Actual source code: mpimatmatmult.c

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

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

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

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

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

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

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

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

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

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

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

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

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

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

118:   /* flag CPU mask for C */
119: #if 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, &dummy1));
143:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy2));
144:   PetscCall(MatSeqAIJGetArrayRead(ptap->P_loc, &dummy3));
145:   if (ptap->P_oth) PetscCall(MatSeqAIJGetArrayRead(ptap->P_oth, &dummy4));
146:   PetscCall(MatSeqAIJGetArrayWrite(c->A, &cda));
147:   PetscCall(MatSeqAIJGetArrayWrite(c->B, &coa));
148:   for (i = 0; i < cm; i++) {
149:     /* compute apa = A[i,:]*P */
150:     AProw_nonscalable(i, ad, ao, p_loc, p_oth, apa);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

330: #if defined(PETSC_USE_INFO)
331:   if (api[am]) {
332:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
333:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
334:   } else {
335:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
336:   }
337: #endif
338:   PetscFunctionReturn(PETSC_SUCCESS);
339: }

341: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat, Mat, PetscReal, Mat);
342: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat, Mat, Mat);

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

349:   PetscFunctionBegin;
350:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
351:     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);

353:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIAIJ_MPIDense;
354:   C->ops->productsymbolic = MatProductSymbolic_AB;
355:   PetscFunctionReturn(PETSC_SUCCESS);
356: }

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

363:   PetscFunctionBegin;
364:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
365:     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);

367:   C->ops->transposematmultsymbolic = MatTransposeMatMultSymbolic_MPIAIJ_MPIDense;
368:   C->ops->productsymbolic          = MatProductSymbolic_AtB;
369:   PetscFunctionReturn(PETSC_SUCCESS);
370: }

372: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIDense(Mat C)
373: {
374:   Mat_Product *product = C->product;

376:   PetscFunctionBegin;
377:   switch (product->type) {
378:   case MATPRODUCT_AB:
379:     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AB(C));
380:     break;
381:   case MATPRODUCT_AtB:
382:     PetscCall(MatProductSetFromOptions_MPIAIJ_MPIDense_AtB(C));
383:     break;
384:   default:
385:     break;
386:   }
387:   PetscFunctionReturn(PETSC_SUCCESS);
388: }

390: typedef struct {
391:   Mat           workB, workB1;
392:   MPI_Request  *rwaits, *swaits;
393:   PetscInt      nsends, nrecvs;
394:   MPI_Datatype *stype, *rtype;
395:   PetscInt      blda;
396: } MPIAIJ_MPIDense;

398: static PetscErrorCode MatMPIAIJ_MPIDenseDestroy(void **ctx)
399: {
400:   MPIAIJ_MPIDense *contents = *(MPIAIJ_MPIDense **)ctx;
401:   PetscInt         i;

403:   PetscFunctionBegin;
404:   PetscCall(MatDestroy(&contents->workB));
405:   PetscCall(MatDestroy(&contents->workB1));
406:   for (i = 0; i < contents->nsends; i++) PetscCallMPI(MPI_Type_free(&contents->stype[i]));
407:   for (i = 0; i < contents->nrecvs; i++) PetscCallMPI(MPI_Type_free(&contents->rtype[i]));
408:   PetscCall(PetscFree4(contents->stype, contents->rtype, contents->rwaits, contents->swaits));
409:   PetscCall(PetscFree(contents));
410:   PetscFunctionReturn(PETSC_SUCCESS);
411: }

413: static PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIDense(Mat A, Mat B, PetscReal fill, Mat C)
414: {
415:   Mat_MPIAIJ      *aij = (Mat_MPIAIJ *)A->data;
416:   PetscInt         nz  = aij->B->cmap->n, blda, m, M, n, N;
417:   MPIAIJ_MPIDense *contents;
418:   VecScatter       ctx = aij->Mvctx;
419:   PetscInt         Am = A->rmap->n, Bm = B->rmap->n, BN = B->cmap->N, Bbn, Bbn1, bs, numBb;
420:   MPI_Comm         comm;
421:   MPI_Datatype     type1, *stype, *rtype;
422:   const PetscInt  *sindices, *sstarts, *rstarts;
423:   PetscMPIInt     *disp, nsends, nrecvs, nrows_to, nrows_from;
424:   PetscBool        cisdense;

426:   PetscFunctionBegin;
427:   MatCheckProduct(C, 4);
428:   PetscCheck(!C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
429:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
430:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)C, MATMPIDENSE, &cisdense));
431:   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)B)->type_name));
432:   PetscCall(MatGetLocalSize(C, &m, &n));
433:   PetscCall(MatGetSize(C, &M, &N));
434:   if (m == PETSC_DECIDE || n == PETSC_DECIDE || M == PETSC_DECIDE || N == PETSC_DECIDE) PetscCall(MatSetSizes(C, Am, B->cmap->n, A->rmap->N, BN));
435:   PetscCall(MatSetBlockSizesFromMats(C, A, B));
436:   PetscCall(MatSetUp(C));
437:   PetscCall(MatDenseGetLDA(B, &blda));
438:   PetscCall(PetscNew(&contents));

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

443:   /* Create column block of B and C for memory scalability when BN is too large */
444:   /* Estimate Bbn, column size of Bb */
445:   if (nz) {
446:     Bbn1 = 2 * Am * BN / nz;
447:     if (!Bbn1) Bbn1 = 1;
448:   } else Bbn1 = BN;

