Date: 2022-08-02T03:13:48+00:00

Actual source code: mpimatmatmult.c

      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>
      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>
     12: #include <petsc/private/sfimpl.h>

     14: #if defined(PETSC_HAVE_HYPRE)
     15: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat,Mat,PetscReal,Mat);
     16: #endif

     18: PETSC_INTERN PetscErrorCode MatProductSymbolic_AB_MPIAIJ_MPIAIJ(Mat C)
     19: {
     20:   Mat_Product         *product = C->product;
     21:   Mat                 A=product->A,B=product->B;
     22:   MatProductAlgorithm alg=product->alg;
     23:   PetscReal           fill=product->fill;
     24:   PetscBool           flg;

     26:   /* scalable */
     27:   PetscStrcmp(alg,"scalable",&flg);
     28:   if (flg) {
     29:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
     30:     return 0;
     31:   }

     33:   /* nonscalable */
     34:   PetscStrcmp(alg,"nonscalable",&flg);
     35:   if (flg) {
     36:     MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
     37:     return 0;
     38:   }

     40:   /* seqmpi */
     41:   PetscStrcmp(alg,"seqmpi",&flg);
     42:   if (flg) {
     43:     MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C);
     44:     return 0;
     45:   }

     47:   /* backend general code */
     48:   PetscStrcmp(alg,"backend",&flg);
     49:   if (flg) {
     50:     MatProductSymbolic_MPIAIJBACKEND(C);
     51:     return 0;
     52:   }

     54: #if defined(PETSC_HAVE_HYPRE)
     55:   PetscStrcmp(alg,"hypre",&flg);
     56:   if (flg) {
     57:     MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
     58:     return 0;
     59:   }
     60: #endif
     61:   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
     62: }

     64: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
     65: {
     66:   Mat_APMPI      *ptap = (Mat_APMPI*)data;

     68:   PetscFree2(ptap->startsj_s,ptap->startsj_r);
     69:   PetscFree(ptap->bufa);
     70:   MatDestroy(&ptap->P_loc);
     71:   MatDestroy(&ptap->P_oth);
     72:   MatDestroy(&ptap->Pt);
     73:   PetscFree(ptap->api);
     74:   PetscFree(ptap->apj);
     75:   PetscFree(ptap->apa);
     76:   PetscFree(ptap);
     77:   return 0;
     78: }

     80: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
     81: {
     82:   Mat_MPIAIJ        *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
     83:   Mat_SeqAIJ        *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
     84:   Mat_SeqAIJ        *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
     85:   PetscScalar       *cda=cd->a,*coa=co->a;
     86:   Mat_SeqAIJ        *p_loc,*p_oth;
     87:   PetscScalar       *apa,*ca;
     88:   PetscInt          cm =C->rmap->n;
     89:   Mat_APMPI         *ptap;
     90:   PetscInt          *api,*apj,*apJ,i,k;
     91:   PetscInt          cstart=C->cmap->rstart;
     92:   PetscInt          cdnz,conz,k0,k1;
     93:   const PetscScalar *dummy;
     94:   MPI_Comm          comm;
     95:   PetscMPIInt       size;

     97:   MatCheckProduct(C,3);
     98:   ptap = (Mat_APMPI*)C->product->data;
    100:   PetscObjectGetComm((PetscObject)A,&comm);
    101:   MPI_Comm_size(comm,&size);

    105:   /* flag CPU mask for C */
    106: #if defined(PETSC_HAVE_DEVICE)
    107:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
    108:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
    109:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
    110: #endif

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

    118:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    119:   /*----------------------------------------------------------*/
    120:   /* get data from symbolic products */
    121:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    122:   p_oth = NULL;
    123:   if (size >1) {
    124:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    125:   }

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

    130:   api = ptap->api;
    131:   apj = ptap->apj;
    132:   /* trigger copy to CPU */
    133:   MatSeqAIJGetArrayRead(a->A,&dummy);
    134:   MatSeqAIJRestoreArrayRead(a->A,&dummy);
    135:   MatSeqAIJGetArrayRead(a->B,&dummy);
    136:   MatSeqAIJRestoreArrayRead(a->B,&dummy);
    137:   for (i=0; i<cm; i++) {
    138:     /* compute apa = A[i,:]*P */
    139:     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);

    141:     /* set values in C */
    142:     apJ  = apj + api[i];
    143:     cdnz = cd->i[i+1] - cd->i[i];
    144:     conz = co->i[i+1] - co->i[i];

    146:     /* 1st off-diagonal part of C */
    147:     ca = coa + co->i[i];
    148:     k  = 0;
    149:     for (k0=0; k0<conz; k0++) {
    150:       if (apJ[k] >= cstart) break;
    151:       ca[k0]      = apa[apJ[k]];
    152:       apa[apJ[k++]] = 0.0;
    153:     }

    155:     /* diagonal part of C */
    156:     ca = cda + cd->i[i];
    157:     for (k1=0; k1<cdnz; k1++) {
    158:       ca[k1]      = apa[apJ[k]];
    159:       apa[apJ[k++]] = 0.0;
    160:     }

    162:     /* 2nd off-diagonal part of C */
    163:     ca = coa + co->i[i];
    164:     for (; k0<conz; k0++) {
    165:       ca[k0]      = apa[apJ[k]];
    166:       apa[apJ[k++]] = 0.0;
    167:     }
    168:   }
    169:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    170:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    171:   return 0;
    172: }

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

    191:   MatCheckProduct(C,4);
    193:   PetscObjectGetComm((PetscObject)A,&comm);
    194:   MPI_Comm_size(comm,&size);

    196:   /* create struct Mat_APMPI and attached it to C later */
    197:   PetscNew(&ptap);

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

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

    205:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    206:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    207:   if (size > 1) {
    208:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    209:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    210:   } else {
    211:     p_oth = NULL;
    212:     pi_oth = NULL; pj_oth = NULL;
    213:   }

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

    221:   /* create and initialize a linked list */
    222:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);

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

    228:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    229:   for (i=0; i<am; i++) {
    230:     /* diagonal portion of A */
    231:     nzi = adi[i+1] - adi[i];
    232:     for (j=0; j<nzi; j++) {
    233:       row  = *adj++;
    234:       pnz  = pi_loc[row+1] - pi_loc[row];
    235:       Jptr = pj_loc + pi_loc[row];
    236:       /* add non-zero cols of P into the sorted linked list lnk */
    237:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    238:     }
    239:     /* off-diagonal portion of A */
    240:     nzi = aoi[i+1] - aoi[i];
    241:     for (j=0; j<nzi; j++) {
    242:       row  = *aoj++;
    243:       pnz  = pi_oth[row+1] - pi_oth[row];
    244:       Jptr = pj_oth + pi_oth[row];
    245:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
    246:     }
    247:     /* add possible missing diagonal entry */
    248:     if (C->force_diagonals) {
    249:       j = i + rstart; /* column index */
    250:       PetscLLCondensedAddSorted(1,&j,lnk,lnkbt);
    251:     }

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

    256:     /* if free space is not available, double the total space in the list */
    257:     if (current_space->local_remaining<apnz) {
    258:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    259:       nspacedouble++;
    260:     }

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

    266:     current_space->array           += apnz;
    267:     current_space->local_used      += apnz;
    268:     current_space->local_remaining -= apnz;
    269:   }

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

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

    281:   /* set and assemble symbolic parallel matrix C */
    282:   /*---------------------------------------------*/
    283:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    284:   MatSetBlockSizesFromMats(C,A,P);

    286:   MatGetType(A,&mtype);
    287:   MatSetType(C,mtype);
    288:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    289:   MatPreallocateFinalize(dnz,onz);

    291:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    292:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    293:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    294:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    296:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    297:   C->ops->productnumeric = MatProductNumeric_AB;

    299:   /* attach the supporting struct to C for reuse */
    300:   C->product->data    = ptap;
    301:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    303:   /* set MatInfo */
    304:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    305:   if (afill < 1.0) afill = 1.0;
    306:   C->info.mallocs           = nspacedouble;
    307:   C->info.fill_ratio_given  = fill;
    308:   C->info.fill_ratio_needed = afill;

    310: #if defined(PETSC_USE_INFO)
    311:   if (api[am]) {
    312:     PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    313:     PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    314:   } else {
    315:     PetscInfo(C,"Empty matrix product\n");
    316:   }
    317: #endif
    318:   return 0;
    319: }

    321: /* ------------------------------------------------------- */
    322: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
    323: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);

    325: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
    326: {
    327:   Mat_Product *product = C->product;
    328:   Mat         A = product->A,B=product->B;

    330:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
    331:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);

    333:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
    334:   C->ops->productsymbolic = MatProductSymbolic_AB;
    335:   return 0;
    336: }
    337: /* -------------------------------------------------------------------- */
    338: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
    339: {
    340:   Mat_Product *product = C->product;
    341:   Mat         A = product->A,B=product->B;

    343:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
    344:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);

    346:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
    347:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
    348:   return 0;
    349: }

    351: /* --------------------------------------------------------------------- */
    352: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
    353: {
    354:   Mat_Product    *product = C->product;

    356:   switch (product->type) {
    357:   case MATPRODUCT_AB:
    358:     MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
    359:     break;
    360:   case MATPRODUCT_AtB:
    361:     MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
    362:     break;
    363:   default:
    364:     break;
    365:   }
    366:   return 0;
    367: }
    368: /* ------------------------------------------------------- */

    370: typedef struct {
    371:   Mat          workB,workB1;
    372:   MPI_Request  *rwaits,*swaits;
    373:   PetscInt     nsends,nrecvs;
    374:   MPI_Datatype *stype,*rtype;
    375:   PetscInt     blda;
    376: } MPIAIJ_MPIDense;

