Actual source code: mpimatmatmult.c
petsc-3.13.6 2020-09-29
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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/vecscatterimpl.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:     goto next;
     33:   }

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

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

     49: #if defined(PETSC_HAVE_HYPRE)
     50:   PetscStrcmp(alg,"hypre",&flg);
     51:   if (flg) {
     52:     MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A,B,fill,C);
     53:     return(0);
     54:   }
     55: #endif
     56:   SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");

     58: next:
     59:   {
     60:     Mat_MPIAIJ *c  = (Mat_MPIAIJ*)C->data;
     61:     Mat_APMPI  *ap = c->ap;
     62:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatFreeIntermediateDataStructures","Mat");
     63:     ap->freestruct = PETSC_FALSE;
     64:     PetscOptionsBool("-mat_freeintermediatedatastructures","Free intermediate data structures", "MatFreeIntermediateDataStructures",ap->freestruct,&ap->freestruct, NULL);
     65:     PetscOptionsEnd();
     66:   }
     67:   return(0);
     68: }

     70: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
     71: {
     73:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
     74:   Mat_APMPI      *ptap = a->ap;

     77:   PetscFree2(ptap->startsj_s,ptap->startsj_r);
     78:   PetscFree(ptap->bufa);
     79:   MatDestroy(&ptap->P_loc);
     80:   MatDestroy(&ptap->P_oth);
     81:   MatDestroy(&ptap->Pt);
     82:   PetscFree(ptap->api);
     83:   PetscFree(ptap->apj);
     84:   PetscFree(ptap->apa);
     85:   ptap->destroy(A);
     86:   PetscFree(ptap);
     87:   return(0);
     88: }

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

    108:   PetscObjectGetComm((PetscObject)A,&comm);
    109:   MPI_Comm_size(comm,&size);

    111:   if (!ptap->P_oth && size>1) SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");

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

    119:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    120:   /*----------------------------------------------------------*/
    121:   /* get data from symbolic products */
    122:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    123:   p_oth = NULL;
    124:   if (size >1) {
    125:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    126:   }

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

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

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

    142:     /* 1st off-diagonal part of C */
    143:     ca = coa + co->i[i];
    144:     k  = 0;
    145:     for (k0=0; k0<conz; k0++) {
    146:       if (apJ[k] >= cstart) break;
    147:       ca[k0]      = apa[apJ[k]];
    148:       apa[apJ[k++]] = 0.0;
    149:     }

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

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

    168:   if (ptap->freestruct) {
    169:     MatFreeIntermediateDataStructures(C);
    170:   }
    171:   return(0);
    172: }

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

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

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

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

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

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

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

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

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

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

    247:     apnz     = lnk[0];
    248:     api[i+1] = api[i] + apnz;

    250:     /* if free space is not available, double the total space in the list */
    251:     if (current_space->local_remaining<apnz) {
    252:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    253:       nspacedouble++;
    254:     }

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

    260:     current_space->array           += apnz;
    261:     current_space->local_used      += apnz;
    262:     current_space->local_remaining -= apnz;
    263:   }

    265:   /* Allocate space for apj, initialize apj, and */
    266:   /* destroy list of free space and other temporary array(s) */
    267:   PetscMalloc1(api[am]+1,&ptap->apj);
    268:   apj  = ptap->apj;
    269:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    270:   PetscLLDestroy(lnk,lnkbt);

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

    275:   /* set and assemble symbolic parallel matrix C */
    276:   /*---------------------------------------------*/
    277:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    278:   MatSetBlockSizesFromMats(C,A,P);

    280:   MatGetType(A,&mtype);
    281:   MatSetType(C,mtype);
    282:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);

    284:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    285:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    286:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    287:   MatPreallocateFinalize(dnz,onz);

    289:   ptap->destroy        = C->ops->destroy;
    290:   ptap->duplicate      = C->ops->duplicate;
    291:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    292:   C->ops->productnumeric = MatProductNumeric_AB;
    293:   C->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
    294:   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;

    296:   /* attach the supporting struct to C for reuse */
    297:   c     = (Mat_MPIAIJ*)C->data;
    298:   c->ap = ptap;

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

    307: #if defined(PETSC_USE_INFO)
    308:   if (api[am]) {
    309:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    310:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    311:   } else {
    312:     PetscInfo(C,"Empty matrix product\n");
    313:   }
    314: #endif
    315:   return(0);
    316: }

    318: /* ------------------------------------------------------- */
    319: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
    320: {
    321:   Mat_Product *product = C->product;
    322:   Mat         A = product->A,B=product->B;

    325:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
    326:     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);

    328:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
    329:   C->ops->productsymbolic = MatProductSymbolic_AB;
    330:   C->ops->productnumeric  = MatProductNumeric_AB;
    331:   return(0);
    332: }
    333: /* -------------------------------------------------------------------- */
    334: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
    335: {
    336:   Mat_Product *product = C->product;
    337:   Mat         A = product->A,B=product->B;

    340:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
    341:     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);

    343:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
    344:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
    345:   return(0);
    346: }

    348: /* --------------------------------------------------------------------- */
    349: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
    350: {
    352:   Mat_Product    *product = C->product;

    355:   switch (product->type) {
    356:   case MATPRODUCT_AB:
    357:     MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
    358:     break;
    359:   case MATPRODUCT_AtB:
    360:     MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
    361:     break;
    362:   default:
    363:     /* Use MatProduct_Basic() if there is no specific implementation */
    364:     C->ops->productsymbolic = MatProductSymbolic_Basic;
    365:   }
    366:   return(0);
    367: }
    368: /* ------------------------------------------------------- */

    370: typedef struct {
    371:   Mat          workB,Bb,Cb,workB1,Bb1,Cb1;
    372:   MPI_Request  *rwaits,*swaits;
    373:   PetscInt     numBb;  /* num of Bb matrices */
    374:   PetscInt     nsends,nrecvs;
    375:   MPI_Datatype *stype,*rtype;
    376: } MPIAIJ_MPIDense;

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

    385:   MatDestroy(&contents->workB);

    387:   if (contents->numBb) {
    388:     MatDestroy(&contents->Bb);
    389:     MatDestroy(&contents->Cb);

    391:     MatDestroy(&contents->workB1);
    392:     MatDestroy(&contents->Bb1);
    393:     MatDestroy(&contents->Cb1);
    394:   }
    395:   for (i=0; i<contents->nsends; i++) {
    396:     MPI_Type_free(&contents->stype[i]);
    397:   }
    398:   for (i=0; i<contents->nrecvs; i++) {
    399:     MPI_Type_free(&contents->rtype[i]);
    400:   }
    401:   PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
    402:   PetscFree(contents);
    403:   return(0);
    404: }

    406: /*
    407:     This is a "dummy function" that handles the case where matrix C was created as a dense matrix
    408:   directly by the user and passed to MatMatMult() with the MAT_REUSE_MATRIX option

    410:   It is the same as MatMatMultSymbolic_MPIAIJ_MPIDense() except does not create C
    411: */
    412: PETSC_INTERN PetscErrorCode MatMatMultNumeric_MPIDense(Mat A,Mat B,Mat C)
    413: {
    414:   PetscBool      flg;

    418:   PetscObjectTypeCompare((PetscObject)A,MATNEST,&flg);
    419:   if (flg) {
    420:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
    421:     MatMatMultSymbolic_Nest_Dense(A,B,PETSC_DEFAULT,&C);
    422:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
    423:     C->ops->matmultnumeric = MatMatMultNumeric_Nest_Dense;
    424:   } else {
    425:     MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,PETSC_DEFAULT,C);
    426:   }
    427:   (*C->ops->matmultnumeric)(A,B,C);
    428:   return(0);
    429: }

    431: /*
    432:   Create Bb, Cb, Bb1 and Cb1 matrices to be used by MatMatMultSymbolic_MPIAIJ_MPIDense().
    433:   These matrices are used as wrappers for sub-columns of B and C, thus their own matrix operations are not used.
    434:   Modified from MatCreateDense().
    435: */
    436: PETSC_STATIC_INLINE PetscErrorCode MatCreateSubMPIDense_private(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt rbs,PetscInt cbs,PetscScalar *data,Mat *A)
    437: {

    441:   MatCreate(comm,A);
    442:   MatSetSizes(*A,m,n,M,N);
    443:   MatSetBlockSizes(*A,rbs,cbs);
    444:   MatSetType(*A,MATMPIDENSE);
    445:   MatMPIDenseSetPreallocation(*A,data);
    446:   (*A)->assembled = PETSC_TRUE;
    447:   return(0);
    448: }

    450: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
    451: {
    452:   PetscErrorCode  ierr;
    453:   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
    454:   Mat_MPIDense    *b=(Mat_MPIDense*)B->data;
    455:   Mat_SeqDense    *bseq=(Mat_SeqDense*)(b->A)->data;
    456:   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,lda=bseq->lda;
    457:   PetscContainer  container;
    458:   MPIAIJ_MPIDense *contents;
    459:   VecScatter      ctx=aij->Mvctx;
    460:   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from;
    461:   MPI_Comm        comm;
    462:   MPI_Datatype    type1,*stype,*rtype;
    463:   const PetscInt  *sindices,*sstarts,*rstarts;
    464:   PetscMPIInt     *disp;

    467:   PetscObjectGetComm((PetscObject)A,&comm);
    468:   if (!C->preallocated) {
    469:     MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
    470:     MatSetBlockSizesFromMats(C,A,B);
    471:     MatSetType(C,MATMPIDENSE);
    472:     MatMPIDenseSetPreallocation(C,NULL);
    473:   }

    475:   PetscNew(&contents);
    476:   contents->numBb = 0;

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

    481:   /* Create column block of B and C for memory scalability when BN is too large */
    482:   /* Estimate Bbn, column size of Bb */
    483:   if (nz) {
    484:     Bbn1 = 2*Am*BN/nz;
    485:   } else Bbn1 = BN;

