Actual source code: mpimatmatmult.c

petsc-master 2020-10-26
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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:     return(0);
 33:   }

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

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

 49: #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");
 57: }

 59: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
 60: {
 62:   Mat_APMPI      *ptap = (Mat_APMPI*)data;

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

 77: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
 78: {
 80:   Mat_MPIAIJ     *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
 81:   Mat_SeqAIJ     *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
 82:   Mat_SeqAIJ     *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
 83:   PetscScalar    *cda=cd->a,*coa=co->a;
 84:   Mat_SeqAIJ     *p_loc,*p_oth;
 85:   PetscScalar    *apa,*ca;
 86:   PetscInt       cm =C->rmap->n;
 87:   Mat_APMPI      *ptap;
 88:   PetscInt       *api,*apj,*apJ,i,k;
 89:   PetscInt       cstart=C->cmap->rstart;
 90:   PetscInt       cdnz,conz,k0,k1;
 91:   MPI_Comm       comm;
 92:   PetscMPIInt    size;

 95:   MatCheckProduct(C,3);
 96:   ptap = (Mat_APMPI*)C->product->data;
 97:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
 98:   PetscObjectGetComm((PetscObject)A,&comm);
 99:   MPI_Comm_size(comm,&size);

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

103:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
104:   /*-----------------------------------------------------*/
105:   /* update numerical values of P_oth and P_loc */
106:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
107:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

109:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
110:   /*----------------------------------------------------------*/
111:   /* get data from symbolic products */
112:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
113:   p_oth = NULL;
114:   if (size >1) {
115:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
116:   }

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

121:   api = ptap->api;
122:   apj = ptap->apj;
123:   for (i=0; i<cm; i++) {
124:     /* compute apa = A[i,:]*P */
125:     AProw_nonscalable(i,ad,ao,p_loc,p_oth,apa);

127:     /* set values in C */
128:     apJ  = apj + api[i];
129:     cdnz = cd->i[i+1] - cd->i[i];
130:     conz = co->i[i+1] - co->i[i];

132:     /* 1st off-diagonal part of C */
133:     ca = coa + co->i[i];
134:     k  = 0;
135:     for (k0=0; k0<conz; k0++) {
136:       if (apJ[k] >= cstart) break;
137:       ca[k0]      = apa[apJ[k]];
138:       apa[apJ[k++]] = 0.0;
139:     }

141:     /* diagonal part of C */
142:     ca = cda + cd->i[i];
143:     for (k1=0; k1<cdnz; k1++) {
144:       ca[k1]      = apa[apJ[k]];
145:       apa[apJ[k++]] = 0.0;
146:     }

148:     /* 2nd off-diagonal part of C */
149:     ca = coa + co->i[i];
150:     for (; k0<conz; k0++) {
151:       ca[k0]      = apa[apJ[k]];
152:       apa[apJ[k++]] = 0.0;
153:     }
154:   }
155:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
156:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
157:   return(0);
158: }

160: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat C)
161: {
162:   PetscErrorCode     ierr;
163:   MPI_Comm           comm;
164:   PetscMPIInt        size;
165:   Mat_APMPI          *ptap;
166:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
167:   Mat_MPIAIJ         *a=(Mat_MPIAIJ*)A->data;
168:   Mat_SeqAIJ         *ad=(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
169:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
170:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
171:   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
172:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
173:   PetscBT            lnkbt;
174:   PetscReal          afill;
175:   MatType            mtype;

178:   MatCheckProduct(C,4);
179:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
180:   PetscObjectGetComm((PetscObject)A,&comm);
181:   MPI_Comm_size(comm,&size);

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

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

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

192:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
193:   pi_loc = p_loc->i; pj_loc = p_loc->j;
194:   if (size > 1) {
195:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
196:     pi_oth = p_oth->i; pj_oth = p_oth->j;
197:   } else {
198:     p_oth = NULL;
199:     pi_oth = NULL; pj_oth = NULL;
200:   }

202:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
203:   /*-------------------------------------------------------------------*/
204:   PetscMalloc1(am+2,&api);
205:   ptap->api = api;
206:   api[0]    = 0;

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

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

215:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
216:   for (i=0; i<am; i++) {
217:     /* diagonal portion of A */
218:     nzi = adi[i+1] - adi[i];
219:     for (j=0; j<nzi; j++) {
220:       row  = *adj++;
221:       pnz  = pi_loc[row+1] - pi_loc[row];
222:       Jptr = pj_loc + pi_loc[row];
223:       /* add non-zero cols of P into the sorted linked list lnk */
224:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
225:     }
226:     /* off-diagonal portion of A */
227:     nzi = aoi[i+1] - aoi[i];
228:     for (j=0; j<nzi; j++) {
229:       row  = *aoj++;
230:       pnz  = pi_oth[row+1] - pi_oth[row];
231:       Jptr = pj_oth + pi_oth[row];
232:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
233:     }

235:     apnz     = lnk[0];
236:     api[i+1] = api[i] + apnz;

238:     /* if free space is not available, double the total space in the list */
239:     if (current_space->local_remaining<apnz) {
240:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
241:       nspacedouble++;
242:     }

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

248:     current_space->array           += apnz;
249:     current_space->local_used      += apnz;
250:     current_space->local_remaining -= apnz;
251:   }

253:   /* Allocate space for apj, initialize apj, and */
254:   /* destroy list of free space and other temporary array(s) */
255:   PetscMalloc1(api[am]+1,&ptap->apj);
256:   apj  = ptap->apj;
257:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
258:   PetscLLDestroy(lnk,lnkbt);

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

263:   /* set and assemble symbolic parallel matrix C */
264:   /*---------------------------------------------*/
265:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
266:   MatSetBlockSizesFromMats(C,A,P);

268:   MatGetType(A,&mtype);
269:   MatSetType(C,mtype);
270:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
271:   MatPreallocateFinalize(dnz,onz);

273:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
274:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
275:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
276:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

278:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
279:   C->ops->productnumeric = MatProductNumeric_AB;

281:   /* attach the supporting struct to C for reuse */
282:   C->product->data    = ptap;
283:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

285:   /* set MatInfo */
286:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
287:   if (afill < 1.0) afill = 1.0;
288:   C->info.mallocs           = nspacedouble;
289:   C->info.fill_ratio_given  = fill;
290:   C->info.fill_ratio_needed = afill;

292: #if defined(PETSC_USE_INFO)
293:   if (api[am]) {
294:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
295:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
296:   } else {
297:     PetscInfo(C,"Empty matrix product\n");
298:   }
299: #endif
300:   return(0);
301: }

303: /* ------------------------------------------------------- */
304: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat,Mat,PetscReal,Mat);
305: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat,Mat,Mat);

307: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
308: {
309:   Mat_Product *product = C->product;
310:   Mat         A = product->A,B=product->B;

313:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
314:     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);

316:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
317:   C->ops->productsymbolic = MatProductSymbolic_AB;
318:   return(0);
319: }
320: /* -------------------------------------------------------------------- */
321: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
322: {
323:   Mat_Product *product = C->product;
324:   Mat         A = product->A,B=product->B;

327:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
328:     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);

330:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
331:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
332:   return(0);
333: }

335: /* --------------------------------------------------------------------- */
336: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
337: {
339:   Mat_Product    *product = C->product;

342:   switch (product->type) {
343:   case MATPRODUCT_AB:
344:     MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C);
345:     break;
346:   case MATPRODUCT_AtB:
347:     MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C);
348:     break;
349:   default:
350:     break;
351:   }
352:   return(0);
353: }
354: /* ------------------------------------------------------- */

356: typedef struct {
357:   Mat          workB,workB1;
358:   MPI_Request  *rwaits,*swaits;
359:   PetscInt     nsends,nrecvs;
360:   MPI_Datatype *stype,*rtype;
361:   PetscInt     blda;
362: } MPIAIJ_MPIDense;

364: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
365: {
366:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*)ctx;
367:   PetscErrorCode  ierr;
368:   PetscInt        i;

371:   MatDestroy(&contents->workB);
372:   MatDestroy(&contents->workB1);
373:   for (i=0; i<contents->nsends; i++) {
374:     MPI_Type_free(&contents->stype[i]);
375:   }
376:   for (i=0; i<contents->nrecvs; i++) {
377:     MPI_Type_free(&contents->rtype[i]);
378:   }
379:   PetscFree4(contents->stype,contents->rtype,contents->rwaits,contents->swaits);
380:   PetscFree(contents);
381:   return(0);
382: }

384: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat C)
385: {
386:   PetscErrorCode  ierr;
387:   Mat_MPIAIJ      *aij=(Mat_MPIAIJ*)A->data;
388:   PetscInt        nz=aij->B->cmap->n,nsends,nrecvs,i,nrows_to,j,blda,clda;
389:   MPIAIJ_MPIDense *contents;
390:   VecScatter      ctx=aij->Mvctx;
391:   PetscInt        Am=A->rmap->n,Bm=B->rmap->n,BN=B->cmap->N,Bbn,Bbn1,bs,nrows_from,numBb;
392:   MPI_Comm        comm;
393:   MPI_Datatype    type1,*stype,*rtype;
394:   const PetscInt  *sindices,*sstarts,*rstarts;
395:   PetscMPIInt     *disp;
396:   PetscBool       cisdense;

399:   MatCheckProduct(C,4);
400:   if (C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data not empty");
401:   PetscObjectGetComm((PetscObject)A,&comm);
402:   PetscObjectBaseTypeCompare((PetscObject)C,MATMPIDENSE,&cisdense);
403:   if (!cisdense) {
404:     MatSetType(C,((PetscObject)B)->type_name);
405:   }
406:   MatSetSizes(C,Am,B->cmap->n,A->rmap->N,BN);
407:   MatSetBlockSizesFromMats(C,A,B);
408:   MatSetUp(C);
409:   MatDenseGetLDA(B,&blda);
410:   MatDenseGetLDA(C,&clda);
411:   PetscNew(&contents);

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

416:   /* Create column block of B and C for memory scalability when BN is too large */
417:   /* Estimate Bbn, column size of Bb */
418:   if (nz) {
419:     Bbn1 = 2*Am*BN/nz;
420:   } else Bbn1 = BN;

