Actual source code: mpimatmatmult.c

  1: /*
  2:   Defines matrix-matrix product routines for pairs of MPIAIJ matrices
  3:           C = A * B
  4: */
  5: #include <../src/mat/impls/aij/seq/aij.h>
  6: #include <../src/mat/utils/freespace.h>
  7: #include <../src/mat/impls/aij/mpi/mpiaij.h>
  8: #include <petscbt.h>
  9: #include <../src/mat/impls/dense/mpi/mpidense.h>
 10: #include <petsc/private/vecimpl.h>
 11: #include <petsc/private/sfimpl.h>

 13: #if PetscDefined(HAVE_HYPRE)
 14: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat, Mat, PetscReal, Mat);
 15: #endif

 17: PETSC_INTERN PetscErrorCode MatProductSymbolic_ABt_MPIAIJ_MPIAIJ(Mat C)
 18: {
 19:   Mat_Product *product = C->product;
 20:   Mat          B       = product->B;

 22:   PetscFunctionBegin;
 23:   PetscCall(MatTranspose(B, MAT_INITIAL_MATRIX, &product->B));
 24:   PetscCall(MatDestroy(&B));
 25:   PetscCall(MatProductSymbolic_AB_MPIAIJ_MPIAIJ(C));
 26:   PetscFunctionReturn(PETSC_SUCCESS);
 27: }

 29: PETSC_INTERN PetscErrorCode MatProductSymbolic_AB_MPIAIJ_MPIAIJ(Mat C)
 30: {
 31:   Mat_Product        *product = C->product;
 32:   Mat                 A = product->A, B = product->B;
 33:   MatProductAlgorithm alg  = product->alg;
 34:   PetscReal           fill = product->fill;
 35:   PetscBool           flg;

 37:   PetscFunctionBegin;
 38:   /* scalable */
 39:   PetscCall(PetscStrcmp(alg, "scalable", &flg));
 40:   if (flg) {
 41:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
 42:     PetscFunctionReturn(PETSC_SUCCESS);
 43:   }

 45:   /* nonscalable */
 46:   PetscCall(PetscStrcmp(alg, "nonscalable", &flg));
 47:   if (flg) {
 48:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
 49:     PetscFunctionReturn(PETSC_SUCCESS);
 50:   }

 52:   /* seqmpi */
 53:   PetscCall(PetscStrcmp(alg, "seqmpi", &flg));
 54:   if (flg) {
 55:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(A, B, fill, C));
 56:     PetscFunctionReturn(PETSC_SUCCESS);
 57:   }

 59:   /* backend general code */
 60:   PetscCall(PetscStrcmp(alg, "backend", &flg));
 61:   if (flg) {
 62:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
 63:     PetscFunctionReturn(PETSC_SUCCESS);
 64:   }

 66: #if PetscDefined(HAVE_HYPRE)
 67:   PetscCall(PetscStrcmp(alg, "hypre", &flg));
 68:   if (flg) {
 69:     PetscCall(MatMatMultSymbolic_AIJ_AIJ_wHYPRE(A, B, fill, C));
 70:     PetscFunctionReturn(PETSC_SUCCESS);
 71:   }
 72: #endif
 73:   SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_SUP, "Mat Product Algorithm is not supported");
 74: }

 76: PetscErrorCode MatProductCtxDestroy_MPIAIJ_MatMatMult(PetscCtxRt data)
 77: {
 78:   MatProductCtx_APMPI *ptap = *(MatProductCtx_APMPI **)data;

 80:   PetscFunctionBegin;
 81:   PetscCall(PetscFree2(ptap->startsj_s, ptap->startsj_r));
 82:   PetscCall(PetscFree(ptap->bufa));
 83:   PetscCall(MatDestroy(&ptap->P_loc));
 84:   PetscCall(MatDestroy(&ptap->P_oth));
 85:   PetscCall(MatDestroy(&ptap->Pt));
 86:   PetscCall(PetscFree(ptap->api));
 87:   PetscCall(PetscFree(ptap->apj));
 88:   PetscCall(PetscFree(ptap->apa));
 89:   PetscCall(PetscFree(ptap));
 90:   PetscFunctionReturn(PETSC_SUCCESS);
 91: }

 93: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat A, Mat P, Mat C)
 94: {
 95:   Mat_MPIAIJ          *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
 96:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
 97:   Mat_SeqAIJ          *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
 98:   PetscScalar         *cda, *coa;
 99:   Mat_SeqAIJ          *p_loc, *p_oth;
100:   PetscScalar         *apa, *ca;
101:   PetscInt             cm = C->rmap->n;
102:   MatProductCtx_APMPI *ptap;
103:   PetscInt            *api, *apj, *apJ, i, k;
104:   PetscInt             cstart = C->cmap->rstart;
105:   PetscInt             cdnz, conz, k0, k1;
106:   const PetscScalar   *dummy1, *dummy2, *dummy3, *dummy4;
107:   MPI_Comm             comm;
108:   PetscMPIInt          size;

110:   PetscFunctionBegin;
111:   MatCheckProduct(C, 3);
112:   ptap = (MatProductCtx_APMPI *)C->product->data;
113:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
114:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
115:   PetscCallMPI(MPI_Comm_size(comm, &size));
116:   PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");

118:   /* flag CPU mask for C */
119: #if PetscDefined(HAVE_DEVICE)
120:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
121:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
122:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
123: #endif

125:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
126:   /* update numerical values of P_oth and P_loc */
127:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_REUSE_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
128:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_REUSE_MATRIX, &ptap->P_loc));

130:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
131:   /* get data from symbolic products */
132:   p_loc = (Mat_SeqAIJ *)ptap->P_loc->data;
133:   p_oth = NULL;
134:   if (size > 1) p_oth = (Mat_SeqAIJ *)ptap->P_oth->data;

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

139:   api = ptap->api;
140:   apj = ptap->apj;
141:   /* trigger copy to CPU */
142:   PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy1));
143:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy2));
144:   PetscCall(MatSeqAIJGetArrayRead(ptap->P_loc, &dummy3));
145:   if (ptap->P_oth) PetscCall(MatSeqAIJGetArrayRead(ptap->P_oth, &dummy4));
146:   PetscCall(MatSeqAIJGetArrayWrite(c->A, &cda));
147:   PetscCall(MatSeqAIJGetArrayWrite(c->B, &coa));
148:   for (i = 0; i < cm; i++) {
149:     /* compute apa = A[i,:]*P */
150:     AProw_nonscalable(i, ad, ao, p_loc, p_oth, apa);

152:     /* set values in C */
153:     apJ  = PetscSafePointerPlusOffset(apj, api[i]);
154:     cdnz = cd->i[i + 1] - cd->i[i];
155:     conz = co->i[i + 1] - co->i[i];

157:     /* 1st off-diagonal part of C */
158:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
159:     k  = 0;
160:     for (k0 = 0; k0 < conz; k0++) {
161:       if (apJ[k] >= cstart) break;
162:       ca[k0]        = apa[apJ[k]];
163:       apa[apJ[k++]] = 0.0;
164:     }

166:     /* diagonal part of C */
167:     ca = PetscSafePointerPlusOffset(cda, cd->i[i]);
168:     for (k1 = 0; k1 < cdnz; k1++) {
169:       ca[k1]        = apa[apJ[k]];
170:       apa[apJ[k++]] = 0.0;
171:     }

173:     /* 2nd off-diagonal part of C */
174:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
175:     for (; k0 < conz; k0++) {
176:       ca[k0]        = apa[apJ[k]];
177:       apa[apJ[k++]] = 0.0;
178:     }
179:   }
180:   PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy1));
181:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy2));
182:   PetscCall(MatSeqAIJRestoreArrayRead(ptap->P_loc, &dummy3));
183:   if (ptap->P_oth) PetscCall(MatSeqAIJRestoreArrayRead(ptap->P_oth, &dummy4));
184:   PetscCall(MatSeqAIJRestoreArrayWrite(c->A, &cda));
185:   PetscCall(MatSeqAIJRestoreArrayWrite(c->B, &coa));

187:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
188:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
189:   PetscFunctionReturn(PETSC_SUCCESS);
190: }

192: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A, Mat P, PetscReal fill, Mat C)
193: {
194:   MPI_Comm             comm;
195:   PetscMPIInt          size;
196:   MatProductCtx_APMPI *ptap;
197:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
198:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
199:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
200:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
201:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
202:   PetscInt            *lnk, i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi;
203:   PetscInt             am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n;
204:   PetscBT              lnkbt;
205:   PetscReal            afill;
206:   MatType              mtype;

208:   PetscFunctionBegin;
209:   MatCheckProduct(C, 4);
210:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
211:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
212:   PetscCallMPI(MPI_Comm_size(comm, &size));

214:   /* create struct MatProductCtx_APMPI and attached it to C later */
215:   PetscCall(PetscNew(&ptap));

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

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

223:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
224:   pi_loc = p_loc->i;
225:   pj_loc = p_loc->j;
226:   if (size > 1) {
227:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
228:     pi_oth = p_oth->i;
229:     pj_oth = p_oth->j;
230:   } else {
231:     p_oth  = NULL;
232:     pi_oth = NULL;
233:     pj_oth = NULL;
234:   }

236:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
237:   PetscCall(PetscMalloc1(am + 1, &api));
238:   ptap->api = api;
239:   api[0]    = 0;

241:   /* create and initialize a linked list */
242:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));

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

248:   MatPreallocateBegin(comm, am, pn, dnz, onz);
249:   for (i = 0; i < am; i++) {
250:     /* diagonal portion of A */
251:     nzi = adi[i + 1] - adi[i];
252:     for (j = 0; j < nzi; j++) {
253:       row  = *adj++;
254:       pnz  = pi_loc[row + 1] - pi_loc[row];
255:       Jptr = pj_loc + pi_loc[row];
256:       /* add non-zero cols of P into the sorted linked list lnk */
257:       PetscCall(PetscLLCondensedAddSorted(pnz, Jptr, lnk, lnkbt));
258:     }
259:     /* off-diagonal portion of A */
260:     nzi = aoi[i + 1] - aoi[i];
261:     for (j = 0; j < nzi; j++) {
262:       row  = *aoj++;
263:       pnz  = pi_oth[row + 1] - pi_oth[row];
264:       Jptr = pj_oth + pi_oth[row];
265:       PetscCall(PetscLLCondensedAddSorted(pnz, Jptr, lnk, lnkbt));
266:     }
267:     /* add possible missing diagonal entry */
268:     if (C->force_diagonals) {
269:       j = i + rstart; /* column index */
270:       PetscCall(PetscLLCondensedAddSorted(1, &j, lnk, lnkbt));
271:     }