    487:   bs = PetscAbs(B->cmap->bs);
    488:   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
    489:   if (Bbn1 > BN) Bbn1 = BN;
    490:   MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);

    492:   /* Enable runtime option for Bbn */
    493:   PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
    494:   PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);
    495:   if (Bbn > BN) SETERRQ2(comm,PETSC_ERR_ARG_SIZ,"Bbn=%D cannot be larger than %D, column size of B",Bbn,BN);
    496:   PetscOptionsEnd();

    498:   if (Bbn < BN) {
    499:     contents->numBb = BN/Bbn;
    500:     Bbn1 = BN - contents->numBb*Bbn;
    501:   }

    503:   if (contents->numBb) {
    504:     PetscScalar data[1]; /* fake array for Bb and Cb */
    505:     PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,contents->numBb);
    506:     MatCreateSubMPIDense_private(comm,B->rmap->n,PETSC_DECIDE,A->rmap->N,Bbn,B->rmap->bs,B->cmap->bs,data,&contents->Bb);
    507:     MatCreateSubMPIDense_private(comm,Am,PETSC_DECIDE,A->rmap->N,Bbn,C->rmap->bs,C->cmap->bs,data,&contents->Cb);

    509:     if (Bbn1) { /* Create Bb1 and Cb1 for the remaining columns */
    510:       PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);
    511:       MatCreateSubMPIDense_private(comm,B->rmap->n,PETSC_DECIDE,A->rmap->N,Bbn1,B->rmap->bs,B->cmap->bs,data,&contents->Bb1);
    512:       MatCreateSubMPIDense_private(comm,Am,PETSC_DECIDE,A->rmap->N,Bbn1,C->rmap->bs,C->cmap->bs,data,&contents->Cb1);

    514:       /* Create work matrix used to store off processor rows of B needed for local product */
    515:       MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
    516:     }
    517:   }

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

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

    527:   contents->rtype  = rtype;
    528:   contents->nrecvs = nrecvs;

    530:   PetscMalloc1(Bm+1,&disp);
    531:   for (i=0; i<nsends; i++) {
    532:     nrows_to = sstarts[i+1]-sstarts[i];
    533:     for (j=0; j<nrows_to; j++){
    534:       disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
    535:     }
    536:     MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);

    538:     MPI_Type_create_resized(type1,0,lda*sizeof(PetscScalar),&stype[i]);
    539:     MPI_Type_commit(&stype[i]);
    540:     MPI_Type_free(&type1);
    541:   }

    543:   for (i=0; i<nrecvs; i++) {
    544:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
    545:     nrows_from = rstarts[i+1]-rstarts[i];
    546:     disp[0] = 0;
    547:     MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);
    548:     MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);
    549:     MPI_Type_commit(&rtype[i]);
    550:     MPI_Type_free(&type1);
    551:   }

    553:   PetscFree(disp);
    554:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
    555:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);

    557:   PetscContainerCreate(comm,&container);
    558:   PetscContainerSetPointer(container,contents);
    559:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
    560:   PetscObjectCompose((PetscObject)C,"workB",(PetscObject)container);
    561:   PetscContainerDestroy(&container);
    562:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
    563:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    564:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    565:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
    566:   return(0);
    567: }

    569: extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);
    570: /*
    571:     Performs an efficient scatter on the rows of B needed by this process; this is
    572:     a modification of the VecScatterBegin_() routines.

    574:     Input: Bbidx = 0: B = Bb
    575:                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
    576: */
    577: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
    578: {
    579:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
    580:   PetscErrorCode    ierr;
    581:   const PetscScalar *b;
    582:   PetscScalar       *rvalues;
    583:   VecScatter        ctx = aij->Mvctx;
    584:   const PetscInt    *sindices,*sstarts,*rstarts;
    585:   const PetscMPIInt *sprocs,*rprocs;
    586:   PetscInt          i,nsends,nrecvs,nrecvs2;
    587:   MPI_Request       *swaits,*rwaits;
    588:   MPI_Comm          comm;
    589:   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,imdex,nsends_mpi,nrecvs_mpi;
    590:   MPI_Status        status;
    591:   MPIAIJ_MPIDense   *contents;
    592:   PetscContainer    container;
    593:   Mat               workB;
    594:   MPI_Datatype      *stype,*rtype;

    597:   PetscObjectGetComm((PetscObject)A,&comm);
    598:   PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);
    599:   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
    600:   PetscContainerGetPointer(container,(void**)&contents);

    602:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
    603:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
    604:   PetscMPIIntCast(nsends,&nsends_mpi);
    605:   PetscMPIIntCast(nrecvs,&nrecvs_mpi);
    606:   if (Bbidx == 0) {
    607:     workB = *outworkB = contents->workB;
    608:   } else {
    609:     workB = *outworkB = contents->workB1;
    610:   }
    611:   if (nrows != workB->rmap->n) SETERRQ2(comm,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",workB->cmap->n,nrows);
    612:   swaits  = contents->swaits;
    613:   rwaits  = contents->rwaits;

    615:   MatDenseGetArrayRead(B,&b);
    616:   MatDenseGetArray(workB,&rvalues);

    618:   /* Post recv, use MPI derived data type to save memory */
    619:   rtype = contents->rtype;
    620:   for (i=0; i<nrecvs; i++) {
    621:     MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
    622:   }

    624:   stype = contents->stype;
    625:   for (i=0; i<nsends; i++) {
    626:     MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
    627:   }

    629:   nrecvs2 = nrecvs;
    630:   while (nrecvs2) {
    631:     MPI_Waitany(nrecvs_mpi,rwaits,&imdex,&status);
    632:     nrecvs2--;
    633:   }
    634:   if (nsends) {MPI_Waitall(nsends_mpi,swaits,MPI_STATUSES_IGNORE);}

    636:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
    637:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
    638:   MatDenseRestoreArrayRead(B,&b);
    639:   MatDenseRestoreArray(workB,&rvalues);
    640:   MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);
    641:   MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);
    642:   return(0);
    643: }

    645: /*
    646:   Compute Cb = A*Bb
    647: */
    648: PETSC_STATIC_INLINE PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense_private(Mat A,Mat Bb,PetscInt Bbidx,PetscInt start,Mat C,const PetscScalar *barray,PetscScalar *carray,Mat Cb)
    649: {
    650:   PetscErrorCode  ierr;
    651:   PetscInt        start1;
    652:   Mat             workB;
    653:   Mat_MPIAIJ      *aij = (Mat_MPIAIJ*)A->data;
    654:   Mat_MPIDense    *cbdense = (Mat_MPIDense*)Cb->data;

    657:   /* Place barray to Bb */
    658:   start1 = start*Bb->rmap->n;
    659:   MatDensePlaceArray(Bb,barray+start1);

    661:   /* get off processor parts of Bb needed to complete Cb=A*Bb */
    662:   MatMPIDenseScatter(A,Bb,Bbidx,C,&workB);
    663:   MatDenseResetArray(Bb);

    665:   /* off-diagonal block of A times nonlocal rows of Bb */
    666:   /* Place carray to Cb */
    667:   start1 = start*Cb->rmap->n;
    668:   MatDensePlaceArray(Cb,carray+start1);
    669:   MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cbdense->A);
    670:   MatDenseResetArray(Cb);
    671:   return(0);
    672: }

    674: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
    675: {
    676:   PetscErrorCode  ierr;
    677:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
    678:   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
    679:   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
    680:   Mat             workB;
    681:   MPIAIJ_MPIDense *contents;
    682:   PetscContainer  container;
    683:   MPI_Comm        comm;
    684:   PetscInt        numBb;

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

    690:   PetscObjectGetComm((PetscObject)A,&comm);
    691:   PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);
    692:   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
    693:   PetscContainerGetPointer(container,(void**)&contents);
    694:   numBb = contents->numBb;

    696:   if (!numBb) {
    697:     /* get off processor parts of B needed to complete C=A*B */
    698:     MatMPIDenseScatter(A,B,0,C,&workB);

    700:     /* off-diagonal block of A times nonlocal rows of B */
    701:     MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);

    703:   } else {
    704:     const PetscScalar *barray;
    705:     PetscScalar       *carray;
    706:     Mat               Bb=contents->Bb,Cb=contents->Cb;
    707:     PetscInt          BbN=Bb->cmap->N,start,i;

    709:     MatDenseGetArrayRead(B,&barray);
    710:     MatDenseGetArray(C,&carray);
    711:     for (i=0; i<numBb; i++) {
    712:       start = i*BbN;
    713:       MatMatMultNumeric_MPIAIJ_MPIDense_private(A,Bb,0,start,C,barray,carray,Cb);
    714:     }

    716:     if (contents->Bb1) {
    717:       Bb = contents->Bb1; Cb = contents->Cb1;
    718:       start = i*BbN;
    719:       MatMatMultNumeric_MPIAIJ_MPIDense_private(A,Bb,1,start,C,barray,carray,Cb);
    720:     }
    721:     MatDenseRestoreArrayRead(B,&barray);
    722:     MatDenseRestoreArray(C,&carray);
    723:   }
    724:   return(0);
    725: }

    727: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
    728: {
    730:   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
    731:   Mat_SeqAIJ     *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
    732:   Mat_SeqAIJ     *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
    733:   PetscInt       *adi = ad->i,*adj,*aoi=ao->i,*aoj;
    734:   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
    735:   Mat_SeqAIJ     *p_loc,*p_oth;
    736:   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
    737:   PetscScalar    *pa_loc,*pa_oth,*pa,valtmp,*ca;
    738:   PetscInt       cm    = C->rmap->n,anz,pnz;
    739:   Mat_APMPI      *ptap = c->ap;
    740:   PetscScalar    *apa_sparse;
    741:   PetscInt       *api,*apj,*apJ,i,j,k,row;
    742:   PetscInt       cstart = C->cmap->rstart;
    743:   PetscInt       cdnz,conz,k0,k1,nextp;
    744:   MPI_Comm       comm;
    745:   PetscMPIInt    size;

