Actual source code: mpimatmatmult.c

petsc-3.6.4 2016-04-12
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  2: /*
  3:   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
  4:           C = A * B
  5: */
  6: #include <../src/mat/impls/aij/seq/aij.h> /*I "petscmat.h" I*/
  7: #include <../src/mat/utils/freespace.h>
  8: #include <../src/mat/impls/aij/mpi/mpiaij.h>
  9: #include <petscbt.h>
 10: #include <../src/mat/impls/dense/mpi/mpidense.h>
 11: #include <petsc/private/vecimpl.h>

 15: PetscErrorCode MatMatMult_MPIAIJ_MPIAIJ(Mat A,Mat B,MatReuse scall,PetscReal fill, Mat *C)
 16: {
 18:   const char     *algTypes[2] = {"scalable","nonscalable"};
 19:   PetscInt       alg=0; /* set default algorithm */

 22:   if (scall == MAT_INITIAL_MATRIX) {
 23:     PetscObjectOptionsBegin((PetscObject)A);
 24:     PetscOptionsEList("-matmatmult_via","Algorithmic approach","MatMatMult",algTypes,2,algTypes[0],&alg,NULL);
 25:     PetscOptionsEnd();

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

 46: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(Mat A)
 47: {
 49:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
 50:   Mat_PtAPMPI    *ptap = a->ptap;

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

 68: PetscErrorCode MatDuplicate_MPIAIJ_MatMatMult(Mat A, MatDuplicateOption op, Mat *M)
 69: {
 71:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ*)A->data;
 72:   Mat_PtAPMPI    *ptap = a->ptap;

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

 77:   (*M)->ops->destroy   = ptap->destroy;   /* = MatDestroy_MPIAIJ, *M doesn't duplicate A's special structure! */
 78:   (*M)->ops->duplicate = ptap->duplicate; /* = MatDuplicate_MPIAIJ */
 79:   return(0);
 80: }

 84: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,Mat C)
 85: {
 87:   Mat_MPIAIJ     *a  =(Mat_MPIAIJ*)A->data,*c=(Mat_MPIAIJ*)C->data;
 88:   Mat_SeqAIJ     *ad =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data;
 89:   Mat_SeqAIJ     *cd =(Mat_SeqAIJ*)(c->A)->data,*co=(Mat_SeqAIJ*)(c->B)->data;
 90:   PetscInt       *adi=ad->i,*adj,*aoi=ao->i,*aoj;
 91:   PetscScalar    *ada,*aoa,*cda=cd->a,*coa=co->a;
 92:   Mat_SeqAIJ     *p_loc,*p_oth;
 93:   PetscInt       *pi_loc,*pj_loc,*pi_oth,*pj_oth,*pj;
 94:   PetscScalar    *pa_loc,*pa_oth,*pa,*apa,valtmp,*ca;
 95:   PetscInt       cm   =C->rmap->n,anz,pnz;
 96:   Mat_PtAPMPI    *ptap=c->ptap;
 97:   PetscInt       *api,*apj,*apJ,i,j,k,row;
 98:   PetscInt       cstart=C->cmap->rstart;
 99:   PetscInt       cdnz,conz,k0,k1;
100:   MPI_Comm       comm;
101:   PetscMPIInt    size;

104:   PetscObjectGetComm((PetscObject)A,&comm);
105:   MPI_Comm_size(comm,&size);

107:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
108:   /*-----------------------------------------------------*/
109:   /* update numerical values of P_oth and P_loc */
110:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
111:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

113:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
114:   /*----------------------------------------------------------*/
115:   /* get data from symbolic products */
116:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
117:   pi_loc=p_loc->i; pj_loc=p_loc->j; pa_loc=p_loc->a;
118:   if (size >1) {
119:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
120:     pi_oth=p_oth->i; pj_oth=p_oth->j; pa_oth=p_oth->a;
121:   } else {
122:     pi_oth=NULL; pj_oth=NULL; pa_oth=NULL;
123:   }

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

128:   api = ptap->api;
129:   apj = ptap->apj;
130:   for (i=0; i<cm; i++) {
131:     /* diagonal portion of A */
132:     anz = adi[i+1] - adi[i];
133:     adj = ad->j + adi[i];
134:     ada = ad->a + adi[i];
135:     for (j=0; j<anz; j++) {
136:       row = adj[j];
137:       pnz = pi_loc[row+1] - pi_loc[row];
138:       pj  = pj_loc + pi_loc[row];
139:       pa  = pa_loc + pi_loc[row];

141:       /* perform dense axpy */
142:       valtmp = ada[j];
143:       for (k=0; k<pnz; k++) {
144:         apa[pj[k]] += valtmp*pa[k];
145:       }
146:       PetscLogFlops(2.0*pnz);
147:     }

149:     /* off-diagonal portion of A */
150:     anz = aoi[i+1] - aoi[i];
151:     aoj = ao->j + aoi[i];
152:     aoa = ao->a + aoi[i];
153:     for (j=0; j<anz; j++) {
154:       row = aoj[j];
155:       pnz = pi_oth[row+1] - pi_oth[row];
156:       pj  = pj_oth + pi_oth[row];
157:       pa  = pa_oth + pi_oth[row];

159:       /* perform dense axpy */
160:       valtmp = aoa[j];
161:       for (k=0; k<pnz; k++) {
162:         apa[pj[k]] += valtmp*pa[k];
163:       }
164:       PetscLogFlops(2.0*pnz);
165:     }

167:     /* set values in C */
168:     apJ  = apj + api[i];
169:     cdnz = cd->i[i+1] - cd->i[i];
170:     conz = co->i[i+1] - co->i[i];

172:     /* 1st off-diagoanl part of C */
173:     ca = coa + co->i[i];
174:     k  = 0;
175:     for (k0=0; k0<conz; k0++) {
176:       if (apJ[k] >= cstart) break;
177:       ca[k0]      = apa[apJ[k]];
178:       apa[apJ[k]] = 0.0;
179:       k++;
180:     }

182:     /* diagonal part of C */
183:     ca = cda + cd->i[i];
184:     for (k1=0; k1<cdnz; k1++) {
185:       ca[k1]      = apa[apJ[k]];
186:       apa[apJ[k]] = 0.0;
187:       k++;
188:     }

190:     /* 2nd off-diagoanl part of C */
191:     ca = coa + co->i[i];
192:     for (; k0<conz; k0++) {
193:       ca[k0]      = apa[apJ[k]];
194:       apa[apJ[k]] = 0.0;
195:       k++;
196:     }
197:   }
198:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
199:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
200:   return(0);
201: }

205: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A,Mat P,PetscReal fill,Mat *C)
206: {
207:   PetscErrorCode     ierr;
208:   MPI_Comm           comm;
209:   PetscMPIInt        size;
210:   Mat                Cmpi;
211:   Mat_PtAPMPI        *ptap;
212:   PetscFreeSpaceList free_space=NULL,current_space=NULL;
213:   Mat_MPIAIJ         *a        =(Mat_MPIAIJ*)A->data,*c;
214:   Mat_SeqAIJ         *ad       =(Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
215:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
216:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
217:   PetscInt           *lnk,i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi;
218:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
219:   PetscBT            lnkbt;
220:   PetscScalar        *apa;
221:   PetscReal          afill;
222:   PetscInt           nlnk_max,armax,prmax;

225:   PetscObjectGetComm((PetscObject)A,&comm);
226:   MPI_Comm_size(comm,&size);

228:   if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) {
229:     SETERRQ4(comm,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, (%D, %D) != (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);
230:   }
231: 
232:   /* create struct Mat_PtAPMPI and attached it to C later */
233:   PetscNew(&ptap);

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

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

241:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
242:   pi_loc = p_loc->i; pj_loc = p_loc->j;
243:   if (size > 1) {
244:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
245:     pi_oth = p_oth->i; pj_oth = p_oth->j;
246:   } else {
247:     p_oth = NULL;
248:     pi_oth = NULL; pj_oth = NULL;
249:   }

251:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
252:   /*-------------------------------------------------------------------*/
253:   PetscMalloc1(am+2,&api);
254:   ptap->api = api;
255:   api[0]    = 0;

257:   /* create and initialize a linked list */
258:   armax    = ad->rmax+ao->rmax;
259:   if (size >1) {
260:     prmax    = PetscMax(p_loc->rmax,p_oth->rmax);
261:   } else {
262:     prmax = p_loc->rmax;
263:   }
264:   nlnk_max = armax*prmax;
265:   if (!nlnk_max || nlnk_max > pN) nlnk_max = pN;
266:   PetscLLCondensedCreate(nlnk_max,pN,&lnk,&lnkbt);

268:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
269:   PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);

271:   current_space = free_space;

273:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
274:   for (i=0; i<am; i++) {
275:     /* diagonal portion of A */
276:     nzi = adi[i+1] - adi[i];
277:     for (j=0; j<nzi; j++) {
278:       row  = *adj++;
279:       pnz  = pi_loc[row+1] - pi_loc[row];
280:       Jptr = pj_loc + pi_loc[row];
281:       /* add non-zero cols of P into the sorted linked list lnk */
282:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
283:     }
284:     /* off-diagonal portion of A */
285:     nzi = aoi[i+1] - aoi[i];
286:     for (j=0; j<nzi; j++) {
287:       row  = *aoj++;
288:       pnz  = pi_oth[row+1] - pi_oth[row];
289:       Jptr = pj_oth + pi_oth[row];
290:       PetscLLCondensedAddSorted(pnz,Jptr,lnk,lnkbt);
291:     }

