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 MatDestroy_MPIAIJ_MatMatMult(void *data)
 77: {
 78:   Mat_APMPI *ptap = (Mat_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:   Mat_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 = (Mat_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  = 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:   Mat_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 Mat_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 + 2, &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] + 1, &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(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
303:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
304:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

512: /*
513:     Performs an efficient scatter on the rows of B needed by this process; this is
514:     a modification of the VecScatterBegin_() routines.

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

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

536:   PetscFunctionBegin;
537:   MatCheckProduct(C, 4);
538:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
539:   contents = (MPIAIJ_MPIDense *)C->product->data;
540:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL /*bs*/));
541:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL /*bs*/));
542:   PetscCall(PetscMPIIntCast(nsends, &nsends_mpi));
543:   PetscCall(PetscMPIIntCast(nrecvs, &nrecvs_mpi));
544:   if (Bbidx == 0) workB = *outworkB = contents->workB;
545:   else workB = *outworkB = contents->workB1;
546:   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);
547:   swaits = contents->swaits;
548:   rwaits = contents->rwaits;

550:   PetscCall(MatDenseGetArrayRead(B, &b));
551:   PetscCall(MatDenseGetLDA(B, &blda));
552:   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);
553:   PetscCall(MatDenseGetArray(workB, &rvalues));

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

560:   stype = contents->stype;
561:   for (i = 0; i < nsends; i++) PetscCallMPI(MPI_Isend(b, ncols, stype[i], sprocs[i], tag, comm, swaits + i));

563:   if (nrecvs) PetscCallMPI(MPI_Waitall(nrecvs_mpi, rwaits, MPI_STATUSES_IGNORE));
564:   if (nsends) PetscCallMPI(MPI_Waitall(nsends_mpi, swaits, MPI_STATUSES_IGNORE));

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

573: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A, Mat B, Mat C)
574: {
575:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ *)A->data;
576:   Mat_MPIDense    *bdense = (Mat_MPIDense *)B->data;
577:   Mat_MPIDense    *cdense = (Mat_MPIDense *)C->data;
578:   Mat              workB;
579:   MPIAIJ_MPIDense *contents;

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

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

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

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

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

623: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A, Mat P, Mat C)
624: {
625:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
626:   Mat_SeqAIJ        *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
627:   Mat_SeqAIJ        *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
628:   PetscInt          *adi = ad->i, *adj, *aoi = ao->i, *aoj;
629:   PetscScalar       *ada, *aoa, *cda = cd->a, *coa = co->a;
630:   Mat_SeqAIJ        *p_loc, *p_oth;
631:   PetscInt          *pi_loc, *pj_loc, *pi_oth, *pj_oth, *pj;
632:   PetscScalar       *pa_loc, *pa_oth, *pa, valtmp, *ca;
633:   PetscInt           cm = C->rmap->n, anz, pnz;
634:   Mat_APMPI         *ptap;
635:   PetscScalar       *apa_sparse;
636:   const PetscScalar *dummy;
637:   PetscInt          *api, *apj, *apJ, i, j, k, row;
638:   PetscInt           cstart = C->cmap->rstart;
639:   PetscInt           cdnz, conz, k0, k1, nextp;
640:   MPI_Comm           comm;
641:   PetscMPIInt        size;

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

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

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

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

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

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

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

732:     /* set values in C */
733:     cdnz = cd->i[i + 1] - cd->i[i];
734:     conz = co->i[i + 1] - co->i[i];

736:     /* 1st off-diagonal part of C */
737:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
738:     k  = 0;
739:     for (k0 = 0; k0 < conz; k0++) {
740:       if (apJ[k] >= cstart) break;
741:       ca[k0]        = apa_sparse[k];
742:       apa_sparse[k] = 0.0;
743:       k++;
744:     }

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

754:     /* 2nd off-diagonal part of C */
755:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
756:     for (; k0 < conz; k0++) {
757:       ca[k0]        = apa_sparse[k];
758:       apa_sparse[k] = 0.0;
759:       k++;
760:     }
761:   }
762:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
763:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
764:   PetscFunctionReturn(PETSC_SUCCESS);
765: }

767: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
768: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A, Mat P, PetscReal fill, Mat C)
769: {
770:   MPI_Comm           comm;
771:   PetscMPIInt        size;
772:   Mat_APMPI         *ptap;
773:   PetscFreeSpaceList free_space = NULL, current_space = NULL;
774:   Mat_MPIAIJ        *a  = (Mat_MPIAIJ *)A->data;
775:   Mat_SeqAIJ        *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
776:   PetscInt          *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
777:   PetscInt          *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
778:   PetscInt           i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi, *lnk, apnz_max = 1;
779:   PetscInt           am = A->rmap->n, pn = P->cmap->n, pm = P->rmap->n, lsize = pn + 20;
780:   PetscReal          afill;
781:   MatType            mtype;

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

789:   /* create struct Mat_APMPI and attached it to C later */
790:   PetscCall(PetscNew(&ptap));

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

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

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

811:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
812:   PetscCall(PetscMalloc1(am + 2, &api));
813:   ptap->api = api;
814:   api[0]    = 0;

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

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

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

864:     apnz       = *lnk;
865:     api[i + 1] = api[i] + apnz;
866:     if (apnz > apnz_max) apnz_max = apnz;

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

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

878:     current_space->array += apnz;
879:     current_space->local_used += apnz;
880:     current_space->local_remaining -= apnz;
881:   }

883:   /* Allocate space for apj, initialize apj, and */
884:   /* destroy list of free space and other temporary array(s) */
885:   PetscCall(PetscMalloc1(api[am] + 1, &ptap->apj));
886:   apj = ptap->apj;
887:   PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
888:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));

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

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

901:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
902:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
903:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
904:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

906:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
907:   C->ops->productnumeric = MatProductNumeric_AB;

909:   /* attach the supporting struct to C for reuse */
910:   C->product->data    = ptap;
911:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

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

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

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

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

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

973:   while (i < size1 && k < size3) {
974:     if (in1[i] < in3[k]) {
975:       out[l++] = in1[i++];
976:     } else if (in1[i] > in3[k]) {
977:       out[l++] = in3[k++];
978:     } else {
979:       out[l++] = in1[i];
980:       i++, k++;
981:     }
982:   }