273:     apnz       = lnk[0];
274:     api[i + 1] = api[i] + apnz;

276:     /* if free space is not available, double the total space in the list */
277:     if (current_space->local_remaining < apnz) {
278:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), &current_space));
279:       nspacedouble++;
280:     }

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

286:     current_space->array += apnz;
287:     current_space->local_used += apnz;
288:     current_space->local_remaining -= apnz;
289:   }

291:   /* Allocate space for apj, initialize apj, and */
292:   /* destroy list of free space and other temporary array(s) */
293:   PetscCall(PetscMalloc1(api[am], &ptap->apj));
294:   apj = ptap->apj;
295:   PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
296:   PetscCall(PetscLLDestroy(lnk, lnkbt));

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

301:   /* set and assemble symbolic parallel matrix C */
302:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
303:   PetscCall(MatSetBlockSizesFromMats(C, A, P));

305:   PetscCall(MatGetType(A, &mtype));
306:   PetscCall(MatSetType(C, mtype));
307:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
308:   MatPreallocateEnd(dnz, onz);

310:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
311:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
312:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
313:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
314:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

316:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
317:   C->ops->productnumeric = MatProductNumeric_AB;

319:   /* attach the supporting struct to C for reuse */
320:   C->product->data    = ptap;
321:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

323:   /* set MatInfo */
324:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
325:   if (afill < 1.0) afill = 1.0;
326:   C->info.mallocs           = nspacedouble;
327:   C->info.fill_ratio_given  = fill;
328:   C->info.fill_ratio_needed = afill;

330:   if (PetscDefined(USE_INFO)) {
331:     if (api[am]) {
332:       PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
333:       PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
334:     } else PetscCall(PetscInfo(C, "Empty matrix product\n"));
335:   }
336:   PetscFunctionReturn(PETSC_SUCCESS);
337: }

339: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat, Mat, PetscReal, Mat);
340: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat, Mat, Mat);

342: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
343: {
344:   Mat_Product *product = C->product;
345:   Mat          A = product->A, B = product->B;

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

351:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
352:   C->ops->productsymbolic = MatProductSymbolic_AB;
353:   PetscFunctionReturn(PETSC_SUCCESS);
354: }

356: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
357: {
358:   Mat_Product *product = C->product;
359:   Mat          A = product->A, B = product->B;

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

365:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
366:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
367:   PetscFunctionReturn(PETSC_SUCCESS);
368: }

370: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
371: {
372:   Mat_Product *product = C->product;

374:   PetscFunctionBegin;
375:   switch (product->type) {
376:   case MATPRODUCT_AB:
377:     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C));
378:     break;
379:   case MATPRODUCT_AtB:
380:     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C));
381:     break;
382:   default:
383:     break;
384:   }
385:   PetscFunctionReturn(PETSC_SUCCESS);
386: }

388: PETSC_INTERN PetscErrorCode MatMPIDenseScatterDestroy_Private(MPIAIJ_MPIDense *contents)
389: {
390:   PetscFunctionBegin;
391:   PetscCall(MatDestroy(&contents->workB));
392:   for (PetscInt i = 0; i < contents->nsends; i++) PetscCallMPI(MPI_Type_free(&contents->stype[i]));
393:   for (PetscInt i = 0; i < contents->nrecvs; i++) PetscCallMPI(MPI_Type_free(&contents->rtype[i]));
394:   PetscCall(PetscFree4(contents->stype, contents->rtype, contents->rwaits, contents->swaits));
395:   PetscFunctionReturn(PETSC_SUCCESS);
396: }

398: static PetscErrorCode MatMPIAIJ_MPIDenseDestroy(PetscCtxRt ctx)
399: {
400:   MPIAIJ_MPIDense *contents = *(MPIAIJ_MPIDense **)ctx;

402:   PetscFunctionBegin;
403:   PetscCall(MatMPIDenseScatterDestroy_Private(contents));
404:   PetscCall(PetscFree(contents));
405:   PetscFunctionReturn(PETSC_SUCCESS);
406: }

408: PETSC_INTERN PetscErrorCode MatMPIDenseScatterSetUp_Private(VecScatter ctx, PetscInt nrows, PetscInt bs, PetscInt Am, Mat B, Mat C, MPIAIJ_MPIDense *contents, PetscInt *batchSize, PetscInt *numBatches)
409: {
410:   PetscInt        Bm = B->rmap->n, BN = B->cmap->N, Bbn, Bbs, numBb;
411:   MPI_Comm        comm;
412:   MPI_Datatype    type1;
413:   const PetscInt *sindices, *sstarts, *rstarts;
414:   PetscMPIInt    *disp;
415:   PetscMPIInt     nsends, nrecvs, nrows_to, nrows_from, bs_mpi;

417:   PetscFunctionBegin;
418:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
419:   PetscCall(MatDenseGetLDA(B, &contents->blda));
420:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE, &nsends, &sstarts, &sindices, NULL, NULL));
421:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE, &nrecvs, &rstarts, NULL, NULL, NULL));

423:   /* Create column block of B and C for memory scalability when BN is too large */
424:   /* Estimate Bbn, column size of Bb */
425:   if (nrows) {
426:     Bbn = 2 * Am * BN / nrows;
427:     if (!Bbn) Bbn = 1;
428:   } else Bbn = BN;
429:   Bbs = B->cmap->bs;
430:   Bbn = Bbn / Bbs * Bbs;
431:   if (Bbn > BN) Bbn = BN;
432:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &Bbn, 1, MPIU_INT, MPI_MAX, comm));

434:   /* Enable runtime option for Bbn */
435:   PetscOptionsBegin(comm, ((PetscObject)C)->prefix, "MatProduct", "Mat");
436:   PetscCall(PetscOptionsDeprecated("-matmatmult_Bbn", "-matproduct_batch_size", "3.25", NULL));
437:   PetscCall(PetscOptionsBoundedInt("-matproduct_batch_size", "Number of dense columns per batch", "MatProduct", Bbn, &Bbn, NULL, 0));
438:   PetscOptionsEnd();
439:   Bbn = PetscMin(Bbn, BN);

441:   if (Bbn > 0 && Bbn < BN) numBb = BN / Bbn;
442:   else numBb = 0;
443:   if (numBb) PetscCall(PetscInfo(C, "Using column batches of size %" PetscInt_FMT " for %" PetscInt_FMT " dense columns\n", Bbn, BN));
444:   /* Create work matrix used to store off processor rows of B needed for local product */
445:   PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nrows, Bbn ? Bbn : BN, NULL, &contents->workB));

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

452:   PetscCall(PetscMalloc1(PetscMax(Bm, 1), &disp));
453:   PetscCall(PetscMPIIntCast(bs, &bs_mpi));
454:   for (PetscMPIInt i = 0; i < nsends; i++) {
455:     PetscCall(PetscMPIIntCast(sstarts[i + 1] - sstarts[i], &nrows_to));
456:     for (PetscInt j = 0; j < nrows_to; j++) PetscCall(PetscMPIIntCast(sindices[sstarts[i] + j] * bs, &disp[j]));
457:     PetscCallMPI(MPI_Type_create_indexed_block(nrows_to, bs_mpi, disp, MPIU_SCALAR, &type1));
458:     PetscCallMPI(MPI_Type_create_resized(type1, 0, contents->blda * sizeof(PetscScalar), &contents->stype[i]));
459:     PetscCallMPI(MPI_Type_commit(&contents->stype[i]));
460:     PetscCallMPI(MPI_Type_free(&type1));
461:   }

463:   for (PetscMPIInt i = 0; i < nrecvs; i++) {
464:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
465:     PetscCall(PetscMPIIntCast((rstarts[i + 1] - rstarts[i]) * bs, &nrows_from));
466:     disp[0] = 0;
467:     PetscCallMPI(MPI_Type_create_indexed_block(1, nrows_from, disp, MPIU_SCALAR, &type1));
468:     PetscCallMPI(MPI_Type_create_resized(type1, 0, nrows * sizeof(PetscScalar), &contents->rtype[i]));
469:     PetscCallMPI(MPI_Type_commit(&contents->rtype[i]));
470:     PetscCallMPI(MPI_Type_free(&type1));
471:   }

473:   PetscCall(PetscFree(disp));
474:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, NULL, NULL));
475:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, NULL, NULL));
476:   if (batchSize) *batchSize = Bbn;
477:   if (numBatches) *numBatches = numBb;
478:   PetscFunctionReturn(PETSC_SUCCESS);
479: }

481: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A, Mat B, PetscReal fill, Mat C)
482: {
483:   Mat_MPIAIJ      *aij = (Mat_MPIAIJ *)A->data;
484:   MPIAIJ_MPIDense *contents;
485:   PetscInt         nz  = aij->B->cmap->n, m, M, n, N;
486:   VecScatter       ctx = aij->Mvctx;
487:   PetscInt         Am = A->rmap->n, BN = B->cmap->N;
488:   PetscBool        cisdense;

490:   PetscFunctionBegin;
491:   MatCheckProduct(C, 4);
492:   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
493:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)C, MATMPIDENSE, &cisdense));
494:   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)B)->type_name));
495:   PetscCall(MatGetLocalSize(C, &m, &n));
496:   PetscCall(MatGetSize(C, &M, &N));
497:   if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) PetscCall(MatSetSizes(C, Am, B->cmap->n, A->rmap->N, BN));
498:   PetscCall(MatSetBlockSizesFromMats(C, A, B));
499:   PetscCall(MatSetUp(C));
500:   PetscCall(PetscNew(&contents));
501:   PetscCall(MatMPIDenseScatterSetUp_Private(ctx, nz, 1, Am, B, C, contents, NULL, NULL));
502:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
503:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
504:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
505:   PetscCall(MatProductClear(aij->A));
506:   PetscCall(MatProductClear(((Mat_MPIDense *)B->data)->A));
507:   PetscCall(MatProductClear(((Mat_MPIDense *)C->data)->A));
508:   PetscCall(MatProductCreateWithMat(aij->A, ((Mat_MPIDense *)B->data)->A, NULL, ((Mat_MPIDense *)C->data)->A));
509:   PetscCall(MatProductSetType(((Mat_MPIDense *)C->data)->A, MATPRODUCT_AB));
510:   PetscCall(MatProductSetFromOptions(((Mat_MPIDense *)C->data)->A));
511:   PetscCall(MatProductSymbolic(((Mat_MPIDense *)C->data)->A));
512:   C->product->data       = contents;
513:   C->product->destroy    = MatMPIAIJ_MPIDenseDestroy;
514:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
515:   PetscFunctionReturn(PETSC_SUCCESS);
516: }

