+1] - po->i[i];
    996:     poJ = po->j + po->i[i];
    997:     pA  = po->a + po->i[i];
    998:     for (j=0; j<pnz; j++) {
    999:       row = poJ[j];
    1000:       cnz = coi[row+1] - coi[row];
    1001:       cj  = coj + coi[row];
    1002:       ca  = coa + coi[row];
    1003:       /* perform dense axpy */
    1004:       valtmp = pA[j];
    1005:       for (k=0; k<cnz; k++) {
    1006:         ca[k] += valtmp*aval[cj[k]];
    1007:       }
    1008:       PetscLogFlops(2.0*cnz);
    1009:     }

    1011:     /* put the value into Cd (diagonal part) */
    1012:     pnz = pd->i[i+1] - pd->i[i];
    1013:     pdJ = pd->j + pd->i[i];
    1014:     pA  = pd->a + pd->i[i];
    1015:     for (j=0; j<pnz; j++) {
    1016:       row = pdJ[j];
    1017:       cnz = bi[row+1] - bi[row];
    1018:       cj  = bj + bi[row];
    1019:       ca  = ba + bi[row];
    1020:       /* perform dense axpy */
    1021:       valtmp = pA[j];
    1022:       for (k=0; k<cnz; k++) {
    1023:         ca[k] += valtmp*aval[cj[k]];
    1024:       }
    1025:       PetscLogFlops(2.0*cnz);
    1026:     }

    1028:     /* zero the current row of Pt*A */
    1029:     aJ = aj + ai[i];
    1030:     for (k=0; k<anz; k++) aval[aJ[k]] = 0.0;
    1031:   }

    1033:   /* 3) send and recv matrix values coa */
    1034:   /*------------------------------------*/
    1035:   buf_ri = merge->buf_ri;
    1036:   buf_rj = merge->buf_rj;
    1037:   len_s  = merge->len_s;
    1038:   PetscCommGetNewTag(comm,&taga);
    1039:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1041:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1042:   for (proc=0,k=0; proc<size; proc++) {
    1043:     if (!len_s[proc]) continue;
    1044:     i    = merge->owners_co[proc];
    1045:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1046:     k++;
    1047:   }
    1048:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
    1049:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

    1051:   PetscFree2(s_waits,status);
    1052:   PetscFree(r_waits);
    1053:   PetscFree(coa);

    1055:   /* 4) insert local Cseq and received values into Cmpi */
    1056:   /*----------------------------------------------------*/
    1057:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1058:   for (k=0; k<merge->nrecv; k++) {
    1059:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1060:     nrows       = *(buf_ri_k[k]);
    1061:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1062:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1063:   }

    1065:   for (i=0; i<cm; i++) {
    1066:     row  = owners[rank] + i; /* global row index of C_seq */
    1067:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1068:     ba_i = ba + bi[i];
    1069:     bnz  = bi[i+1] - bi[i];
    1070:     /* add received vals into ba */
    1071:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1072:       /* i-th row */
    1073:       if (i == *nextrow[k]) {
    1074:         cnz    = *(nextci[k]+1) - *nextci[k];
    1075:         cj     = buf_rj[k] + *(nextci[k]);
    1076:         ca     = abuf_r[k] + *(nextci[k]);
    1077:         nextcj = 0;
    1078:         for (j=0; nextcj<cnz; j++) {
    1079:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1080:             ba_i[j] += ca[nextcj++];
    1081:           }
    1082:         }
    1083:         nextrow[k]++; nextci[k]++;
    1084:         PetscLogFlops(2.0*cnz);
    1085:       }
    1086:     }
    1087:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1088:   }
    1089:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1090:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1092:   PetscFree(ba);
    1093:   PetscFree(abuf_r[0]);
    1094:   PetscFree(abuf_r);
    1095:   PetscFree3(buf_ri_k,nextrow,nextci);
    1096:   PetscFree(aval);
    1097:   return(0);
    1098: }

