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 defined(PETSC_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 defined(PETSC_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(void **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 = cd->a, *coa = co->a;
 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   *dummy;
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 defined(PETSC_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, &dummy));
143:   PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy));
144:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy));
145:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy));
146:   for (i = 0; i < cm; i++) {
147:     /* compute apa = A[i,:]*P */
148:     AProw_nonscalable(i, ad, ao, p_loc, p_oth, apa);

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

155:     /* 1st off-diagonal part of C */
156:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
157:     k  = 0;
158:     for (k0 = 0; k0 < conz; k0++) {
159:       if (apJ[k] >= cstart) break;
160:       ca[k0]        = apa[apJ[k]];
161:       apa[apJ[k++]] = 0.0;
162:     }

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

171:     /* 2nd off-diagonal part of C */
172:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
173:     for (; k0 < conz; k0++) {
174:       ca[k0]        = apa[apJ[k]];
175:       apa[apJ[k++]] = 0.0;
176:     }
177:   }
178:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
179:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
180:   PetscFunctionReturn(PETSC_SUCCESS);
181: }

183: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat A, Mat P, PetscReal fill, Mat C)
184: {
185:   MPI_Comm             comm;
186:   PetscMPIInt          size;
187:   MatProductCtx_APMPI *ptap;
188:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
189:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
190:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
191:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
192:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
193:   PetscInt            *lnk, i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi;
194:   PetscInt             am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n;
195:   PetscBT              lnkbt;
196:   PetscReal            afill;
197:   MatType              mtype;

199:   PetscFunctionBegin;
200:   MatCheckProduct(C, 4);
201:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
202:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
203:   PetscCallMPI(MPI_Comm_size(comm, &size));

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

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

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

214:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
215:   pi_loc = p_loc->i;
216:   pj_loc = p_loc->j;
217:   if (size > 1) {
218:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
219:     pi_oth = p_oth->i;
220:     pj_oth = p_oth->j;
221:   } else {
222:     p_oth  = NULL;
223:     pi_oth = NULL;
224:     pj_oth = NULL;
225:   }

227:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
228:   PetscCall(PetscMalloc1(am + 1, &api));
229:   ptap->api = api;
230:   api[0]    = 0;

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

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

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

264:     apnz       = lnk[0];
265:     api[i + 1] = api[i] + apnz;

267:     /* if free space is not available, double the total space in the list */
268:     if (current_space->local_remaining < apnz) {
269:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), &current_space));
270:       nspacedouble++;
271:     }

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

277:     current_space->array += apnz;
278:     current_space->local_used += apnz;
279:     current_space->local_remaining -= apnz;
280:   }

282:   /* Allocate space for apj, initialize apj, and */
283:   /* destroy list of free space and other temporary array(s) */
284:   PetscCall(PetscMalloc1(api[am], &ptap->apj));
285:   apj = ptap->apj;
286:   PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
287:   PetscCall(PetscLLDestroy(lnk, lnkbt));

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

292:   /* set and assemble symbolic parallel matrix C */
293:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
294:   PetscCall(MatSetBlockSizesFromMats(C, A, P));

296:   PetscCall(MatGetType(A, &mtype));
297:   PetscCall(MatSetType(C, mtype));
298:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
299:   MatPreallocateEnd(dnz, onz);

301:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
302:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
303:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
304:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
305:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

307:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
308:   C->ops->productnumeric = MatProductNumeric_AB;

310:   /* attach the supporting struct to C for reuse */
311:   C->product->data    = ptap;
312:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

314:   /* set MatInfo */
315:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
316:   if (afill < 1.0) afill = 1.0;
317:   C->info.mallocs           = nspacedouble;
318:   C->info.fill_ratio_given  = fill;
319:   C->info.fill_ratio_needed = afill;

321: #if defined(PETSC_USE_INFO)
322:   if (api[am]) {
323:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
324:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
325:   } else {
326:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
327:   }
328: #endif
329:   PetscFunctionReturn(PETSC_SUCCESS);
330: }

332: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat, Mat, PetscReal, Mat);
333: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat, Mat, Mat);

335: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AB(Mat C)
336: {
337:   Mat_Product *product = C->product;
338:   Mat          A = product->A, B = product->B;

340:   PetscFunctionBegin;
341:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
342:     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);

344:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
345:   C->ops->productsymbolic = MatProductSymbolic_AB;
346:   PetscFunctionReturn(PETSC_SUCCESS);
347: }

349: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(Mat C)
350: {
351:   Mat_Product *product = C->product;
352:   Mat          A = product->A, B = product->B;

354:   PetscFunctionBegin;
355:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
356:     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);

358:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
359:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
360:   PetscFunctionReturn(PETSC_SUCCESS);
361: }

363: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
364: {
365:   Mat_Product *product = C->product;

367:   PetscFunctionBegin;
368:   switch (product->type) {
369:   case MATPRODUCT_AB:
370:     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C));
371:     break;
372:   case MATPRODUCT_AtB:
373:     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C));
374:     break;
375:   default:
376:     break;
377:   }
378:   PetscFunctionReturn(PETSC_SUCCESS);
379: }

381: typedef struct {
382:   Mat           workB, workB1;
383:   MPI_Request  *rwaits, *swaits;
384:   PetscInt      nsends, nrecvs;
385:   MPI_Datatype *stype, *rtype;
386:   PetscInt      blda;
387: } MPIAIJ_MPIDense;

389: static PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void **ctx)
390: {
391:   MPIAIJ_MPIDense *contents = *(MPIAIJ_MPIDense **)ctx;
392:   PetscInt         i;

394:   PetscFunctionBegin;
395:   PetscCall(MatDestroy(&contents->workB));
396:   PetscCall(MatDestroy(&contents->workB1));
397:   for (i = 0; i < contents->nsends; i++) PetscCallMPI(MPI_Type_free(&contents->stype[i]));
398:   for (i = 0; i < contents->nrecvs; i++) PetscCallMPI(MPI_Type_free(&contents->rtype[i]));
399:   PetscCall(PetscFree4(contents->stype, contents->rtype, contents->rwaits, contents->swaits));
400:   PetscCall(PetscFree(contents));
401:   PetscFunctionReturn(PETSC_SUCCESS);
402: }

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

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

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

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

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

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

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

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

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

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

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

478:   PetscCall(PetscMalloc1(Bm + 1, &disp));
479:   for (PetscMPIInt i = 0; i < nsends; i++) {
480:     PetscCall(PetscMPIIntCast(sstarts[i + 1] - sstarts[i], &nrows_to));
481:     for (PetscInt j = 0; j < nrows_to; j++) PetscCall(PetscMPIIntCast(sindices[sstarts[i] + j], &disp[j])); /* rowB to be sent */
482:     PetscCallMPI(MPI_Type_create_indexed_block(nrows_to, 1, disp, MPIU_SCALAR, &type1));
483:     PetscCallMPI(MPI_Type_create_resized(type1, 0, blda * sizeof(PetscScalar), &stype[i]));
484:     PetscCallMPI(MPI_Type_commit(&stype[i]));
485:     PetscCallMPI(MPI_Type_free(&type1));
486:   }

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

498:   PetscCall(PetscFree(disp));
499:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, NULL, NULL));
500:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, NULL, NULL));
501:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
502:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
503:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

505:   C->product->data       = contents;
506:   C->product->destroy    = MatMPIAIJ_MPIDenseDestroy;
507:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
508:   PetscFunctionReturn(PETSC_SUCCESS);
509: }

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

513: /*
514:     Performs an efficient scatter on the rows of B needed by this process; this is
515:     a modification of the VecScatterBegin_() routines.