518: PETSC_INTERN PetscErrorCode MatMatMultNumericAdd_SeqAIJ_SeqDense(Mat, Mat, Mat, const PetscBool);

520: /*
521:     Performs an efficient scatter on the rows of B needed by this process; this is
522:     a modification of the VecScatterBegin_() routines.
523: */

525: PETSC_INTERN PetscErrorCode MatMPIDenseScatter_Private(VecScatter ctx, PetscInt nrows, PetscInt bs, Mat workB, MPIAIJ_MPIDense *contents, Mat B, Mat C)
526: {
527:   const PetscScalar *b;
528:   PetscScalar       *rvalues;
529:   const PetscInt    *sindices, *sstarts, *rstarts;
530:   const PetscMPIInt *sprocs, *rprocs;
531:   PetscMPIInt        nsends, nrecvs;
532:   MPI_Comm           comm;
533:   PetscMPIInt        tag = ((PetscObject)ctx)->tag, ncols, nsends_mpi, nrecvs_mpi;
534:   PetscInt           blda;

536:   PetscFunctionBegin;
537:   MatCheckProduct(C, 7);
538:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
539:   PetscCall(PetscMPIIntCast(B->cmap->N, &ncols));
540:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL /*bs*/));
541:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL /*bs*/));
542:   PetscCall(PetscMPIIntCast(nsends, &nsends_mpi));
543:   PetscCall(PetscMPIIntCast(nrecvs, &nrecvs_mpi));
544:   PetscCheck(nrows == workB->rmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of rows of workB %" PetscInt_FMT " not equal to columns of off-diagonal block %" PetscInt_FMT, workB->rmap->n, nrows);

546:   PetscCall(MatDenseGetArrayRead(B, &b));
547:   PetscCall(MatDenseGetLDA(B, &blda));
548:   PetscCheck(blda == contents->blda, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Cannot reuse an input matrix with lda %" PetscInt_FMT " != %" PetscInt_FMT, blda, contents->blda);
549:   PetscCall(MatDenseGetArray(workB, &rvalues));

551:   /* Post recv, use MPI derived data type to save memory */
552:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
553:   for (PetscMPIInt i = 0; i < nrecvs; i++) PetscCallMPI(MPIU_Irecv(rvalues + ((rstarts[i] - rstarts[0]) * bs), ncols, contents->rtype[i], rprocs[i], tag, comm, contents->rwaits + i));
554:   for (PetscMPIInt i = 0; i < nsends; i++) PetscCallMPI(MPIU_Isend(b, ncols, contents->stype[i], sprocs[i], tag, comm, contents->swaits + i));

556:   if (nrecvs) PetscCallMPI(MPI_Waitall(nrecvs_mpi, contents->rwaits, MPI_STATUSES_IGNORE));
557:   if (nsends) PetscCallMPI(MPI_Waitall(nsends_mpi, contents->swaits, MPI_STATUSES_IGNORE));

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

566: static PetscErrorCode MatMPIDenseScatter(Mat A, Mat B, Mat workB, Mat C)
567: {
568:   Mat_MPIAIJ      *aij = (Mat_MPIAIJ *)A->data;
569:   MPIAIJ_MPIDense *contents;

571:   PetscFunctionBegin;
572:   contents = (MPIAIJ_MPIDense *)C->product->data;
573:   PetscCall(MatMPIDenseScatter_Private(aij->Mvctx, aij->B->cmap->n, 1, workB, contents, B, C));
574:   PetscFunctionReturn(PETSC_SUCCESS);
575: }

577: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A, Mat B, Mat C)
578: {
579:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ *)A->data;
580:   Mat_MPIDense    *bdense = (Mat_MPIDense *)B->data;
581:   Mat_MPIDense    *cdense = (Mat_MPIDense *)C->data;
582:   Mat              workB;
583:   MPIAIJ_MPIDense *contents;

585:   PetscFunctionBegin;
586:   MatCheckProduct(C, 3);
587:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
588:   contents = (MPIAIJ_MPIDense *)C->product->data;
589:   /* diagonal block of A times all local rows of B, first make sure that everything is up-to-date */
590:   if (!cdense->A->product) {
591:     PetscCall(MatProductCreateWithMat(aij->A, bdense->A, NULL, cdense->A));
592:     PetscCall(MatProductSetType(cdense->A, MATPRODUCT_AB));
593:     PetscCall(MatProductSetFromOptions(cdense->A));
594:     PetscCall(MatProductSymbolic(cdense->A));
595:   } else PetscCall(MatProductReplaceMats(aij->A, bdense->A, NULL, cdense->A));
596:   if (PetscDefined(HAVE_CUPM) && !cdense->A->product->clear) {
597:     PetscBool flg;

599:     PetscCall(PetscObjectTypeCompare((PetscObject)C, MATMPIDENSE, &flg));
600:     if (flg) PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &flg));
601:     if (!flg) cdense->A->product->clear = PETSC_TRUE; /* if either A or C is a device Mat, make sure MatProductClear() is called */
602:   }
603:   PetscCall(MatProductNumeric(cdense->A));
604:   if (contents->workB->cmap->n == B->cmap->N) {
605:     /* get off processor parts of B needed to complete C=A*B */
606:     workB = contents->workB;
607:     PetscCall(MatMPIDenseScatter(A, B, workB, C));

609:     /* off-diagonal block of A times nonlocal rows of B */
610:     PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
611:   } else {
612:     Mat       Bb, Cb;
613:     PetscInt  BN = B->cmap->N, n = contents->workB->cmap->n, cols;
614:     PetscBool ccpu;

616:     PetscCheck(n > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Column block size %" PetscInt_FMT " must be positive", n);
617:     /* Prevent from unneeded copies back and forth from the GPU
618:        when getting and restoring the submatrix
619:        We need a proper GPU code for AIJ * dense in parallel */
620:     PetscCall(MatBoundToCPU(C, &ccpu));
621:     PetscCall(MatBindToCPU(C, PETSC_TRUE));
622:     for (PetscInt i = 0; i < BN; i += n) {
623:       cols  = PetscMin(n, BN - i);
624:       workB = contents->workB;
625:       if (cols != n) PetscCall(MatDenseGetSubMatrix(contents->workB, PETSC_DECIDE, PETSC_DECIDE, 0, cols, &workB));
626:       PetscCall(MatDenseGetSubMatrix(B, PETSC_DECIDE, PETSC_DECIDE, i, i + cols, &Bb));
627:       PetscCall(MatDenseGetSubMatrix(C, PETSC_DECIDE, PETSC_DECIDE, i, i + cols, &Cb));

629:       /* get off processor parts of B needed to complete C=A*B */
630:       PetscCall(MatMPIDenseScatter(A, Bb, workB, C));

632:       /* off-diagonal block of A times nonlocal rows of B */
633:       cdense = (Mat_MPIDense *)Cb->data;
634:       PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
635:       if (cols != n) PetscCall(MatDenseRestoreSubMatrix(contents->workB, &workB));
636:       PetscCall(MatDenseRestoreSubMatrix(B, &Bb));
637:       PetscCall(MatDenseRestoreSubMatrix(C, &Cb));
638:     }
639:     PetscCall(MatBindToCPU(C, ccpu));
640:   }
641:   PetscFunctionReturn(PETSC_SUCCESS);
642: }

644: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A, Mat P, Mat C)
645: {
646:   Mat_MPIAIJ          *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
647:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
648:   Mat_SeqAIJ          *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
649:   PetscInt            *adi = ad->i, *adj, *aoi = ao->i, *aoj;
650:   PetscScalar         *ada, *aoa, *cda = cd->a, *coa = co->a;
651:   Mat_SeqAIJ          *p_loc, *p_oth;
652:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *pj;
653:   PetscScalar         *pa_loc, *pa_oth, *pa, valtmp, *ca;
654:   PetscInt             cm = C->rmap->n, anz, pnz;
655:   MatProductCtx_APMPI *ptap;
656:   PetscScalar         *apa_sparse;
657:   const PetscScalar   *dummy;
658:   PetscInt            *api, *apj, *apJ, i, j, k, row;
659:   PetscInt             cstart = C->cmap->rstart;
660:   PetscInt             cdnz, conz, k0, k1, nextp;
661:   MPI_Comm             comm;
662:   PetscMPIInt          size;

664:   PetscFunctionBegin;
665:   MatCheckProduct(C, 3);
666:   ptap = (MatProductCtx_APMPI *)C->product->data;
667:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
668:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
669:   PetscCallMPI(MPI_Comm_size(comm, &size));
670:   PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");

672:   /* flag CPU mask for C */
673: #if PetscDefined(HAVE_DEVICE)
674:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
675:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
676:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
677: #endif
678:   apa_sparse = ptap->apa;

680:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
681:   /* update numerical values of P_oth and P_loc */
682:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_REUSE_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
683:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_REUSE_MATRIX, &ptap->P_loc));

685:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
686:   /* get data from symbolic products */
687:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
688:   pi_loc = p_loc->i;
689:   pj_loc = p_loc->j;
690:   pa_loc = p_loc->a;
691:   if (size > 1) {
692:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
693:     pi_oth = p_oth->i;
694:     pj_oth = p_oth->j;
695:     pa_oth = p_oth->a;
696:   } else {
697:     p_oth  = NULL;
698:     pi_oth = NULL;
699:     pj_oth = NULL;
700:     pa_oth = NULL;
701:   }

703:   /* trigger copy to CPU */
704:   PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy));
705:   PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy));
706:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy));
707:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy));
708:   api = ptap->api;
709:   apj = ptap->apj;
710:   for (i = 0; i < cm; i++) {
711:     apJ = apj + api[i];

713:     /* diagonal portion of A */
714:     anz = adi[i + 1] - adi[i];
715:     adj = ad->j + adi[i];
716:     ada = ad->a + adi[i];
717:     for (j = 0; j < anz; j++) {
718:       row = adj[j];
719:       pnz = pi_loc[row + 1] - pi_loc[row];
720:       pj  = pj_loc + pi_loc[row];
721:       pa  = pa_loc + pi_loc[row];
722:       /* perform sparse axpy */
723:       valtmp = ada[j];
724:       nextp  = 0;
725:       for (k = 0; nextp < pnz; k++) {
726:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
727:           apa_sparse[k] += valtmp * pa[nextp++];
728:         }
729:       }
730:       PetscCall(PetscLogFlops(2.0 * pnz));
731:     }

