Actual source code: mpimatmatmult.c
petsc-3.15.0 2021-03-30
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      2: /*
      3:   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
      4:           C = A * B
      5: */
      6: #include <../src/mat/impls/aij/seq/aij.h>
      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:   PetscErrorCode      ierr;
     21:   Mat_Product         *product = C->product;
     22:   Mat                 A=product->A,B=product->B;
     23:   MatProductAlgorithm alg=product->alg;
     24:   PetscReal           fill=product->fill;
     25:   PetscBool           flg;

     28:   /* scalable */
     29:   PetscStrcmp(alg,"scalable",&flg);
     30:   if (flg) {
     31:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
     32:     return(0);
     33:   }

     35:   /* nonscalable */
     36:   PetscStrcmp(alg,"nonscalable",&flg);
     37:   if (flg) {
     38:     MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
     39:     return(0);
     40:   }

     42:   /* seqmpi */
     43:   PetscStrcmp(alg,"seqmpi",&flg);
     44:   if (flg) {
     45:     MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A,B,fill,C);
     46:     return(0);
     47:   }

     49:   /* backend general code */
     50:   PetscStrcmp(alg,"backend",&flg);
     51:   if (flg) {
     52:     MatProductSymbolic_MPIAIJBACKEND(C);
     53:     return(0);
     54:   }

     56: #if defined(PETSC_HAVE_HYPRE)
     57:   PetscStrcmp(alg,"hypre",&flg);
     58:   if (flg) {
     59:     MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
     60:     return(0);
     61:   }
     62: #endif
     63:   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
     64: }

     66: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
     67: {
     69:   Mat_APMPI      *ptap = (Mat_APMPI*)data;

     72:   PetscFree2(ptap->startsj_s,ptap->startsj_r);
     73:   PetscFree(ptap->bufa);
     74:   MatDestroy(&ptap->P_loc);
     75:   MatDestroy(&ptap->P_oth);
     76:   MatDestroy(&ptap->Pt);
     77:   PetscFree(ptap->api);
     78:   PetscFree(ptap->apj);
     79:   PetscFree(ptap->apa);
     80:   PetscFree(ptap);
     81:   return(0);
     82: }

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

    103:   MatCheckProduct(C,3);
    104:   ptap = (Mat_APMPI*)C->product->data;
    105:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    106:   PetscObjectGetComm((PetscObject)A,&comm);
    107:   MPI_Comm_size(comm,&size);

    109:   if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");

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

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

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

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

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

    145:     /* 1st off-diagonal part of C */
    146:     ca = coa + co->i[i];
    147:     k  = 0;
    148:     for (k0=0; k0<conz; k0++) {
    149:       if (apJ[k] >= cstart) break;
    150:       ca[k0]      = apa[apJ[k]];
    151:       apa[apJ[k++]] = 0.0;
    152:     }

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

    161:     /* 2nd off-diagonal part of C */
    162:     ca = coa + co->i[i];
    163:     for (; k0<conz; k0++) {
    164:       ca[k0]      = apa[apJ[k]];
    165:       apa[apJ[k++]] = 0.0;
    166:     }
    167:   }
    168:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    169:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    170:   return(0);
    171: }

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

    191:   MatCheckProduct(C,4);
    192:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    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:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    313:     PetscInfo1(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;

    331:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
    332:     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);

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

    345:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
    346:     SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);

    348:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
    349:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
    350:   return(0);
    351: }

    353: /* --------------------------------------------------------------------- */
    354: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
    355: {
    357:   Mat_Product    *product = C->product;

    360:   switch (product->type) {
    361:   case MATPRODUCT_AB:
    362:     MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
    363:     break;
    364:   case MATPRODUCT_AtB:
    365:     MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
    366:     break;
    367:   default:
    368:     break;
    369:   }
    370:   return(0);
    371: }
    372: /* ------------------------------------------------------- */

    374: typedef struct {
    375:   Mat          workB,workB1;
    376:   MPI_Request  *rwaits,*swaits;
    377:   PetscInt     nsends,nrecvs;
    378:   MPI_Datatype *stype,*rtype;
    379:   PetscInt     blda;
    380: } MPIAIJ_MPIDense;

    382: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
    383: {
    384:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
    385:   PetscErrorCode  ierr;
    386:   PetscInt        i;

    389:   MatDestroy(&contents->workB);
    390:   MatDestroy(&contents->workB1);
    391:   for (i=0; i<contents->nsends; i++) {
    392:     MPI_Type_free(&contents->stype[i]);
    393:   }
    394:   for (i=0; i<contents->nrecvs; i++) {
    395:     MPI_Type_free(&contents->rtype[i]);
    396:   }
    397:   PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
    398:   PetscFree(contents);
    399:   return(0);
    400: }

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

    417:   MatCheckProduct(C,4);
    418:   if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
    419:   PetscObjectGetComm((PetscObject)A,&comm);
    420:   PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);
    421:   if (!cisdense) {
    422:     MatSetType(C,((PetscObject)B)->type_name);
    423:   }
    424:   MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
    425:   MatSetBlockSizesFromMats(C,A,B);
    426:   MatSetUp(C);
    427:   MatDenseGetLDA(B,&blda);
    428:   MatDenseGetLDA(C,&clda);
    429:   PetscNew(&contents);

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

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

    441:   bs = PetscAbs(B->cmap->bs);
    442:   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
    443:   if (Bbn1 > BN) Bbn1 = BN;
    444:   MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);

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

    452:   if (Bbn > 0 && Bbn < BN) {
    453:     numBb = BN/Bbn;
    454:     Bbn1 = BN - numBb*Bbn;
    455:   } else numBb = 0;

    457:   if (numBb) {
    458:     PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,numBb);
    459:     if (Bbn1) { /* Create workB1 for the remaining columns */
    460:       PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);
    461:       /* Create work matrix used to store off processor rows of B needed for local product */
    462:       MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
    463:     } else contents->workB1 = NULL;
    464:   }

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

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

    474:   contents->rtype  = rtype;
    475:   contents->nrecvs = nrecvs;
    476:   contents->blda   = blda;

    478:   PetscMalloc1(Bm+1,&disp);
    479:   for (i=0; i<nsends; i++) {
    480:     nrows_to = sstarts[i+1]-sstarts[i];
    481:     for (j=0; j<nrows_to; j++){
    482:       disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
    483:     }
    484:     MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);

    486:     MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);
    487:     MPI_Type_commit(&stype[i]);
    488:     MPI_Type_free(&type1);
    489:   }

    491:   for (i=0; i<nrecvs; i++) {
    492:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
    493:     nrows_from = rstarts[i+1]-rstarts[i];
    494:     disp[0] = 0;
    495:     MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);
    496:     MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);
    497:     MPI_Type_commit(&rtype[i]);
    498:     MPI_Type_free(&type1);
    499:   }

    501:   PetscFree(disp);
    502:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
    503:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
    504:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    505:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    506:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    507:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    509:   C->product->data = contents;
    510:   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
    511:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
    512:   return(0);
    513: }

    515: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
    516: /*
    517:     Performs an efficient scatter on the rows of B needed by this process; this is
    518:     a modification of the VecScatterBegin_() routines.

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

    542:   MatCheckProduct(C,4);
    543:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
    544:   contents = (MPIAIJ_MPIDense*)C->product->data;
    545:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
    546:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
    547:   PetscMPIIntCast(nsends,&nsends_mpi);
    548:   PetscMPIIntCast(nrecvs,&nrecvs_mpi);
    549:   if (Bbidx == 0) {
    550:     workB = *outworkB = contents->workB;
    551:   } else {
    552:     workB = *outworkB = contents->workB1;
    553:   }
    554:   if (nrows != workB->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",workB->cmap->n,nrows);
    555:   swaits = contents->swaits;
    556:   rwaits = contents->rwaits;

    558:   MatDenseGetArrayRead(B,&b);
    559:   MatDenseGetLDA(B,&blda);
    560:   if (blda != contents->blda) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot reuse an input matrix with lda %D != %D",blda,contents->blda);
    561:   MatDenseGetArray(workB,&rvalues);

    563:   /* Post recv, use MPI derived data type to save memory */
    564:   PetscObjectGetComm((PetscObject)C,&comm);
    565:   rtype = contents->rtype;
    566:   for (i=0; i<nrecvs; i++) {
    567:     MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
    568:   }

    570:   stype = contents->stype;
    571:   for (i=0; i<nsends; i++) {
    572:     MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
    573:   }