293:     apnz     = lnk[0];
294:     api[i+1] = api[i] + apnz;

296:     /* if free space is not available, double the total space in the list */
297:     if (current_space->local_remaining<apnz) {
298:       PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);
299:       nspacedouble++;
300:     }

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

306:     current_space->array           += apnz;
307:     current_space->local_used      += apnz;
308:     current_space->local_remaining -= apnz;
309:   }

311:   /* Allocate space for apj, initialize apj, and */
312:   /* destroy list of free space and other temporary array(s) */
313:   PetscMalloc1(api[am]+1,&ptap->apj);
314:   apj  = ptap->apj;
315:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
316:   PetscLLDestroy(lnk,lnkbt);

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

321:   ptap->apa = apa;

323:   /* create and assemble symbolic parallel matrix Cmpi */
324:   /*----------------------------------------------------*/
325:   MatCreate(comm,&Cmpi);
326:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
327:   MatSetBlockSizesFromMats(Cmpi,A,P);

329:   MatSetType(Cmpi,MATMPIAIJ);
330:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
331:   MatPreallocateFinalize(dnz,onz);
332:   for (i=0; i<am; i++) {
333:     row  = i + rstart;
334:     apnz = api[i+1] - api[i];
335:     MatSetValues(Cmpi,1,&row,apnz,apj,apa,INSERT_VALUES);
336:     apj += apnz;
337:   }
338:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
339:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);

341:   ptap->destroy        = Cmpi->ops->destroy;
342:   ptap->duplicate      = Cmpi->ops->duplicate;
343:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
344:   Cmpi->ops->destroy   = MatDestroy_MPIAIJ_MatMatMult;
345:   Cmpi->ops->duplicate = MatDuplicate_MPIAIJ_MatMatMult;

347:   /* attach the supporting struct to Cmpi for reuse */
348:   c       = (Mat_MPIAIJ*)Cmpi->data;
349:   c->ptap = ptap;

351:   *C = Cmpi;

353:   /* set MatInfo */
354:   afill = (PetscReal)api[am]/(adi[am]+aoi[am]+pi_loc[pm]+1) + 1.e-5;
355:   if (afill < 1.0) afill = 1.0;
356:   Cmpi->info.mallocs           = nspacedouble;
357:   Cmpi->info.fill_ratio_given  = fill;
358:   Cmpi->info.fill_ratio_needed = afill;

360: #if defined(PETSC_USE_INFO)
361:   if (api[am]) {
362:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
363:     PetscInfo1(Cmpi,"Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n",(double)afill);
364:   } else {
365:     PetscInfo(Cmpi,"Empty matrix product\n");
366:   }
367: #endif
368:   return(0);
369: }

373: PetscErrorCode MatMatMult_MPIAIJ_MPIDense(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat *C)
374: {

378:   if (scall == MAT_INITIAL_MATRIX) {
379:     PetscLogEventBegin(MAT_MatMultSymbolic,A,B,0,0);
380:     MatMatMultSymbolic_MPIAIJ_MPIDense(A,B,fill,C);
381:     PetscLogEventEnd(MAT_MatMultSymbolic,A,B,0,0);
382:   }
383:   PetscLogEventBegin(MAT_MatMultNumeric,A,B,0,0);
384:   MatMatMultNumeric_MPIAIJ_MPIDense(A,B,*C);
385:   PetscLogEventEnd(MAT_MatMultNumeric,A,B,0,0);
386:   return(0);
387: }

389: typedef struct {
390:   Mat         workB;
391:   PetscScalar *rvalues,*svalues;
392:   MPI_Request *rwaits,*swaits;
393: } MPIAIJ_MPIDense;

397: PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void *ctx)
398: {
399:   MPIAIJ_MPIDense *contents = (MPIAIJ_MPIDense*) ctx;
400:   PetscErrorCode  ierr;

403:   MatDestroy(&contents->workB);
404:   PetscFree4(contents->rvalues,contents->svalues,contents->rwaits,contents->swaits);
405:   PetscFree(contents);
406:   return(0);
407: }

411: /*
412:     This is a "dummy function" that handles the case where matrix C was created as a dense matrix
413:   directly by the user and passed to MatMatMult() with the MAT_REUSE_MATRIX option

415:   It is the same as MatMatMultSymbolic_MPIAIJ_MPIDense() except does not create C
416: */
417: PetscErrorCode MatMatMultNumeric_MPIDense(Mat A,Mat B,Mat C)
418: {
419:   PetscErrorCode         ierr;
420:   PetscBool              flg;
421:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
422:   PetscInt               nz   = aij->B->cmap->n;
423:   PetscContainer         container;
424:   MPIAIJ_MPIDense        *contents;
425:   VecScatter             ctx   = aij->Mvctx;
426:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
427:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;

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

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

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

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

448:   PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);
449:   PetscContainerSetPointer(container,contents);
450:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
451:   PetscObjectCompose((PetscObject)C,"workB",(PetscObject)container);
452:   PetscContainerDestroy(&container);

454:   (*C->ops->matmultnumeric)(A,B,C);
455:   return(0);
456: }

460: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A,Mat B,PetscReal fill,Mat *C)
461: {
462:   PetscErrorCode         ierr;
463:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*) A->data;
464:   PetscInt               nz   = aij->B->cmap->n;
465:   PetscContainer         container;
466:   MPIAIJ_MPIDense        *contents;
467:   VecScatter             ctx   = aij->Mvctx;
468:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
469:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;
470:   PetscInt               m     = A->rmap->n,n=B->cmap->n;

473:   MatCreate(PetscObjectComm((PetscObject)B),C);
474:   MatSetSizes(*C,m,n,A->rmap->N,B->cmap->N);
475:   MatSetBlockSizesFromMats(*C,A,B);
476:   MatSetType(*C,MATMPIDENSE);
477:   MatMPIDenseSetPreallocation(*C,NULL);
478:   MatAssemblyBegin(*C,MAT_FINAL_ASSEMBLY);
479:   MatAssemblyEnd(*C,MAT_FINAL_ASSEMBLY);

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

483:   PetscNew(&contents);
484:   /* Create work matrix used to store off processor rows of B needed for local product */
485:   MatCreateSeqDense(PETSC_COMM_SELF,nz,B->cmap->N,NULL,&contents->workB);
486:   /* Create work arrays needed */
487:   PetscMalloc4(B->cmap->N*from->starts[from->n],&contents->rvalues,
488:                       B->cmap->N*to->starts[to->n],&contents->svalues,
489:                       from->n,&contents->rwaits,
490:                       to->n,&contents->swaits);

492:   PetscContainerCreate(PetscObjectComm((PetscObject)A),&container);
493:   PetscContainerSetPointer(container,contents);
494:   PetscContainerSetUserDestroy(container,MatMPIAIJ_MPIDenseDestroy);
495:   PetscObjectCompose((PetscObject)(*C),"workB",(PetscObject)container);
496:   PetscContainerDestroy(&container);
497:   return(0);
498: }

502: /*
503:     Performs an efficient scatter on the rows of B needed by this process; this is
504:     a modification of the VecScatterBegin_() routines.
505: */
506: PetscErrorCode MatMPIDenseScatter(Mat A,Mat B,Mat C,Mat *outworkB)
507: {
508:   Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)A->data;
509:   PetscErrorCode         ierr;
510:   PetscScalar            *b,*w,*svalues,*rvalues;
511:   VecScatter             ctx   = aij->Mvctx;
512:   VecScatter_MPI_General *from = (VecScatter_MPI_General*) ctx->fromdata;
513:   VecScatter_MPI_General *to   = (VecScatter_MPI_General*) ctx->todata;
514:   PetscInt               i,j,k;
515:   PetscInt               *sindices,*sstarts,*rindices,*rstarts;
516:   PetscMPIInt            *sprocs,*rprocs,nrecvs;
517:   MPI_Request            *swaits,*rwaits;
518:   MPI_Comm               comm;
519:   PetscMPIInt            tag  = ((PetscObject)ctx)->tag,ncols = B->cmap->N, nrows = aij->B->cmap->n,imdex,nrowsB = B->rmap->n;
520:   MPI_Status             status;
521:   MPIAIJ_MPIDense        *contents;
522:   PetscContainer         container;
523:   Mat                    workB;

526:   PetscObjectGetComm((PetscObject)A,&comm);
527:   PetscObjectQuery((PetscObject)C,"workB",(PetscObject*)&container);
528:   if (!container) SETERRQ(comm,PETSC_ERR_PLIB,"Container does not exist");
529:   PetscContainerGetPointer(container,(void**)&contents);

531:   workB = *outworkB = contents->workB;
532:   if (nrows != workB->rmap->n) SETERRQ2(comm,PETSC_ERR_PLIB,"Number of rows of workB %D not equal to columns of aij->B %D",nrows,workB->cmap->n);
533:   sindices = to->indices;
534:   sstarts  = to->starts;
535:   sprocs   = to->procs;
536:   swaits   = contents->swaits;
537:   svalues  = contents->svalues;

539:   rindices = from->indices;
540:   rstarts  = from->starts;
541:   rprocs   = from->procs;
542:   rwaits   = contents->rwaits;
543:   rvalues  = contents->rvalues;

545:   MatDenseGetArray(B,&b);
546:   MatDenseGetArray(workB,&w);