422:   bs = PetscAbs(B->cmap->bs);
423:   Bbn1 = Bbn1/bs *bs; /* Bbn1 is a multiple of bs */
424:   if (Bbn1 > BN) Bbn1 = BN;
425:   MPI_Allreduce(&Bbn1,&Bbn,1,MPIU_INT,MPI_MAX,comm);

427:   /* Enable runtime option for Bbn */
428:   PetscOptionsBegin(comm,((PetscObject)C)->prefix,"MatMatMult","Mat");
429:   PetscOptionsInt("-matmatmult_Bbn","Number of columns in Bb","MatMatMult",Bbn,&Bbn,NULL);
430:   PetscOptionsEnd();
431:   Bbn  = PetscMin(Bbn,BN);

433:   if (Bbn > 0 && Bbn < BN) {
434:     numBb = BN/Bbn;
435:     Bbn1 = BN - numBb*Bbn;
436:   } else numBb = 0;

438:   if (numBb) {
439:     PetscInfo3(C,"use Bb, BN=%D, Bbn=%D; numBb=%D\n",BN,Bbn,numBb);
440:     if (Bbn1) { /* Create workB1 for the remaining columns */
441:       PetscInfo2(C,"use Bb1, BN=%D, Bbn1=%D\n",BN,Bbn1);
442:       /* Create work matrix used to store off processor rows of B needed for local product */
443:       MatCreateSeqDense(PETSC_COMM_SELF,nz,Bbn1,NULL,&contents->workB1);
444:     } else contents->workB1 = NULL;
445:   }

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

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

455:   contents->rtype  = rtype;
456:   contents->nrecvs = nrecvs;
457:   contents->blda   = blda;

459:   PetscMalloc1(Bm+1,&disp);
460:   for (i=0; i<nsends; i++) {
461:     nrows_to = sstarts[i+1]-sstarts[i];
462:     for (j=0; j<nrows_to; j++){
463:       disp[j] = sindices[sstarts[i]+j]; /* rowB to be sent */
464:     }
465:     MPI_Type_create_indexed_block(nrows_to,1,(const PetscMPIInt *)disp,MPIU_SCALAR,&type1);

467:     MPI_Type_create_resized(type1,0,blda*sizeof(PetscScalar),&stype[i]);
468:     MPI_Type_commit(&stype[i]);
469:     MPI_Type_free(&type1);
470:   }

472:   for (i=0; i<nrecvs; i++) {
473:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
474:     nrows_from = rstarts[i+1]-rstarts[i];
475:     disp[0] = 0;
476:     MPI_Type_create_indexed_block(1, nrows_from, (const PetscMPIInt *)disp, MPIU_SCALAR, &type1);
477:     MPI_Type_create_resized(type1, 0, nz*sizeof(PetscScalar), &rtype[i]);
478:     MPI_Type_commit(&rtype[i]);
479:     MPI_Type_free(&type1);
480:   }

482:   PetscFree(disp);
483:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,NULL,NULL);
484:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,NULL,NULL);
485:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
486:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
487:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
488:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

490:   C->product->data = contents;
491:   C->product->destroy = MatMPIAIJ_MPIDenseDestroy;
492:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
493:   return(0);
494: }

496: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat,const PetscBool);
497: /*
498:     Performs an efficient scatter on the rows of B needed by this process; this is
499:     a modification of the VecScatterBegin_() routines.

501:     Input: Bbidx = 0: B = Bb
502:                  = 1: B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
503: */
504: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,PetscInt Bbidx,Mat C,Mat *outworkB)
505: {
506:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ*)A->data;
507:   PetscErrorCode    ierr;
508:   const PetscScalar *b;
509:   PetscScalar       *rvalues;
510:   VecScatter        ctx = aij->Mvctx;
511:   const PetscInt    *sindices,*sstarts,*rstarts;
512:   const PetscMPIInt *sprocs,*rprocs;
513:   PetscInt          i,nsends,nrecvs;
514:   MPI_Request       *swaits,*rwaits;
515:   MPI_Comm          comm;
516:   PetscMPIInt       tag=((PetscObject)ctx)->tag,ncols=B->cmap->N,nrows=aij->B->cmap->n,nsends_mpi,nrecvs_mpi;
517:   MPIAIJ_MPIDense   *contents;
518:   Mat               workB;
519:   MPI_Datatype      *stype,*rtype;
520:   PetscInt          blda;

523:   MatCheckProduct(C,4);
524:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
525:   contents = (MPIAIJ_MPIDense*)C->product->data;
526:   VecScatterGetRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL/*bs*/);
527:   VecScatterGetRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL/*bs*/);
528:   PetscMPIIntCast(nsends,&nsends_mpi);
529:   PetscMPIIntCast(nrecvs,&nrecvs_mpi);
530:   if (Bbidx == 0) {
531:     workB = *outworkB = contents->workB;
532:   } else {
533:     workB = *outworkB = contents->workB1;
534:   }
535:   if (nrows != workB->rmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",workB->cmap->n,nrows);
536:   swaits = contents->swaits;
537:   rwaits = contents->rwaits;

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

544:   /* Post recv, use MPI derived data type to save memory */
545:   PetscObjectGetComm((PetscObject)C,&comm);
546:   rtype = contents->rtype;
547:   for (i=0; i<nrecvs; i++) {
548:     MPI_Irecv(rvalues+(rstarts[i]-rstarts[0]),ncols,rtype[i],rprocs[i],tag,comm,rwaits+i);
549:   }

551:   stype = contents->stype;
552:   for (i=0; i<nsends; i++) {
553:     MPI_Isend(b,ncols,stype[i],sprocs[i],tag,comm,swaits+i);
554:   }

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

559:   VecScatterRestoreRemote_Private(ctx,PETSC_TRUE/*send*/,&nsends,&sstarts,&sindices,&sprocs,NULL);
560:   VecScatterRestoreRemoteOrdered_Private(ctx,PETSC_FALSE/*recv*/,&nrecvs,&rstarts,NULL,&rprocs,NULL);
561:   MatDenseRestoreArrayRead(B,&b);
562:   MatDenseRestoreArray(workB,&rvalues);
563:   return(0);
564: }

566: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A,Mat B,Mat C)
567: {
568:   PetscErrorCode  ierr;
569:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ*)A->data;
570:   Mat_MPIDense    *bdense = (Mat_MPIDense*)B->data;
571:   Mat_MPIDense    *cdense = (Mat_MPIDense*)C->data;
572:   Mat             workB;
573:   MPIAIJ_MPIDense *contents;

576:   MatCheckProduct(C,3);
577:   if (!C->product->data) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_PLIB,"Product data empty");
578:   contents = (MPIAIJ_MPIDense*)C->product->data;
579:   /* diagonal block of A times all local rows of B */
580:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
581:   MatMatMult(aij->A,bdense->A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&cdense->A);
582:   if (contents->workB->cmap->n == B->cmap->N) {
583:     /* get off processor parts of B needed to complete C=A*B */
584:     MatMPIDenseScatter(A,B,0,C,&workB);

586:     /* off-diagonal block of A times nonlocal rows of B */
587:     MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A,PETSC_TRUE);
588:   } else {
589:     Mat      Bb,Cb;
590:     PetscInt BN=B->cmap->N,n=contents->workB->cmap->n,i;

592:     for (i=0; i<BN; i+=n) {
593:       MatDenseGetSubMatrix(B,i,PetscMin(i+n,BN),&Bb);
594:       MatDenseGetSubMatrix(C,i,PetscMin(i+n,BN),&Cb);

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

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

603:       MatDenseRestoreSubMatrix(B,&Bb);
604:       MatDenseRestoreSubMatrix(C,&Cb);
605:     }
606:   }
607:   return(0);
608: }

610: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A,Mat P,Mat C)
611: {
613:   Mat_MPIAIJ     *a   = (Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
614:   Mat_SeqAIJ     *ad  = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
615:   Mat_SeqAIJ     *cd  = (Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
616:   PetscInt       *adi = ad->i,*adj,*aoi=ao->i,*aoj;
617:   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
618:   Mat_SeqAIJ     *p_loc,*p_oth;
619:   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
620:   PetscScalar    *pa_loc,*pa_oth,*pa,valtmp,*ca;
621:   PetscInt       cm    = C->rmap->n,anz,pnz;
622:   Mat_APMPI      *ptap;
623:   PetscScalar    *apa_sparse;
624:   PetscInt       *api,*apj,*apJ,i,j,k,row;
625:   PetscInt       cstart = C->cmap->rstart;
626:   PetscInt       cdnz,conz,k0,k1,nextp;
627:   MPI_Comm       comm;
628:   PetscMPIInt    size;

631:   MatCheckProduct(C,3);
632:   ptap = (Mat_APMPI*)C->product->data;
633:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
634:   PetscObjectGetComm((PetscObject)C,&comm);
635:   MPI_Comm_size(comm,&size);
636:   if (!ptap->P_oth && size>1) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"AP cannot be reused. Do not call MatProductClear()");

638:   apa_sparse = ptap->apa;

640:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
641:   /*-----------------------------------------------------*/
642:   /* update numerical values of P_oth and P_loc */
643:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
644:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

646:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
647:   /*----------------------------------------------------------*/
648:   /* get data from symbolic products */
649:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
650:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
651:   if (size >1) {
652:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
653:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
654:   } else {
655:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
656:   }

658:   api = ptap->api;
659:   apj = ptap->apj;
660:   for (i=0; i<cm; i++) {
661:     apJ = apj + api[i];

663:     /* diagonal portion of A */
664:     anz = adi[i+1] - adi[i];
665:     adj = ad->j + adi[i];
666:     ada = ad->a + adi[i];
667:     for (j=0; j<anz; j++) {
668:       row = adj[j];
669:       pnz = pi_loc[row+1] - pi_loc[row];
670:       pj  = pj_loc + pi_loc[row];
671:       pa  = pa_loc + pi_loc[row];
672:       /* perform sparse axpy */
673:       valtmp = ada[j];
674:       nextp  = 0;
675:       for (k=0; nextp<pnz; k++) {
676:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
677:           apa_sparse[k] += valtmp*pa[nextp++];
678:         }
679:       }
680:       PetscLogFlops(2.0*pnz);
681:     }