517:     Input: If Bbidx = 0, uses B = Bb, else B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
518: */

520: static PetscErrorCode MatMPIDenseScatter(Mat A, Mat B, PetscInt Bbidx, Mat C, Mat *outworkB)
521: {
522:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)A->data;
523:   const PetscScalar *b;
524:   PetscScalar       *rvalues;
525:   VecScatter         ctx = aij->Mvctx;
526:   const PetscInt    *sindices, *sstarts, *rstarts;
527:   const PetscMPIInt *sprocs, *rprocs;
528:   PetscMPIInt        nsends, nrecvs;
529:   MPI_Request       *swaits, *rwaits;
530:   MPI_Comm           comm;
531:   PetscMPIInt        tag = ((PetscObject)ctx)->tag, ncols, nrows, nsends_mpi, nrecvs_mpi;
532:   MPIAIJ_MPIDense   *contents;
533:   Mat                workB;
534:   MPI_Datatype      *stype, *rtype;
535:   PetscInt           blda;

537:   PetscFunctionBegin;
538:   MatCheckProduct(C, 4);
539:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
540:   PetscCall(PetscMPIIntCast(B->cmap->N, &ncols));
541:   PetscCall(PetscMPIIntCast(aij->B->cmap->n, &nrows));
542:   contents = (MPIAIJ_MPIDense *)C->product->data;
543:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL /*bs*/));
544:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL /*bs*/));
545:   PetscCall(PetscMPIIntCast(nsends, &nsends_mpi));
546:   PetscCall(PetscMPIIntCast(nrecvs, &nrecvs_mpi));
547:   if (Bbidx == 0) workB = *outworkB = contents->workB;
548:   else workB = *outworkB = contents->workB1;
549:   PetscCheck(nrows == workB->rmap->n, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Number of rows of workB %" PetscInt_FMT " not equal to columns of aij->B %d", workB->cmap->n, nrows);
550:   swaits = contents->swaits;
551:   rwaits = contents->rwaits;

553:   PetscCall(MatDenseGetArrayRead(B, &b));
554:   PetscCall(MatDenseGetLDA(B, &blda));
555:   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);
556:   PetscCall(MatDenseGetArray(workB, &rvalues));

558:   /* Post recv, use MPI derived data type to save memory */
559:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
560:   rtype = contents->rtype;
561:   for (PetscMPIInt i = 0; i < nrecvs; i++) PetscCallMPI(MPIU_Irecv(rvalues + (rstarts[i] - rstarts[0]), ncols, rtype[i], rprocs[i], tag, comm, rwaits + i));

563:   stype = contents->stype;
564:   for (PetscMPIInt i = 0; i < nsends; i++) PetscCallMPI(MPIU_Isend(b, ncols, stype[i], sprocs[i], tag, comm, swaits + i));

566:   if (nrecvs) PetscCallMPI(MPI_Waitall(nrecvs_mpi, rwaits, MPI_STATUSES_IGNORE));
567:   if (nsends) PetscCallMPI(MPI_Waitall(nsends_mpi, swaits, MPI_STATUSES_IGNORE));

569:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL));
570:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL));
571:   PetscCall(MatDenseRestoreArrayRead(B, &b));
572:   PetscCall(MatDenseRestoreArray(workB, &rvalues));
573:   PetscFunctionReturn(PETSC_SUCCESS);
574: }

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

584:   PetscFunctionBegin;
585:   MatCheckProduct(C, 3);
586:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
587:   contents = (MPIAIJ_MPIDense *)C->product->data;
588:   /* diagonal block of A times all local rows of B */
589:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
590:   PetscCall(MatMatMult(aij->A, bdense->A, MAT_REUSE_MATRIX, PETSC_CURRENT, &cdense->A));
591:   if (contents->workB->cmap->n == B->cmap->N) {
592:     /* get off processor parts of B needed to complete C=A*B */
593:     PetscCall(MatMPIDenseScatter(A, B, 0, C, &workB));

595:     /* off-diagonal block of A times nonlocal rows of B */
596:     PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
597:   } else {
598:     Mat       Bb, Cb;
599:     PetscInt  BN = B->cmap->N, n = contents->workB->cmap->n;
600:     PetscBool ccpu;

602:     PetscCheck(n > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Column block size %" PetscInt_FMT " must be positive", n);
603:     /* Prevent from unneeded copies back and forth from the GPU
604:        when getting and restoring the submatrix
605:        We need a proper GPU code for AIJ * dense in parallel */
606:     PetscCall(MatBoundToCPU(C, &ccpu));
607:     PetscCall(MatBindToCPU(C, PETSC_TRUE));
608:     for (PetscInt i = 0; i < BN; i += n) {
609:       PetscCall(MatDenseGetSubMatrix(B, PETSC_DECIDE, PETSC_DECIDE, i, PetscMin(i + n, BN), &Bb));
610:       PetscCall(MatDenseGetSubMatrix(C, PETSC_DECIDE, PETSC_DECIDE, i, PetscMin(i + n, BN), &Cb));

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

615:       /* off-diagonal block of A times nonlocal rows of B */
616:       cdense = (Mat_MPIDense *)Cb->data;
617:       PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
618:       PetscCall(MatDenseRestoreSubMatrix(B, &Bb));
619:       PetscCall(MatDenseRestoreSubMatrix(C, &Cb));
620:     }
621:     PetscCall(MatBindToCPU(C, ccpu));
622:   }
623:   PetscFunctionReturn(PETSC_SUCCESS);
624: }

626: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A, Mat P, Mat C)
627: {
628:   Mat_MPIAIJ          *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
629:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
630:   Mat_SeqAIJ          *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
631:   PetscInt            *adi = ad->i, *adj, *aoi = ao->i, *aoj;
632:   PetscScalar         *ada, *aoa, *cda = cd->a, *coa = co->a;
633:   Mat_SeqAIJ          *p_loc, *p_oth;
634:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *pj;
635:   PetscScalar         *pa_loc, *pa_oth, *pa, valtmp, *ca;
636:   PetscInt             cm = C->rmap->n, anz, pnz;
637:   MatProductCtx_APMPI *ptap;
638:   PetscScalar         *apa_sparse;
639:   const PetscScalar   *dummy;
640:   PetscInt            *api, *apj, *apJ, i, j, k, row;
641:   PetscInt             cstart = C->cmap->rstart;
642:   PetscInt             cdnz, conz, k0, k1, nextp;
643:   MPI_Comm             comm;
644:   PetscMPIInt          size;

646:   PetscFunctionBegin;
647:   MatCheckProduct(C, 3);
648:   ptap = (MatProductCtx_APMPI *)C->product->data;
649:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
650:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
651:   PetscCallMPI(MPI_Comm_size(comm, &size));
652:   PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");

654:   /* flag CPU mask for C */
655: #if defined(PETSC_HAVE_DEVICE)
656:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
657:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
658:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
659: #endif
660:   apa_sparse = ptap->apa;

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

667:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
668:   /* get data from symbolic products */
669:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
670:   pi_loc = p_loc->i;
671:   pj_loc = p_loc->j;
672:   pa_loc = p_loc->a;
673:   if (size > 1) {
674:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
675:     pi_oth = p_oth->i;
676:     pj_oth = p_oth->j;
677:     pa_oth = p_oth->a;
678:   } else {
679:     p_oth  = NULL;
680:     pi_oth = NULL;
681:     pj_oth = NULL;
682:     pa_oth = NULL;
683:   }

685:   /* trigger copy to CPU */
686:   PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy));
687:   PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy));
688:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy));
689:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy));
690:   api = ptap->api;
691:   apj = ptap->apj;
692:   for (i = 0; i < cm; i++) {
693:     apJ = apj + api[i];

695:     /* diagonal portion of A */
696:     anz = adi[i + 1] - adi[i];
697:     adj = ad->j + adi[i];
698:     ada = ad->a + adi[i];
699:     for (j = 0; j < anz; j++) {
700:       row = adj[j];
701:       pnz = pi_loc[row + 1] - pi_loc[row];
702:       pj  = pj_loc + pi_loc[row];
703:       pa  = pa_loc + pi_loc[row];
704:       /* perform sparse axpy */
705:       valtmp = ada[j];
706:       nextp  = 0;
707:       for (k = 0; nextp < pnz; k++) {
708:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
709:           apa_sparse[k] += valtmp * pa[nextp++];
710:         }
711:       }
712:       PetscCall(PetscLogFlops(2.0 * pnz));
713:     }

715:     /* off-diagonal portion of A */
716:     anz = aoi[i + 1] - aoi[i];
717:     aoj = PetscSafePointerPlusOffset(ao->j, aoi[i]);
718:     aoa = PetscSafePointerPlusOffset(ao->a, aoi[i]);
719:     for (j = 0; j < anz; j++) {
720:       row = aoj[j];
721:       pnz = pi_oth[row + 1] - pi_oth[row];
722:       pj  = pj_oth + pi_oth[row];
723:       pa  = pa_oth + pi_oth[row];
724:       /* perform sparse axpy */
725:       valtmp = aoa[j];
726:       nextp  = 0;
727:       for (k = 0; nextp < pnz; k++) {
728:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
729:           apa_sparse[k] += valtmp * pa[nextp++];
730:         }
731:       }
732:       PetscCall(PetscLogFlops(2.0 * pnz));
733:     }