    378: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
    379: {
    380:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
    381:   PetscInt        i;

    383:   MatDestroy(&contents->workB);
    384:   MatDestroy(&contents->workB1);
    385:   for (i=0; i<contents->nsends; i++) {
    386:     MPI_Type_free(&contents->stype[i]);
    387:   }
    388:   for (i=0; i<contents->nrecvs; i++) {
    389:     MPI_Type_free(&contents->rtype[i]);
    390:   }
    391:   PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
    392:   PetscFree(contents);
    393:   return 0;
    394: }

    396: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
    397: {
    398:   PetscErrorCode  ierr;
    399:   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
    400:   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,m,M,n,N;
    401:   MPIAIJ_MPIDense *contents;
    402:   VecScatter      ctx=aij->Mvctx;
    403:   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
    404:   MPI_Comm        comm;
    405:   MPI_Datatype    type1,*stype,*rtype;
    406:   const PetscInt  *sindices,*sstarts,*rstarts;
    407:   PetscMPIInt     *disp;
    408:   PetscBool       cisdense;

    410:   MatCheckProduct(C,4);
    412:   PetscObjectGetComm((PetscObject)A,&comm);
    413:   PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);
    414:   if (!cisdense) {
    415:     MatSetType(C,((PetscObject)B)->type_name);
    416:   }
    417:   MatGetLocalSize(C,&m,&n);
    418:   MatGetSize(C,&M,&N);
    419:   if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) {
    420:     MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
    421:   }
    422:   MatSetBlockSizesFromMats(C,A,B);
    423:   MatSetUp(C);
    424:   MatDenseGetLDA(B,&blda);
    425:   PetscNew(&contents);

    427:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
    428:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);

    430:   /* Create column block of B and C for memory scalability when BN is too large */
    431:   /* Estimate Bbn, column size of Bb */
    432:   if (nz) {
    433:     Bbn1 = 2*Am*BN/nz;
    434:     if (!Bbn1) Bbn1 = 1;
    435:   } else Bbn1 = BN;

    437:   bs = PetscAbs(B->cmap->bs);
    438:   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
    439:   if (Bbn1 > BN) Bbn1 = BN;
    440:   MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);

    442:   /* Enable runtime option for Bbn */
    443:   PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
    444:   PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);
    445:   PetscOptionsEnd();
    446:   Bbn  = PetscMin(Bbn,BN);

    448:   if (Bbn > 0 && Bbn < BN) {
    449:     numBb = BN/Bbn;
    450:     Bbn1 = BN - numBb*Bbn;
    451:   } else numBb = 0;

    453:   if (numBb) {
    454:     PetscInfo(C,"use Bb, BN=%" PetscInt_FMT ", Bbn=%" PetscInt_FMT "; numBb=%" PetscInt_FMT "\n",BN,Bbn,numBb);
    455:     if (Bbn1) { /* Create workB1 for the remaining columns */
    456:       PetscInfo(C,"use Bb1, BN=%" PetscInt_FMT ", Bbn1=%" PetscInt_FMT "\n",BN,Bbn1);
    457:       /* Create work matrix used to store off processor rows of B needed for local product */
    458:       MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
    459:     } else contents->workB1 = NULL;
    460:   }

    462:   /* Create work matrix used to store off processor rows of B needed for local product */
    463:   MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn,NULL,&contents->workB);

    465:   /* Use MPI derived data type to reduce memory required by the send/recv buffers */
    466:   PetscMalloc4(nsends,&stype,nrecvs,&rtype,nrecvs,&contents->rwaits,nsends,&contents->swaits);
    467:   contents->stype  = stype;
    468:   contents->nsends = nsends;

    470:   contents->rtype  = rtype;
    471:   contents->nrecvs = nrecvs;
    472:   contents->blda   = blda;

    474:   PetscMalloc1(Bm+1,&disp);
    475:   for (i=0; i<nsends; i++) {
    476:     nrows_to = sstarts[i+1]-sstarts[i];
    477:     for (j=0; j<nrows_to; j++) disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
    478:     MPI_Type_create_indexed_block(nrows_to,1,disp,MPIU_SCALAR,&type1);
    479:     MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);
    480:     MPI_Type_commit(&stype[i]);
    481:     MPI_Type_free(&type1);
    482:   }

    484:   for (i=0; i<nrecvs; i++) {
    485:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
    486:     nrows_from = rstarts[i+1]-rstarts[i];
    487:     disp[0] = 0;
    488:     MPI_Type_create_indexed_block(1,nrows_from,disp,MPIU_SCALAR,&type1);
    489:     MPI_Type_create_resized(type1,0,nz*sizeof(PetscScalar),&rtype[i]);
    490:     MPI_Type_commit(&rtype[i]);
    491:     MPI_Type_free(&type1);
    492:   }

    494:   PetscFree(disp);
    495:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
    496:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
    497:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    498:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    499:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    500:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    502:   C->product->data = contents;
    503:   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
    504:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
    505:   return 0;
    506: }

    508: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
    509: /*
    510:     Performs an efficient scatter on the rows of B needed by this process; this is
    511:     a modification of the VecScatterBegin_() routines.

    513:     Input: Bbidx = 0: B = Bb
    514:                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
    515: */
    516: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
    517: {
    518:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
    519:   const PetscScalar *b;
    520:   PetscScalar       *rvalues;
    521:   VecScatter        ctx = aij->Mvctx;
    522:   const PetscInt    *sindices,*sstarts,*rstarts;
    523:   const PetscMPIInt *sprocs,*rprocs;
    524:   PetscInt          i,nsends,nrecvs;
    525:   MPI_Request       *swaits,*rwaits;
    526:   MPI_Comm          comm;
    527:   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
    528:   MPIAIJ_MPIDense   *contents;
    529:   Mat               workB;
    530:   MPI_Datatype      *stype,*rtype;
    531:   PetscInt          blda;

    533:   MatCheckProduct(C,4);
    535:   contents = (MPIAIJ_MPIDense*)C->product->data;
    536:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
    537:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
    538:   PetscMPIIntCast(nsends,&nsends_mpi);
    539:   PetscMPIIntCast(nrecvs,&nrecvs_mpi);
    540:   if (Bbidx == 0) workB = *outworkB = contents->workB;
    541:   else workB = *outworkB = contents->workB1;
    543:   swaits = contents->swaits;
    544:   rwaits = contents->rwaits;

    546:   MatDenseGetArrayRead(B,&b);
    547:   MatDenseGetLDA(B,&blda);
    549:   MatDenseGetArray(workB,&rvalues);

    551:   /* Post recv, use MPI derived data type to save memory */
    552:   PetscObjectGetComm((PetscObject)C,&comm);
    553:   rtype = contents->rtype;
    554:   for (i=0; i<nrecvs; i++) {
    555:     MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
    556:   }

    558:   stype = contents->stype;
    559:   for (i=0; i<nsends; i++) {
    560:     MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
    561:   }

    563:   if (nrecvs) MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE);
    564:   if (nsends) MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);

    566:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
    567:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
    568:   MatDenseRestoreArrayRead(B,&b);
    569:   MatDenseRestoreArray(workB,&rvalues);
    570:   return 0;
    571: }

    573: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
    574: {
    575:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
    576:   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
    577:   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
    578:   Mat             workB;
    579:   MPIAIJ_MPIDense *contents;

    581:   MatCheckProduct(C,3);
    583:   contents = (MPIAIJ_MPIDense*)C->product->data;
    584:   /* diagonal block of A times all local rows of B */
    585:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
    586:   MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);
    587:   if (contents->workB->cmap->n == B->cmap->N) {
    588:     /* get off processor parts of B needed to complete C=A*B */
    589:     MatMPIDenseScatter(A,B,0,C,&workB);

    591:     /* off-diagonal block of A times nonlocal rows of B */
    592:     MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
    593:   } else {
    594:     Mat       Bb,Cb;
    595:     PetscInt  BN=B->cmap->N,n=contents->workB->cmap->n,i;
    596:     PetscBool ccpu;

    599:     /* Prevent from unneeded copies back and forth from the GPU
    600:        when getting and restoring the submatrix
    601:        We need a proper GPU code for AIJ * dense in parallel */
    602:     MatBoundToCPU(C,&ccpu);
    603:     MatBindToCPU(C,PETSC_TRUE);
    604:     for (i=0; i<BN; i+=n) {
    605:       MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);
    606:       MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);

    608:       /* get off processor parts of B needed to complete C=A*B */
    609:       MatMPIDenseScatter(A,Bb,(i+n)>BN,C,&workB);

    611:       /* off-diagonal block of A times nonlocal rows of B */
    612:       cdense = (Mat_MPIDense*)Cb->data;
    613:       MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
    614:       MatDenseRestoreSubMatrix(B,&Bb);
    615:       MatDenseRestoreSubMatrix(C,&Cb);
    616:     }
    617:     MatBindToCPU(C,ccpu);
    618:   }
    619:   return 0;
    620: }

    622: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
    623: {
    624:   Mat_MPIAIJ        *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
    625:   Mat_SeqAIJ        *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
    626:   Mat_SeqAIJ        *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
    627:   PetscInt          *adi = ad->i,*adj,*aoi=ao->i,*aoj;
    628:   PetscScalar       *ada,*aoa,*cda=cd->a,*coa=co->a;
    629:   Mat_SeqAIJ        *p_loc,*p_oth;
    630:   PetscInt          *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
    631:   PetscScalar       *pa_loc,*pa_oth,*pa,valtmp,*ca;
    632:   PetscInt          cm    = C->rmap->n,anz,pnz;
    633:   Mat_APMPI         *ptap;
    634:   PetscScalar       *apa_sparse;
    635:   const PetscScalar *dummy;
    636:   PetscInt          *api,*apj,*apJ,i,j,k,row;
    637:   PetscInt          cstart = C->cmap->rstart;
    638:   PetscInt          cdnz,conz,k0,k1,nextp;
    639:   MPI_Comm          comm;
    640:   PetscMPIInt       size;