984:   while (k < size3 && j < size2) {
985:     if (in3[k] < in2[j]) {
986:       out[l++] = in3[k++];
987:     } else if (in3[k] > in2[j]) {
988:       out[l++] = in2[j++];
989:     } else {
990:       out[l++] = in3[k];
991:       k++, j++;
992:     }
993:   }

995:   /* Traverse one remaining array */
996:   while (i < size1) out[l++] = in1[i++];
997:   while (j < size2) out[l++] = in2[j++];
998:   while (k < size3) out[l++] = in3[k++];

1000:   *size4 = l;
1001: }

1003: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1004: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1005: /* matrix-matrix multiplications.  */
1006: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1007: {
1008:   MPI_Comm           comm;
1009:   PetscMPIInt        size;
1010:   Mat_APMPI         *ptap;
1011:   PetscFreeSpaceList free_space_diag = NULL, current_space = NULL;
1012:   Mat_MPIAIJ        *a  = (Mat_MPIAIJ *)A->data;
1013:   Mat_SeqAIJ        *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
1014:   Mat_MPIAIJ        *p = (Mat_MPIAIJ *)P->data;
1015:   Mat_SeqAIJ        *adpd_seq, *p_off, *aopoth_seq;
1016:   PetscInt           adponz, adpdnz;
1017:   PetscInt          *pi_loc, *dnz, *onz;
1018:   PetscInt          *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
1019:   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;
1020:   PetscInt           am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
1021:   PetscBT            lnkbt;
1022:   PetscReal          afill;
1023:   PetscMPIInt        rank;
1024:   Mat                adpd, aopoth;
1025:   MatType            mtype;
1026:   const char        *prefix;

1028:   PetscFunctionBegin;
1029:   MatCheckProduct(C, 4);
1030:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1031:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1032:   PetscCallMPI(MPI_Comm_size(comm, &size));
1033:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1034:   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));

1036:   /* create struct Mat_APMPI and attached it to C later */
1037:   PetscCall(PetscNew(&ptap));

1039:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1040:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));

1042:   /* get P_loc by taking all local rows of P */
1043:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));

1045:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
1046:   pi_loc = p_loc->i;

1048:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1049:   PetscCall(PetscMalloc1(am + 2, &api));
1050:   PetscCall(PetscMalloc1(am + 2, &adpoi));

1052:   adpoi[0]  = 0;
1053:   ptap->api = api;
1054:   api[0]    = 0;

1056:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1057:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
1058:   MatPreallocateBegin(comm, am, pn, dnz, onz);

1060:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1061:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1062:   PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
1063:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1064:   PetscCall(MatSetOptionsPrefix(adpd, prefix));
1065:   PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));

1067:   PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
1068:   PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
1069:   PetscCall(MatProductSetFill(adpd, fill));
1070:   PetscCall(MatProductSetFromOptions(adpd));

1072:   adpd->force_diagonals = C->force_diagonals;
1073:   PetscCall(MatProductSymbolic(adpd));

1075:   adpd_seq = (Mat_SeqAIJ *)((adpd)->data);
1076:   adpdi    = adpd_seq->i;
1077:   adpdj    = adpd_seq->j;
1078:   p_off    = (Mat_SeqAIJ *)p->B->data;
1079:   poff_i   = p_off->i;
1080:   poff_j   = p_off->j;

1082:   /* j_temp stores indices of a result row before they are added to the linked list */
1083:   PetscCall(PetscMalloc1(pN + 2, &j_temp));

1085:   /* Symbolic calc of the A_diag * p_loc_off */
1086:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1087:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
1088:   current_space = free_space_diag;

1090:   for (i = 0; i < am; i++) {
1091:     /* A_diag * P_loc_off */
1092:     nzi = adi[i + 1] - adi[i];
1093:     for (j = 0; j < nzi; j++) {
1094:       row  = *adj++;
1095:       pnz  = poff_i[row + 1] - poff_i[row];
1096:       Jptr = poff_j + poff_i[row];
1097:       for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
1098:       /* add non-zero cols of P into the sorted linked list lnk */
1099:       PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
1100:     }

1102:     adponz       = lnk[0];
1103:     adpoi[i + 1] = adpoi[i] + adponz;

1105:     /* if free space is not available, double the total space in the list */
1106:     if (current_space->local_remaining < adponz) {
1107:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), &current_space));
1108:       nspacedouble++;
1109:     }

1111:     /* Copy data into free space, then initialize lnk */
1112:     PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));

1114:     current_space->array += adponz;
1115:     current_space->local_used += adponz;
1116:     current_space->local_remaining -= adponz;
1117:   }

1119:   /* Symbolic calc of A_off * P_oth */
1120:   PetscCall(MatSetOptionsPrefix(a->B, prefix));
1121:   PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
1122:   PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
1123:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1124:   aopoth_seq = (Mat_SeqAIJ *)((aopoth)->data);
1125:   aopothi    = aopoth_seq->i;
1126:   aopothj    = aopoth_seq->j;

1128:   /* Allocate space for apj, adpj, aopj, ... */
1129:   /* destroy lists of free space and other temporary array(s) */

1131:   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am] + 2, &ptap->apj));
1132:   PetscCall(PetscMalloc1(adpoi[am] + 2, &adpoj));

1134:   /* Copy from linked list to j-array */
1135:   PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
1136:   PetscCall(PetscLLDestroy(lnk, lnkbt));

1138:   adpoJ = adpoj;
1139:   adpdJ = adpdj;
1140:   aopJ  = aopothj;
1141:   apj   = ptap->apj;
1142:   apJ   = apj; /* still empty */

1144:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1145:   /* A_diag * P_loc_diag to get A*P */
1146:   for (i = 0; i < am; i++) {
1147:     aopnz  = aopothi[i + 1] - aopothi[i];
1148:     adponz = adpoi[i + 1] - adpoi[i];
1149:     adpdnz = adpdi[i + 1] - adpdi[i];

1151:     /* Correct indices from A_diag*P_diag */
1152:     for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
1153:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1154:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1155:     PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));

1157:     aopJ += aopnz;
1158:     adpoJ += adponz;
1159:     adpdJ += adpdnz;
1160:     apJ += apnz;
1161:     api[i + 1] = api[i] + apnz;
1162:   }