    575:   if (nrecvs) {MPI_Waitall(nrecvs_mpi,rwaits,MPI_STATUSES_IGNORE);}
    576:   if (nsends) {MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);}

    578:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
    579:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
    580:   MatDenseRestoreArrayRead(B,&b);
    581:   MatDenseRestoreArray(workB,&rvalues);
    582:   return(0);
    583: }

    585: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
    586: {
    587:   PetscErrorCode  ierr;
    588:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
    589:   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
    590:   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
    591:   Mat             workB;
    592:   MPIAIJ_MPIDense *contents;

    595:   MatCheckProduct(C,3);
    596:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
    597:   contents = (MPIAIJ_MPIDense*)C->product->data;
    598:   /* diagonal block of A times all local rows of B */
    599:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
    600:   MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);
    601:   if (contents->workB->cmap->n == B->cmap->N) {
    602:     /* get off processor parts of B needed to complete C=A*B */
    603:     MatMPIDenseScatter(A,B,0,C,&workB);

    605:     /* off-diagonal block of A times nonlocal rows of B */
    606:     MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
    607:   } else {
    608:     Mat      Bb,Cb;
    609:     PetscInt BN=B->cmap->N,n=contents->workB->cmap->n,i;
    610:     if (n <= 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Column block size %D must be positive",n);

    612:     for (i=0; i<BN; i+=n) {
    613:       MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);
    614:       MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);

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

    619:       /* off-diagonal block of A times nonlocal rows of B */
    620:       cdense = (Mat_MPIDense*)Cb->data;
    621:       MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);

    623:       MatDenseRestoreSubMatrix(B,&Bb);
    624:       MatDenseRestoreSubMatrix(C,&Cb);
    625:     }
    626:   }
    627:   return(0);
    628: }

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

    652:   MatCheckProduct(C,3);
    653:   ptap = (Mat_APMPI*)C->product->data;
    654:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    655:   PetscObjectGetComm((PetscObject)C,&comm);
    656:   MPI_Comm_size(comm,&size);
    657:   if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");

    659:   apa_sparse = ptap->apa;

    661:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    662:   /*-----------------------------------------------------*/
    663:   /* update numerical values of P_oth and P_loc */
    664:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    665:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    667:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    668:   /*----------------------------------------------------------*/
    669:   /* get data from symbolic products */
    670:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    671:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
    672:   if (size >1) {
    673:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    674:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
    675:   } else {
    676:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
    677:   }

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

    689:     /* diagonal portion of A */
    690:     anz = adi[i+1] - adi[i];
    691:     adj = ad->j + adi[i];
    692:     ada = ad->a + adi[i];
    693:     for (j=0; j<anz; j++) {
    694:       row = adj[j];
    695:       pnz = pi_loc[row+1] - pi_loc[row];
    696:       pj  = pj_loc + pi_loc[row];
    697:       pa  = pa_loc + pi_loc[row];
    698:       /* perform sparse axpy */
    699:       valtmp = ada[j];
    700:       nextp  = 0;
    701:       for (k=0; nextp<pnz; k++) {
    702:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    703:           apa_sparse[k] += valtmp*pa[nextp++];
    704:         }
    705:       }
    706:       PetscLogFlops(2.0*pnz);
    707:     }

    709:     /* off-diagonal portion of A */
    710:     anz = aoi[i+1] - aoi[i];
    711:     aoj = ao->j + aoi[i];
    712:     aoa = ao->a + aoi[i];
    713:     for (j=0; j<anz; j++) {
    714:       row = aoj[j];
    715:       pnz = pi_oth[row+1] - pi_oth[row];
    716:       pj  = pj_oth + pi_oth[row];
    717:       pa  = pa_oth + pi_oth[row];
    718:       /* perform sparse axpy */
    719:       valtmp = aoa[j];
    720:       nextp  = 0;
    721:       for (k=0; nextp<pnz; k++) {
    722:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    723:           apa_sparse[k] += valtmp*pa[nextp++];
    724:         }
    725:       }
    726:       PetscLogFlops(2.0*pnz);
    727:     }

    729:     /* set values in C */
    730:     cdnz = cd->i[i+1] - cd->i[i];
    731:     conz = co->i[i+1] - co->i[i];

    733:     /* 1st off-diagonal part of C */
    734:     ca = coa + co->i[i];
    735:     k  = 0;
    736:     for (k0=0; k0<conz; k0++) {
    737:       if (apJ[k] >= cstart) break;
    738:       ca[k0]        = apa_sparse[k];
    739:       apa_sparse[k] = 0.0;
    740:       k++;
    741:     }

    743:     /* diagonal part of C */
    744:     ca = cda + cd->i[i];
    745:     for (k1=0; k1<cdnz; k1++) {
    746:       ca[k1]        = apa_sparse[k];
    747:       apa_sparse[k] = 0.0;
    748:       k++;
    749:     }

    751:     /* 2nd off-diagonal part of C */
    752:     ca = coa + co->i[i];
    753:     for (; k0<conz; k0++) {
    754:       ca[k0]        = apa_sparse[k];
    755:       apa_sparse[k] = 0.0;
    756:       k++;
    757:     }
    758:   }
    759:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    760:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    761:   return(0);
    762: }

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

    782:   MatCheckProduct(C,4);
    783:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    784:   PetscObjectGetComm((PetscObject)A,&comm);
    785:   MPI_Comm_size(comm,&size);

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

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

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

    796:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    797:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    798:   if (size > 1) {
    799:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    800:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    801:   } else {
    802:     p_oth  = NULL;
    803:     pi_oth = NULL; pj_oth = NULL;
    804:   }

    806:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    807:   /*-------------------------------------------------------------------*/
    808:   PetscMalloc1(am+2,&api);
    809:   ptap->api = api;
    810:   api[0]    = 0;

    812:   PetscLLCondensedCreate_Scalable(lsize,&lnk);

    814:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    815:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
    816:   current_space = free_space;
    817:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    818:   for (i=0; i<am; i++) {
    819:     /* diagonal portion of A */
    820:     nzi = adi[i+1] - adi[i];
    821:     for (j=0; j<nzi; j++) {
    822:       row  = *adj++;
    823:       pnz  = pi_loc[row+1] - pi_loc[row];
    824:       Jptr = pj_loc + pi_loc[row];
    825:       /* Expand list if it is not long enough */
    826:       if (pnz+apnz_max > lsize) {
    827:         lsize = pnz+apnz_max;
    828:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    829:       }
    830:       /* add non-zero cols of P into the sorted linked list lnk */
    831:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    832:       apnz     = *lnk; /* The first element in the list is the number of items in the list */
    833:       api[i+1] = api[i] + apnz;
    834:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
    835:     }
    836:     /* off-diagonal portion of A */
    837:     nzi = aoi[i+1] - aoi[i];
    838:     for (j=0; j<nzi; j++) {
    839:       row  = *aoj++;
    840:       pnz  = pi_oth[row+1] - pi_oth[row];
    841:       Jptr = pj_oth + pi_oth[row];
    842:       /* Expand list if it is not long enough */
    843:       if (pnz+apnz_max > lsize) {
    844:         lsize = pnz + apnz_max;
    845:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    846:       }
    847:       /* add non-zero cols of P into the sorted linked list lnk */
    848:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    849:       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
    850:       api[i+1] = api[i] + apnz;
    851:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
    852:     }

    854:     /* add missing diagonal entry */
    855:     if (C->force_diagonals) {
    856:       j = i + rstart; /* column index */
    857:       PetscLLCondensedAddSorted_Scalable(1,&j,lnk);
    858:     }

    860:     apnz     = *lnk;
    861:     api[i+1] = api[i] + apnz;
    862:     if (apnz > apnz_max) apnz_max = apnz;

    864:     /* if free space is not available, double the total space in the list */
    865:     if (current_space->local_remaining<apnz) {
    866:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    867:       nspacedouble++;
    868:     }

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

    874:     current_space->array           += apnz;
    875:     current_space->local_used      += apnz;
    876:     current_space->local_remaining -= apnz;
    877:   }

    879:   /* Allocate space for apj, initialize apj, and */
    880:   /* destroy list of free space and other temporary array(s) */
    881:   PetscMalloc1(api[am]+1,&ptap->apj);
    882:   apj  = ptap->apj;
    883:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    884:   PetscLLCondensedDestroy_Scalable(lnk);