    642:   MatCheckProduct(C,3);
    643:   ptap = (Mat_APMPI*)C->product->data;
    645:   PetscObjectGetComm((PetscObject)C,&comm);
    646:   MPI_Comm_size(comm,&size);

    649:   /* flag CPU mask for C */
    650: #if defined(PETSC_HAVE_DEVICE)
    651:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
    652:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
    653:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
    654: #endif
    655:   apa_sparse = ptap->apa;

    657:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    658:   /*-----------------------------------------------------*/
    659:   /* update numerical values of P_oth and P_loc */
    660:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    661:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    663:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    664:   /*----------------------------------------------------------*/
    665:   /* get data from symbolic products */
    666:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    667:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
    668:   if (size >1) {
    669:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    670:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
    671:   } else {
    672:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
    673:   }

    675:   /* trigger copy to CPU */
    676:   MatSeqAIJGetArrayRead(a->A,&dummy);
    677:   MatSeqAIJRestoreArrayRead(a->A,&dummy);
    678:   MatSeqAIJGetArrayRead(a->B,&dummy);
    679:   MatSeqAIJRestoreArrayRead(a->B,&dummy);
    680:   api = ptap->api;
    681:   apj = ptap->apj;
    682:   for (i=0; i<cm; i++) {
    683:     apJ = apj + api[i];

    685:     /* diagonal portion of A */
    686:     anz = adi[i+1] - adi[i];
    687:     adj = ad->j + adi[i];
    688:     ada = ad->a + adi[i];
    689:     for (j=0; j<anz; j++) {
    690:       row = adj[j];
    691:       pnz = pi_loc[row+1] - pi_loc[row];
    692:       pj  = pj_loc + pi_loc[row];
    693:       pa  = pa_loc + pi_loc[row];
    694:       /* perform sparse axpy */
    695:       valtmp = ada[j];
    696:       nextp  = 0;
    697:       for (k=0; nextp<pnz; k++) {
    698:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    699:           apa_sparse[k] += valtmp*pa[nextp++];
    700:         }
    701:       }
    702:       PetscLogFlops(2.0*pnz);
    703:     }

    705:     /* off-diagonal portion of A */
    706:     anz = aoi[i+1] - aoi[i];
    707:     aoj = ao->j + aoi[i];
    708:     aoa = ao->a + aoi[i];
    709:     for (j=0; j<anz; j++) {
    710:       row = aoj[j];
    711:       pnz = pi_oth[row+1] - pi_oth[row];
    712:       pj  = pj_oth + pi_oth[row];
    713:       pa  = pa_oth + pi_oth[row];
    714:       /* perform sparse axpy */
    715:       valtmp = aoa[j];
    716:       nextp  = 0;
    717:       for (k=0; nextp<pnz; k++) {
    718:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    719:           apa_sparse[k] += valtmp*pa[nextp++];
    720:         }
    721:       }
    722:       PetscLogFlops(2.0*pnz);
    723:     }

    725:     /* set values in C */
    726:     cdnz = cd->i[i+1] - cd->i[i];
    727:     conz = co->i[i+1] - co->i[i];

    729:     /* 1st off-diagonal part of C */
    730:     ca = coa + co->i[i];
    731:     k  = 0;
    732:     for (k0=0; k0<conz; k0++) {
    733:       if (apJ[k] >= cstart) break;
    734:       ca[k0]        = apa_sparse[k];
    735:       apa_sparse[k] = 0.0;
    736:       k++;
    737:     }

    739:     /* diagonal part of C */
    740:     ca = cda + cd->i[i];
    741:     for (k1=0; k1<cdnz; k1++) {
    742:       ca[k1]        = apa_sparse[k];
    743:       apa_sparse[k] = 0.0;
    744:       k++;
    745:     }

    747:     /* 2nd off-diagonal part of C */
    748:     ca = coa + co->i[i];
    749:     for (; k0<conz; k0++) {
    750:       ca[k0]        = apa_sparse[k];
    751:       apa_sparse[k] = 0.0;
    752:       k++;
    753:     }
    754:   }
    755:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    756:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    757:   return 0;
    758: }

    760: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
    761: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
    762: {
    763:   PetscErrorCode     ierr;
    764:   MPI_Comm           comm;
    765:   PetscMPIInt        size;
    766:   Mat_APMPI          *ptap;
    767:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
    768:   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
    769:   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    770:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    771:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    772:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=1;
    773:   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
    774:   PetscReal          afill;
    775:   MatType            mtype;

    777:   MatCheckProduct(C,4);
    779:   PetscObjectGetComm((PetscObject)A,&comm);
    780:   MPI_Comm_size(comm,&size);

    782:   /* create struct Mat_APMPI and attached it to C later */
    783:   PetscNew(&ptap);

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

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

    791:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    792:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    793:   if (size > 1) {
    794:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    795:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    796:   } else {
    797:     p_oth  = NULL;
    798:     pi_oth = NULL; pj_oth = NULL;
    799:   }

    801:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    802:   /*-------------------------------------------------------------------*/
    803:   PetscMalloc1(am+2,&api);
    804:   ptap->api = api;
    805:   api[0]    = 0;

    807:   PetscLLCondensedCreate_Scalable(lsize,&lnk);

    809:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    810:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
    811:   current_space = free_space;
    812:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    813:   for (i=0; i<am; i++) {
    814:     /* diagonal portion of A */
    815:     nzi = adi[i+1] - adi[i];
    816:     for (j=0; j<nzi; j++) {
    817:       row  = *adj++;
    818:       pnz  = pi_loc[row+1] - pi_loc[row];
    819:       Jptr = pj_loc + pi_loc[row];
    820:       /* Expand list if it is not long enough */
    821:       if (pnz+apnz_max > lsize) {
    822:         lsize = pnz+apnz_max;
    823:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    824:       }
    825:       /* add non-zero cols of P into the sorted linked list lnk */
    826:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    827:       apnz     = *lnk; /* The first element in the list is the number of items in the list */
    828:       api[i+1] = api[i] + apnz;
    829:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
    830:     }
    831:     /* off-diagonal portion of A */
    832:     nzi = aoi[i+1] - aoi[i];
    833:     for (j=0; j<nzi; j++) {
    834:       row  = *aoj++;
    835:       pnz  = pi_oth[row+1] - pi_oth[row];
    836:       Jptr = pj_oth + pi_oth[row];
    837:       /* Expand list if it is not long enough */
    838:       if (pnz+apnz_max > lsize) {
    839:         lsize = pnz + apnz_max;
    840:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    841:       }
    842:       /* add non-zero cols of P into the sorted linked list lnk */
    843:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    844:       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
    845:       api[i+1] = api[i] + apnz;
    846:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
    847:     }

    849:     /* add missing diagonal entry */
    850:     if (C->force_diagonals) {
    851:       j = i + rstart; /* column index */
    852:       PetscLLCondensedAddSorted_Scalable(1,&j,lnk);
    853:     }

    855:     apnz     = *lnk;
    856:     api[i+1] = api[i] + apnz;
    857:     if (apnz > apnz_max) apnz_max = apnz;

    859:     /* if free space is not available, double the total space in the list */
    860:     if (current_space->local_remaining<apnz) {
    861:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    862:       nspacedouble++;
    863:     }

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

    869:     current_space->array           += apnz;
    870:     current_space->local_used      += apnz;
    871:     current_space->local_remaining -= apnz;
    872:   }

    874:   /* Allocate space for apj, initialize apj, and */
    875:   /* destroy list of free space and other temporary array(s) */
    876:   PetscMalloc1(api[am]+1,&ptap->apj);
    877:   apj  = ptap->apj;
    878:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    879:   PetscLLCondensedDestroy_Scalable(lnk);

    881:   /* create and assemble symbolic parallel matrix C */
    882:   /*----------------------------------------------------*/
    883:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    884:   MatSetBlockSizesFromMats(C,A,P);
    885:   MatGetType(A,&mtype);
    886:   MatSetType(C,mtype);
    887:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    888:   MatPreallocateFinalize(dnz,onz);

    890:   /* malloc apa for assembly C */
    891:   PetscCalloc1(apnz_max,&ptap->apa);

    893:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    894:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    895:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    896:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    898:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
    899:   C->ops->productnumeric = MatProductNumeric_AB;

    901:   /* attach the supporting struct to C for reuse */
    902:   C->product->data    = ptap;
    903:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    905:   /* set MatInfo */
    906:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    907:   if (afill < 1.0) afill = 1.0;
    908:   C->info.mallocs           = nspacedouble;
    909:   C->info.fill_ratio_given  = fill;
    910:   C->info.fill_ratio_needed = afill;

    912: #if defined(PETSC_USE_INFO)
    913:   if (api[am]) {
    914:     PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    915:     PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    916:   } else {
    917:     PetscInfo(C,"Empty matrix product\n");
    918:   }
    919: #endif
    920:   return 0;
    921: }

    923: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
    924: /* Three input arrays are merged to one output array. The size of the    */
    925: /* output array is also output. Duplicate entries only show up once.     */
    926: static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
    927:                                PetscInt  size2, PetscInt *in2,
    928:                                PetscInt  size3, PetscInt *in3,
    929:                                PetscInt *size4, PetscInt *out)
    930: {
    931:   int i = 0, j = 0, k = 0, l = 0;