548:   for (i=0; i<from->n; i++) {
549:     MPI_Irecv(rvalues+ncols*rstarts[i],ncols*(rstarts[i+1]-rstarts[i]),MPIU_SCALAR,rprocs[i],tag,comm,rwaits+i);
550:   }

552:   for (i=0; i<to->n; i++) {
553:     /* pack a message at a time */
554:     for (j=0; j<sstarts[i+1]-sstarts[i]; j++) {
555:       for (k=0; k<ncols; k++) {
556:         svalues[ncols*(sstarts[i] + j) + k] = b[sindices[sstarts[i]+j] + nrowsB*k];
557:       }
558:     }
559:     MPI_Isend(svalues+ncols*sstarts[i],ncols*(sstarts[i+1]-sstarts[i]),MPIU_SCALAR,sprocs[i],tag,comm,swaits+i);
560:   }

562:   nrecvs = from->n;
563:   while (nrecvs) {
564:     MPI_Waitany(from->n,rwaits,&imdex,&status);
565:     nrecvs--;
566:     /* unpack a message at a time */
567:     for (j=0; j<rstarts[imdex+1]-rstarts[imdex]; j++) {
568:       for (k=0; k<ncols; k++) {
569:         w[rindices[rstarts[imdex]+j] + nrows*k] = rvalues[ncols*(rstarts[imdex] + j) + k];
570:       }
571:     }
572:   }
573:   if (to->n) {MPI_Waitall(to->n,swaits,to->sstatus);}

575:   MatDenseRestoreArray(B,&b);
576:   MatDenseRestoreArray(workB,&w);
577:   MatAssemblyBegin(workB,MAT_FINAL_ASSEMBLY);
578:   MatAssemblyEnd(workB,MAT_FINAL_ASSEMBLY);
579:   return(0);
580: }
581: extern PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat,Mat,Mat);

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

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

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

600:   /* off-diagonal block of A times nonlocal rows of B */
601:   MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B,workB,cdense->A);
602:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
603:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
604:   return(0);
605: }

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

630:   PetscObjectGetComm((PetscObject)A,&comm);
631:   MPI_Comm_size(comm,&size);

633:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
634:   /*-----------------------------------------------------*/
635:   /* update numerical values of P_oth and P_loc */
636:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_REUSE_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
637:   MatMPIAIJGetLocalMat(P,MAT_REUSE_MATRIX,&ptap->P_loc);

639:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
640:   /*----------------------------------------------------------*/
641:   /* get data from symbolic products */
642:   p_loc = (Mat_SeqAIJ*)(ptap->P_loc)->data;
643:   pi_loc = p_loc->i; pj_loc = p_loc->j; pa_loc = p_loc->a;
644:   if (size >1) {
645:     p_oth = (Mat_SeqAIJ*)(ptap->P_oth)->data;
646:     pi_oth = p_oth->i; pj_oth = p_oth->j; pa_oth = p_oth->a;
647:   } else {
648:     p_oth = NULL; pi_oth = NULL; pj_oth = NULL; pa_oth = NULL;
649:   }

651:   api = ptap->api;
652:   apj = ptap->apj;
653:   for (i=0; i<cm; i++) {
654:     apJ = apj + api[i];

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

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

696:     /* set values in C */
697:     cdnz = cd->i[i+1] - cd->i[i];
698:     conz = co->i[i+1] - co->i[i];

700:     /* 1st off-diagoanl part of C */
701:     ca = coa + co->i[i];
702:     k  = 0;
703:     for (k0=0; k0<conz; k0++) {
704:       if (apJ[k] >= cstart) break;
705:       ca[k0]        = apa_sparse[k];
706:       apa_sparse[k] = 0.0;
707:       k++;
708:     }

710:     /* diagonal part of C */
711:     ca = cda + cd->i[i];
712:     for (k1=0; k1<cdnz; k1++) {
713:       ca[k1]        = apa_sparse[k];
714:       apa_sparse[k] = 0.0;
715:       k++;
716:     }

718:     /* 2nd off-diagoanl part of C */
719:     ca = coa + co->i[i];
720:     for (; k0<conz; k0++) {
721:       ca[k0]        = apa_sparse[k];
722:       apa_sparse[k] = 0.0;
723:       k++;
724:     }
725:   }
726:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
727:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
728:   return(0);
729: }

731: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
734: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A,Mat P,PetscReal fill,Mat *C)
735: {
736:   PetscErrorCode     ierr;
737:   MPI_Comm           comm;
738:   PetscMPIInt        size;
739:   Mat                Cmpi;
740:   Mat_PtAPMPI        *ptap;
741:   PetscFreeSpaceList free_space = NULL,current_space=NULL;
742:   Mat_MPIAIJ         *a         = (Mat_MPIAIJ*)A->data,*c;
743:   Mat_SeqAIJ         *ad        = (Mat_SeqAIJ*)(a->A)->data,*ao=(Mat_SeqAIJ*)(a->B)->data,*p_loc,*p_oth;
744:   PetscInt           *pi_loc,*pj_loc,*pi_oth,*pj_oth,*dnz,*onz;
745:   PetscInt           *adi=ad->i,*adj=ad->j,*aoi=ao->i,*aoj=ao->j,rstart=A->rmap->rstart;
746:   PetscInt           i,pnz,row,*api,*apj,*Jptr,apnz,nspacedouble=0,j,nzi,*lnk,apnz_max=0;
747:   PetscInt           am=A->rmap->n,pN=P->cmap->N,pn=P->cmap->n,pm=P->rmap->n;
748:   PetscInt           nlnk_max,armax,prmax;
749:   PetscReal          afill;
750:   PetscScalar        *apa;

753:   PetscObjectGetComm((PetscObject)A,&comm);
754:   MPI_Comm_size(comm,&size);

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

759:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
760:   MatGetBrowsOfAoCols_MPIAIJ(A,P,MAT_INITIAL_MATRIX,&ptap->startsj_s,&ptap->startsj_r,&ptap->bufa,&ptap->P_oth);
761: 
762:   /* get P_loc by taking all local rows of P */
763:   MatMPIAIJGetLocalMat(P,MAT_INITIAL_MATRIX,&ptap->P_loc);

765:   p_loc  = (Mat_SeqAIJ*)(ptap->P_loc)->data;
766:   pi_loc = p_loc->i; pj_loc = p_loc->j;
767:   if (size > 1) {
768:     p_oth  = (Mat_SeqAIJ*)(ptap->P_oth)->data;
769:     pi_oth = p_oth->i; pj_oth = p_oth->j;
770:   } else {
771:     p_oth  = NULL;
772:     pi_oth = NULL; pj_oth = NULL;
773:   }

775:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
776:   /*-------------------------------------------------------------------*/
777:   PetscMalloc1(am+2,&api);
778:   ptap->api = api;
779:   api[0]    = 0;

781:   /* create and initialize a linked list */
782:   armax = ad->rmax+ao->rmax;
783:   if (size >1) {
784:     prmax = PetscMax(p_loc->rmax,p_oth->rmax);
785:   } else {
786:     prmax = p_loc->rmax;
787:   }
788:   nlnk_max = armax*prmax;
789:   if (!nlnk_max || nlnk_max > pN) nlnk_max = pN;
790:   PetscLLCondensedCreate_Scalable(nlnk_max,&lnk);

792:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
793:   PetscFreeSpaceGet((PetscInt)(fill*(adi[am]+aoi[am]+pi_loc[pm])),&free_space);

795:   current_space = free_space;

797:   MatPreallocateInitialize(comm,am,pn,dnz,onz);
798:   for (i=0; i<am; i++) {
799:     /* diagonal portion of A */
800:     nzi = adi[i+1] - adi[i];
801:     for (j=0; j<nzi; j++) {
802:       row  = *adj++;
803:       pnz  = pi_loc[row+1] - pi_loc[row];
804:       Jptr = pj_loc + pi_loc[row];
805:       /* add non-zero cols of P into the sorted linked list lnk */
806:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
807:     }
808:     /* off-diagonal portion of A */
809:     nzi = aoi[i+1] - aoi[i];
810:     for (j=0; j<nzi; j++) {
811:       row  = *aoj++;
812:       pnz  = pi_oth[row+1] - pi_oth[row];
813:       Jptr = pj_oth + pi_oth[row];
814:       PetscLLCondensedAddSorted_Scalable(pnz,Jptr,lnk);
815:     }

817:     apnz     = *lnk;
818:     api[i+1] = api[i] + apnz;
819:     if (apnz > apnz_max) apnz_max = apnz;

821:     /* if free space is not available, double the total space in the list */
822:     if (current_space->local_remaining<apnz) {
823:       PetscFreeSpaceGet(apnz+current_space->total_array_size,&current_space);
824:       nspacedouble++;
825:     }

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

831:     current_space->array           += apnz;
832:     current_space->local_used      += apnz;
833:     current_space->local_remaining -= apnz;
834:   }

836:   /* Allocate space for apj, initialize apj, and */
837:   /* destroy list of free space and other temporary array(s) */
838:   PetscMalloc1(api[am]+1,&ptap->apj);
839:   apj  = ptap->apj;
840:   PetscFreeSpaceContiguous(&free_space,ptap->apj);
841:   PetscLLCondensedDestroy_Scalable(lnk);