683:     /* off-diagonal portion of A */
684:     anz = aoi[i+1] - aoi[i];
685:     aoj = ao->j + aoi[i];
686:     aoa = ao->a + aoi[i];
687:     for (j=0; j<anz; j++) {
688:       row = aoj[j];
689:       pnz = pi_oth[row+1] - pi_oth[row];
690:       pj  = pj_oth + pi_oth[row];
691:       pa  = pa_oth + pi_oth[row];
692:       /* perform sparse axpy */
693:       valtmp = aoa[j];
694:       nextp  = 0;
695:       for (k=0; nextp<pnz; k++) {
696:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
697:           apa_sparse[k] += valtmp*pa[nextp++];
698:         }
699:       }
700:       PetscLogFlops(2.0*pnz);
701:     }

703:     /* set values in C */
704:     cdnz = cd->i[i+1] - cd->i[i];
705:     conz = co->i[i+1] - co->i[i];

707:     /* 1st off-diagonal part of C */
708:     ca = coa + co->i[i];
709:     k  = 0;
710:     for (k0=0; k0<conz; k0++) {
711:       if (apJ[k] >= cstart) break;
712:       ca[k0]        = apa_sparse[k];
713:       apa_sparse[k] = 0.0;
714:       k++;
715:     }

717:     /* diagonal part of C */
718:     ca = cda + cd->i[i];
719:     for (k1=0; k1<cdnz; k1++) {
720:       ca[k1]        = apa_sparse[k];
721:       apa_sparse[k] = 0.0;
722:       k++;
723:     }

725:     /* 2nd off-diagonal part of C */
726:     ca = coa + co->i[i];
727:     for (; k0<conz; k0++) {
728:       ca[k0]        = apa_sparse[k];
729:       apa_sparse[k] = 0.0;
730:       k++;
731:     }
732:   }
733:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
734:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
735:   return(0);
736: }

738: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
739: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat C)
740: {
741:   PetscErrorCode     ierr;
742:   MPI_Comm           comm;
743:   PetscMPIInt        size;
744:   Mat_APMPI          *ptap;
745:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
746:   Mat_MPIAIJ         *a  = (Mat_MPIAIJ*)A->data;
747:   Mat_SeqAIJ         *ad = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
748:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
749:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
750:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
751:   PetscInt           am=A->rmap->n,pn=P->cmap->n,pm=P->rmap->n,lsize=pn+20;
752:   PetscReal          afill;
753:   MatType            mtype;

756:   MatCheckProduct(C,4);
757:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
758:   PetscObjectGetComm((PetscObject)A,&comm);
759:   MPI_Comm_size(comm,&size);

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

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

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

770:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
771:   pi_loc = p_loc->i; pj_loc = p_loc->j;
772:   if (size > 1) {
773:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
774:     pi_oth = p_oth->i; pj_oth = p_oth->j;
775:   } else {
776:     p_oth  = NULL;
777:     pi_oth = NULL; pj_oth = NULL;
778:   }

780:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
781:   /*-------------------------------------------------------------------*/
782:   PetscMalloc1(am+2,&api);
783:   ptap->api = api;
784:   api[0]    = 0;

786:   PetscLLCondensedCreate_Scalable(lsize,&lnk);

788:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
789:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space);
790:   current_space = free_space;
791:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
792:   for (i=0; i<am; i++) {
793:     /* diagonal portion of A */
794:     nzi = adi[i+1] - adi[i];
795:     for (j=0; j<nzi; j++) {
796:       row  = *adj++;
797:       pnz  = pi_loc[row+1] - pi_loc[row];
798:       Jptr = pj_loc + pi_loc[row];
799:       /* Expand list if it is not long enough */
800:       if (pnz+apnz_max > lsize) {
801:         lsize = pnz+apnz_max;
802:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
803:       }
804:       /* add non-zero cols of P into the sorted linked list lnk */
805:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
806:       apnz     = *lnk; /* The first element in the list is the number of items in the list */
807:       api[i+1] = api[i] + apnz;
808:       if (apnz > apnz_max) apnz_max = apnz;
809:     }
810:     /* off-diagonal portion of A */
811:     nzi = aoi[i+1] - aoi[i];
812:     for (j=0; j<nzi; j++) {
813:       row  = *aoj++;
814:       pnz  = pi_oth[row+1] - pi_oth[row];
815:       Jptr = pj_oth + pi_oth[row];
816:       /* Expand list if it is not long enough */
817:       if (pnz+apnz_max > lsize) {
818:         lsize = pnz + apnz_max;
819:         PetscLLCondensedExpand_Scalable(lsize, &lnk);
820:       }
821:       /* add non-zero cols of P into the sorted linked list lnk */
822:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
823:       apnz     = *lnk;  /* The first element in the list is the number of items in the list */
824:       api[i+1] = api[i] + apnz;
825:       if (apnz > apnz_max) apnz_max = apnz;
826:     }
827:     apnz     = *lnk;
828:     api[i+1] = api[i] + apnz;
829:     if (apnz > apnz_max) apnz_max = apnz;

831:     /* if free space is not available, double the total space in the list */
832:     if (current_space->local_remaining<apnz) {
833:       PetscFreeSpaceGet(PetscIntSumTruncate(apnz,current_space->total_array_size),&current_space);
834:       nspacedouble++;
835:     }

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

841:     current_space->array           += apnz;
842:     current_space->local_used      += apnz;
843:     current_space->local_remaining -= apnz;
844:   }

846:   /* Allocate space for apj, initialize apj, and */
847:   /* destroy list of free space and other temporary array(s) */
848:   PetscMalloc1(api[am]+1,&ptap->apj);
849:   apj  = ptap->apj;
850:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
851:   PetscLLCondensedDestroy_Scalable(lnk);

853:   /* create and assemble symbolic parallel matrix C */
854:   /*----------------------------------------------------*/
855:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
856:   MatSetBlockSizesFromMats(C,A,P);
857:   MatGetType(A,&mtype);
858:   MatSetType(C,mtype);
859:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
860:   MatPreallocateFinalize(dnz,onz);

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

865:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
866:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
867:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
868:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

870:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
871:   C->ops->productnumeric = MatProductNumeric_AB;

873:   /* attach the supporting struct to C for reuse */
874:   C->product->data    = ptap;
875:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

877:   /* set MatInfo */
878:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
879:   if (afill < 1.0) afill = 1.0;
880:   C->info.mallocs           = nspacedouble;
881:   C->info.fill_ratio_given  = fill;
882:   C->info.fill_ratio_needed = afill;

884: #if defined(PETSC_USE_INFO)
885:   if (api[am]) {
886:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
887:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
888:   } else {
889:     PetscInfo(C,"Empty matrix product\n");
890:   }
891: #endif
892:   return(0);
893: }

895: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
896: /* Three input arrays are merged to one output array. The size of the    */
897: /* output array is also output. Duplicate entries only show up once.     */
898: static void Merge3SortedArrays(PetscInt  size1, PetscInt *in1,
899:                                PetscInt  size2, PetscInt *in2,
900:                                PetscInt  size3, PetscInt *in3,
901:                                PetscInt *size4, PetscInt *out)
902: {
903:   int i = 0, j = 0, k = 0, l = 0;

905:   /* Traverse all three arrays */
906:   while (i<size1 && j<size2 && k<size3) {
907:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
908:       out[l++] = in1[i++];
909:     }
910:     else if (in2[j] < in1[i] && in2[j] < in3[k]) {
911:       out[l++] = in2[j++];
912:     }
913:     else if (in3[k] < in1[i] && in3[k] < in2[j]) {
914:       out[l++] = in3[k++];
915:     }
916:     else if (in1[i] == in2[j] && in1[i] < in3[k]) {
917:       out[l++] = in1[i];
918:       i++, j++;
919:     }
920:     else if (in1[i] == in3[k] && in1[i] < in2[j]) {
921:       out[l++] = in1[i];
922:       i++, k++;
923:     }
924:     else if (in3[k] == in2[j] && in2[j] < in1[i])  {
925:       out[l++] = in2[j];
926:       k++, j++;
927:     }
928:     else if (in1[i] == in2[j] && in1[i] == in3[k]) {
929:       out[l++] = in1[i];
930:       i++, j++, k++;
931:     }
932:   }

934:   /* Traverse two remaining arrays */
935:   while (i<size1 && j<size2) {
936:     if (in1[i] < in2[j]) {
937:       out[l++] = in1[i++];
938:     }
939:     else if (in1[i] > in2[j]) {
940:       out[l++] = in2[j++];
941:     }
942:     else {
943:       out[l++] = in1[i];
944:       i++, j++;
945:     }
946:   }

948:   while (i<size1 && k<size3) {
949:     if (in1[i] < in3[k]) {
950:       out[l++] = in1[i++];
951:     }
952:     else if (in1[i] > in3[k]) {
953:       out[l++] = in3[k++];
954:     }
955:     else {
956:       out[l++] = in1[i];
957:       i++, k++;
958:     }
959:   }

961:   while (k<size3 && j<size2)  {
962:     if (in3[k] < in2[j]) {
963:       out[l++] = in3[k++];
964:     }
965:     else if (in3[k] > in2[j]) {
966:       out[l++] = in2[j++];
967:     }
968:     else {
969:       out[l++] = in3[k];
970:       k++, j++;
971:     }
972:   }

974:   /* Traverse one remaining array */
975:   while (i<size1) out[l++] = in1[i++];
976:   while (j<size2) out[l++] = in2[j++];
977:   while (k<size3) out[l++] = in3[k++];