    933:   /* Traverse all three arrays */
    934:   while (i<size1 && j<size2 && k<size3) {
    935:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
    936:       out[l++] = in1[i++];
    937:     }
    938:     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
    939:       out[l++] = in2[j++];
    940:     }
    941:     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
    942:       out[l++] = in3[k++];
    943:     }
    944:     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
    945:       out[l++] = in1[i];
    946:       i++, j++;
    947:     }
    948:     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
    949:       out[l++] = in1[i];
    950:       i++, k++;
    951:     }
    952:     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
    953:       out[l++] = in2[j];
    954:       k++, j++;
    955:     }
    956:     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
    957:       out[l++] = in1[i];
    958:       i++, j++, k++;
    959:     }
    960:   }

    962:   /* Traverse two remaining arrays */
    963:   while (i<size1 && j<size2) {
    964:     if (in1[i] < in2[j]) {
    965:       out[l++] = in1[i++];
    966:     }
    967:     else if (in1[i] > in2[j]) {
    968:       out[l++] = in2[j++];
    969:     }
    970:     else {
    971:       out[l++] = in1[i];
    972:       i++, j++;
    973:     }
    974:   }

    976:   while (i<size1 && k<size3) {
    977:     if (in1[i] < in3[k]) {
    978:       out[l++] = in1[i++];
    979:     }
    980:     else if (in1[i] > in3[k]) {
    981:       out[l++] = in3[k++];
    982:     }
    983:     else {
    984:       out[l++] = in1[i];
    985:       i++, k++;
    986:     }
    987:   }

    989:   while (k<size3 && j<size2)  {
    990:     if (in3[k] < in2[j]) {
    991:       out[l++] = in3[k++];
    992:     }
    993:     else if (in3[k] > in2[j]) {
    994:       out[l++] = in2[j++];
    995:     }
    996:     else {
    997:       out[l++] = in3[k];
    998:       k++, j++;
    999:     }
    1000:   }

    1002:   /* Traverse one remaining array */
    1003:   while (i<size1) out[l++] = in1[i++];
    1004:   while (j<size2) out[l++] = in2[j++];
    1005:   while (k<size3) out[l++] = in3[k++];

    1007:   *size4 = l;
    1008: }

    1010: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
    1011: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
    1012: /* matrix-matrix multiplications.  */
    1013: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
    1014: {
    1015:   PetscErrorCode     ierr;
    1016:   MPI_Comm           comm;
    1017:   PetscMPIInt        size;
    1018:   Mat_APMPI          *ptap;
    1019:   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
    1020:   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
    1021:   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
    1022:   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
    1023:   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
    1024:   PetscInt           adponz, adpdnz;
    1025:   PetscInt           *pi_loc,*dnz,*onz;
    1026:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
    1027:   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
    1028:                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
    1029:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
    1030:   PetscBT            lnkbt;
    1031:   PetscReal          afill;
    1032:   PetscMPIInt        rank;
    1033:   Mat                adpd, aopoth;
    1034:   MatType            mtype;
    1035:   const char         *prefix;

    1037:   MatCheckProduct(C,4);
    1039:   PetscObjectGetComm((PetscObject)A,&comm);
    1040:   MPI_Comm_size(comm,&size);
    1041:   MPI_Comm_rank(comm, &rank);
    1042:   MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);

    1044:   /* create struct Mat_APMPI and attached it to C later */
    1045:   PetscNew(&ptap);

    1047:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    1048:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

    1050:   /* get P_loc by taking all local rows of P */
    1051:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    1053:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    1054:   pi_loc = p_loc->i;

    1056:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
    1057:   PetscMalloc1(am+2,&api);
    1058:   PetscMalloc1(am+2,&adpoi);

    1060:   adpoi[0]    = 0;
    1061:   ptap->api = api;
    1062:   api[0] = 0;

    1064:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
    1065:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
    1066:   MatPreallocateInitialize(comm,am,pn,dnz,onz);

    1068:   /* Symbolic calc of A_loc_diag * P_loc_diag */
    1069:   MatGetOptionsPrefix(A,&prefix);
    1070:   MatProductCreate(a->A,p->A,NULL,&adpd);
    1071:   MatGetOptionsPrefix(A,&prefix);
    1072:   MatSetOptionsPrefix(adpd,prefix);
    1073:   MatAppendOptionsPrefix(adpd,"inner_diag_");

    1075:   MatProductSetType(adpd,MATPRODUCT_AB);
    1076:   MatProductSetAlgorithm(adpd,"sorted");
    1077:   MatProductSetFill(adpd,fill);
    1078:   MatProductSetFromOptions(adpd);

    1080:   adpd->force_diagonals = C->force_diagonals;
    1081:   MatProductSymbolic(adpd);

    1083:   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
    1084:   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
    1085:   p_off = (Mat_SeqAIJ*)((p->B)->data);
    1086:   poff_i = p_off->i; poff_j = p_off->j;

    1088:   /* j_temp stores indices of a result row before they are added to the linked list */
    1089:   PetscMalloc1(pN+2,&j_temp);

    1091:   /* Symbolic calc of the A_diag * p_loc_off */
    1092:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    1093:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
    1094:   current_space = free_space_diag;

    1096:   for (i=0; i<am; i++) {
    1097:     /* A_diag * P_loc_off */
    1098:     nzi = adi[i+1] - adi[i];
    1099:     for (j=0; j<nzi; j++) {
    1100:       row  = *adj++;
    1101:       pnz  = poff_i[row+1] - poff_i[row];
    1102:       Jptr = poff_j + poff_i[row];
    1103:       for (i1 = 0; i1 < pnz; i1++) {
    1104:         j_temp[i1] = p->garray[Jptr[i1]];
    1105:       }
    1106:       /* add non-zero cols of P into the sorted linked list lnk */
    1107:       PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
    1108:     }

    1110:     adponz     = lnk[0];
    1111:     adpoi[i+1] = adpoi[i] + adponz;

    1113:     /* if free space is not available, double the total space in the list */
    1114:     if (current_space->local_remaining<adponz) {
    1115:       PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);
    1116:       nspacedouble++;
    1117:     }

    1119:     /* Copy data into free space, then initialize lnk */
    1120:     PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);

    1122:     current_space->array           += adponz;
    1123:     current_space->local_used      += adponz;
    1124:     current_space->local_remaining -= adponz;
    1125:   }

    1127:   /* Symbolic calc of A_off * P_oth */
    1128:   MatSetOptionsPrefix(a->B,prefix);
    1129:   MatAppendOptionsPrefix(a->B,"inner_offdiag_");
    1130:   MatCreate(PETSC_COMM_SELF,&aopoth);
    1131:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
    1132:   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
    1133:   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;

    1135:   /* Allocate space for apj, adpj, aopj, ... */
    1136:   /* destroy lists of free space and other temporary array(s) */

    1138:   PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
    1139:   PetscMalloc1(adpoi[am]+2, &adpoj);

    1141:   /* Copy from linked list to j-array */
    1142:   PetscFreeSpaceContiguous(&free_space_diag,adpoj);
    1143:   PetscLLDestroy(lnk,lnkbt);

    1145:   adpoJ = adpoj;
    1146:   adpdJ = adpdj;
    1147:   aopJ = aopothj;
    1148:   apj  = ptap->apj;
    1149:   apJ = apj; /* still empty */

    1151:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
    1152:   /* A_diag * P_loc_diag to get A*P */
    1153:   for (i = 0; i < am; i++) {
    1154:     aopnz  =  aopothi[i+1] -  aopothi[i];
    1155:     adponz = adpoi[i+1] - adpoi[i];
    1156:     adpdnz = adpdi[i+1] - adpdi[i];

    1158:     /* Correct indices from A_diag*P_diag */
    1159:     for (i1 = 0; i1 < adpdnz; i1++) {
    1160:       adpdJ[i1] += p_colstart;
    1161:     }
    1162:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
    1163:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
    1164:     MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);

    1166:     aopJ += aopnz;
    1167:     adpoJ += adponz;
    1168:     adpdJ += adpdnz;
    1169:     apJ += apnz;
    1170:     api[i+1] = api[i] + apnz;
    1171:   }

    1173:   /* malloc apa to store dense row A[i,:]*P */
    1174:   PetscCalloc1(pN+2,&ptap->apa);

    1176:   /* create and assemble symbolic parallel matrix C */
    1177:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    1178:   MatSetBlockSizesFromMats(C,A,P);
    1179:   MatGetType(A,&mtype);
    1180:   MatSetType(C,mtype);
    1181:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1182:   MatPreallocateFinalize(dnz,onz);

    1184:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    1185:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1186:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1187:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1189:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    1190:   C->ops->productnumeric = MatProductNumeric_AB;

    1192:   /* attach the supporting struct to C for reuse */
    1193:   C->product->data    = ptap;
    1194:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    1196:   /* set MatInfo */
    1197:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    1198:   if (afill < 1.0) afill = 1.0;
    1199:   C->info.mallocs           = nspacedouble;
    1200:   C->info.fill_ratio_given  = fill;
    1201:   C->info.fill_ratio_needed = afill;

    1203: #if defined(PETSC_USE_INFO)
    1204:   if (api[am]) {
    1205:     PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1206:     PetscInfo(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    1207:   } else {
    1208:     PetscInfo(C,"Empty matrix product\n");
    1209:   }
    1210: #endif

    1212:   MatDestroy(&aopoth);
    1213:   MatDestroy(&adpd);
    1214:   PetscFree(j_temp);
    1215:   PetscFree(adpoj);
    1216:   PetscFree(adpoi);
    1217:   return 0;
    1218: }