735:     /* set values in C */
736:     cdnz = cd->i[i + 1] - cd->i[i];
737:     conz = co->i[i + 1] - co->i[i];

739:     /* 1st off-diagonal part of C */
740:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
741:     k  = 0;
742:     for (k0 = 0; k0 < conz; k0++) {
743:       if (apJ[k] >= cstart) break;
744:       ca[k0]        = apa_sparse[k];
745:       apa_sparse[k] = 0.0;
746:       k++;
747:     }

749:     /* diagonal part of C */
750:     ca = cda + cd->i[i];
751:     for (k1 = 0; k1 < cdnz; k1++) {
752:       ca[k1]        = apa_sparse[k];
753:       apa_sparse[k] = 0.0;
754:       k++;
755:     }

757:     /* 2nd off-diagonal part of C */
758:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
759:     for (; k0 < conz; k0++) {
760:       ca[k0]        = apa_sparse[k];
761:       apa_sparse[k] = 0.0;
762:       k++;
763:     }
764:   }
765:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
766:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
767:   PetscFunctionReturn(PETSC_SUCCESS);
768: }

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

786:   PetscFunctionBegin;
787:   MatCheckProduct(C, 4);
788:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
789:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
790:   PetscCallMPI(MPI_Comm_size(comm, &size));

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

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

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

801:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
802:   pi_loc = p_loc->i;
803:   pj_loc = p_loc->j;
804:   if (size > 1) {
805:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
806:     pi_oth = p_oth->i;
807:     pj_oth = p_oth->j;
808:   } else {
809:     p_oth  = NULL;
810:     pi_oth = NULL;
811:     pj_oth = NULL;
812:   }

814:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
815:   PetscCall(PetscMalloc1(am + 1, &api));
816:   ptap->api = api;
817:   api[0]    = 0;

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

821:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
822:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space));
823:   current_space = free_space;
824:   MatPreallocateBegin(comm, am, pn, dnz, onz);
825:   for (i = 0; i < am; i++) {
826:     /* diagonal portion of A */
827:     nzi = adi[i + 1] - adi[i];
828:     for (j = 0; j < nzi; j++) {
829:       row  = *adj++;
830:       pnz  = pi_loc[row + 1] - pi_loc[row];
831:       Jptr = pj_loc + pi_loc[row];
832:       /* Expand list if it is not long enough */
833:       if (pnz + apnz_max > lsize) {
834:         lsize = pnz + apnz_max;
835:         PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
836:       }
837:       /* add non-zero cols of P into the sorted linked list lnk */
838:       PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
839:       apnz       = *lnk; /* The first element in the list is the number of items in the list */
840:       api[i + 1] = api[i] + apnz;
841:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
842:     }
843:     /* off-diagonal portion of A */
844:     nzi = aoi[i + 1] - aoi[i];
845:     for (j = 0; j < nzi; j++) {
846:       row  = *aoj++;
847:       pnz  = pi_oth[row + 1] - pi_oth[row];
848:       Jptr = pj_oth + pi_oth[row];
849:       /* Expand list if it is not long enough */
850:       if (pnz + apnz_max > lsize) {
851:         lsize = pnz + apnz_max;
852:         PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
853:       }
854:       /* add non-zero cols of P into the sorted linked list lnk */
855:       PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
856:       apnz       = *lnk; /* The first element in the list is the number of items in the list */
857:       api[i + 1] = api[i] + apnz;
858:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
859:     }

861:     /* add missing diagonal entry */
862:     if (C->force_diagonals) {
863:       j = i + rstart; /* column index */
864:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &j, lnk));
865:     }

867:     apnz       = *lnk;
868:     api[i + 1] = api[i] + apnz;
869:     if (apnz > apnz_max) apnz_max = apnz;

871:     /* if free space is not available, double the total space in the list */
872:     if (current_space->local_remaining < apnz) {
873:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), &current_space));
874:       nspacedouble++;
875:     }

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

881:     current_space->array += apnz;
882:     current_space->local_used += apnz;
883:     current_space->local_remaining -= apnz;
884:   }

886:   /* Allocate space for apj, initialize apj, and */
887:   /* destroy list of free space and other temporary array(s) */
888:   PetscCall(PetscMalloc1(api[am], &ptap->apj));
889:   apj = ptap->apj;
890:   PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
891:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));

893:   /* create and assemble symbolic parallel matrix C */
894:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
895:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
896:   PetscCall(MatGetType(A, &mtype));
897:   PetscCall(MatSetType(C, mtype));
898:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
899:   MatPreallocateEnd(dnz, onz);

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

904:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
905:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
906:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
907:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
908:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

910:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
911:   C->ops->productnumeric = MatProductNumeric_AB;

913:   /* attach the supporting struct to C for reuse */
914:   C->product->data    = ptap;
915:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

917:   /* set MatInfo */
918:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
919:   if (afill < 1.0) afill = 1.0;
920:   C->info.mallocs           = nspacedouble;
921:   C->info.fill_ratio_given  = fill;
922:   C->info.fill_ratio_needed = afill;

924: #if defined(PETSC_USE_INFO)
925:   if (api[am]) {
926:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
927:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
928:   } else {
929:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
930:   }
931: #endif
932:   PetscFunctionReturn(PETSC_SUCCESS);
933: }

935: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
936: /* Three input arrays are merged to one output array. The size of the    */
937: /* output array is also output. Duplicate entries only show up once.     */
938: static void Merge3SortedArrays(PetscInt size1, PetscInt *in1, PetscInt size2, PetscInt *in2, PetscInt size3, PetscInt *in3, PetscInt *size4, PetscInt *out)
939: {
940:   int i = 0, j = 0, k = 0, l = 0;

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

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

977:   while (i < size1 && k < size3) {
978:     if (in1[i] < in3[k]) {
979:       out[l++] = in1[i++];
980:     } else if (in1[i] > in3[k]) {
981:       out[l++] = in3[k++];
982:     } else {
983:       out[l++] = in1[i];
984:       i++, k++;
985:     }
986:   }

988:   while (k < size3 && j < size2) {
989:     if (in3[k] < in2[j]) {
990:       out[l++] = in3[k++];
991:     } else if (in3[k] > in2[j]) {
992:       out[l++] = in2[j++];
993:     } else {
994:       out[l++] = in3[k];
995:       k++, j++;
996:     }
997:   }

999:   /* Traverse one remaining array */
1000:   while (i < size1) out[l++] = in1[i++];
1001:   while (j < size2) out[l++] = in2[j++];
1002:   while (k < size3) out[l++] = in3[k++];

1004:   *size4 = l;
1005: }

1007: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1008: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1009: /* matrix-matrix multiplications.  */
1010: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1011: {
1012:   MPI_Comm             comm;
1013:   PetscMPIInt          size;
1014:   MatProductCtx_APMPI *ptap;
1015:   PetscFreeSpaceList   free_space_diag = NULL, current_space = NULL;
1016:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
1017:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
1018:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
1019:   Mat_SeqAIJ          *adpd_seq, *p_off, *aopoth_seq;
1020:   PetscInt             adponz, adpdnz;
1021:   PetscInt            *pi_loc, *dnz, *onz;
1022:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
1023:   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;
1024:   PetscInt             am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
1025:   PetscBT              lnkbt;
1026:   PetscReal            afill;
1027:   PetscMPIInt          rank;
1028:   Mat                  adpd, aopoth;
1029:   MatType              mtype;
1030:   const char          *prefix;

1032:   PetscFunctionBegin;
1033:   MatCheckProduct(C, 4);
1034:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1035:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1036:   PetscCallMPI(MPI_Comm_size(comm, &size));
1037:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1038:   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));

1040:   /* create struct MatProductCtx_APMPI and attached it to C later */
1041:   PetscCall(PetscNew(&ptap));

1043:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1044:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));

1046:   /* get P_loc by taking all local rows of P */
1047:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));

1049:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
1050:   pi_loc = p_loc->i;

1052:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1053:   PetscCall(PetscMalloc1(am + 1, &api));
1054:   PetscCall(PetscMalloc1(am + 1, &adpoi));

