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, 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, numBb;
410:   MPI_Comm         comm;
411:   MPI_Datatype     type1, *stype, *rtype;
412:   const PetscInt  *sindices, *sstarts, *rstarts;
413:   PetscMPIInt     *disp, nsends, nrecvs, nrows_to, nrows_from;
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:   PetscCallMPI(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 (PetscMPIInt i = 0; i < nsends; i++) {
479:     PetscCall(PetscMPIIntCast(sstarts[i + 1] - sstarts[i], &nrows_to));
480:     for (PetscInt j = 0; j < nrows_to; j++) PetscCall(PetscMPIIntCast(sindices[sstarts[i] + j], &disp[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 (PetscMPIInt i = 0; i < nrecvs; i++) {
488:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
489:     PetscCall(PetscMPIIntCast(rstarts[i + 1] - rstarts[i], &nrows_from));
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:   PetscMPIInt        nsends, nrecvs;
528:   MPI_Request       *swaits, *rwaits;
529:   MPI_Comm           comm;
530:   PetscMPIInt        tag = ((PetscObject)ctx)->tag, ncols, nrows, 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:   PetscCall(PetscMPIIntCast(B->cmap->N, &ncols));
540:   PetscCall(PetscMPIIntCast(aij->B->cmap->n, &nrows));
541:   contents = (MPIAIJ_MPIDense *)C->product->data;
542:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL /*bs*/));
543:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL /*bs*/));
544:   PetscCall(PetscMPIIntCast(nsends, &nsends_mpi));
545:   PetscCall(PetscMPIIntCast(nrecvs, &nrecvs_mpi));
546:   if (Bbidx == 0) workB = *outworkB = contents->workB;
547:   else workB = *outworkB = contents->workB1;
548:   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);
549:   swaits = contents->swaits;
550:   rwaits = contents->rwaits;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

738:     /* 1st off-diagonal part of C */
739:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
740:     k  = 0;
741:     for (k0 = 0; k0 < conz; k0++) {
742:       if (apJ[k] >= cstart) break;
743:       ca[k0]        = apa_sparse[k];
744:       apa_sparse[k] = 0.0;
745:       k++;
746:     }

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

756:     /* 2nd off-diagonal part of C */
757:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
758:     for (; k0 < conz; k0++) {
759:       ca[k0]        = apa_sparse[k];
760:       apa_sparse[k] = 0.0;
761:       k++;
762:     }
763:   }
764:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
765:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
766:   PetscFunctionReturn(PETSC_SUCCESS);
767: }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

908:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
909:   C->ops->productnumeric = MatProductNumeric_AB;

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

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

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

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

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

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

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

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

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

1002:   *size4 = l;
1003: }

1005: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1006: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1007: /* matrix-matrix multiplications.  */
1008: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1009: {
1010:   MPI_Comm           comm;
1011:   PetscMPIInt        size;
1012:   Mat_APMPI         *ptap;
1013:   PetscFreeSpaceList free_space_diag = NULL, current_space = NULL;
1014:   Mat_MPIAIJ        *a  = (Mat_MPIAIJ *)A->data;
1015:   Mat_SeqAIJ        *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
1016:   Mat_MPIAIJ        *p = (Mat_MPIAIJ *)P->data;
1017:   Mat_SeqAIJ        *adpd_seq, *p_off, *aopoth_seq;
1018:   PetscInt           adponz, adpdnz;
1019:   PetscInt          *pi_loc, *dnz, *onz;
1020:   PetscInt          *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
1021:   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;
1022:   PetscInt           am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
1023:   PetscBT            lnkbt;
1024:   PetscReal          afill;
1025:   PetscMPIInt        rank;
1026:   Mat                adpd, aopoth;
1027:   MatType            mtype;
1028:   const char        *prefix;

1030:   PetscFunctionBegin;
1031:   MatCheckProduct(C, 4);
1032:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1033:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1034:   PetscCallMPI(MPI_Comm_size(comm, &size));
1035:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1036:   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));

1038:   /* create struct Mat_APMPI and attached it to C later */
1039:   PetscCall(PetscNew(&ptap));

1041:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1042:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));

1044:   /* get P_loc by taking all local rows of P */
1045:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));

1047:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
1048:   pi_loc = p_loc->i;

1050:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1051:   PetscCall(PetscMalloc1(am + 2, &api));
1052:   PetscCall(PetscMalloc1(am + 2, &adpoi));

1054:   adpoi[0]  = 0;
1055:   ptap->api = api;
1056:   api[0]    = 0;

1058:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1059:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
1060:   MatPreallocateBegin(comm, am, pn, dnz, onz);

1062:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1063:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1064:   PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
1065:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1066:   PetscCall(MatSetOptionsPrefix(adpd, prefix));
1067:   PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));

1069:   PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
1070:   PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
1071:   PetscCall(MatProductSetFill(adpd, fill));
1072:   PetscCall(MatProductSetFromOptions(adpd));

1074:   adpd->force_diagonals = C->force_diagonals;
1075:   PetscCall(MatProductSymbolic(adpd));

1077:   adpd_seq = (Mat_SeqAIJ *)((adpd)->data);
1078:   adpdi    = adpd_seq->i;
1079:   adpdj    = adpd_seq->j;
1080:   p_off    = (Mat_SeqAIJ *)p->B->data;
1081:   poff_i   = p_off->i;
1082:   poff_j   = p_off->j;

1084:   /* j_temp stores indices of a result row before they are added to the linked list */
1085:   PetscCall(PetscMalloc1(pN + 2, &j_temp));

1087:   /* Symbolic calc of the A_diag * p_loc_off */
1088:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1089:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
1090:   current_space = free_space_diag;