979:   *size4 = l;
980: }

982: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
983: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
984: /* matrix-matrix multiplications.  */
985: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
986: {
987:   PetscErrorCode     ierr;
988:   MPI_Comm           comm;
989:   PetscMPIInt        size;
990:   Mat_APMPI          *ptap;
991:   PetscFreeSpaceList free_space_diag=NULL, current_space=NULL;
992:   Mat_MPIAIJ         *a  =(Mat_MPIAIJ*)A->data;
993:   Mat_SeqAIJ         *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc;
994:   Mat_MPIAIJ         *p  =(Mat_MPIAIJ*)P->data;
995:   Mat_SeqAIJ         *adpd_seq, *p_off, *aopoth_seq;
996:   PetscInt           adponz, adpdnz;
997:   PetscInt           *pi_loc,*dnz,*onz;
998:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,rstart=A->rmap->rstart;
999:   PetscInt           *lnk,i, i1=0,pnz,row,*adpoi,*adpoj, *api, *adpoJ, *aopJ, *apJ,*Jptr, aopnz, nspacedouble=0,j,nzi,
1000:                      *apj,apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1001:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n, p_colstart, p_colend;
1002:   PetscBT            lnkbt;
1003:   PetscReal          afill;
1004:   PetscMPIInt        rank;
1005:   Mat                adpd, aopoth;
1006:   MatType            mtype;
1007:   const char         *prefix;

1010:   MatCheckProduct(C,4);
1011:   if (C->product->data) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Extra product struct not empty");
1012:   PetscObjectGetComm((PetscObject)A,&comm);
1013:   MPI_Comm_size(comm,&size);
1014:   MPI_Comm_rank(comm, &rank);
1015:   MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend);

1017:   /* create struct Mat_APMPI and attached it to C later */
1018:   PetscNew(&ptap);

1020:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1021:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);

1023:   /* get P_loc by taking all local rows of P */
1024:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);


1027:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
1028:   pi_loc = p_loc->i;

1030:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1031:   PetscMalloc1(am+2,&api);
1032:   PetscMalloc1(am+2,&adpoi);

1034:   adpoi[0]    = 0;
1035:   ptap->api = api;
1036:   api[0] = 0;

1038:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1039:   PetscLLCondensedCreate(pN,pN,&lnk,&lnkbt);
1040:   MatPreallocateInitialize(comm,am,pn,dnz,onz);

1042:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1043:   MatGetOptionsPrefix(A,&prefix);
1044:   MatProductCreate(a->A,p->A,NULL,&adpd);
1045:   MatGetOptionsPrefix(A,&prefix);
1046:   MatSetOptionsPrefix(adpd,prefix);
1047:   MatAppendOptionsPrefix(adpd,"inner_diag_");

1049:   MatProductSetType(adpd,MATPRODUCT_AB);
1050:   MatProductSetAlgorithm(adpd,"sorted");
1051:   MatProductSetFill(adpd,fill);
1052:   MatProductSetFromOptions(adpd);
1053:   MatProductSymbolic(adpd);

1055:   adpd_seq = (Mat_SeqAIJ*)((adpd)->data);
1056:   adpdi = adpd_seq->i; adpdj = adpd_seq->j;
1057:   p_off = (Mat_SeqAIJ*)((p->B)->data);
1058:   poff_i = p_off->i; poff_j = p_off->j;

1060:   /* j_temp stores indices of a result row before they are added to the linked list */
1061:   PetscMalloc1(pN+2,&j_temp);


1064:   /* Symbolic calc of the A_diag * p_loc_off */
1065:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1066:   PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,PetscIntSumTruncate(adi[am],PetscIntSumTruncate(aoi[am],pi_loc[pm]))),&free_space_diag);
1067:   current_space = free_space_diag;

1069:   for (i=0; i<am; i++) {
1070:     /* A_diag * P_loc_off */
1071:     nzi = adi[i+1] - adi[i];
1072:     for (j=0; j<nzi; j++) {
1073:       row  = *adj++;
1074:       pnz  = poff_i[row+1] - poff_i[row];
1075:       Jptr = poff_j + poff_i[row];
1076:       for (i1 = 0; i1 < pnz; i1++) {
1077:         j_temp[i1] = p->garray[Jptr[i1]];
1078:       }
1079:       /* add non-zero cols of P into the sorted linked list lnk */
1080:       PetscLLCondensedAddSorted(pnz,j_temp,lnk,lnkbt);
1081:     }

1083:     adponz     = lnk[0];
1084:     adpoi[i+1] = adpoi[i] + adponz;

1086:     /* if free space is not available, double the total space in the list */
1087:     if (current_space->local_remaining<adponz) {
1088:       PetscFreeSpaceGet(PetscIntSumTruncate(adponz,current_space->total_array_size),&current_space);
1089:       nspacedouble++;
1090:     }

1092:     /* Copy data into free space, then initialize lnk */
1093:     PetscLLCondensedClean(pN,adponz,current_space->array,lnk,lnkbt);

1095:     current_space->array           += adponz;
1096:     current_space->local_used      += adponz;
1097:     current_space->local_remaining -= adponz;
1098:   }

1100:   /* Symbolic calc of A_off * P_oth */
1101:   MatSetOptionsPrefix(a->B,prefix);
1102:   MatAppendOptionsPrefix(a->B,"inner_offdiag_");
1103:   MatCreate(PETSC_COMM_SELF,&aopoth);
1104:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth);
1105:   aopoth_seq = (Mat_SeqAIJ*)((aopoth)->data);
1106:   aopothi = aopoth_seq->i; aopothj = aopoth_seq->j;

1108:   /* Allocate space for apj, adpj, aopj, ... */
1109:   /* destroy lists of free space and other temporary array(s) */

1111:   PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am]+2, &ptap->apj);
1112:   PetscMalloc1(adpoi[am]+2, &adpoj);

1114:   /* Copy from linked list to j-array */
1115:   PetscFreeSpaceContiguous(&free_space_diag,adpoj);
1116:   PetscLLDestroy(lnk,lnkbt);

1118:   adpoJ = adpoj;
1119:   adpdJ = adpdj;
1120:   aopJ = aopothj;
1121:   apj  = ptap->apj;
1122:   apJ = apj; /* still empty */

1124:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1125:   /* A_diag * P_loc_diag to get A*P */
1126:   for (i = 0; i < am; i++) {
1127:     aopnz  =  aopothi[i+1] -  aopothi[i];
1128:     adponz = adpoi[i+1] - adpoi[i];
1129:     adpdnz = adpdi[i+1] - adpdi[i];

1131:     /* Correct indices from A_diag*P_diag */
1132:     for (i1 = 0; i1 < adpdnz; i1++) {
1133:       adpdJ[i1] += p_colstart;
1134:     }
1135:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1136:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1137:     MatPreallocateSet(i+rstart, apnz, apJ, dnz, onz);

1139:     aopJ += aopnz;
1140:     adpoJ += adponz;
1141:     adpdJ += adpdnz;
1142:     apJ += apnz;
1143:     api[i+1] = api[i] + apnz;
1144:   }

1146:   /* malloc apa to store dense row A[i,:]*P */
1147:   PetscCalloc1(pN+2,&ptap->apa);

1149:   /* create and assemble symbolic parallel matrix C */
1150:   MatSetSizes(C,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
1151:   MatSetBlockSizesFromMats(C,A,P);
1152:   MatGetType(A,&mtype);
1153:   MatSetType(C,mtype);
1154:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
1155:   MatPreallocateFinalize(dnz,onz);

1157:   MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api);
1158:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1159:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1160:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

1162:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1163:   C->ops->productnumeric = MatProductNumeric_AB;

1165:   /* attach the supporting struct to C for reuse */
1166:   C->product->data    = ptap;
1167:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

1169:   /* set MatInfo */
1170:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
1171:   if (afill < 1.0) afill = 1.0;
1172:   C->info.mallocs           = nspacedouble;
1173:   C->info.fill_ratio_given  = fill;
1174:   C->info.fill_ratio_needed = afill;

1176: #if defined(PETSC_USE_INFO)
1177:   if (api[am]) {
1178:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
1179:     PetscInfo1(C,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
1180:   } else {
1181:     PetscInfo(C,"Empty matrix product\n");
1182:   }
1183: #endif

1185:   MatDestroy(&aopoth);
1186:   MatDestroy(&adpd);
1187:   PetscFree(j_temp);
1188:   PetscFree(adpoj);
1189:   PetscFree(adpoi);
1190:   return(0);
1191: }

1193: /*-------------------------------------------------------------------------*/
1194: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1195: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
1196: {
1198:   Mat_APMPI      *ptap;
1199:   Mat            Pt;

1202:   MatCheckProduct(C,3);
1203:   ptap = (Mat_APMPI*)C->product->data;
1204:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1205:   if (!ptap->Pt) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");

1207:   Pt   = ptap->Pt;
1208:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
1209:   MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt,A,C);
1210:   return(0);
1211: }

1213: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1214: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat C)
1215: {
1216:   PetscErrorCode      ierr;
1217:   Mat_APMPI           *ptap;
1218:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data;
1219:   MPI_Comm            comm;
1220:   PetscMPIInt         size,rank;
1221:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1222:   PetscInt            pn=P->cmap->n,aN=A->cmap->N,an=A->cmap->n;
1223:   PetscInt            *lnk,i,k,nsend,rstart;
1224:   PetscBT             lnkbt;
1225:   PetscMPIInt         tagi,tagj,*len_si,*len_s,*len_ri,icompleted=0,nrecv;
1226:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1227:   PetscInt            len,proc,*dnz,*onz,*owners,nzi;
1228:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1229:   MPI_Request         *swaits,*rwaits;
1230:   MPI_Status          *sstatus,rstatus;
1231:   PetscLayout         rowmap;
1232:   PetscInt            *owners_co,*coi,*coj;    /* i and j array of (p->B)^T*A*P - used in the communication */
1233:   PetscMPIInt         *len_r,*id_r;    /* array of length of comm->size, store send/recv matrix values */
1234:   PetscInt            *Jptr,*prmap=p->garray,con,j,Crmax;
1235:   Mat_SeqAIJ          *a_loc,*c_loc,*c_oth;
1236:   PetscTable          ta;
1237:   MatType             mtype;
1238:   const char          *prefix;

1241:   PetscObjectGetComm((PetscObject)A,&comm);
1242:   MPI_Comm_size(comm,&size);
1243:   MPI_Comm_rank(comm,&rank);

1245:   /* create symbolic parallel matrix C */
1246:   MatGetType(A,&mtype);
1247:   MatSetType(C,mtype);