    886:   /* create and assemble symbolic parallel matrix C */
    887:   /*----------------------------------------------------*/
    888:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    889:   MatSetBlockSizesFromMats(C,A,P);
    890:   MatGetType(A,&mtype);
    891:   MatSetType(C,mtype);
    892:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    893:   MatPreallocateFinalize(dnz,onz);

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

    898:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    899:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    900:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    901:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    903:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
    904:   C->ops->productnumeric = MatProductNumeric_AB;

    906:   /* attach the supporting struct to C for reuse */
    907:   C->product->data    = ptap;
    908:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    910:   /* set MatInfo */
    911:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    912:   if (afill < 1.0) afill = 1.0;
    913:   C->info.mallocs           = nspacedouble;
    914:   C->info.fill_ratio_given  = fill;
    915:   C->info.fill_ratio_needed = afill;

    917: #if defined(PETSC_USE_INFO)
    918:   if (api[am]) {
    919:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    920:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    921:   } else {
    922:     PetscInfo(C,"Empty matrix product\n");
    923:   }
    924: #endif
    925:   return(0);
    926: }

    928: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
    929: /* Three input arrays are merged to one output array. The size of the    */
    930: /* output array is also output. Duplicate entries only show up once.     */
    931: static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
    932:                                PetscInt  size2, PetscInt *in2,
    933:                                PetscInt  size3, PetscInt *in3,
    934:                                PetscInt *size4, PetscInt *out)
    935: {
    936:   int i = 0, j = 0, k = 0, l = 0;

    938:   /* Traverse all three arrays */
    939:   while (i<size1 && j<size2 && k<size3) {
    940:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
    941:       out[l++] = in1[i++];
    942:     }
    943:     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
    944:       out[l++] = in2[j++];
    945:     }
    946:     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
    947:       out[l++] = in3[k++];
    948:     }
    949:     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
    950:       out[l++] = in1[i];
    951:       i++, j++;
    952:     }
    953:     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
    954:       out[l++] = in1[i];
    955:       i++, k++;
    956:     }
    957:     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
    958:       out[l++] = in2[j];
    959:       k++, j++;
    960:     }
    961:     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
    962:       out[l++] = in1[i];
    963:       i++, j++, k++;
    964:     }
    965:   }

    967:   /* Traverse two remaining arrays */
    968:   while (i<size1 && j<size2) {
    969:     if (in1[i] < in2[j]) {
    970:       out[l++] = in1[i++];
    971:     }
    972:     else if (in1[i] > in2[j]) {
    973:       out[l++] = in2[j++];
    974:     }
    975:     else {
    976:       out[l++] = in1[i];
    977:       i++, j++;
    978:     }
    979:   }

    981:   while (i<size1 && k<size3) {
    982:     if (in1[i] < in3[k]) {
    983:       out[l++] = in1[i++];
    984:     }
    985:     else if (in1[i] > in3[k]) {
    986:       out[l++] = in3[k++];
    987:     }
    988:     else {
    989:       out[l++] = in1[i];
    990:       i++, k++;
    991:     }
    992:   }

    994:   while (k<size3 && j<size2)  {
    995:     if (in3[k] < in2[j]) {
    996:       out[l++] = in3[k++];
    997:     }
    998:     else if (in3[k] > in2[j]) {
    999:       out[l++] = in2[j++];
    1000:     }
    1001:     else {
    1002:       out[l++] = in3[k];
    1003:       k++, j++;
    1004:     }
    1005:   }

    1007:   /* Traverse one remaining array */
    1008:   while (i<size1) out[l++] = in1[i++];
    1009:   while (j<size2) out[l++] = in2[j++];
    1010:   while (k<size3) out[l++] = in3[k++];

    1012:   *size4 = l;
    1013: }

    1015: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
    1016: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
    1017: /* matrix-matrix multiplications.  */
    1018: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
    1019: {
    1020:   PetscErrorCode     ierr;
    1021:   MPI_Comm           comm;
    1022:   PetscMPIInt        size;
    1023:   Mat_APMPI          *ptap;
    1024:   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
    1025:   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
    1026:   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
    1027:   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
    1028:   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
    1029:   PetscInt           adponz, adpdnz;
    1030:   PetscInt           *pi_loc,*dnz,*onz;
    1031:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
    1032:   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
    1033:                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
    1034:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
    1035:   PetscBT            lnkbt;
    1036:   PetscReal          afill;
    1037:   PetscMPIInt        rank;
    1038:   Mat                adpd, aopoth;
    1039:   MatType            mtype;
    1040:   const char         *prefix;

    1043:   MatCheckProduct(C,4);
    1044:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
    1045:   PetscObjectGetComm((PetscObject)A,&comm);
    1046:   MPI_Comm_size(comm,&size);
    1047:   MPI_Comm_rank(comm, &rank);
    1048:   MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);

    1050:   /* create struct Mat_APMPI and attached it to C later */
    1051:   PetscNew(&ptap);

    1053:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    1054:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

    1056:   /* get P_loc by taking all local rows of P */
    1057:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    1060:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    1061:   pi_loc = p_loc->i;

    1063:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
    1064:   PetscMalloc1(am+2,&api);
    1065:   PetscMalloc1(am+2,&adpoi);

    1067:   adpoi[0]    = 0;
    1068:   ptap->api = api;
    1069:   api[0] = 0;

    1071:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
    1072:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
    1073:   MatPreallocateInitialize(comm,am,pn,dnz,onz);

    1075:   /* Symbolic calc of A_loc_diag * P_loc_diag */
    1076:   MatGetOptionsPrefix(A,&prefix);
    1077:   MatProductCreate(a->A,p->A,NULL,&adpd);
    1078:   MatGetOptionsPrefix(A,&prefix);
    1079:   MatSetOptionsPrefix(adpd,prefix);
    1080:   MatAppendOptionsPrefix(adpd,"inner_diag_");

    1082:   MatProductSetType(adpd,MATPRODUCT_AB);
    1083:   MatProductSetAlgorithm(adpd,"sorted");
    1084:   MatProductSetFill(adpd,fill);
    1085:   MatProductSetFromOptions(adpd);

    1087:   adpd->force_diagonals = C->force_diagonals;
    1088:   MatProductSymbolic(adpd);

    1090:   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
    1091:   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
    1092:   p_off = (Mat_SeqAIJ*)((p->B)->data);
    1093:   poff_i = p_off->i; poff_j = p_off->j;

    1095:   /* j_temp stores indices of a result row before they are added to the linked list */
    1096:   PetscMalloc1(pN+2,&j_temp);

    1099:   /* Symbolic calc of the A_diag * p_loc_off */
    1100:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    1101:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
    1102:   current_space = free_space_diag;

    1104:   for (i=0; i<am; i++) {
    1105:     /* A_diag * P_loc_off */
    1106:     nzi = adi[i+1] - adi[i];
    1107:     for (j=0; j<nzi; j++) {
    1108:       row  = *adj++;
    1109:       pnz  = poff_i[row+1] - poff_i[row];
    1110:       Jptr = poff_j + poff_i[row];
    1111:       for (i1 = 0; i1 < pnz; i1++) {
    1112:         j_temp[i1] = p->garray[Jptr[i1]];
    1113:       }
    1114:       /* add non-zero cols of P into the sorted linked list lnk */
    1115:       PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
    1116:     }

    1118:     adponz     = lnk[0];
    1119:     adpoi[i+1] = adpoi[i] + adponz;

    1121:     /* if free space is not available, double the total space in the list */
    1122:     if (current_space->local_remaining<adponz) {
    1123:       PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);
    1124:       nspacedouble++;
    1125:     }

    1127:     /* Copy data into free space, then initialize lnk */
    1128:     PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);

    1130:     current_space->array           += adponz;
    1131:     current_space->local_used      += adponz;
    1132:     current_space->local_remaining -= adponz;
    1133:   }

    1135:   /* Symbolic calc of A_off * P_oth */
    1136:   MatSetOptionsPrefix(a->B,prefix);
    1137:   MatAppendOptionsPrefix(a->B,"inner_offdiag_");
    1138:   MatCreate(PETSC_COMM_SELF,&aopoth);
    1139:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
    1140:   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
    1141:   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;

    1143:   /* Allocate space for apj, adpj, aopj, ... */
    1144:   /* destroy lists of free space and other temporary array(s) */

    1146:   PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
    1147:   PetscMalloc1(adpoi[am]+2, &adpoj);

    1149:   /* Copy from linked list to j-array */
    1150:   PetscFreeSpaceContiguous(&free_space_diag,adpoj);
    1151:   PetscLLDestroy(lnk,lnkbt);