1164:   /* malloc apa to store dense row A[i,:]*P */
1165:   PetscCall(PetscCalloc1(pN + 2, &ptap->apa));

1167:   /* create and assemble symbolic parallel matrix C */
1168:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1169:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
1170:   PetscCall(MatGetType(A, &mtype));
1171:   PetscCall(MatSetType(C, mtype));
1172:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1173:   MatPreallocateEnd(dnz, onz);

1175:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1176:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1177:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1178:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1180:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1181:   C->ops->productnumeric = MatProductNumeric_AB;

1183:   /* attach the supporting struct to C for reuse */
1184:   C->product->data    = ptap;
1185:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

1187:   /* set MatInfo */
1188:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1189:   if (afill < 1.0) afill = 1.0;
1190:   C->info.mallocs           = nspacedouble;
1191:   C->info.fill_ratio_given  = fill;
1192:   C->info.fill_ratio_needed = afill;

1194: #if defined(PETSC_USE_INFO)
1195:   if (api[am]) {
1196:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1197:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1198:   } else {
1199:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1200:   }
1201: #endif

1203:   PetscCall(MatDestroy(&aopoth));
1204:   PetscCall(MatDestroy(&adpd));
1205:   PetscCall(PetscFree(j_temp));
1206:   PetscCall(PetscFree(adpoj));
1207:   PetscCall(PetscFree(adpoi));
1208:   PetscFunctionReturn(PETSC_SUCCESS);
1209: }

1211: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1212: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
1213: {
1214:   Mat_APMPI *ptap;
1215:   Mat        Pt;

1217:   PetscFunctionBegin;
1218:   MatCheckProduct(C, 3);
1219:   ptap = (Mat_APMPI *)C->product->data;
1220:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1221:   PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");

1223:   Pt = ptap->Pt;
1224:   PetscCall(MatTransposeSetPrecursor(P, Pt));
1225:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
1226:   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
1227:   PetscFunctionReturn(PETSC_SUCCESS);
1228: }

1230: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1231: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, PetscReal fill, Mat C)
1232: {
1233:   Mat_APMPI               *ptap;
1234:   Mat_MPIAIJ              *p = (Mat_MPIAIJ *)P->data;
1235:   MPI_Comm                 comm;
1236:   PetscMPIInt              size, rank;
1237:   PetscFreeSpaceList       free_space = NULL, current_space = NULL;
1238:   PetscInt                 pn = P->cmap->n, aN = A->cmap->N, an = A->cmap->n;
1239:   PetscInt                *lnk, i, k, nsend, rstart;
1240:   PetscBT                  lnkbt;
1241:   PetscMPIInt              tagi, tagj, *len_si, *len_s, *len_ri, nrecv;
1242:   PETSC_UNUSED PetscMPIInt icompleted = 0;
1243:   PetscInt               **buf_rj, **buf_ri, **buf_ri_k, row, ncols, *cols;
1244:   PetscInt                 len, proc, *dnz, *onz, *owners, nzi;
1245:   PetscInt                 nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1246:   MPI_Request             *swaits, *rwaits;
1247:   MPI_Status              *sstatus, rstatus;
1248:   PetscLayout              rowmap;
1249:   PetscInt                *owners_co, *coi, *coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1250:   PetscMPIInt             *len_r, *id_r;          /* array of length of comm->size, store send/recv matrix values */
1251:   PetscInt                *Jptr, *prmap = p->garray, con, j, Crmax;
1252:   Mat_SeqAIJ              *a_loc, *c_loc, *c_oth;
1253:   PetscHMapI               ta;
1254:   MatType                  mtype;
1255:   const char              *prefix;

1257:   PetscFunctionBegin;
1258:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1259:   PetscCallMPI(MPI_Comm_size(comm, &size));
1260:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1262:   /* create symbolic parallel matrix C */
1263:   PetscCall(MatGetType(A, &mtype));
1264:   PetscCall(MatSetType(C, mtype));

1266:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1268:   /* create struct Mat_APMPI and attached it to C later */
1269:   PetscCall(PetscNew(&ptap));

1271:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1272:   PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
1273:   PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));

1275:   /* (1) compute symbolic A_loc */
1276:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));

1278:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1279:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1280:   PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
1281:   PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
1282:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
1283:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));

1285:   /* (3) send coj of C_oth to other processors  */
1286:   /* determine row ownership */
1287:   PetscCall(PetscLayoutCreate(comm, &rowmap));
1288:   rowmap->n  = pn;
1289:   rowmap->bs = 1;
1290:   PetscCall(PetscLayoutSetUp(rowmap));
1291:   owners = rowmap->range;

1293:   /* determine the number of messages to send, their lengths */
1294:   PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 2, &owners_co));
1295:   PetscCall(PetscArrayzero(len_s, size));
1296:   PetscCall(PetscArrayzero(len_si, size));

1298:   c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
1299:   coi   = c_oth->i;
1300:   coj   = c_oth->j;
1301:   con   = ptap->C_oth->rmap->n;
1302:   proc  = 0;
1303:   for (i = 0; i < con; i++) {
1304:     while (prmap[i] >= owners[proc + 1]) proc++;
1305:     len_si[proc]++;                     /* num of rows in Co(=Pt*A) to be sent to [proc] */
1306:     len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1307:   }

1309:   len          = 0; /* max length of buf_si[], see (4) */
1310:   owners_co[0] = 0;
1311:   nsend        = 0;
1312:   for (proc = 0; proc < size; proc++) {
1313:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1314:     if (len_s[proc]) {
1315:       nsend++;
1316:       len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1317:       len += len_si[proc];
1318:     }
1319:   }

1321:   /* determine the number and length of messages to receive for coi and coj  */
1322:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
1323:   PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));

1325:   /* post the Irecv and Isend of coj */
1326:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1327:   PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
1328:   PetscCall(PetscMalloc1(nsend + 1, &swaits));
1329:   for (proc = 0, k = 0; proc < size; proc++) {
1330:     if (!len_s[proc]) continue;
1331:     i = owners_co[proc];
1332:     PetscCallMPI(MPI_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1333:     k++;
1334:   }