    1100: PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat, MatDuplicateOption,Mat*);
    1101: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
    1104: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat *C)
    1105: {
    1106:   PetscErrorCode      ierr;
    1107:   Mat                 Cmpi,A_loc,POt,PDt;
    1108:   Mat_PtAPMPI         *ptap;
    1109:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1110:   Mat_MPIAIJ          *p        =(Mat_MPIAIJ*)P->data,*c;
    1111:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1112:   PetscInt            nnz;
    1113:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1114:   PetscInt            am=A->rmap->n,pn=P->cmap->n;
    1115:   PetscBT             lnkbt;
    1116:   MPI_Comm            comm;
    1117:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1118:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1119:   PetscInt            len,proc,*dnz,*onz,*owners;
    1120:   PetscInt            nzi,*bi,*bj;
    1121:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1122:   MPI_Request         *swaits,*rwaits;
    1123:   MPI_Status          *sstatus,rstatus;
    1124:   Mat_Merge_SeqsToMPI *merge;
    1125:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1126:   PetscReal           afill  =1.0,afill_tmp;
    1127:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N;
    1128:   PetscScalar         *vals;
    1129:   Mat_SeqAIJ          *a_loc, *pdt,*pot;

    1132:   PetscObjectGetComm((PetscObject)A,&comm);
    1133:   /* check if matrix local sizes are compatible */
    1134:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != P (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);

    1136:   MPI_Comm_size(comm,&size);
    1137:   MPI_Comm_rank(comm,&rank);

    1139:   /* create struct Mat_PtAPMPI and attached it to C later */
    1140:   PetscNew(&ptap);

    1142:   /* get A_loc by taking all local rows of A */
    1143:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1145:   ptap->A_loc = A_loc;

    1147:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1148:   ai    = a_loc->i;
    1149:   aj    = a_loc->j;

    1151:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1152:   /*----------------------------------------------------*/
    1153:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
    1154:   pdt  = (Mat_SeqAIJ*)PDt->data;
    1155:   pdti = pdt->i; pdtj = pdt->j;

    1157:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
    1158:   pot  = (Mat_SeqAIJ*)POt->data;
    1159:   poti = pot->i; potj = pot->j;

    1161:   /* then, compute symbolic Co = (p->B)^T*A */
    1162:   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors >= (num of nonzero rows of C_seq) - pn */
    1163:   PetscMalloc1(pon+1,&coi);
    1164:   coi[0] = 0;

    1166:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1167:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
    1168:   PetscFreeSpaceGet(nnz,&free_space);
    1169:   current_space = free_space;

    1171:   /* create and initialize a linked list */
    1172:   PetscLLCondensedCreate(aN,aN,&lnk,&lnkbt);

    1174:   for (i=0; i<pon; i++) {
    1175:     pnz = poti[i+1] - poti[i];
    1176:     ptJ = potj + poti[i];
    1177:     for (j=0; j<pnz; j++) {
    1178:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1179:       anz  = ai[row+1] - ai[row];
    1180:       Jptr = aj + ai[row];
    1181:       /* add non-zero cols of AP into the sorted linked list lnk */
    1182:       PetscLLCondensedAddSorted(anz,Jptr,lnk,lnkbt);
    1183:     }
    1184:     nnz = lnk[0];

    1186:     /* If free space is not available, double the total space in the list */
    1187:     if (current_space->local_remaining<nnz) {
    1188:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1189:       nspacedouble++;
    1190:     }

    1192:     /* Copy data into free space, and zero out denserows */
    1193:     PetscLLCondensedClean(aN,nnz,current_space->array,lnk,lnkbt);

    1195:     current_space->array           += nnz;
    1196:     current_space->local_used      += nnz;
    1197:     current_space->local_remaining -= nnz;

    1199:     coi[i+1] = coi[i] + nnz;
    1200:   }

    1202:   PetscMalloc1(coi[pon]+1,&coj);
    1203:   PetscFreeSpaceContiguous(&free_space,coj);

    1205:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1206:   if (afill_tmp > afill) afill = afill_tmp;

    1208:   /* send j-array (coj) of Co to other processors */
    1209:   /*----------------------------------------------*/
    1210:   /* determine row ownership */
    1211:   PetscNew(&merge);
    1212:   PetscLayoutCreate(comm,&merge->rowmap);

    1214:   merge->rowmap->n  = pn;
    1215:   merge->rowmap->bs = 1;

    1217:   PetscLayoutSetUp(merge->rowmap);
    1218:   owners = merge->rowmap->range;

    1220:   /* determine the number of messages to send, their lengths */
    1221:   PetscCalloc1(size,&len_si);
    1222:   PetscMalloc1(size,&merge->len_s);

    1224:   len_s        = merge->len_s;
    1225:   merge->nsend = 0;

    1227:   PetscMalloc1(size+2,&owners_co);
    1228:   PetscMemzero(len_s,size*sizeof(PetscMPIInt));