450:   bs   = B->cmap->bs;
451:   Bbn1 = Bbn1 / bs * bs; /* Bbn1 is a multiple of bs */
452:   if (Bbn1 > BN) Bbn1 = BN;
453:   PetscCallMPI(MPIU_Allreduce(&Bbn1, &Bbn, 1, MPIU_INT, MPI_MAX, comm));

455:   /* Enable runtime option for Bbn */
456:   PetscOptionsBegin(comm, ((PetscObject)C)->prefix, "MatMatMult", "Mat");
457:   PetscCall(PetscOptionsInt("-matmatmult_Bbn", "Number of columns in Bb", "MatMatMult", Bbn, &Bbn, NULL));
458:   PetscOptionsEnd();
459:   Bbn = PetscMin(Bbn, BN);

461:   if (Bbn > 0 && Bbn < BN) {
462:     numBb = BN / Bbn;
463:     Bbn1  = BN - numBb * Bbn;
464:   } else numBb = 0;

466:   if (numBb) {
467:     PetscCall(PetscInfo(C, "use Bb, BN=%" PetscInt_FMT ", Bbn=%" PetscInt_FMT "; numBb=%" PetscInt_FMT "\n", BN, Bbn, numBb));
468:     if (Bbn1) { /* Create workB1 for the remaining columns */
469:       PetscCall(PetscInfo(C, "use Bb1, BN=%" PetscInt_FMT ", Bbn1=%" PetscInt_FMT "\n", BN, Bbn1));
470:       /* Create work matrix used to store off processor rows of B needed for local product */
471:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nz, Bbn1, NULL, &contents->workB1));
472:     } else contents->workB1 = NULL;
473:   }

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

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

483:   contents->rtype  = rtype;
484:   contents->nrecvs = nrecvs;
485:   contents->blda   = blda;

487:   PetscCall(PetscMalloc1(Bm + 1, &disp));
488:   for (PetscMPIInt i = 0; i < nsends; i++) {
489:     PetscCall(PetscMPIIntCast(sstarts[i + 1] - sstarts[i], &nrows_to));
490:     for (PetscInt j = 0; j < nrows_to; j++) PetscCall(PetscMPIIntCast(sindices[sstarts[i] + j], &disp[j])); /* rowB to be sent */
491:     PetscCallMPI(MPI_Type_create_indexed_block(nrows_to, 1, disp, MPIU_SCALAR, &type1));
492:     PetscCallMPI(MPI_Type_create_resized(type1, 0, blda * sizeof(PetscScalar), &stype[i]));
493:     PetscCallMPI(MPI_Type_commit(&stype[i]));
494:     PetscCallMPI(MPI_Type_free(&type1));
495:   }

497:   for (PetscMPIInt i = 0; i < nrecvs; i++) {
498:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
499:     PetscCall(PetscMPIIntCast(rstarts[i + 1] - rstarts[i], &nrows_from));
500:     disp[0] = 0;
501:     PetscCallMPI(MPI_Type_create_indexed_block(1, nrows_from, disp, MPIU_SCALAR, &type1));
502:     PetscCallMPI(MPI_Type_create_resized(type1, 0, nz * sizeof(PetscScalar), &rtype[i]));
503:     PetscCallMPI(MPI_Type_commit(&rtype[i]));
504:     PetscCallMPI(MPI_Type_free(&type1));
505:   }

507:   PetscCall(PetscFree(disp));
508:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, NULL, NULL));
509:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, NULL, NULL));
510:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
511:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
512:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

514:   C->product->data       = contents;
515:   C->product->destroy    = MatMPIAIJ_MPIDenseDestroy;
516:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
517:   PetscFunctionReturn(PETSC_SUCCESS);
518: }

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

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

526:     Input: If Bbidx = 0, uses B = Bb, else B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
527: */

529: static PetscErrorCode MatMPIDenseScatter(Mat A, Mat B, PetscInt Bbidx, Mat C, Mat *outworkB)
530: {
531:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)A->data;
532:   const PetscScalar *b;
533:   PetscScalar       *rvalues;
534:   VecScatter         ctx = aij->Mvctx;
535:   const PetscInt    *sindices, *sstarts, *rstarts;
536:   const PetscMPIInt *sprocs, *rprocs;
537:   PetscMPIInt        nsends, nrecvs;
538:   MPI_Request       *swaits, *rwaits;
539:   MPI_Comm           comm;
540:   PetscMPIInt        tag = ((PetscObject)ctx)->tag, ncols, nrows, nsends_mpi, nrecvs_mpi;
541:   MPIAIJ_MPIDense   *contents;
542:   Mat                workB;
543:   MPI_Datatype      *stype, *rtype;
544:   PetscInt           blda;

546:   PetscFunctionBegin;
547:   MatCheckProduct(C, 4);
548:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
549:   PetscCall(PetscMPIIntCast(B->cmap->N, &ncols));
550:   PetscCall(PetscMPIIntCast(aij->B->cmap->n, &nrows));
551:   contents = (MPIAIJ_MPIDense *)C->product->data;
552:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL /*bs*/));
553:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL /*bs*/));
554:   PetscCall(PetscMPIIntCast(nsends, &nsends_mpi));
555:   PetscCall(PetscMPIIntCast(nrecvs, &nrecvs_mpi));
556:   if (Bbidx == 0) workB = *outworkB = contents->workB;
557:   else workB = *outworkB = contents->workB1;
558:   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);
559:   swaits = contents->swaits;
560:   rwaits = contents->rwaits;

562:   PetscCall(MatDenseGetArrayRead(B, &b));
563:   PetscCall(MatDenseGetLDA(B, &blda));
564:   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);
565:   PetscCall(MatDenseGetArray(workB, &rvalues));