1336:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1337:   PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
1338:   PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
1339:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
1340:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
1341:   c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;

1343:   /* receives coj are complete */
1344:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1345:   PetscCall(PetscFree(rwaits));
1346:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1348:   /* add received column indices into ta to update Crmax */
1349:   a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;

1351:   /* create and initialize a linked list */
1352:   PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
1353:   MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);

1355:   for (k = 0; k < nrecv; k++) { /* k-th received message */
1356:     Jptr = buf_rj[k];
1357:     for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1358:   }
1359:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
1360:   PetscCall(PetscHMapIDestroy(&ta));

1362:   /* (4) send and recv coi */
1363:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1364:   PetscCall(PetscPostIrecvInt(comm, tagi, nrecv, id_r, len_ri, &buf_ri, &rwaits));
1365:   PetscCall(PetscMalloc1(len + 1, &buf_s));
1366:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1367:   for (proc = 0, k = 0; proc < size; proc++) {
1368:     if (!len_s[proc]) continue;
1369:     /* form outgoing message for i-structure:
1370:          buf_si[0]:                 nrows to be sent
1371:                [1:nrows]:           row index (global)
1372:                [nrows+1:2*nrows+1]: i-structure index
1373:     */
1374:     nrows       = len_si[proc] / 2 - 1; /* num of rows in Co to be sent to [proc] */
1375:     buf_si_i    = buf_si + nrows + 1;
1376:     buf_si[0]   = nrows;
1377:     buf_si_i[0] = 0;
1378:     nrows       = 0;
1379:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1380:       nzi                 = coi[i + 1] - coi[i];
1381:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1382:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1383:       nrows++;
1384:     }
1385:     PetscCallMPI(MPI_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1386:     k++;
1387:     buf_si += len_si[proc];
1388:   }
1389:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1390:   PetscCall(PetscFree(rwaits));
1391:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1393:   PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
1394:   PetscCall(PetscFree(len_ri));
1395:   PetscCall(PetscFree(swaits));
1396:   PetscCall(PetscFree(buf_s));

1398:   /* (5) compute the local portion of C      */
1399:   /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
1400:   PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
1401:   current_space = free_space;

1403:   PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
1404:   for (k = 0; k < nrecv; k++) {
1405:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1406:     nrows       = *buf_ri_k[k];
1407:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1408:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1409:   }

1411:   MatPreallocateBegin(comm, pn, an, dnz, onz);
1412:   PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
1413:   for (i = 0; i < pn; i++) { /* for each local row of C */
1414:     /* add C_loc into C */
1415:     nzi  = c_loc->i[i + 1] - c_loc->i[i];
1416:     Jptr = c_loc->j + c_loc->i[i];
1417:     PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));

1419:     /* add received col data into lnk */
1420:     for (k = 0; k < nrecv; k++) { /* k-th received message */
1421:       if (i == *nextrow[k]) {     /* i-th row */
1422:         nzi  = *(nextci[k] + 1) - *nextci[k];
1423:         Jptr = buf_rj[k] + *nextci[k];
1424:         PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1425:         nextrow[k]++;
1426:         nextci[k]++;
1427:       }
1428:     }

1430:     /* add missing diagonal entry */
1431:     if (C->force_diagonals) {
1432:       k = i + owners[rank]; /* column index */
1433:       PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
1434:     }

1436:     nzi = lnk[0];

1438:     /* copy data into free space, then initialize lnk */
1439:     PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
1440:     PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
1441:   }
1442:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1443:   PetscCall(PetscLLDestroy(lnk, lnkbt));
1444:   PetscCall(PetscFreeSpaceDestroy(free_space));

1446:   /* local sizes and preallocation */
1447:   PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
1448:   if (P->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
1449:   if (A->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
1450:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1451:   MatPreallocateEnd(dnz, onz);

1453:   /* add C_loc and C_oth to C */
1454:   PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
1455:   for (i = 0; i < pn; i++) {
1456:     ncols = c_loc->i[i + 1] - c_loc->i[i];
1457:     cols  = c_loc->j + c_loc->i[i];
1458:     row   = rstart + i;
1459:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));

1461:     if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
1462:   }
1463:   for (i = 0; i < con; i++) {
1464:     ncols = c_oth->i[i + 1] - c_oth->i[i];
1465:     cols  = c_oth->j + c_oth->i[i];
1466:     row   = prmap[i];
1467:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1468:   }
1469:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1470:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1471:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1473:   /* members in merge */
1474:   PetscCall(PetscFree(id_r));
1475:   PetscCall(PetscFree(len_r));
1476:   PetscCall(PetscFree(buf_ri[0]));
1477:   PetscCall(PetscFree(buf_ri));
1478:   PetscCall(PetscFree(buf_rj[0]));
1479:   PetscCall(PetscFree(buf_rj));
1480:   PetscCall(PetscLayoutDestroy(&rowmap));

1482:   /* attach the supporting struct to C for reuse */
1483:   C->product->data    = ptap;
1484:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1485:   PetscFunctionReturn(PETSC_SUCCESS);
1486: }

1488: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
1489: {
1490:   Mat_MPIAIJ        *p = (Mat_MPIAIJ *)P->data;
1491:   Mat_SeqAIJ        *c_seq;
1492:   Mat_APMPI         *ptap;
1493:   Mat                A_loc, C_loc, C_oth;
1494:   PetscInt           i, rstart, rend, cm, ncols, row;
1495:   const PetscInt    *cols;
1496:   const PetscScalar *vals;

1498:   PetscFunctionBegin;
1499:   MatCheckProduct(C, 3);
1500:   ptap = (Mat_APMPI *)C->product->data;
1501:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1502:   PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1503:   PetscCall(MatZeroEntries(C));

1505:   /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1506:   /* 1) get R = Pd^T, Ro = Po^T */
1507:   PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
1508:   PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
1509:   PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
1510:   PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));

1512:   /* 2) compute numeric A_loc */
1513:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));

1515:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1516:   A_loc = ptap->A_loc;
1517:   PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
1518:   PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
1519:   C_loc = ptap->C_loc;
1520:   C_oth = ptap->C_oth;

1522:   /* add C_loc and C_oth to C */
1523:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));