1092:   for (i = 0; i < am; i++) {
1093:     /* A_diag * P_loc_off */
1094:     nzi = adi[i + 1] - adi[i];
1095:     for (j = 0; j < nzi; j++) {
1096:       row  = *adj++;
1097:       pnz  = poff_i[row + 1] - poff_i[row];
1098:       Jptr = poff_j + poff_i[row];
1099:       for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
1100:       /* add non-zero cols of P into the sorted linked list lnk */
1101:       PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
1102:     }

1104:     adponz       = lnk[0];
1105:     adpoi[i + 1] = adpoi[i] + adponz;

1107:     /* if free space is not available, double the total space in the list */
1108:     if (current_space->local_remaining < adponz) {
1109:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), &current_space));
1110:       nspacedouble++;
1111:     }

1113:     /* Copy data into free space, then initialize lnk */
1114:     PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));

1116:     current_space->array += adponz;
1117:     current_space->local_used += adponz;
1118:     current_space->local_remaining -= adponz;
1119:   }

1121:   /* Symbolic calc of A_off * P_oth */
1122:   PetscCall(MatSetOptionsPrefix(a->B, prefix));
1123:   PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
1124:   PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
1125:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1126:   aopoth_seq = (Mat_SeqAIJ *)((aopoth)->data);
1127:   aopothi    = aopoth_seq->i;
1128:   aopothj    = aopoth_seq->j;

1130:   /* Allocate space for apj, adpj, aopj, ... */
1131:   /* destroy lists of free space and other temporary array(s) */

1133:   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am] + 2, &ptap->apj));
1134:   PetscCall(PetscMalloc1(adpoi[am] + 2, &adpoj));

1136:   /* Copy from linked list to j-array */
1137:   PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
1138:   PetscCall(PetscLLDestroy(lnk, lnkbt));

1140:   adpoJ = adpoj;
1141:   adpdJ = adpdj;
1142:   aopJ  = aopothj;
1143:   apj   = ptap->apj;
1144:   apJ   = apj; /* still empty */

1146:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1147:   /* A_diag * P_loc_diag to get A*P */
1148:   for (i = 0; i < am; i++) {
1149:     aopnz  = aopothi[i + 1] - aopothi[i];
1150:     adponz = adpoi[i + 1] - adpoi[i];
1151:     adpdnz = adpdi[i + 1] - adpdi[i];

1153:     /* Correct indices from A_diag*P_diag */
1154:     for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
1155:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1156:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1157:     PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));

1159:     aopJ += aopnz;
1160:     adpoJ += adponz;
1161:     adpdJ += adpdnz;
1162:     apJ += apnz;
1163:     api[i + 1] = api[i] + apnz;
1164:   }

1166:   /* malloc apa to store dense row A[i,:]*P */
1167:   PetscCall(PetscCalloc1(pN + 2, &ptap->apa));

1169:   /* create and assemble symbolic parallel matrix C */
1170:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1171:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
1172:   PetscCall(MatGetType(A, &mtype));
1173:   PetscCall(MatSetType(C, mtype));
1174:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1175:   MatPreallocateEnd(dnz, onz);

1177:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1178:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1179:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1180:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1182:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1183:   C->ops->productnumeric = MatProductNumeric_AB;

1185:   /* attach the supporting struct to C for reuse */
1186:   C->product->data    = ptap;
1187:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

1189:   /* set MatInfo */
1190:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1191:   if (afill < 1.0) afill = 1.0;
1192:   C->info.mallocs           = nspacedouble;
1193:   C->info.fill_ratio_given  = fill;
1194:   C->info.fill_ratio_needed = afill;

1196: #if defined(PETSC_USE_INFO)
1197:   if (api[am]) {
1198:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1199:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1200:   } else {
1201:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1202:   }
1203: #endif

1205:   PetscCall(MatDestroy(&aopoth));
1206:   PetscCall(MatDestroy(&adpd));
1207:   PetscCall(PetscFree(j_temp));
1208:   PetscCall(PetscFree(adpoj));
1209:   PetscCall(PetscFree(adpoi));
1210:   PetscFunctionReturn(PETSC_SUCCESS);
1211: }

1213: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1214: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
1215: {
1216:   Mat_APMPI *ptap;
1217:   Mat        Pt;

1219:   PetscFunctionBegin;
1220:   MatCheckProduct(C, 3);
1221:   ptap = (Mat_APMPI *)C->product->data;
1222:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1223:   PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");

1225:   Pt = ptap->Pt;
1226:   PetscCall(MatTransposeSetPrecursor(P, Pt));
1227:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
1228:   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
1229:   PetscFunctionReturn(PETSC_SUCCESS);
1230: }

1232: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1233: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, PetscReal fill, Mat C)
1234: {
1235:   Mat_APMPI               *ptap;
1236:   Mat_MPIAIJ              *p = (Mat_MPIAIJ *)P->data;
1237:   MPI_Comm                 comm;
1238:   PetscMPIInt              size, rank;
1239:   PetscFreeSpaceList       free_space = NULL, current_space = NULL;
1240:   PetscInt                 pn = P->cmap->n, aN = A->cmap->N, an = A->cmap->n;
1241:   PetscInt                *lnk, i, k, rstart;
1242:   PetscBT                  lnkbt;
1243:   PetscMPIInt              tagi, tagj, *len_si, *len_s, *len_ri, nrecv, proc, nsend;
1244:   PETSC_UNUSED PetscMPIInt icompleted = 0;
1245:   PetscInt               **buf_rj, **buf_ri, **buf_ri_k, row, ncols, *cols;
1246:   PetscInt                 len, *dnz, *onz, *owners, nzi;
1247:   PetscInt                 nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1248:   MPI_Request             *swaits, *rwaits;
1249:   MPI_Status              *sstatus, rstatus;
1250:   PetscLayout              rowmap;
1251:   PetscInt                *owners_co, *coi, *coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1252:   PetscMPIInt             *len_r, *id_r;          /* array of length of comm->size, store send/recv matrix values */
1253:   PetscInt                *Jptr, *prmap = p->garray, con, j, Crmax;
1254:   Mat_SeqAIJ              *a_loc, *c_loc, *c_oth;
1255:   PetscHMapI               ta;
1256:   MatType                  mtype;
1257:   const char              *prefix;