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

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

575:   if (nrecvs) PetscCallMPI(MPI_Waitall(nrecvs_mpi, rwaits, MPI_STATUSES_IGNORE));
576:   if (nsends) PetscCallMPI(MPI_Waitall(nsends_mpi, swaits, MPI_STATUSES_IGNORE));

578:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL));
579:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL));
580:   PetscCall(MatDenseRestoreArrayRead(B, &b));
581:   PetscCall(MatDenseRestoreArray(workB, &rvalues));
582:   PetscFunctionReturn(PETSC_SUCCESS);
583: }

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

593:   PetscFunctionBegin;
594:   MatCheckProduct(C, 3);
595:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
596:   contents = (MPIAIJ_MPIDense *)C->product->data;
597:   /* diagonal block of A times all local rows of B */
598:   /* TODO: this calls a symbolic multiplication every time, which could be avoided */
599:   PetscCall(MatMatMult(aij->A, bdense->A, MAT_REUSE_MATRIX, PETSC_CURRENT, &cdense->A));
600:   if (contents->workB->cmap->n == B->cmap->N) {
601:     /* get off processor parts of B needed to complete C=A*B */
602:     PetscCall(MatMPIDenseScatter(A, B, 0, C, &workB));

604:     /* off-diagonal block of A times nonlocal rows of B */
605:     PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
606:   } else {
607:     Mat       Bb, Cb;
608:     PetscInt  BN = B->cmap->N, n = contents->workB->cmap->n;
609:     PetscBool ccpu;

611:     PetscCheck(n > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Column block size %" PetscInt_FMT " must be positive", n);
612:     /* Prevent from unneeded copies back and forth from the GPU
613:        when getting and restoring the submatrix
614:        We need a proper GPU code for AIJ * dense in parallel */
615:     PetscCall(MatBoundToCPU(C, &ccpu));
616:     PetscCall(MatBindToCPU(C, PETSC_TRUE));
617:     for (PetscInt i = 0; i < BN; i += n) {
618:       PetscCall(MatDenseGetSubMatrix(B, PETSC_DECIDE, PETSC_DECIDE, i, PetscMin(i + n, BN), &Bb));
619:       PetscCall(MatDenseGetSubMatrix(C, PETSC_DECIDE, PETSC_DECIDE, i, PetscMin(i + n, BN), &Cb));

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

624:       /* off-diagonal block of A times nonlocal rows of B */
625:       cdense = (Mat_MPIDense *)Cb->data;
626:       PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
627:       PetscCall(MatDenseRestoreSubMatrix(B, &Bb));
628:       PetscCall(MatDenseRestoreSubMatrix(C, &Cb));
629:     }
630:     PetscCall(MatBindToCPU(C, ccpu));
631:   }
632:   PetscFunctionReturn(PETSC_SUCCESS);
633: }

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

655:   PetscFunctionBegin;
656:   MatCheckProduct(C, 3);
657:   ptap = (MatProductCtx_APMPI *)C->product->data;
658:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
659:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
660:   PetscCallMPI(MPI_Comm_size(comm, &size));
661:   PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");

663:   /* flag CPU mask for C */
664: #if defined(PETSC_HAVE_DEVICE)
665:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
666:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
667:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
668: #endif
669:   apa_sparse = ptap->apa;

671:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
672:   /* update numerical values of P_oth and P_loc */
673:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_REUSE_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
674:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_REUSE_MATRIX, &ptap->P_loc));

676:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
677:   /* get data from symbolic products */
678:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
679:   pi_loc = p_loc->i;
680:   pj_loc = p_loc->j;
681:   pa_loc = p_loc->a;
682:   if (size > 1) {
683:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
684:     pi_oth = p_oth->i;
685:     pj_oth = p_oth->j;
686:     pa_oth = p_oth->a;
687:   } else {
688:     p_oth  = NULL;
689:     pi_oth = NULL;
690:     pj_oth = NULL;
691:     pa_oth = NULL;
692:   }

694:   /* trigger copy to CPU */
695:   PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy));
696:   PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy));
697:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy));
698:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy));
699:   api = ptap->api;
700:   apj = ptap->apj;
701:   for (i = 0; i < cm; i++) {
702:     apJ = apj + api[i];

704:     /* diagonal portion of A */
705:     anz = adi[i + 1] - adi[i];
706:     adj = ad->j + adi[i];
707:     ada = ad->a + adi[i];
708:     for (j = 0; j < anz; j++) {
709:       row = adj[j];
710:       pnz = pi_loc[row + 1] - pi_loc[row];
711:       pj  = pj_loc + pi_loc[row];
712:       pa  = pa_loc + pi_loc[row];
713:       /* perform sparse axpy */
714:       valtmp = ada[j];
715:       nextp  = 0;
716:       for (k = 0; nextp < pnz; k++) {
717:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
718:           apa_sparse[k] += valtmp * pa[nextp++];
719:         }
720:       }
721:       PetscCall(PetscLogFlops(2.0 * pnz));
722:     }

724:     /* off-diagonal portion of A */
725:     anz = aoi[i + 1] - aoi[i];
726:     aoj = PetscSafePointerPlusOffset(ao->j, aoi[i]);
727:     aoa = PetscSafePointerPlusOffset(ao->a, aoi[i]);
728:     for (j = 0; j < anz; j++) {
729:       row = aoj[j];
730:       pnz = pi_oth[row + 1] - pi_oth[row];
731:       pj  = pj_oth + pi_oth[row];
732:       pa  = pa_oth + pi_oth[row];
733:       /* perform sparse axpy */
734:       valtmp = aoa[j];
735:       nextp  = 0;
736:       for (k = 0; nextp < pnz; k++) {
737:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
738:           apa_sparse[k] += valtmp * pa[nextp++];
739:         }
740:       }
741:       PetscCall(PetscLogFlops(2.0 * pnz));
742:     }