    1220: /*-------------------------------------------------------------------------*/
    1221: /* This routine only works when scall=MAT_REUSE_MATRIX! */
    1222: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
    1223: {
    1224:   Mat_APMPI      *ptap;
    1225:   Mat            Pt;

    1227:   MatCheckProduct(C,3);
    1228:   ptap = (Mat_APMPI*)C->product->data;

    1232:   Pt   = ptap->Pt;
    1233:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
    1234:   MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);
    1235:   return 0;
    1236: }

    1238: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
    1239: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
    1240: {
    1241:   PetscErrorCode      ierr;
    1242:   Mat_APMPI           *ptap;
    1243:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
    1244:   MPI_Comm            comm;
    1245:   PetscMPIInt         size,rank;
    1246:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1247:   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
    1248:   PetscInt            *lnk,i,k,nsend,rstart;
    1249:   PetscBT             lnkbt;
    1250:   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
    1251:   PETSC_UNUSED PetscMPIInt icompleted=0;
    1252:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
    1253:   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
    1254:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1255:   MPI_Request         *swaits,*rwaits;
    1256:   MPI_Status          *sstatus,rstatus;
    1257:   PetscLayout         rowmap;
    1258:   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
    1259:   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
    1260:   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
    1261:   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
    1262:   PetscTable          ta;
    1263:   MatType             mtype;
    1264:   const char          *prefix;

    1266:   PetscObjectGetComm((PetscObject)A,&comm);
    1267:   MPI_Comm_size(comm,&size);
    1268:   MPI_Comm_rank(comm,&rank);

    1270:   /* create symbolic parallel matrix C */
    1271:   MatGetType(A,&mtype);
    1272:   MatSetType(C,mtype);

    1274:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

    1276:   /* create struct Mat_APMPI and attached it to C later */
    1277:   PetscNew(&ptap);
    1278:   ptap->reuse = MAT_INITIAL_MATRIX;

    1280:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
    1281:   /* --------------------------------- */
    1282:   MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
    1283:   MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);

    1285:   /* (1) compute symbolic A_loc */
    1286:   /* ---------------------------*/
    1287:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);

    1289:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
    1290:   /* ------------------------------------ */
    1291:   MatGetOptionsPrefix(A,&prefix);
    1292:   MatSetOptionsPrefix(ptap->Ro,prefix);
    1293:   MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
    1294:   MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
    1295:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);

    1297:   /* (3) send coj of C_oth to other processors  */
    1298:   /* ------------------------------------------ */
    1299:   /* determine row ownership */
    1300:   PetscLayoutCreate(comm,&rowmap);
    1301:   rowmap->n  = pn;
    1302:   rowmap->bs = 1;
    1303:   PetscLayoutSetUp(rowmap);
    1304:   owners = rowmap->range;

    1306:   /* determine the number of messages to send, their lengths */
    1307:   PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
    1308:   PetscArrayzero(len_s,size);
    1309:   PetscArrayzero(len_si,size);

    1311:   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
    1312:   coi   = c_oth->i; coj = c_oth->j;
    1313:   con   = ptap->C_oth->rmap->n;
    1314:   proc  = 0;
    1315:   for (i=0; i<con; i++) {
    1316:     while (prmap[i] >= owners[proc+1]) proc++;
    1317:     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
    1318:     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
    1319:   }

    1321:   len          = 0; /* max length of buf_si[], see (4) */
    1322:   owners_co[0] = 0;
    1323:   nsend        = 0;
    1324:   for (proc=0; proc<size; proc++) {
    1325:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1326:     if (len_s[proc]) {
    1327:       nsend++;
    1328:       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
    1329:       len         += len_si[proc];
    1330:     }
    1331:   }

    1333:   /* determine the number and length of messages to receive for coi and coj  */
    1334:   PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
    1335:   PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);

    1337:   /* post the Irecv and Isend of coj */
    1338:   PetscCommGetNewTag(comm,&tagj);
    1339:   PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
    1340:   PetscMalloc1(nsend+1,&swaits);
    1341:   for (proc=0, k=0; proc<size; proc++) {
    1342:     if (!len_s[proc]) continue;
    1343:     i    = owners_co[proc];
    1344:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1345:     k++;
    1346:   }

    1348:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
    1349:   /* ---------------------------------------- */
    1350:   MatSetOptionsPrefix(ptap->Rd,prefix);
    1351:   MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
    1352:   MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
    1353:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
    1354:   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;

    1356:   /* receives coj are complete */
    1357:   for (i=0; i<nrecv; i++) {
    1358:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1359:   }
    1360:   PetscFree(rwaits);
    1361:   if (nsend) MPI_Waitall(nsend,swaits,sstatus);

    1363:   /* add received column indices into ta to update Crmax */
    1364:   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;

    1366:   /* create and initialize a linked list */
    1367:   PetscTableCreate(an,aN,&ta); /* for compute Crmax */
    1368:   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);

    1370:   for (k=0; k<nrecv; k++) {/* k-th received message */
    1371:     Jptr = buf_rj[k];
    1372:     for (j=0; j<len_r[k]; j++) {
    1373:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1374:     }
    1375:   }
    1376:   PetscTableGetCount(ta,&Crmax);
    1377:   PetscTableDestroy(&ta);

    1379:   /* (4) send and recv coi */
    1380:   /*-----------------------*/
    1381:   PetscCommGetNewTag(comm,&tagi);
    1382:   PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
    1383:   PetscMalloc1(len+1,&buf_s);
    1384:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1385:   for (proc=0,k=0; proc<size; proc++) {
    1386:     if (!len_s[proc]) continue;
    1387:     /* form outgoing message for i-structure:
    1388:          buf_si[0]:                 nrows to be sent
    1389:                [1:nrows]:           row index (global)
    1390:                [nrows+1:2*nrows+1]: i-structure index
    1391:     */
    1392:     /*-------------------------------------------*/
    1393:     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
    1394:     buf_si_i    = buf_si + nrows+1;
    1395:     buf_si[0]   = nrows;
    1396:     buf_si_i[0] = 0;
    1397:     nrows       = 0;
    1398:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1399:       nzi = coi[i+1] - coi[i];
    1400:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1401:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1402:       nrows++;
    1403:     }
    1404:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1405:     k++;
    1406:     buf_si += len_si[proc];
    1407:   }
    1408:   for (i=0; i<nrecv; i++) {
    1409:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1410:   }
    1411:   PetscFree(rwaits);
    1412:   if (nsend) MPI_Waitall(nsend,swaits,sstatus);

    1414:   PetscFree4(len_s,len_si,sstatus,owners_co);
    1415:   PetscFree(len_ri);
    1416:   PetscFree(swaits);
    1417:   PetscFree(buf_s);

    1419:   /* (5) compute the local portion of C      */
    1420:   /* ------------------------------------------ */
    1421:   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
    1422:   PetscFreeSpaceGet(Crmax,&free_space);
    1423:   current_space = free_space;

    1425:   PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
    1426:   for (k=0; k<nrecv; k++) {
    1427:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1428:     nrows       = *buf_ri_k[k];
    1429:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1430:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    1431:   }

    1433:   MatPreallocateInitialize(comm,pn,an,dnz,onz);
    1434:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
    1435:   for (i=0; i<pn; i++) { /* for each local row of C */
    1436:     /* add C_loc into C */
    1437:     nzi  = c_loc->i[i+1] - c_loc->i[i];
    1438:     Jptr = c_loc->j + c_loc->i[i];
    1439:     PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);

    1441:     /* add received col data into lnk */
    1442:     for (k=0; k<nrecv; k++) { /* k-th received message */
    1443:       if (i == *nextrow[k]) { /* i-th row */
    1444:         nzi  = *(nextci[k]+1) - *nextci[k];
    1445:         Jptr = buf_rj[k] + *nextci[k];
    1446:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
    1447:         nextrow[k]++; nextci[k]++;
    1448:       }
    1449:     }

    1451:     /* add missing diagonal entry */
    1452:     if (C->force_diagonals) {
    1453:       k = i + owners[rank]; /* column index */
    1454:       PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);
    1455:     }

    1457:     nzi = lnk[0];

    1459:     /* copy data into free space, then initialize lnk */
    1460:     PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
    1461:     MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
    1462:   }
    1463:   PetscFree3(buf_ri_k,nextrow,nextci);
    1464:   PetscLLDestroy(lnk,lnkbt);
    1465:   PetscFreeSpaceDestroy(free_space);

    1467:   /* local sizes and preallocation */
    1468:   MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
    1469:   if (P->cmap->bs > 0) PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);
    1470:   if (A->cmap->bs > 0) PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);
    1471:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1472:   MatPreallocateFinalize(dnz,onz);

    1474:   /* add C_loc and C_oth to C */
    1475:   MatGetOwnershipRange(C,&rstart,NULL);
    1476:   for (i=0; i<pn; i++) {
    1477:     ncols = c_loc->i[i+1] - c_loc->i[i];
    1478:     cols  = c_loc->j + c_loc->i[i];
    1479:     row   = rstart + i;
    1480:     MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);

    1482:     if (C->force_diagonals) {
    1483:       MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);
    1484:     }
    1485:   }
    1486:   for (i=0; i<con; i++) {
    1487:     ncols = c_oth->i[i+1] - c_oth->i[i];
    1488:     cols  = c_oth->j + c_oth->i[i];
    1489:     row   = prmap[i];
    1490:     MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);
    1491:   }
    1492:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1493:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1494:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1496:   /* members in merge */
    1497:   PetscFree(id_r);
    1498:   PetscFree(len_r);
    1499:   PetscFree(buf_ri[0]);
    1500:   PetscFree(buf_ri);
    1501:   PetscFree(buf_rj[0]);
    1502:   PetscFree(buf_rj);
    1503:   PetscLayoutDestroy(&rowmap);