1056:   adpoi[0]  = 0;
1057:   ptap->api = api;
1058:   api[0]    = 0;

1060:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1061:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
1062:   MatPreallocateBegin(comm, am, pn, dnz, onz);

1064:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1065:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1066:   PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
1067:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1068:   PetscCall(MatSetOptionsPrefix(adpd, prefix));
1069:   PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));

1071:   PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
1072:   PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
1073:   PetscCall(MatProductSetFill(adpd, fill));
1074:   PetscCall(MatProductSetFromOptions(adpd));

1076:   adpd->force_diagonals = C->force_diagonals;
1077:   PetscCall(MatProductSymbolic(adpd));

1079:   adpd_seq = (Mat_SeqAIJ *)((adpd)->data);
1080:   adpdi    = adpd_seq->i;
1081:   adpdj    = adpd_seq->j;
1082:   p_off    = (Mat_SeqAIJ *)p->B->data;
1083:   poff_i   = p_off->i;
1084:   poff_j   = p_off->j;

1086:   /* j_temp stores indices of a result row before they are added to the linked list */
1087:   PetscCall(PetscMalloc1(pN, &j_temp));

1089:   /* Symbolic calc of the A_diag * p_loc_off */
1090:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1091:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
1092:   current_space = free_space_diag;

1094:   for (i = 0; i < am; i++) {
1095:     /* A_diag * P_loc_off */
1096:     nzi = adi[i + 1] - adi[i];
1097:     for (j = 0; j < nzi; j++) {
1098:       row  = *adj++;
1099:       pnz  = poff_i[row + 1] - poff_i[row];
1100:       Jptr = poff_j + poff_i[row];
1101:       for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
1102:       /* add non-zero cols of P into the sorted linked list lnk */
1103:       PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
1104:     }

1106:     adponz       = lnk[0];
1107:     adpoi[i + 1] = adpoi[i] + adponz;

1109:     /* if free space is not available, double the total space in the list */
1110:     if (current_space->local_remaining < adponz) {
1111:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), &current_space));
1112:       nspacedouble++;
1113:     }

1115:     /* Copy data into free space, then initialize lnk */
1116:     PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));

1118:     current_space->array += adponz;
1119:     current_space->local_used += adponz;
1120:     current_space->local_remaining -= adponz;
1121:   }

1123:   /* Symbolic calc of A_off * P_oth */
1124:   PetscCall(MatSetOptionsPrefix(a->B, prefix));
1125:   PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
1126:   PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
1127:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1128:   aopoth_seq = (Mat_SeqAIJ *)((aopoth)->data);
1129:   aopothi    = aopoth_seq->i;
1130:   aopothj    = aopoth_seq->j;

1132:   /* Allocate space for apj, adpj, aopj, ... */
1133:   /* destroy lists of free space and other temporary array(s) */

1135:   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am], &ptap->apj));
1136:   PetscCall(PetscMalloc1(adpoi[am], &adpoj));

1138:   /* Copy from linked list to j-array */
1139:   PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
1140:   PetscCall(PetscLLDestroy(lnk, lnkbt));

1142:   adpoJ = adpoj;
1143:   adpdJ = adpdj;
1144:   aopJ  = aopothj;
1145:   apj   = ptap->apj;
1146:   apJ   = apj; /* still empty */

1148:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1149:   /* A_diag * P_loc_diag to get A*P */
1150:   for (i = 0; i < am; i++) {
1151:     aopnz  = aopothi[i + 1] - aopothi[i];
1152:     adponz = adpoi[i + 1] - adpoi[i];
1153:     adpdnz = adpdi[i + 1] - adpdi[i];

1155:     /* Correct indices from A_diag*P_diag */
1156:     for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
1157:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1158:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1159:     PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));

1161:     aopJ += aopnz;
1162:     adpoJ += adponz;
1163:     adpdJ += adpdnz;
1164:     apJ += apnz;
1165:     api[i + 1] = api[i] + apnz;
1166:   }

1168:   /* malloc apa to store dense row A[i,:]*P */
1169:   PetscCall(PetscCalloc1(pN, &ptap->apa));

1171:   /* create and assemble symbolic parallel matrix C */
1172:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1173:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
1174:   PetscCall(MatGetType(A, &mtype));
1175:   PetscCall(MatSetType(C, mtype));
1176:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1177:   MatPreallocateEnd(dnz, onz);

1179:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1180:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
1181:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1182:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1183:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1185:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1186:   C->ops->productnumeric = MatProductNumeric_AB;

1188:   /* attach the supporting struct to C for reuse */
1189:   C->product->data    = ptap;
1190:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

1192:   /* set MatInfo */
1193:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1194:   if (afill < 1.0) afill = 1.0;
1195:   C->info.mallocs           = nspacedouble;
1196:   C->info.fill_ratio_given  = fill;
1197:   C->info.fill_ratio_needed = afill;

1199: #if defined(PETSC_USE_INFO)
1200:   if (api[am]) {
1201:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1202:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1203:   } else {
1204:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1205:   }
1206: #endif

1208:   PetscCall(MatDestroy(&aopoth));
1209:   PetscCall(MatDestroy(&adpd));
1210:   PetscCall(PetscFree(j_temp));
1211:   PetscCall(PetscFree(adpoj));
1212:   PetscCall(PetscFree(adpoi));
1213:   PetscFunctionReturn(PETSC_SUCCESS);
1214: }

1216: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1217: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
1218: {
1219:   MatProductCtx_APMPI *ptap;
1220:   Mat                  Pt;

1222:   PetscFunctionBegin;
1223:   MatCheckProduct(C, 3);
1224:   ptap = (MatProductCtx_APMPI *)C->product->data;
1225:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1226:   PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");

1228:   Pt = ptap->Pt;
1229:   PetscCall(MatTransposeSetPrecursor(P, Pt));
1230:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
1231:   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
1232:   PetscFunctionReturn(PETSC_SUCCESS);
1233: }

1235: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1236: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, PetscReal fill, Mat C)
1237: {
1238:   MatProductCtx_APMPI     *ptap;
1239:   Mat_MPIAIJ              *p = (Mat_MPIAIJ *)P->data;
1240:   MPI_Comm                 comm;
1241:   PetscMPIInt              size, rank;
1242:   PetscFreeSpaceList       free_space = NULL, current_space = NULL;
1243:   PetscInt                 pn = P->cmap->n, aN = A->cmap->N, an = A->cmap->n;
1244:   PetscInt                *lnk, i, k, rstart;
1245:   PetscBT                  lnkbt;
1246:   PetscMPIInt              tagi, tagj, *len_si, *len_s, *len_ri, nrecv, proc, nsend;
1247:   PETSC_UNUSED PetscMPIInt icompleted = 0;
1248:   PetscInt               **buf_rj, **buf_ri, **buf_ri_k, row, ncols, *cols;
1249:   PetscInt                 len, *dnz, *onz, *owners, nzi;
1250:   PetscInt                 nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1251:   MPI_Request             *swaits, *rwaits;
1252:   MPI_Status              *sstatus, rstatus;
1253:   PetscLayout              rowmap;
1254:   PetscInt                *owners_co, *coi, *coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1255:   PetscMPIInt             *len_r, *id_r;          /* array of length of comm->size, store send/recv matrix values */
1256:   PetscInt                *Jptr, *prmap = p->garray, con, j, Crmax;
1257:   Mat_SeqAIJ              *a_loc, *c_loc, *c_oth;
1258:   PetscHMapI               ta;
1259:   MatType                  mtype;
1260:   const char              *prefix;

1262:   PetscFunctionBegin;
1263:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1264:   PetscCallMPI(MPI_Comm_size(comm, &size));
1265:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1267:   /* create symbolic parallel matrix C */
1268:   PetscCall(MatGetType(A, &mtype));
1269:   PetscCall(MatSetType(C, mtype));

1271:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1273:   /* create struct MatProductCtx_APMPI and attached it to C later */
1274:   PetscCall(PetscNew(&ptap));

1276:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1277:   PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
1278:   PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));

1280:   /* (1) compute symbolic A_loc */
1281:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));

1283:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1284:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1285:   PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
1286:   PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
1287:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
1288:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));

1290:   /* (3) send coj of C_oth to other processors  */
1291:   /* determine row ownership */
1292:   PetscCall(PetscLayoutCreate(comm, &rowmap));
1293:   rowmap->n  = pn;
1294:   rowmap->bs = 1;
1295:   PetscCall(PetscLayoutSetUp(rowmap));
1296:   owners = rowmap->range;