744:     /* set values in C */
745:     cdnz = cd->i[i + 1] - cd->i[i];
746:     conz = co->i[i + 1] - co->i[i];

748:     /* 1st off-diagonal part of C */
749:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
750:     k  = 0;
751:     for (k0 = 0; k0 < conz; k0++) {
752:       if (apJ[k] >= cstart) break;
753:       ca[k0]        = apa_sparse[k];
754:       apa_sparse[k] = 0.0;
755:       k++;
756:     }

758:     /* diagonal part of C */
759:     ca = cda + cd->i[i];
760:     for (k1 = 0; k1 < cdnz; k1++) {
761:       ca[k1]        = apa_sparse[k];
762:       apa_sparse[k] = 0.0;
763:       k++;
764:     }

766:     /* 2nd off-diagonal part of C */
767:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
768:     for (; k0 < conz; k0++) {
769:       ca[k0]        = apa_sparse[k];
770:       apa_sparse[k] = 0.0;
771:       k++;
772:     }
773:   }
774:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
775:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
776:   PetscFunctionReturn(PETSC_SUCCESS);
777: }

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

795:   PetscFunctionBegin;
796:   MatCheckProduct(C, 4);
797:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
798:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
799:   PetscCallMPI(MPI_Comm_size(comm, &size));

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

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

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

810:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
811:   pi_loc = p_loc->i;
812:   pj_loc = p_loc->j;
813:   if (size > 1) {
814:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
815:     pi_oth = p_oth->i;
816:     pj_oth = p_oth->j;
817:   } else {
818:     p_oth  = NULL;
819:     pi_oth = NULL;
820:     pj_oth = NULL;
821:   }

823:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
824:   PetscCall(PetscMalloc1(am + 1, &api));
825:   ptap->api = api;
826:   api[0]    = 0;

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

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

870:     /* add missing diagonal entry */
871:     if (C->force_diagonals) {
872:       j = i + rstart; /* column index */
873:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &j, lnk));
874:     }

876:     apnz       = *lnk;
877:     api[i + 1] = api[i] + apnz;
878:     if (apnz > apnz_max) apnz_max = apnz;

880:     /* if free space is not available, double the total space in the list */
881:     if (current_space->local_remaining < apnz) {
882:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), &current_space));
883:       nspacedouble++;
884:     }

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

890:     current_space->array += apnz;
891:     current_space->local_used += apnz;
892:     current_space->local_remaining -= apnz;
893:   }

895:   /* Allocate space for apj, initialize apj, and */
896:   /* destroy list of free space and other temporary array(s) */
897:   PetscCall(PetscMalloc1(api[am], &ptap->apj));
898:   apj = ptap->apj;
899:   PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
900:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));

902:   /* create and assemble symbolic parallel matrix C */
903:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
904:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
905:   PetscCall(MatGetType(A, &mtype));
906:   PetscCall(MatSetType(C, mtype));
907:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
908:   MatPreallocateEnd(dnz, onz);

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

913:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
914:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
915:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
916:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
917:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

919:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
920:   C->ops->productnumeric = MatProductNumeric_AB;

922:   /* attach the supporting struct to C for reuse */
923:   C->product->data    = ptap;
924:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

926:   /* set MatInfo */
927:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
928:   if (afill < 1.0) afill = 1.0;
929:   C->info.mallocs           = nspacedouble;
930:   C->info.fill_ratio_given  = fill;
931:   C->info.fill_ratio_needed = afill;

933: #if defined(PETSC_USE_INFO)
934:   if (api[am]) {
935:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
936:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
937:   } else {
938:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
939:   }
940: #endif
941:   PetscFunctionReturn(PETSC_SUCCESS);
942: }

944: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
945: /* Three input arrays are merged to one output array. The size of the    */
946: /* output array is also output. Duplicate entries only show up once.     */
947: static void Merge3SortedArrays(PetscInt size1, PetscInt *in1, PetscInt size2, PetscInt *in2, PetscInt size3, PetscInt *in3, PetscInt *size4, PetscInt *out)
948: {
949:   int i = 0, j = 0, k = 0, l = 0;

951:   /* Traverse all three arrays */
952:   while (i < size1 && j < size2 && k < size3) {
953:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
954:       out[l++] = in1[i++];
955:     } else if (in2[j] < in1[i] && in2[j] < in3[k]) {
956:       out[l++] = in2[j++];
957:     } else if (in3[k] < in1[i] && in3[k] < in2[j]) {
958:       out[l++] = in3[k++];
959:     } else if (in1[i] == in2[j] && in1[i] < in3[k]) {
960:       out[l++] = in1[i];
961:       i++, j++;
962:     } else if (in1[i] == in3[k] && in1[i] < in2[j]) {
963:       out[l++] = in1[i];
964:       i++, k++;
965:     } else if (in3[k] == in2[j] && in2[j] < in1[i]) {
966:       out[l++] = in2[j];
967:       k++, j++;
968:     } else if (in1[i] == in2[j] && in1[i] == in3[k]) {
969:       out[l++] = in1[i];
970:       i++, j++, k++;
971:     }
972:   }

974:   /* Traverse two remaining arrays */
975:   while (i < size1 && j < size2) {
976:     if (in1[i] < in2[j]) {
977:       out[l++] = in1[i++];
978:     } else if (in1[i] > in2[j]) {
979:       out[l++] = in2[j++];
980:     } else {
981:       out[l++] = in1[i];
982:       i++, j++;
983:     }
984:   }