733:     /* off-diagonal portion of A */
734:     anz = aoi[i + 1] - aoi[i];
735:     aoj = PetscSafePointerPlusOffset(ao->j, aoi[i]);
736:     aoa = PetscSafePointerPlusOffset(ao->a, aoi[i]);
737:     for (j = 0; j < anz; j++) {
738:       row = aoj[j];
739:       pnz = pi_oth[row + 1] - pi_oth[row];
740:       pj  = pj_oth + pi_oth[row];
741:       pa  = pa_oth + pi_oth[row];
742:       /* perform sparse axpy */
743:       valtmp = aoa[j];
744:       nextp  = 0;
745:       for (k = 0; nextp < pnz; k++) {
746:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
747:           apa_sparse[k] += valtmp * pa[nextp++];
748:         }
749:       }
750:       PetscCall(PetscLogFlops(2.0 * pnz));
751:     }

753:     /* set values in C */
754:     cdnz = cd->i[i + 1] - cd->i[i];
755:     conz = co->i[i + 1] - co->i[i];

757:     /* 1st off-diagonal part of C */
758:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
759:     k  = 0;
760:     for (k0 = 0; k0 < conz; k0++) {
761:       if (apJ[k] >= cstart) break;
762:       ca[k0]        = apa_sparse[k];
763:       apa_sparse[k] = 0.0;
764:       k++;
765:     }

767:     /* diagonal part of C */
768:     ca = cda + cd->i[i];
769:     for (k1 = 0; k1 < cdnz; k1++) {
770:       ca[k1]        = apa_sparse[k];
771:       apa_sparse[k] = 0.0;
772:       k++;
773:     }

775:     /* 2nd off-diagonal part of C */
776:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
777:     for (; k0 < conz; k0++) {
778:       ca[k0]        = apa_sparse[k];
779:       apa_sparse[k] = 0.0;
780:       k++;
781:     }
782:   }
783:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
784:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
785:   PetscFunctionReturn(PETSC_SUCCESS);
786: }

788: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
789: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A, Mat P, PetscReal fill, Mat C)
790: {
791:   MPI_Comm             comm;
792:   PetscMPIInt          size;
793:   MatProductCtx_APMPI *ptap;
794:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
795:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
796:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
797:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
798:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
799:   PetscInt             i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi, *lnk, apnz_max = 1;
800:   PetscInt             am = A->rmap->n, pn = P->cmap->n, pm = P->rmap->n, lsize = pn + 20;
801:   PetscReal            afill;
802:   MatType              mtype;

804:   PetscFunctionBegin;
805:   MatCheckProduct(C, 4);
806:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
807:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
808:   PetscCallMPI(MPI_Comm_size(comm, &size));

810:   /* create struct MatProductCtx_APMPI and attached it to C later */
811:   PetscCall(PetscNew(&ptap));

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

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

819:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
820:   pi_loc = p_loc->i;
821:   pj_loc = p_loc->j;
822:   if (size > 1) {
823:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
824:     pi_oth = p_oth->i;
825:     pj_oth = p_oth->j;
826:   } else {
827:     p_oth  = NULL;
828:     pi_oth = NULL;
829:     pj_oth = NULL;
830:   }

832:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
833:   PetscCall(PetscMalloc1(am + 1, &api));
834:   ptap->api = api;
835:   api[0]    = 0;

837:   PetscCall(PetscLLCondensedCreate_Scalable(lsize, &lnk));

839:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
840:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space));
841:   current_space = free_space;
842:   MatPreallocateBegin(comm, am, pn, dnz, onz);
843:   for (i = 0; i < am; i++) {
844:     /* diagonal portion of A */
845:     nzi = adi[i + 1] - adi[i];
846:     for (j = 0; j < nzi; j++) {
847:       row  = *adj++;
848:       pnz  = pi_loc[row + 1] - pi_loc[row];
849:       Jptr = pj_loc + pi_loc[row];
850:       /* Expand list if it is not long enough */
851:       if (pnz + apnz_max > lsize) {
852:         lsize = pnz + apnz_max;
853:         PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
854:       }
855:       /* add non-zero cols of P into the sorted linked list lnk */
856:       PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
857:       apnz       = *lnk; /* The first element in the list is the number of items in the list */
858:       api[i + 1] = api[i] + apnz;
859:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
860:     }
861:     /* off-diagonal portion of A */
862:     nzi = aoi[i + 1] - aoi[i];
863:     for (j = 0; j < nzi; j++) {
864:       row  = *aoj++;
865:       pnz  = pi_oth[row + 1] - pi_oth[row];
866:       Jptr = pj_oth + pi_oth[row];
867:       /* Expand list if it is not long enough */
868:       if (pnz + apnz_max > lsize) {
869:         lsize = pnz + apnz_max;
870:         PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
871:       }
872:       /* add non-zero cols of P into the sorted linked list lnk */
873:       PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
874:       apnz       = *lnk; /* The first element in the list is the number of items in the list */
875:       api[i + 1] = api[i] + apnz;
876:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
877:     }

879:     /* add missing diagonal entry */
880:     if (C->force_diagonals) {
881:       j = i + rstart; /* column index */
882:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &j, lnk));
883:     }

885:     apnz       = *lnk;
886:     api[i + 1] = api[i] + apnz;
887:     if (apnz > apnz_max) apnz_max = apnz;

889:     /* if free space is not available, double the total space in the list */
890:     if (current_space->local_remaining < apnz) {
891:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), &current_space));
892:       nspacedouble++;
893:     }

895:     /* Copy data into free space, then initialize lnk */
896:     PetscCall(PetscLLCondensedClean_Scalable(apnz, current_space->array, lnk));
897:     PetscCall(MatPreallocateSet(i + rstart, apnz, current_space->array, dnz, onz));

899:     current_space->array += apnz;
900:     current_space->local_used += apnz;
901:     current_space->local_remaining -= apnz;
902:   }

904:   /* Allocate space for apj, initialize apj, and */
905:   /* destroy list of free space and other temporary array(s) */
906:   PetscCall(PetscMalloc1(api[am], &ptap->apj));
907:   apj = ptap->apj;
908:   PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
909:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));

911:   /* create and assemble symbolic parallel matrix C */
912:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
913:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
914:   PetscCall(MatGetType(A, &mtype));
915:   PetscCall(MatSetType(C, mtype));
916:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
917:   MatPreallocateEnd(dnz, onz);

919:   /* malloc apa for assembly C */
920:   PetscCall(PetscCalloc1(apnz_max, &ptap->apa));

922:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
923:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
924:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
925:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
926:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

928:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
929:   C->ops->productnumeric = MatProductNumeric_AB;

931:   /* attach the supporting struct to C for reuse */
932:   C->product->data    = ptap;
933:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

935:   /* set MatInfo */
936:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
937:   if (afill < 1.0) afill = 1.0;
938:   C->info.mallocs           = nspacedouble;
939:   C->info.fill_ratio_given  = fill;
940:   C->info.fill_ratio_needed = afill;

942:   if (PetscDefined(USE_INFO)) {
943:     if (api[am]) {
944:       PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
945:       PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
946:     } else PetscCall(PetscInfo(C, "Empty matrix product\n"));
947:   }
948:   PetscFunctionReturn(PETSC_SUCCESS);
949: }

951: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
952: /* Three input arrays are merged to one output array. The size of the    */
953: /* output array is also output. Duplicate entries only show up once.     */
954: static void Merge3SortedArrays(PetscInt size1, PetscInt *in1, PetscInt size2, PetscInt *in2, PetscInt size3, PetscInt *in3, PetscInt *size4, PetscInt *out)
955: {
956:   int i = 0, j = 0, k = 0, l = 0;

958:   /* Traverse all three arrays */
959:   while (i < size1 && j < size2 && k < size3) {
960:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
961:       out[l++] = in1[i++];
962:     } else if (in2[j] < in1[i] && in2[j] < in3[k]) {
963:       out[l++] = in2[j++];
964:     } else if (in3[k] < in1[i] && in3[k] < in2[j]) {
965:       out[l++] = in3[k++];
966:     } else if (in1[i] == in2[j] && in1[i] < in3[k]) {
967:       out[l++] = in1[i];
968:       i++, j++;
969:     } else if (in1[i] == in3[k] && in1[i] < in2[j]) {
970:       out[l++] = in1[i];
971:       i++, k++;
972:     } else if (in3[k] == in2[j] && in2[j] < in1[i]) {
973:       out[l++] = in2[j];
974:       k++, j++;
975:     } else if (in1[i] == in2[j] && in1[i] == in3[k]) {
976:       out[l++] = in1[i];
977:       i++, j++, k++;
978:     }
979:   }

981:   /* Traverse two remaining arrays */
982:   while (i < size1 && j < size2) {
983:     if (in1[i] < in2[j]) {
984:       out[l++] = in1[i++];
985:     } else if (in1[i] > in2[j]) {
986:       out[l++] = in2[j++];
987:     } else {
988:       out[l++] = in1[i];
989:       i++, j++;
990:     }
991:   }

993:   while (i < size1 && k < size3) {
994:     if (in1[i] < in3[k]) {
995:       out[l++] = in1[i++];
996:     } else if (in1[i] > in3[k]) {
997:       out[l++] = in3[k++];
998:     } else {
999:       out[l++] = in1[i];
1000:       i++, k++;
1001:     }
1002:   }

1004:   while (k < size3 && j < size2) {
1005:     if (in3[k] < in2[j]) {
1006:       out[l++] = in3[k++];
1007:     } else if (in3[k] > in2[j]) {
1008:       out[l++] = in2[j++];
1009:     } else {
1010:       out[l++] = in3[k];
1011:       k++, j++;
1012:     }
1013:   }

1015:   /* Traverse one remaining array */
1016:   while (i < size1) out[l++] = in1[i++];
1017:   while (j < size2) out[l++] = in2[j++];
1018:   while (k < size3) out[l++] = in3[k++];