    748:   PetscObjectGetComm((PetscObject)C,&comm);
    749:   MPI_Comm_size(comm,&size);

    751:   if (!ptap->P_oth && size>1) {
    752:     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
    753:   }
    754:   apa_sparse = ptap->apa;

    756:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    757:   /*-----------------------------------------------------*/
    758:   /* update numerical values of P_oth and P_loc */
    759:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
    760:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

    762:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    763:   /*----------------------------------------------------------*/
    764:   /* get data from symbolic products */
    765:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    766:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
    767:   if (size >1) {
    768:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    769:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
    770:   } else {
    771:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
    772:   }

    774:   api = ptap->api;
    775:   apj = ptap->apj;
    776:   for (i=0; i<cm; i++) {
    777:     apJ = apj + api[i];

    779:     /* diagonal portion of A */
    780:     anz = adi[i+1] - adi[i];
    781:     adj = ad->j + adi[i];
    782:     ada = ad->a + adi[i];
    783:     for (j=0; j<anz; j++) {
    784:       row = adj[j];
    785:       pnz = pi_loc[row+1] - pi_loc[row];
    786:       pj  = pj_loc + pi_loc[row];
    787:       pa  = pa_loc + pi_loc[row];
    788:       /* perform sparse axpy */
    789:       valtmp = ada[j];
    790:       nextp  = 0;
    791:       for (k=0; nextp<pnz; k++) {
    792:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    793:           apa_sparse[k] += valtmp*pa[nextp++];
    794:         }
    795:       }
    796:       PetscLogFlops(2.0*pnz);
    797:     }

    799:     /* off-diagonal portion of A */
    800:     anz = aoi[i+1] - aoi[i];
    801:     aoj = ao->j + aoi[i];
    802:     aoa = ao->a + aoi[i];
    803:     for (j=0; j<anz; j++) {
    804:       row = aoj[j];
    805:       pnz = pi_oth[row+1] - pi_oth[row];
    806:       pj  = pj_oth + pi_oth[row];
    807:       pa  = pa_oth + pi_oth[row];
    808:       /* perform sparse axpy */
    809:       valtmp = aoa[j];
    810:       nextp  = 0;
    811:       for (k=0; nextp<pnz; k++) {
    812:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    813:           apa_sparse[k] += valtmp*pa[nextp++];
    814:         }
    815:       }
    816:       PetscLogFlops(2.0*pnz);
    817:     }

    819:     /* set values in C */
    820:     cdnz = cd->i[i+1] - cd->i[i];
    821:     conz = co->i[i+1] - co->i[i];

    823:     /* 1st off-diagonal part of C */
    824:     ca = coa + co->i[i];
    825:     k  = 0;
    826:     for (k0=0; k0<conz; k0++) {
    827:       if (apJ[k] >= cstart) break;
    828:       ca[k0]        = apa_sparse[k];
    829:       apa_sparse[k] = 0.0;
    830:       k++;
    831:     }

    833:     /* diagonal part of C */
    834:     ca = cda + cd->i[i];
    835:     for (k1=0; k1<cdnz; k1++) {
    836:       ca[k1]        = apa_sparse[k];
    837:       apa_sparse[k] = 0.0;
    838:       k++;
    839:     }

    841:     /* 2nd off-diagonal part of C */
    842:     ca = coa + co->i[i];
    843:     for (; k0<conz; k0++) {
    844:       ca[k0]        = apa_sparse[k];
    845:       apa_sparse[k] = 0.0;
    846:       k++;
    847:     }
    848:   }
    849:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    850:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    852:   if (ptap->freestruct) {
    853:     MatFreeIntermediateDataStructures(C);
    854:   }
    855:   return(0);
    856: }

    858: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
    859: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
    860: {
    861:   PetscErrorCode     ierr;
    862:   MPI_Comm           comm;
    863:   PetscMPIInt        size;
    864:   Mat_APMPI          *ptap;
    865:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
    866:   Mat_MPIAIJ         *a         = (Mat_MPIAIJ*)A->data,*c;
    867:   Mat_SeqAIJ         *ad        = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
    868:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
    869:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
    870:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
    871:   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
    872:   PetscReal          afill;
    873:   MatType            mtype;

    876:   PetscObjectGetComm((PetscObject)A,&comm);
    877:   MPI_Comm_size(comm,&size);

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

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

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

    888:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    889:   pi_loc = p_loc->i; pj_loc = p_loc->j;
    890:   if (size > 1) {
    891:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
    892:     pi_oth = p_oth->i; pj_oth = p_oth->j;
    893:   } else {
    894:     p_oth  = NULL;
    895:     pi_oth = NULL; pj_oth = NULL;
    896:   }

    898:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    899:   /*-------------------------------------------------------------------*/
    900:   PetscMalloc1(am+2,&api);
    901:   ptap->api = api;
    902:   api[0]    = 0;

    904:   PetscLLCondensedCreate_Scalable(lsize,&lnk);

    906:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    907:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
    908:   current_space = free_space;
    909:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
    910:   for (i=0; i<am; i++) {
    911:     /* diagonal portion of A */
    912:     nzi = adi[i+1] - adi[i];
    913:     for (j=0; j<nzi; j++) {
    914:       row  = *adj++;
    915:       pnz  = pi_loc[row+1] - pi_loc[row];
    916:       Jptr = pj_loc + pi_loc[row];
    917:       /* Expand list if it is not long enough */
    918:       if (pnz+apnz_max > lsize) {
    919:         lsize = pnz+apnz_max;
    920:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    921:       }
    922:       /* add non-zero cols of P into the sorted linked list lnk */
    923:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    924:       apnz     = *lnk; /* The first element in the list is the number of items in the list */
    925:       api[i+1] = api[i] + apnz;
    926:       if (apnz > apnz_max) apnz_max = apnz;
    927:     }
    928:     /* off-diagonal portion of A */
    929:     nzi = aoi[i+1] - aoi[i];
    930:     for (j=0; j<nzi; j++) {
    931:       row  = *aoj++;
    932:       pnz  = pi_oth[row+1] - pi_oth[row];
    933:       Jptr = pj_oth + pi_oth[row];
    934:       /* Expand list if it is not long enough */
    935:       if (pnz+apnz_max > lsize) {
    936:         lsize = pnz + apnz_max;
    937:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
    938:       }
    939:       /* add non-zero cols of P into the sorted linked list lnk */
    940:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
    941:       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
    942:       api[i+1] = api[i] + apnz;
    943:       if (apnz > apnz_max) apnz_max = apnz;
    944:     }
    945:     apnz     = *lnk;
    946:     api[i+1] = api[i] + apnz;
    947:     if (apnz > apnz_max) apnz_max = apnz;

    949:     /* if free space is not available, double the total space in the list */
    950:     if (current_space->local_remaining<apnz) {
    951:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
    952:       nspacedouble++;
    953:     }

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

    959:     current_space->array           += apnz;
    960:     current_space->local_used      += apnz;
    961:     current_space->local_remaining -= apnz;
    962:   }

    964:   /* Allocate space for apj, initialize apj, and */
    965:   /* destroy list of free space and other temporary array(s) */
    966:   PetscMalloc1(api[am]+1,&ptap->apj);
    967:   apj  = ptap->apj;
    968:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
    969:   PetscLLCondensedDestroy_Scalable(lnk);

    971:   /* create and assemble symbolic parallel matrix C */
    972:   /*----------------------------------------------------*/
    973:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    974:   MatSetBlockSizesFromMats(C,A,P);
    975:   MatGetType(A,&mtype);
    976:   MatSetType(C,mtype);
    977:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);

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

    982:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    983:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    984:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    985:   MatPreallocateFinalize(dnz,onz);

    987:   ptap->destroy             = C->ops->destroy;
    988:   ptap->duplicate           = C->ops->duplicate;
    989:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
    990:   C->ops->productnumeric = MatProductNumeric_AB;
    991:   C->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
    992:   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;

    994:   /* attach the supporting struct to C for reuse */
    995:   c     = (Mat_MPIAIJ*)C->data;
    996:   c->ap = ptap;

    998:   /* set MatInfo */
    999:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    1000:   if (afill < 1.0) afill = 1.0;
    1001:   C->info.mallocs           = nspacedouble;
    1002:   C->info.fill_ratio_given  = fill;
    1003:   C->info.fill_ratio_needed = afill;

    1005: #if defined(PETSC_USE_INFO)
    1006:   if (api[am]) {
    1007:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1008:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    1009:   } else {
    1010:     PetscInfo(C,"Empty matrix product\n");
    1011:   }
    1012: #endif
    1013:   return(0);
    1014: }

    1016: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
    1017: /* Three input arrays are merged to one output array. The size of the    */
    1018: /* output array is also output. Duplicate entries only show up once.     */
    1019: static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
    1020:                                PetscInt  size2, PetscInt *in2,
    1021:                                PetscInt  size3, PetscInt *in3,
    1022:                                PetscInt *size4, PetscInt *out)
    1023: {
    1024:   int i = 0, j = 0, k = 0, l = 0;

    1026:   /* Traverse all three arrays */
    1027:   while (i<size1 && j<size2 && k<size3) {
    1028:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
    1029:       out[l++] = in1[i++];
    1030:     }
    1031:     else if(in2[j] < in1[i] && in2[j] < in3[k]) {
    1032:       out[l++] = in2[j++];
    1033:     }
    1034:     else if(in3[k] < in1[i] && in3[k] < in2[j]) {
    1035:       out[l++] = in3[k++];
    1036:     }
    1037:     else if(in1[i] == in2[j] && in1[i] < in3[k]) {
    1038:       out[l++] = in1[i];
    1039:       i++, j++;
    1040:     }
    1041:     else if(in1[i] == in3[k] && in1[i] < in2[j]) {
    1042:       out[l++] = in1[i];
    1043:       i++, k++;
    1044:     }
    1045:     else if(in3[k] == in2[j] && in2[j] < in1[i])  {
    1046:       out[l++] = in2[j];
    1047:       k++, j++;
    1048:     }
    1049:     else if(in1[i] == in2[j] && in1[i] == in3[k]) {
    1050:       out[l++] = in1[i];
    1051:       i++, j++, k++;
    1052:     }
    1053:   }