986:   while (i < size1 && k < size3) {
987:     if (in1[i] < in3[k]) {
988:       out[l++] = in1[i++];
989:     } else if (in1[i] > in3[k]) {
990:       out[l++] = in3[k++];
991:     } else {
992:       out[l++] = in1[i];
993:       i++, k++;
994:     }
995:   }

997:   while (k < size3 && j < size2) {
998:     if (in3[k] < in2[j]) {
999:       out[l++] = in3[k++];
1000:     } else if (in3[k] > in2[j]) {
1001:       out[l++] = in2[j++];
1002:     } else {
1003:       out[l++] = in3[k];
1004:       k++, j++;
1005:     }
1006:   }

1008:   /* Traverse one remaining array */
1009:   while (i < size1) out[l++] = in1[i++];
1010:   while (j < size2) out[l++] = in2[j++];
1011:   while (k < size3) out[l++] = in3[k++];

1013:   *size4 = l;
1014: }

1016: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1017: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1018: /* matrix-matrix multiplications.  */
1019: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1020: {
1021:   MPI_Comm             comm;
1022:   PetscMPIInt          size;
1023:   MatProductCtx_APMPI *ptap;
1024:   PetscFreeSpaceList   free_space_diag = NULL, current_space = NULL;
1025:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
1026:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
1027:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
1028:   Mat_SeqAIJ          *adpd_seq, *p_off, *aopoth_seq;
1029:   PetscInt             adponz, adpdnz;
1030:   PetscInt            *pi_loc, *dnz, *onz;
1031:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
1032:   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;
1033:   PetscInt             am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
1034:   PetscBT              lnkbt;
1035:   PetscReal            afill;
1036:   PetscMPIInt          rank;
1037:   Mat                  adpd, aopoth;
1038:   MatType              mtype;
1039:   const char          *prefix;

1041:   PetscFunctionBegin;
1042:   MatCheckProduct(C, 4);
1043:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1044:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1045:   PetscCallMPI(MPI_Comm_size(comm, &size));
1046:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1047:   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));

1049:   /* create struct MatProductCtx_APMPI and attached it to C later */
1050:   PetscCall(PetscNew(&ptap));

1052:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1053:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));

1055:   /* get P_loc by taking all local rows of P */
1056:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));

1058:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
1059:   pi_loc = p_loc->i;

1061:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1062:   PetscCall(PetscMalloc1(am + 1, &api));
1063:   PetscCall(PetscMalloc1(am + 1, &adpoi));

1065:   adpoi[0]  = 0;
1066:   ptap->api = api;
1067:   api[0]    = 0;

1069:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1070:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
1071:   MatPreallocateBegin(comm, am, pn, dnz, onz);

1073:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1074:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1075:   PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
1076:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1077:   PetscCall(MatSetOptionsPrefix(adpd, prefix));
1078:   PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));

1080:   PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
1081:   PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
1082:   PetscCall(MatProductSetFill(adpd, fill));
1083:   PetscCall(MatProductSetFromOptions(adpd));

1085:   adpd->force_diagonals = C->force_diagonals;
1086:   PetscCall(MatProductSymbolic(adpd));

1088:   adpd_seq = (Mat_SeqAIJ *)((adpd)->data);
1089:   adpdi    = adpd_seq->i;
1090:   adpdj    = adpd_seq->j;
1091:   p_off    = (Mat_SeqAIJ *)p->B->data;
1092:   poff_i   = p_off->i;
1093:   poff_j   = p_off->j;

1095:   /* j_temp stores indices of a result row before they are added to the linked list */
1096:   PetscCall(PetscMalloc1(pN, &j_temp));

1098:   /* Symbolic calc of the A_diag * p_loc_off */
1099:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1100:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
1101:   current_space = free_space_diag;

1103:   for (i = 0; i < am; i++) {
1104:     /* A_diag * P_loc_off */
1105:     nzi = adi[i + 1] - adi[i];
1106:     for (j = 0; j < nzi; j++) {
1107:       row  = *adj++;
1108:       pnz  = poff_i[row + 1] - poff_i[row];
1109:       Jptr = poff_j + poff_i[row];
1110:       for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
1111:       /* add non-zero cols of P into the sorted linked list lnk */
1112:       PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
1113:     }

1115:     adponz       = lnk[0];
1116:     adpoi[i + 1] = adpoi[i] + adponz;

1118:     /* if free space is not available, double the total space in the list */
1119:     if (current_space->local_remaining < adponz) {
1120:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), &current_space));
1121:       nspacedouble++;
1122:     }

1124:     /* Copy data into free space, then initialize lnk */
1125:     PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));

1127:     current_space->array += adponz;
1128:     current_space->local_used += adponz;
1129:     current_space->local_remaining -= adponz;
1130:   }

1132:   /* Symbolic calc of A_off * P_oth */
1133:   PetscCall(MatSetOptionsPrefix(a->B, prefix));
1134:   PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
1135:   PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
1136:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1137:   aopoth_seq = (Mat_SeqAIJ *)((aopoth)->data);
1138:   aopothi    = aopoth_seq->i;
1139:   aopothj    = aopoth_seq->j;

1141:   /* Allocate space for apj, adpj, aopj, ... */
1142:   /* destroy lists of free space and other temporary array(s) */

1144:   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am], &ptap->apj));
1145:   PetscCall(PetscMalloc1(adpoi[am], &adpoj));

1147:   /* Copy from linked list to j-array */
1148:   PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
1149:   PetscCall(PetscLLDestroy(lnk, lnkbt));