    1230:   proc = 0;
    1231:   for (i=0; i<pon; i++) {
    1232:     while (prmap[i] >= owners[proc+1]) proc++;
    1233:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1234:     len_s[proc] += coi[i+1] - coi[i];
    1235:   }

    1237:   len          = 0; /* max length of buf_si[] */
    1238:   owners_co[0] = 0;
    1239:   for (proc=0; proc<size; proc++) {
    1240:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1241:     if (len_si[proc]) {
    1242:       merge->nsend++;
    1243:       len_si[proc] = 2*(len_si[proc] + 1);
    1244:       len         += len_si[proc];
    1245:     }
    1246:   }

    1248:   /* determine the number and length of messages to receive for coi and coj  */
    1249:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1250:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1252:   /* post the Irecv and Isend of coj */
    1253:   PetscCommGetNewTag(comm,&tagj);
    1254:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1255:   PetscMalloc1(merge->nsend+1,&swaits);
    1256:   for (proc=0, k=0; proc<size; proc++) {
    1257:     if (!len_s[proc]) continue;
    1258:     i    = owners_co[proc];
    1259:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1260:     k++;
    1261:   }

    1263:   /* receives and sends of coj are complete */
    1264:   PetscMalloc1(size,&sstatus);
    1265:   for (i=0; i<merge->nrecv; i++) {
    1266:     PetscMPIInt icompleted;
    1267:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1268:   }
    1269:   PetscFree(rwaits);
    1270:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

    1272:   /* send and recv coi */
    1273:   /*-------------------*/
    1274:   PetscCommGetNewTag(comm,&tagi);
    1275:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    1276:   PetscMalloc1(len+1,&buf_s);
    1277:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1278:   for (proc=0,k=0; proc<size; proc++) {
    1279:     if (!len_s[proc]) continue;
    1280:     /* form outgoing message for i-structure:
    1281:          buf_si[0]:                 nrows to be sent
    1282:                [1:nrows]:           row index (global)
    1283:                [nrows+1:2*nrows+1]: i-structure index
    1284:     */
    1285:     /*-------------------------------------------*/
    1286:     nrows       = len_si[proc]/2 - 1;
    1287:     buf_si_i    = buf_si + nrows+1;
    1288:     buf_si[0]   = nrows;
    1289:     buf_si_i[0] = 0;
    1290:     nrows       = 0;
    1291:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1292:       nzi               = coi[i+1] - coi[i];
    1293:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
    1294:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1295:       nrows++;
    1296:     }
    1297:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1298:     k++;
    1299:     buf_si += len_si[proc];
    1300:   }
    1301:   i = merge->nrecv;
    1302:   while (i--) {
    1303:     PetscMPIInt icompleted;
    1304:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1305:   }
    1306:   PetscFree(rwaits);
    1307:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
    1308:   PetscFree(len_si);
    1309:   PetscFree(len_ri);
    1310:   PetscFree(swaits);
    1311:   PetscFree(sstatus);
    1312:   PetscFree(buf_s);

    1314:   /* compute the local portion of C (mpi mat) */
    1315:   /*------------------------------------------*/
    1316:   /* allocate bi array and free space for accumulating nonzero column info */
    1317:   PetscMalloc1(pn+1,&bi);
    1318:   bi[0] = 0;

    1320:   /* set initial free space to be fill*(nnz(P) + nnz(A)) */
    1321:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
    1322:   PetscFreeSpaceGet(nnz,&free_space);
    1323:   current_space = free_space;

    1325:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1326:   for (k=0; k<merge->nrecv; k++) {
    1327:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1328:     nrows       = *buf_ri_k[k];
    1329:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1330:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1331:   }

    1333:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    1334:   rmax = 0;
    1335:   for (i=0; i<pn; i++) {
    1336:     /* add pdt[i,:]*AP into lnk */
    1337:     pnz = pdti[i+1] - pdti[i];
    1338:     ptJ = pdtj + pdti[i];
    1339:     for (j=0; j<pnz; j++) {
    1340:       row  = ptJ[j];  /* row of AP == col of Pt */
    1341:       anz  = ai[row+1] - ai[row];
    1342:       Jptr = aj + ai[row];
    1343:       /* add non-zero cols of AP into the sorted linked list lnk */
    1344:       PetscLLCondensedAddSorted(anz,Jptr,lnk,lnkbt);
    1345:     }