1020:   *size4 = l;
1021: }

1023: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1024: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1025: /* matrix-matrix multiplications.  */
1026: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1027: {
1028:   MPI_Comm             comm;
1029:   PetscMPIInt          size;
1030:   MatProductCtx_APMPI *ptap;
1031:   PetscFreeSpaceList   free_space_diag = NULL, current_space = NULL;
1032:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
1033:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
1034:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
1035:   Mat_SeqAIJ          *adpd_seq, *p_off, *aopoth_seq;
1036:   PetscInt             adponz, adpdnz;
1037:   PetscInt            *pi_loc, *dnz, *onz;
1038:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
1039:   PetscInt            *lnk, i, i1 = 0, pnz, row, *adpoi, *adpoj, *api, *adpoJ, *aopJ, *apJ, *Jptr, aopnz, nspacedouble = 0, j, nzi, *apj, apnz, *adpdi, *adpdj, *adpdJ, *poff_i, *poff_j, *j_temp, *aopothi, *aopothj;
1040:   PetscInt             am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
1041:   PetscBT              lnkbt;
1042:   PetscReal            afill;
1043:   PetscMPIInt          rank;
1044:   Mat                  adpd, aopoth;
1045:   MatType              mtype;
1046:   const char          *prefix;

1048:   PetscFunctionBegin;
1049:   MatCheckProduct(C, 4);
1050:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1051:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1052:   PetscCallMPI(MPI_Comm_size(comm, &size));
1053:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1054:   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));

1056:   /* create struct MatProductCtx_APMPI and attached it to C later */
1057:   PetscCall(PetscNew(&ptap));

1059:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1060:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));

1062:   /* get P_loc by taking all local rows of P */
1063:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));

1065:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
1066:   pi_loc = p_loc->i;

1068:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1069:   PetscCall(PetscMalloc1(am + 1, &api));
1070:   PetscCall(PetscMalloc1(am + 1, &adpoi));

1072:   adpoi[0]  = 0;
1073:   ptap->api = api;
1074:   api[0]    = 0;

1076:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1077:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
1078:   MatPreallocateBegin(comm, am, pn, dnz, onz);

1080:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1081:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1082:   PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
1083:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1084:   PetscCall(MatSetOptionsPrefix(adpd, prefix));
1085:   PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));

1087:   PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
1088:   PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
1089:   PetscCall(MatProductSetFill(adpd, fill));
1090:   PetscCall(MatProductSetFromOptions(adpd));

1092:   adpd->force_diagonals = C->force_diagonals;
1093:   PetscCall(MatProductSymbolic(adpd));

1095:   adpd_seq = (Mat_SeqAIJ *)((adpd)->data);
1096:   adpdi    = adpd_seq->i;
1097:   adpdj    = adpd_seq->j;
1098:   p_off    = (Mat_SeqAIJ *)p->B->data;
1099:   poff_i   = p_off->i;
1100:   poff_j   = p_off->j;

1102:   /* j_temp stores indices of a result row before they are added to the linked list */
1103:   PetscCall(PetscMalloc1(pN, &j_temp));

1105:   /* Symbolic calc of the A_diag * p_loc_off */
1106:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1107:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
1108:   current_space = free_space_diag;

1110:   for (i = 0; i < am; i++) {
1111:     /* A_diag * P_loc_off */
1112:     nzi = adi[i + 1] - adi[i];
1113:     for (j = 0; j < nzi; j++) {
1114:       row  = *adj++;
1115:       pnz  = poff_i[row + 1] - poff_i[row];
1116:       Jptr = poff_j + poff_i[row];
1117:       for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
1118:       /* add non-zero cols of P into the sorted linked list lnk */
1119:       PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
1120:     }

1122:     adponz       = lnk[0];
1123:     adpoi[i + 1] = adpoi[i] + adponz;

1125:     /* if free space is not available, double the total space in the list */
1126:     if (current_space->local_remaining < adponz) {
1127:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), &current_space));
1128:       nspacedouble++;
1129:     }

1131:     /* Copy data into free space, then initialize lnk */
1132:     PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));

1134:     current_space->array += adponz;
1135:     current_space->local_used += adponz;
1136:     current_space->local_remaining -= adponz;
1137:   }

1139:   /* Symbolic calc of A_off * P_oth */
1140:   PetscCall(MatSetOptionsPrefix(a->B, prefix));
1141:   PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
1142:   PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
1143:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1144:   aopoth_seq = (Mat_SeqAIJ *)((aopoth)->data);
1145:   aopothi    = aopoth_seq->i;
1146:   aopothj    = aopoth_seq->j;

1148:   /* Allocate space for apj, adpj, aopj, ... */
1149:   /* destroy lists of free space and other temporary array(s) */

1151:   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am], &ptap->apj));
1152:   PetscCall(PetscMalloc1(adpoi[am], &adpoj));

1154:   /* Copy from linked list to j-array */
1155:   PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
1156:   PetscCall(PetscLLDestroy(lnk, lnkbt));

1158:   adpoJ = adpoj;
1159:   adpdJ = adpdj;
1160:   aopJ  = aopothj;
1161:   apj   = ptap->apj;
1162:   apJ   = apj; /* still empty */

1164:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1165:   /* A_diag * P_loc_diag to get A*P */
1166:   for (i = 0; i < am; i++) {
1167:     aopnz  = aopothi[i + 1] - aopothi[i];
1168:     adponz = adpoi[i + 1] - adpoi[i];
1169:     adpdnz = adpdi[i + 1] - adpdi[i];

1171:     /* Correct indices from A_diag*P_diag */
1172:     for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
1173:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1174:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1175:     PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));

1177:     aopJ += aopnz;
1178:     adpoJ += adponz;
1179:     adpdJ += adpdnz;
1180:     apJ += apnz;
1181:     api[i + 1] = api[i] + apnz;
1182:   }

1184:   /* malloc apa to store dense row A[i,:]*P */
1185:   PetscCall(PetscCalloc1(pN, &ptap->apa));

1187:   /* create and assemble symbolic parallel matrix C */
1188:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1189:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
1190:   PetscCall(MatGetType(A, &mtype));
1191:   PetscCall(MatSetType(C, mtype));
1192:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1193:   MatPreallocateEnd(dnz, onz);

1195:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1196:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
1197:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1198:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1199:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1201:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1202:   C->ops->productnumeric = MatProductNumeric_AB;

1204:   /* attach the supporting struct to C for reuse */
1205:   C->product->data    = ptap;
1206:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

1208:   /* set MatInfo */
1209:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1210:   if (afill < 1.0) afill = 1.0;
1211:   C->info.mallocs           = nspacedouble;
1212:   C->info.fill_ratio_given  = fill;
1213:   C->info.fill_ratio_needed = afill;

1215:   if (PetscDefined(USE_INFO)) {
1216:     if (api[am]) {
1217:       PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1218:       PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1219:     } else PetscCall(PetscInfo(C, "Empty matrix product\n"));
1220:   }

1222:   PetscCall(MatDestroy(&aopoth));
1223:   PetscCall(MatDestroy(&adpd));
1224:   PetscCall(PetscFree(j_temp));
1225:   PetscCall(PetscFree(adpoj));
1226:   PetscCall(PetscFree(adpoi));
1227:   PetscFunctionReturn(PETSC_SUCCESS);
1228: }

1230: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1231: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
1232: {
1233:   MatProductCtx_APMPI *ptap;
1234:   Mat                  Pt;

1236:   PetscFunctionBegin;
1237:   MatCheckProduct(C, 3);
1238:   ptap = (MatProductCtx_APMPI *)C->product->data;
1239:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1240:   PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");

1242:   Pt = ptap->Pt;
1243:   PetscCall(MatTransposeSetPrecursor(P, Pt));
1244:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
1245:   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
1246:   PetscFunctionReturn(PETSC_SUCCESS);
1247: }

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

1276:   PetscFunctionBegin;
1277:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1278:   PetscCallMPI(MPI_Comm_size(comm, &size));
1279:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

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

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

1287:   /* create struct MatProductCtx_APMPI and attached it to C later */
1288:   PetscCall(PetscNew(&ptap));

1290:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1291:   PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
1292:   PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));

1294:   /* (1) compute symbolic A_loc */
1295:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));

1297:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1298:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1299:   PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
1300:   PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
1301:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
1302:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));

1304:   /* (3) send coj of C_oth to other processors  */
1305:   /* determine row ownership */
1306:   PetscCall(PetscLayoutCreate(comm, &rowmap));
1307:   rowmap->n  = pn;
1308:   rowmap->bs = 1;
1309:   PetscCall(PetscLayoutSetUp(rowmap));
1310:   owners = rowmap->range;

1312:   /* determine the number of messages to send, their lengths */
1313:   PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 1, &owners_co));
1314:   PetscCall(PetscArrayzero(len_s, size));
1315:   PetscCall(PetscArrayzero(len_si, size));

1317:   c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
1318:   coi   = c_oth->i;
1319:   coj   = c_oth->j;
1320:   con   = ptap->C_oth->rmap->n;
1321:   proc  = 0;
1322:   for (i = 0; i < con; i++) {
1323:     while (prmap[i] >= owners[proc + 1]) proc++;
1324:     len_si[proc]++;                     /* num of rows in Co(=Pt*A) to be sent to [proc] */
1325:     len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1326:   }

1328:   len          = 0; /* max length of buf_si[], see (4) */
1329:   owners_co[0] = 0;
1330:   nsend        = 0;
1331:   for (proc = 0; proc < size; proc++) {
1332:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1333:     if (len_s[proc]) {
1334:       nsend++;
1335:       len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1336:       len += len_si[proc];
1337:     }
1338:   }

1340:   /* determine the number and length of messages to receive for coi and coj  */
1341:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
1342:   PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));

1344:   /* post the Irecv and Isend of coj */
1345:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1346:   PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
1347:   PetscCall(PetscMalloc1(nsend, &swaits));
1348:   for (proc = 0, k = 0; proc < size; proc++) {
1349:     if (!len_s[proc]) continue;
1350:     i = owners_co[proc];
1351:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1352:     k++;
1353:   }

1355:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1356:   PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
1357:   PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
1358:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
1359:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
1360:   c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;

1362:   /* receives coj are complete */
1363:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1364:   PetscCall(PetscFree(rwaits));
1365:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1367:   /* add received column indices into ta to update Crmax */
1368:   a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;

1370:   /* create and initialize a linked list */
1371:   PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
1372:   MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);

1374:   for (k = 0; k < nrecv; k++) { /* k-th received message */
1375:     Jptr = buf_rj[k];
1376:     for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1377:   }
1378:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
1379:   PetscCall(PetscHMapIDestroy(&ta));