    1055:   /* Traverse two remaining arrays */
    1056:   while (i<size1 && j<size2) {
    1057:     if (in1[i] < in2[j]) {
    1058:       out[l++] = in1[i++];
    1059:     }
    1060:     else if(in1[i] > in2[j]) {
    1061:       out[l++] = in2[j++];
    1062:     }
    1063:     else {
    1064:       out[l++] = in1[i];
    1065:       i++, j++;
    1066:     }
    1067:   }

    1069:   while (i<size1 && k<size3) {
    1070:     if (in1[i] < in3[k]) {
    1071:       out[l++] = in1[i++];
    1072:     }
    1073:     else if(in1[i] > in3[k]) {
    1074:       out[l++] = in3[k++];
    1075:     }
    1076:     else {
    1077:       out[l++] = in1[i];
    1078:       i++, k++;
    1079:     }
    1080:   }

    1082:   while (k<size3 && j<size2)  {
    1083:     if (in3[k] < in2[j]) {
    1084:       out[l++] = in3[k++];
    1085:     }
    1086:     else if(in3[k] > in2[j]) {
    1087:       out[l++] = in2[j++];
    1088:     }
    1089:     else {
    1090:       out[l++] = in3[k];
    1091:       k++, j++;
    1092:     }
    1093:   }

    1095:   /* Traverse one remaining array */
    1096:   while (i<size1) out[l++] = in1[i++];
    1097:   while (j<size2) out[l++] = in2[j++];
    1098:   while (k<size3) out[l++] = in3[k++];

    1100:   *size4 = l;
    1101: }

    1103: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
    1104: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
    1105: /* matrix-matrix multiplications.  */
    1106: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
    1107: {
    1108:   PetscErrorCode     ierr;
    1109:   MPI_Comm           comm;
    1110:   PetscMPIInt        size;
    1111:   Mat_APMPI          *ptap;
    1112:   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
    1113:   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data;
    1114:   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
    1115:   Mat_MPIAIJ         *p        =(Mat_MPIAIJ*)P->data;
    1116:   Mat_MPIAIJ         *c;
    1117:   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
    1118:   PetscInt           adponz, adpdnz;
    1119:   PetscInt           *pi_loc,*dnz,*onz;
    1120:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
    1121:   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
    1122:                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
    1123:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
    1124:   PetscBT            lnkbt;
    1125:   PetscReal          afill;
    1126:   PetscMPIInt        rank;
    1127:   Mat                adpd, aopoth;
    1128:   MatType            mtype;
    1129:   const char         *prefix;

    1132:   PetscObjectGetComm((PetscObject)A,&comm);
    1133:   MPI_Comm_size(comm,&size);
    1134:   MPI_Comm_rank(comm, &rank);
    1135:   MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);

    1137:   /* create struct Mat_APMPI and attached it to C later */
    1138:   PetscNew(&ptap);

    1140:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    1141:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

    1143:   /* get P_loc by taking all local rows of P */
    1144:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

    1147:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
    1148:   pi_loc = p_loc->i;

    1150:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
    1151:   PetscMalloc1(am+2,&api);
    1152:   PetscMalloc1(am+2,&adpoi);

    1154:   adpoi[0]    = 0;
    1155:   ptap->api = api;
    1156:   api[0] = 0;

    1158:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
    1159:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
    1160:   MatPreallocateInitialize(comm,am,pn,dnz,onz);

    1162:   /* Symbolic calc of A_loc_diag * P_loc_diag */
    1163:   MatGetOptionsPrefix(A,&prefix);
    1164:   MatProductCreate(a->A,p->A,NULL,&adpd);
    1165:   MatGetOptionsPrefix(A,&prefix);
    1166:   MatSetOptionsPrefix(adpd,prefix);
    1167:   MatAppendOptionsPrefix(adpd,"inner_diag_");

    1169:   MatProductSetType(adpd,MATPRODUCT_AB);
    1170:   MatProductSetAlgorithm(adpd,"sorted");
    1171:   MatProductSetFill(adpd,fill);
    1172:   MatProductSetFromOptions(adpd);
    1173:   MatProductSymbolic(adpd);

    1175:   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
    1176:   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
    1177:   p_off = (Mat_SeqAIJ*)((p->B)->data);
    1178:   poff_i = p_off->i; poff_j = p_off->j;

    1180:   /* j_temp stores indices of a result row before they are added to the linked list */
    1181:   PetscMalloc1(pN+2,&j_temp);

    1184:   /* Symbolic calc of the A_diag * p_loc_off */
    1185:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    1186:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
    1187:   current_space = free_space_diag;

    1189:   for (i=0; i<am; i++) {
    1190:     /* A_diag * P_loc_off */
    1191:     nzi = adi[i+1] - adi[i];
    1192:     for (j=0; j<nzi; j++) {
    1193:       row  = *adj++;
    1194:       pnz  = poff_i[row+1] - poff_i[row];
    1195:       Jptr = poff_j + poff_i[row];
    1196:       for(i1 = 0; i1 < pnz; i1++) {
    1197:         j_temp[i1] = p->garray[Jptr[i1]];
    1198:       }
    1199:       /* add non-zero cols of P into the sorted linked list lnk */
    1200:       PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
    1201:     }

    1203:     adponz     = lnk[0];
    1204:     adpoi[i+1] = adpoi[i] + adponz;

    1206:     /* if free space is not available, double the total space in the list */
    1207:     if (current_space->local_remaining<adponz) {
    1208:       PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);
    1209:       nspacedouble++;
    1210:     }

    1212:     /* Copy data into free space, then initialize lnk */
    1213:     PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);

    1215:     current_space->array           += adponz;
    1216:     current_space->local_used      += adponz;
    1217:     current_space->local_remaining -= adponz;
    1218:   }

    1220:   /* Symbolic calc of A_off * P_oth */
    1221:   MatSetOptionsPrefix(a->B,prefix);
    1222:   MatAppendOptionsPrefix(a->B,"inner_offdiag_");
    1223:   MatCreate(PETSC_COMM_SELF,&aopoth);
    1224:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
    1225:   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
    1226:   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;

    1228:   /* Allocate space for apj, adpj, aopj, ... */
    1229:   /* destroy lists of free space and other temporary array(s) */

    1231:   PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
    1232:   PetscMalloc1(adpoi[am]+2, &adpoj);

    1234:   /* Copy from linked list to j-array */
    1235:   PetscFreeSpaceContiguous(&free_space_diag,adpoj);
    1236:   PetscLLDestroy(lnk,lnkbt);

    1238:   adpoJ = adpoj;
    1239:   adpdJ = adpdj;
    1240:   aopJ = aopothj;
    1241:   apj  = ptap->apj;
    1242:   apJ = apj; /* still empty */

    1244:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
    1245:   /* A_diag * P_loc_diag to get A*P */
    1246:   for (i = 0; i < am; i++) {
    1247:     aopnz  =  aopothi[i+1] -  aopothi[i];
    1248:     adponz = adpoi[i+1] - adpoi[i];
    1249:     adpdnz = adpdi[i+1] - adpdi[i];

    1251:     /* Correct indices from A_diag*P_diag */
    1252:     for(i1 = 0; i1 < adpdnz; i1++) {
    1253:       adpdJ[i1] += p_colstart;
    1254:     }
    1255:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
    1256:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
    1257:     MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);

    1259:     aopJ += aopnz;
    1260:     adpoJ += adponz;
    1261:     adpdJ += adpdnz;
    1262:     apJ += apnz;
    1263:     api[i+1] = api[i] + apnz;
    1264:   }

    1266:   /* malloc apa to store dense row A[i,:]*P */
    1267:   PetscCalloc1(pN+2,&ptap->apa);

    1269:   /* create and assemble symbolic parallel matrix C */
    1270:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
    1271:   MatSetBlockSizesFromMats(C,A,P);
    1272:   MatGetType(A,&mtype);
    1273:   MatSetType(C,mtype);
    1274:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);

    1277:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
    1278:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1279:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    1280:   MatPreallocateFinalize(dnz,onz);

    1283:   ptap->destroy        = C->ops->destroy;
    1284:   ptap->duplicate      = C->ops->duplicate;
    1285:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    1286:   C->ops->productnumeric = MatProductNumeric_AB;
    1287:   C->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;

    1289:   /* attach the supporting struct to C for reuse */
    1290:   c       = (Mat_MPIAIJ*)C->data;
    1291:   c->ap = ptap;

    1293:   /* set MatInfo */
    1294:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
    1295:   if (afill < 1.0) afill = 1.0;
    1296:   C->info.mallocs           = nspacedouble;
    1297:   C->info.fill_ratio_given  = fill;
    1298:   C->info.fill_ratio_needed = afill;

    1300: #if defined(PETSC_USE_INFO)
    1301:   if (api[am]) {
    1302:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    1303:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
    1304:   } else {
    1305:     PetscInfo(C,"Empty matrix product\n");
    1306:   }
    1307: #endif

    1309:   MatDestroy(&aopoth);
    1310:   MatDestroy(&adpd);
    1311:   PetscFree(j_temp);
    1312:   PetscFree(adpoj);
    1313:   PetscFree(adpoi);
    1314:   return(0);
    1315: }