1151:   adpoJ = adpoj;
1152:   adpdJ = adpdj;
1153:   aopJ  = aopothj;
1154:   apj   = ptap->apj;
1155:   apJ   = apj; /* still empty */

1157:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1158:   /* A_diag * P_loc_diag to get A*P */
1159:   for (i = 0; i < am; i++) {
1160:     aopnz  = aopothi[i + 1] - aopothi[i];
1161:     adponz = adpoi[i + 1] - adpoi[i];
1162:     adpdnz = adpdi[i + 1] - adpdi[i];

1164:     /* Correct indices from A_diag*P_diag */
1165:     for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
1166:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1167:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1168:     PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));

1170:     aopJ += aopnz;
1171:     adpoJ += adponz;
1172:     adpdJ += adpdnz;
1173:     apJ += apnz;
1174:     api[i + 1] = api[i] + apnz;
1175:   }

1177:   /* malloc apa to store dense row A[i,:]*P */
1178:   PetscCall(PetscCalloc1(pN, &ptap->apa));

1180:   /* create and assemble symbolic parallel matrix C */
1181:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1182:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
1183:   PetscCall(MatGetType(A, &mtype));
1184:   PetscCall(MatSetType(C, mtype));
1185:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1186:   MatPreallocateEnd(dnz, onz);

1188:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1189:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
1190:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1191:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1192:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1194:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1195:   C->ops->productnumeric = MatProductNumeric_AB;

1197:   /* attach the supporting struct to C for reuse */
1198:   C->product->data    = ptap;
1199:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

1201:   /* set MatInfo */
1202:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1203:   if (afill < 1.0) afill = 1.0;
1204:   C->info.mallocs           = nspacedouble;
1205:   C->info.fill_ratio_given  = fill;
1206:   C->info.fill_ratio_needed = afill;

1208: #if defined(PETSC_USE_INFO)
1209:   if (api[am]) {
1210:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1211:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1212:   } else {
1213:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1214:   }
1215: #endif

1217:   PetscCall(MatDestroy(&aopoth));
1218:   PetscCall(MatDestroy(&adpd));
1219:   PetscCall(PetscFree(j_temp));
1220:   PetscCall(PetscFree(adpoj));
1221:   PetscCall(PetscFree(adpoi));
1222:   PetscFunctionReturn(PETSC_SUCCESS);
1223: }

1225: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1226: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
1227: {
1228:   MatProductCtx_APMPI *ptap;
1229:   Mat                  Pt;

1231:   PetscFunctionBegin;
1232:   MatCheckProduct(C, 3);
1233:   ptap = (MatProductCtx_APMPI *)C->product->data;
1234:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1235:   PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");

1237:   Pt = ptap->Pt;
1238:   PetscCall(MatTransposeSetPrecursor(P, Pt));
1239:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
1240:   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
1241:   PetscFunctionReturn(PETSC_SUCCESS);
1242: }

1244: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1245: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, PetscReal fill, Mat C)
1246: {
1247:   MatProductCtx_APMPI     *ptap;
1248:   Mat_MPIAIJ              *p = (Mat_MPIAIJ *)P->data;
1249:   MPI_Comm                 comm;
1250:   PetscMPIInt              size, rank;
1251:   PetscFreeSpaceList       free_space = NULL, current_space = NULL;
1252:   PetscInt                 pn = P->cmap->n, aN = A->cmap->N, an = A->cmap->n;
1253:   PetscInt                *lnk, i, k, rstart;
1254:   PetscBT                  lnkbt;
1255:   PetscMPIInt              tagi, tagj, *len_si, *len_s, *len_ri, nrecv, proc, nsend;
1256:   PETSC_UNUSED PetscMPIInt icompleted = 0;
1257:   PetscInt               **buf_rj, **buf_ri, **buf_ri_k, row, ncols, *cols;
1258:   PetscInt                 len, *dnz, *onz, *owners, nzi;
1259:   PetscInt                 nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1260:   MPI_Request             *swaits, *rwaits;
1261:   MPI_Status              *sstatus, rstatus;
1262:   PetscLayout              rowmap;
1263:   PetscInt                *owners_co, *coi, *coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1264:   PetscMPIInt             *len_r, *id_r;          /* array of length of comm->size, store send/recv matrix values */
1265:   PetscInt                *Jptr, *prmap = p->garray, con, j, Crmax;
1266:   Mat_SeqAIJ              *a_loc, *c_loc, *c_oth;
1267:   PetscHMapI               ta;
1268:   MatType                  mtype;
1269:   const char              *prefix;

1271:   PetscFunctionBegin;
1272:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1273:   PetscCallMPI(MPI_Comm_size(comm, &size));
1274:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1276:   /* create symbolic parallel matrix C */
1277:   PetscCall(MatGetType(A, &mtype));
1278:   PetscCall(MatSetType(C, mtype));

1280:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1282:   /* create struct MatProductCtx_APMPI and attached it to C later */
1283:   PetscCall(PetscNew(&ptap));

1285:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1286:   PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
1287:   PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));

1289:   /* (1) compute symbolic A_loc */
1290:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));

1292:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1293:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1294:   PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
1295:   PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
1296:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
1297:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));

1299:   /* (3) send coj of C_oth to other processors  */
1300:   /* determine row ownership */
1301:   PetscCall(PetscLayoutCreate(comm, &rowmap));
1302:   rowmap->n  = pn;
1303:   rowmap->bs = 1;
1304:   PetscCall(PetscLayoutSetUp(rowmap));
1305:   owners = rowmap->range;