1249:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1251:   /* create struct Mat_APMPI and attached it to C later */
1252:   PetscNew(&ptap);
1253:   ptap->reuse = MAT_INITIAL_MATRIX;

1255:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1256:   /* --------------------------------- */
1257:   MatTranspose_SeqAIJ(p->A,MAT_INITIAL_MATRIX,&ptap->Rd);
1258:   MatTranspose_SeqAIJ(p->B,MAT_INITIAL_MATRIX,&ptap->Ro);

1260:   /* (1) compute symbolic A_loc */
1261:   /* ---------------------------*/
1262:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&ptap->A_loc);

1264:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1265:   /* ------------------------------------ */
1266:   MatGetOptionsPrefix(A,&prefix);
1267:   MatSetOptionsPrefix(ptap->Ro,prefix);
1268:   MatAppendOptionsPrefix(ptap->Ro,"inner_offdiag_");
1269:   MatCreate(PETSC_COMM_SELF,&ptap->C_oth);
1270:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro,ptap->A_loc,fill,ptap->C_oth);

1272:   /* (3) send coj of C_oth to other processors  */
1273:   /* ------------------------------------------ */
1274:   /* determine row ownership */
1275:   PetscLayoutCreate(comm,&rowmap);
1276:   rowmap->n  = pn;
1277:   rowmap->bs = 1;
1278:   PetscLayoutSetUp(rowmap);
1279:   owners = rowmap->range;

1281:   /* determine the number of messages to send, their lengths */
1282:   PetscMalloc4(size,&len_s,size,&len_si,size,&sstatus,size+2,&owners_co);
1283:   PetscArrayzero(len_s,size);
1284:   PetscArrayzero(len_si,size);

1286:   c_oth = (Mat_SeqAIJ*)ptap->C_oth->data;
1287:   coi   = c_oth->i; coj = c_oth->j;
1288:   con   = ptap->C_oth->rmap->n;
1289:   proc  = 0;
1290:   for (i=0; i<con; i++) {
1291:     while (prmap[i] >= owners[proc+1]) proc++;
1292:     len_si[proc]++;               /* num of rows in Co(=Pt*A) to be sent to [proc] */
1293:     len_s[proc] += coi[i+1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1294:   }

1296:   len          = 0; /* max length of buf_si[], see (4) */
1297:   owners_co[0] = 0;
1298:   nsend        = 0;
1299:   for (proc=0; proc<size; proc++) {
1300:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1301:     if (len_s[proc]) {
1302:       nsend++;
1303:       len_si[proc] = 2*(len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1304:       len         += len_si[proc];
1305:     }
1306:   }

1308:   /* determine the number and length of messages to receive for coi and coj  */
1309:   PetscGatherNumberOfMessages(comm,NULL,len_s,&nrecv);
1310:   PetscGatherMessageLengths2(comm,nsend,nrecv,len_s,len_si,&id_r,&len_r,&len_ri);

1312:   /* post the Irecv and Isend of coj */
1313:   PetscCommGetNewTag(comm,&tagj);
1314:   PetscPostIrecvInt(comm,tagj,nrecv,id_r,len_r,&buf_rj,&rwaits);
1315:   PetscMalloc1(nsend+1,&swaits);
1316:   for (proc=0, k=0; proc<size; proc++) {
1317:     if (!len_s[proc]) continue;
1318:     i    = owners_co[proc];
1319:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1320:     k++;
1321:   }

1323:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1324:   /* ---------------------------------------- */
1325:   MatSetOptionsPrefix(ptap->Rd,prefix);
1326:   MatAppendOptionsPrefix(ptap->Rd,"inner_diag_");
1327:   MatCreate(PETSC_COMM_SELF,&ptap->C_loc);
1328:   MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd,ptap->A_loc,fill,ptap->C_loc);
1329:   c_loc = (Mat_SeqAIJ*)ptap->C_loc->data;

1331:   /* receives coj are complete */
1332:   for (i=0; i<nrecv; i++) {
1333:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1334:   }
1335:   PetscFree(rwaits);
1336:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

1338:   /* add received column indices into ta to update Crmax */
1339:   a_loc = (Mat_SeqAIJ*)(ptap->A_loc)->data;

1341:   /* create and initialize a linked list */
1342:   PetscTableCreate(an,aN,&ta); /* for compute Crmax */
1343:   MatRowMergeMax_SeqAIJ(a_loc,ptap->A_loc->rmap->N,ta);

1345:   for (k=0; k<nrecv; k++) {/* k-th received message */
1346:     Jptr = buf_rj[k];
1347:     for (j=0; j<len_r[k]; j++) {
1348:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1349:     }
1350:   }
1351:   PetscTableGetCount(ta,&Crmax);
1352:   PetscTableDestroy(&ta);

1354:   /* (4) send and recv coi */
1355:   /*-----------------------*/
1356:   PetscCommGetNewTag(comm,&tagi);
1357:   PetscPostIrecvInt(comm,tagi,nrecv,id_r,len_ri,&buf_ri,&rwaits);
1358:   PetscMalloc1(len+1,&buf_s);
1359:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1360:   for (proc=0,k=0; proc<size; proc++) {
1361:     if (!len_s[proc]) continue;
1362:     /* form outgoing message for i-structure:
1363:          buf_si[0]:                 nrows to be sent
1364:                [1:nrows]:           row index (global)
1365:                [nrows+1:2*nrows+1]: i-structure index
1366:     */
1367:     /*-------------------------------------------*/
1368:     nrows       = len_si[proc]/2 - 1; /* num of rows in Co to be sent to [proc] */
1369:     buf_si_i    = buf_si + nrows+1;
1370:     buf_si[0]   = nrows;
1371:     buf_si_i[0] = 0;
1372:     nrows       = 0;
1373:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1374:       nzi = coi[i+1] - coi[i];
1375:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1376:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1377:       nrows++;
1378:     }
1379:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1380:     k++;
1381:     buf_si += len_si[proc];
1382:   }
1383:   for (i=0; i<nrecv; i++) {
1384:     MPI_Waitany(nrecv,rwaits,&icompleted,&rstatus);
1385:   }
1386:   PetscFree(rwaits);
1387:   if (nsend) {MPI_Waitall(nsend,swaits,sstatus);}

1389:   PetscFree4(len_s,len_si,sstatus,owners_co);
1390:   PetscFree(len_ri);
1391:   PetscFree(swaits);
1392:   PetscFree(buf_s);

1394:   /* (5) compute the local portion of C      */
1395:   /* ------------------------------------------ */
1396:   /* set initial free space to be Crmax, sufficient for holding nozeros in each row of C */
1397:   PetscFreeSpaceGet(Crmax,&free_space);
1398:   current_space = free_space;

1400:   PetscMalloc3(nrecv,&buf_ri_k,nrecv,&nextrow,nrecv,&nextci);
1401:   for (k=0; k<nrecv; k++) {
1402:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1403:     nrows       = *buf_ri_k[k];
1404:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1405:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1406:   }

1408:   MatPreallocateInitialize(comm,pn,an,dnz,onz);
1409:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);
1410:   for (i=0; i<pn; i++) {
1411:     /* add C_loc into C */
1412:     nzi  = c_loc->i[i+1] - c_loc->i[i];
1413:     Jptr = c_loc->j + c_loc->i[i];
1414:     PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);

1416:     /* add received col data into lnk */
1417:     for (k=0; k<nrecv; k++) { /* k-th received message */
1418:       if (i == *nextrow[k]) { /* i-th row */
1419:         nzi  = *(nextci[k]+1) - *nextci[k];
1420:         Jptr = buf_rj[k] + *nextci[k];
1421:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
1422:         nextrow[k]++; nextci[k]++;
1423:       }
1424:     }
1425:     nzi = lnk[0];

1427:     /* copy data into free space, then initialize lnk */
1428:     PetscLLCondensedClean(aN,nzi,current_space->array,lnk,lnkbt);
1429:     MatPreallocateSet(i+owners[rank],nzi,current_space->array,dnz,onz);
1430:   }
1431:   PetscFree3(buf_ri_k,nextrow,nextci);
1432:   PetscLLDestroy(lnk,lnkbt);
1433:   PetscFreeSpaceDestroy(free_space);

1435:   /* local sizes and preallocation */
1436:   MatSetSizes(C,pn,an,PETSC_DETERMINE,PETSC_DETERMINE);
1437:   if (P->cmap->bs > 0) {PetscLayoutSetBlockSize(C->rmap,P->cmap->bs);}
1438:   if (A->cmap->bs > 0) {PetscLayoutSetBlockSize(C->cmap,A->cmap->bs);}
1439:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
1440:   MatPreallocateFinalize(dnz,onz);

1442:   /* add C_loc and C_oth to C */
1443:   MatGetOwnershipRange(C,&rstart,NULL);
1444:   for (i=0; i<pn; i++) {
1445:     const PetscInt ncols = c_loc->i[i+1] - c_loc->i[i];
1446:     const PetscInt *cols = c_loc->j + c_loc->i[i];
1447:     const PetscInt row = rstart + i;
1448:     MatSetValues(C,1,&row,ncols,cols,NULL,INSERT_VALUES);
1449:   }
1450:   for (i=0; i<con; i++) {
1451:     const PetscInt ncols = c_oth->i[i+1] - c_oth->i[i];
1452:     const PetscInt *cols = c_oth->j + c_oth->i[i];
1453:     const PetscInt row = prmap[i];
1454:     MatSetValues(C,1,&row,ncols,cols,NULL,INSERT_VALUES);
1455:   }
1456:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1457:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1458:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

1460:   /* members in merge */
1461:   PetscFree(id_r);
1462:   PetscFree(len_r);
1463:   PetscFree(buf_ri[0]);
1464:   PetscFree(buf_ri);
1465:   PetscFree(buf_rj[0]);
1466:   PetscFree(buf_rj);
1467:   PetscLayoutDestroy(&rowmap);

1469:   /* attach the supporting struct to C for reuse */
1470:   C->product->data    = ptap;
1471:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1472:   return(0);
1473: }