843:   /* create and assemble symbolic parallel matrix Cmpi */
844:   /*----------------------------------------------------*/
845:   MatCreate(comm,&Cmpi);
846:   MatSetSizes(Cmpi,am,pn,PETSC_DETERMINE,PETSC_DETERMINE);
847:   MatSetBlockSizesFromMats(Cmpi,A,P);
848:   MatSetType(Cmpi,MATMPIAIJ);
849:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
850:   MatPreallocateFinalize(dnz,onz);

852:   /* malloc apa for assembly Cmpi */
853:   PetscCalloc1(apnz_max,&apa);

855:   ptap->apa = apa;
856:   for (i=0; i<am; i++) {
857:     row  = i + rstart;
858:     apnz = api[i+1] - api[i];
859:     MatSetValues(Cmpi,1,&row,apnz,apj,apa,INSERT_VALUES);
860:     apj += apnz;
861:   }
862:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
863:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);

865:   ptap->destroy             = Cmpi->ops->destroy;
866:   ptap->duplicate           = Cmpi->ops->duplicate;
867:   Cmpi->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
868:   Cmpi->ops->destroy        = MatDestroy_MPIAIJ_MatMatMult;
869:   Cmpi->ops->duplicate      = MatDuplicate_MPIAIJ_MatMatMult;

871:   /* attach the supporting struct to Cmpi for reuse */
872:   c       = (Mat_MPIAIJ*)Cmpi->data;
873:   c->ptap = ptap;

875:   *C = Cmpi;

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:   Cmpi->info.mallocs           = nspacedouble;
881:   Cmpi->info.fill_ratio_given  = fill;
882:   Cmpi->info.fill_ratio_needed = afill;

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

895: /*-------------------------------------------------------------------------*/
898: PetscErrorCode MatTransposeMatMult_MPIAIJ_MPIAIJ(Mat P,Mat A,MatReuse scall,PetscReal fill,Mat *C)
899: {
901:   const char     *algTypes[3] = {"scalable","nonscalable","matmatmult"};
902:   PetscInt       alg=0; /* set default algorithm */

905:   if (scall == MAT_INITIAL_MATRIX) {
906:     PetscObjectOptionsBegin((PetscObject)A);
907:     PetscOptionsEList("-mattransposematmult_via","Algorithmic approach","MatTransposeMatMult",algTypes,3,algTypes[0],&alg,NULL);
908:     PetscOptionsEnd();

910:     PetscLogEventBegin(MAT_TransposeMatMultSymbolic,P,A,0,0);
911:     switch (alg) {
912:     case 1:
913:       MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(P,A,fill,C);
914:       break;
915:     case 2:
916:     {
917:       Mat         Pt;
918:       Mat_PtAPMPI *ptap;
919:       Mat_MPIAIJ  *c;
920:       MatTranspose(P,MAT_INITIAL_MATRIX,&Pt);
921:       MatMatMult(Pt,A,MAT_INITIAL_MATRIX,fill,C);
922:       c        = (Mat_MPIAIJ*)(*C)->data;
923:       ptap     = c->ptap;
924:       ptap->Pt = Pt;
925:       (*C)->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
926:       return(0);
927:     }
928:       break;
929:     default:
930:       MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(P,A,fill,C);
931:       break;
932:     }
933:     PetscLogEventEnd(MAT_TransposeMatMultSymbolic,P,A,0,0);
934:   }
935:   PetscLogEventBegin(MAT_TransposeMatMultNumeric,P,A,0,0);
936:   (*(*C)->ops->mattransposemultnumeric)(P,A,*C);
937:   PetscLogEventEnd(MAT_TransposeMatMultNumeric,P,A,0,0);
938:   return(0);
939: }

941: /* This routine only works when scall=MAT_REUSE_MATRIX! */
944: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P,Mat A,Mat C)
945: {
947:   Mat_MPIAIJ     *c=(Mat_MPIAIJ*)C->data;
948:   Mat_PtAPMPI    *ptap= c->ptap;
949:   Mat            Pt=ptap->Pt;

952:   MatTranspose(P,MAT_REUSE_MATRIX,&Pt);
953:   MatMatMultNumeric(Pt,A,C);
954:   return(0);
955: }

957: /* Non-scalable version, use dense axpy */
960: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,Mat C)
961: {
962:   PetscErrorCode      ierr;
963:   Mat_Merge_SeqsToMPI *merge;
964:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
965:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
966:   Mat_PtAPMPI         *ptap;
967:   PetscInt            *adj,*aJ;
968:   PetscInt            i,j,k,anz,pnz,row,*cj;
969:   MatScalar           *ada,*aval,*ca,valtmp;
970:   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
971:   MPI_Comm            comm;
972:   PetscMPIInt         size,rank,taga,*len_s;
973:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
974:   PetscInt            **buf_ri,**buf_rj;
975:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
976:   MPI_Request         *s_waits,*r_waits;
977:   MPI_Status          *status;
978:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
979:   PetscInt            *ai,*aj,*coi,*coj;
980:   PetscInt            *poJ,*pdJ;
981:   Mat                 A_loc;
982:   Mat_SeqAIJ          *a_loc;

985:   PetscObjectGetComm((PetscObject)C,&comm);
986:   MPI_Comm_size(comm,&size);
987:   MPI_Comm_rank(comm,&rank);

989:   ptap  = c->ptap;
990:   merge = ptap->merge;

992:   /* 2) compute numeric C_seq = P_loc^T*A_loc*P - dominating part */
993:   /*--------------------------------------------------------------*/
994:   /* get data from symbolic products */
995:   coi  = merge->coi; coj = merge->coj;
996:   PetscCalloc1(coi[pon]+1,&coa);

998:   bi     = merge->bi; bj = merge->bj;
999:   owners = merge->rowmap->range;
1000:   PetscCalloc1(bi[cm]+1,&ba);

1002:   /* get A_loc by taking all local rows of A */
1003:   A_loc = ptap->A_loc;
1004:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
1005:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1006:   ai    = a_loc->i;
1007:   aj    = a_loc->j;

1009:   PetscCalloc1(A->cmap->N,&aval); /* non-scalable!!! */

1011:   for (i=0; i<am; i++) {
1012:     /* 2-a) put A[i,:] to dense array aval */
1013:     anz = ai[i+1] - ai[i];
1014:     adj = aj + ai[i];
1015:     ada = a_loc->a + ai[i];
1016:     for (j=0; j<anz; j++) {
1017:       aval[adj[j]] = ada[j];
1018:     }

1020:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1021:     /*--------------------------------------------------------------*/
1022:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1023:     pnz = po->i[i+1] - po->i[i];
1024:     poJ = po->j + po->i[i];
1025:     pA  = po->a + po->i[i];
1026:     for (j=0; j<pnz; j++) {
1027:       row = poJ[j];
1028:       cnz = coi[row+1] - coi[row];
1029:       cj  = coj + coi[row];
1030:       ca  = coa + coi[row];
1031:       /* perform dense axpy */
1032:       valtmp = pA[j];
1033:       for (k=0; k<cnz; k++) {
1034:         ca[k] += valtmp*aval[cj[k]];
1035:       }
1036:       PetscLogFlops(2.0*cnz);
1037:     }

1039:     /* put the value into Cd (diagonal part) */
1040:     pnz = pd->i[i+1] - pd->i[i];
1041:     pdJ = pd->j + pd->i[i];
1042:     pA  = pd->a + pd->i[i];
1043:     for (j=0; j<pnz; j++) {
1044:       row = pdJ[j];
1045:       cnz = bi[row+1] - bi[row];
1046:       cj  = bj + bi[row];
1047:       ca  = ba + bi[row];
1048:       /* perform dense axpy */
1049:       valtmp = pA[j];
1050:       for (k=0; k<cnz; k++) {
1051:         ca[k] += valtmp*aval[cj[k]];
1052:       }
1053:       PetscLogFlops(2.0*cnz);
1054:     }

1056:     /* zero the current row of Pt*A */
1057:     aJ = aj + ai[i];
1058:     for (k=0; k<anz; k++) aval[aJ[k]] = 0.0;
1059:   }

1061:   /* 3) send and recv matrix values coa */
1062:   /*------------------------------------*/
1063:   buf_ri = merge->buf_ri;
1064:   buf_rj = merge->buf_rj;
1065:   len_s  = merge->len_s;
1066:   PetscCommGetNewTag(comm,&taga);
1067:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

1069:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
1070:   for (proc=0,k=0; proc<size; proc++) {
1071:     if (!len_s[proc]) continue;
1072:     i    = merge->owners_co[proc];
1073:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
1074:     k++;
1075:   }
1076:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
1077:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

1079:   PetscFree2(s_waits,status);
1080:   PetscFree(r_waits);
1081:   PetscFree(coa);

1083:   /* 4) insert local Cseq and received values into Cmpi */
1084:   /*----------------------------------------------------*/
1085:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1086:   for (k=0; k<merge->nrecv; k++) {
1087:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1088:     nrows       = *(buf_ri_k[k]);
1089:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1090:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1091:   }