1307:   /* determine the number of messages to send, their lengths */
1308:   PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 1, &owners_co));
1309:   PetscCall(PetscArrayzero(len_s, size));
1310:   PetscCall(PetscArrayzero(len_si, size));

1312:   c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
1313:   coi   = c_oth->i;
1314:   coj   = c_oth->j;
1315:   con   = ptap->C_oth->rmap->n;
1316:   proc  = 0;
1317:   for (i = 0; i < con; i++) {
1318:     while (prmap[i] >= owners[proc + 1]) proc++;
1319:     len_si[proc]++;                     /* num of rows in Co(=Pt*A) to be sent to [proc] */
1320:     len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1321:   }

1323:   len          = 0; /* max length of buf_si[], see (4) */
1324:   owners_co[0] = 0;
1325:   nsend        = 0;
1326:   for (proc = 0; proc < size; proc++) {
1327:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1328:     if (len_s[proc]) {
1329:       nsend++;
1330:       len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1331:       len += len_si[proc];
1332:     }
1333:   }

1335:   /* determine the number and length of messages to receive for coi and coj  */
1336:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
1337:   PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));

1339:   /* post the Irecv and Isend of coj */
1340:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1341:   PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
1342:   PetscCall(PetscMalloc1(nsend, &swaits));
1343:   for (proc = 0, k = 0; proc < size; proc++) {
1344:     if (!len_s[proc]) continue;
1345:     i = owners_co[proc];
1346:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1347:     k++;
1348:   }

1350:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1351:   PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
1352:   PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
1353:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
1354:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
1355:   c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;

1357:   /* receives coj are complete */
1358:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1359:   PetscCall(PetscFree(rwaits));
1360:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1362:   /* add received column indices into ta to update Crmax */
1363:   a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;

1365:   /* create and initialize a linked list */
1366:   PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
1367:   MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);

1369:   for (k = 0; k < nrecv; k++) { /* k-th received message */
1370:     Jptr = buf_rj[k];
1371:     for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1372:   }
1373:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
1374:   PetscCall(PetscHMapIDestroy(&ta));

1376:   /* (4) send and recv coi */
1377:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1378:   PetscCall(PetscPostIrecvInt(comm, tagi, nrecv, id_r, len_ri, &buf_ri, &rwaits));
1379:   PetscCall(PetscMalloc1(len, &buf_s));
1380:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1381:   for (proc = 0, k = 0; proc < size; proc++) {
1382:     if (!len_s[proc]) continue;
1383:     /* form outgoing message for i-structure:
1384:          buf_si[0]:                 nrows to be sent
1385:                [1:nrows]:           row index (global)
1386:                [nrows+1:2*nrows+1]: i-structure index
1387:     */
1388:     nrows       = len_si[proc] / 2 - 1; /* num of rows in Co to be sent to [proc] */
1389:     buf_si_i    = buf_si + nrows + 1;
1390:     buf_si[0]   = nrows;
1391:     buf_si_i[0] = 0;
1392:     nrows       = 0;
1393:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1394:       nzi                 = coi[i + 1] - coi[i];
1395:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1396:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1397:       nrows++;
1398:     }
1399:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1400:     k++;
1401:     buf_si += len_si[proc];
1402:   }
1403:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1404:   PetscCall(PetscFree(rwaits));
1405:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1407:   PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
1408:   PetscCall(PetscFree(len_ri));
1409:   PetscCall(PetscFree(swaits));
1410:   PetscCall(PetscFree(buf_s));

1412:   /* (5) compute the local portion of C      */
1413:   /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
1414:   PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
1415:   current_space = free_space;

1417:   PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
1418:   for (k = 0; k < nrecv; k++) {
1419:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1420:     nrows       = *buf_ri_k[k];
1421:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1422:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1423:   }

1425:   MatPreallocateBegin(comm, pn, an, dnz, onz);
1426:   PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
1427:   for (i = 0; i < pn; i++) { /* for each local row of C */
1428:     /* add C_loc into C */
1429:     nzi  = c_loc->i[i + 1] - c_loc->i[i];
1430:     Jptr = c_loc->j + c_loc->i[i];
1431:     PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));

1433:     /* add received col data into lnk */
1434:     for (k = 0; k < nrecv; k++) { /* k-th received message */
1435:       if (i == *nextrow[k]) {     /* i-th row */
1436:         nzi  = *(nextci[k] + 1) - *nextci[k];
1437:         Jptr = buf_rj[k] + *nextci[k];
1438:         PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1439:         nextrow[k]++;
1440:         nextci[k]++;
1441:       }
1442:     }

1444:     /* add missing diagonal entry */
1445:     if (C->force_diagonals) {
1446:       k = i + owners[rank]; /* column index */
1447:       PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
1448:     }

1450:     nzi = lnk[0];

1452:     /* copy data into free space, then initialize lnk */
1453:     PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
1454:     PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
1455:   }
1456:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1457:   PetscCall(PetscLLDestroy(lnk, lnkbt));
1458:   PetscCall(PetscFreeSpaceDestroy(free_space));

1460:   /* local sizes and preallocation */
1461:   PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
1462:   PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
1463:   PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
1464:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1465:   MatPreallocateEnd(dnz, onz);

1467:   /* add C_loc and C_oth to C */
1468:   PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
1469:   for (i = 0; i < pn; i++) {
1470:     ncols = c_loc->i[i + 1] - c_loc->i[i];
1471:     cols  = c_loc->j + c_loc->i[i];
1472:     row   = rstart + i;
1473:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));