    1317: /*-------------------------------------------------------------------------*/
    1318: /* This routine only works when scall=MAT_REUSE_MATRIX! */
    1319: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
    1320: {
    1322:   Mat_MPIAIJ     *c=(Mat_MPIAIJ*)C->data;
    1323:   Mat_APMPI      *ptap= c->ap;
    1324:   Mat            Pt;

    1327:   if (!ptap->Pt) {
    1328:     MPI_Comm comm;
    1329:     PetscObjectGetComm((PetscObject)C,&comm);
    1330:     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
    1331:   }

    1333:   Pt = ptap->Pt;
    1334:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
    1335:   MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);

    1337:   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
    1338:   if (ptap->freestruct) {
    1339:     MatFreeIntermediateDataStructures(C);
    1340:   }
    1341:   return(0);
    1342: }

    1344: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
    1345: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
    1346: {
    1347:   PetscErrorCode      ierr;
    1348:   Mat_APMPI           *ptap;
    1349:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*c;
    1350:   MPI_Comm            comm;
    1351:   PetscMPIInt         size,rank;
    1352:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1353:   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
    1354:   PetscInt            *lnk,i,k,nsend;
    1355:   PetscBT             lnkbt;
    1356:   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
    1357:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1358:   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
    1359:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1360:   MPI_Request         *swaits,*rwaits;
    1361:   MPI_Status          *sstatus,rstatus;
    1362:   PetscLayout         rowmap;
    1363:   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
    1364:   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
    1365:   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
    1366:   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
    1367:   PetscTable          ta;
    1368:   MatType             mtype;
    1369:   const char          *prefix;

    1372:   PetscObjectGetComm((PetscObject)A,&comm);
    1373:   MPI_Comm_size(comm,&size);
    1374:   MPI_Comm_rank(comm,&rank);

    1376:   /* create symbolic parallel matrix C */
    1377:   MatGetType(A,&mtype);
    1378:   MatSetType(C,mtype);

    1380:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

    1382:   /* create struct Mat_APMPI and attached it to C later */
    1383:   PetscNew(&ptap);
    1384:   ptap->reuse = MAT_INITIAL_MATRIX;

    1386:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
    1387:   /* --------------------------------- */
    1388:   MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
    1389:   MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);

    1391:   /* (1) compute symbolic A_loc */
    1392:   /* ---------------------------*/
    1393:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);

    1395:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
    1396:   /* ------------------------------------ */
    1397:   MatGetOptionsPrefix(A,&prefix);
    1398:   MatSetOptionsPrefix(ptap->Ro,prefix);
    1399:   MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
    1400:   MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
    1401:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);

    1403:   /* (3) send coj of C_oth to other processors  */
    1404:   /* ------------------------------------------ */
    1405:   /* determine row ownership */
    1406:   PetscLayoutCreate(comm,&rowmap);
    1407:   rowmap->n  = pn;
    1408:   rowmap->bs = 1;
    1409:   PetscLayoutSetUp(rowmap);
    1410:   owners = rowmap->range;

    1412:   /* determine the number of messages to send, their lengths */
    1413:   PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
    1414:   PetscArrayzero(len_s,size);
    1415:   PetscArrayzero(len_si,size);

    1417:   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
    1418:   coi   = c_oth->i; coj = c_oth->j;
    1419:   con   = ptap->C_oth->rmap->n;
    1420:   proc  = 0;
    1421:   for (i=0; i<con; i++) {
    1422:     while (prmap[i] >= owners[proc+1]) proc++;
    1423:     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
    1424:     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
    1425:   }

    1427:   len          = 0; /* max length of buf_si[], see (4) */
    1428:   owners_co[0] = 0;
    1429:   nsend        = 0;
    1430:   for (proc=0; proc<size; proc++) {
    1431:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1432:     if (len_s[proc]) {
    1433:       nsend++;
    1434:       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
    1435:       len         += len_si[proc];
    1436:     }
    1437:   }

    1439:   /* determine the number and length of messages to receive for coi and coj  */
    1440:   PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
    1441:   PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);

    1443:   /* post the Irecv and Isend of coj */
    1444:   PetscCommGetNewTag(comm,&tagj);
    1445:   PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
    1446:   PetscMalloc1(nsend+1,&swaits);
    1447:   for (proc=0, k=0; proc<size; proc++) {
    1448:     if (!len_s[proc]) continue;
    1449:     i    = owners_co[proc];
    1450:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1451:     k++;
    1452:   }

    1454:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
    1455:   /* ---------------------------------------- */
    1456:   MatSetOptionsPrefix(ptap->Rd,prefix);
    1457:   MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
    1458:   MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
    1459:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
    1460:   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;

    1462:   /* receives coj are complete */
    1463:   for (i=0; i<nrecv; i++) {
    1464:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1465:   }
    1466:   PetscFree(rwaits);
    1467:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

    1469:   /* add received column indices into ta to update Crmax */
    1470:   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;

    1472:   /* create and initialize a linked list */
    1473:   PetscTableCreate(an,aN,&ta); /* for compute Crmax */
    1474:   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);

    1476:   for (k=0; k<nrecv; k++) {/* k-th received message */
    1477:     Jptr = buf_rj[k];
    1478:     for (j=0; j<len_r[k]; j++) {
    1479:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    1480:     }
    1481:   }
    1482:   PetscTableGetCount(ta,&Crmax);
    1483:   PetscTableDestroy(&ta);

    1485:   /* (4) send and recv coi */
    1486:   /*-----------------------*/
    1487:   PetscCommGetNewTag(comm,&tagi);
    1488:   PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
    1489:   PetscMalloc1(len+1,&buf_s);
    1490:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    1491:   for (proc=0,k=0; proc<size; proc++) {
    1492:     if (!len_s[proc]) continue;
    1493:     /* form outgoing message for i-structure:
    1494:          buf_si[0]:                 nrows to be sent
    1495:                [1:nrows]:           row index (global)
    1496:                [nrows+1:2*nrows+1]: i-structure index
    1497:     */
    1498:     /*-------------------------------------------*/
    1499:     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
    1500:     buf_si_i    = buf_si + nrows+1;
    1501:     buf_si[0]   = nrows;
    1502:     buf_si_i[0] = 0;
    1503:     nrows       = 0;
    1504:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    1505:       nzi = coi[i+1] - coi[i];
    1506:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    1507:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    1508:       nrows++;
    1509:     }
    1510:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    1511:     k++;
    1512:     buf_si += len_si[proc];
    1513:   }
    1514:   for (i=0; i<nrecv; i++) {
    1515:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
    1516:   }
    1517:   PetscFree(rwaits);
    1518:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

    1520:   PetscFree4(len_s,len_si,sstatus,owners_co);
    1521:   PetscFree(len_ri);
    1522:   PetscFree(swaits);
    1523:   PetscFree(buf_s);

    1525:   /* (5) compute the local portion of C      */
    1526:   /* ------------------------------------------ */
    1527:   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
    1528:   PetscFreeSpaceGet(Crmax,&free_space);
    1529:   current_space = free_space;

    1531:   PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
    1532:   for (k=0; k<nrecv; k++) {
    1533:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1534:     nrows       = *buf_ri_k[k];
    1535:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    1536:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1537:   }

    1539:   MatPreallocateInitialize(comm,pn,an,dnz,onz);
    1540:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
    1541:   for (i=0; i<pn; i++) {
    1542:     /* add C_loc into C */
    1543:     nzi  = c_loc->i[i+1] - c_loc->i[i];
    1544:     Jptr = c_loc->j + c_loc->i[i];
    1545:     PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);

    1547:     /* add received col data into lnk */
    1548:     for (k=0; k<nrecv; k++) { /* k-th received message */
    1549:       if (i == *nextrow[k]) { /* i-th row */
    1550:         nzi  = *(nextci[k]+1) - *nextci[k];
    1551:         Jptr = buf_rj[k] + *nextci[k];
    1552:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
    1553:         nextrow[k]++; nextci[k]++;
    1554:       }
    1555:     }
    1556:     nzi = lnk[0];

    1558:     /* copy data into free space, then initialize lnk */
    1559:     PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
    1560:     MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
    1561:   }
    1562:   PetscFree3(buf_ri_k,nextrow,nextci);
    1563:   PetscLLDestroy(lnk,lnkbt);
    1564:   PetscFreeSpaceDestroy(free_space);

    1566:   /* local sizes and preallocation */
    1567:   MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
    1568:   if (P->cmap->bs > 0) {PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);}
    1569:   if (A->cmap->bs > 0) {PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);}
    1570:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    1571:   MatPreallocateFinalize(dnz,onz);

    1573:   /* members in merge */
    1574:   PetscFree(id_r);
    1575:   PetscFree(len_r);
    1576:   PetscFree(buf_ri[0]);
    1577:   PetscFree(buf_ri);
    1578:   PetscFree(buf_rj[0]);
    1579:   PetscFree(buf_rj);
    1580:   PetscLayoutDestroy(&rowmap);

    1582:   /* attach the supporting struct to C for reuse */
    1583:   c = (Mat_MPIAIJ*)C->data;
    1584:   c->ap         = ptap;
    1585:   ptap->destroy = C->ops->destroy;

    1587:   /* C is not ready for use - assembly will be done by MatPtAPNumeric() */
    1588:   C->assembled        = PETSC_FALSE;
    1589:   C->ops->destroy     = MatDestroy_MPIAIJ_PtAP;
    1590:   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
    1591:   return(0);
    1592: }

    1594: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
    1595: {
    1596:   PetscErrorCode    ierr;
    1597:   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
    1598:   Mat_SeqAIJ        *c_seq;
    1599:   Mat_APMPI         *ptap = c->ap;
    1600:   Mat               A_loc,C_loc,C_oth;
    1601:   PetscInt          i,rstart,rend,cm,ncols,row;
    1602:   const PetscInt    *cols;
    1603:   const PetscScalar *vals;

    1606:   if (!ptap->A_loc) {
    1607:     MPI_Comm comm;
    1608:     PetscObjectGetComm((PetscObject)C,&comm);
    1609:     SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
    1610:   }