1259:   PetscFunctionBegin;
1260:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1261:   PetscCallMPI(MPI_Comm_size(comm, &size));
1262:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1264:   /* create symbolic parallel matrix C */
1265:   PetscCall(MatGetType(A, &mtype));
1266:   PetscCall(MatSetType(C, mtype));

1268:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1270:   /* create struct Mat_APMPI and attached it to C later */
1271:   PetscCall(PetscNew(&ptap));

1273:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1274:   PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
1275:   PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));

1277:   /* (1) compute symbolic A_loc */
1278:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));

1280:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1281:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1282:   PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
1283:   PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
1284:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
1285:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));

1287:   /* (3) send coj of C_oth to other processors  */
1288:   /* determine row ownership */
1289:   PetscCall(PetscLayoutCreate(comm, &rowmap));
1290:   rowmap->n  = pn;
1291:   rowmap->bs = 1;
1292:   PetscCall(PetscLayoutSetUp(rowmap));
1293:   owners = rowmap->range;

1295:   /* determine the number of messages to send, their lengths */
1296:   PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 2, &owners_co));
1297:   PetscCall(PetscArrayzero(len_s, size));
1298:   PetscCall(PetscArrayzero(len_si, size));

1300:   c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
1301:   coi   = c_oth->i;
1302:   coj   = c_oth->j;
1303:   con   = ptap->C_oth->rmap->n;
1304:   proc  = 0;
1305:   for (i = 0; i < con; i++) {
1306:     while (prmap[i] >= owners[proc + 1]) proc++;
1307:     len_si[proc]++;                     /* num of rows in Co(=Pt*A) to be sent to [proc] */
1308:     len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1309:   }

1311:   len          = 0; /* max length of buf_si[], see (4) */
1312:   owners_co[0] = 0;
1313:   nsend        = 0;
1314:   for (proc = 0; proc < size; proc++) {
1315:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1316:     if (len_s[proc]) {
1317:       nsend++;
1318:       len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1319:       len += len_si[proc];
1320:     }
1321:   }

1323:   /* determine the number and length of messages to receive for coi and coj  */
1324:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
1325:   PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));

1327:   /* post the Irecv and Isend of coj */
1328:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1329:   PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
1330:   PetscCall(PetscMalloc1(nsend + 1, &swaits));
1331:   for (proc = 0, k = 0; proc < size; proc++) {
1332:     if (!len_s[proc]) continue;
1333:     i = owners_co[proc];
1334:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1335:     k++;
1336:   }

1338:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1339:   PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
1340:   PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
1341:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
1342:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
1343:   c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;

1345:   /* receives coj are complete */
1346:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1347:   PetscCall(PetscFree(rwaits));
1348:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1350:   /* add received column indices into ta to update Crmax */
1351:   a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;

1353:   /* create and initialize a linked list */
1354:   PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
1355:   MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);

1357:   for (k = 0; k < nrecv; k++) { /* k-th received message */
1358:     Jptr = buf_rj[k];
1359:     for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1360:   }
1361:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
1362:   PetscCall(PetscHMapIDestroy(&ta));

1364:   /* (4) send and recv coi */
1365:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1366:   PetscCall(PetscPostIrecvInt(comm, tagi, nrecv, id_r, len_ri, &buf_ri, &rwaits));
1367:   PetscCall(PetscMalloc1(len + 1, &buf_s));
1368:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1369:   for (proc = 0, k = 0; proc < size; proc++) {
1370:     if (!len_s[proc]) continue;
1371:     /* form outgoing message for i-structure:
1372:          buf_si[0]:                 nrows to be sent
1373:                [1:nrows]:           row index (global)
1374:                [nrows+1:2*nrows+1]: i-structure index
1375:     */
1376:     nrows       = len_si[proc] / 2 - 1; /* num of rows in Co to be sent to [proc] */
1377:     buf_si_i    = buf_si + nrows + 1;
1378:     buf_si[0]   = nrows;
1379:     buf_si_i[0] = 0;
1380:     nrows       = 0;
1381:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1382:       nzi                 = coi[i + 1] - coi[i];
1383:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1384:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1385:       nrows++;
1386:     }
1387:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1388:     k++;
1389:     buf_si += len_si[proc];
1390:   }
1391:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1392:   PetscCall(PetscFree(rwaits));
1393:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1395:   PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
1396:   PetscCall(PetscFree(len_ri));
1397:   PetscCall(PetscFree(swaits));
1398:   PetscCall(PetscFree(buf_s));

1400:   /* (5) compute the local portion of C      */
1401:   /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
1402:   PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
1403:   current_space = free_space;

1405:   PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
1406:   for (k = 0; k < nrecv; k++) {
1407:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1408:     nrows       = *buf_ri_k[k];
1409:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1410:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1411:   }

1413:   MatPreallocateBegin(comm, pn, an, dnz, onz);
1414:   PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
1415:   for (i = 0; i < pn; i++) { /* for each local row of C */
1416:     /* add C_loc into C */
1417:     nzi  = c_loc->i[i + 1] - c_loc->i[i];
1418:     Jptr = c_loc->j + c_loc->i[i];
1419:     PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));

1421:     /* add received col data into lnk */
1422:     for (k = 0; k < nrecv; k++) { /* k-th received message */
1423:       if (i == *nextrow[k]) {     /* i-th row */
1424:         nzi  = *(nextci[k] + 1) - *nextci[k];
1425:         Jptr = buf_rj[k] + *nextci[k];
1426:         PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1427:         nextrow[k]++;
1428:         nextci[k]++;
1429:       }
1430:     }