    1153:   adpoJ = adpoj;
    1154:   adpdJ = adpdj;
    1155:   aopJ = aopothj;
    1156:   apj  = ptap->apj;
    1157:   apJ = apj; /* still empty */

    1159:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
    1160:   /* A_diag * P_loc_diag to get A*P */
    1161:   for (i = 0; i < am; i++) {
    1162:     aopnz  =  aopothi[i+1] -  aopothi[i];
    1163:     adponz = adpoi[i+1] - adpoi[i];
    1164:     adpdnz = adpdi[i+1] - adpdi[i];

    1166:     /* Correct indices from A_diag*P_diag */
    1167:     for (i1 = 0; i1 < adpdnz; i1++) {
    1168:       adpdJ[i1] += p_colstart;
    1169:     }
    1170:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
    1171:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
    1172:     MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);

    1174:     aopJ += aopnz;
    1175:     adpoJ += adponz;
    1176:     adpdJ += adpdnz;
    1177:     apJ += apnz;
    1178:     api[i+1] = api[i] + apnz;
    1179:   }

    1181:   /* malloc apa to store dense row A[i,:]*P */
    1182:   PetscCalloc1(pN+2,&ptap->apa);

    1184:   /* create and assemble symbolic parallel matrix C */
    1185:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    1186:   MatSetBlockSizesFromMats(C,A,P);
    1187:   MatGetType(A,&mtype);
    1188:   MatSetType(C,mtype);
    1189:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1190:   MatPreallocateFinalize(dnz,onz);

    1192:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    1193:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1194:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1195:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1197:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    1198:   C->ops->productnumeric = MatProductNumeric_AB;

    1200:   /* attach the supporting struct to C for reuse */
    1201:   C->product->data    = ptap;
    1202:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

    1204:   /* set MatInfo */
    1205:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    1206:   if (afill < 1.0) afill = 1.0;
    1207:   C->info.mallocs           = nspacedouble;
    1208:   C->info.fill_ratio_given  = fill;
    1209:   C->info.fill_ratio_needed = afill;

    1211: #if defined(PETSC_USE_INFO)
    1212:   if (api[am]) {
    1213:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1214:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    1215:   } else {
    1216:     PetscInfo(C,"Empty matrix product\n");
    1217:   }
    1218: #endif

    1220:   MatDestroy(&aopoth);
    1221:   MatDestroy(&adpd);
    1222:   PetscFree(j_temp);
    1223:   PetscFree(adpoj);
    1224:   PetscFree(adpoi);
    1225:   return(0);
    1226: }

    1228: /*-------------------------------------------------------------------------*/
    1229: /* This routine only works when scall=MAT_REUSE_MATRIX! */
    1230: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
    1231: {
    1233:   Mat_APMPI      *ptap;
    1234:   Mat            Pt;

    1237:   MatCheckProduct(C,3);
    1238:   ptap = (Mat_APMPI*)C->product->data;
    1239:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1240:   if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");

    1242:   Pt   = ptap->Pt;
    1243:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
    1244:   MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);
    1245:   return(0);
    1246: }

    1248: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
    1249: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
    1250: {
    1251:   PetscErrorCode      ierr;
    1252:   Mat_APMPI           *ptap;
    1253:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
    1254:   MPI_Comm            comm;
    1255:   PetscMPIInt         size,rank;
    1256:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1257:   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
    1258:   PetscInt            *lnk,i,k,nsend,rstart;
    1259:   PetscBT             lnkbt;
    1260:   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,nrecv;
    1261:   PETSC_UNUSED PetscMPIInt icompleted=0;
    1262:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k,row,ncols,*cols;
    1263:   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
    1264:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1265:   MPI_Request         *swaits,*rwaits;
    1266:   MPI_Status          *sstatus,rstatus;
    1267:   PetscLayout         rowmap;
    1268:   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
    1269:   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
    1270:   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
    1271:   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
    1272:   PetscTable          ta;
    1273:   MatType             mtype;
    1274:   const char          *prefix;

    1277:   PetscObjectGetComm((PetscObject)A,&comm);
    1278:   MPI_Comm_size(comm,&size);
    1279:   MPI_Comm_rank(comm,&rank);

    1281:   /* create symbolic parallel matrix C */
    1282:   MatGetType(A,&mtype);
    1283:   MatSetType(C,mtype);

    1285:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

    1287:   /* create struct Mat_APMPI and attached it to C later */
    1288:   PetscNew(&ptap);
    1289:   ptap->reuse = MAT_INITIAL_MATRIX;

    1291:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
    1292:   /* --------------------------------- */
    1293:   MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
    1294:   MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);

    1296:   /* (1) compute symbolic A_loc */
    1297:   /* ---------------------------*/
    1298:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);

    1300:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
    1301:   /* ------------------------------------ */
    1302:   MatGetOptionsPrefix(A,&prefix);
    1303:   MatSetOptionsPrefix(ptap->Ro,prefix);
    1304:   MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
    1305:   MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
    1306:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);

    1308:   /* (3) send coj of C_oth to other processors  */
    1309:   /* ------------------------------------------ */
    1310:   /* determine row ownership */
    1311:   PetscLayoutCreate(comm,&rowmap);
    1312:   rowmap->n  = pn;
    1313:   rowmap->bs = 1;
    1314:   PetscLayoutSetUp(rowmap);
    1315:   owners = rowmap->range;

    1317:   /* determine the number of messages to send, their lengths */
    1318:   PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
    1319:   PetscArrayzero(len_s,size);
    1320:   PetscArrayzero(len_si,size);

    1322:   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
    1323:   coi   = c_oth->i; coj = c_oth->j;
    1324:   con   = ptap->C_oth->rmap->n;
    1325:   proc  = 0;
    1326:   for (i=0; i<con; i++) {
    1327:     while (prmap[i] >= owners[proc+1]) proc++;
    1328:     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
    1329:     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
    1330:   }

    1332:   len          = 0; /* max length of buf_si[], see (4) */
    1333:   owners_co[0] = 0;
    1334:   nsend        = 0;
    1335:   for (proc=0; proc<size; proc++) {
    1336:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1337:     if (len_s[proc]) {
    1338:       nsend++;
    1339:       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
    1340:       len         += len_si[proc];
    1341:     }
    1342:   }

    1344:   /* determine the number and length of messages to receive for coi and coj  */
    1345:   PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
    1346:   PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);

    1348:   /* post the Irecv and Isend of coj */
    1349:   PetscCommGetNewTag(comm,&tagj);
    1350:   PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
    1351:   PetscMalloc1(nsend+1,&swaits);
    1352:   for (proc=0, k=0; proc<size; proc++) {
    1353:     if (!len_s[proc]) continue;
    1354:     i    = owners_co[proc];
    1355:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1356:     k++;
    1357:   }

    1359:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
    1360:   /* ---------------------------------------- */
    1361:   MatSetOptionsPrefix(ptap->Rd,prefix);
    1362:   MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
    1363:   MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
    1364:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
    1365:   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;

    1367:   /* receives coj are complete */
    1368:   for (i=0; i<nrecv; i++) {
    1369:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1370:   }
    1371:   PetscFree(rwaits);
    1372:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

    1374:   /* add received column indices into ta to update Crmax */
    1375:   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;

    1377:   /* create and initialize a linked list */
    1378:   PetscTableCreate(an,aN,&ta); /* for compute Crmax */
    1379:   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);

    1381:   for (k=0; k<nrecv; k++) {/* k-th received message */
    1382:     Jptr = buf_rj[k];
    1383:     for (j=0; j<len_r[k]; j++) {
    1384:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1385:     }
    1386:   }
    1387:   PetscTableGetCount(ta,&Crmax);
    1388:   PetscTableDestroy(&ta);

    1390:   /* (4) send and recv coi */
    1391:   /*-----------------------*/
    1392:   PetscCommGetNewTag(comm,&tagi);
    1393:   PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
    1394:   PetscMalloc1(len+1,&buf_s);
    1395:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1396:   for (proc=0,k=0; proc<size; proc++) {
    1397:     if (!len_s[proc]) continue;
    1398:     /* form outgoing message for i-structure:
    1399:          buf_si[0]:                 nrows to be sent
    1400:                [1:nrows]:           row index (global)
    1401:                [nrows+1:2*nrows+1]: i-structure index
    1402:     */
    1403:     /*-------------------------------------------*/
    1404:     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
    1405:     buf_si_i    = buf_si + nrows+1;
    1406:     buf_si[0]   = nrows;
    1407:     buf_si_i[0] = 0;
    1408:     nrows       = 0;
    1409:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1410:       nzi = coi[i+1] - coi[i];
    1411:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1412:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1413:       nrows++;
    1414:     }
    1415:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1416:     k++;
    1417:     buf_si += len_si[proc];
    1418:   }
    1419:   for (i=0; i<nrecv; i++) {
    1420:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1421:   }
    1422:   PetscFree(rwaits);
    1423:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