    1612:   MatZeroEntries(C);

    1614:   if (ptap->reuse == MAT_REUSE_MATRIX) {
    1615:     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
    1616:     /* 1) get R = Pd^T, Ro = Po^T */
    1617:     /*----------------------------*/
    1618:     MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
    1619:     MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);

    1621:     /* 2) compute numeric A_loc */
    1622:     /*--------------------------*/
    1623:     MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
    1624:   }

    1626:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
    1627:   A_loc = ptap->A_loc;
    1628:   ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
    1629:   ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
    1630:   C_loc = ptap->C_loc;
    1631:   C_oth = ptap->C_oth;

    1633:   /* add C_loc and Co to to C */
    1634:   MatGetOwnershipRange(C,&rstart,&rend);

    1636:   /* C_loc -> C */
    1637:   cm    = C_loc->rmap->N;
    1638:   c_seq = (Mat_SeqAIJ*)C_loc->data;
    1639:   cols = c_seq->j;
    1640:   vals = c_seq->a;
    1641:   for (i=0; i<cm; i++) {
    1642:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1643:     row = rstart + i;
    1644:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1645:     cols += ncols; vals += ncols;
    1646:   }

    1648:   /* Co -> C, off-processor part */
    1649:   cm    = C_oth->rmap->N;
    1650:   c_seq = (Mat_SeqAIJ*)C_oth->data;
    1651:   cols  = c_seq->j;
    1652:   vals  = c_seq->a;
    1653:   for (i=0; i<cm; i++) {
    1654:     ncols = c_seq->i[i+1] - c_seq->i[i];
    1655:     row = p->garray[i];
    1656:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
    1657:     cols += ncols; vals += ncols;
    1658:   }
    1659:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1660:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1662:   ptap->reuse = MAT_REUSE_MATRIX;

    1664:   /* supporting struct ptap consumes almost same amount of memory as C=PtAP, release it if C will not be updated by A and P */
    1665:   if (ptap->freestruct) {
    1666:     MatFreeIntermediateDataStructures(C);
    1667:   }
    1668:   return(0);
    1669: }

    1671: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
    1672: {
    1673:   PetscErrorCode      ierr;
    1674:   Mat_Merge_SeqsToMPI *merge;
    1675:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
    1676:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
    1677:   Mat_APMPI           *ptap;
    1678:   PetscInt            *adj;
    1679:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
    1680:   MatScalar           *ada,*ca,valtmp;
    1681:   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
    1682:   MPI_Comm            comm;
    1683:   PetscMPIInt         size,rank,taga,*len_s;
    1684:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
    1685:   PetscInt            **buf_ri,**buf_rj;
    1686:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
    1687:   MPI_Request         *s_waits,*r_waits;
    1688:   MPI_Status          *status;
    1689:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
    1690:   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
    1691:   Mat                 A_loc;
    1692:   Mat_SeqAIJ          *a_loc;

    1695:   PetscObjectGetComm((PetscObject)C,&comm);
    1696:   MPI_Comm_size(comm,&size);
    1697:   MPI_Comm_rank(comm,&rank);

    1699:   ptap  = c->ap;
    1700:   if (!ptap->A_loc) SETERRQ(comm,PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatFreeIntermediateDataStructures() or use '-mat_freeintermediatedatastructures'");
    1701:   merge = ptap->merge;

    1703:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
    1704:   /*------------------------------------------*/
    1705:   /* get data from symbolic products */
    1706:   coi    = merge->coi; coj = merge->coj;
    1707:   PetscCalloc1(coi[pon]+1,&coa);
    1708:   bi     = merge->bi; bj = merge->bj;
    1709:   owners = merge->rowmap->range;
    1710:   PetscCalloc1(bi[cm]+1,&ba);

    1712:   /* get A_loc by taking all local rows of A */
    1713:   A_loc = ptap->A_loc;
    1714:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
    1715:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
    1716:   ai    = a_loc->i;
    1717:   aj    = a_loc->j;

    1719:   for (i=0; i<am; i++) {
    1720:     anz = ai[i+1] - ai[i];
    1721:     adj = aj + ai[i];
    1722:     ada = a_loc->a + ai[i];

    1724:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1725:     /*-------------------------------------------------------------*/
    1726:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1727:     pnz = po->i[i+1] - po->i[i];
    1728:     poJ = po->j + po->i[i];
    1729:     pA  = po->a + po->i[i];
    1730:     for (j=0; j<pnz; j++) {
    1731:       row = poJ[j];
    1732:       cj  = coj + coi[row];
    1733:       ca  = coa + coi[row];
    1734:       /* perform sparse axpy */
    1735:       nexta  = 0;
    1736:       valtmp = pA[j];
    1737:       for (k=0; nexta<anz; k++) {
    1738:         if (cj[k] == adj[nexta]) {
    1739:           ca[k] += valtmp*ada[nexta];
    1740:           nexta++;
    1741:         }
    1742:       }
    1743:       PetscLogFlops(2.0*anz);
    1744:     }

    1746:     /* put the value into Cd (diagonal part) */
    1747:     pnz = pd->i[i+1] - pd->i[i];
    1748:     pdJ = pd->j + pd->i[i];
    1749:     pA  = pd->a + pd->i[i];
    1750:     for (j=0; j<pnz; j++) {
    1751:       row = pdJ[j];
    1752:       cj  = bj + bi[row];
    1753:       ca  = ba + bi[row];
    1754:       /* perform sparse axpy */
    1755:       nexta  = 0;
    1756:       valtmp = pA[j];
    1757:       for (k=0; nexta<anz; k++) {
    1758:         if (cj[k] == adj[nexta]) {
    1759:           ca[k] += valtmp*ada[nexta];
    1760:           nexta++;
    1761:         }
    1762:       }
    1763:       PetscLogFlops(2.0*anz);
    1764:     }
    1765:   }

    1767:   /* 3) send and recv matrix values coa */
    1768:   /*------------------------------------*/
    1769:   buf_ri = merge->buf_ri;
    1770:   buf_rj = merge->buf_rj;
    1771:   len_s  = merge->len_s;
    1772:   PetscCommGetNewTag(comm,&taga);
    1773:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

    1775:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
    1776:   for (proc=0,k=0; proc<size; proc++) {
    1777:     if (!len_s[proc]) continue;
    1778:     i    = merge->owners_co[proc];
    1779:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
    1780:     k++;
    1781:   }
    1782:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
    1783:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

    1785:   PetscFree2(s_waits,status);
    1786:   PetscFree(r_waits);
    1787:   PetscFree(coa);

    1789:   /* 4) insert local Cseq and received values into Cmpi */
    1790:   /*----------------------------------------------------*/
    1791:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    1792:   for (k=0; k<merge->nrecv; k++) {
    1793:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1794:     nrows       = *(buf_ri_k[k]);
    1795:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
    1796:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
    1797:   }

    1799:   for (i=0; i<cm; i++) {
    1800:     row  = owners[rank] + i; /* global row index of C_seq */
    1801:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
    1802:     ba_i = ba + bi[i];
    1803:     bnz  = bi[i+1] - bi[i];
    1804:     /* add received vals into ba */
    1805:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    1806:       /* i-th row */
    1807:       if (i == *nextrow[k]) {
    1808:         cnz    = *(nextci[k]+1) - *nextci[k];
    1809:         cj     = buf_rj[k] + *(nextci[k]);
    1810:         ca     = abuf_r[k] + *(nextci[k]);
    1811:         nextcj = 0;
    1812:         for (j=0; nextcj<cnz; j++) {
    1813:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1814:             ba_i[j] += ca[nextcj++];
    1815:           }
    1816:         }
    1817:         nextrow[k]++; nextci[k]++;
    1818:         PetscLogFlops(2.0*cnz);
    1819:       }
    1820:     }
    1821:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
    1822:   }
    1823:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    1824:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

    1826:   PetscFree(ba);
    1827:   PetscFree(abuf_r[0]);
    1828:   PetscFree(abuf_r);
    1829:   PetscFree3(buf_ri_k,nextrow,nextci);

    1831:   if (ptap->freestruct) {
    1832:     MatFreeIntermediateDataStructures(C);
    1833:   }
    1834:   return(0);
    1835: }

    1837: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
    1838: {
    1839:   PetscErrorCode      ierr;
    1840:   Mat                 A_loc,POt,PDt;
    1841:   Mat_APMPI           *ptap;
    1842:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
    1843:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data,*c;
    1844:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
    1845:   PetscInt            nnz;
    1846:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
    1847:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
    1848:   MPI_Comm            comm;
    1849:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
    1850:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
    1851:   PetscInt            len,proc,*dnz,*onz,*owners;
    1852:   PetscInt            nzi,*bi,*bj;
    1853:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
    1854:   MPI_Request         *swaits,*rwaits;
    1855:   MPI_Status          *sstatus,rstatus;
    1856:   Mat_Merge_SeqsToMPI *merge;
    1857:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
    1858:   PetscReal           afill  =1.0,afill_tmp;
    1859:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
    1860:   Mat_SeqAIJ          *a_loc,*pdt,*pot;
    1861:   PetscTable          ta;
    1862:   MatType             mtype;

    1865:   PetscObjectGetComm((PetscObject)A,&comm);
    1866:   /* check if matrix local sizes are compatible */
    1867:   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);

    1869:   MPI_Comm_size(comm,&size);
    1870:   MPI_Comm_rank(comm,&rank);

    1872:   /* create struct Mat_APMPI and attached it to C later */
    1873:   PetscNew(&ptap);

    1875:   /* get A_loc by taking all local rows of A */
    1876:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

    1878:   ptap->A_loc = A_loc;
    1879:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
    1880:   ai          = a_loc->i;
    1881:   aj          = a_loc->j;