1432:     /* add missing diagonal entry */
1433:     if (C->force_diagonals) {
1434:       k = i + owners[rank]; /* column index */
1435:       PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
1436:     }

1438:     nzi = lnk[0];

1440:     /* copy data into free space, then initialize lnk */
1441:     PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
1442:     PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
1443:   }
1444:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1445:   PetscCall(PetscLLDestroy(lnk, lnkbt));
1446:   PetscCall(PetscFreeSpaceDestroy(free_space));

1448:   /* local sizes and preallocation */
1449:   PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
1450:   if (P->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
1451:   if (A->cmap->bs > 0) PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
1452:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1453:   MatPreallocateEnd(dnz, onz);

1455:   /* add C_loc and C_oth to C */
1456:   PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
1457:   for (i = 0; i < pn; i++) {
1458:     ncols = c_loc->i[i + 1] - c_loc->i[i];
1459:     cols  = c_loc->j + c_loc->i[i];
1460:     row   = rstart + i;
1461:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));

1463:     if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
1464:   }
1465:   for (i = 0; i < con; i++) {
1466:     ncols = c_oth->i[i + 1] - c_oth->i[i];
1467:     cols  = c_oth->j + c_oth->i[i];
1468:     row   = prmap[i];
1469:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1470:   }
1471:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1472:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1473:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1475:   /* members in merge */
1476:   PetscCall(PetscFree(id_r));
1477:   PetscCall(PetscFree(len_r));
1478:   PetscCall(PetscFree(buf_ri[0]));
1479:   PetscCall(PetscFree(buf_ri));
1480:   PetscCall(PetscFree(buf_rj[0]));
1481:   PetscCall(PetscFree(buf_rj));
1482:   PetscCall(PetscLayoutDestroy(&rowmap));

1484:   /* attach the supporting struct to C for reuse */
1485:   C->product->data    = ptap;
1486:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1487:   PetscFunctionReturn(PETSC_SUCCESS);
1488: }

1490: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
1491: {
1492:   Mat_MPIAIJ        *p = (Mat_MPIAIJ *)P->data;
1493:   Mat_SeqAIJ        *c_seq;
1494:   Mat_APMPI         *ptap;
1495:   Mat                A_loc, C_loc, C_oth;
1496:   PetscInt           i, rstart, rend, cm, ncols, row;
1497:   const PetscInt    *cols;
1498:   const PetscScalar *vals;

1500:   PetscFunctionBegin;
1501:   MatCheckProduct(C, 3);
1502:   ptap = (Mat_APMPI *)C->product->data;
1503:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1504:   PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1505:   PetscCall(MatZeroEntries(C));

1507:   /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1508:   /* 1) get R = Pd^T, Ro = Po^T */
1509:   PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
1510:   PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
1511:   PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
1512:   PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));

1514:   /* 2) compute numeric A_loc */
1515:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));

1517:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1518:   A_loc = ptap->A_loc;
1519:   PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
1520:   PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
1521:   C_loc = ptap->C_loc;
1522:   C_oth = ptap->C_oth;

1524:   /* add C_loc and C_oth to C */
1525:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));

1527:   /* C_loc -> C */
1528:   cm    = C_loc->rmap->N;
1529:   c_seq = (Mat_SeqAIJ *)C_loc->data;
1530:   cols  = c_seq->j;
1531:   vals  = c_seq->a;
1532:   for (i = 0; i < cm; i++) {
1533:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1534:     row   = rstart + i;
1535:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1536:     cols += ncols;
1537:     vals += ncols;
1538:   }

1540:   /* Co -> C, off-processor part */
1541:   cm    = C_oth->rmap->N;
1542:   c_seq = (Mat_SeqAIJ *)C_oth->data;
1543:   cols  = c_seq->j;
1544:   vals  = c_seq->a;
1545:   for (i = 0; i < cm; i++) {
1546:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1547:     row   = p->garray[i];
1548:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1549:     cols += ncols;
1550:     vals += ncols;
1551:   }
1552:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1553:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1554:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1555:   PetscFunctionReturn(PETSC_SUCCESS);
1556: }

1558: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
1559: {
1560:   Mat_Merge_SeqsToMPI *merge;
1561:   Mat_MPIAIJ          *p  = (Mat_MPIAIJ *)P->data;
1562:   Mat_SeqAIJ          *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
1563:   Mat_APMPI           *ap;
1564:   PetscInt            *adj;
1565:   PetscInt             i, j, k, anz, pnz, row, *cj, nexta;
1566:   MatScalar           *ada, *ca, valtmp;
1567:   PetscInt             am = A->rmap->n, cm = C->rmap->n, pon = (p->B)->cmap->n;
1568:   MPI_Comm             comm;
1569:   PetscMPIInt          size, rank, taga, *len_s, proc;
1570:   PetscInt            *owners, nrows, **buf_ri_k, **nextrow, **nextci;
1571:   PetscInt           **buf_ri, **buf_rj;
1572:   PetscInt             cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1573:   MPI_Request         *s_waits, *r_waits;
1574:   MPI_Status          *status;
1575:   MatScalar          **abuf_r, *ba_i, *pA, *coa, *ba;
1576:   const PetscScalar   *dummy;
1577:   PetscInt            *ai, *aj, *coi, *coj, *poJ, *pdJ;
1578:   Mat                  A_loc;
1579:   Mat_SeqAIJ          *a_loc;

1581:   PetscFunctionBegin;
1582:   MatCheckProduct(C, 3);
1583:   ap = (Mat_APMPI *)C->product->data;
1584:   PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
1585:   PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1586:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
1587:   PetscCallMPI(MPI_Comm_size(comm, &size));
1588:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1590:   merge = ap->merge;

1592:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1593:   /* get data from symbolic products */
1594:   coi = merge->coi;
1595:   coj = merge->coj;
1596:   PetscCall(PetscCalloc1(coi[pon] + 1, &coa));
1597:   bi     = merge->bi;
1598:   bj     = merge->bj;
1599:   owners = merge->rowmap->range;
1600:   PetscCall(PetscCalloc1(bi[cm] + 1, &ba));