    1505:   /* attach the supporting struct to C for reuse */
    1506:   C->product->data    = ptap;
    1507:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    1508:   return 0;
    1509: }

    1511: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
    1512: {
    1513:   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
    1514:   Mat_SeqAIJ        *c_seq;
    1515:   Mat_APMPI         *ptap;
    1516:   Mat               A_loc,C_loc,C_oth;
    1517:   PetscInt          i,rstart,rend,cm,ncols,row;
    1518:   const PetscInt    *cols;
    1519:   const PetscScalar *vals;

    1521:   MatCheckProduct(C,3);
    1522:   ptap = (Mat_APMPI*)C->product->data;
    1525:   MatZeroEntries(C);

    1527:   if (ptap->reuse == MAT_REUSE_MATRIX) {
    1528:     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
    1529:     /* 1) get R = Pd^T, Ro = Po^T */
    1530:     /*----------------------------*/
    1531:     MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
    1532:     MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);

    1534:     /* 2) compute numeric A_loc */
    1535:     /*--------------------------*/
    1536:     MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
    1537:   }

    1539:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
    1540:   A_loc = ptap->A_loc;
    1541:   ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
    1542:   ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
    1543:   C_loc = ptap->C_loc;
    1544:   C_oth = ptap->C_oth;

    1546:   /* add C_loc and C_oth to C */
    1547:   MatGetOwnershipRange(C,&rstart,&rend);

    1549:   /* C_loc -> C */
    1550:   cm    = C_loc->rmap->N;
    1551:   c_seq = (Mat_SeqAIJ*)C_loc->data;
    1552:   cols = c_seq->j;
    1553:   vals = c_seq->a;
    1554:   for (i=0; i<cm; i++) {
    1555:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1556:     row = rstart + i;
    1557:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1558:     cols += ncols; vals += ncols;
    1559:   }

    1561:   /* Co -> C, off-processor part */
    1562:   cm    = C_oth->rmap->N;
    1563:   c_seq = (Mat_SeqAIJ*)C_oth->data;
    1564:   cols  = c_seq->j;
    1565:   vals  = c_seq->a;
    1566:   for (i=0; i<cm; i++) {
    1567:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1568:     row = p->garray[i];
    1569:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1570:     cols += ncols; vals += ncols;
    1571:   }
    1572:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1573:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1574:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1576:   ptap->reuse = MAT_REUSE_MATRIX;
    1577:   return 0;
    1578: }

    1580: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
    1581: {
    1582:   Mat_Merge_SeqsToMPI *merge;
    1583:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
    1584:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    1585:   Mat_APMPI           *ptap;
    1586:   PetscInt            *adj;
    1587:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
    1588:   MatScalar           *ada,*ca,valtmp;
    1589:   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    1590:   MPI_Comm            comm;
    1591:   PetscMPIInt         size,rank,taga,*len_s;
    1592:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    1593:   PetscInt            **buf_ri,**buf_rj;
    1594:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    1595:   MPI_Request         *s_waits,*r_waits;
    1596:   MPI_Status          *status;
    1597:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    1598:   const PetscScalar   *dummy;
    1599:   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
    1600:   Mat                 A_loc;
    1601:   Mat_SeqAIJ          *a_loc;

    1603:   MatCheckProduct(C,3);
    1604:   ptap = (Mat_APMPI*)C->product->data;
    1607:   PetscObjectGetComm((PetscObject)C,&comm);
    1608:   MPI_Comm_size(comm,&size);
    1609:   MPI_Comm_rank(comm,&rank);

    1611:   merge = ptap->merge;

    1613:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
    1614:   /*------------------------------------------*/
    1615:   /* get data from symbolic products */
    1616:   coi    = merge->coi; coj = merge->coj;
    1617:   PetscCalloc1(coi[pon]+1,&coa);
    1618:   bi     = merge->bi; bj = merge->bj;
    1619:   owners = merge->rowmap->range;
    1620:   PetscCalloc1(bi[cm]+1,&ba);

    1622:   /* get A_loc by taking all local rows of A */
    1623:   A_loc = ptap->A_loc;
    1624:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    1625:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1626:   ai    = a_loc->i;
    1627:   aj    = a_loc->j;

    1629:   /* trigger copy to CPU */
    1630:   MatSeqAIJGetArrayRead(p->A,&dummy);
    1631:   MatSeqAIJRestoreArrayRead(p->A,&dummy);
    1632:   MatSeqAIJGetArrayRead(p->B,&dummy);
    1633:   MatSeqAIJRestoreArrayRead(p->B,&dummy);
    1634:   for (i=0; i<am; i++) {
    1635:     anz = ai[i+1] - ai[i];
    1636:     adj = aj + ai[i];
    1637:     ada = a_loc->a + ai[i];

    1639:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1640:     /*-------------------------------------------------------------*/
    1641:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1642:     pnz = po->i[i+1] - po->i[i];
    1643:     poJ = po->j + po->i[i];
    1644:     pA  = po->a + po->i[i];
    1645:     for (j=0; j<pnz; j++) {
    1646:       row = poJ[j];
    1647:       cj  = coj + coi[row];
    1648:       ca  = coa + coi[row];
    1649:       /* perform sparse axpy */
    1650:       nexta  = 0;
    1651:       valtmp = pA[j];
    1652:       for (k=0; nexta<anz; k++) {
    1653:         if (cj[k] == adj[nexta]) {
    1654:           ca[k] += valtmp*ada[nexta];
    1655:           nexta++;
    1656:         }
    1657:       }
    1658:       PetscLogFlops(2.0*anz);
    1659:     }

    1661:     /* put the value into Cd (diagonal part) */
    1662:     pnz = pd->i[i+1] - pd->i[i];
    1663:     pdJ = pd->j + pd->i[i];
    1664:     pA  = pd->a + pd->i[i];
    1665:     for (j=0; j<pnz; j++) {
    1666:       row = pdJ[j];
    1667:       cj  = bj + bi[row];
    1668:       ca  = ba + bi[row];
    1669:       /* perform sparse axpy */
    1670:       nexta  = 0;
    1671:       valtmp = pA[j];
    1672:       for (k=0; nexta<anz; k++) {
    1673:         if (cj[k] == adj[nexta]) {
    1674:           ca[k] += valtmp*ada[nexta];
    1675:           nexta++;
    1676:         }
    1677:       }
    1678:       PetscLogFlops(2.0*anz);
    1679:     }
    1680:   }

    1682:   /* 3) send and recv matrix values coa */
    1683:   /*------------------------------------*/
    1684:   buf_ri = merge->buf_ri;
    1685:   buf_rj = merge->buf_rj;
    1686:   len_s  = merge->len_s;
    1687:   PetscCommGetNewTag(comm,&taga);
    1688:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1690:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1691:   for (proc=0,k=0; proc<size; proc++) {
    1692:     if (!len_s[proc]) continue;
    1693:     i    = merge->owners_co[proc];
    1694:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1695:     k++;
    1696:   }
    1697:   if (merge->nrecv) MPI_Waitall(merge->nrecv,r_waits,status);
    1698:   if (merge->nsend) MPI_Waitall(merge->nsend,s_waits,status);

    1700:   PetscFree2(s_waits,status);
    1701:   PetscFree(r_waits);
    1702:   PetscFree(coa);

    1704:   /* 4) insert local Cseq and received values into Cmpi */
    1705:   /*----------------------------------------------------*/
    1706:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1707:   for (k=0; k<merge->nrecv; k++) {
    1708:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1709:     nrows       = *(buf_ri_k[k]);
    1710:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1711:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    1712:   }

    1714:   for (i=0; i<cm; i++) {
    1715:     row  = owners[rank] + i; /* global row index of C_seq */
    1716:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1717:     ba_i = ba + bi[i];
    1718:     bnz  = bi[i+1] - bi[i];
    1719:     /* add received vals into ba */
    1720:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1721:       /* i-th row */
    1722:       if (i == *nextrow[k]) {
    1723:         cnz    = *(nextci[k]+1) - *nextci[k];
    1724:         cj     = buf_rj[k] + *(nextci[k]);
    1725:         ca     = abuf_r[k] + *(nextci[k]);
    1726:         nextcj = 0;
    1727:         for (j=0; nextcj<cnz; j++) {
    1728:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1729:             ba_i[j] += ca[nextcj++];
    1730:           }
    1731:         }
    1732:         nextrow[k]++; nextci[k]++;
    1733:         PetscLogFlops(2.0*cnz);
    1734:       }
    1735:     }
    1736:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1737:   }
    1738:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1739:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1741:   PetscFree(ba);
    1742:   PetscFree(abuf_r[0]);
    1743:   PetscFree(abuf_r);
    1744:   PetscFree3(buf_ri_k,nextrow,nextci);
    1745:   return 0;
    1746: }

    1748: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
    1749: {
    1750:   PetscErrorCode      ierr;
    1751:   Mat                 A_loc;
    1752:   Mat_APMPI           *ptap;
    1753:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1754:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
    1755:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1756:   PetscInt            nnz;
    1757:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1758:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
    1759:   MPI_Comm            comm;
    1760:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1761:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1762:   PetscInt            len,proc,*dnz,*onz,*owners;
    1763:   PetscInt            nzi,*bi,*bj;
    1764:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1765:   MPI_Request         *swaits,*rwaits;
    1766:   MPI_Status          *sstatus,rstatus;
    1767:   Mat_Merge_SeqsToMPI *merge;
    1768:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1769:   PetscReal           afill  =1.0,afill_tmp;
    1770:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
    1771:   Mat_SeqAIJ          *a_loc;
    1772:   PetscTable          ta;
    1773:   MatType             mtype;