1525:   /* C_loc -> C */
1526:   cm    = C_loc->rmap->N;
1527:   c_seq = (Mat_SeqAIJ *)C_loc->data;
1528:   cols  = c_seq->j;
1529:   vals  = c_seq->a;
1530:   for (i = 0; i < cm; i++) {
1531:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1532:     row   = rstart + i;
1533:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1534:     cols += ncols;
1535:     vals += ncols;
1536:   }

1538:   /* Co -> C, off-processor part */
1539:   cm    = C_oth->rmap->N;
1540:   c_seq = (Mat_SeqAIJ *)C_oth->data;
1541:   cols  = c_seq->j;
1542:   vals  = c_seq->a;
1543:   for (i = 0; i < cm; i++) {
1544:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1545:     row   = p->garray[i];
1546:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1547:     cols += ncols;
1548:     vals += ncols;
1549:   }
1550:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1551:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1552:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1553:   PetscFunctionReturn(PETSC_SUCCESS);
1554: }

1556: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
1557: {
1558:   Mat_Merge_SeqsToMPI *merge;
1559:   Mat_MPIAIJ          *p  = (Mat_MPIAIJ *)P->data;
1560:   Mat_SeqAIJ          *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
1561:   Mat_APMPI           *ap;
1562:   PetscInt            *adj;
1563:   PetscInt             i, j, k, anz, pnz, row, *cj, nexta;
1564:   MatScalar           *ada, *ca, valtmp;
1565:   PetscInt             am = A->rmap->n, cm = C->rmap->n, pon = (p->B)->cmap->n;
1566:   MPI_Comm             comm;
1567:   PetscMPIInt          size, rank, taga, *len_s;
1568:   PetscInt            *owners, proc, nrows, **buf_ri_k, **nextrow, **nextci;
1569:   PetscInt           **buf_ri, **buf_rj;
1570:   PetscInt             cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1571:   MPI_Request         *s_waits, *r_waits;
1572:   MPI_Status          *status;
1573:   MatScalar          **abuf_r, *ba_i, *pA, *coa, *ba;
1574:   const PetscScalar   *dummy;
1575:   PetscInt            *ai, *aj, *coi, *coj, *poJ, *pdJ;
1576:   Mat                  A_loc;
1577:   Mat_SeqAIJ          *a_loc;

1579:   PetscFunctionBegin;
1580:   MatCheckProduct(C, 3);
1581:   ap = (Mat_APMPI *)C->product->data;
1582:   PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
1583:   PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1584:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
1585:   PetscCallMPI(MPI_Comm_size(comm, &size));
1586:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1588:   merge = ap->merge;

1590:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1591:   /* get data from symbolic products */
1592:   coi = merge->coi;
1593:   coj = merge->coj;
1594:   PetscCall(PetscCalloc1(coi[pon] + 1, &coa));
1595:   bi     = merge->bi;
1596:   bj     = merge->bj;
1597:   owners = merge->rowmap->range;
1598:   PetscCall(PetscCalloc1(bi[cm] + 1, &ba));

1600:   /* get A_loc by taking all local rows of A */
1601:   A_loc = ap->A_loc;
1602:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
1603:   a_loc = (Mat_SeqAIJ *)(A_loc)->data;
1604:   ai    = a_loc->i;
1605:   aj    = a_loc->j;

1607:   /* trigger copy to CPU */
1608:   PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
1609:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
1610:   PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
1611:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
1612:   for (i = 0; i < am; i++) {
1613:     anz = ai[i + 1] - ai[i];
1614:     adj = aj + ai[i];
1615:     ada = a_loc->a + ai[i];

1617:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1618:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1619:     pnz = po->i[i + 1] - po->i[i];
1620:     poJ = po->j + po->i[i];
1621:     pA  = po->a + po->i[i];
1622:     for (j = 0; j < pnz; j++) {
1623:       row = poJ[j];
1624:       cj  = coj + coi[row];
1625:       ca  = coa + coi[row];
1626:       /* perform sparse axpy */
1627:       nexta  = 0;
1628:       valtmp = pA[j];
1629:       for (k = 0; nexta < anz; k++) {
1630:         if (cj[k] == adj[nexta]) {
1631:           ca[k] += valtmp * ada[nexta];
1632:           nexta++;
1633:         }
1634:       }
1635:       PetscCall(PetscLogFlops(2.0 * anz));
1636:     }

1638:     /* put the value into Cd (diagonal part) */
1639:     pnz = pd->i[i + 1] - pd->i[i];
1640:     pdJ = pd->j + pd->i[i];
1641:     pA  = pd->a + pd->i[i];
1642:     for (j = 0; j < pnz; j++) {
1643:       row = pdJ[j];
1644:       cj  = bj + bi[row];
1645:       ca  = ba + bi[row];
1646:       /* perform sparse axpy */
1647:       nexta  = 0;
1648:       valtmp = pA[j];
1649:       for (k = 0; nexta < anz; k++) {
1650:         if (cj[k] == adj[nexta]) {
1651:           ca[k] += valtmp * ada[nexta];
1652:           nexta++;
1653:         }
1654:       }
1655:       PetscCall(PetscLogFlops(2.0 * anz));
1656:     }
1657:   }

1659:   /* 3) send and recv matrix values coa */
1660:   buf_ri = merge->buf_ri;
1661:   buf_rj = merge->buf_rj;
1662:   len_s  = merge->len_s;
1663:   PetscCall(PetscCommGetNewTag(comm, &taga));
1664:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

1666:   PetscCall(PetscMalloc2(merge->nsend + 1, &s_waits, size, &status));
1667:   for (proc = 0, k = 0; proc < size; proc++) {
1668:     if (!len_s[proc]) continue;
1669:     i = merge->owners_co[proc];
1670:     PetscCallMPI(MPI_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
1671:     k++;
1672:   }
1673:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
1674:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));

1676:   PetscCall(PetscFree2(s_waits, status));
1677:   PetscCall(PetscFree(r_waits));
1678:   PetscCall(PetscFree(coa));

1680:   /* 4) insert local Cseq and received values into Cmpi */
1681:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1682:   for (k = 0; k < merge->nrecv; k++) {
1683:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1684:     nrows       = *buf_ri_k[k];
1685:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1686:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1687:   }