1602:   /* get A_loc by taking all local rows of A */
1603:   A_loc = ap->A_loc;
1604:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
1605:   a_loc = (Mat_SeqAIJ *)A_loc->data;
1606:   ai    = a_loc->i;
1607:   aj    = a_loc->j;

1609:   /* trigger copy to CPU */
1610:   PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
1611:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
1612:   PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
1613:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
1614:   for (i = 0; i < am; i++) {
1615:     anz = ai[i + 1] - ai[i];
1616:     adj = aj + ai[i];
1617:     ada = a_loc->a + ai[i];

1619:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1620:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1621:     pnz = po->i[i + 1] - po->i[i];
1622:     poJ = po->j + po->i[i];
1623:     pA  = po->a + po->i[i];
1624:     for (j = 0; j < pnz; j++) {
1625:       row = poJ[j];
1626:       cj  = coj + coi[row];
1627:       ca  = coa + coi[row];
1628:       /* perform sparse axpy */
1629:       nexta  = 0;
1630:       valtmp = pA[j];
1631:       for (k = 0; nexta < anz; k++) {
1632:         if (cj[k] == adj[nexta]) {
1633:           ca[k] += valtmp * ada[nexta];
1634:           nexta++;
1635:         }
1636:       }
1637:       PetscCall(PetscLogFlops(2.0 * anz));
1638:     }

1640:     /* put the value into Cd (diagonal part) */
1641:     pnz = pd->i[i + 1] - pd->i[i];
1642:     pdJ = pd->j + pd->i[i];
1643:     pA  = pd->a + pd->i[i];
1644:     for (j = 0; j < pnz; j++) {
1645:       row = pdJ[j];
1646:       cj  = bj + bi[row];
1647:       ca  = ba + bi[row];
1648:       /* perform sparse axpy */
1649:       nexta  = 0;
1650:       valtmp = pA[j];
1651:       for (k = 0; nexta < anz; k++) {
1652:         if (cj[k] == adj[nexta]) {
1653:           ca[k] += valtmp * ada[nexta];
1654:           nexta++;
1655:         }
1656:       }
1657:       PetscCall(PetscLogFlops(2.0 * anz));
1658:     }
1659:   }

1661:   /* 3) send and recv matrix values coa */
1662:   buf_ri = merge->buf_ri;
1663:   buf_rj = merge->buf_rj;
1664:   len_s  = merge->len_s;
1665:   PetscCall(PetscCommGetNewTag(comm, &taga));
1666:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

1668:   PetscCall(PetscMalloc2(merge->nsend + 1, &s_waits, size, &status));
1669:   for (proc = 0, k = 0; proc < size; proc++) {
1670:     if (!len_s[proc]) continue;
1671:     i = merge->owners_co[proc];
1672:     PetscCallMPI(MPIU_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
1673:     k++;
1674:   }
1675:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
1676:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));

1678:   PetscCall(PetscFree2(s_waits, status));
1679:   PetscCall(PetscFree(r_waits));
1680:   PetscCall(PetscFree(coa));

1682:   /* 4) insert local Cseq and received values into Cmpi */
1683:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1684:   for (k = 0; k < merge->nrecv; k++) {
1685:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1686:     nrows       = *buf_ri_k[k];
1687:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1688:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1689:   }

1691:   for (i = 0; i < cm; i++) {
1692:     row  = owners[rank] + i; /* global row index of C_seq */
1693:     bj_i = bj + bi[i];       /* col indices of the i-th row of C */
1694:     ba_i = ba + bi[i];
1695:     bnz  = bi[i + 1] - bi[i];
1696:     /* add received vals into ba */
1697:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1698:       /* i-th row */
1699:       if (i == *nextrow[k]) {
1700:         cnz    = *(nextci[k] + 1) - *nextci[k];
1701:         cj     = buf_rj[k] + *nextci[k];
1702:         ca     = abuf_r[k] + *nextci[k];
1703:         nextcj = 0;
1704:         for (j = 0; nextcj < cnz; j++) {
1705:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1706:             ba_i[j] += ca[nextcj++];
1707:           }
1708:         }
1709:         nextrow[k]++;
1710:         nextci[k]++;
1711:         PetscCall(PetscLogFlops(2.0 * cnz));
1712:       }
1713:     }
1714:     PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
1715:   }
1716:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1717:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

1719:   PetscCall(PetscFree(ba));
1720:   PetscCall(PetscFree(abuf_r[0]));
1721:   PetscCall(PetscFree(abuf_r));
1722:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1723:   PetscFunctionReturn(PETSC_SUCCESS);
1724: }

1726: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
1727: {
1728:   Mat                  A_loc;
1729:   Mat_APMPI           *ap;
1730:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
1731:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
1732:   PetscInt            *pdti, *pdtj, *poti, *potj, *ptJ;
1733:   PetscInt             nnz;
1734:   PetscInt            *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
1735:   PetscInt             am = A->rmap->n, pn = P->cmap->n;
1736:   MPI_Comm             comm;
1737:   PetscMPIInt          size, rank, tagi, tagj, *len_si, *len_s, *len_ri, proc;
1738:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
1739:   PetscInt             len, *dnz, *onz, *owners;
1740:   PetscInt             nzi, *bi, *bj;
1741:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1742:   MPI_Request         *swaits, *rwaits;
1743:   MPI_Status          *sstatus, rstatus;
1744:   Mat_Merge_SeqsToMPI *merge;
1745:   PetscInt            *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
1746:   PetscReal            afill  = 1.0, afill_tmp;
1747:   PetscInt             rstart = P->cmap->rstart, rmax, Armax;
1748:   Mat_SeqAIJ          *a_loc;
1749:   PetscHMapI           ta;
1750:   MatType              mtype;