1093:   for (i=0; i<cm; i++) {
1094:     row  = owners[rank] + i; /* global row index of C_seq */
1095:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1096:     ba_i = ba + bi[i];
1097:     bnz  = bi[i+1] - bi[i];
1098:     /* add received vals into ba */
1099:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1100:       /* i-th row */
1101:       if (i == *nextrow[k]) {
1102:         cnz    = *(nextci[k]+1) - *nextci[k];
1103:         cj     = buf_rj[k] + *(nextci[k]);
1104:         ca     = abuf_r[k] + *(nextci[k]);
1105:         nextcj = 0;
1106:         for (j=0; nextcj<cnz; j++) {
1107:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1108:             ba_i[j] += ca[nextcj++];
1109:           }
1110:         }
1111:         nextrow[k]++; nextci[k]++;
1112:         PetscLogFlops(2.0*cnz);
1113:       }
1114:     }
1115:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
1116:   }
1117:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1118:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

1120:   PetscFree(ba);
1121:   PetscFree(abuf_r[0]);
1122:   PetscFree(abuf_r);
1123:   PetscFree3(buf_ri_k,nextrow,nextci);
1124:   PetscFree(aval);
1125:   return(0);
1126: }

1128: PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat, MatDuplicateOption,Mat*);
1129: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1132: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P,Mat A,PetscReal fill,Mat *C)
1133: {
1134:   PetscErrorCode      ierr;
1135:   Mat                 Cmpi,A_loc,POt,PDt;
1136:   Mat_PtAPMPI         *ptap;
1137:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1138:   Mat_MPIAIJ          *p        =(Mat_MPIAIJ*)P->data,*c;
1139:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1140:   PetscInt            nnz;
1141:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1142:   PetscInt            am=A->rmap->n,pn=P->cmap->n;
1143:   PetscBT             lnkbt;
1144:   MPI_Comm            comm;
1145:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1146:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1147:   PetscInt            len,proc,*dnz,*onz,*owners;
1148:   PetscInt            nzi,*bi,*bj;
1149:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1150:   MPI_Request         *swaits,*rwaits;
1151:   MPI_Status          *sstatus,rstatus;
1152:   Mat_Merge_SeqsToMPI *merge;
1153:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1154:   PetscReal           afill  =1.0,afill_tmp;
1155:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Crmax;
1156:   PetscScalar         *vals;
1157:   Mat_SeqAIJ          *a_loc, *pdt,*pot;

1160:   PetscObjectGetComm((PetscObject)A,&comm);
1161:   /* check if matrix local sizes are compatible */
1162:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) {
1163:     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);
1164:   }

1166:   MPI_Comm_size(comm,&size);
1167:   MPI_Comm_rank(comm,&rank);

1169:   /* create struct Mat_PtAPMPI and attached it to C later */
1170:   PetscNew(&ptap);

1172:   /* get A_loc by taking all local rows of A */
1173:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

1175:   ptap->A_loc = A_loc;

1177:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1178:   ai    = a_loc->i;
1179:   aj    = a_loc->j;

1181:   /* determine symbolic Co=(p->B)^T*A - send to others */
1182:   /*----------------------------------------------------*/
1183:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
1184:   pdt  = (Mat_SeqAIJ*)PDt->data;
1185:   pdti = pdt->i; pdtj = pdt->j;

1187:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
1188:   pot  = (Mat_SeqAIJ*)POt->data;
1189:   poti = pot->i; potj = pot->j;

1191:   /* then, compute symbolic Co = (p->B)^T*A */
1192:   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors >= (num of nonzero rows of C_seq) - pn */
1193:   PetscMalloc1(pon+1,&coi);
1194:   coi[0] = 0;

1196:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1197:   nnz           = fill*(poti[pon] + ai[am]);
1198:   PetscFreeSpaceGet(nnz,&free_space);
1199:   current_space = free_space;

1201:   /* create and initialize a linked list */
1202:   i     = PetscMax(pdt->rmax,pot->rmax);
1203:   Crmax = i*a_loc->rmax*size;
1204:   if (!Crmax || Crmax > aN) Crmax = aN;
1205:   PetscLLCondensedCreate(Crmax,aN,&lnk,&lnkbt);

1207:   for (i=0; i<pon; i++) {
1208:     pnz = poti[i+1] - poti[i];
1209:     ptJ = potj + poti[i];
1210:     for (j=0; j<pnz; j++) {
1211:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1212:       anz  = ai[row+1] - ai[row];
1213:       Jptr = aj + ai[row];
1214:       /* add non-zero cols of AP into the sorted linked list lnk */
1215:       PetscLLCondensedAddSorted(anz,Jptr,lnk,lnkbt);
1216:     }
1217:     nnz = lnk[0];

1219:     /* If free space is not available, double the total space in the list */
1220:     if (current_space->local_remaining<nnz) {
1221:       PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);
1222:       nspacedouble++;
1223:     }

1225:     /* Copy data into free space, and zero out denserows */
1226:     PetscLLCondensedClean(aN,nnz,current_space->array,lnk,lnkbt);

1228:     current_space->array           += nnz;
1229:     current_space->local_used      += nnz;
1230:     current_space->local_remaining -= nnz;

1232:     coi[i+1] = coi[i] + nnz;
1233:   }

1235:   PetscMalloc1(coi[pon]+1,&coj);
1236:   PetscFreeSpaceContiguous(&free_space,coj);

1238:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1239:   if (afill_tmp > afill) afill = afill_tmp;

1241:   /* send j-array (coj) of Co to other processors */
1242:   /*----------------------------------------------*/
1243:   /* determine row ownership */
1244:   PetscNew(&merge);
1245:   PetscLayoutCreate(comm,&merge->rowmap);

1247:   merge->rowmap->n  = pn;
1248:   merge->rowmap->bs = 1;

1250:   PetscLayoutSetUp(merge->rowmap);
1251:   owners = merge->rowmap->range;

1253:   /* determine the number of messages to send, their lengths */
1254:   PetscCalloc1(size,&len_si);
1255:   PetscMalloc1(size,&merge->len_s);

1257:   len_s        = merge->len_s;
1258:   merge->nsend = 0;

1260:   PetscMalloc1(size+2,&owners_co);
1261:   PetscMemzero(len_s,size*sizeof(PetscMPIInt));

1263:   proc = 0;
1264:   for (i=0; i<pon; i++) {
1265:     while (prmap[i] >= owners[proc+1]) proc++;
1266:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1267:     len_s[proc] += coi[i+1] - coi[i];
1268:   }

1270:   len          = 0; /* max length of buf_si[] */
1271:   owners_co[0] = 0;
1272:   for (proc=0; proc<size; proc++) {
1273:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1274:     if (len_si[proc]) {
1275:       merge->nsend++;
1276:       len_si[proc] = 2*(len_si[proc] + 1);
1277:       len         += len_si[proc];
1278:     }
1279:   }

1281:   /* determine the number and length of messages to receive for coi and coj  */
1282:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
1283:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

1285:   /* post the Irecv and Isend of coj */
1286:   PetscCommGetNewTag(comm,&tagj);
1287:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
1288:   PetscMalloc1(merge->nsend+1,&swaits);
1289:   for (proc=0, k=0; proc<size; proc++) {
1290:     if (!len_s[proc]) continue;
1291:     i    = owners_co[proc];
1292:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1293:     k++;
1294:   }

1296:   /* receives and sends of coj are complete */
1297:   PetscMalloc1(size,&sstatus);
1298:   for (i=0; i<merge->nrecv; i++) {
1299:     PetscMPIInt icompleted;
1300:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1301:   }
1302:   PetscFree(rwaits);
1303:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

1305:   /* send and recv coi */
1306:   /*-------------------*/
1307:   PetscCommGetNewTag(comm,&tagi);
1308:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
1309:   PetscMalloc1(len+1,&buf_s);
1310:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1311:   for (proc=0,k=0; proc<size; proc++) {
1312:     if (!len_s[proc]) continue;
1313:     /* form outgoing message for i-structure:
1314:          buf_si[0]:                 nrows to be sent
1315:                [1:nrows]:           row index (global)
1316:                [nrows+1:2*nrows+1]: i-structure index
1317:     */
1318:     /*-------------------------------------------*/
1319:     nrows       = len_si[proc]/2 - 1;
1320:     buf_si_i    = buf_si + nrows+1;
1321:     buf_si[0]   = nrows;
1322:     buf_si_i[0] = 0;
1323:     nrows       = 0;
1324:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1325:       nzi               = coi[i+1] - coi[i];
1326:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi; /* i-structure */
1327:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1328:       nrows++;
1329:     }
1330:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1331:     k++;
1332:     buf_si += len_si[proc];
1333:   }
1334:   i = merge->nrecv;
1335:   while (i--) {
1336:     PetscMPIInt icompleted;
1337:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1338:   }
1339:   PetscFree(rwaits);
1340:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1341:   PetscFree(len_si);
1342:   PetscFree(len_ri);
1343:   PetscFree(swaits);
1344:   PetscFree(sstatus);
1345:   PetscFree(buf_s);

1347:   /* compute the local portion of C (mpi mat) */
1348:   /*------------------------------------------*/
1349:   /* allocate bi array and free space for accumulating nonzero column info */
1350:   PetscMalloc1(pn+1,&bi);
1351:   bi[0] = 0;

1353:   /* set initial free space to be fill*(nnz(P) + nnz(A)) */
1354:   nnz           = fill*(pdti[pn] + poti[pon] + ai[am]);
1355:   PetscFreeSpaceGet(nnz,&free_space);
1356:   current_space = free_space;

1358:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1359:   for (k=0; k<merge->nrecv; k++) {
1360:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1361:     nrows       = *buf_ri_k[k];
1362:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1363:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1364:   }