1689:   for (i = 0; i < cm; i++) {
1690:     row  = owners[rank] + i; /* global row index of C_seq */
1691:     bj_i = bj + bi[i];       /* col indices of the i-th row of C */
1692:     ba_i = ba + bi[i];
1693:     bnz  = bi[i + 1] - bi[i];
1694:     /* add received vals into ba */
1695:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1696:       /* i-th row */
1697:       if (i == *nextrow[k]) {
1698:         cnz    = *(nextci[k] + 1) - *nextci[k];
1699:         cj     = buf_rj[k] + *nextci[k];
1700:         ca     = abuf_r[k] + *nextci[k];
1701:         nextcj = 0;
1702:         for (j = 0; nextcj < cnz; j++) {
1703:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1704:             ba_i[j] += ca[nextcj++];
1705:           }
1706:         }
1707:         nextrow[k]++;
1708:         nextci[k]++;
1709:         PetscCall(PetscLogFlops(2.0 * cnz));
1710:       }
1711:     }
1712:     PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
1713:   }
1714:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1715:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

1717:   PetscCall(PetscFree(ba));
1718:   PetscCall(PetscFree(abuf_r[0]));
1719:   PetscCall(PetscFree(abuf_r));
1720:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1721:   PetscFunctionReturn(PETSC_SUCCESS);
1722: }

1724: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
1725: {
1726:   Mat                  A_loc;
1727:   Mat_APMPI           *ap;
1728:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
1729:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
1730:   PetscInt            *pdti, *pdtj, *poti, *potj, *ptJ;
1731:   PetscInt             nnz;
1732:   PetscInt            *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
1733:   PetscInt             am = A->rmap->n, pn = P->cmap->n;
1734:   MPI_Comm             comm;
1735:   PetscMPIInt          size, rank, tagi, tagj, *len_si, *len_s, *len_ri;
1736:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
1737:   PetscInt             len, proc, *dnz, *onz, *owners;
1738:   PetscInt             nzi, *bi, *bj;
1739:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1740:   MPI_Request         *swaits, *rwaits;
1741:   MPI_Status          *sstatus, rstatus;
1742:   Mat_Merge_SeqsToMPI *merge;
1743:   PetscInt            *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
1744:   PetscReal            afill  = 1.0, afill_tmp;
1745:   PetscInt             rstart = P->cmap->rstart, rmax, Armax;
1746:   Mat_SeqAIJ          *a_loc;
1747:   PetscHMapI           ta;
1748:   MatType              mtype;

1750:   PetscFunctionBegin;
1751:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1752:   /* check if matrix local sizes are compatible */
1753:   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,
1754:              A->rmap->rend, P->rmap->rstart, P->rmap->rend);

1756:   PetscCallMPI(MPI_Comm_size(comm, &size));
1757:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1759:   /* create struct Mat_APMPI and attached it to C later */
1760:   PetscCall(PetscNew(&ap));

1762:   /* get A_loc by taking all local rows of A */
1763:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));

1765:   ap->A_loc = A_loc;
1766:   a_loc     = (Mat_SeqAIJ *)(A_loc)->data;
1767:   ai        = a_loc->i;
1768:   aj        = a_loc->j;

1770:   /* determine symbolic Co=(p->B)^T*A - send to others */
1771:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
1772:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
1773:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1774:                          >= (num of nonzero rows of C_seq) - pn */
1775:   PetscCall(PetscMalloc1(pon + 1, &coi));
1776:   coi[0] = 0;

1778:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1779:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
1780:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1781:   current_space = free_space;

1783:   /* create and initialize a linked list */
1784:   PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
1785:   MatRowMergeMax_SeqAIJ(a_loc, am, ta);
1786:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1788:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));

1790:   for (i = 0; i < pon; i++) {
1791:     pnz = poti[i + 1] - poti[i];
1792:     ptJ = potj + poti[i];
1793:     for (j = 0; j < pnz; j++) {
1794:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1795:       anz  = ai[row + 1] - ai[row];
1796:       Jptr = aj + ai[row];
1797:       /* add non-zero cols of AP into the sorted linked list lnk */
1798:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1799:     }
1800:     nnz = lnk[0];

1802:     /* If free space is not available, double the total space in the list */
1803:     if (current_space->local_remaining < nnz) {
1804:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1805:       nspacedouble++;
1806:     }

1808:     /* Copy data into free space, and zero out denserows */
1809:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));

1811:     current_space->array += nnz;
1812:     current_space->local_used += nnz;
1813:     current_space->local_remaining -= nnz;

1815:     coi[i + 1] = coi[i] + nnz;
1816:   }

1818:   PetscCall(PetscMalloc1(coi[pon] + 1, &coj));
1819:   PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
1820:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */

1822:   afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
1823:   if (afill_tmp > afill) afill = afill_tmp;

1825:   /* send j-array (coj) of Co to other processors */
1826:   /* determine row ownership */
1827:   PetscCall(PetscNew(&merge));
1828:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));

1830:   merge->rowmap->n  = pn;
1831:   merge->rowmap->bs = 1;

1833:   PetscCall(PetscLayoutSetUp(merge->rowmap));
1834:   owners = merge->rowmap->range;

1836:   /* determine the number of messages to send, their lengths */
1837:   PetscCall(PetscCalloc1(size, &len_si));
1838:   PetscCall(PetscCalloc1(size, &merge->len_s));

1840:   len_s        = merge->len_s;
1841:   merge->nsend = 0;

1843:   PetscCall(PetscMalloc1(size + 2, &owners_co));

1845:   proc = 0;
1846:   for (i = 0; i < pon; i++) {
1847:     while (prmap[i] >= owners[proc + 1]) proc++;
1848:     len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1849:     len_s[proc] += coi[i + 1] - coi[i];
1850:   }

1852:   len          = 0; /* max length of buf_si[] */
1853:   owners_co[0] = 0;
1854:   for (proc = 0; proc < size; proc++) {
1855:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1856:     if (len_si[proc]) {
1857:       merge->nsend++;
1858:       len_si[proc] = 2 * (len_si[proc] + 1);
1859:       len += len_si[proc];
1860:     }
1861:   }

1863:   /* determine the number and length of messages to receive for coi and coj  */
1864:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
1865:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