1752:   PetscFunctionBegin;
1753:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1754:   /* check if matrix local sizes are compatible */
1755:   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,
1756:              A->rmap->rend, P->rmap->rstart, P->rmap->rend);

1758:   PetscCallMPI(MPI_Comm_size(comm, &size));
1759:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1761:   /* create struct Mat_APMPI and attached it to C later */
1762:   PetscCall(PetscNew(&ap));

1764:   /* get A_loc by taking all local rows of A */
1765:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));

1767:   ap->A_loc = A_loc;
1768:   a_loc     = (Mat_SeqAIJ *)A_loc->data;
1769:   ai        = a_loc->i;
1770:   aj        = a_loc->j;

1772:   /* determine symbolic Co=(p->B)^T*A - send to others */
1773:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
1774:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
1775:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1776:                          >= (num of nonzero rows of C_seq) - pn */
1777:   PetscCall(PetscMalloc1(pon + 1, &coi));
1778:   coi[0] = 0;

1780:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1781:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
1782:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1783:   current_space = free_space;

1785:   /* create and initialize a linked list */
1786:   PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
1787:   MatRowMergeMax_SeqAIJ(a_loc, am, ta);
1788:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1790:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));

1792:   for (i = 0; i < pon; i++) {
1793:     pnz = poti[i + 1] - poti[i];
1794:     ptJ = potj + poti[i];
1795:     for (j = 0; j < pnz; j++) {
1796:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1797:       anz  = ai[row + 1] - ai[row];
1798:       Jptr = aj + ai[row];
1799:       /* add non-zero cols of AP into the sorted linked list lnk */
1800:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1801:     }
1802:     nnz = lnk[0];

1804:     /* If free space is not available, double the total space in the list */
1805:     if (current_space->local_remaining < nnz) {
1806:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1807:       nspacedouble++;
1808:     }

1810:     /* Copy data into free space, and zero out denserows */
1811:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));

1813:     current_space->array += nnz;
1814:     current_space->local_used += nnz;
1815:     current_space->local_remaining -= nnz;

1817:     coi[i + 1] = coi[i] + nnz;
1818:   }

1820:   PetscCall(PetscMalloc1(coi[pon] + 1, &coj));
1821:   PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
1822:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */

1824:   afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
1825:   if (afill_tmp > afill) afill = afill_tmp;

1827:   /* send j-array (coj) of Co to other processors */
1828:   /* determine row ownership */
1829:   PetscCall(PetscNew(&merge));
1830:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));

1832:   merge->rowmap->n  = pn;
1833:   merge->rowmap->bs = 1;

1835:   PetscCall(PetscLayoutSetUp(merge->rowmap));
1836:   owners = merge->rowmap->range;

1838:   /* determine the number of messages to send, their lengths */
1839:   PetscCall(PetscCalloc1(size, &len_si));
1840:   PetscCall(PetscCalloc1(size, &merge->len_s));

1842:   len_s        = merge->len_s;
1843:   merge->nsend = 0;

1845:   PetscCall(PetscMalloc1(size + 2, &owners_co));

1847:   proc = 0;
1848:   for (i = 0; i < pon; i++) {
1849:     while (prmap[i] >= owners[proc + 1]) proc++;
1850:     len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1851:     len_s[proc] += coi[i + 1] - coi[i];
1852:   }

1854:   len          = 0; /* max length of buf_si[] */
1855:   owners_co[0] = 0;
1856:   for (proc = 0; proc < size; proc++) {
1857:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1858:     if (len_si[proc]) {
1859:       merge->nsend++;
1860:       len_si[proc] = 2 * (len_si[proc] + 1);
1861:       len += len_si[proc];
1862:     }
1863:   }

1865:   /* determine the number and length of messages to receive for coi and coj  */
1866:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
1867:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

1869:   /* post the Irecv and Isend of coj */
1870:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1871:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
1872:   PetscCall(PetscMalloc1(merge->nsend + 1, &swaits));
1873:   for (proc = 0, k = 0; proc < size; proc++) {
1874:     if (!len_s[proc]) continue;
1875:     i = owners_co[proc];
1876:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1877:     k++;
1878:   }

1880:   /* receives and sends of coj are complete */
1881:   PetscCall(PetscMalloc1(size, &sstatus));
1882:   for (i = 0; i < merge->nrecv; i++) {
1883:     PETSC_UNUSED PetscMPIInt icompleted;
1884:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1885:   }
1886:   PetscCall(PetscFree(rwaits));
1887:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));

1889:   /* add received column indices into table to update Armax */
1890:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1891:   for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1892:     Jptr = buf_rj[k];
1893:     for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1894:   }
1895:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1897:   /* send and recv coi */
1898:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1899:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &rwaits));
1900:   PetscCall(PetscMalloc1(len + 1, &buf_s));
1901:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1902:   for (proc = 0, k = 0; proc < size; proc++) {
1903:     if (!len_s[proc]) continue;
1904:     /* form outgoing message for i-structure:
1905:          buf_si[0]:                 nrows to be sent
1906:                [1:nrows]:           row index (global)
1907:                [nrows+1:2*nrows+1]: i-structure index
1908:     */
1909:     nrows       = len_si[proc] / 2 - 1;
1910:     buf_si_i    = buf_si + nrows + 1;
1911:     buf_si[0]   = nrows;
1912:     buf_si_i[0] = 0;
1913:     nrows       = 0;
1914:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1915:       nzi                 = coi[i + 1] - coi[i];
1916:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1917:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1918:       nrows++;
1919:     }
1920:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1921:     k++;
1922:     buf_si += len_si[proc];
1923:   }
1924:   i = merge->nrecv;
1925:   while (i--) {
1926:     PETSC_UNUSED PetscMPIInt icompleted;
1927:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1928:   }
1929:   PetscCall(PetscFree(rwaits));
1930:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
1931:   PetscCall(PetscFree(len_si));
1932:   PetscCall(PetscFree(len_ri));
1933:   PetscCall(PetscFree(swaits));
1934:   PetscCall(PetscFree(sstatus));
1935:   PetscCall(PetscFree(buf_s));