1366:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
1367:   rmax = 0;
1368:   for (i=0; i<pn; i++) {
1369:     /* add pdt[i,:]*AP into lnk */
1370:     pnz = pdti[i+1] - pdti[i];
1371:     ptJ = pdtj + pdti[i];
1372:     for (j=0; j<pnz; j++) {
1373:       row  = ptJ[j];  /* row of AP == col of Pt */
1374:       anz  = ai[row+1] - ai[row];
1375:       Jptr = aj + ai[row];
1376:       /* add non-zero cols of AP into the sorted linked list lnk */
1377:       PetscLLCondensedAddSorted(anz,Jptr,lnk,lnkbt);
1378:     }

1380:     /* add received col data into lnk */
1381:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1382:       if (i == *nextrow[k]) { /* i-th row */
1383:         nzi  = *(nextci[k]+1) - *nextci[k];
1384:         Jptr = buf_rj[k] + *nextci[k];
1385:         PetscLLCondensedAddSorted(nzi,Jptr,lnk,lnkbt);
1386:         nextrow[k]++; nextci[k]++;
1387:       }
1388:     }
1389:     nnz = lnk[0];

1391:     /* if free space is not available, make more free space */
1392:     if (current_space->local_remaining<nnz) {
1393:       PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);
1394:       nspacedouble++;
1395:     }
1396:     /* copy data into free space, then initialize lnk */
1397:     PetscLLCondensedClean(aN,nnz,current_space->array,lnk,lnkbt);
1398:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

1400:     current_space->array           += nnz;
1401:     current_space->local_used      += nnz;
1402:     current_space->local_remaining -= nnz;

1404:     bi[i+1] = bi[i] + nnz;
1405:     if (nnz > rmax) rmax = nnz;
1406:   }
1407:   PetscFree3(buf_ri_k,nextrow,nextci);

1409:   PetscMalloc1(bi[pn]+1,&bj);
1410:   PetscFreeSpaceContiguous(&free_space,bj);

1412:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
1413:   if (afill_tmp > afill) afill = afill_tmp;
1414:   PetscLLCondensedDestroy(lnk,lnkbt);
1415:   MatDestroy(&POt);
1416:   MatDestroy(&PDt);

1418:   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
1419:   /*----------------------------------------------------------------------------------*/
1420:   PetscCalloc1(rmax+1,&vals);

1422:   MatCreate(comm,&Cmpi);
1423:   MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
1424:   MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
1425:   MatSetType(Cmpi,MATMPIAIJ);
1426:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
1427:   MatPreallocateFinalize(dnz,onz);
1428:   MatSetBlockSize(Cmpi,1);
1429:   for (i=0; i<pn; i++) {
1430:     row  = i + rstart;
1431:     nnz  = bi[i+1] - bi[i];
1432:     Jptr = bj + bi[i];
1433:     MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);
1434:   }
1435:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
1436:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
1437:   PetscFree(vals);

1439:   merge->bi        = bi;
1440:   merge->bj        = bj;
1441:   merge->coi       = coi;
1442:   merge->coj       = coj;
1443:   merge->buf_ri    = buf_ri;
1444:   merge->buf_rj    = buf_rj;
1445:   merge->owners_co = owners_co;
1446:   merge->destroy   = Cmpi->ops->destroy;
1447:   merge->duplicate = Cmpi->ops->duplicate;

1449:   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1450:   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
1451:   Cmpi->ops->duplicate               = MatDuplicate_MPIAIJ_MatPtAP;

1453:   /* attach the supporting struct to Cmpi for reuse */
1454:   c           = (Mat_MPIAIJ*)Cmpi->data;
1455:   c->ptap     = ptap;
1456:   ptap->api   = NULL;
1457:   ptap->apj   = NULL;
1458:   ptap->merge = merge;
1459:   ptap->rmax  = rmax;

1461:   *C = Cmpi;
1462: #if defined(PETSC_USE_INFO)
1463:   if (bi[pn] != 0) {
1464:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
1465:     PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
1466:   } else {
1467:     PetscInfo(Cmpi,"Empty matrix product\n");
1468:   }
1469: #endif
1470:   return(0);
1471: }

1475: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P,Mat A,Mat C)
1476: {
1477:   PetscErrorCode      ierr;
1478:   Mat_Merge_SeqsToMPI *merge;
1479:   Mat_MPIAIJ          *p =(Mat_MPIAIJ*)P->data,*c=(Mat_MPIAIJ*)C->data;
1480:   Mat_SeqAIJ          *pd=(Mat_SeqAIJ*)(p->A)->data,*po=(Mat_SeqAIJ*)(p->B)->data;
1481:   Mat_PtAPMPI         *ptap;
1482:   PetscInt            *adj;
1483:   PetscInt            i,j,k,anz,pnz,row,*cj,nexta;
1484:   MatScalar           *ada,*ca,valtmp;
1485:   PetscInt            am  =A->rmap->n,cm=C->rmap->n,pon=(p->B)->cmap->n;
1486:   MPI_Comm            comm;
1487:   PetscMPIInt         size,rank,taga,*len_s;
1488:   PetscInt            *owners,proc,nrows,**buf_ri_k,**nextrow,**nextci;
1489:   PetscInt            **buf_ri,**buf_rj;
1490:   PetscInt            cnz=0,*bj_i,*bi,*bj,bnz,nextcj;  /* bi,bj,ba: local array of C(mpi mat) */
1491:   MPI_Request         *s_waits,*r_waits;
1492:   MPI_Status          *status;
1493:   MatScalar           **abuf_r,*ba_i,*pA,*coa,*ba;
1494:   PetscInt            *ai,*aj,*coi,*coj;
1495:   PetscInt            *poJ,*pdJ;
1496:   Mat                 A_loc;
1497:   Mat_SeqAIJ          *a_loc;

1500:   PetscObjectGetComm((PetscObject)C,&comm);
1501:   MPI_Comm_size(comm,&size);
1502:   MPI_Comm_rank(comm,&rank);

1504:   ptap  = c->ptap;
1505:   merge = ptap->merge;

1507:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1508:   /*------------------------------------------*/
1509:   /* get data from symbolic products */
1510:   coi    = merge->coi; coj = merge->coj;
1511:   PetscCalloc1(coi[pon]+1,&coa);
1512:   bi     = merge->bi; bj = merge->bj;
1513:   owners = merge->rowmap->range;
1514:   PetscCalloc1(bi[cm]+1,&ba);

1516:   /* get A_loc by taking all local rows of A */
1517:   A_loc = ptap->A_loc;
1518:   MatMPIAIJGetLocalMat(A,MAT_REUSE_MATRIX,&A_loc);
1519:   a_loc = (Mat_SeqAIJ*)(A_loc)->data;
1520:   ai    = a_loc->i;
1521:   aj    = a_loc->j;

1523:   for (i=0; i<am; i++) {
1524:     anz = ai[i+1] - ai[i];
1525:     adj = aj + ai[i];
1526:     ada = a_loc->a + ai[i];

1528:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1529:     /*-------------------------------------------------------------*/
1530:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1531:     pnz = po->i[i+1] - po->i[i];
1532:     poJ = po->j + po->i[i];
1533:     pA  = po->a + po->i[i];
1534:     for (j=0; j<pnz; j++) {
1535:       row = poJ[j];
1536:       cj  = coj + coi[row];
1537:       ca  = coa + coi[row];
1538:       /* perform sparse axpy */
1539:       nexta  = 0;
1540:       valtmp = pA[j];
1541:       for (k=0; nexta<anz; k++) {
1542:         if (cj[k] == adj[nexta]) {
1543:           ca[k] += valtmp*ada[nexta];
1544:           nexta++;
1545:         }
1546:       }
1547:       PetscLogFlops(2.0*anz);
1548:     }

1550:     /* put the value into Cd (diagonal part) */
1551:     pnz = pd->i[i+1] - pd->i[i];
1552:     pdJ = pd->j + pd->i[i];
1553:     pA  = pd->a + pd->i[i];
1554:     for (j=0; j<pnz; j++) {
1555:       row = pdJ[j];
1556:       cj  = bj + bi[row];
1557:       ca  = ba + bi[row];
1558:       /* perform sparse axpy */
1559:       nexta  = 0;
1560:       valtmp = pA[j];
1561:       for (k=0; nexta<anz; k++) {
1562:         if (cj[k] == adj[nexta]) {
1563:           ca[k] += valtmp*ada[nexta];
1564:           nexta++;
1565:         }
1566:       }
1567:       PetscLogFlops(2.0*anz);
1568:     }
1569:   }

1571:   /* 3) send and recv matrix values coa */
1572:   /*------------------------------------*/
1573:   buf_ri = merge->buf_ri;
1574:   buf_rj = merge->buf_rj;
1575:   len_s  = merge->len_s;
1576:   PetscCommGetNewTag(comm,&taga);
1577:   PetscPostIrecvScalar(comm,taga,merge->nrecv,merge->id_r,merge->len_r,&abuf_r,&r_waits);

1579:   PetscMalloc2(merge->nsend+1,&s_waits,size,&status);
1580:   for (proc=0,k=0; proc<size; proc++) {
1581:     if (!len_s[proc]) continue;
1582:     i    = merge->owners_co[proc];
1583:     MPI_Isend(coa+coi[i],len_s[proc],MPIU_MATSCALAR,proc,taga,comm,s_waits+k);
1584:     k++;
1585:   }
1586:   if (merge->nrecv) {MPI_Waitall(merge->nrecv,r_waits,status);}
1587:   if (merge->nsend) {MPI_Waitall(merge->nsend,s_waits,status);}