1298:   /* determine the number of messages to send, their lengths */
1299:   PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 1, &owners_co));
1300:   PetscCall(PetscArrayzero(len_s, size));
1301:   PetscCall(PetscArrayzero(len_si, size));

1303:   c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
1304:   coi   = c_oth->i;
1305:   coj   = c_oth->j;
1306:   con   = ptap->C_oth->rmap->n;
1307:   proc  = 0;
1308:   for (i = 0; i < con; i++) {
1309:     while (prmap[i] >= owners[proc + 1]) proc++;
1310:     len_si[proc]++;                     /* num of rows in Co(=Pt*A) to be sent to [proc] */
1311:     len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1312:   }

1314:   len          = 0; /* max length of buf_si[], see (4) */
1315:   owners_co[0] = 0;
1316:   nsend        = 0;
1317:   for (proc = 0; proc < size; proc++) {
1318:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1319:     if (len_s[proc]) {
1320:       nsend++;
1321:       len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1322:       len += len_si[proc];
1323:     }
1324:   }

1326:   /* determine the number and length of messages to receive for coi and coj  */
1327:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
1328:   PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));

1330:   /* post the Irecv and Isend of coj */
1331:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1332:   PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
1333:   PetscCall(PetscMalloc1(nsend, &swaits));
1334:   for (proc = 0, k = 0; proc < size; proc++) {
1335:     if (!len_s[proc]) continue;
1336:     i = owners_co[proc];
1337:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1338:     k++;
1339:   }

1341:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1342:   PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
1343:   PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
1344:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
1345:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
1346:   c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;

1348:   /* receives coj are complete */
1349:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1350:   PetscCall(PetscFree(rwaits));
1351:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1353:   /* add received column indices into ta to update Crmax */
1354:   a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;

1356:   /* create and initialize a linked list */
1357:   PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
1358:   MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);

1360:   for (k = 0; k < nrecv; k++) { /* k-th received message */
1361:     Jptr = buf_rj[k];
1362:     for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1363:   }
1364:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
1365:   PetscCall(PetscHMapIDestroy(&ta));

1367:   /* (4) send and recv coi */
1368:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1369:   PetscCall(PetscPostIrecvInt(comm, tagi, nrecv, id_r, len_ri, &buf_ri, &rwaits));
1370:   PetscCall(PetscMalloc1(len, &buf_s));
1371:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1372:   for (proc = 0, k = 0; proc < size; proc++) {
1373:     if (!len_s[proc]) continue;
1374:     /* form outgoing message for i-structure:
1375:          buf_si[0]:                 nrows to be sent
1376:                [1:nrows]:           row index (global)
1377:                [nrows+1:2*nrows+1]: i-structure index
1378:     */
1379:     nrows       = len_si[proc] / 2 - 1; /* num of rows in Co to be sent to [proc] */
1380:     buf_si_i    = buf_si + nrows + 1;
1381:     buf_si[0]   = nrows;
1382:     buf_si_i[0] = 0;
1383:     nrows       = 0;
1384:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1385:       nzi                 = coi[i + 1] - coi[i];
1386:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1387:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1388:       nrows++;
1389:     }
1390:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1391:     k++;
1392:     buf_si += len_si[proc];
1393:   }
1394:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1395:   PetscCall(PetscFree(rwaits));
1396:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1398:   PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
1399:   PetscCall(PetscFree(len_ri));
1400:   PetscCall(PetscFree(swaits));
1401:   PetscCall(PetscFree(buf_s));

1403:   /* (5) compute the local portion of C      */
1404:   /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
1405:   PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
1406:   current_space = free_space;

1408:   PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
1409:   for (k = 0; k < nrecv; k++) {
1410:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1411:     nrows       = *buf_ri_k[k];
1412:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1413:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1414:   }

1416:   MatPreallocateBegin(comm, pn, an, dnz, onz);
1417:   PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
1418:   for (i = 0; i < pn; i++) { /* for each local row of C */
1419:     /* add C_loc into C */
1420:     nzi  = c_loc->i[i + 1] - c_loc->i[i];
1421:     Jptr = c_loc->j + c_loc->i[i];
1422:     PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));

1424:     /* add received col data into lnk */
1425:     for (k = 0; k < nrecv; k++) { /* k-th received message */
1426:       if (i == *nextrow[k]) {     /* i-th row */
1427:         nzi  = *(nextci[k] + 1) - *nextci[k];
1428:         Jptr = buf_rj[k] + *nextci[k];
1429:         PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1430:         nextrow[k]++;
1431:         nextci[k]++;
1432:       }
1433:     }

1435:     /* add missing diagonal entry */
1436:     if (C->force_diagonals) {
1437:       k = i + owners[rank]; /* column index */
1438:       PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
1439:     }

1441:     nzi = lnk[0];

1443:     /* copy data into free space, then initialize lnk */
1444:     PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
1445:     PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
1446:   }
1447:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1448:   PetscCall(PetscLLDestroy(lnk, lnkbt));
1449:   PetscCall(PetscFreeSpaceDestroy(free_space));

1451:   /* local sizes and preallocation */
1452:   PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
1453:   PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
1454:   PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
1455:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1456:   MatPreallocateEnd(dnz, onz);

1458:   /* add C_loc and C_oth to C */
1459:   PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
1460:   for (i = 0; i < pn; i++) {
1461:     ncols = c_loc->i[i + 1] - c_loc->i[i];
1462:     cols  = c_loc->j + c_loc->i[i];
1463:     row   = rstart + i;
1464:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));

1466:     if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
1467:   }
1468:   for (i = 0; i < con; i++) {
1469:     ncols = c_oth->i[i + 1] - c_oth->i[i];
1470:     cols  = c_oth->j + c_oth->i[i];
1471:     row   = prmap[i];
1472:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1473:   }
1474:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1475:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1476:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1478:   /* members in merge */
1479:   PetscCall(PetscFree(id_r));
1480:   PetscCall(PetscFree(len_r));
1481:   PetscCall(PetscFree(buf_ri[0]));
1482:   PetscCall(PetscFree(buf_ri));
1483:   PetscCall(PetscFree(buf_rj[0]));
1484:   PetscCall(PetscFree(buf_rj));
1485:   PetscCall(PetscLayoutDestroy(&rowmap));

1487:   /* attach the supporting struct to C for reuse */
1488:   C->product->data    = ptap;
1489:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
1490:   PetscFunctionReturn(PETSC_SUCCESS);
1491: }

1493: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
1494: {
1495:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
1496:   Mat_SeqAIJ          *c_seq;
1497:   MatProductCtx_APMPI *ptap;
1498:   Mat                  A_loc, C_loc, C_oth;
1499:   PetscInt             i, rstart, rend, cm, ncols, row;
1500:   const PetscInt      *cols;
1501:   const PetscScalar   *vals;

1503:   PetscFunctionBegin;
1504:   MatCheckProduct(C, 3);
1505:   ptap = (MatProductCtx_APMPI *)C->product->data;
1506:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1507:   PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1508:   PetscCall(MatZeroEntries(C));

1510:   /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1511:   /* 1) get R = Pd^T, Ro = Po^T */
1512:   PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
1513:   PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
1514:   PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
1515:   PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));

1517:   /* 2) compute numeric A_loc */
1518:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));

1520:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1521:   A_loc = ptap->A_loc;
1522:   PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
1523:   PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
1524:   C_loc = ptap->C_loc;
1525:   C_oth = ptap->C_oth;

1527:   /* add C_loc and C_oth to C */
1528:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));

1530:   /* C_loc -> C */
1531:   cm    = C_loc->rmap->N;
1532:   c_seq = (Mat_SeqAIJ *)C_loc->data;
1533:   cols  = c_seq->j;
1534:   vals  = c_seq->a;
1535:   for (i = 0; i < cm; i++) {
1536:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1537:     row   = rstart + i;
1538:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1539:     cols += ncols;
1540:     vals += ncols;
1541:   }