    1883:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1884:   /*----------------------------------------------------*/
    1885:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
    1886:   pdt  = (Mat_SeqAIJ*)PDt->data;
    1887:   pdti = pdt->i; pdtj = pdt->j;

    1889:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
    1890:   pot  = (Mat_SeqAIJ*)POt->data;
    1891:   poti = pot->i; potj = pot->j;

    1893:   /* then, compute symbolic Co = (p->B)^T*A */
    1894:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
    1895:                          >= (num of nonzero rows of C_seq) - pn */
    1896:   PetscMalloc1(pon+1,&coi);
    1897:   coi[0] = 0;

    1899:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1900:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
    1901:   PetscFreeSpaceGet(nnz,&free_space);
    1902:   current_space = free_space;

    1904:   /* create and initialize a linked list */
    1905:   PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
    1906:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
    1907:   PetscTableGetCount(ta,&Armax);

    1909:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

    1911:   for (i=0; i<pon; i++) {
    1912:     pnz = poti[i+1] - poti[i];
    1913:     ptJ = potj + poti[i];
    1914:     for (j=0; j<pnz; j++) {
    1915:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1916:       anz  = ai[row+1] - ai[row];
    1917:       Jptr = aj + ai[row];
    1918:       /* add non-zero cols of AP into the sorted linked list lnk */
    1919:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    1920:     }
    1921:     nnz = lnk[0];

    1923:     /* If free space is not available, double the total space in the list */
    1924:     if (current_space->local_remaining<nnz) {
    1925:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    1926:       nspacedouble++;
    1927:     }

    1929:     /* Copy data into free space, and zero out denserows */
    1930:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

    1932:     current_space->array           += nnz;
    1933:     current_space->local_used      += nnz;
    1934:     current_space->local_remaining -= nnz;

    1936:     coi[i+1] = coi[i] + nnz;
    1937:   }

    1939:   PetscMalloc1(coi[pon]+1,&coj);
    1940:   PetscFreeSpaceContiguous(&free_space,coj);
    1941:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

    1943:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
    1944:   if (afill_tmp > afill) afill = afill_tmp;

    1946:   /* send j-array (coj) of Co to other processors */
    1947:   /*----------------------------------------------*/
    1948:   /* determine row ownership */
    1949:   PetscNew(&merge);
    1950:   PetscLayoutCreate(comm,&merge->rowmap);

    1952:   merge->rowmap->n  = pn;
    1953:   merge->rowmap->bs = 1;

    1955:   PetscLayoutSetUp(merge->rowmap);
    1956:   owners = merge->rowmap->range;

    1958:   /* determine the number of messages to send, their lengths */
    1959:   PetscCalloc1(size,&len_si);
    1960:   PetscCalloc1(size,&merge->len_s);

    1962:   len_s        = merge->len_s;
    1963:   merge->nsend = 0;

    1965:   PetscMalloc1(size+2,&owners_co);

    1967:   proc = 0;
    1968:   for (i=0; i<pon; i++) {
    1969:     while (prmap[i] >= owners[proc+1]) proc++;
    1970:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
    1971:     len_s[proc] += coi[i+1] - coi[i];
    1972:   }

    1974:   len          = 0; /* max length of buf_si[] */
    1975:   owners_co[0] = 0;
    1976:   for (proc=0; proc<size; proc++) {
    1977:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
    1978:     if (len_si[proc]) {
    1979:       merge->nsend++;
    1980:       len_si[proc] = 2*(len_si[proc] + 1);
    1981:       len         += len_si[proc];
    1982:     }
    1983:   }

    1985:   /* determine the number and length of messages to receive for coi and coj  */
    1986:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
    1987:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

    1989:   /* post the Irecv and Isend of coj */
    1990:   PetscCommGetNewTag(comm,&tagj);
    1991:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
    1992:   PetscMalloc1(merge->nsend+1,&swaits);
    1993:   for (proc=0, k=0; proc<size; proc++) {
    1994:     if (!len_s[proc]) continue;
    1995:     i    = owners_co[proc];
    1996:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
    1997:     k++;
    1998:   }

    2000:   /* receives and sends of coj are complete */
    2001:   PetscMalloc1(size,&sstatus);
    2002:   for (i=0; i<merge->nrecv; i++) {
    2003:     PetscMPIInt icompleted;
    2004:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    2005:   }
    2006:   PetscFree(rwaits);
    2007:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

    2009:   /* add received column indices into table to update Armax */
    2010:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
    2011:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
    2012:     Jptr = buf_rj[k];
    2013:     for (j=0; j<merge->len_r[k]; j++) {
    2014:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
    2015:     }
    2016:   }
    2017:   PetscTableGetCount(ta,&Armax);
    2018:   /* 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); */

    2020:   /* send and recv coi */
    2021:   /*-------------------*/
    2022:   PetscCommGetNewTag(comm,&tagi);
    2023:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
    2024:   PetscMalloc1(len+1,&buf_s);
    2025:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
    2026:   for (proc=0,k=0; proc<size; proc++) {
    2027:     if (!len_s[proc]) continue;
    2028:     /* form outgoing message for i-structure:
    2029:          buf_si[0]:                 nrows to be sent
    2030:                [1:nrows]:           row index (global)
    2031:                [nrows+1:2*nrows+1]: i-structure index
    2032:     */
    2033:     /*-------------------------------------------*/
    2034:     nrows       = len_si[proc]/2 - 1;
    2035:     buf_si_i    = buf_si + nrows+1;
    2036:     buf_si[0]   = nrows;
    2037:     buf_si_i[0] = 0;
    2038:     nrows       = 0;
    2039:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
    2040:       nzi               = coi[i+1] - coi[i];
    2041:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
    2042:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
    2043:       nrows++;
    2044:     }
    2045:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
    2046:     k++;
    2047:     buf_si += len_si[proc];
    2048:   }
    2049:   i = merge->nrecv;
    2050:   while (i--) {
    2051:     PetscMPIInt icompleted;
    2052:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
    2053:   }
    2054:   PetscFree(rwaits);
    2055:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
    2056:   PetscFree(len_si);
    2057:   PetscFree(len_ri);
    2058:   PetscFree(swaits);
    2059:   PetscFree(sstatus);
    2060:   PetscFree(buf_s);

    2062:   /* compute the local portion of C (mpi mat) */
    2063:   /*------------------------------------------*/
    2064:   /* allocate bi array and free space for accumulating nonzero column info */
    2065:   PetscMalloc1(pn+1,&bi);
    2066:   bi[0] = 0;

    2068:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
    2069:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
    2070:   PetscFreeSpaceGet(nnz,&free_space);
    2071:   current_space = free_space;

    2073:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
    2074:   for (k=0; k<merge->nrecv; k++) {
    2075:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    2076:     nrows       = *buf_ri_k[k];
    2077:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
    2078:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
    2079:   }

    2081:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
    2082:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
    2083:   rmax = 0;
    2084:   for (i=0; i<pn; i++) {
    2085:     /* add pdt[i,:]*AP into lnk */
    2086:     pnz = pdti[i+1] - pdti[i];
    2087:     ptJ = pdtj + pdti[i];
    2088:     for (j=0; j<pnz; j++) {
    2089:       row  = ptJ[j];  /* row of AP == col of Pt */
    2090:       anz  = ai[row+1] - ai[row];
    2091:       Jptr = aj + ai[row];
    2092:       /* add non-zero cols of AP into the sorted linked list lnk */
    2093:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
    2094:     }

    2096:     /* add received col data into lnk */
    2097:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
    2098:       if (i == *nextrow[k]) { /* i-th row */
    2099:         nzi  = *(nextci[k]+1) - *nextci[k];
    2100:         Jptr = buf_rj[k] + *nextci[k];
    2101:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
    2102:         nextrow[k]++; nextci[k]++;
    2103:       }
    2104:     }
    2105:     nnz = lnk[0];

    2107:     /* if free space is not available, make more free space */
    2108:     if (current_space->local_remaining<nnz) {
    2109:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
    2110:       nspacedouble++;
    2111:     }
    2112:     /* copy data into free space, then initialize lnk */
    2113:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
    2114:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

    2116:     current_space->array           += nnz;
    2117:     current_space->local_used      += nnz;
    2118:     current_space->local_remaining -= nnz;

    2120:     bi[i+1] = bi[i] + nnz;
    2121:     if (nnz > rmax) rmax = nnz;
    2122:   }
    2123:   PetscFree3(buf_ri_k,nextrow,nextci);

    2125:   PetscMalloc1(bi[pn]+1,&bj);
    2126:   PetscFreeSpaceContiguous(&free_space,bj);
    2127:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
    2128:   if (afill_tmp > afill) afill = afill_tmp;
    2129:   PetscLLCondensedDestroy_Scalable(lnk);
    2130:   PetscTableDestroy(&ta);

    2132:   MatDestroy(&POt);
    2133:   MatDestroy(&PDt);

    2135:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
    2136:   /*-------------------------------------------------------------------------------*/
    2137:   MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
    2138:   MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
    2139:   MatGetType(A,&mtype);
    2140:   MatSetType(C,mtype);
    2141:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
    2142:   MatPreallocateFinalize(dnz,onz);
    2143:   MatSetBlockSize(C,1);
    2144:   for (i=0; i<pn; i++) {
    2145:     row  = i + rstart;
    2146:     nnz  = bi[i+1] - bi[i];
    2147:     Jptr = bj + bi[i];
    2148:     MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
    2149:   }
    2150:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    2151:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    2152:   merge->bi        = bi;
    2153:   merge->bj        = bj;
    2154:   merge->coi       = coi;
    2155:   merge->coj       = coj;
    2156:   merge->buf_ri    = buf_ri;
    2157:   merge->buf_rj    = buf_rj;
    2158:   merge->owners_co = owners_co;

    2160:   /* attach the supporting struct to C for reuse */
    2161:   c = (Mat_MPIAIJ*)C->data;