1589:   PetscFree2(s_waits,status);
1590:   PetscFree(r_waits);
1591:   PetscFree(coa);

1593:   /* 4) insert local Cseq and received values into Cmpi */
1594:   /*----------------------------------------------------*/
1595:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1596:   for (k=0; k<merge->nrecv; k++) {
1597:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1598:     nrows       = *(buf_ri_k[k]);
1599:     nextrow[k]  = buf_ri_k[k]+1;  /* next row number of k-th recved i-structure */
1600:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* poins to the next i-structure of k-th recved i-structure  */
1601:   }

1603:   for (i=0; i<cm; i++) {
1604:     row  = owners[rank] + i; /* global row index of C_seq */
1605:     bj_i = bj + bi[i];  /* col indices of the i-th row of C */
1606:     ba_i = ba + bi[i];
1607:     bnz  = bi[i+1] - bi[i];
1608:     /* add received vals into ba */
1609:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1610:       /* i-th row */
1611:       if (i == *nextrow[k]) {
1612:         cnz    = *(nextci[k]+1) - *nextci[k];
1613:         cj     = buf_rj[k] + *(nextci[k]);
1614:         ca     = abuf_r[k] + *(nextci[k]);
1615:         nextcj = 0;
1616:         for (j=0; nextcj<cnz; j++) {
1617:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1618:             ba_i[j] += ca[nextcj++];
1619:           }
1620:         }
1621:         nextrow[k]++; nextci[k]++;
1622:         PetscLogFlops(2.0*cnz);
1623:       }
1624:     }
1625:     MatSetValues(C,1,&row,bnz,bj_i,ba_i,INSERT_VALUES);
1626:   }
1627:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
1628:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);

1630:   PetscFree(ba);
1631:   PetscFree(abuf_r[0]);
1632:   PetscFree(abuf_r);
1633:   PetscFree3(buf_ri_k,nextrow,nextci);
1634:   return(0);
1635: }

1637: PetscErrorCode MatDuplicate_MPIAIJ_MatPtAP(Mat, MatDuplicateOption,Mat*);
1638: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ();
1639:    differ from MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable in using LLCondensedCreate_Scalable() */
1642: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P,Mat A,PetscReal fill,Mat *C)
1643: {
1644:   PetscErrorCode      ierr;
1645:   Mat                 Cmpi,A_loc,POt,PDt;
1646:   Mat_PtAPMPI         *ptap;
1647:   PetscFreeSpaceList  free_space=NULL,current_space=NULL;
1648:   Mat_MPIAIJ          *p        =(Mat_MPIAIJ*)P->data,*c;
1649:   PetscInt            *pdti,*pdtj,*poti,*potj,*ptJ;
1650:   PetscInt            nnz;
1651:   PetscInt            *lnk,*owners_co,*coi,*coj,i,k,pnz,row;
1652:   PetscInt            am  =A->rmap->n,pn=P->cmap->n;
1653:   MPI_Comm            comm;
1654:   PetscMPIInt         size,rank,tagi,tagj,*len_si,*len_s,*len_ri;
1655:   PetscInt            **buf_rj,**buf_ri,**buf_ri_k;
1656:   PetscInt            len,proc,*dnz,*onz,*owners;
1657:   PetscInt            nzi,*bi,*bj;
1658:   PetscInt            nrows,*buf_s,*buf_si,*buf_si_i,**nextrow,**nextci;
1659:   MPI_Request         *swaits,*rwaits;
1660:   MPI_Status          *sstatus,rstatus;
1661:   Mat_Merge_SeqsToMPI *merge;
1662:   PetscInt            *ai,*aj,*Jptr,anz,*prmap=p->garray,pon,nspacedouble=0,j;
1663:   PetscReal           afill  =1.0,afill_tmp;
1664:   PetscInt            rstart = P->cmap->rstart,rmax,aN=A->cmap->N,Crmax;
1665:   PetscScalar         *vals;
1666:   Mat_SeqAIJ          *a_loc, *pdt,*pot;

1669:   PetscObjectGetComm((PetscObject)A,&comm);
1670:   /* check if matrix local sizes are compatible */
1671:   if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) {
1672:     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);
1673:   }

1675:   MPI_Comm_size(comm,&size);
1676:   MPI_Comm_rank(comm,&rank);

1678:   /* create struct Mat_PtAPMPI and attached it to C later */
1679:   PetscNew(&ptap);

1681:   /* get A_loc by taking all local rows of A */
1682:   MatMPIAIJGetLocalMat(A,MAT_INITIAL_MATRIX,&A_loc);

1684:   ptap->A_loc = A_loc;
1685:   a_loc       = (Mat_SeqAIJ*)(A_loc)->data;
1686:   ai          = a_loc->i;
1687:   aj          = a_loc->j;

1689:   /* determine symbolic Co=(p->B)^T*A - send to others */
1690:   /*----------------------------------------------------*/
1691:   MatTransposeSymbolic_SeqAIJ(p->A,&PDt);
1692:   pdt  = (Mat_SeqAIJ*)PDt->data;
1693:   pdti = pdt->i; pdtj = pdt->j;

1695:   MatTransposeSymbolic_SeqAIJ(p->B,&POt);
1696:   pot  = (Mat_SeqAIJ*)POt->data;
1697:   poti = pot->i; potj = pot->j;

1699:   /* then, compute symbolic Co = (p->B)^T*A */
1700:   pon    = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1701:                          >= (num of nonzero rows of C_seq) - pn */
1702:   PetscMalloc1(pon+1,&coi);
1703:   coi[0] = 0;

1705:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1706:   nnz           = fill*(poti[pon] + ai[am]);
1707:   PetscFreeSpaceGet(nnz,&free_space);
1708:   current_space = free_space;

1710:   /* create and initialize a linked list */
1711:   i     = PetscMax(pdt->rmax,pot->rmax);
1712:   Crmax = i*a_loc->rmax*size; /* non-scalable! */
1713:   if (!Crmax || Crmax > aN) Crmax = aN;
1714:   PetscLLCondensedCreate_Scalable(Crmax,&lnk);

1716:   for (i=0; i<pon; i++) {
1717:     pnz = poti[i+1] - poti[i];
1718:     ptJ = potj + poti[i];
1719:     for (j=0; j<pnz; j++) {
1720:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1721:       anz  = ai[row+1] - ai[row];
1722:       Jptr = aj + ai[row];
1723:       /* add non-zero cols of AP into the sorted linked list lnk */
1724:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1725:     }
1726:     nnz = lnk[0];

1728:     /* If free space is not available, double the total space in the list */
1729:     if (current_space->local_remaining<nnz) {
1730:       PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);
1731:       nspacedouble++;
1732:     }

1734:     /* Copy data into free space, and zero out denserows */
1735:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);

1737:     current_space->array           += nnz;
1738:     current_space->local_used      += nnz;
1739:     current_space->local_remaining -= nnz;

1741:     coi[i+1] = coi[i] + nnz;
1742:   }

1744:   PetscMalloc1(coi[pon]+1,&coj);
1745:   PetscFreeSpaceContiguous(&free_space,coj);

1747:   afill_tmp = (PetscReal)coi[pon]/(poti[pon] + ai[am]+1);
1748:   if (afill_tmp > afill) afill = afill_tmp;

1750:   /* send j-array (coj) of Co to other processors */
1751:   /*----------------------------------------------*/
1752:   /* determine row ownership */
1753:   PetscNew(&merge);
1754:   PetscLayoutCreate(comm,&merge->rowmap);

1756:   merge->rowmap->n  = pn;
1757:   merge->rowmap->bs = 1;

1759:   PetscLayoutSetUp(merge->rowmap);
1760:   owners = merge->rowmap->range;

1762:   /* determine the number of messages to send, their lengths */
1763:   PetscCalloc1(size,&len_si);
1764:   PetscMalloc1(size,&merge->len_s);

1766:   len_s        = merge->len_s;
1767:   merge->nsend = 0;

1769:   PetscMalloc1(size+2,&owners_co);
1770:   PetscMemzero(len_s,size*sizeof(PetscMPIInt));

1772:   proc = 0;
1773:   for (i=0; i<pon; i++) {
1774:     while (prmap[i] >= owners[proc+1]) proc++;
1775:     len_si[proc]++;  /* num of rows in Co to be sent to [proc] */
1776:     len_s[proc] += coi[i+1] - coi[i];
1777:   }

1779:   len          = 0; /* max length of buf_si[] */
1780:   owners_co[0] = 0;
1781:   for (proc=0; proc<size; proc++) {
1782:     owners_co[proc+1] = owners_co[proc] + len_si[proc];
1783:     if (len_si[proc]) {
1784:       merge->nsend++;
1785:       len_si[proc] = 2*(len_si[proc] + 1);
1786:       len         += len_si[proc];
1787:     }
1788:   }

1790:   /* determine the number and length of messages to receive for coi and coj  */
1791:   PetscGatherNumberOfMessages(comm,NULL,len_s,&merge->nrecv);
1792:   PetscGatherMessageLengths2(comm,merge->nsend,merge->nrecv,len_s,len_si,&merge->id_r,&merge->len_r,&len_ri);