    1775:   PetscObjectGetComm((PetscObject)A,&comm);
    1776:   /* check if matrix local sizes are compatible */

    1779:   MPI_Comm_size(comm,&size);
    1780:   MPI_Comm_rank(comm,&rank);

    1782:   /* create struct Mat_APMPI and attached it to C later */
    1783:   PetscNew(&ptap);

    1785:   /* get A_loc by taking all local rows of A */
    1786:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1788:   ptap->A_loc = A_loc;
    1789:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
    1790:   ai          = a_loc->i;
    1791:   aj          = a_loc->j;

    1793:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1794:   /*----------------------------------------------------*/
    1795:   MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
    1796:   MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);
    1797:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
    1798:                          >= (num of nonzero rows of C_seq) - pn */
    1799:   PetscMalloc1(pon+1,&coi);
    1800:   coi[0] = 0;

    1802:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1803:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
    1804:   PetscFreeSpaceGet(nnz,&free_space);
    1805:   current_space = free_space;

    1807:   /* create and initialize a linked list */
    1808:   PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
    1809:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
    1810:   PetscTableGetCount(ta,&Armax);

    1812:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

    1814:   for (i=0; i<pon; i++) {
    1815:     pnz = poti[i+1] - poti[i];
    1816:     ptJ = potj + poti[i];
    1817:     for (j=0; j<pnz; j++) {
    1818:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1819:       anz  = ai[row+1] - ai[row];
    1820:       Jptr = aj + ai[row];
    1821:       /* add non-zero cols of AP into the sorted linked list lnk */
    1822:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1823:     }
    1824:     nnz = lnk[0];

    1826:     /* If free space is not available, double the total space in the list */
    1827:     if (current_space->local_remaining<nnz) {
    1828:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1829:       nspacedouble++;
    1830:     }

    1832:     /* Copy data into free space, and zero out denserows */
    1833:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

    1835:     current_space->array           += nnz;
    1836:     current_space->local_used      += nnz;
    1837:     current_space->local_remaining -= nnz;

    1839:     coi[i+1] = coi[i] + nnz;
    1840:   }

    1842:   PetscMalloc1(coi[pon]+1,&coj);
    1843:   PetscFreeSpaceContiguous(&free_space,coj);
    1844:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

    1846:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1847:   if (afill_tmp > afill) afill = afill_tmp;

    1849:   /* send j-array (coj) of Co to other processors */
    1850:   /*----------------------------------------------*/
    1851:   /* determine row ownership */
    1852:   PetscNew(&merge);
    1853:   PetscLayoutCreate(comm,&merge->rowmap);

    1855:   merge->rowmap->n  = pn;
    1856:   merge->rowmap->bs = 1;

    1858:   PetscLayoutSetUp(merge->rowmap);
    1859:   owners = merge->rowmap->range;

    1861:   /* determine the number of messages to send, their lengths */
    1862:   PetscCalloc1(size,&len_si);
    1863:   PetscCalloc1(size,&merge->len_s);

    1865:   len_s        = merge->len_s;
    1866:   merge->nsend = 0;

    1868:   PetscMalloc1(size+2,&owners_co);

    1870:   proc = 0;
    1871:   for (i=0; i<pon; i++) {
    1872:     while (prmap[i] >= owners[proc+1]) proc++;
    1873:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1874:     len_s[proc] += coi[i+1] - coi[i];
    1875:   }

    1877:   len          = 0; /* max length of buf_si[] */
    1878:   owners_co[0] = 0;
    1879:   for (proc=0; proc<size; proc++) {
    1880:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1881:     if (len_si[proc]) {
    1882:       merge->nsend++;
    1883:       len_si[proc] = 2*(len_si[proc] + 1);
    1884:       len         += len_si[proc];
    1885:     }
    1886:   }

    1888:   /* determine the number and length of messages to receive for coi and coj  */
    1889:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1890:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1892:   /* post the Irecv and Isend of coj */
    1893:   PetscCommGetNewTag(comm,&tagj);
    1894:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1895:   PetscMalloc1(merge->nsend+1,&swaits);
    1896:   for (proc=0, k=0; proc<size; proc++) {
    1897:     if (!len_s[proc]) continue;
    1898:     i    = owners_co[proc];
    1899:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1900:     k++;
    1901:   }

    1903:   /* receives and sends of coj are complete */
    1904:   PetscMalloc1(size,&sstatus);
    1905:   for (i=0; i<merge->nrecv; i++) {
    1906:     PETSC_UNUSED PetscMPIInt icompleted;
    1907:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1908:   }
    1909:   PetscFree(rwaits);
    1910:   if (merge->nsend) MPI_Waitall(merge->nsend,swaits,sstatus);

    1912:   /* add received column indices into table to update Armax */
    1913:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
    1914:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
    1915:     Jptr = buf_rj[k];
    1916:     for (j=0; j<merge->len_r[k]; j++) {
    1917:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1918:     }
    1919:   }
    1920:   PetscTableGetCount(ta,&Armax);

    1922:   /* send and recv coi */
    1923:   /*-------------------*/
    1924:   PetscCommGetNewTag(comm,&tagi);
    1925:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    1926:   PetscMalloc1(len+1,&buf_s);
    1927:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1928:   for (proc=0,k=0; proc<size; proc++) {
    1929:     if (!len_s[proc]) continue;
    1930:     /* form outgoing message for i-structure:
    1931:          buf_si[0]:                 nrows to be sent
    1932:                [1:nrows]:           row index (global)
    1933:                [nrows+1:2*nrows+1]: i-structure index
    1934:     */
    1935:     /*-------------------------------------------*/
    1936:     nrows       = len_si[proc]/2 - 1;
    1937:     buf_si_i    = buf_si + nrows+1;
    1938:     buf_si[0]   = nrows;
    1939:     buf_si_i[0] = 0;
    1940:     nrows       = 0;
    1941:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1942:       nzi               = coi[i+1] - coi[i];
    1943:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1944:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1945:       nrows++;
    1946:     }
    1947:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1948:     k++;
    1949:     buf_si += len_si[proc];
    1950:   }
    1951:   i = merge->nrecv;
    1952:   while (i--) {
    1953:     PETSC_UNUSED PetscMPIInt icompleted;
    1954:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1955:   }
    1956:   PetscFree(rwaits);
    1957:   if (merge->nsend) MPI_Waitall(merge->nsend,swaits,sstatus);
    1958:   PetscFree(len_si);
    1959:   PetscFree(len_ri);
    1960:   PetscFree(swaits);
    1961:   PetscFree(sstatus);
    1962:   PetscFree(buf_s);

    1964:   /* compute the local portion of C (mpi mat) */
    1965:   /*------------------------------------------*/
    1966:   /* allocate bi array and free space for accumulating nonzero column info */
    1967:   PetscMalloc1(pn+1,&bi);
    1968:   bi[0] = 0;

    1970:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
    1971:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
    1972:   PetscFreeSpaceGet(nnz,&free_space);
    1973:   current_space = free_space;

    1975:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1976:   for (k=0; k<merge->nrecv; k++) {
    1977:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1978:     nrows       = *buf_ri_k[k];
    1979:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1980:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
    1981:   }

    1983:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
    1984:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    1985:   rmax = 0;
    1986:   for (i=0; i<pn; i++) {
    1987:     /* add pdt[i,:]*AP into lnk */
    1988:     pnz = pdti[i+1] - pdti[i];
    1989:     ptJ = pdtj + pdti[i];
    1990:     for (j=0; j<pnz; j++) {
    1991:       row  = ptJ[j];  /* row of AP == col of Pt */
    1992:       anz  = ai[row+1] - ai[row];
    1993:       Jptr = aj + ai[row];
    1994:       /* add non-zero cols of AP into the sorted linked list lnk */
    1995:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1996:     }

    1998:     /* add received col data into lnk */
    1999:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    2000:       if (i == *nextrow[k]) { /* i-th row */
    2001:         nzi  = *(nextci[k]+1) - *nextci[k];
    2002:         Jptr = buf_rj[k] + *nextci[k];
    2003:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
    2004:         nextrow[k]++; nextci[k]++;
    2005:       }
    2006:     }

    2008:     /* add missing diagonal entry */
    2009:     if (C->force_diagonals) {
    2010:       k = i + owners[rank]; /* column index */
    2011:       PetscLLCondensedAddSorted_Scalable(1,&k,lnk);
    2012:     }

    2014:     nnz = lnk[0];

    2016:     /* if free space is not available, make more free space */
    2017:     if (current_space->local_remaining<nnz) {
    2018:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    2019:       nspacedouble++;
    2020:     }
    2021:     /* copy data into free space, then initialize lnk */
    2022:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
    2023:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    2025:     current_space->array           += nnz;
    2026:     current_space->local_used      += nnz;
    2027:     current_space->local_remaining -= nnz;

    2029:     bi[i+1] = bi[i] + nnz;
    2030:     if (nnz > rmax) rmax = nnz;
    2031:   }
    2032:   PetscFree3(buf_ri_k,nextrow,nextci);

    2034:   PetscMalloc1(bi[pn]+1,&bj);
    2035:   PetscFreeSpaceContiguous(&free_space,bj);
    2036:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    2037:   if (afill_tmp > afill) afill = afill_tmp;
    2038:   PetscLLCondensedDestroy_Scalable(lnk);
    2039:   PetscTableDestroy(&ta);
    2040:   MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
    2041:   MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);