1867:   /* post the Irecv and Isend of coj */
1868:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1869:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
1870:   PetscCall(PetscMalloc1(merge->nsend + 1, &swaits));
1871:   for (proc = 0, k = 0; proc < size; proc++) {
1872:     if (!len_s[proc]) continue;
1873:     i = owners_co[proc];
1874:     PetscCallMPI(MPI_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1875:     k++;
1876:   }

1878:   /* receives and sends of coj are complete */
1879:   PetscCall(PetscMalloc1(size, &sstatus));
1880:   for (i = 0; i < merge->nrecv; i++) {
1881:     PETSC_UNUSED PetscMPIInt icompleted;
1882:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1883:   }
1884:   PetscCall(PetscFree(rwaits));
1885:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));

1887:   /* add received column indices into table to update Armax */
1888:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1889:   for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1890:     Jptr = buf_rj[k];
1891:     for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1892:   }
1893:   PetscCall(PetscHMapIGetSize(ta, &Armax));

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

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

1940:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1941:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
1942:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1943:   current_space = free_space;

1945:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1946:   for (k = 0; k < merge->nrecv; k++) {
1947:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1948:     nrows       = *buf_ri_k[k];
1949:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1950:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1951:   }

1953:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
1954:   MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
1955:   rmax = 0;
1956:   for (i = 0; i < pn; i++) {
1957:     /* add pdt[i,:]*AP into lnk */
1958:     pnz = pdti[i + 1] - pdti[i];
1959:     ptJ = pdtj + pdti[i];
1960:     for (j = 0; j < pnz; j++) {
1961:       row  = ptJ[j]; /* row of AP == col of Pt */
1962:       anz  = ai[row + 1] - ai[row];
1963:       Jptr = aj + ai[row];
1964:       /* add non-zero cols of AP into the sorted linked list lnk */
1965:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1966:     }

1968:     /* add received col data into lnk */
1969:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1970:       if (i == *nextrow[k]) {            /* i-th row */
1971:         nzi  = *(nextci[k] + 1) - *nextci[k];
1972:         Jptr = buf_rj[k] + *nextci[k];
1973:         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
1974:         nextrow[k]++;
1975:         nextci[k]++;
1976:       }
1977:     }

1979:     /* add missing diagonal entry */
1980:     if (C->force_diagonals) {
1981:       k = i + owners[rank]; /* column index */
1982:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
1983:     }

1985:     nnz = lnk[0];

1987:     /* if free space is not available, make more free space */
1988:     if (current_space->local_remaining < nnz) {
1989:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1990:       nspacedouble++;
1991:     }
1992:     /* copy data into free space, then initialize lnk */
1993:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
1994:     PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));

1996:     current_space->array += nnz;
1997:     current_space->local_used += nnz;
1998:     current_space->local_remaining -= nnz;

2000:     bi[i + 1] = bi[i] + nnz;
2001:     if (nnz > rmax) rmax = nnz;
2002:   }
2003:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));

2005:   PetscCall(PetscMalloc1(bi[pn] + 1, &bj));
2006:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
2007:   afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
2008:   if (afill_tmp > afill) afill = afill_tmp;
2009:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2010:   PetscCall(PetscHMapIDestroy(&ta));
2011:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
2012:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));

2014:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2015:   PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
2016:   PetscCall(MatSetBlockSizes(C, PetscAbs(P->cmap->bs), PetscAbs(A->cmap->bs)));
2017:   PetscCall(MatGetType(A, &mtype));
2018:   PetscCall(MatSetType(C, mtype));
2019:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
2020:   MatPreallocateEnd(dnz, onz);
2021:   PetscCall(MatSetBlockSize(C, 1));
2022:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2023:   for (i = 0; i < pn; i++) {
2024:     row  = i + rstart;
2025:     nnz  = bi[i + 1] - bi[i];
2026:     Jptr = bj + bi[i];
2027:     PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
2028:   }
2029:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2030:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2031:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
2032:   merge->bi        = bi;
2033:   merge->bj        = bj;
2034:   merge->coi       = coi;
2035:   merge->coj       = coj;
2036:   merge->buf_ri    = buf_ri;
2037:   merge->buf_rj    = buf_rj;
2038:   merge->owners_co = owners_co;

2040:   /* attach the supporting struct to C for reuse */
2041:   C->product->data    = ap;
2042:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2043:   ap->merge           = merge;

2045:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2047: #if defined(PETSC_USE_INFO)
2048:   if (bi[pn] != 0) {
2049:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
2050:     PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
2051:   } else {
2052:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
2053:   }
2054: #endif
2055:   PetscFunctionReturn(PETSC_SUCCESS);
2056: }

2058: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2059: {
2060:   Mat_Product *product = C->product;
2061:   Mat          A = product->A, B = product->B;
2062:   PetscReal    fill = product->fill;
2063:   PetscBool    flg;

2065:   PetscFunctionBegin;
2066:   /* scalable */
2067:   PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
2068:   if (flg) {
2069:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
2070:     goto next;
2071:   }

2073:   /* nonscalable */
2074:   PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
2075:   if (flg) {
2076:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
2077:     goto next;
2078:   }

2080:   /* matmatmult */
2081:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
2082:   if (flg) {
2083:     Mat        At;
2084:     Mat_APMPI *ptap;

2086:     PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
2087:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
2088:     ptap = (Mat_APMPI *)C->product->data;
2089:     if (ptap) {
2090:       ptap->Pt            = At;
2091:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2092:     }
2093:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2094:     goto next;
2095:   }

2097:   /* backend general code */
2098:   PetscCall(PetscStrcmp(product->alg, "backend", &flg));
2099:   if (flg) {
2100:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2101:     PetscFunctionReturn(PETSC_SUCCESS);
2102:   }

2104:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");

2106: next:
2107:   C->ops->productnumeric = MatProductNumeric_AtB;
2108:   PetscFunctionReturn(PETSC_SUCCESS);
2109: }