    1347:     /* add received col data into lnk */
    1348:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1349:       if (i == *nextrow[k]) { /* i-th row */
    1350:         nzi  = *(nextci[k]+1) - *nextci[k];
    1351:         Jptr = buf_rj[k] + *nextci[k];
    1352:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
    1353:         nextrow[k]++; nextci[k]++;
    1354:       }
    1355:     }
    1356:     nnz = lnk[0];

    1358:     /* if free space is not available, make more free space */
    1359:     if (current_space->local_remaining<nnz) {
    1360:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1361:       nspacedouble++;
    1362:     }
    1363:     /* copy data into free space, then initialize lnk */
    1364:     PetscLLCondensedClean(aN,nnz,current_space->array,lnk,lnkbt);
    1365:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    1367:     current_space->array           += nnz;
    1368:     current_space->local_used      += nnz;
    1369:     current_space->local_remaining -= nnz;

    1371:     bi[i+1] = bi[i] + nnz;
    1372:     if (nnz > rmax) rmax = nnz;
    1373:   }
    1374:   PetscFree3(buf_ri_k,nextrow,nextci);

    1376:   PetscMalloc1(bi[pn]+1,&bj);
    1377:   PetscFreeSpaceContiguous(&free_space,bj);

    1379:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    1380:   if (afill_tmp > afill) afill = afill_tmp;
    1381:   PetscLLCondensedDestroy(lnk,lnkbt);
    1382:   MatDestroy(&POt);
    1383:   MatDestroy(&PDt);

    1385:   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
    1386:   /*----------------------------------------------------------------------------------*/
    1387:   PetscCalloc1(rmax+1,&vals);

    1389:   MatCreate(comm,&Cmpi);
    1390:   MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    1391:   MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    1392:   MatSetType(Cmpi,MATMPIAIJ);
    1393:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
    1394:   MatPreallocateFinalize(dnz,onz);
    1395:   MatSetBlockSize(Cmpi,1);
    1396:   for (i=0; i<pn; i++) {
    1397:     row  = i + rstart;
    1398:     nnz  = bi[i+1] - bi[i];
    1399:     Jptr = bj + bi[i];
    1400:     MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);
    1401:   }
    1402:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
    1403:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
    1404:   PetscFree(vals);

    1406:   merge->bi        = bi;
    1407:   merge->bj        = bj;
    1408:   merge->coi       = coi;
    1409:   merge->coj       = coj;
    1410:   merge->buf_ri    = buf_ri;
    1411:   merge->buf_rj    = buf_rj;
    1412:   merge->owners_co = owners_co;

    1414:   /* attach the supporting struct to Cmpi for reuse */
    1415:   c           = (Mat_MPIAIJ*)Cmpi->data;
    1416:   c->ptap     = ptap;
    1417:   ptap->api   = NULL;
    1418:   ptap->apj   = NULL;
    1419:   ptap->merge = merge;
    1420:   ptap->destroy   = Cmpi->ops->destroy;
    1421:   ptap->duplicate = Cmpi->ops->duplicate;

    1423:   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    1424:   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
    1425:   Cmpi->ops->duplicate               = MatDuplicate_MPIAIJ_MatPtAP;

    1427:   *C = Cmpi;
    1428: #if defined(PETSC_USE_INFO)
    1429:   if (bi[pn] != 0) {
    1430:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1431:     PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    1432:   } else {
    1433:     PetscInfo(Cmpi,"Empty matrix product\n");
    1434:   }
    1435: #endif
    1436:   return(0);
    1437: }

    1441: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
    1442: {
    1443:   PetscErrorCode      ierr;
    1444:   Mat_Merge_SeqsToMPI *merge;
    1445:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
    1446:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    1447:   Mat_PtAPMPI         *ptap;
    1448:   PetscInt            *adj;
    1449:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
    1450:   MatScalar           *ada,*ca,valtmp;
    1451:   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    1452:   MPI_Comm            comm;
    1453:   PetscMPIInt         size,rank,taga,*len_s;
    1454:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    1455:   PetscInt            **buf_ri,**buf_rj;
    1456:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    1457:   MPI_Request         *s_waits,*r_waits;
    1458:   MPI_Status          *status;
    1459:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    1460:   PetscInt            *ai,*aj,*coi,*coj;
    1461:   PetscInt            *poJ,*pdJ;
    1462:   Mat                 A_loc;
    1463:   Mat_SeqAIJ          *a_loc;

    1466:   PetscObjectGetComm((PetscObject)C,&comm);
    1467:   MPI_Comm_size(comm,&size);
    1468:   MPI_Comm_rank(comm,&rank);