    1425:   PetscFree4(len_s,len_si,sstatus,owners_co);
    1426:   PetscFree(len_ri);
    1427:   PetscFree(swaits);
    1428:   PetscFree(buf_s);

    1430:   /* (5) compute the local portion of C      */
    1431:   /* ------------------------------------------ */
    1432:   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
    1433:   PetscFreeSpaceGet(Crmax,&free_space);
    1434:   current_space = free_space;

    1436:   PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
    1437:   for (k=0; k<nrecv; k++) {
    1438:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1439:     nrows       = *buf_ri_k[k];
    1440:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1441:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1442:   }

    1444:   MatPreallocateInitialize(comm,pn,an,dnz,onz);
    1445:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
    1446:   for (i=0; i<pn; i++) { /* for each local row of C */
    1447:     /* add C_loc into C */
    1448:     nzi  = c_loc->i[i+1] - c_loc->i[i];
    1449:     Jptr = c_loc->j + c_loc->i[i];
    1450:     PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);

    1452:     /* add received col data into lnk */
    1453:     for (k=0; k<nrecv; k++) { /* k-th received message */
    1454:       if (i == *nextrow[k]) { /* i-th row */
    1455:         nzi  = *(nextci[k]+1) - *nextci[k];
    1456:         Jptr = buf_rj[k] + *nextci[k];
    1457:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
    1458:         nextrow[k]++; nextci[k]++;
    1459:       }
    1460:     }

    1462:     /* add missing diagonal entry */
    1463:     if (C->force_diagonals) {
    1464:       k = i + owners[rank]; /* column index */
    1465:       PetscLLCondensedAddSorted(1,&k,lnk,lnkbt);
    1466:     }

    1468:     nzi = lnk[0];

    1470:     /* copy data into free space, then initialize lnk */
    1471:     PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
    1472:     MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
    1473:   }
    1474:   PetscFree3(buf_ri_k,nextrow,nextci);
    1475:   PetscLLDestroy(lnk,lnkbt);
    1476:   PetscFreeSpaceDestroy(free_space);

    1478:   /* local sizes and preallocation */
    1479:   MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
    1480:   if (P->cmap->bs > 0) {PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);}
    1481:   if (A->cmap->bs > 0) {PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);}
    1482:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1483:   MatPreallocateFinalize(dnz,onz);

    1485:   /* add C_loc and C_oth to C */
    1486:   MatGetOwnershipRange(C,&rstart,NULL);
    1487:   for (i=0; i<pn; i++) {
    1488:     ncols = c_loc->i[i+1] - c_loc->i[i];
    1489:     cols  = c_loc->j + c_loc->i[i];
    1490:     row   = rstart + i;
    1491:     MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);

    1493:     if (C->force_diagonals) {
    1494:       MatSetValues(C,1,(const PetscInt*)&row,1,(const PetscInt*)&row,NULL,INSERT_VALUES);
    1495:     }
    1496:   }
    1497:   for (i=0; i<con; i++) {
    1498:     ncols = c_oth->i[i+1] - c_oth->i[i];
    1499:     cols  = c_oth->j + c_oth->i[i];
    1500:     row   = prmap[i];
    1501:     MatSetValues(C,1,(const PetscInt*)&row,ncols,(const PetscInt*)cols,NULL,INSERT_VALUES);
    1502:   }
    1503:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1504:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1505:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1507:   /* members in merge */
    1508:   PetscFree(id_r);
    1509:   PetscFree(len_r);
    1510:   PetscFree(buf_ri[0]);
    1511:   PetscFree(buf_ri);
    1512:   PetscFree(buf_rj[0]);
    1513:   PetscFree(buf_rj);
    1514:   PetscLayoutDestroy(&rowmap);

    1516:   /* attach the supporting struct to C for reuse */
    1517:   C->product->data    = ptap;
    1518:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    1519:   return(0);
    1520: }

    1522: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
    1523: {
    1524:   PetscErrorCode    ierr;
    1525:   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
    1526:   Mat_SeqAIJ        *c_seq;
    1527:   Mat_APMPI         *ptap;
    1528:   Mat               A_loc,C_loc,C_oth;
    1529:   PetscInt          i,rstart,rend,cm,ncols,row;
    1530:   const PetscInt    *cols;
    1531:   const PetscScalar *vals;

    1534:   MatCheckProduct(C,3);
    1535:   ptap = (Mat_APMPI*)C->product->data;
    1536:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1537:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
    1538:   MatZeroEntries(C);

    1540:   if (ptap->reuse == MAT_REUSE_MATRIX) {
    1541:     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
    1542:     /* 1) get R = Pd^T, Ro = Po^T */
    1543:     /*----------------------------*/
    1544:     MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
    1545:     MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);

    1547:     /* 2) compute numeric A_loc */
    1548:     /*--------------------------*/
    1549:     MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
    1550:   }

    1552:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
    1553:   A_loc = ptap->A_loc;
    1554:   ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
    1555:   ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
    1556:   C_loc = ptap->C_loc;
    1557:   C_oth = ptap->C_oth;

    1559:   /* add C_loc and C_oth to C */
    1560:   MatGetOwnershipRange(C,&rstart,&rend);

    1562:   /* C_loc -> C */
    1563:   cm    = C_loc->rmap->N;
    1564:   c_seq = (Mat_SeqAIJ*)C_loc->data;
    1565:   cols = c_seq->j;
    1566:   vals = c_seq->a;
    1567:   for (i=0; i<cm; i++) {
    1568:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1569:     row = rstart + i;
    1570:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1571:     cols += ncols; vals += ncols;
    1572:   }

    1574:   /* Co -> C, off-processor part */
    1575:   cm    = C_oth->rmap->N;
    1576:   c_seq = (Mat_SeqAIJ*)C_oth->data;
    1577:   cols  = c_seq->j;
    1578:   vals  = c_seq->a;
    1579:   for (i=0; i<cm; i++) {
    1580:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1581:     row = p->garray[i];
    1582:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1583:     cols += ncols; vals += ncols;
    1584:   }
    1585:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1586:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1587:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

    1589:   ptap->reuse = MAT_REUSE_MATRIX;
    1590:   return(0);
    1591: }

    1593: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
    1594: {
    1595:   PetscErrorCode      ierr;
    1596:   Mat_Merge_SeqsToMPI *merge;
    1597:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
    1598:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    1599:   Mat_APMPI           *ptap;
    1600:   PetscInt            *adj;
    1601:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
    1602:   MatScalar           *ada,*ca,valtmp;
    1603:   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    1604:   MPI_Comm            comm;
    1605:   PetscMPIInt         size,rank,taga,*len_s;
    1606:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    1607:   PetscInt            **buf_ri,**buf_rj;
    1608:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    1609:   MPI_Request         *s_waits,*r_waits;
    1610:   MPI_Status          *status;
    1611:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    1612:   const PetscScalar   *dummy;
    1613:   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
    1614:   Mat                 A_loc;
    1615:   Mat_SeqAIJ          *a_loc;

    1618:   MatCheckProduct(C,3);
    1619:   ptap = (Mat_APMPI*)C->product->data;
    1620:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
    1621:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
    1622:   PetscObjectGetComm((PetscObject)C,&comm);
    1623:   MPI_Comm_size(comm,&size);
    1624:   MPI_Comm_rank(comm,&rank);

    1626:   merge = ptap->merge;

    1628:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
    1629:   /*------------------------------------------*/
    1630:   /* get data from symbolic products */
    1631:   coi    = merge->coi; coj = merge->coj;
    1632:   PetscCalloc1(coi[pon]+1,&coa);
    1633:   bi     = merge->bi; bj = merge->bj;
    1634:   owners = merge->rowmap->range;
    1635:   PetscCalloc1(bi[cm]+1,&ba);

    1637:   /* get A_loc by taking all local rows of A */
    1638:   A_loc = ptap->A_loc;
    1639:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    1640:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1641:   ai    = a_loc->i;
    1642:   aj    = a_loc->j;