1794:   /* post the Irecv and Isend of coj */
1795:   PetscCommGetNewTag(comm,&tagj);
1796:   PetscPostIrecvInt(comm,tagj,merge->nrecv,merge->id_r,merge->len_r,&buf_rj,&rwaits);
1797:   PetscMalloc1(merge->nsend+1,&swaits);
1798:   for (proc=0, k=0; proc<size; proc++) {
1799:     if (!len_s[proc]) continue;
1800:     i    = owners_co[proc];
1801:     MPI_Isend(coj+coi[i],len_s[proc],MPIU_INT,proc,tagj,comm,swaits+k);
1802:     k++;
1803:   }

1805:   /* receives and sends of coj are complete */
1806:   PetscMalloc1(size,&sstatus);
1807:   for (i=0; i<merge->nrecv; i++) {
1808:     PetscMPIInt icompleted;
1809:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1810:   }
1811:   PetscFree(rwaits);
1812:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}

1814:   /* send and recv coi */
1815:   /*-------------------*/
1816:   PetscCommGetNewTag(comm,&tagi);
1817:   PetscPostIrecvInt(comm,tagi,merge->nrecv,merge->id_r,len_ri,&buf_ri,&rwaits);
1818:   PetscMalloc1(len+1,&buf_s);
1819:   buf_si = buf_s;  /* points to the beginning of k-th msg to be sent */
1820:   for (proc=0,k=0; proc<size; proc++) {
1821:     if (!len_s[proc]) continue;
1822:     /* form outgoing message for i-structure:
1823:          buf_si[0]:                 nrows to be sent
1824:                [1:nrows]:           row index (global)
1825:                [nrows+1:2*nrows+1]: i-structure index
1826:     */
1827:     /*-------------------------------------------*/
1828:     nrows       = len_si[proc]/2 - 1;
1829:     buf_si_i    = buf_si + nrows+1;
1830:     buf_si[0]   = nrows;
1831:     buf_si_i[0] = 0;
1832:     nrows       = 0;
1833:     for (i=owners_co[proc]; i<owners_co[proc+1]; i++) {
1834:       nzi               = coi[i+1] - coi[i];
1835:       buf_si_i[nrows+1] = buf_si_i[nrows] + nzi;  /* i-structure */
1836:       buf_si[nrows+1]   = prmap[i] -owners[proc]; /* local row index */
1837:       nrows++;
1838:     }
1839:     MPI_Isend(buf_si,len_si[proc],MPIU_INT,proc,tagi,comm,swaits+k);
1840:     k++;
1841:     buf_si += len_si[proc];
1842:   }
1843:   i = merge->nrecv;
1844:   while (i--) {
1845:     PetscMPIInt icompleted;
1846:     MPI_Waitany(merge->nrecv,rwaits,&icompleted,&rstatus);
1847:   }
1848:   PetscFree(rwaits);
1849:   if (merge->nsend) {MPI_Waitall(merge->nsend,swaits,sstatus);}
1850:   PetscFree(len_si);
1851:   PetscFree(len_ri);
1852:   PetscFree(swaits);
1853:   PetscFree(sstatus);
1854:   PetscFree(buf_s);

1856:   /* compute the local portion of C (mpi mat) */
1857:   /*------------------------------------------*/
1858:   /* allocate bi array and free space for accumulating nonzero column info */
1859:   PetscMalloc1(pn+1,&bi);
1860:   bi[0] = 0;

1862:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1863:   nnz           = fill*(pdti[pn] + poti[pon] + ai[am]);
1864:   PetscFreeSpaceGet(nnz,&free_space);
1865:   current_space = free_space;

1867:   PetscMalloc3(merge->nrecv,&buf_ri_k,merge->nrecv,&nextrow,merge->nrecv,&nextci);
1868:   for (k=0; k<merge->nrecv; k++) {
1869:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1870:     nrows       = *buf_ri_k[k];
1871:     nextrow[k]  = buf_ri_k[k] + 1;  /* next row number of k-th recved i-structure */
1872:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recieved i-structure  */
1873:   }

1875:   MatPreallocateInitialize(comm,pn,A->cmap->n,dnz,onz);
1876:   rmax = 0;
1877:   for (i=0; i<pn; i++) {
1878:     /* add pdt[i,:]*AP into lnk */
1879:     pnz = pdti[i+1] - pdti[i];
1880:     ptJ = pdtj + pdti[i];
1881:     for (j=0; j<pnz; j++) {
1882:       row  = ptJ[j];  /* row of AP == col of Pt */
1883:       anz  = ai[row+1] - ai[row];
1884:       Jptr = aj + ai[row];
1885:       /* add non-zero cols of AP into the sorted linked list lnk */
1886:       PetscLLCondensedAddSorted_Scalable(anz,Jptr,lnk);
1887:     }

1889:     /* add received col data into lnk */
1890:     for (k=0; k<merge->nrecv; k++) { /* k-th received message */
1891:       if (i == *nextrow[k]) { /* i-th row */
1892:         nzi  = *(nextci[k]+1) - *nextci[k];
1893:         Jptr = buf_rj[k] + *nextci[k];
1894:         PetscLLCondensedAddSorted_Scalable(nzi,Jptr,lnk);
1895:         nextrow[k]++; nextci[k]++;
1896:       }
1897:     }
1898:     nnz = lnk[0];

1900:     /* if free space is not available, make more free space */
1901:     if (current_space->local_remaining<nnz) {
1902:       PetscFreeSpaceGet(nnz+current_space->total_array_size,&current_space);
1903:       nspacedouble++;
1904:     }
1905:     /* copy data into free space, then initialize lnk */
1906:     PetscLLCondensedClean_Scalable(nnz,current_space->array,lnk);
1907:     MatPreallocateSet(i+owners[rank],nnz,current_space->array,dnz,onz);

1909:     current_space->array           += nnz;
1910:     current_space->local_used      += nnz;
1911:     current_space->local_remaining -= nnz;

1913:     bi[i+1] = bi[i] + nnz;
1914:     if (nnz > rmax) rmax = nnz;
1915:   }
1916:   PetscFree3(buf_ri_k,nextrow,nextci);

1918:   PetscMalloc1(bi[pn]+1,&bj);
1919:   PetscFreeSpaceContiguous(&free_space,bj);
1920:   afill_tmp = (PetscReal)bi[pn]/(pdti[pn] + poti[pon] + ai[am]+1);
1921:   if (afill_tmp > afill) afill = afill_tmp;
1922:   PetscLLCondensedDestroy_Scalable(lnk);
1923:   MatDestroy(&POt);
1924:   MatDestroy(&PDt);

1926:   /* create symbolic parallel matrix Cmpi - why cannot be assembled in Numeric part   */
1927:   /*----------------------------------------------------------------------------------*/
1928:   PetscCalloc1(rmax+1,&vals);

1930:   MatCreate(comm,&Cmpi);
1931:   MatSetSizes(Cmpi,pn,A->cmap->n,PETSC_DETERMINE,PETSC_DETERMINE);
1932:   MatSetBlockSizes(Cmpi,PetscAbs(P->cmap->bs),PetscAbs(A->cmap->bs));
1933:   MatSetType(Cmpi,MATMPIAIJ);
1934:   MatMPIAIJSetPreallocation(Cmpi,0,dnz,0,onz);
1935:   MatPreallocateFinalize(dnz,onz);
1936:   MatSetBlockSize(Cmpi,1);
1937:   for (i=0; i<pn; i++) {
1938:     row  = i + rstart;
1939:     nnz  = bi[i+1] - bi[i];
1940:     Jptr = bj + bi[i];
1941:     MatSetValues(Cmpi,1,&row,nnz,Jptr,vals,INSERT_VALUES);
1942:   }
1943:   MatAssemblyBegin(Cmpi,MAT_FINAL_ASSEMBLY);
1944:   MatAssemblyEnd(Cmpi,MAT_FINAL_ASSEMBLY);
1945:   PetscFree(vals);

1947:   merge->bi        = bi;
1948:   merge->bj        = bj;
1949:   merge->coi       = coi;
1950:   merge->coj       = coj;
1951:   merge->buf_ri    = buf_ri;
1952:   merge->buf_rj    = buf_rj;
1953:   merge->owners_co = owners_co;
1954:   merge->destroy   = Cmpi->ops->destroy;
1955:   merge->duplicate = Cmpi->ops->duplicate;

1957:   Cmpi->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;
1958:   Cmpi->ops->destroy                 = MatDestroy_MPIAIJ_PtAP;
1959:   Cmpi->ops->duplicate               = MatDuplicate_MPIAIJ_MatPtAP;

1961:   /* attach the supporting struct to Cmpi for reuse */
1962:   c = (Mat_MPIAIJ*)Cmpi->data;

1964:   c->ptap     = ptap;
1965:   ptap->api   = NULL;
1966:   ptap->apj   = NULL;
1967:   ptap->merge = merge;
1968:   ptap->rmax  = rmax;
1969:   ptap->apa   = NULL;

1971:   *C = Cmpi;
1972: #if defined(PETSC_USE_INFO)
1973:   if (bi[pn] != 0) {
1974:     PetscInfo3(Cmpi,"Reallocs %D; Fill ratio: given %g needed %g.\n",nspacedouble,(double)fill,(double)afill);
1975:     PetscInfo1(Cmpi,"Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n",(double)afill);
1976:   } else {
1977:     PetscInfo(Cmpi,"Empty matrix product\n");
1978:   }
1979: #endif
1980:   return(0);
1981: }