1543:   /* Co -> C, off-processor part */
1544:   cm    = C_oth->rmap->N;
1545:   c_seq = (Mat_SeqAIJ *)C_oth->data;
1546:   cols  = c_seq->j;
1547:   vals  = c_seq->a;
1548:   for (i = 0; i < cm; i++) {
1549:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1550:     row   = p->garray[i];
1551:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1552:     cols += ncols;
1553:     vals += ncols;
1554:   }
1555:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1556:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1557:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1558:   PetscFunctionReturn(PETSC_SUCCESS);
1559: }

1561: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
1562: {
1563:   MatMergeSeqsToMPI   *merge;
1564:   Mat_MPIAIJ          *p  = (Mat_MPIAIJ *)P->data;
1565:   Mat_SeqAIJ          *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
1566:   MatProductCtx_APMPI *ap;
1567:   PetscInt            *adj;
1568:   PetscInt             i, j, k, anz, pnz, row, *cj, nexta;
1569:   MatScalar           *ada, *ca, valtmp;
1570:   PetscInt             am = A->rmap->n, cm = C->rmap->n, pon = (p->B)->cmap->n;
1571:   MPI_Comm             comm;
1572:   PetscMPIInt          size, rank, taga, *len_s, proc;
1573:   PetscInt            *owners, nrows, **buf_ri_k, **nextrow, **nextci;
1574:   PetscInt           **buf_ri, **buf_rj;
1575:   PetscInt             cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1576:   MPI_Request         *s_waits, *r_waits;
1577:   MPI_Status          *status;
1578:   MatScalar          **abuf_r, *ba_i, *pA, *coa, *ba;
1579:   const PetscScalar   *dummy;
1580:   PetscInt            *ai, *aj, *coi, *coj, *poJ, *pdJ;
1581:   Mat                  A_loc;
1582:   Mat_SeqAIJ          *a_loc;

1584:   PetscFunctionBegin;
1585:   MatCheckProduct(C, 3);
1586:   ap = (MatProductCtx_APMPI *)C->product->data;
1587:   PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
1588:   PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1589:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
1590:   PetscCallMPI(MPI_Comm_size(comm, &size));
1591:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1593:   merge = ap->merge;

1595:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1596:   /* get data from symbolic products */
1597:   coi = merge->coi;
1598:   coj = merge->coj;
1599:   PetscCall(PetscCalloc1(coi[pon], &coa));
1600:   bi     = merge->bi;
1601:   bj     = merge->bj;
1602:   owners = merge->rowmap->range;
1603:   PetscCall(PetscCalloc1(bi[cm], &ba));

1605:   /* get A_loc by taking all local rows of A */
1606:   A_loc = ap->A_loc;
1607:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
1608:   a_loc = (Mat_SeqAIJ *)A_loc->data;
1609:   ai    = a_loc->i;
1610:   aj    = a_loc->j;

1612:   /* trigger copy to CPU */
1613:   PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
1614:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
1615:   PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
1616:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
1617:   for (i = 0; i < am; i++) {
1618:     anz = ai[i + 1] - ai[i];
1619:     adj = aj + ai[i];
1620:     ada = a_loc->a + ai[i];

1622:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1623:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1624:     pnz = po->i[i + 1] - po->i[i];
1625:     poJ = po->j + po->i[i];
1626:     pA  = po->a + po->i[i];
1627:     for (j = 0; j < pnz; j++) {
1628:       row = poJ[j];
1629:       cj  = coj + coi[row];
1630:       ca  = coa + coi[row];
1631:       /* perform sparse axpy */
1632:       nexta  = 0;
1633:       valtmp = pA[j];
1634:       for (k = 0; nexta < anz; k++) {
1635:         if (cj[k] == adj[nexta]) {
1636:           ca[k] += valtmp * ada[nexta];
1637:           nexta++;
1638:         }
1639:       }
1640:       PetscCall(PetscLogFlops(2.0 * anz));
1641:     }

1643:     /* put the value into Cd (diagonal part) */
1644:     pnz = pd->i[i + 1] - pd->i[i];
1645:     pdJ = pd->j + pd->i[i];
1646:     pA  = pd->a + pd->i[i];
1647:     for (j = 0; j < pnz; j++) {
1648:       row = pdJ[j];
1649:       cj  = bj + bi[row];
1650:       ca  = ba + bi[row];
1651:       /* perform sparse axpy */
1652:       nexta  = 0;
1653:       valtmp = pA[j];
1654:       for (k = 0; nexta < anz; k++) {
1655:         if (cj[k] == adj[nexta]) {
1656:           ca[k] += valtmp * ada[nexta];
1657:           nexta++;
1658:         }
1659:       }
1660:       PetscCall(PetscLogFlops(2.0 * anz));
1661:     }
1662:   }

1664:   /* 3) send and recv matrix values coa */
1665:   buf_ri = merge->buf_ri;
1666:   buf_rj = merge->buf_rj;
1667:   len_s  = merge->len_s;
1668:   PetscCall(PetscCommGetNewTag(comm, &taga));
1669:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

1671:   PetscCall(PetscMalloc2(merge->nsend, &s_waits, size, &status));
1672:   for (proc = 0, k = 0; proc < size; proc++) {
1673:     if (!len_s[proc]) continue;
1674:     i = merge->owners_co[proc];
1675:     PetscCallMPI(MPIU_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
1676:     k++;
1677:   }
1678:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
1679:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));

1681:   PetscCall(PetscFree2(s_waits, status));
1682:   PetscCall(PetscFree(r_waits));
1683:   PetscCall(PetscFree(coa));

1685:   /* 4) insert local Cseq and received values into Cmpi */
1686:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1687:   for (k = 0; k < merge->nrecv; k++) {
1688:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1689:     nrows       = *buf_ri_k[k];
1690:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1691:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1692:   }

1694:   for (i = 0; i < cm; i++) {
1695:     row  = owners[rank] + i; /* global row index of C_seq */
1696:     bj_i = bj + bi[i];       /* col indices of the i-th row of C */
1697:     ba_i = ba + bi[i];
1698:     bnz  = bi[i + 1] - bi[i];
1699:     /* add received vals into ba */
1700:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1701:       /* i-th row */
1702:       if (i == *nextrow[k]) {
1703:         cnz    = *(nextci[k] + 1) - *nextci[k];
1704:         cj     = buf_rj[k] + *nextci[k];
1705:         ca     = abuf_r[k] + *nextci[k];
1706:         nextcj = 0;
1707:         for (j = 0; nextcj < cnz; j++) {
1708:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1709:             ba_i[j] += ca[nextcj++];
1710:           }
1711:         }
1712:         nextrow[k]++;
1713:         nextci[k]++;
1714:         PetscCall(PetscLogFlops(2.0 * cnz));
1715:       }
1716:     }
1717:     PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
1718:   }
1719:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1720:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

1722:   PetscCall(PetscFree(ba));
1723:   PetscCall(PetscFree(abuf_r[0]));
1724:   PetscCall(PetscFree(abuf_r));
1725:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1726:   PetscFunctionReturn(PETSC_SUCCESS);
1727: }

1729: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
1730: {
1731:   Mat                  A_loc;
1732:   MatProductCtx_APMPI *ap;
1733:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
1734:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
1735:   PetscInt            *pdti, *pdtj, *poti, *potj, *ptJ;
1736:   PetscInt             nnz;
1737:   PetscInt            *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
1738:   PetscInt             am = A->rmap->n, pn = P->cmap->n;
1739:   MPI_Comm             comm;
1740:   PetscMPIInt          size, rank, tagi, tagj, *len_si, *len_s, *len_ri, proc;
1741:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
1742:   PetscInt             len, *dnz, *onz, *owners;
1743:   PetscInt             nzi, *bi, *bj;
1744:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1745:   MPI_Request         *swaits, *rwaits;
1746:   MPI_Status          *sstatus, rstatus;
1747:   MatMergeSeqsToMPI   *merge;
1748:   PetscInt            *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
1749:   PetscReal            afill  = 1.0, afill_tmp;
1750:   PetscInt             rstart = P->cmap->rstart, rmax, Armax;
1751:   Mat_SeqAIJ          *a_loc;
1752:   PetscHMapI           ta;
1753:   MatType              mtype;

1755:   PetscFunctionBegin;
1756:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1757:   /* check if matrix local sizes are compatible */
1758:   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,
1759:              A->rmap->rend, P->rmap->rstart, P->rmap->rend);

1761:   PetscCallMPI(MPI_Comm_size(comm, &size));
1762:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1764:   /* create struct MatProductCtx_APMPI and attached it to C later */
1765:   PetscCall(PetscNew(&ap));