    1644:   /* trigger copy to CPU */
    1645:   MatSeqAIJGetArrayRead(p->A,&dummy);
    1646:   MatSeqAIJRestoreArrayRead(p->A,&dummy);
    1647:   MatSeqAIJGetArrayRead(p->B,&dummy);
    1648:   MatSeqAIJRestoreArrayRead(p->B,&dummy);
    1649:   for (i=0; i<am; i++) {
    1650:     anz = ai[i+1] - ai[i];
    1651:     adj = aj + ai[i];
    1652:     ada = a_loc->a + ai[i];

    1654:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1655:     /*-------------------------------------------------------------*/
    1656:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1657:     pnz = po->i[i+1] - po->i[i];
    1658:     poJ = po->j + po->i[i];
    1659:     pA  = po->a + po->i[i];
    1660:     for (j=0; j<pnz; j++) {
    1661:       row = poJ[j];
    1662:       cj  = coj + coi[row];
    1663:       ca  = coa + coi[row];
    1664:       /* perform sparse axpy */
    1665:       nexta  = 0;
    1666:       valtmp = pA[j];
    1667:       for (k=0; nexta<anz; k++) {
    1668:         if (cj[k] == adj[nexta]) {
    1669:           ca[k] += valtmp*ada[nexta];
    1670:           nexta++;
    1671:         }
    1672:       }
    1673:       PetscLogFlops(2.0*anz);
    1674:     }

    1676:     /* put the value into Cd (diagonal part) */
    1677:     pnz = pd->i[i+1] - pd->i[i];
    1678:     pdJ = pd->j + pd->i[i];
    1679:     pA  = pd->a + pd->i[i];
    1680:     for (j=0; j<pnz; j++) {
    1681:       row = pdJ[j];
    1682:       cj  = bj + bi[row];
    1683:       ca  = ba + bi[row];
    1684:       /* perform sparse axpy */
    1685:       nexta  = 0;
    1686:       valtmp = pA[j];
    1687:       for (k=0; nexta<anz; k++) {
    1688:         if (cj[k] == adj[nexta]) {
    1689:           ca[k] += valtmp*ada[nexta];
    1690:           nexta++;
    1691:         }
    1692:       }
    1693:       PetscLogFlops(2.0*anz);
    1694:     }
    1695:   }

    1697:   /* 3) send and recv matrix values coa */
    1698:   /*------------------------------------*/
    1699:   buf_ri = merge->buf_ri;
    1700:   buf_rj = merge->buf_rj;
    1701:   len_s  = merge->len_s;
    1702:   PetscCommGetNewTag(comm,&taga);
    1703:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1705:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1706:   for (proc=0,k=0; proc<size; proc++) {
    1707:     if (!len_s[proc]) continue;
    1708:     i    = merge->owners_co[proc];
    1709:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1710:     k++;
    1711:   }
    1712:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
    1713:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

    1715:   PetscFree2(s_waits,status);
    1716:   PetscFree(r_waits);
    1717:   PetscFree(coa);

    1719:   /* 4) insert local Cseq and received values into Cmpi */
    1720:   /*----------------------------------------------------*/
    1721:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1722:   for (k=0; k<merge->nrecv; k++) {
    1723:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1724:     nrows       = *(buf_ri_k[k]);
    1725:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1726:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1727:   }

    1729:   for (i=0; i<cm; i++) {
    1730:     row  = owners[rank] + i; /* global row index of C_seq */
    1731:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1732:     ba_i = ba + bi[i];
    1733:     bnz  = bi[i+1] - bi[i];
    1734:     /* add received vals into ba */
    1735:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1736:       /* i-th row */
    1737:       if (i == *nextrow[k]) {
    1738:         cnz    = *(nextci[k]+1) - *nextci[k];
    1739:         cj     = buf_rj[k] + *(nextci[k]);
    1740:         ca     = abuf_r[k] + *(nextci[k]);
    1741:         nextcj = 0;
    1742:         for (j=0; nextcj<cnz; j++) {
    1743:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1744:             ba_i[j] += ca[nextcj++];
    1745:           }
    1746:         }
    1747:         nextrow[k]++; nextci[k]++;
    1748:         PetscLogFlops(2.0*cnz);
    1749:       }
    1750:     }
    1751:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1752:   }
    1753:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1754:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1756:   PetscFree(ba);
    1757:   PetscFree(abuf_r[0]);
    1758:   PetscFree(abuf_r);
    1759:   PetscFree3(buf_ri_k,nextrow,nextci);
    1760:   return(0);
    1761: }

    1763: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
    1764: {
    1765:   PetscErrorCode      ierr;
    1766:   Mat                 A_loc;
    1767:   Mat_APMPI           *ptap;
    1768:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1769:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
    1770:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1771:   PetscInt            nnz;
    1772:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1773:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
    1774:   MPI_Comm            comm;
    1775:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1776:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1777:   PetscInt            len,proc,*dnz,*onz,*owners;
    1778:   PetscInt            nzi,*bi,*bj;
    1779:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1780:   MPI_Request         *swaits,*rwaits;
    1781:   MPI_Status          *sstatus,rstatus;
    1782:   Mat_Merge_SeqsToMPI *merge;
    1783:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1784:   PetscReal           afill  =1.0,afill_tmp;
    1785:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
    1786:   Mat_SeqAIJ          *a_loc;
    1787:   PetscTable          ta;
    1788:   MatType             mtype;

    1791:   PetscObjectGetComm((PetscObject)A,&comm);
    1792:   /* check if matrix local sizes are compatible */
    1793:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != P (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);

    1795:   MPI_Comm_size(comm,&size);
    1796:   MPI_Comm_rank(comm,&rank);

    1798:   /* create struct Mat_APMPI and attached it to C later */
    1799:   PetscNew(&ptap);

    1801:   /* get A_loc by taking all local rows of A */
    1802:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1804:   ptap->A_loc = A_loc;
    1805:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
    1806:   ai          = a_loc->i;
    1807:   aj          = a_loc->j;

    1809:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1810:   /*----------------------------------------------------*/
    1811:   MatGetSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
    1812:   MatGetSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);
    1813:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
    1814:                          >= (num of nonzero rows of C_seq) - pn */
    1815:   PetscMalloc1(pon+1,&coi);
    1816:   coi[0] = 0;

    1818:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1819:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
    1820:   PetscFreeSpaceGet(nnz,&free_space);
    1821:   current_space = free_space;

    1823:   /* create and initialize a linked list */
    1824:   PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
    1825:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
    1826:   PetscTableGetCount(ta,&Armax);

    1828:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

    1830:   for (i=0; i<pon; i++) {
    1831:     pnz = poti[i+1] - poti[i];
    1832:     ptJ = potj + poti[i];
    1833:     for (j=0; j<pnz; j++) {
    1834:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1835:       anz  = ai[row+1] - ai[row];
    1836:       Jptr = aj + ai[row];
    1837:       /* add non-zero cols of AP into the sorted linked list lnk */
    1838:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1839:     }
    1840:     nnz = lnk[0];

    1842:     /* If free space is not available, double the total space in the list */
    1843:     if (current_space->local_remaining<nnz) {
    1844:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1845:       nspacedouble++;
    1846:     }

    1848:     /* Copy data into free space, and zero out denserows */
    1849:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

    1851:     current_space->array           += nnz;
    1852:     current_space->local_used      += nnz;
    1853:     current_space->local_remaining -= nnz;

    1855:     coi[i+1] = coi[i] + nnz;
    1856:   }

    1858:   PetscMalloc1(coi[pon]+1,&coj);
    1859:   PetscFreeSpaceContiguous(&free_space,coj);
    1860:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

    1862:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1863:   if (afill_tmp > afill) afill = afill_tmp;

    1865:   /* send j-array (coj) of Co to other processors */
    1866:   /*----------------------------------------------*/
    1867:   /* determine row ownership */
    1868:   PetscNew(&merge);
    1869:   PetscLayoutCreate(comm,&merge->rowmap);

    1871:   merge->rowmap->n  = pn;
    1872:   merge->rowmap->bs = 1;

    1874:   PetscLayoutSetUp(merge->rowmap);
    1875:   owners = merge->rowmap->range;

    1877:   /* determine the number of messages to send, their lengths */
    1878:   PetscCalloc1(size,&len_si);
    1879:   PetscCalloc1(size,&merge->len_s);

    1881:   len_s        = merge->len_s;
    1882:   merge->nsend = 0;

    1884:   PetscMalloc1(size+2,&owners_co);