1937:   /* compute the local portion of C (mpi mat) */
1938:   /* allocate bi array and free space for accumulating nonzero column info */
1939:   PetscCall(PetscMalloc1(pn + 1, &bi));
1940:   bi[0] = 0;

1942:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1943:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
1944:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1945:   current_space = free_space;

1947:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1948:   for (k = 0; k < merge->nrecv; k++) {
1949:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1950:     nrows       = *buf_ri_k[k];
1951:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1952:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1953:   }

1955:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
1956:   MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
1957:   rmax = 0;
1958:   for (i = 0; i < pn; i++) {
1959:     /* add pdt[i,:]*AP into lnk */
1960:     pnz = pdti[i + 1] - pdti[i];
1961:     ptJ = pdtj + pdti[i];
1962:     for (j = 0; j < pnz; j++) {
1963:       row  = ptJ[j]; /* row of AP == col of Pt */
1964:       anz  = ai[row + 1] - ai[row];
1965:       Jptr = aj + ai[row];
1966:       /* add non-zero cols of AP into the sorted linked list lnk */
1967:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1968:     }

1970:     /* add received col data into lnk */
1971:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1972:       if (i == *nextrow[k]) {            /* i-th row */
1973:         nzi  = *(nextci[k] + 1) - *nextci[k];
1974:         Jptr = buf_rj[k] + *nextci[k];
1975:         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
1976:         nextrow[k]++;
1977:         nextci[k]++;
1978:       }
1979:     }

1981:     /* add missing diagonal entry */
1982:     if (C->force_diagonals) {
1983:       k = i + owners[rank]; /* column index */
1984:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
1985:     }

1987:     nnz = lnk[0];

1989:     /* if free space is not available, make more free space */
1990:     if (current_space->local_remaining < nnz) {
1991:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1992:       nspacedouble++;
1993:     }
1994:     /* copy data into free space, then initialize lnk */
1995:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
1996:     PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));

1998:     current_space->array += nnz;
1999:     current_space->local_used += nnz;
2000:     current_space->local_remaining -= nnz;

2002:     bi[i + 1] = bi[i] + nnz;
2003:     if (nnz > rmax) rmax = nnz;
2004:   }
2005:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));

2007:   PetscCall(PetscMalloc1(bi[pn] + 1, &bj));
2008:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
2009:   afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
2010:   if (afill_tmp > afill) afill = afill_tmp;
2011:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2012:   PetscCall(PetscHMapIDestroy(&ta));
2013:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
2014:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));

2016:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2017:   PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
2018:   PetscCall(MatSetBlockSizes(C, PetscAbs(P->cmap->bs), PetscAbs(A->cmap->bs)));
2019:   PetscCall(MatGetType(A, &mtype));
2020:   PetscCall(MatSetType(C, mtype));
2021:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
2022:   MatPreallocateEnd(dnz, onz);
2023:   PetscCall(MatSetBlockSize(C, 1));
2024:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2025:   for (i = 0; i < pn; i++) {
2026:     row  = i + rstart;
2027:     nnz  = bi[i + 1] - bi[i];
2028:     Jptr = bj + bi[i];
2029:     PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
2030:   }
2031:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2032:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2033:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
2034:   merge->bi        = bi;
2035:   merge->bj        = bj;
2036:   merge->coi       = coi;
2037:   merge->coj       = coj;
2038:   merge->buf_ri    = buf_ri;
2039:   merge->buf_rj    = buf_rj;
2040:   merge->owners_co = owners_co;

2042:   /* attach the supporting struct to C for reuse */
2043:   C->product->data    = ap;
2044:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2045:   ap->merge           = merge;

2047:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2049: #if defined(PETSC_USE_INFO)
2050:   if (bi[pn] != 0) {
2051:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
2052:     PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
2053:   } else {
2054:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
2055:   }
2056: #endif
2057:   PetscFunctionReturn(PETSC_SUCCESS);
2058: }

2060: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2061: {
2062:   Mat_Product *product = C->product;
2063:   Mat          A = product->A, B = product->B;
2064:   PetscReal    fill = product->fill;
2065:   PetscBool    flg;

2067:   PetscFunctionBegin;
2068:   /* scalable */
2069:   PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
2070:   if (flg) {
2071:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
2072:     goto next;
2073:   }

2075:   /* nonscalable */
2076:   PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
2077:   if (flg) {
2078:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
2079:     goto next;
2080:   }

2082:   /* matmatmult */
2083:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
2084:   if (flg) {
2085:     Mat        At;
2086:     Mat_APMPI *ptap;

2088:     PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
2089:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
2090:     ptap = (Mat_APMPI *)C->product->data;
2091:     if (ptap) {
2092:       ptap->Pt            = At;
2093:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2094:     }
2095:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2096:     goto next;
2097:   }

2099:   /* backend general code */
2100:   PetscCall(PetscStrcmp(product->alg, "backend", &flg));
2101:   if (flg) {
2102:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2103:     PetscFunctionReturn(PETSC_SUCCESS);
2104:   }

2106:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");

2108: next:
2109:   C->ops->productnumeric = MatProductNumeric_AtB;
2110:   PetscFunctionReturn(PETSC_SUCCESS);
2111: }

2113: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2114: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2115: {
2116:   Mat_Product *product = C->product;
2117:   Mat          A = product->A, B = product->B;
2118: #if defined(PETSC_HAVE_HYPRE)
2119:   const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
2120:   PetscInt    nalg        = 5;
2121: #else
2122:   const char *algTypes[4] = {
2123:     "scalable",
2124:     "nonscalable",
2125:     "seqmpi",
2126:     "backend",
2127:   };
2128:   PetscInt nalg = 4;
2129: #endif
2130:   PetscInt  alg = 1; /* set nonscalable algorithm as default */
2131:   PetscBool flg;
2132:   MPI_Comm  comm;