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

1412:   PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
1413:   PetscCall(PetscFree(len_ri));
1414:   PetscCall(PetscFree(swaits));
1415:   PetscCall(PetscFree(buf_s));

1417:   /* (5) compute the local portion of C      */
1418:   /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
1419:   PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
1420:   current_space = free_space;

1422:   PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
1423:   for (k = 0; k < nrecv; k++) {
1424:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1425:     nrows       = *buf_ri_k[k];
1426:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1427:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1428:   }

1430:   MatPreallocateBegin(comm, pn, an, dnz, onz);
1431:   PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
1432:   for (i = 0; i < pn; i++) { /* for each local row of C */
1433:     /* add C_loc into C */
1434:     nzi  = c_loc->i[i + 1] - c_loc->i[i];
1435:     Jptr = c_loc->j + c_loc->i[i];
1436:     PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));

1438:     /* add received col data into lnk */
1439:     for (k = 0; k < nrecv; k++) { /* k-th received message */
1440:       if (i == *nextrow[k]) {     /* i-th row */
1441:         nzi  = *(nextci[k] + 1) - *nextci[k];
1442:         Jptr = buf_rj[k] + *nextci[k];
1443:         PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1444:         nextrow[k]++;
1445:         nextci[k]++;
1446:       }
1447:     }

1449:     /* add missing diagonal entry */
1450:     if (C->force_diagonals) {
1451:       k = i + owners[rank]; /* column index */
1452:       PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
1453:     }

1455:     nzi = lnk[0];

1457:     /* copy data into free space, then initialize lnk */
1458:     PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
1459:     PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
1460:   }
1461:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1462:   PetscCall(PetscLLDestroy(lnk, lnkbt));
1463:   PetscCall(PetscFreeSpaceDestroy(free_space));

1465:   /* local sizes and preallocation */
1466:   PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
1467:   PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
1468:   PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
1469:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1470:   MatPreallocateEnd(dnz, onz);

1472:   /* add C_loc and C_oth to C */
1473:   PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
1474:   for (i = 0; i < pn; i++) {
1475:     ncols = c_loc->i[i + 1] - c_loc->i[i];
1476:     cols  = c_loc->j + c_loc->i[i];
1477:     row   = rstart + i;
1478:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));

1480:     if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
1481:   }
1482:   for (i = 0; i < con; i++) {
1483:     ncols = c_oth->i[i + 1] - c_oth->i[i];
1484:     cols  = c_oth->j + c_oth->i[i];
1485:     row   = prmap[i];
1486:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1487:   }
1488:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1489:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1490:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1492:   /* members in merge */
1493:   PetscCall(PetscFree(id_r));
1494:   PetscCall(PetscFree(len_r));
1495:   PetscCall(PetscFree(buf_ri[0]));
1496:   PetscCall(PetscFree(buf_ri));
1497:   PetscCall(PetscFree(buf_rj[0]));
1498:   PetscCall(PetscFree(buf_rj));
1499:   PetscCall(PetscLayoutDestroy(&rowmap));

1501:   /* attach the supporting struct to C for reuse */
1502:   C->product->data    = ptap;
1503:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
1504:   PetscFunctionReturn(PETSC_SUCCESS);
1505: }

1507: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
1508: {
1509:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
1510:   Mat_SeqAIJ          *c_seq;
1511:   MatProductCtx_APMPI *ptap;
1512:   Mat                  A_loc, C_loc, C_oth;
1513:   PetscInt             i, rstart, rend, cm, ncols, row;
1514:   const PetscInt      *cols;
1515:   const PetscScalar   *vals;

1517:   PetscFunctionBegin;
1518:   MatCheckProduct(C, 3);
1519:   ptap = (MatProductCtx_APMPI *)C->product->data;
1520:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1521:   PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1522:   PetscCall(MatZeroEntries(C));

1524:   /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1525:   /* 1) get R = Pd^T, Ro = Po^T */
1526:   PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
1527:   PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
1528:   PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
1529:   PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));

1531:   /* 2) compute numeric A_loc */
1532:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));

1534:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1535:   A_loc = ptap->A_loc;
1536:   PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
1537:   PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
1538:   C_loc = ptap->C_loc;
1539:   C_oth = ptap->C_oth;

1541:   /* add C_loc and C_oth to C */
1542:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));

1544:   /* C_loc -> C */
1545:   cm    = C_loc->rmap->N;
1546:   c_seq = (Mat_SeqAIJ *)C_loc->data;
1547:   cols  = c_seq->j;
1548:   vals  = c_seq->a;
1549:   for (i = 0; i < cm; i++) {
1550:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1551:     row   = rstart + i;
1552:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1553:     cols += ncols;
1554:     vals += ncols;
1555:   }

1557:   /* Co -> C, off-processor part */
1558:   cm    = C_oth->rmap->N;
1559:   c_seq = (Mat_SeqAIJ *)C_oth->data;
1560:   cols  = c_seq->j;
1561:   vals  = c_seq->a;
1562:   for (i = 0; i < cm; i++) {
1563:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1564:     row   = p->garray[i];
1565:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1566:     cols += ncols;
1567:     vals += ncols;
1568:   }
1569:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1570:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1571:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1572:   PetscFunctionReturn(PETSC_SUCCESS);
1573: }

1575: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
1576: {
1577:   MatMergeSeqsToMPI   *merge;
1578:   Mat_MPIAIJ          *p  = (Mat_MPIAIJ *)P->data;
1579:   Mat_SeqAIJ          *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
1580:   MatProductCtx_APMPI *ap;
1581:   PetscInt            *adj;
1582:   PetscInt             i, j, k, anz, pnz, row, *cj, nexta;
1583:   MatScalar           *ada, *ca, valtmp;
1584:   PetscInt             am = A->rmap->n, cm = C->rmap->n, pon = (p->B)->cmap->n;
1585:   MPI_Comm             comm;
1586:   PetscMPIInt          size, rank, taga, *len_s, proc;
1587:   PetscInt            *owners, nrows, **buf_ri_k, **nextrow, **nextci;
1588:   PetscInt           **buf_ri, **buf_rj;
1589:   PetscInt             cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1590:   MPI_Request         *s_waits, *r_waits;
1591:   MPI_Status          *status;
1592:   MatScalar          **abuf_r, *ba_i, *pA, *coa, *ba;
1593:   const PetscScalar   *dummy;
1594:   PetscInt            *ai, *aj, *coi, *coj, *poJ, *pdJ;
1595:   Mat                  A_loc;
1596:   Mat_SeqAIJ          *a_loc;

1598:   PetscFunctionBegin;
1599:   MatCheckProduct(C, 3);
1600:   ap = (MatProductCtx_APMPI *)C->product->data;
1601:   PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
1602:   PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1603:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
1604:   PetscCallMPI(MPI_Comm_size(comm, &size));
1605:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1607:   merge = ap->merge;

1609:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1610:   /* get data from symbolic products */
1611:   coi = merge->coi;
1612:   coj = merge->coj;
1613:   PetscCall(PetscCalloc1(coi[pon], &coa));
1614:   bi     = merge->bi;
1615:   bj     = merge->bj;
1616:   owners = merge->rowmap->range;
1617:   PetscCall(PetscCalloc1(bi[cm], &ba));

1619:   /* get A_loc by taking all local rows of A */
1620:   A_loc = ap->A_loc;
1621:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
1622:   a_loc = (Mat_SeqAIJ *)A_loc->data;
1623:   ai    = a_loc->i;
1624:   aj    = a_loc->j;

1626:   /* trigger copy to CPU */
1627:   PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
1628:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
1629:   PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
1630:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
1631:   for (i = 0; i < am; i++) {
1632:     anz = ai[i + 1] - ai[i];
1633:     adj = aj + ai[i];
1634:     ada = a_loc->a + ai[i];

1636:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1637:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1638:     pnz = po->i[i + 1] - po->i[i];
1639:     poJ = po->j + po->i[i];
1640:     pA  = po->a + po->i[i];
1641:     for (j = 0; j < pnz; j++) {
1642:       row = poJ[j];
1643:       cj  = coj + coi[row];
1644:       ca  = coa + coi[row];
1645:       /* perform sparse axpy */
1646:       nexta  = 0;
1647:       valtmp = pA[j];
1648:       for (k = 0; nexta < anz; k++) {
1649:         if (cj[k] == adj[nexta]) {
1650:           ca[k] += valtmp * ada[nexta];
1651:           nexta++;
1652:         }
1653:       }
1654:       PetscCall(PetscLogFlops(2.0 * anz));
1655:     }

1657:     /* put the value into Cd (diagonal part) */
1658:     pnz = pd->i[i + 1] - pd->i[i];
1659:     pdJ = pd->j + pd->i[i];
1660:     pA  = pd->a + pd->i[i];
1661:     for (j = 0; j < pnz; j++) {
1662:       row = pdJ[j];
1663:       cj  = bj + bi[row];
1664:       ca  = ba + bi[row];
1665:       /* perform sparse axpy */
1666:       nexta  = 0;
1667:       valtmp = pA[j];
1668:       for (k = 0; nexta < anz; k++) {
1669:         if (cj[k] == adj[nexta]) {
1670:           ca[k] += valtmp * ada[nexta];
1671:           nexta++;
1672:         }
1673:       }
1674:       PetscCall(PetscLogFlops(2.0 * anz));
1675:     }
1676:   }

1678:   /* 3) send and recv matrix values coa */
1679:   buf_ri = merge->buf_ri;
1680:   buf_rj = merge->buf_rj;
1681:   len_s  = merge->len_s;
1682:   PetscCall(PetscCommGetNewTag(comm, &taga));
1683:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

1685:   PetscCall(PetscMalloc2(merge->nsend, &s_waits, size, &status));
1686:   for (proc = 0, k = 0; proc < size; proc++) {
1687:     if (!len_s[proc]) continue;
1688:     i = merge->owners_co[proc];
1689:     PetscCallMPI(MPIU_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
1690:     k++;
1691:   }
1692:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
1693:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));

1695:   PetscCall(PetscFree2(s_waits, status));
1696:   PetscCall(PetscFree(r_waits));
1697:   PetscCall(PetscFree(coa));

1699:   /* 4) insert local Cseq and received values into Cmpi */
1700:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1701:   for (k = 0; k < merge->nrecv; k++) {
1702:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1703:     nrows       = *buf_ri_k[k];
1704:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1705:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1706:   }