    1886:   proc = 0;
    1887:   for (i=0; i<pon; i++) {
    1888:     while (prmap[i] >= owners[proc+1]) proc++;
    1889:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1890:     len_s[proc] += coi[i+1] - coi[i];
    1891:   }

    1893:   len          = 0; /* max length of buf_si[] */
    1894:   owners_co[0] = 0;
    1895:   for (proc=0; proc<size; proc++) {
    1896:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1897:     if (len_si[proc]) {
    1898:       merge->nsend++;
    1899:       len_si[proc] = 2*(len_si[proc] + 1);
    1900:       len         += len_si[proc];
    1901:     }
    1902:   }

    1904:   /* determine the number and length of messages to receive for coi and coj  */
    1905:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1906:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1908:   /* post the Irecv and Isend of coj */
    1909:   PetscCommGetNewTag(comm,&tagj);
    1910:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1911:   PetscMalloc1(merge->nsend+1,&swaits);
    1912:   for (proc=0, k=0; proc<size; proc++) {
    1913:     if (!len_s[proc]) continue;
    1914:     i    = owners_co[proc];
    1915:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1916:     k++;
    1917:   }

    1919:   /* receives and sends of coj are complete */
    1920:   PetscMalloc1(size,&sstatus);
    1921:   for (i=0; i<merge->nrecv; i++) {
    1922:     PETSC_UNUSED PetscMPIInt icompleted;
    1923:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1924:   }
    1925:   PetscFree(rwaits);
    1926:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

    1928:   /* add received column indices into table to update Armax */
    1929:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
    1930:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
    1931:     Jptr = buf_rj[k];
    1932:     for (j=0; j<merge->len_r[k]; j++) {
    1933:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1934:     }
    1935:   }
    1936:   PetscTableGetCount(ta,&Armax);
    1937:   /* printf("Armax %d, an %d + Bn %d = %d, aN %d\n",Armax,A->cmap->n,a->B->cmap->N,A->cmap->n+a->B->cmap->N,aN); */

    1939:   /* send and recv coi */
    1940:   /*-------------------*/
    1941:   PetscCommGetNewTag(comm,&tagi);
    1942:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    1943:   PetscMalloc1(len+1,&buf_s);
    1944:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1945:   for (proc=0,k=0; proc<size; proc++) {
    1946:     if (!len_s[proc]) continue;
    1947:     /* form outgoing message for i-structure:
    1948:          buf_si[0]:                 nrows to be sent
    1949:                [1:nrows]:           row index (global)
    1950:                [nrows+1:2*nrows+1]: i-structure index
    1951:     */
    1952:     /*-------------------------------------------*/
    1953:     nrows       = len_si[proc]/2 - 1;
    1954:     buf_si_i    = buf_si + nrows+1;
    1955:     buf_si[0]   = nrows;
    1956:     buf_si_i[0] = 0;
    1957:     nrows       = 0;
    1958:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1959:       nzi               = coi[i+1] - coi[i];
    1960:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1961:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1962:       nrows++;
    1963:     }
    1964:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1965:     k++;
    1966:     buf_si += len_si[proc];
    1967:   }
    1968:   i = merge->nrecv;
    1969:   while (i--) {
    1970:     PETSC_UNUSED PetscMPIInt icompleted;
    1971:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    1972:   }
    1973:   PetscFree(rwaits);
    1974:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
    1975:   PetscFree(len_si);
    1976:   PetscFree(len_ri);
    1977:   PetscFree(swaits);
    1978:   PetscFree(sstatus);
    1979:   PetscFree(buf_s);

    1981:   /* compute the local portion of C (mpi mat) */
    1982:   /*------------------------------------------*/
    1983:   /* allocate bi array and free space for accumulating nonzero column info */
    1984:   PetscMalloc1(pn+1,&bi);
    1985:   bi[0] = 0;

    1987:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
    1988:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
    1989:   PetscFreeSpaceGet(nnz,&free_space);
    1990:   current_space = free_space;

    1992:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1993:   for (k=0; k<merge->nrecv; k++) {
    1994:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1995:     nrows       = *buf_ri_k[k];
    1996:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1997:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
    1998:   }

    2000:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
    2001:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    2002:   rmax = 0;
    2003:   for (i=0; i<pn; i++) {
    2004:     /* add pdt[i,:]*AP into lnk */
    2005:     pnz = pdti[i+1] - pdti[i];
    2006:     ptJ = pdtj + pdti[i];
    2007:     for (j=0; j<pnz; j++) {
    2008:       row  = ptJ[j];  /* row of AP == col of Pt */
    2009:       anz  = ai[row+1] - ai[row];
    2010:       Jptr = aj + ai[row];
    2011:       /* add non-zero cols of AP into the sorted linked list lnk */
    2012:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    2013:     }

    2015:     /* add received col data into lnk */
    2016:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    2017:       if (i == *nextrow[k]) { /* i-th row */
    2018:         nzi  = *(nextci[k]+1) - *nextci[k];
    2019:         Jptr = buf_rj[k] + *nextci[k];
    2020:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
    2021:         nextrow[k]++; nextci[k]++;
    2022:       }
    2023:     }

    2025:     /* add missing diagonal entry */
    2026:     if (C->force_diagonals) {
    2027:       k = i + owners[rank]; /* column index */
    2028:       PetscLLCondensedAddSorted_Scalable(1,&k,lnk);
    2029:     }

    2031:     nnz = lnk[0];

    2033:     /* if free space is not available, make more free space */
    2034:     if (current_space->local_remaining<nnz) {
    2035:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    2036:       nspacedouble++;
    2037:     }
    2038:     /* copy data into free space, then initialize lnk */
    2039:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
    2040:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    2042:     current_space->array           += nnz;
    2043:     current_space->local_used      += nnz;
    2044:     current_space->local_remaining -= nnz;

    2046:     bi[i+1] = bi[i] + nnz;
    2047:     if (nnz > rmax) rmax = nnz;
    2048:   }
    2049:   PetscFree3(buf_ri_k,nextrow,nextci);

    2051:   PetscMalloc1(bi[pn]+1,&bj);
    2052:   PetscFreeSpaceContiguous(&free_space,bj);
    2053:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    2054:   if (afill_tmp > afill) afill = afill_tmp;
    2055:   PetscLLCondensedDestroy_Scalable(lnk);
    2056:   PetscTableDestroy(&ta);
    2057:   MatRestoreSymbolicTranspose_SeqAIJ(p->A,&pdti,&pdtj);
    2058:   MatRestoreSymbolicTranspose_SeqAIJ(p->B,&poti,&potj);

    2060:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
    2061:   /*-------------------------------------------------------------------------------*/
    2062:   MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    2063:   MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    2064:   MatGetType(A,&mtype);
    2065:   MatSetType(C,mtype);
    2066:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    2067:   MatPreallocateFinalize(dnz,onz);
    2068:   MatSetBlockSize(C,1);
    2069:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    2070:   for (i=0; i<pn; i++) {
    2071:     row  = i + rstart;
    2072:     nnz  = bi[i+1] - bi[i];
    2073:     Jptr = bj + bi[i];
    2074:     MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
    2075:   }
    2076:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    2077:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    2078:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
    2079:   merge->bi        = bi;
    2080:   merge->bj        = bj;
    2081:   merge->coi       = coi;
    2082:   merge->coj       = coj;
    2083:   merge->buf_ri    = buf_ri;
    2084:   merge->buf_rj    = buf_rj;
    2085:   merge->owners_co = owners_co;

    2087:   /* attach the supporting struct to C for reuse */
    2088:   C->product->data    = ptap;
    2089:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    2090:   ptap->merge         = merge;

    2092:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

    2094: #if defined(PETSC_USE_INFO)
    2095:   if (bi[pn] != 0) {
    2096:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    2097:     PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    2098:   } else {
    2099:     PetscInfo(C,"Empty matrix product\n");
    2100:   }
    2101: #endif
    2102:   return(0);
    2103: }

    2105: /* ---------------------------------------------------------------- */
    2106: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
    2107: {
    2109:   Mat_Product    *product = C->product;
    2110:   Mat            A=product->A,B=product->B;
    2111:   PetscReal      fill=product->fill;
    2112:   PetscBool      flg;

    2115:   /* scalable */
    2116:   PetscStrcmp(product->alg,"scalable",&flg);
    2117:   if (flg) {
    2118:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
    2119:     goto next;
    2120:   }

    2122:   /* nonscalable */
    2123:   PetscStrcmp(product->alg,"nonscalable",&flg);
    2124:   if (flg) {
    2125:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
    2126:     goto next;
    2127:   }