2134:   PetscFunctionBegin;
2135:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));

2137:   /* Set "nonscalable" as default algorithm */
2138:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2139:   if (flg) {
2140:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2142:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2143:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2144:       MatInfo   Ainfo, Binfo;
2145:       PetscInt  nz_local;
2146:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2148:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2149:       PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2150:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2152:       if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2153:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPIU_BOOL, MPI_LOR, comm));

2155:       if (alg_scalable) {
2156:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2157:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2158:         PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2159:       }
2160:     }
2161:   }

2163:   /* Get runtime option */
2164:   if (product->api_user) {
2165:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2166:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2167:     PetscOptionsEnd();
2168:   } else {
2169:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2170:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2171:     PetscOptionsEnd();
2172:   }
2173:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2175:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2176:   PetscFunctionReturn(PETSC_SUCCESS);
2177: }

2179: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2180: {
2181:   PetscFunctionBegin;
2182:   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2183:   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2184:   PetscFunctionReturn(PETSC_SUCCESS);
2185: }

2187: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2188: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2189: {
2190:   Mat_Product *product = C->product;
2191:   Mat          A = product->A, B = product->B;
2192:   const char  *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
2193:   PetscInt     nalg        = 4;
2194:   PetscInt     alg         = 1; /* set default algorithm  */
2195:   PetscBool    flg;
2196:   MPI_Comm     comm;

2198:   PetscFunctionBegin;
2199:   /* Check matrix local sizes */
2200:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2201:   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 ")",
2202:              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

2204:   /* Set default algorithm */
2205:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2206:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2208:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2209:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2210:     MatInfo   Ainfo, Binfo;
2211:     PetscInt  nz_local;
2212:     PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2214:     PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2215:     PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2216:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2218:     if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2219:     PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPIU_BOOL, MPI_LOR, comm));

2221:     if (alg_scalable) {
2222:       alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2223:       PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2224:       PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2225:     }
2226:   }

2228:   /* Get runtime option */
2229:   if (product->api_user) {
2230:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2231:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2232:     PetscOptionsEnd();
2233:   } else {
2234:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2235:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2236:     PetscOptionsEnd();
2237:   }
2238:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2240:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2241:   PetscFunctionReturn(PETSC_SUCCESS);
2242: }

2244: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2245: {
2246:   Mat_Product *product = C->product;
2247:   Mat          A = product->A, P = product->B;
2248:   MPI_Comm     comm;
2249:   PetscBool    flg;
2250:   PetscInt     alg = 1; /* set default algorithm */
2251: #if !defined(PETSC_HAVE_HYPRE)
2252:   const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
2253:   PetscInt    nalg        = 5;
2254: #else
2255:   const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
2256:   PetscInt    nalg        = 6;
2257: #endif
2258:   PetscInt pN = P->cmap->N;

2260:   PetscFunctionBegin;
2261:   /* Check matrix local sizes */
2262:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2263:   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 ")",
2264:              A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
2265:   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 ")",
2266:              A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);

2268:   /* Set "nonscalable" as default algorithm */
2269:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2270:   if (flg) {
2271:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2273:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2274:     if (pN > 100000) {
2275:       MatInfo   Ainfo, Pinfo;
2276:       PetscInt  nz_local;
2277:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2279:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2280:       PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
2281:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2283:       if (pN > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2284:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPIU_BOOL, MPI_LOR, comm));

2286:       if (alg_scalable) {
2287:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2288:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2289:       }
2290:     }
2291:   }

2293:   /* Get runtime option */
2294:   if (product->api_user) {
2295:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2296:     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2297:     PetscOptionsEnd();
2298:   } else {
2299:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2300:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2301:     PetscOptionsEnd();
2302:   }
2303:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2305:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2306:   PetscFunctionReturn(PETSC_SUCCESS);
2307: }

2309: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2310: {
2311:   Mat_Product *product = C->product;
2312:   Mat          A = product->A, R = product->B;

2314:   PetscFunctionBegin;
2315:   /* Check matrix local sizes */
2316:   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,
2317:              A->rmap->n, R->rmap->n, R->cmap->n);

2319:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2320:   PetscFunctionReturn(PETSC_SUCCESS);
2321: }

2323: /*
2324:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2325: */
2326: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2327: {
2328:   Mat_Product *product     = C->product;
2329:   PetscBool    flg         = PETSC_FALSE;
2330:   PetscInt     alg         = 1; /* default algorithm */
2331:   const char  *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
2332:   PetscInt     nalg        = 3;

2334:   PetscFunctionBegin;
2335:   /* Set default algorithm */
2336:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2337:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2339:   /* Get runtime option */
2340:   if (product->api_user) {
2341:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2342:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2343:     PetscOptionsEnd();
2344:   } else {
2345:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2346:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2347:     PetscOptionsEnd();
2348:   }
2349:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2351:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2352:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2353:   PetscFunctionReturn(PETSC_SUCCESS);
2354: }

2356: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2357: {
2358:   Mat_Product *product = C->product;

2360:   PetscFunctionBegin;
2361:   switch (product->type) {
2362:   case MATPRODUCT_AB:
2363:     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2364:     break;
2365:   case MATPRODUCT_ABt:
2366:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2367:     break;
2368:   case MATPRODUCT_AtB:
2369:     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2370:     break;
2371:   case MATPRODUCT_PtAP:
2372:     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2373:     break;
2374:   case MATPRODUCT_RARt:
2375:     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2376:     break;
2377:   case MATPRODUCT_ABC:
2378:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2379:     break;
2380:   default:
2381:     break;
2382:   }
2383:   PetscFunctionReturn(PETSC_SUCCESS);
2384: }