1475: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
1476: {
1477:   PetscErrorCode    ierr;
1478:   Mat_MPIAIJ        *p=(Mat_MPIAIJ*)P->data;
1479:   Mat_SeqAIJ        *c_seq;
1480:   Mat_APMPI         *ptap;
1481:   Mat               A_loc,C_loc,C_oth;
1482:   PetscInt          i,rstart,rend,cm,ncols,row;
1483:   const PetscInt    *cols;
1484:   const PetscScalar *vals;

1487:   MatCheckProduct(C,3);
1488:   ptap = (Mat_APMPI*)C->product->data;
1489:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1490:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1491:   MatZeroEntries(C);

1493:   if (ptap->reuse == MAT_REUSE_MATRIX) {
1494:     /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1495:     /* 1) get R = Pd^T, Ro = Po^T */
1496:     /*----------------------------*/
1497:     MatTranspose_SeqAIJ(p->A,MAT_REUSE_MATRIX,&ptap->Rd);
1498:     MatTranspose_SeqAIJ(p->B,MAT_REUSE_MATRIX,&ptap->Ro);

1500:     /* 2) compute numeric A_loc */
1501:     /*--------------------------*/
1502:     MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&ptap->A_loc);
1503:   }

1505:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1506:   A_loc = ptap->A_loc;
1507:   ((ptap->C_loc)->ops->matmultnumeric)(ptap->Rd,A_loc,ptap->C_loc);
1508:   ((ptap->C_oth)->ops->matmultnumeric)(ptap->Ro,A_loc,ptap->C_oth);
1509:   C_loc = ptap->C_loc;
1510:   C_oth = ptap->C_oth;

1512:   /* add C_loc and C_oth to C */
1513:   MatGetOwnershipRange(C,&rstart,&rend);

1515:   /* C_loc -> C */
1516:   cm    = C_loc->rmap->N;
1517:   c_seq = (Mat_SeqAIJ*)C_loc->data;
1518:   cols = c_seq->j;
1519:   vals = c_seq->a;
1520:   for (i=0; i<cm; i++) {
1521:     ncols = c_seq->i[i+1] - c_seq->i[i];
1522:     row = rstart + i;
1523:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1524:     cols += ncols; vals += ncols;
1525:   }

1527:   /* Co -> C, off-processor part */
1528:   cm    = C_oth->rmap->N;
1529:   c_seq = (Mat_SeqAIJ*)C_oth->data;
1530:   cols  = c_seq->j;
1531:   vals  = c_seq->a;
1532:   for (i=0; i<cm; i++) {
1533:     ncols = c_seq->i[i+1] - c_seq->i[i];
1534:     row = p->garray[i];
1535:     MatSetValues(C,1,&row,ncols,cols,vals,ADD_VALUES);
1536:     cols += ncols; vals += ncols;
1537:   }
1538:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1539:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
1540:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);

1542:   ptap->reuse = MAT_REUSE_MATRIX;
1543:   return(0);
1544: }

1546: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1547: {
1548:   PetscErrorCode      ierr;
1549:   Mat_Merge_SeqsToMPI *merge;
1550:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data;
1551:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1552:   Mat_APMPI           *ptap;
1553:   PetscInt            *adj;
1554:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1555:   MatScalar           *ada,*ca,valtmp;
1556:   PetscInt            am=A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1557:   MPI_Comm            comm;
1558:   PetscMPIInt         size,rank,taga,*len_s;
1559:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1560:   PetscInt            **buf_ri,**buf_rj;
1561:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1562:   MPI_Request         *s_waits,*r_waits;
1563:   MPI_Status          *status;
1564:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1565:   PetscInt            *ai,*aj,*coi,*coj,*poJ,*pdJ;
1566:   Mat                 A_loc;
1567:   Mat_SeqAIJ          *a_loc;

1570:   MatCheckProduct(C,3);
1571:   ptap = (Mat_APMPI*)C->product->data;
1572:   if (!ptap) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtAP cannot be computed. Missing data");
1573:   if (!ptap->A_loc) SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_ARG_WRONGSTATE,"PtA cannot be reused. Do not call MatProductClear()");
1574:   PetscObjectGetComm((PetscObject)C,&comm);
1575:   MPI_Comm_size(comm,&size);
1576:   MPI_Comm_rank(comm,&rank);

1578:   merge = ptap->merge;

1580:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1581:   /*------------------------------------------*/
1582:   /* get data from symbolic products */
1583:   coi    = merge->coi; coj = merge->coj;
1584:   PetscCalloc1(coi[pon]+1,&coa);
1585:   bi     = merge->bi; bj = merge->bj;
1586:   owners = merge->rowmap->range;
1587:   PetscCalloc1(bi[cm]+1,&ba);

1589:   /* get A_loc by taking all local rows of A */
1590:   A_loc = ptap->A_loc;
1591:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
1592:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1593:   ai    = a_loc->i;
1594:   aj    = a_loc->j;

1596:   for (i=0; i<am; i++) {
1597:     anz = ai[i+1] - ai[i];
1598:     adj = aj + ai[i];
1599:     ada = a_loc->a + ai[i];

1601:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1602:     /*-------------------------------------------------------------*/
1603:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1604:     pnz = po->i[i+1] - po->i[i];
1605:     poJ = po->j + po->i[i];
1606:     pA  = po->a + po->i[i];
1607:     for (j=0; j<pnz; j++) {
1608:       row = poJ[j];
1609:       cj  = coj + coi[row];
1610:       ca  = coa + coi[row];
1611:       /* perform sparse axpy */
1612:       nexta  = 0;
1613:       valtmp = pA[j];
1614:       for (k=0; nexta<anz; k++) {
1615:         if (cj[k] == adj[nexta]) {
1616:           ca[k] += valtmp*ada[nexta];
1617:           nexta++;
1618:         }
1619:       }
1620:       PetscLogFlops(2.0*anz);
1621:     }

1623:     /* put the value into Cd (diagonal part) */
1624:     pnz = pd->i[i+1] - pd->i[i];
1625:     pdJ = pd->j + pd->i[i];
1626:     pA  = pd->a + pd->i[i];
1627:     for (j=0; j<pnz; j++) {
1628:       row = pdJ[j];
1629:       cj  = bj + bi[row];
1630:       ca  = ba + bi[row];
1631:       /* perform sparse axpy */
1632:       nexta  = 0;
1633:       valtmp = pA[j];
1634:       for (k=0; nexta<anz; k++) {
1635:         if (cj[k] == adj[nexta]) {
1636:           ca[k] += valtmp*ada[nexta];
1637:           nexta++;
1638:         }
1639:       }
1640:       PetscLogFlops(2.0*anz);
1641:     }
1642:   }

1644:   /* 3) send and recv matrix values coa */
1645:   /*------------------------------------*/
1646:   buf_ri = merge->buf_ri;
1647:   buf_rj = merge->buf_rj;
1648:   len_s  = merge->len_s;
1649:   PetscCommGetNewTag(comm,&taga);
1650:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

1652:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
1653:   for (proc=0,k=0; proc<size; proc++) {
1654:     if (!len_s[proc]) continue;
1655:     i    = merge->owners_co[proc];
1656:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
1657:     k++;
1658:   }
1659:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
1660:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

1662:   PetscFree2(s_waits,status);
1663:   PetscFree(r_waits);
1664:   PetscFree(coa);

1666:   /* 4) insert local Cseq and received values into Cmpi */
1667:   /*----------------------------------------------------*/
1668:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1669:   for (k=0; k<merge->nrecv; k++) {
1670:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1671:     nrows       = *(buf_ri_k[k]);
1672:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1673:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1674:   }

1676:   for (i=0; i<cm; i++) {
1677:     row  = owners[rank] + i; /* global row index of C_seq */
1678:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1679:     ba_i = ba + bi[i];
1680:     bnz  = bi[i+1] - bi[i];
1681:     /* add received vals into ba */
1682:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1683:       /* i-th row */
1684:       if (i == *nextrow[k]) {
1685:         cnz    = *(nextci[k]+1) - *nextci[k];
1686:         cj     = buf_rj[k] + *(nextci[k]);
1687:         ca     = abuf_r[k] + *(nextci[k]);
1688:         nextcj = 0;
1689:         for (j=0; nextcj<cnz; j++) {
1690:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1691:             ba_i[j] += ca[nextcj++];
1692:           }
1693:         }
1694:         nextrow[k]++; nextci[k]++;
1695:         PetscLogFlops(2.0*cnz);
1696:       }
1697:     }
1698:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
1699:   }
1700:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1701:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

1703:   PetscFree(ba);
1704:   PetscFree(abuf_r[0]);
1705:   PetscFree(abuf_r);
1706:   PetscFree3(buf_ri_k,nextrow,nextci);
1707:   return(0);
1708: }

1710: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat C)
1711: {
1712:   PetscErrorCode      ierr;
1713:   Mat                 A_loc,POt,PDt;
1714:   Mat_APMPI           *ptap;
1715:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1716:   Mat_MPIAIJ          *p=(Mat_MPIAIJ*)P->data,*a=(Mat_MPIAIJ*)A->data;
1717:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1718:   PetscInt            nnz;
1719:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1720:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1721:   MPI_Comm            comm;
1722:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1723:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1724:   PetscInt            len,proc,*dnz,*onz,*owners;
1725:   PetscInt            nzi,*bi,*bj;
1726:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1727:   MPI_Request         *swaits,*rwaits;
1728:   MPI_Status          *sstatus,rstatus;
1729:   Mat_Merge_SeqsToMPI *merge;
1730:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1731:   PetscReal           afill  =1.0,afill_tmp;
1732:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Armax;
1733:   Mat_SeqAIJ          *a_loc,*pdt,*pot;
1734:   PetscTable          ta;
1735:   MatType             mtype;

1738:   PetscObjectGetComm((PetscObject)A,&comm);
1739:   /* check if matrix local sizes are compatible */
1740:   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);

1742:   MPI_Comm_size(comm,&size);
1743:   MPI_Comm_rank(comm,&rank);

1745:   /* create struct Mat_APMPI and attached it to C later */
1746:   PetscNew(&ptap);

1748:   /* get A_loc by taking all local rows of A */
1749:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