    2129:   /* matmatmult */
    2130:   PetscStrcmp(product->alg,"at*b",&flg);
    2131:   if (flg) {
    2132:     Mat       At;
    2133:     Mat_APMPI *ptap;

    2135:     MatTranspose(A,MAT_INITIAL_MATRIX,&At);
    2136:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
    2137:     ptap = (Mat_APMPI*)C->product->data;
    2138:     if (ptap) {
    2139:       ptap->Pt = At;
    2140:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
    2141:     }
    2142:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
    2143:     goto next;
    2144:   }

    2146:   /* backend general code */
    2147:   PetscStrcmp(product->alg,"backend",&flg);
    2148:   if (flg) {
    2149:     MatProductSymbolic_MPIAIJBACKEND(C);
    2150:     return(0);
    2151:   }

    2153:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");

    2155: next:
    2156:   C->ops->productnumeric = MatProductNumeric_AtB;
    2157:   return(0);
    2158: }

    2160: /* ---------------------------------------------------------------- */
    2161: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
    2162: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
    2163: {
    2165:   Mat_Product    *product = C->product;
    2166:   Mat            A=product->A,B=product->B;
    2167: #if defined(PETSC_HAVE_HYPRE)
    2168:   const char     *algTypes[5] = {"scalable","nonscalable","seqmpi","backend","hypre"};
    2169:   PetscInt       nalg = 5;
    2170: #else
    2171:   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","backend",};
    2172:   PetscInt       nalg = 4;
    2173: #endif
    2174:   PetscInt       alg = 1; /* set nonscalable algorithm as default */
    2175:   PetscBool      flg;
    2176:   MPI_Comm       comm;

    2179:   /* Check matrix local sizes */
    2180:   PetscObjectGetComm((PetscObject)C,&comm);
    2181:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,B->rmap->rstart,B->rmap->rend);

    2183:   /* Set "nonscalable" as default algorithm */
    2184:   PetscStrcmp(C->product->alg,"default",&flg);
    2185:   if (flg) {
    2186:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2188:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2189:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2190:       MatInfo     Ainfo,Binfo;
    2191:       PetscInt    nz_local;
    2192:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2194:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2195:       MatGetInfo(B,MAT_LOCAL,&Binfo);
    2196:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2198:       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2199:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2201:       if (alg_scalable) {
    2202:         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2203:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2204:         PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
    2205:       }
    2206:     }
    2207:   }

    2209:   /* Get runtime option */
    2210:   if (product->api_user) {
    2211:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
    2212:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2213:     PetscOptionsEnd();
    2214:   } else {
    2215:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
    2216:     PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2217:     PetscOptionsEnd();
    2218:   }
    2219:   if (flg) {
    2220:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2221:   }

    2223:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
    2224:   return(0);
    2225: }

    2227: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
    2228: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
    2229: {
    2231:   Mat_Product    *product = C->product;
    2232:   Mat            A=product->A,B=product->B;
    2233:   const char     *algTypes[4] = {"scalable","nonscalable","at*b","backend"};
    2234:   PetscInt       nalg = 4;
    2235:   PetscInt       alg = 1; /* set default algorithm  */
    2236:   PetscBool      flg;
    2237:   MPI_Comm       comm;

    2240:   /* Check matrix local sizes */
    2241:   PetscObjectGetComm((PetscObject)C,&comm);
    2242:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A (%D, %D) != B (%D,%D)",A->rmap->rstart,A->rmap->rend,B->rmap->rstart,B->rmap->rend);

    2244:   /* Set default algorithm */
    2245:   PetscStrcmp(C->product->alg,"default",&flg);
    2246:   if (flg) {
    2247:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2248:   }

    2250:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2251:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2252:     MatInfo     Ainfo,Binfo;
    2253:     PetscInt    nz_local;
    2254:     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2256:     MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2257:     MatGetInfo(B,MAT_LOCAL,&Binfo);
    2258:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2260:     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2261:     MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2263:     if (alg_scalable) {
    2264:       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2265:       MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2266:       PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
    2267:     }
    2268:   }

    2270:   /* Get runtime option */
    2271:   if (product->api_user) {
    2272:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
    2273:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2274:     PetscOptionsEnd();
    2275:   } else {
    2276:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
    2277:     PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2278:     PetscOptionsEnd();
    2279:   }
    2280:   if (flg) {
    2281:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2282:   }

    2284:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
    2285:   return(0);
    2286: }

    2288: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
    2289: {
    2291:   Mat_Product    *product = C->product;
    2292:   Mat            A=product->A,P=product->B;
    2293:   MPI_Comm       comm;
    2294:   PetscBool      flg;
    2295:   PetscInt       alg=1; /* set default algorithm */
    2296: #if !defined(PETSC_HAVE_HYPRE)
    2297:   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","backend"};
    2298:   PetscInt       nalg=5;
    2299: #else
    2300:   const char     *algTypes[6] = {"scalable","nonscalable","allatonce","allatonce_merged","backend","hypre"};
    2301:   PetscInt       nalg=6;
    2302: #endif
    2303:   PetscInt       pN=P->cmap->N;

    2306:   /* Check matrix local sizes */
    2307:   PetscObjectGetComm((PetscObject)C,&comm);
    2308:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
    2309:   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);

    2311:   /* Set "nonscalable" as default algorithm */
    2312:   PetscStrcmp(C->product->alg,"default",&flg);
    2313:   if (flg) {
    2314:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2316:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2317:     if (pN > 100000) {
    2318:       MatInfo     Ainfo,Pinfo;
    2319:       PetscInt    nz_local;
    2320:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2322:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2323:       MatGetInfo(P,MAT_LOCAL,&Pinfo);
    2324:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

    2326:       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2327:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2329:       if (alg_scalable) {
    2330:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2331:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2332:       }
    2333:     }
    2334:   }

    2336:   /* Get runtime option */
    2337:   if (product->api_user) {
    2338:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
    2339:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2340:     PetscOptionsEnd();
    2341:   } else {
    2342:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
    2343:     PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2344:     PetscOptionsEnd();
    2345:   }
    2346:   if (flg) {
    2347:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2348:   }

    2350:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
    2351:   return(0);
    2352: }

    2354: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
    2355: {
    2356:   Mat_Product *product = C->product;
    2357:   Mat         A = product->A,R=product->B;

    2360:   /* Check matrix local sizes */
    2361:   if (A->cmap->n != R->cmap->n || A->rmap->n != R->cmap->n) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, A local (%D, %D), R local (%D,%D)",A->rmap->n,A->rmap->n,R->rmap->n,R->cmap->n);

    2363:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
    2364:   return(0);
    2365: }

    2367: /*
    2368:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
    2369: */
    2370: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
    2371: {
    2373:   Mat_Product    *product = C->product;
    2374:   PetscBool      flg = PETSC_FALSE;
    2375:   PetscInt       alg = 1; /* default algorithm */
    2376:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
    2377:   PetscInt       nalg = 3;

    2380:   /* Set default algorithm */
    2381:   PetscStrcmp(C->product->alg,"default",&flg);
    2382:   if (flg) {
    2383:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2384:   }

    2386:   /* Get runtime option */
    2387:   if (product->api_user) {
    2388:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
    2389:     PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2390:     PetscOptionsEnd();
    2391:   } else {
    2392:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
    2393:     PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
    2394:     PetscOptionsEnd();
    2395:   }
    2396:   if (flg) {
    2397:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2398:   }

    2400:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
    2401:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
    2402:   return(0);
    2403: }

    2405: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
    2406: {
    2408:   Mat_Product    *product = C->product;

    2411:   switch (product->type) {
    2412:   case MATPRODUCT_AB:
    2413:     MatProductSetFromOptions_MPIAIJ_AB(C);
    2414:     break;
    2415:   case MATPRODUCT_AtB:
    2416:     MatProductSetFromOptions_MPIAIJ_AtB(C);
    2417:     break;
    2418:   case MATPRODUCT_PtAP:
    2419:     MatProductSetFromOptions_MPIAIJ_PtAP(C);
    2420:     break;
    2421:   case MATPRODUCT_RARt:
    2422:     MatProductSetFromOptions_MPIAIJ_RARt(C);
    2423:     break;
    2424:   case MATPRODUCT_ABC:
    2425:     MatProductSetFromOptions_MPIAIJ_ABC(C);
    2426:     break;
    2427:   default:
    2428:     break;
    2429:   }
    2430:   return(0);
    2431: }