    1470:   ptap  = c->ptap;
    1471:   merge = ptap->merge;

    1473:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
    1474:   /*------------------------------------------*/
    1475:   /* get data from symbolic products */
    1476:   coi    = merge->coi; coj = merge->coj;
    1477:   PetscCalloc1(coi[pon]+1,&coa);
    1478:   bi     = merge->bi; bj = merge->bj;
    1479:   owners = merge->rowmap->range;
    1480:   PetscCalloc1(bi[cm]+1,&ba);

    1482:   /* get A_loc by taking all local rows of A */
    1483:   A_loc = ptap->A_loc;
    1484:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    1485:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1486:   ai    = a_loc->i;
    1487:   aj    = a_loc->j;

    1489:   for (i=0; i<am; i++) {
    1490:     anz = ai[i+1] - ai[i];
    1491:     adj = aj + ai[i];
    1492:     ada = a_loc->a + ai[i];

    1494:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1495:     /*-------------------------------------------------------------*/
    1496:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1497:     pnz = po->i[i+1] - po->i[i];
    1498:     poJ = po->j + po->i[i];
    1499:     pA  = po->a + po->i[i];
    1500:     for (j=0; j<pnz; j++) {
    1501:       row = poJ[j];
    1502:       cj  = coj + coi[row];
    1503:       ca  = coa + coi[row];
    1504:       /* perform sparse axpy */
    1505:       nexta  = 0;
    1506:       valtmp = pA[j];
    1507:       for (k=0; nexta<anz; k++) {
    1508:         if (cj[k] == adj[nexta]) {
    1509:           ca[k] += valtmp*ada[nexta];
    1510:           nexta++;
    1511:         }
    1512:       }
    1513:       PetscLogFlops(2.0*anz);
    1514:     }

    1516:     /* put the value into Cd (diagonal part) */
    1517:     pnz = pd->i[i+1] - pd->i[i];
    1518:     pdJ = pd->j + pd->i[i];
    1519:     pA  = pd->a + pd->i[i];
    1520:     for (j=0; j<pnz; j++) {
    1521:       row = pdJ[j];
    1522:       cj  = bj + bi[row];
    1523:       ca  = ba + bi[row];
    1524:       /* perform sparse axpy */
    1525:       nexta  = 0;
    1526:       valtmp = pA[j];
    1527:       for (k=0; nexta<anz; k++) {
    1528:         if (cj[k] == adj[nexta]) {
    1529:           ca[k] += valtmp*ada[nexta];
    1530:           nexta++;
    1531:         }
    1532:       }
    1533:       PetscLogFlops(2.0*anz);
    1534:     }
    1535:   }

    1537:   /* 3) send and recv matrix values coa */
    1538:   /*------------------------------------*/
    1539:   buf_ri = merge->buf_ri;
    1540:   buf_rj = merge->buf_rj;
    1541:   len_s  = merge->len_s;
    1542:   PetscCommGetNewTag(comm,&taga);
    1543:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1545:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1546:   for (proc=0,k=0; proc<size; proc++) {
    1547:     if (!len_s[proc]) continue;
    1548:     i    = merge->owners_co[proc];
    1549:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1550:     k++;
    1551:   }
    1552:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
    1553:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

    1555:   PetscFree2(s_waits,status);
    1556:   PetscFree(r_waits);
    1557:   PetscFree(coa);

    1559:   /* 4) insert local Cseq and received values into Cmpi */
    1560:   /*----------------------------------------------------*/
    1561:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1562:   for (k=0; k<merge->nrecv; k++) {
    1563:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1564:     nrows       = *(buf_ri_k[k]);
    1565:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1566:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1567:   }

    1569:   for (i=0; i<cm; i++) {
    1570:     row  = owners[rank] + i; /* global row index of C_seq */
    1571:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1572:     ba_i = ba + bi[i];
    1573:     bnz  = bi[i+1] - bi[i];
    1574:     /* add received vals into ba */
    1575:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1576:       /* i-th row */
    1577:       if (i == *nextrow[k]) {
    1578:         cnz    = *(nextci[k]+1) - *nextci[k];
    1579:         cj     = buf_rj[k] + *(nextci[k]);
    1580:         ca     = abuf_r[k] + *(nextci[k]);
    1581:         nextcj = 0;
    1582:         for (j=0; nextcj<cnz; j++) {
    1583:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1584:             ba_i[j] += ca[nextcj++];
    1585:           }
    1586:         }
    1587:         nextrow[k]++; nextci[k]++;
    1588:         PetscLogFlops(2.0*cnz);
    1589:       }
    1590:     }
    1591:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1592:   }
    1593:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1594:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1596:   PetscFree(ba);
    1597:   PetscFree(abuf_r[0]);
    1598:   PetscFree(abuf_r);
    1599:   PetscFree3(buf_ri_k,nextrow,nextci);
    1600:   return(0);
    1601: }