    2043:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
    2044:   /*-------------------------------------------------------------------------------*/
    2045:   MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    2046:   MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    2047:   MatGetType(A,&mtype);
    2048:   MatSetType(C,mtype);
    2049:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    2050:   MatPreallocateFinalize(dnz,onz);
    2051:   MatSetBlockSize(C,1);
    2052:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    2053:   for (i=0; i<pn; i++) {
    2054:     row  = i + rstart;
    2055:     nnz  = bi[i+1] - bi[i];
    2056:     Jptr = bj + bi[i];
    2057:     MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
    2058:   }
    2059:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    2060:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    2061:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    2062:   merge->bi        = bi;
    2063:   merge->bj        = bj;
    2064:   merge->coi       = coi;
    2065:   merge->coj       = coj;
    2066:   merge->buf_ri    = buf_ri;
    2067:   merge->buf_rj    = buf_rj;
    2068:   merge->owners_co = owners_co;

    2070:   /* attach the supporting struct to C for reuse */
    2071:   C->product->data    = ptap;
    2072:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    2073:   ptap->merge         = merge;

    2075:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

    2077: #if defined(PETSC_USE_INFO)
    2078:   if (bi[pn] != 0) {
    2079:     PetscInfo(C,"Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    2080:     PetscInfo(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    2081:   } else {
    2082:     PetscInfo(C,"Empty matrix product\n");
    2083:   }
    2084: #endif
    2085:   return 0;
    2086: }

    2088: /* ---------------------------------------------------------------- */
    2089: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
    2090: {
    2091:   Mat_Product    *product = C->product;
    2092:   Mat            A=product->A,B=product->B;
    2093:   PetscReal      fill=product->fill;
    2094:   PetscBool      flg;

    2096:   /* scalable */
    2097:   PetscStrcmp(product->alg,"scalable",&flg);
    2098:   if (flg) {
    2099:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
    2100:     goto next;
    2101:   }

    2103:   /* nonscalable */
    2104:   PetscStrcmp(product->alg,"nonscalable",&flg);
    2105:   if (flg) {
    2106:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
    2107:     goto next;
    2108:   }

    2110:   /* matmatmult */
    2111:   PetscStrcmp(product->alg,"at*b",&flg);
    2112:   if (flg) {
    2113:     Mat       At;
    2114:     Mat_APMPI *ptap;

    2116:     MatTranspose(A,MAT_INITIAL_MATRIX,&At);
    2117:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
    2118:     ptap = (Mat_APMPI*)C->product->data;
    2119:     if (ptap) {
    2120:       ptap->Pt = At;
    2121:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    2122:     }
    2123:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
    2124:     goto next;
    2125:   }

    2127:   /* backend general code */
    2128:   PetscStrcmp(product->alg,"backend",&flg);
    2129:   if (flg) {
    2130:     MatProductSymbolic_MPIAIJBACKEND(C);
    2131:     return 0;
    2132:   }

    2134:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");

    2136: next:
    2137:   C->ops->productnumeric = MatProductNumeric_AtB;
    2138:   return 0;
    2139: }

    2141: /* ---------------------------------------------------------------- */
    2142: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
    2143: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
    2144: {
    2146:   Mat_Product    *product = C->product;
    2147:   Mat            A=product->A,B=product->B;
    2148: #if defined(PETSC_HAVE_HYPRE)
    2149:   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
    2150:   PetscInt       nalg = 5;
    2151: #else
    2152:   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
    2153:   PetscInt       nalg = 4;
    2154: #endif
    2155:   PetscInt       alg = 1; /* set nonscalable algorithm as default */
    2156:   PetscBool      flg;
    2157:   MPI_Comm       comm;

    2159:   /* Check matrix local sizes */
    2160:   PetscObjectGetComm((PetscObject)C,&comm);

    2163:   /* Set "nonscalable" as default algorithm */
    2164:   PetscStrcmp(C->product->alg,"default",&flg);
    2165:   if (flg) {
    2166:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2168:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2169:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2170:       MatInfo     Ainfo,Binfo;
    2171:       PetscInt    nz_local;
    2172:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2174:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2175:       MatGetInfo(B,MAT_LOCAL,&Binfo);
    2176:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2178:       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2179:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2181:       if (alg_scalable) {
    2182:         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2183:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2184:         PetscInfo(B,"Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n",B->cmap->N,(double)(product->fill*nz_local));
    2185:       }
    2186:     }
    2187:   }

    2189:   /* Get runtime option */
    2190:   if (product->api_user) {
    2191:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
    2192:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2193:     PetscOptionsEnd();
    2194:   } else {
    2195:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
    2196:     PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2197:     PetscOptionsEnd();
    2198:   }
    2199:   if (flg) {
    2200:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2201:   }

    2203:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
    2204:   return 0;
    2205: }

    2207: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
    2208: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
    2209: {
    2211:   Mat_Product    *product = C->product;
    2212:   Mat            A=product->A,B=product->B;
    2213:   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
    2214:   PetscInt       nalg = 4;
    2215:   PetscInt       alg = 1; /* set default algorithm  */
    2216:   PetscBool      flg;
    2217:   MPI_Comm       comm;

    2219:   /* Check matrix local sizes */
    2220:   PetscObjectGetComm((PetscObject)C,&comm);

    2223:   /* Set default algorithm */
    2224:   PetscStrcmp(C->product->alg,"default",&flg);
    2225:   if (flg) {
    2226:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2227:   }

    2229:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2230:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2231:     MatInfo     Ainfo,Binfo;
    2232:     PetscInt    nz_local;
    2233:     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2235:     MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2236:     MatGetInfo(B,MAT_LOCAL,&Binfo);
    2237:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2239:     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2240:     MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2242:     if (alg_scalable) {
    2243:       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2244:       MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2245:       PetscInfo(B,"Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n",B->cmap->N,(double)(product->fill*nz_local));
    2246:     }
    2247:   }

    2249:   /* Get runtime option */
    2250:   if (product->api_user) {
    2251:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
    2252:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2253:     PetscOptionsEnd();
    2254:   } else {
    2255:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
    2256:     PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2257:     PetscOptionsEnd();
    2258:   }
    2259:   if (flg) {
    2260:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2261:   }

    2263:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
    2264:   return 0;
    2265: }

    2267: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
    2268: {
    2270:   Mat_Product    *product = C->product;
    2271:   Mat            A=product->A,P=product->B;
    2272:   MPI_Comm       comm;
    2273:   PetscBool      flg;
    2274:   PetscInt       alg=1; /* set default algorithm */
    2275: #if !defined(PETSC_HAVE_HYPRE)
    2276:   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
    2277:   PetscInt       nalg=5;
    2278: #else
    2279:   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
    2280:   PetscInt       nalg=6;
    2281: #endif
    2282:   PetscInt       pN=P->cmap->N;

    2284:   /* Check matrix local sizes */
    2285:   PetscObjectGetComm((PetscObject)C,&comm);

    2289:   /* Set "nonscalable" as default algorithm */
    2290:   PetscStrcmp(C->product->alg,"default",&flg);
    2291:   if (flg) {
    2292:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2294:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2295:     if (pN > 100000) {
    2296:       MatInfo     Ainfo,Pinfo;
    2297:       PetscInt    nz_local;
    2298:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2300:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2301:       MatGetInfo(P,MAT_LOCAL,&Pinfo);
    2302:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

    2304:       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2305:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2307:       if (alg_scalable) {
    2308:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2309:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2310:       }
    2311:     }
    2312:   }

    2314:   /* Get runtime option */
    2315:   if (product->api_user) {
    2316:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
    2317:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2318:     PetscOptionsEnd();
    2319:   } else {
    2320:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
    2321:     PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2322:     PetscOptionsEnd();
    2323:   }
    2324:   if (flg) {
    2325:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2326:   }

    2328:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
    2329:   return 0;
    2330: }

    2332: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
    2333: {
    2334:   Mat_Product *product = C->product;
    2335:   Mat         A = product->A,R=product->B;

    2337:   /* Check matrix local sizes */

    2340:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
    2341:   return 0;
    2342: }

    2344: /*
    2345:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
    2346: */
    2347: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
    2348: {
    2350:   Mat_Product    *product = C->product;
    2351:   PetscBool      flg = PETSC_FALSE;
    2352:   PetscInt       alg = 1; /* default algorithm */
    2353:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
    2354:   PetscInt       nalg = 3;

    2356:   /* Set default algorithm */
    2357:   PetscStrcmp(C->product->alg,"default",&flg);
    2358:   if (flg) {
    2359:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2360:   }

    2362:   /* Get runtime option */
    2363:   if (product->api_user) {
    2364:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
    2365:     PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2366:     PetscOptionsEnd();
    2367:   } else {
    2368:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
    2369:     PetscOptionsEList("-mat_product_algorithm","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
    2370:     PetscOptionsEnd();
    2371:   }
    2372:   if (flg) {
    2373:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2374:   }

    2376:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
    2377:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
    2378:   return 0;
    2379: }

    2381: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
    2382: {
    2383:   Mat_Product    *product = C->product;

    2385:   switch (product->type) {
    2386:   case MATPRODUCT_AB:
    2387:     MatProductSetFromOptions_MPIAIJ_AB(C);
    2388:     break;
    2389:   case MATPRODUCT_AtB:
    2390:     MatProductSetFromOptions_MPIAIJ_AtB(C);
    2391:     break;
    2392:   case MATPRODUCT_PtAP:
    2393:     MatProductSetFromOptions_MPIAIJ_PtAP(C);
    2394:     break;
    2395:   case MATPRODUCT_RARt:
    2396:     MatProductSetFromOptions_MPIAIJ_RARt(C);
    2397:     break;
    2398:   case MATPRODUCT_ABC:
    2399:     MatProductSetFromOptions_MPIAIJ_ABC(C);
    2400:     break;
    2401:   default:
    2402:     break;
    2403:   }
    2404:   return 0;
    2405: }