1708:   for (i = 0; i < cm; i++) {
1709:     row  = owners[rank] + i; /* global row index of C_seq */
1710:     bj_i = bj + bi[i];       /* col indices of the i-th row of C */
1711:     ba_i = ba + bi[i];
1712:     bnz  = bi[i + 1] - bi[i];
1713:     /* add received vals into ba */
1714:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1715:       /* i-th row */
1716:       if (i == *nextrow[k]) {
1717:         cnz    = *(nextci[k] + 1) - *nextci[k];
1718:         cj     = buf_rj[k] + *nextci[k];
1719:         ca     = abuf_r[k] + *nextci[k];
1720:         nextcj = 0;
1721:         for (j = 0; nextcj < cnz; j++) {
1722:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1723:             ba_i[j] += ca[nextcj++];
1724:           }
1725:         }
1726:         nextrow[k]++;
1727:         nextci[k]++;
1728:         PetscCall(PetscLogFlops(2.0 * cnz));
1729:       }
1730:     }
1731:     PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
1732:   }
1733:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1734:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

1736:   PetscCall(PetscFree(ba));
1737:   PetscCall(PetscFree(abuf_r[0]));
1738:   PetscCall(PetscFree(abuf_r));
1739:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1740:   PetscFunctionReturn(PETSC_SUCCESS);
1741: }

1743: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
1744: {
1745:   Mat                  A_loc;
1746:   MatProductCtx_APMPI *ap;
1747:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
1748:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
1749:   PetscInt            *pdti, *pdtj, *poti, *potj, *ptJ;
1750:   PetscInt             nnz;
1751:   PetscInt            *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
1752:   PetscInt             am = A->rmap->n, pn = P->cmap->n;
1753:   MPI_Comm             comm;
1754:   PetscMPIInt          size, rank, tagi, tagj, *len_si, *len_s, *len_ri, proc;
1755:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
1756:   PetscInt             len, *dnz, *onz, *owners;
1757:   PetscInt             nzi, *bi, *bj;
1758:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1759:   MPI_Request         *swaits, *rwaits;
1760:   MPI_Status          *sstatus, rstatus;
1761:   MatMergeSeqsToMPI   *merge;
1762:   PetscInt            *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
1763:   PetscReal            afill  = 1.0, afill_tmp;
1764:   PetscInt             rstart = P->cmap->rstart, rmax, Armax;
1765:   Mat_SeqAIJ          *a_loc;
1766:   PetscHMapI           ta;
1767:   MatType              mtype;

1769:   PetscFunctionBegin;
1770:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1771:   /* check if matrix local sizes are compatible */
1772:   PetscCheck(A->rmap->rstart == P->rmap->rstart && A->rmap->rend == P->rmap->rend, comm, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != P (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->rstart,
1773:              A->rmap->rend, P->rmap->rstart, P->rmap->rend);

1775:   PetscCallMPI(MPI_Comm_size(comm, &size));
1776:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1778:   /* create struct MatProductCtx_APMPI and attached it to C later */
1779:   PetscCall(PetscNew(&ap));

1781:   /* get A_loc by taking all local rows of A */
1782:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));

1784:   ap->A_loc = A_loc;
1785:   a_loc     = (Mat_SeqAIJ *)A_loc->data;
1786:   ai        = a_loc->i;
1787:   aj        = a_loc->j;

1789:   /* determine symbolic Co=(p->B)^T*A - send to others */
1790:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
1791:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
1792:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1793:                          >= (num of nonzero rows of C_seq) - pn */
1794:   PetscCall(PetscMalloc1(pon + 1, &coi));
1795:   coi[0] = 0;

1797:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1798:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
1799:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1800:   current_space = free_space;

1802:   /* create and initialize a linked list */
1803:   PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
1804:   MatRowMergeMax_SeqAIJ(a_loc, am, ta);
1805:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1807:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));

1809:   for (i = 0; i < pon; i++) {
1810:     pnz = poti[i + 1] - poti[i];
1811:     ptJ = potj + poti[i];
1812:     for (j = 0; j < pnz; j++) {
1813:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1814:       anz  = ai[row + 1] - ai[row];
1815:       Jptr = aj + ai[row];
1816:       /* add non-zero cols of AP into the sorted linked list lnk */
1817:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1818:     }
1819:     nnz = lnk[0];

1821:     /* If free space is not available, double the total space in the list */
1822:     if (current_space->local_remaining < nnz) {
1823:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1824:       nspacedouble++;
1825:     }

1827:     /* Copy data into free space, and zero out denserows */
1828:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));

1830:     current_space->array += nnz;
1831:     current_space->local_used += nnz;
1832:     current_space->local_remaining -= nnz;

1834:     coi[i + 1] = coi[i] + nnz;
1835:   }

1837:   PetscCall(PetscMalloc1(coi[pon], &coj));
1838:   PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
1839:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */

1841:   afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
1842:   if (afill_tmp > afill) afill = afill_tmp;

1844:   /* send j-array (coj) of Co to other processors */
1845:   /* determine row ownership */
1846:   PetscCall(PetscNew(&merge));
1847:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));

1849:   merge->rowmap->n  = pn;
1850:   merge->rowmap->bs = 1;

1852:   PetscCall(PetscLayoutSetUp(merge->rowmap));
1853:   owners = merge->rowmap->range;

1855:   /* determine the number of messages to send, their lengths */
1856:   PetscCall(PetscCalloc1(size, &len_si));
1857:   PetscCall(PetscCalloc1(size, &merge->len_s));

1859:   len_s        = merge->len_s;
1860:   merge->nsend = 0;

1862:   PetscCall(PetscMalloc1(size + 1, &owners_co));

1864:   proc = 0;
1865:   for (i = 0; i < pon; i++) {
1866:     while (prmap[i] >= owners[proc + 1]) proc++;
1867:     len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1868:     len_s[proc] += coi[i + 1] - coi[i];
1869:   }

1871:   len          = 0; /* max length of buf_si[] */
1872:   owners_co[0] = 0;
1873:   for (proc = 0; proc < size; proc++) {
1874:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1875:     if (len_s[proc]) {
1876:       merge->nsend++;
1877:       len_si[proc] = 2 * (len_si[proc] + 1);
1878:       len += len_si[proc];
1879:     }
1880:   }

1882:   /* determine the number and length of messages to receive for coi and coj  */
1883:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
1884:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

1886:   /* post the Irecv and Isend of coj */
1887:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1888:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
1889:   PetscCall(PetscMalloc1(merge->nsend, &swaits));
1890:   for (proc = 0, k = 0; proc < size; proc++) {
1891:     if (!len_s[proc]) continue;
1892:     i = owners_co[proc];
1893:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1894:     k++;
1895:   }

1897:   /* receives and sends of coj are complete */
1898:   PetscCall(PetscMalloc1(size, &sstatus));
1899:   for (i = 0; i < merge->nrecv; i++) {
1900:     PETSC_UNUSED PetscMPIInt icompleted;
1901:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1902:   }
1903:   PetscCall(PetscFree(rwaits));
1904:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));

1906:   /* add received column indices into table to update Armax */
1907:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1908:   for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1909:     Jptr = buf_rj[k];
1910:     for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1911:   }
1912:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1914:   /* send and recv coi */
1915:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1916:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &rwaits));
1917:   PetscCall(PetscMalloc1(len, &buf_s));
1918:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1919:   for (proc = 0, k = 0; proc < size; proc++) {
1920:     if (!len_s[proc]) continue;
1921:     /* form outgoing message for i-structure:
1922:          buf_si[0]:                 nrows to be sent
1923:                [1:nrows]:           row index (global)
1924:                [nrows+1:2*nrows+1]: i-structure index
1925:     */
1926:     nrows       = len_si[proc] / 2 - 1;
1927:     buf_si_i    = buf_si + nrows + 1;
1928:     buf_si[0]   = nrows;
1929:     buf_si_i[0] = 0;
1930:     nrows       = 0;
1931:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1932:       nzi                 = coi[i + 1] - coi[i];
1933:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1934:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1935:       nrows++;
1936:     }
1937:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1938:     k++;
1939:     buf_si += len_si[proc];
1940:   }
1941:   i = merge->nrecv;
1942:   while (i--) {
1943:     PETSC_UNUSED PetscMPIInt icompleted;
1944:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1945:   }
1946:   PetscCall(PetscFree(rwaits));
1947:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
1948:   PetscCall(PetscFree(len_si));
1949:   PetscCall(PetscFree(len_ri));
1950:   PetscCall(PetscFree(swaits));
1951:   PetscCall(PetscFree(sstatus));
1952:   PetscCall(PetscFree(buf_s));

1954:   /* compute the local portion of C (mpi mat) */
1955:   /* allocate bi array and free space for accumulating nonzero column info */
1956:   PetscCall(PetscMalloc1(pn + 1, &bi));
1957:   bi[0] = 0;

1959:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1960:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
1961:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1962:   current_space = free_space;

1964:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1965:   for (k = 0; k < merge->nrecv; k++) {
1966:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1967:     nrows       = *buf_ri_k[k];
1968:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1969:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1970:   }

1972:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
1973:   MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
1974:   rmax = 0;
1975:   for (i = 0; i < pn; i++) {
1976:     /* add pdt[i,:]*AP into lnk */
1977:     pnz = pdti[i + 1] - pdti[i];
1978:     ptJ = pdtj + pdti[i];
1979:     for (j = 0; j < pnz; j++) {
1980:       row  = ptJ[j]; /* row of AP == col of Pt */
1981:       anz  = ai[row + 1] - ai[row];
1982:       Jptr = aj + ai[row];
1983:       /* add non-zero cols of AP into the sorted linked list lnk */
1984:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1985:     }

1987:     /* add received col data into lnk */
1988:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1989:       if (i == *nextrow[k]) {            /* i-th row */
1990:         nzi  = *(nextci[k] + 1) - *nextci[k];
1991:         Jptr = buf_rj[k] + *nextci[k];
1992:         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
1993:         nextrow[k]++;
1994:         nextci[k]++;
1995:       }
1996:     }

1998:     /* add missing diagonal entry */
1999:     if (C->force_diagonals) {
2000:       k = i + owners[rank]; /* column index */
2001:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
2002:     }

2004:     nnz = lnk[0];

2006:     /* if free space is not available, make more free space */
2007:     if (current_space->local_remaining < nnz) {
2008:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
2009:       nspacedouble++;
2010:     }
2011:     /* copy data into free space, then initialize lnk */
2012:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
2013:     PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));