    1603: PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat, MatDuplicateOption,Mat*);
    1604: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ();
    1605:    differ from MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable in using LLCondensedCreate_Scalable() */
    1608: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat *C)
    1609: {
    1610:   PetscErrorCode      ierr;
    1611:   Mat                 Cmpi,A_loc,POt,PDt;
    1612:   Mat_PtAPMPI         *ptap;
    1613:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1614:   Mat_MPIAIJ          *p        =(Mat_MPIAIJ*)P->data,*c;
    1615:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1616:   PetscInt            nnz;
    1617:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1618:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
    1619:   MPI_Comm            comm;
    1620:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1621:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1622:   PetscInt            len,proc,*dnz,*onz,*owners;
    1623:   PetscInt            nzi,*bi,*bj;
    1624:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1625:   MPI_Request         *swaits,*rwaits;
    1626:   MPI_Status          *sstatus,rstatus;
    1627:   Mat_Merge_SeqsToMPI *merge;
    1628:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1629:   PetscReal           afill  =1.0,afill_tmp;
    1630:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
    1631:   PetscScalar         *vals;
    1632:   Mat_SeqAIJ          *a_loc,*pdt,*pot;
    1633:   PetscTable          ta;

    1636:   PetscObjectGetComm((PetscObject)A,&comm);
    1637:   /* check if matrix local sizes are compatible */
    1638:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != P (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);

    1640:   MPI_Comm_size(comm,&size);
    1641:   MPI_Comm_rank(comm,&rank);

    1643:   /* create struct Mat_PtAPMPI and attached it to C later */
    1644:   PetscNew(&ptap);

    1646:   /* get A_loc by taking all local rows of A */
    1647:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1649:   ptap->A_loc = A_loc;
    1650:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
    1651:   ai          = a_loc->i;
    1652:   aj          = a_loc->j;

    1654:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1655:   /*----------------------------------------------------*/
    1656:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
    1657:   pdt  = (Mat_SeqAIJ*)PDt->data;
    1658:   pdti = pdt->i; pdtj = pdt->j;

    1660:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
    1661:   pot  = (Mat_SeqAIJ*)POt->data;
    1662:   poti = pot->i; potj = pot->j;

    1664:   /* then, compute symbolic Co = (p->B)^T*A */
    1665:   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors
    1666:                          >= (num of nonzero rows of C_seq) - pn */
    1667:   PetscMalloc1(pon+1,&coi);
    1668:   coi[0] = 0;

    1670:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1671:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
    1672:   PetscFreeSpaceGet(nnz,&free_space);
    1673:   current_space = free_space;

    1675:   /* create and initialize a linked list */
    1676:   PetscTableCreate(aN,aN,&ta);
    1677:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
    1678:   PetscTableGetCount(ta,&Armax);
    1679:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

    1681:   for (i=0; i<pon; i++) {
    1682:     pnz = poti[i+1] - poti[i];
    1683:     ptJ = potj + poti[i];
    1684:     for (j=0; j<pnz; j++) {
    1685:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1686:       anz  = ai[row+1] - ai[row];
    1687:       Jptr = aj + ai[row];
    1688:       /* add non-zero cols of AP into the sorted linked list lnk */
    1689:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1690:     }
    1691:     nnz = lnk[0];

    1693:     /* If free space is not available, double the total space in the list */
    1694:     if (current_space->local_remaining<nnz) {
    1695:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1696:       nspacedouble++;
    1697:     }

    1699:     /* Copy data into free space, and zero out denserows */
    1700:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

    1702:     current_space->array           += nnz;
    1703:     current_space->local_used      += nnz;
    1704:     current_space->local_remaining -= nnz;

    1706:     coi[i+1] = coi[i] + nnz;
    1707:   }

    1709:   PetscMalloc1(coi[pon]+1,&coj);
    1710:   PetscFreeSpaceContiguous(&free_space,coj);
    1711:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

    1713:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1714:   if (afill_tmp > afill) afill = afill_tmp;