1767:   /* get A_loc by taking all local rows of A */
1768:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));

1770:   ap->A_loc = A_loc;
1771:   a_loc     = (Mat_SeqAIJ *)A_loc->data;
1772:   ai        = a_loc->i;
1773:   aj        = a_loc->j;

1775:   /* determine symbolic Co=(p->B)^T*A - send to others */
1776:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
1777:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
1778:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1779:                          >= (num of nonzero rows of C_seq) - pn */
1780:   PetscCall(PetscMalloc1(pon + 1, &coi));
1781:   coi[0] = 0;

1783:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1784:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
1785:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1786:   current_space = free_space;

1788:   /* create and initialize a linked list */
1789:   PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
1790:   MatRowMergeMax_SeqAIJ(a_loc, am, ta);
1791:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1793:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));

1795:   for (i = 0; i < pon; i++) {
1796:     pnz = poti[i + 1] - poti[i];
1797:     ptJ = potj + poti[i];
1798:     for (j = 0; j < pnz; j++) {
1799:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1800:       anz  = ai[row + 1] - ai[row];
1801:       Jptr = aj + ai[row];
1802:       /* add non-zero cols of AP into the sorted linked list lnk */
1803:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1804:     }
1805:     nnz = lnk[0];

1807:     /* If free space is not available, double the total space in the list */
1808:     if (current_space->local_remaining < nnz) {
1809:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1810:       nspacedouble++;
1811:     }

1813:     /* Copy data into free space, and zero out denserows */
1814:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));

1816:     current_space->array += nnz;
1817:     current_space->local_used += nnz;
1818:     current_space->local_remaining -= nnz;

1820:     coi[i + 1] = coi[i] + nnz;
1821:   }

1823:   PetscCall(PetscMalloc1(coi[pon], &coj));
1824:   PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
1825:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */

1827:   afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
1828:   if (afill_tmp > afill) afill = afill_tmp;

1830:   /* send j-array (coj) of Co to other processors */
1831:   /* determine row ownership */
1832:   PetscCall(PetscNew(&merge));
1833:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));

1835:   merge->rowmap->n  = pn;
1836:   merge->rowmap->bs = 1;

1838:   PetscCall(PetscLayoutSetUp(merge->rowmap));
1839:   owners = merge->rowmap->range;

1841:   /* determine the number of messages to send, their lengths */
1842:   PetscCall(PetscCalloc1(size, &len_si));
1843:   PetscCall(PetscCalloc1(size, &merge->len_s));

1845:   len_s        = merge->len_s;
1846:   merge->nsend = 0;

1848:   PetscCall(PetscMalloc1(size + 1, &owners_co));

1850:   proc = 0;
1851:   for (i = 0; i < pon; i++) {
1852:     while (prmap[i] >= owners[proc + 1]) proc++;
1853:     len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1854:     len_s[proc] += coi[i + 1] - coi[i];
1855:   }

1857:   len          = 0; /* max length of buf_si[] */
1858:   owners_co[0] = 0;
1859:   for (proc = 0; proc < size; proc++) {
1860:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1861:     if (len_s[proc]) {
1862:       merge->nsend++;
1863:       len_si[proc] = 2 * (len_si[proc] + 1);
1864:       len += len_si[proc];
1865:     }
1866:   }

1868:   /* determine the number and length of messages to receive for coi and coj  */
1869:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
1870:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

1872:   /* post the Irecv and Isend of coj */
1873:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1874:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
1875:   PetscCall(PetscMalloc1(merge->nsend, &swaits));
1876:   for (proc = 0, k = 0; proc < size; proc++) {
1877:     if (!len_s[proc]) continue;
1878:     i = owners_co[proc];
1879:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1880:     k++;
1881:   }

1883:   /* receives and sends of coj are complete */
1884:   PetscCall(PetscMalloc1(size, &sstatus));
1885:   for (i = 0; i < merge->nrecv; i++) {
1886:     PETSC_UNUSED PetscMPIInt icompleted;
1887:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1888:   }
1889:   PetscCall(PetscFree(rwaits));
1890:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));

1892:   /* add received column indices into table to update Armax */
1893:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1894:   for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1895:     Jptr = buf_rj[k];
1896:     for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1897:   }
1898:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1900:   /* send and recv coi */
1901:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1902:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &rwaits));
1903:   PetscCall(PetscMalloc1(len, &buf_s));
1904:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1905:   for (proc = 0, k = 0; proc < size; proc++) {
1906:     if (!len_s[proc]) continue;
1907:     /* form outgoing message for i-structure:
1908:          buf_si[0]:                 nrows to be sent
1909:                [1:nrows]:           row index (global)
1910:                [nrows+1:2*nrows+1]: i-structure index
1911:     */
1912:     nrows       = len_si[proc] / 2 - 1;
1913:     buf_si_i    = buf_si + nrows + 1;
1914:     buf_si[0]   = nrows;
1915:     buf_si_i[0] = 0;
1916:     nrows       = 0;
1917:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1918:       nzi                 = coi[i + 1] - coi[i];
1919:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1920:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1921:       nrows++;
1922:     }
1923:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1924:     k++;
1925:     buf_si += len_si[proc];
1926:   }
1927:   i = merge->nrecv;
1928:   while (i--) {
1929:     PETSC_UNUSED PetscMPIInt icompleted;
1930:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1931:   }
1932:   PetscCall(PetscFree(rwaits));
1933:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
1934:   PetscCall(PetscFree(len_si));
1935:   PetscCall(PetscFree(len_ri));
1936:   PetscCall(PetscFree(swaits));
1937:   PetscCall(PetscFree(sstatus));
1938:   PetscCall(PetscFree(buf_s));

1940:   /* compute the local portion of C (mpi mat) */
1941:   /* allocate bi array and free space for accumulating nonzero column info */
1942:   PetscCall(PetscMalloc1(pn + 1, &bi));
1943:   bi[0] = 0;

1945:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1946:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
1947:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1948:   current_space = free_space;

1950:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1951:   for (k = 0; k < merge->nrecv; k++) {
1952:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1953:     nrows       = *buf_ri_k[k];
1954:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1955:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1956:   }

1958:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
1959:   MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
1960:   rmax = 0;
1961:   for (i = 0; i < pn; i++) {
1962:     /* add pdt[i,:]*AP into lnk */
1963:     pnz = pdti[i + 1] - pdti[i];
1964:     ptJ = pdtj + pdti[i];
1965:     for (j = 0; j < pnz; j++) {
1966:       row  = ptJ[j]; /* row of AP == col of Pt */
1967:       anz  = ai[row + 1] - ai[row];
1968:       Jptr = aj + ai[row];
1969:       /* add non-zero cols of AP into the sorted linked list lnk */
1970:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1971:     }

1973:     /* add received col data into lnk */
1974:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1975:       if (i == *nextrow[k]) {            /* i-th row */
1976:         nzi  = *(nextci[k] + 1) - *nextci[k];
1977:         Jptr = buf_rj[k] + *nextci[k];
1978:         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
1979:         nextrow[k]++;
1980:         nextci[k]++;
1981:       }
1982:     }

1984:     /* add missing diagonal entry */
1985:     if (C->force_diagonals) {
1986:       k = i + owners[rank]; /* column index */
1987:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
1988:     }

1990:     nnz = lnk[0];

1992:     /* if free space is not available, make more free space */
1993:     if (current_space->local_remaining < nnz) {
1994:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1995:       nspacedouble++;
1996:     }
1997:     /* copy data into free space, then initialize lnk */
1998:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
1999:     PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));

2001:     current_space->array += nnz;
2002:     current_space->local_used += nnz;
2003:     current_space->local_remaining -= nnz;

2005:     bi[i + 1] = bi[i] + nnz;
2006:     if (nnz > rmax) rmax = nnz;
2007:   }
2008:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));

2010:   PetscCall(PetscMalloc1(bi[pn], &bj));
2011:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
2012:   afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
2013:   if (afill_tmp > afill) afill = afill_tmp;
2014:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2015:   PetscCall(PetscHMapIDestroy(&ta));
2016:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
2017:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));