1751:   ptap->A_loc = A_loc;
1752:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1753:   ai          = a_loc->i;
1754:   aj          = a_loc->j;

1756:   /* determine symbolic Co=(p->B)^T*A - send to others */
1757:   /*----------------------------------------------------*/
1758:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
1759:   pdt  = (Mat_SeqAIJ*)PDt->data;
1760:   pdti = pdt->i; pdtj = pdt->j;

1762:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
1763:   pot  = (Mat_SeqAIJ*)POt->data;
1764:   poti = pot->i; potj = pot->j;

1766:   /* then, compute symbolic Co = (p->B)^T*A */
1767:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1768:                          >= (num of nonzero rows of C_seq) - pn */
1769:   PetscMalloc1(pon+1,&coi);
1770:   coi[0] = 0;

1772:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1773:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(poti[pon],ai[am]));
1774:   PetscFreeSpaceGet(nnz,&free_space);
1775:   current_space = free_space;

1777:   /* create and initialize a linked list */
1778:   PetscTableCreate(A->cmap->n + a->B->cmap->N,aN,&ta);
1779:   MatRowMergeMax_SeqAIJ(a_loc,am,ta);
1780:   PetscTableGetCount(ta,&Armax);

1782:   PetscLLCondensedCreate_Scalable(Armax,&lnk);

1784:   for (i=0; i<pon; i++) {
1785:     pnz = poti[i+1] - poti[i];
1786:     ptJ = potj + poti[i];
1787:     for (j=0; j<pnz; j++) {
1788:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1789:       anz  = ai[row+1] - ai[row];
1790:       Jptr = aj + ai[row];
1791:       /* add non-zero cols of AP into the sorted linked list lnk */
1792:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1793:     }
1794:     nnz = lnk[0];

1796:     /* If free space is not available, double the total space in the list */
1797:     if (current_space->local_remaining<nnz) {
1798:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
1799:       nspacedouble++;
1800:     }

1802:     /* Copy data into free space, and zero out denserows */
1803:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

1805:     current_space->array           += nnz;
1806:     current_space->local_used      += nnz;
1807:     current_space->local_remaining -= nnz;

1809:     coi[i+1] = coi[i] + nnz;
1810:   }

1812:   PetscMalloc1(coi[pon]+1,&coj);
1813:   PetscFreeSpaceContiguous(&free_space,coj);
1814:   PetscLLCondensedDestroy_Scalable(lnk); /* must destroy to get a new one for C */

1816:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1817:   if (afill_tmp > afill) afill = afill_tmp;

1819:   /* send j-array (coj) of Co to other processors */
1820:   /*----------------------------------------------*/
1821:   /* determine row ownership */
1822:   PetscNew(&merge);
1823:   PetscLayoutCreate(comm,&merge->rowmap);

1825:   merge->rowmap->n  = pn;
1826:   merge->rowmap->bs = 1;

1828:   PetscLayoutSetUp(merge->rowmap);
1829:   owners = merge->rowmap->range;

1831:   /* determine the number of messages to send, their lengths */
1832:   PetscCalloc1(size,&len_si);
1833:   PetscCalloc1(size,&merge->len_s);

1835:   len_s        = merge->len_s;
1836:   merge->nsend = 0;

1838:   PetscMalloc1(size+2,&owners_co);

1840:   proc = 0;
1841:   for (i=0; i<pon; i++) {
1842:     while (prmap[i] >= owners[proc+1]) proc++;
1843:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1844:     len_s[proc] += coi[i+1] - coi[i];
1845:   }

1847:   len          = 0; /* max length of buf_si[] */
1848:   owners_co[0] = 0;
1849:   for (proc=0; proc<size; proc++) {
1850:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1851:     if (len_si[proc]) {
1852:       merge->nsend++;
1853:       len_si[proc] = 2*(len_si[proc] + 1);
1854:       len         += len_si[proc];
1855:     }
1856:   }

1858:   /* determine the number and length of messages to receive for coi and coj  */
1859:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
1860:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

1862:   /* post the Irecv and Isend of coj */
1863:   PetscCommGetNewTag(comm,&tagj);
1864:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
1865:   PetscMalloc1(merge->nsend+1,&swaits);
1866:   for (proc=0, k=0; proc<size; proc++) {
1867:     if (!len_s[proc]) continue;
1868:     i    = owners_co[proc];
1869:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1870:     k++;
1871:   }

1873:   /* receives and sends of coj are complete */
1874:   PetscMalloc1(size,&sstatus);
1875:   for (i=0; i<merge->nrecv; i++) {
1876:     PetscMPIInt icompleted;
1877:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1878:   }
1879:   PetscFree(rwaits);
1880:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

1882:   /* add received column indices into table to update Armax */
1883:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1884:   for (k=0; k<merge->nrecv; k++) {/* k-th received message */
1885:     Jptr = buf_rj[k];
1886:     for (j=0; j<merge->len_r[k]; j++) {
1887:       PetscTableAdd(ta,*(Jptr+j)+1,1,INSERT_VALUES);
1888:     }
1889:   }
1890:   PetscTableGetCount(ta,&Armax);
1891:   /* 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); */

1893:   /* send and recv coi */
1894:   /*-------------------*/
1895:   PetscCommGetNewTag(comm,&tagi);
1896:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
1897:   PetscMalloc1(len+1,&buf_s);
1898:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1899:   for (proc=0,k=0; proc<size; proc++) {
1900:     if (!len_s[proc]) continue;
1901:     /* form outgoing message for i-structure:
1902:          buf_si[0]:                 nrows to be sent
1903:                [1:nrows]:           row index (global)
1904:                [nrows+1:2*nrows+1]: i-structure index
1905:     */
1906:     /*-------------------------------------------*/
1907:     nrows       = len_si[proc]/2 - 1;
1908:     buf_si_i    = buf_si + nrows+1;
1909:     buf_si[0]   = nrows;
1910:     buf_si_i[0] = 0;
1911:     nrows       = 0;
1912:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1913:       nzi               = coi[i+1] - coi[i];
1914:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1915:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1916:       nrows++;
1917:     }
1918:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1919:     k++;
1920:     buf_si += len_si[proc];
1921:   }
1922:   i = merge->nrecv;
1923:   while (i--) {
1924:     PetscMPIInt icompleted;
1925:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1926:   }
1927:   PetscFree(rwaits);
1928:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1929:   PetscFree(len_si);
1930:   PetscFree(len_ri);
1931:   PetscFree(swaits);
1932:   PetscFree(sstatus);
1933:   PetscFree(buf_s);

1935:   /* compute the local portion of C (mpi mat) */
1936:   /*------------------------------------------*/
1937:   /* allocate bi array and free space for accumulating nonzero column info */
1938:   PetscMalloc1(pn+1,&bi);
1939:   bi[0] = 0;

1941:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1942:   nnz           = PetscRealIntMultTruncate(fill,PetscIntSumTruncate(pdti[pn],PetscIntSumTruncate(poti[pon],ai[am])));
1943:   PetscFreeSpaceGet(nnz,&free_space);
1944:   current_space = free_space;

1946:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1947:   for (k=0; k<merge->nrecv; k++) {
1948:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1949:     nrows       = *buf_ri_k[k];
1950:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1951:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1952:   }

1954:   PetscLLCondensedCreate_Scalable(Armax,&lnk);
1955:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
1956:   rmax = 0;
1957:   for (i=0; i<pn; i++) {
1958:     /* add pdt[i,:]*AP into lnk */
1959:     pnz = pdti[i+1] - pdti[i];
1960:     ptJ = pdtj + pdti[i];
1961:     for (j=0; j<pnz; j++) {
1962:       row  = ptJ[j];  /* row of AP == col of Pt */
1963:       anz  = ai[row+1] - ai[row];
1964:       Jptr = aj + ai[row];
1965:       /* add non-zero cols of AP into the sorted linked list lnk */
1966:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1967:     }

1969:     /* add received col data into lnk */
1970:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1971:       if (i == *nextrow[k]) { /* i-th row */
1972:         nzi  = *(nextci[k]+1) - *nextci[k];
1973:         Jptr = buf_rj[k] + *nextci[k];
1974:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
1975:         nextrow[k]++; nextci[k]++;
1976:       }
1977:     }
1978:     nnz = lnk[0];

1980:     /* if free space is not available, make more free space */
1981:     if (current_space->local_remaining<nnz) {
1982:       PetscFreeSpaceGet(PetscIntSumTruncate(nnz,current_space->total_array_size),&current_space);
1983:       nspacedouble++;
1984:     }
1985:     /* copy data into free space, then initialize lnk */
1986:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
1987:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

1989:     current_space->array           += nnz;
1990:     current_space->local_used      += nnz;
1991:     current_space->local_remaining -= nnz;

1993:     bi[i+1] = bi[i] + nnz;
1994:     if (nnz > rmax) rmax = nnz;
1995:   }
1996:   PetscFree3(buf_ri_k,nextrow,nextci);

1998:   PetscMalloc1(bi[pn]+1,&bj);
1999:   PetscFreeSpaceContiguous(&free_space,bj);
2000:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
2001:   if (afill_tmp > afill) afill = afill_tmp;
2002:   PetscLLCondensedDestroy_Scalable(lnk);
2003:   PetscTableDestroy(&ta);

2005:   MatDestroy(&POt);
2006:   MatDestroy(&PDt);

2008:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2009:   /*-------------------------------------------------------------------------------*/
2010:   MatSetSizes(C,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
2011:   MatSetBlockSizes(C,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
2012:   MatGetType(A,&mtype);
2013:   MatSetType(C,mtype);
2014:   MatMPIAIJSetPreallocation(C,0,dnz,0,onz);
2015:   MatPreallocateFinalize(dnz,onz);
2016:   MatSetBlockSize(C,1);
2017:   MatSetOption(C,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE);
2018:   for (i=0; i<pn; i++) {
2019:     row  = i + rstart;
2020:     nnz  = bi[i+1] - bi[i];
2021:     Jptr = bj + bi[i];
2022:     MatSetValues(C,1,&row,nnz,Jptr,NULL,INSERT_VALUES);
2023:   }
2024:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
2025:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
2026:   MatSetOption(C,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);
2027:   merge->bi        = bi;
2028:   merge->bj        = bj;
2029:   merge->coi       = coi;
2030:   merge->coj       = coj;
2031:   merge->buf_ri    = buf_ri;
2032:   merge->buf_rj    = buf_rj;
2033:   merge->owners_co = owners_co;