    1716:   /* send j-array (coj) of Co to other processors */
    1717:   /*----------------------------------------------*/
    1718:   /* determine row ownership */
    1719:   PetscNew(&merge);
    1720:   PetscLayoutCreate(comm,&merge->rowmap);

    1722:   merge->rowmap->n  = pn;
    1723:   merge->rowmap->bs = 1;

    1725:   PetscLayoutSetUp(merge->rowmap);
    1726:   owners = merge->rowmap->range;

    1728:   /* determine the number of messages to send, their lengths */
    1729:   PetscCalloc1(size,&len_si);
    1730:   PetscMalloc1(size,&merge->len_s);

    1732:   len_s        = merge->len_s;
    1733:   merge->nsend = 0;

    1735:   PetscMalloc1(size+2,&owners_co);
    1736:   PetscMemzero(len_s,size*sizeof(PetscMPIInt));

    1738:   proc = 0;
    1739:   for (i=0; i<pon; i++) {
    1740:     while (prmap[i] >= owners[proc+1]) proc++;
    1741:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1742:     len_s[proc] += coi[i+1] - coi[i];
    1743:   }

    1745:   len          = 0; /* max length of buf_si[] */
    1746:   owners_co[0] = 0;
    1747:   for (proc=0; proc<size; proc++) {
    1748:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1749:     if (len_si[proc]) {
    1750:       merge->nsend++;
    1751:       len_si[proc] = 2*(len_si[proc] + 1);
    1752:       len         += len_si[proc];
    1753:     }
    1754:   }

    1756:   /* determine the number and length of messages to receive for coi and coj  */
    1757:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1758:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1760:   /* post the Irecv and Isend of coj */
    1761:   PetscCommGetNewTag(comm,&tagj);
    1762:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1763:   PetscMalloc1(merge->nsend+1,&swaits);
    1764:   for (proc=0, k=0; proc<size; proc++) {
    1765:     if (!len_s[proc]) continue;
    1766:     i    = owners_co[proc];
    1767:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1768:     k++;
    1769:   }

    1771:   /* receives and sends of coj are complete */
    1772:   PetscMalloc1(size,&sstatus);
    1773:   for (i=0; i<merge->nrecv; i++) {
    1774:     PetscMPIInt icompleted;
    1775:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1776:   }
    1777:   PetscFree(rwaits);
    1778:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

    1780:   /* add received column indices into table to update Armax */
    1781:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
    1782:     Jptr = buf_rj[k];
    1783:     for (j=0; j<merge->len_r[k]; j++) {
    1784:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1785:     }
    1786:   }
    1787:   PetscTableGetCount(ta,&Armax);

    1789:   /* send and recv coi */
    1790:   /*-------------------*/
    1791:   PetscCommGetNewTag(comm,&tagi);
    1792:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    1793:   PetscMalloc1(len+1,&buf_s);
    1794:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1795:   for (proc=0,k=0; proc<size; proc++) {
    1796:     if (!len_s[proc]) continue;
    1797:     /* form outgoing message for i-structure:
    1798:          buf_si[0]:                 nrows to be sent
    1799:                [1:nrows]:           row index (global)
    1800:                [nrows+1:2*nrows+1]: i-structure index
    1801:     */
    1802:     /*-------------------------------------------*/
    1803:     nrows       = len_si[proc]/2 - 1;
    1804:     buf_si_i    = buf_si + nrows+1;
    1805:     buf_si[0]   = nrows;
    1806:     buf_si_i[0] = 0;
    1807:     nrows       = 0;
    1808:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1809:       nzi               = coi[i+1] - coi[i];
    1810:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1811:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1812:       nrows++;
    1813:     }
    1814:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1815:     k++;
    1816:     buf_si += len_si[proc];
    1817:   }
    1818:   i = merge->nrecv;
    1819:   while (i--) {
    1820:     PetscMPIInt icompleted;
    1821:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1822:   }
    1823:   PetscFree(rwaits);
    1824:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
    1825:   PetscFree(len_si);
    1826:   PetscFree(len_ri);
    1827:   PetscFree(swaits);
    1828:   PetscFree(sstatus);
    1829:   PetscFree(buf_s);

    1831:   /* compute the local portion of C (mpi mat) */
    1832:   /*------------------------------------------*/
    1833:   /* allocate bi array and free space for accumulating nonzero column info */
    1834:   PetscMalloc1(pn+1,&bi);
    1835:   bi[0] = 0;