2019:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2020:   PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
2021:   PetscCall(MatSetBlockSizes(C, P->cmap->bs, A->cmap->bs));
2022:   PetscCall(MatGetType(A, &mtype));
2023:   PetscCall(MatSetType(C, mtype));
2024:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
2025:   MatPreallocateEnd(dnz, onz);
2026:   PetscCall(MatSetBlockSize(C, 1));
2027:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2028:   for (i = 0; i < pn; i++) {
2029:     row  = i + rstart;
2030:     nnz  = bi[i + 1] - bi[i];
2031:     Jptr = bj + bi[i];
2032:     PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
2033:   }
2034:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2035:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2036:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
2037:   merge->bi        = bi;
2038:   merge->bj        = bj;
2039:   merge->coi       = coi;
2040:   merge->coj       = coj;
2041:   merge->buf_ri    = buf_ri;
2042:   merge->buf_rj    = buf_rj;
2043:   merge->owners_co = owners_co;

2045:   /* attach the supporting struct to C for reuse */
2046:   C->product->data    = ap;
2047:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2048:   ap->merge           = merge;

2050:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2052: #if defined(PETSC_USE_INFO)
2053:   if (bi[pn] != 0) {
2054:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
2055:     PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
2056:   } else {
2057:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
2058:   }
2059: #endif
2060:   PetscFunctionReturn(PETSC_SUCCESS);
2061: }

2063: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2064: {
2065:   Mat_Product *product = C->product;
2066:   Mat          A = product->A, B = product->B;
2067:   PetscReal    fill = product->fill;
2068:   PetscBool    flg;

2070:   PetscFunctionBegin;
2071:   /* scalable */
2072:   PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
2073:   if (flg) {
2074:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
2075:     goto next;
2076:   }

2078:   /* nonscalable */
2079:   PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
2080:   if (flg) {
2081:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
2082:     goto next;
2083:   }

2085:   /* matmatmult */
2086:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
2087:   if (flg) {
2088:     Mat                  At;
2089:     MatProductCtx_APMPI *ptap;

2091:     PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
2092:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
2093:     ptap = (MatProductCtx_APMPI *)C->product->data;
2094:     if (ptap) {
2095:       ptap->Pt            = At;
2096:       C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2097:     }
2098:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2099:     goto next;
2100:   }

2102:   /* backend general code */
2103:   PetscCall(PetscStrcmp(product->alg, "backend", &flg));
2104:   if (flg) {
2105:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2106:     PetscFunctionReturn(PETSC_SUCCESS);
2107:   }

2109:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");

2111: next:
2112:   C->ops->productnumeric = MatProductNumeric_AtB;
2113:   PetscFunctionReturn(PETSC_SUCCESS);
2114: }

2116: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2117: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2118: {
2119:   Mat_Product *product = C->product;
2120:   Mat          A = product->A, B = product->B;
2121: #if defined(PETSC_HAVE_HYPRE)
2122:   const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
2123:   PetscInt    nalg        = 5;
2124: #else
2125:   const char *algTypes[4] = {
2126:     "scalable",
2127:     "nonscalable",
2128:     "seqmpi",
2129:     "backend",
2130:   };
2131:   PetscInt nalg = 4;
2132: #endif
2133:   PetscInt  alg = 1; /* set nonscalable algorithm as default */
2134:   PetscBool flg;
2135:   MPI_Comm  comm;

2137:   PetscFunctionBegin;
2138:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));

2140:   /* Set "nonscalable" as default algorithm */
2141:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2142:   if (flg) {
2143:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2145:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2146:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2147:       MatInfo   Ainfo, Binfo;
2148:       PetscInt  nz_local;
2149:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2151:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2152:       PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2153:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2155:       if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2156:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2158:       if (alg_scalable) {
2159:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2160:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2161:         PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2162:       }
2163:     }
2164:   }

2166:   /* Get runtime option */
2167:   if (product->api_user) {
2168:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2169:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2170:     PetscOptionsEnd();
2171:   } else {
2172:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2173:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2174:     PetscOptionsEnd();
2175:   }
2176:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2178:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2179:   PetscFunctionReturn(PETSC_SUCCESS);
2180: }

2182: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2183: {
2184:   PetscFunctionBegin;
2185:   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2186:   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2187:   PetscFunctionReturn(PETSC_SUCCESS);
2188: }

2190: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2191: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2192: {
2193:   Mat_Product *product = C->product;
2194:   Mat          A = product->A, B = product->B;
2195:   const char  *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
2196:   PetscInt     nalg        = 4;
2197:   PetscInt     alg         = 1; /* set default algorithm  */
2198:   PetscBool    flg;
2199:   MPI_Comm     comm;

2201:   PetscFunctionBegin;
2202:   /* Check matrix local sizes */
2203:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2204:   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 ")",
2205:              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

2207:   /* Set default algorithm */
2208:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2209:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2211:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2212:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2213:     MatInfo   Ainfo, Binfo;
2214:     PetscInt  nz_local;
2215:     PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2217:     PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2218:     PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2219:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2221:     if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2222:     PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2224:     if (alg_scalable) {
2225:       alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2226:       PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2227:       PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2228:     }
2229:   }

2231:   /* Get runtime option */
2232:   if (product->api_user) {
2233:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2234:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2235:     PetscOptionsEnd();
2236:   } else {
2237:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2238:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2239:     PetscOptionsEnd();
2240:   }
2241:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2243:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2244:   PetscFunctionReturn(PETSC_SUCCESS);
2245: }

2247: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2248: {
2249:   Mat_Product *product = C->product;
2250:   Mat          A = product->A, P = product->B;
2251:   MPI_Comm     comm;
2252:   PetscBool    flg;
2253:   PetscInt     alg = 1; /* set default algorithm */
2254: #if !defined(PETSC_HAVE_HYPRE)
2255:   const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
2256:   PetscInt    nalg        = 5;
2257: #else
2258:   const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
2259:   PetscInt    nalg        = 6;
2260: #endif
2261:   PetscInt pN = P->cmap->N;

2263:   PetscFunctionBegin;
2264:   /* Check matrix local sizes */
2265:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2266:   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 ")",
2267:              A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
2268:   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 ")",
2269:              A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);

2271:   /* Set "nonscalable" as default algorithm */
2272:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2273:   if (flg) {
2274:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2276:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2277:     if (pN > 100000) {
2278:       MatInfo   Ainfo, Pinfo;
2279:       PetscInt  nz_local;
2280:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2282:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2283:       PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
2284:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2286:       if (pN > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2287:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2289:       if (alg_scalable) {
2290:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2291:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2292:       }
2293:     }
2294:   }

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

2308:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2309:   PetscFunctionReturn(PETSC_SUCCESS);
2310: }

2312: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2313: {
2314:   Mat_Product *product = C->product;
2315:   Mat          A = product->A, R = product->B;

2317:   PetscFunctionBegin;
2318:   /* Check matrix local sizes */
2319:   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,
2320:              A->rmap->n, R->rmap->n, R->cmap->n);

2322:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2323:   PetscFunctionReturn(PETSC_SUCCESS);
2324: }

2326: /*
2327:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2328: */
2329: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2330: {
2331:   Mat_Product *product     = C->product;
2332:   PetscBool    flg         = PETSC_FALSE;
2333:   PetscInt     alg         = 1; /* default algorithm */
2334:   const char  *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
2335:   PetscInt     nalg        = 3;

2337:   PetscFunctionBegin;
2338:   /* Set default algorithm */
2339:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2340:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2342:   /* Get runtime option */
2343:   if (product->api_user) {
2344:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2345:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2346:     PetscOptionsEnd();
2347:   } else {
2348:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2349:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2350:     PetscOptionsEnd();
2351:   }
2352:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2354:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2355:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2356:   PetscFunctionReturn(PETSC_SUCCESS);
2357: }

2359: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2360: {
2361:   Mat_Product *product = C->product;

2363:   PetscFunctionBegin;
2364:   switch (product->type) {
2365:   case MATPRODUCT_AB:
2366:     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2367:     break;
2368:   case MATPRODUCT_ABt:
2369:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2370:     break;
2371:   case MATPRODUCT_AtB:
2372:     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2373:     break;
2374:   case MATPRODUCT_PtAP:
2375:     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2376:     break;
2377:   case MATPRODUCT_RARt:
2378:     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2379:     break;
2380:   case MATPRODUCT_ABC:
2381:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2382:     break;
2383:   default:
2384:     break;
2385:   }
2386:   PetscFunctionReturn(PETSC_SUCCESS);
2387: }