2015:     current_space->array += nnz;
2016:     current_space->local_used += nnz;
2017:     current_space->local_remaining -= nnz;

2019:     bi[i + 1] = bi[i] + nnz;
2020:     if (nnz > rmax) rmax = nnz;
2021:   }
2022:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));

2024:   PetscCall(PetscMalloc1(bi[pn], &bj));
2025:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
2026:   afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
2027:   if (afill_tmp > afill) afill = afill_tmp;
2028:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2029:   PetscCall(PetscHMapIDestroy(&ta));
2030:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
2031:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));

2033:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2034:   PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
2035:   PetscCall(MatSetBlockSizes(C, P->cmap->bs, A->cmap->bs));
2036:   PetscCall(MatGetType(A, &mtype));
2037:   PetscCall(MatSetType(C, mtype));
2038:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
2039:   MatPreallocateEnd(dnz, onz);
2040:   PetscCall(MatSetBlockSize(C, 1));
2041:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2042:   for (i = 0; i < pn; i++) {
2043:     row  = i + rstart;
2044:     nnz  = bi[i + 1] - bi[i];
2045:     Jptr = bj + bi[i];
2046:     PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
2047:   }
2048:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2049:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2050:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
2051:   merge->bi        = bi;
2052:   merge->bj        = bj;
2053:   merge->coi       = coi;
2054:   merge->coj       = coj;
2055:   merge->buf_ri    = buf_ri;
2056:   merge->buf_rj    = buf_rj;
2057:   merge->owners_co = owners_co;

2059:   /* attach the supporting struct to C for reuse */
2060:   C->product->data    = ap;
2061:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2062:   ap->merge           = merge;

2064:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2066:   if (PetscDefined(USE_INFO)) {
2067:     if (bi[pn] != 0) {
2068:       PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
2069:       PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
2070:     } else PetscCall(PetscInfo(C, "Empty matrix product\n"));
2071:   }
2072:   PetscFunctionReturn(PETSC_SUCCESS);
2073: }

2075: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2076: {
2077:   Mat_Product *product = C->product;
2078:   Mat          A = product->A, B = product->B;
2079:   PetscReal    fill = product->fill;
2080:   PetscBool    flg;

2082:   PetscFunctionBegin;
2083:   /* scalable */
2084:   PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
2085:   if (flg) {
2086:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
2087:     goto next;
2088:   }

2090:   /* nonscalable */
2091:   PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
2092:   if (flg) {
2093:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
2094:     goto next;
2095:   }

2097:   /* matmatmult */
2098:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
2099:   if (flg) {
2100:     Mat                  At;
2101:     MatProductCtx_APMPI *ptap;

2103:     PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
2104:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
2105:     ptap = (MatProductCtx_APMPI *)C->product->data;
2106:     if (ptap) {
2107:       ptap->Pt            = At;
2108:       C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2109:     }
2110:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2111:     goto next;
2112:   }

2114:   /* backend general code */
2115:   PetscCall(PetscStrcmp(product->alg, "backend", &flg));
2116:   if (flg) {
2117:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2118:     PetscFunctionReturn(PETSC_SUCCESS);
2119:   }

2121:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");

2123: next:
2124:   C->ops->productnumeric = MatProductNumeric_AtB;
2125:   PetscFunctionReturn(PETSC_SUCCESS);
2126: }

2128: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2129: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2130: {
2131:   Mat_Product *product = C->product;
2132:   Mat          A = product->A, B = product->B;
2133: #if PetscDefined(HAVE_HYPRE)
2134:   const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
2135:   PetscInt    nalg        = 5;
2136: #else
2137:   const char *algTypes[4] = {
2138:     "scalable",
2139:     "nonscalable",
2140:     "seqmpi",
2141:     "backend",
2142:   };
2143:   PetscInt nalg = 4;
2144: #endif
2145:   PetscInt  alg = 1; /* set nonscalable algorithm as default */
2146:   PetscBool flg;
2147:   MPI_Comm  comm;

2149:   PetscFunctionBegin;
2150:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));

2152:   /* Set "nonscalable" as default algorithm */
2153:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2154:   if (flg) {
2155:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2157:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2158:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2159:       MatInfo   Ainfo, Binfo;
2160:       PetscInt  nz_local;
2161:       PetscBool alg_scalable = PETSC_FALSE;

2163:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2164:       PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2165:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2167:       if (B->cmap->N > product->fill * nz_local) alg_scalable = PETSC_TRUE;
2168:       PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2170:       if (alg_scalable) {
2171:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2172:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2173:         PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2174:       }
2175:     }
2176:   }

2178:   /* Get runtime option */
2179:   if (product->api_user) {
2180:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2181:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2182:     PetscOptionsEnd();
2183:   } else {
2184:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2185:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2186:     PetscOptionsEnd();
2187:   }
2188:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2190:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2191:   PetscFunctionReturn(PETSC_SUCCESS);
2192: }

2194: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2195: {
2196:   PetscFunctionBegin;
2197:   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2198:   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2199:   PetscFunctionReturn(PETSC_SUCCESS);
2200: }

2202: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2203: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2204: {
2205:   Mat_Product *product = C->product;
2206:   Mat          A = product->A, B = product->B;
2207:   const char  *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
2208:   PetscInt     nalg        = 4;
2209:   PetscInt     alg         = 1; /* set default algorithm  */
2210:   PetscBool    flg;
2211:   MPI_Comm     comm;

2213:   PetscFunctionBegin;
2214:   /* Check matrix local sizes */
2215:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2216:   PetscCheck(A->rmap->rstart == B->rmap->rstart && A->rmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A (%" PetscInt_FMT ", %" PetscInt_FMT ") != B (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2217:              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

2219:   /* Set default algorithm */
2220:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2221:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2223:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2224:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2225:     MatInfo   Ainfo, Binfo;
2226:     PetscInt  nz_local;
2227:     PetscBool alg_scalable = PETSC_FALSE;

2229:     PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2230:     PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2231:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2233:     if (B->cmap->N > product->fill * nz_local) alg_scalable = PETSC_TRUE;
2234:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2236:     if (alg_scalable) {
2237:       alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2238:       PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2239:       PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2240:     }
2241:   }

2243:   /* Get runtime option */
2244:   if (product->api_user) {
2245:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2246:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2247:     PetscOptionsEnd();
2248:   } else {
2249:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2250:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2251:     PetscOptionsEnd();
2252:   }
2253:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2255:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2256:   PetscFunctionReturn(PETSC_SUCCESS);
2257: }

2259: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2260: {
2261:   Mat_Product *product = C->product;
2262:   Mat          A = product->A, P = product->B;
2263:   MPI_Comm     comm;
2264:   PetscBool    flg;
2265:   PetscInt     alg = 1; /* set default algorithm */
2266: #if !PetscDefined(HAVE_HYPRE)
2267:   const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
2268:   PetscInt    nalg        = 5;
2269: #else
2270:   const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
2271:   PetscInt    nalg        = 6;
2272: #endif
2273:   PetscInt pN = P->cmap->N;

2275:   PetscFunctionBegin;
2276:   /* Check matrix local sizes */
2277:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2278:   PetscCheck(A->rmap->rstart == P->rmap->rstart && A->rmap->rend == P->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, Arow (%" PetscInt_FMT ", %" PetscInt_FMT ") != Prow (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2279:              A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
2280:   PetscCheck(A->cmap->rstart == P->rmap->rstart && A->cmap->rend == P->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, Acol (%" PetscInt_FMT ", %" PetscInt_FMT ") != Prow (%" PetscInt_FMT ",%" PetscInt_FMT ")",
2281:              A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);

2283:   /* Set "nonscalable" as default algorithm */
2284:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2285:   if (flg) {
2286:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2288:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2289:     if (pN > 100000) {
2290:       MatInfo   Ainfo, Pinfo;
2291:       PetscInt  nz_local;
2292:       PetscBool alg_scalable = PETSC_FALSE;

2294:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2295:       PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
2296:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2298:       if (pN > product->fill * nz_local) alg_scalable = PETSC_TRUE;
2299:       PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2301:       if (alg_scalable) {
2302:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2303:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2304:       }
2305:     }
2306:   }

2308:   /* Get runtime option */
2309:   if (product->api_user) {
2310:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2311:     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2312:     PetscOptionsEnd();
2313:   } else {
2314:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2315:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2316:     PetscOptionsEnd();
2317:   }
2318:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2320:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2321:   PetscFunctionReturn(PETSC_SUCCESS);
2322: }

2324: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2325: {
2326:   Mat_Product *product = C->product;
2327:   Mat          A = product->A, R = product->B;

2329:   PetscFunctionBegin;
2330:   /* Check matrix local sizes */
2331:   PetscCheck(A->cmap->n == R->cmap->n && A->rmap->n == R->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, A local (%" PetscInt_FMT ", %" PetscInt_FMT "), R local (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->n,
2332:              A->rmap->n, R->rmap->n, R->cmap->n);

2334:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2335:   PetscFunctionReturn(PETSC_SUCCESS);
2336: }

2338: /*
2339:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2340: */
2341: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2342: {
2343:   Mat_Product *product     = C->product;
2344:   PetscBool    flg         = PETSC_FALSE;
2345:   PetscInt     alg         = 1; /* default algorithm */
2346:   const char  *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
2347:   PetscInt     nalg        = 3;

2349:   PetscFunctionBegin;
2350:   /* Set default algorithm */
2351:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2352:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2354:   /* Get runtime option */
2355:   if (product->api_user) {
2356:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2357:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2358:     PetscOptionsEnd();
2359:   } else {
2360:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2361:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2362:     PetscOptionsEnd();
2363:   }
2364:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2366:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2367:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2368:   PetscFunctionReturn(PETSC_SUCCESS);
2369: }

2371: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2372: {
2373:   Mat_Product *product = C->product;

2375:   PetscFunctionBegin;
2376:   switch (product->type) {
2377:   case MATPRODUCT_AB:
2378:     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2379:     break;
2380:   case MATPRODUCT_ABt:
2381:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2382:     break;
2383:   case MATPRODUCT_AtB:
2384:     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2385:     break;
2386:   case MATPRODUCT_PtAP:
2387:     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2388:     break;
2389:   case MATPRODUCT_RARt:
2390:     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2391:     break;
2392:   case MATPRODUCT_ABC:
2393:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2394:     break;
2395:   default:
2396:     break;
2397:   }
2398:   PetscFunctionReturn(PETSC_SUCCESS);
2399: }