    1837:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
    1838:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
    1839:   PetscFreeSpaceGet(nnz,&free_space);
    1840:   current_space = free_space;

    1842:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1843:   for (k=0; k<merge->nrecv; k++) {
    1844:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1845:     nrows       = *buf_ri_k[k];
    1846:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1847:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recieved i-structure  */
    1848:   }

    1850:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
    1851:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    1852:   rmax = 0;
    1853:   for (i=0; i<pn; i++) {
    1854:     /* add pdt[i,:]*AP into lnk */
    1855:     pnz = pdti[i+1] - pdti[i];
    1856:     ptJ = pdtj + pdti[i];
    1857:     for (j=0; j<pnz; j++) {
    1858:       row  = ptJ[j];  /* row of AP == col of Pt */
    1859:       anz  = ai[row+1] - ai[row];
    1860:       Jptr = aj + ai[row];
    1861:       /* add non-zero cols of AP into the sorted linked list lnk */
    1862:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1863:     }

    1865:     /* add received col data into lnk */
    1866:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1867:       if (i == *nextrow[k]) { /* i-th row */
    1868:         nzi  = *(nextci[k]+1) - *nextci[k];
    1869:         Jptr = buf_rj[k] + *nextci[k];
    1870:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
    1871:         nextrow[k]++; nextci[k]++;
    1872:       }
    1873:     }
    1874:     nnz = lnk[0];

    1876:     /* if free space is not available, make more free space */
    1877:     if (current_space->local_remaining<nnz) {
    1878:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1879:       nspacedouble++;
    1880:     }
    1881:     /* copy data into free space, then initialize lnk */
    1882:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
    1883:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    1885:     current_space->array           += nnz;
    1886:     current_space->local_used      += nnz;
    1887:     current_space->local_remaining -= nnz;

    1889:     bi[i+1] = bi[i] + nnz;
    1890:     if (nnz > rmax) rmax = nnz;
    1891:   }
    1892:   PetscFree3(buf_ri_k,nextrow,nextci);

    1894:   PetscMalloc1(bi[pn]+1,&bj);
    1895:   PetscFreeSpaceContiguous(&free_space,bj);
    1896:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    1897:   if (afill_tmp > afill) afill = afill_tmp;
    1898:   PetscLLCondensedDestroy_Scalable(lnk);
    1899:   PetscTableDestroy(&ta);

    1901:   MatDestroy(&POt);
    1902:   MatDestroy(&PDt);

    1904:   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
    1905:   /*----------------------------------------------------------------------------------*/
    1906:   PetscCalloc1(rmax+1,&vals);

    1908:   MatCreate(comm,&Cmpi);
    1909:   MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    1910:   MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    1911:   MatSetType(Cmpi,MATMPIAIJ);
    1912:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
    1913:   MatPreallocateFinalize(dnz,onz);
    1914:   MatSetBlockSize(Cmpi,1);
    1915:   for (i=0; i<pn; i++) {
    1916:     row  = i + rstart;
    1917:     nnz  = bi[i+1] - bi[i];
    1918:     Jptr = bj + bi[i];
    1919:     MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);
    1920:   }
    1921:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
    1922:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
    1923:   PetscFree(vals);

    1925:   merge->bi        = bi;
    1926:   merge->bj        = bj;
    1927:   merge->coi       = coi;
    1928:   merge->coj       = coj;
    1929:   merge->buf_ri    = buf_ri;
    1930:   merge->buf_rj    = buf_rj;
    1931:   merge->owners_co = owners_co;

    1933:   /* attach the supporting struct to Cmpi for reuse */
    1934:   c = (Mat_MPIAIJ*)Cmpi->data;

    1936:   c->ptap     = ptap;
    1937:   ptap->api   = NULL;
    1938:   ptap->apj   = NULL;
    1939:   ptap->merge = merge;
    1940:   ptap->apa   = NULL;
    1941:   ptap->destroy   = Cmpi->ops->destroy;
    1942:   ptap->duplicate = Cmpi->ops->duplicate;

    1944:   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
    1945:   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
    1946:   Cmpi->ops->duplicate               = MatDuplicate_MPIAIJ_MatPtAP;

    1948:   *C = Cmpi;
    1949: #if defined(PETSC_USE_INFO)
    1950:   if (bi[pn] != 0) {
    1951:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1952:     PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    1953:   } else {
    1954:     PetscInfo(Cmpi,"Empty matrix product\n");
    1955:   }
    1956: #endif
    1957:   return(0);
    1958: }