2111: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2112: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2113: {
2114:   Mat_Product *product = C->product;
2115:   Mat          A = product->A, B = product->B;
2116: #if defined(PETSC_HAVE_HYPRE)
2117:   const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
2118:   PetscInt    nalg        = 5;
2119: #else
2120:   const char *algTypes[4] = {
2121:     "scalable",
2122:     "nonscalable",
2123:     "seqmpi",
2124:     "backend",
2125:   };
2126:   PetscInt nalg = 4;
2127: #endif
2128:   PetscInt  alg = 1; /* set nonscalable algorithm as default */
2129:   PetscBool flg;
2130:   MPI_Comm  comm;

2132:   PetscFunctionBegin;
2133:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));

2135:   /* Set "nonscalable" as default algorithm */
2136:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2137:   if (flg) {
2138:     PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));

2140:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2141:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2142:       MatInfo   Ainfo, Binfo;
2143:       PetscInt  nz_local;
2144:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2146:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2147:       PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2148:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2150:       if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2151:       PetscCall(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPIU_BOOL, MPI_LOR, comm));

2153:       if (alg_scalable) {
2154:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2155:         PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2156:         PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2157:       }
2158:     }
2159:   }

2161:   /* Get runtime option */
2162:   if (product->api_user) {
2163:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2164:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2165:     PetscOptionsEnd();
2166:   } else {
2167:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2168:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2169:     PetscOptionsEnd();
2170:   }
2171:   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));

2173:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2174:   PetscFunctionReturn(PETSC_SUCCESS);
2175: }

2177: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2178: {
2179:   PetscFunctionBegin;
2180:   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2181:   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2182:   PetscFunctionReturn(PETSC_SUCCESS);
2183: }

2185: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2186: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2187: {
2188:   Mat_Product *product = C->product;
2189:   Mat          A = product->A, B = product->B;
2190:   const char  *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
2191:   PetscInt     nalg        = 4;
2192:   PetscInt     alg         = 1; /* set default algorithm  */
2193:   PetscBool    flg;
2194:   MPI_Comm     comm;

2196:   PetscFunctionBegin;
2197:   /* Check matrix local sizes */
2198:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2199:   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 ")",
2200:              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

2202:   /* Set default algorithm */
2203:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2204:   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));

2206:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2207:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2208:     MatInfo   Ainfo, Binfo;
2209:     PetscInt  nz_local;
2210:     PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2212:     PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2213:     PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2214:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2216:     if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2217:     PetscCall(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPIU_BOOL, MPI_LOR, comm));

2219:     if (alg_scalable) {
2220:       alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2221:       PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2222:       PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2223:     }
2224:   }

2226:   /* Get runtime option */
2227:   if (product->api_user) {
2228:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2229:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2230:     PetscOptionsEnd();
2231:   } else {
2232:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2233:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2234:     PetscOptionsEnd();
2235:   }
2236:   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));

2238:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2239:   PetscFunctionReturn(PETSC_SUCCESS);
2240: }

2242: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2243: {
2244:   Mat_Product *product = C->product;
2245:   Mat          A = product->A, P = product->B;
2246:   MPI_Comm     comm;
2247:   PetscBool    flg;
2248:   PetscInt     alg = 1; /* set default algorithm */
2249: #if !defined(PETSC_HAVE_HYPRE)
2250:   const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
2251:   PetscInt    nalg        = 5;
2252: #else
2253:   const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
2254:   PetscInt    nalg        = 6;
2255: #endif
2256:   PetscInt pN = P->cmap->N;

2258:   PetscFunctionBegin;
2259:   /* Check matrix local sizes */
2260:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2261:   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 ")",
2262:              A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
2263:   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 ")",
2264:              A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);

2266:   /* Set "nonscalable" as default algorithm */
2267:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2268:   if (flg) {
2269:     PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));

2271:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2272:     if (pN > 100000) {
2273:       MatInfo   Ainfo, Pinfo;
2274:       PetscInt  nz_local;
2275:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2277:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2278:       PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
2279:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2281:       if (pN > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2282:       PetscCall(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPIU_BOOL, MPI_LOR, comm));

2284:       if (alg_scalable) {
2285:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2286:         PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));
2287:       }
2288:     }
2289:   }

2291:   /* Get runtime option */
2292:   if (product->api_user) {
2293:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2294:     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2295:     PetscOptionsEnd();
2296:   } else {
2297:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2298:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2299:     PetscOptionsEnd();
2300:   }
2301:   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));

2303:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2304:   PetscFunctionReturn(PETSC_SUCCESS);
2305: }

2307: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2308: {
2309:   Mat_Product *product = C->product;
2310:   Mat          A = product->A, R = product->B;

2312:   PetscFunctionBegin;
2313:   /* Check matrix local sizes */
2314:   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,
2315:              A->rmap->n, R->rmap->n, R->cmap->n);

2317:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2318:   PetscFunctionReturn(PETSC_SUCCESS);
2319: }

2321: /*
2322:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2323: */
2324: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2325: {
2326:   Mat_Product *product     = C->product;
2327:   PetscBool    flg         = PETSC_FALSE;
2328:   PetscInt     alg         = 1; /* default algorithm */
2329:   const char  *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
2330:   PetscInt     nalg        = 3;

2332:   PetscFunctionBegin;
2333:   /* Set default algorithm */
2334:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2335:   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));

2337:   /* Get runtime option */
2338:   if (product->api_user) {
2339:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2340:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2341:     PetscOptionsEnd();
2342:   } else {
2343:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2344:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2345:     PetscOptionsEnd();
2346:   }
2347:   if (flg) PetscCall(MatProductSetAlgorithm(C, (MatProductAlgorithm)algTypes[alg]));

2349:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2350:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2351:   PetscFunctionReturn(PETSC_SUCCESS);
2352: }

2354: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2355: {
2356:   Mat_Product *product = C->product;

2358:   PetscFunctionBegin;
2359:   switch (product->type) {
2360:   case MATPRODUCT_AB:
2361:     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2362:     break;
2363:   case MATPRODUCT_ABt:
2364:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2365:     break;
2366:   case MATPRODUCT_AtB:
2367:     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2368:     break;
2369:   case MATPRODUCT_PtAP:
2370:     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2371:     break;
2372:   case MATPRODUCT_RARt:
2373:     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2374:     break;
2375:   case MATPRODUCT_ABC:
2376:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2377:     break;
2378:   default:
2379:     break;
2380:   }
2381:   PetscFunctionReturn(PETSC_SUCCESS);
2382: }