    2163:   c->ap       = ptap;
    2164:   ptap->api   = NULL;
    2165:   ptap->apj   = NULL;
    2166:   ptap->merge = merge;
    2167:   ptap->apa   = NULL;
    2168:   ptap->destroy   = C->ops->destroy;
    2169:   ptap->duplicate = C->ops->duplicate;

    2171:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
    2172:   C->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
    2173:   C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;

    2175: #if defined(PETSC_USE_INFO)
    2176:   if (bi[pn] != 0) {
    2177:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
    2178:     PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
    2179:   } else {
    2180:     PetscInfo(C,"Empty matrix product\n");
    2181:   }
    2182: #endif
    2183:   return(0);
    2184: }

    2186: /* ---------------------------------------------------------------- */
    2187: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
    2188: {
    2190:   Mat_Product    *product = C->product;
    2191:   Mat            A=product->A,B=product->B;
    2192:   PetscReal      fill=product->fill;
    2193:   PetscBool      flg;

    2196:   /* scalable */
    2197:   PetscStrcmp(product->alg,"scalable",&flg);
    2198:   if (flg) {
    2199:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
    2200:     goto next;
    2201:   }

    2203:   /* nonscalable */
    2204:   PetscStrcmp(product->alg,"nonscalable",&flg);
    2205:   if (flg) {
    2206:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
    2207:     goto next;
    2208:   }

    2210:   /* matmatmult */
    2211:   PetscStrcmp(product->alg,"at*b",&flg);
    2212:   if (flg) {
    2213:     Mat         At;
    2214:     Mat_APMPI   *ptap;
    2215:     Mat_MPIAIJ  *c;
    2216:     MatTranspose(A,MAT_INITIAL_MATRIX,&At);

    2218:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
    2219:     c    = (Mat_MPIAIJ*)C->data;
    2220:     ptap = c->ap;
    2221:     if (ptap) {
    2222:       ptap->Pt = At;
    2223:       C->ops->freeintermediatedatastructures = MatFreeIntermediateDataStructures_MPIAIJ_AP;
    2224:     }
    2225:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
    2226:     goto next;
    2227:   }

    2229:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");

    2231: next:
    2232:   C->ops->productnumeric = MatProductNumeric_AtB;

    2234:   {
    2235:     Mat_MPIAIJ *c  = (Mat_MPIAIJ*)C->data;
    2236:     Mat_APMPI  *ap = c->ap;
    2237:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatFreeIntermediateDataStructures","Mat");
    2238:     ap->freestruct = PETSC_FALSE;
    2239:     PetscOptionsBool("-mat_freeintermediatedatastructures","Free intermediate data structures", "MatFreeIntermediateDataStructures",ap->freestruct,&ap->freestruct, NULL);
    2240:     PetscOptionsEnd();
    2241:   }
    2242:   return(0);
    2243: }

    2245: /* ---------------------------------------------------------------- */
    2246: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
    2247: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
    2248: {
    2250:   Mat_Product    *product = C->product;
    2251:   Mat            A=product->A,B=product->B;
    2252: #if defined(PETSC_HAVE_HYPRE)
    2253:   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","hypre"};
    2254:   PetscInt       nalg = 4;
    2255: #else
    2256:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
    2257:   PetscInt       nalg = 3;
    2258: #endif
    2259:   PetscInt       alg = 1; /* set nonscalable algorithm as default */
    2260:   PetscBool      flg;
    2261:   MPI_Comm       comm;

    2264:   /* Check matrix local sizes */
    2265:   PetscObjectGetComm((PetscObject)C,&comm);
    2266:   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);

    2268:   /* Set "nonscalable" as default algorithm */
    2269:   PetscStrcmp(C->product->alg,"default",&flg);
    2270:   if (flg) {
    2271:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2273:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2274:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2275:       MatInfo     Ainfo,Binfo;
    2276:       PetscInt    nz_local;
    2277:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2279:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2280:       MatGetInfo(B,MAT_LOCAL,&Binfo);
    2281:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2283:       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2284:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2286:       if (alg_scalable) {
    2287:         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2288:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2289:         PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
    2290:       }
    2291:     }
    2292:   }

    2294:   /* Get runtime option */
    2295:   if (product->api_user) {
    2296:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
    2297:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2298:     PetscOptionsEnd();
    2299:   } else {
    2300:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
    2301:     PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2302:     PetscOptionsEnd();
    2303:   }
    2304:   if (flg) {
    2305:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2306:   }

    2308:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
    2309:   return(0);
    2310: }

    2312: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
    2313: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
    2314: {
    2316:   Mat_Product    *product = C->product;
    2317:   Mat            A=product->A,B=product->B;
    2318:   const char     *algTypes[3] = {"scalable","nonscalable","at*b"};
    2319:   PetscInt       nalg = 3;
    2320:   PetscInt       alg = 1; /* set default algorithm  */
    2321:   PetscBool      flg;
    2322:   MPI_Comm       comm;

    2325:   /* Check matrix local sizes */
    2326:   PetscObjectGetComm((PetscObject)C,&comm);
    2327:   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);

    2329:   /* Set default algorithm */
    2330:   PetscStrcmp(C->product->alg,"default",&flg);
    2331:   if (flg) {
    2332:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2333:   }

    2335:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2336:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2337:     MatInfo     Ainfo,Binfo;
    2338:     PetscInt    nz_local;
    2339:     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2341:     MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2342:     MatGetInfo(B,MAT_LOCAL,&Binfo);
    2343:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2345:     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2346:     MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2348:     if (alg_scalable) {
    2349:       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2350:       MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2351:       PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
    2352:     }
    2353:   }

    2355:   /* Get runtime option */
    2356:   if (product->api_user) {
    2357:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
    2358:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2359:     PetscOptionsEnd();
    2360:   } else {
    2361:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
    2362:     PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2363:     PetscOptionsEnd();
    2364:   }
    2365:   if (flg) {
    2366:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2367:   }

    2369:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
    2370:   return(0);
    2371: }

    2373: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
    2374: {
    2376:   Mat_Product    *product = C->product;
    2377:   Mat            A=product->A,P=product->B;
    2378:   MPI_Comm       comm;
    2379:   PetscBool      flg;
    2380:   PetscInt       alg=1; /* set default algorithm */
    2381: #if !defined(PETSC_HAVE_HYPRE)
    2382:   const char     *algTypes[4] = {"scalable","nonscalable","allatonce","allatonce_merged"};
    2383:   PetscInt       nalg=4;
    2384: #else
    2385:   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","hypre"};
    2386:   PetscInt       nalg=5;
    2387: #endif
    2388:   PetscInt       pN=P->cmap->N;

    2391:   /* Check matrix local sizes */
    2392:   PetscObjectGetComm((PetscObject)C,&comm);
    2393:   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);
    2394:   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);

    2396:   /* Set "nonscalable" as default algorithm */
    2397:   PetscStrcmp(C->product->alg,"default",&flg);
    2398:   if (flg) {
    2399:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

    2401:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2402:     if (pN > 100000) {
    2403:       MatInfo     Ainfo,Pinfo;
    2404:       PetscInt    nz_local;
    2405:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

    2407:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
    2408:       MatGetInfo(P,MAT_LOCAL,&Pinfo);
    2409:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

    2411:       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
    2412:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

    2414:       if (alg_scalable) {
    2415:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2416:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2417:       }
    2418:     }
    2419:   }

    2421:   /* Get runtime option */
    2422:   if (product->api_user) {
    2423:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
    2424:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2425:     PetscOptionsEnd();
    2426:   } else {
    2427:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
    2428:     PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
    2429:     PetscOptionsEnd();
    2430:   }
    2431:   if (flg) {
    2432:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2433:   }

    2435:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
    2436:   return(0);
    2437: }

    2439: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
    2440: {
    2441:   Mat_Product *product = C->product;
    2442:   Mat         A = product->A,R=product->B;

    2445:   /* Check matrix local sizes */
    2446:   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);

    2448:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
    2449:   return(0);
    2450: }

    2452: /*
    2453:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
    2454: */
    2455: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
    2456: {
    2458:   Mat_Product    *product = C->product;
    2459:   PetscBool      flg = PETSC_FALSE;
    2460:   PetscInt       alg = 1; /* default algorithm */
    2461:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
    2462:   PetscInt       nalg = 3;

    2465:   /* Set default algorithm */
    2466:   PetscStrcmp(C->product->alg,"default",&flg);
    2467:   if (flg) {
    2468:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2469:   }

    2471:   /* Get runtime option */
    2472:   if (product->api_user) {
    2473:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
    2474:     PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
    2475:     PetscOptionsEnd();
    2476:   } else {
    2477:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
    2478:     PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
    2479:     PetscOptionsEnd();
    2480:   }
    2481:   if (flg) {
    2482:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
    2483:   }

    2485:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
    2486:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
    2487:   return(0);
    2488: }

    2490: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
    2491: {
    2493:   Mat_Product    *product = C->product;

    2496:   switch (product->type) {
    2497:   case MATPRODUCT_AB:
    2498:     MatProductSetFromOptions_MPIAIJ_AB(C);
    2499:     break;
    2500:   case MATPRODUCT_AtB:
    2501:     MatProductSetFromOptions_MPIAIJ_AtB(C);
    2502:     break;
    2503:   case MATPRODUCT_PtAP:
    2504:     MatProductSetFromOptions_MPIAIJ_PtAP(C);
    2505:     break;
    2506:   case MATPRODUCT_RARt:
    2507:     MatProductSetFromOptions_MPIAIJ_RARt(C);
    2508:     break;
    2509:   case MATPRODUCT_ABC:
    2510:     MatProductSetFromOptions_MPIAIJ_ABC(C);
    2511:     break;
    2512:   default: SETERRQ1(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"MatProduct type %s is not supported for MPIAIJ and MPIAIJ matrices",MatProductTypes[product->type]);
    2513:   }
    2514:   return(0);
    2515: }