2035:   /* attach the supporting struct to C for reuse */
2036:   C->product->data    = ptap;
2037:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2038:   ptap->merge         = merge;

2040:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2042: #if defined(PETSC_USE_INFO)
2043:   if (bi[pn] != 0) {
2044:     PetscInfo3(C,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
2045:     PetscInfo1(C,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
2046:   } else {
2047:     PetscInfo(C,"Empty matrix product\n");
2048:   }
2049: #endif
2050:   return(0);
2051: }

2053: /* ---------------------------------------------------------------- */
2054: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2055: {
2057:   Mat_Product    *product = C->product;
2058:   Mat            A=product->A,B=product->B;
2059:   PetscReal      fill=product->fill;
2060:   PetscBool      flg;

2063:   /* scalable */
2064:   PetscStrcmp(product->alg,"scalable",&flg);
2065:   if (flg) {
2066:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A,B,fill,C);
2067:     goto next;
2068:   }

2070:   /* nonscalable */
2071:   PetscStrcmp(product->alg,"nonscalable",&flg);
2072:   if (flg) {
2073:     MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A,B,fill,C);
2074:     goto next;
2075:   }

2077:   /* matmatmult */
2078:   PetscStrcmp(product->alg,"at*b",&flg);
2079:   if (flg) {
2080:     Mat       At;
2081:     Mat_APMPI *ptap;

2083:     MatTranspose(A,MAT_INITIAL_MATRIX,&At);
2084:     MatMatMultSymbolic_MPIAIJ_MPIAIJ(At,B,fill,C);
2085:     ptap = (Mat_APMPI*)C->product->data;
2086:     if (ptap) {
2087:       ptap->Pt = At;
2088:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2089:     }
2090:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2091:     goto next;
2092:   }

2094:   SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"MatProduct type is not supported");

2096: next:
2097:   C->ops->productnumeric = MatProductNumeric_AtB;
2098:   return(0);
2099: }

2101: /* ---------------------------------------------------------------- */
2102: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2103: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2104: {
2106:   Mat_Product    *product = C->product;
2107:   Mat            A=product->A,B=product->B;
2108: #if defined(PETSC_HAVE_HYPRE)
2109:   const char     *algTypes[4] = {"scalable","nonscalable","seqmpi","hypre"};
2110:   PetscInt       nalg = 4;
2111: #else
2112:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2113:   PetscInt       nalg = 3;
2114: #endif
2115:   PetscInt       alg = 1; /* set nonscalable algorithm as default */
2116:   PetscBool      flg;
2117:   MPI_Comm       comm;

2120:   /* Check matrix local sizes */
2121:   PetscObjectGetComm((PetscObject)C,&comm);
2122:   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);

2124:   /* Set "nonscalable" as default algorithm */
2125:   PetscStrcmp(C->product->alg,"default",&flg);
2126:   if (flg) {
2127:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

2129:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2130:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2131:       MatInfo     Ainfo,Binfo;
2132:       PetscInt    nz_local;
2133:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

2135:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
2136:       MatGetInfo(B,MAT_LOCAL,&Binfo);
2137:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2139:       if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2140:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

2142:       if (alg_scalable) {
2143:         alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2144:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2145:         PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
2146:       }
2147:     }
2148:   }

2150:   /* Get runtime option */
2151:   if (product->api_user) {
2152:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMult","Mat");
2153:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2154:     PetscOptionsEnd();
2155:   } else {
2156:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AB","Mat");
2157:     PetscOptionsEList("-matproduct_ab_via","Algorithmic approach","MatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2158:     PetscOptionsEnd();
2159:   }
2160:   if (flg) {
2161:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2162:   }

2164:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2165:   return(0);
2166: }

2168: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2169: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2170: {
2172:   Mat_Product    *product = C->product;
2173:   Mat            A=product->A,B=product->B;
2174:   const char     *algTypes[3] = {"scalable","nonscalable","at*b"};
2175:   PetscInt       nalg = 3;
2176:   PetscInt       alg = 1; /* set default algorithm  */
2177:   PetscBool      flg;
2178:   MPI_Comm       comm;

2181:   /* Check matrix local sizes */
2182:   PetscObjectGetComm((PetscObject)C,&comm);
2183:   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);

2185:   /* Set default algorithm */
2186:   PetscStrcmp(C->product->alg,"default",&flg);
2187:   if (flg) {
2188:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2189:   }

2191:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2192:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2193:     MatInfo     Ainfo,Binfo;
2194:     PetscInt    nz_local;
2195:     PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

2197:     MatGetInfo(A,MAT_LOCAL,&Ainfo);
2198:     MatGetInfo(B,MAT_LOCAL,&Binfo);
2199:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2201:     if (B->cmap->N > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2202:     MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

2204:     if (alg_scalable) {
2205:       alg  = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2206:       MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2207:       PetscInfo2(B,"Use scalable algorithm, BN %D, fill*nz_allocated %g\n",B->cmap->N,product->fill*nz_local);
2208:     }
2209:   }

2211:   /* Get runtime option */
2212:   if (product->api_user) {
2213:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatTransposeMatMult","Mat");
2214:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2215:     PetscOptionsEnd();
2216:   } else {
2217:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_AtB","Mat");
2218:     PetscOptionsEList("-matproduct_atb_via","Algorithmic approach","MatTransposeMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2219:     PetscOptionsEnd();
2220:   }
2221:   if (flg) {
2222:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2223:   }

2225:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2226:   return(0);
2227: }

2229: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2230: {
2232:   Mat_Product    *product = C->product;
2233:   Mat            A=product->A,P=product->B;
2234:   MPI_Comm       comm;
2235:   PetscBool      flg;
2236:   PetscInt       alg=1; /* set default algorithm */
2237: #if !defined(PETSC_HAVE_HYPRE)
2238:   const char     *algTypes[4] = {"scalable","nonscalable","allatonce","allatonce_merged"};
2239:   PetscInt       nalg=4;
2240: #else
2241:   const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","hypre"};
2242:   PetscInt       nalg=5;
2243: #endif
2244:   PetscInt       pN=P->cmap->N;

2247:   /* Check matrix local sizes */
2248:   PetscObjectGetComm((PetscObject)C,&comm);
2249:   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);
2250:   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);

2252:   /* Set "nonscalable" as default algorithm */
2253:   PetscStrcmp(C->product->alg,"default",&flg);
2254:   if (flg) {
2255:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);

2257:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2258:     if (pN > 100000) {
2259:       MatInfo     Ainfo,Pinfo;
2260:       PetscInt    nz_local;
2261:       PetscBool   alg_scalable_loc=PETSC_FALSE,alg_scalable;

2263:       MatGetInfo(A,MAT_LOCAL,&Ainfo);
2264:       MatGetInfo(P,MAT_LOCAL,&Pinfo);
2265:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2267:       if (pN > product->fill*nz_local) alg_scalable_loc = PETSC_TRUE;
2268:       MPIU_Allreduce(&alg_scalable_loc,&alg_scalable,1,MPIU_BOOL,MPI_LOR,comm);

2270:       if (alg_scalable) {
2271:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2272:         MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2273:       }
2274:     }
2275:   }

2277:   /* Get runtime option */
2278:   if (product->api_user) {
2279:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatPtAP","Mat");
2280:     PetscOptionsEList("-matptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
2281:     PetscOptionsEnd();
2282:   } else {
2283:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");
2284:     PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);
2285:     PetscOptionsEnd();
2286:   }
2287:   if (flg) {
2288:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2289:   }

2291:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2292:   return(0);
2293: }

2295: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2296: {
2297:   Mat_Product *product = C->product;
2298:   Mat         A = product->A,R=product->B;

2301:   /* Check matrix local sizes */
2302:   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);

2304:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2305:   return(0);
2306: }

2308: /*
2309:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2310: */
2311: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2312: {
2314:   Mat_Product    *product = C->product;
2315:   PetscBool      flg = PETSC_FALSE;
2316:   PetscInt       alg = 1; /* default algorithm */
2317:   const char     *algTypes[3] = {"scalable","nonscalable","seqmpi"};
2318:   PetscInt       nalg = 3;

2321:   /* Set default algorithm */
2322:   PetscStrcmp(C->product->alg,"default",&flg);
2323:   if (flg) {
2324:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2325:   }

2327:   /* Get runtime option */
2328:   if (product->api_user) {
2329:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatMatMatMult","Mat");
2330:     PetscOptionsEList("-matmatmatmult_via","Algorithmic approach","MatMatMatMult",algTypes,nalg,algTypes[alg],&alg,&flg);
2331:     PetscOptionsEnd();
2332:   } else {
2333:     PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_ABC","Mat");
2334:     PetscOptionsEList("-matproduct_abc_via","Algorithmic approach","MatProduct_ABC",algTypes,nalg,algTypes[alg],&alg,&flg);
2335:     PetscOptionsEnd();
2336:   }
2337:   if (flg) {
2338:     MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);
2339:   }

2341:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2342:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2343:   return(0);
2344: }

2346: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2347: {
2349:   Mat_Product    *product = C->product;

2352:   switch (product->type) {
2353:   case MATPRODUCT_AB:
2354:     MatProductSetFromOptions_MPIAIJ_AB(C);
2355:     break;
2356:   case MATPRODUCT_AtB:
2357:     MatProductSetFromOptions_MPIAIJ_AtB(C);
2358:     break;
2359:   case MATPRODUCT_PtAP:
2360:     MatProductSetFromOptions_MPIAIJ_PtAP(C);
2361:     break;
2362:   case MATPRODUCT_RARt:
2363:     MatProductSetFromOptions_MPIAIJ_RARt(C);
2364:     break;
2365:   case MATPRODUCT_ABC:
2366:     MatProductSetFromOptions_MPIAIJ_ABC(C);
2367:     break;
2368:   default:
2369:     break;
2370:   }
2371:   return(0);
2372: }