1475:     if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
1476:   }
1477:   for (i = 0; i < con; i++) {
1478:     ncols = c_oth->i[i + 1] - c_oth->i[i];
1479:     cols  = c_oth->j + c_oth->i[i];
1480:     row   = prmap[i];
1481:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1482:   }
1483:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1484:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1485:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1487:   /* members in merge */
1488:   PetscCall(PetscFree(id_r));
1489:   PetscCall(PetscFree(len_r));
1490:   PetscCall(PetscFree(buf_ri[0]));
1491:   PetscCall(PetscFree(buf_ri));
1492:   PetscCall(PetscFree(buf_rj[0]));
1493:   PetscCall(PetscFree(buf_rj));
1494:   PetscCall(PetscLayoutDestroy(&rowmap));

1496:   /* attach the supporting struct to C for reuse */
1497:   C->product->data    = ptap;
1498:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
1499:   PetscFunctionReturn(PETSC_SUCCESS);
1500: }

1502: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
1503: {
1504:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
1505:   Mat_SeqAIJ          *c_seq;
1506:   MatProductCtx_APMPI *ptap;
1507:   Mat                  A_loc, C_loc, C_oth;
1508:   PetscInt             i, rstart, rend, cm, ncols, row;
1509:   const PetscInt      *cols;
1510:   const PetscScalar   *vals;

1512:   PetscFunctionBegin;
1513:   MatCheckProduct(C, 3);
1514:   ptap = (MatProductCtx_APMPI *)C->product->data;
1515:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1516:   PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1517:   PetscCall(MatZeroEntries(C));

1519:   /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1520:   /* 1) get R = Pd^T, Ro = Po^T */
1521:   PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
1522:   PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
1523:   PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
1524:   PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));

1526:   /* 2) compute numeric A_loc */
1527:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));

1529:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1530:   A_loc = ptap->A_loc;
1531:   PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
1532:   PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
1533:   C_loc = ptap->C_loc;
1534:   C_oth = ptap->C_oth;

1536:   /* add C_loc and C_oth to C */
1537:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));

1539:   /* C_loc -> C */
1540:   cm    = C_loc->rmap->N;
1541:   c_seq = (Mat_SeqAIJ *)C_loc->data;
1542:   cols  = c_seq->j;
1543:   vals  = c_seq->a;
1544:   for (i = 0; i < cm; i++) {
1545:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1546:     row   = rstart + i;
1547:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1548:     cols += ncols;
1549:     vals += ncols;
1550:   }

1552:   /* Co -> C, off-processor part */
1553:   cm    = C_oth->rmap->N;
1554:   c_seq = (Mat_SeqAIJ *)C_oth->data;
1555:   cols  = c_seq->j;
1556:   vals  = c_seq->a;
1557:   for (i = 0; i < cm; i++) {
1558:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1559:     row   = p->garray[i];
1560:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1561:     cols += ncols;
1562:     vals += ncols;
1563:   }
1564:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1565:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1566:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1567:   PetscFunctionReturn(PETSC_SUCCESS);
1568: }

1570: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
1571: {
1572:   MatMergeSeqsToMPI   *merge;
1573:   Mat_MPIAIJ          *p  = (Mat_MPIAIJ *)P->data;
1574:   Mat_SeqAIJ          *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
1575:   MatProductCtx_APMPI *ap;
1576:   PetscInt            *adj;
1577:   PetscInt             i, j, k, anz, pnz, row, *cj, nexta;
1578:   MatScalar           *ada, *ca, valtmp;
1579:   PetscInt             am = A->rmap->n, cm = C->rmap->n, pon = (p->B)->cmap->n;
1580:   MPI_Comm             comm;
1581:   PetscMPIInt          size, rank, taga, *len_s, proc;
1582:   PetscInt            *owners, nrows, **buf_ri_k, **nextrow, **nextci;
1583:   PetscInt           **buf_ri, **buf_rj;
1584:   PetscInt             cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1585:   MPI_Request         *s_waits, *r_waits;
1586:   MPI_Status          *status;
1587:   MatScalar          **abuf_r, *ba_i, *pA, *coa, *ba;
1588:   const PetscScalar   *dummy;
1589:   PetscInt            *ai, *aj, *coi, *coj, *poJ, *pdJ;
1590:   Mat                  A_loc;
1591:   Mat_SeqAIJ          *a_loc;

1593:   PetscFunctionBegin;
1594:   MatCheckProduct(C, 3);
1595:   ap = (MatProductCtx_APMPI *)C->product->data;
1596:   PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
1597:   PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1598:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
1599:   PetscCallMPI(MPI_Comm_size(comm, &size));
1600:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1602:   merge = ap->merge;

1604:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1605:   /* get data from symbolic products */
1606:   coi = merge->coi;
1607:   coj = merge->coj;
1608:   PetscCall(PetscCalloc1(coi[pon], &coa));
1609:   bi     = merge->bi;
1610:   bj     = merge->bj;
1611:   owners = merge->rowmap->range;
1612:   PetscCall(PetscCalloc1(bi[cm], &ba));

1614:   /* get A_loc by taking all local rows of A */
1615:   A_loc = ap->A_loc;
1616:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
1617:   a_loc = (Mat_SeqAIJ *)A_loc->data;
1618:   ai    = a_loc->i;
1619:   aj    = a_loc->j;

1621:   /* trigger copy to CPU */
1622:   PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
1623:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
1624:   PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
1625:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
1626:   for (i = 0; i < am; i++) {
1627:     anz = ai[i + 1] - ai[i];
1628:     adj = aj + ai[i];
1629:     ada = a_loc->a + ai[i];

1631:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1632:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1633:     pnz = po->i[i + 1] - po->i[i];
1634:     poJ = po->j + po->i[i];
1635:     pA  = po->a + po->i[i];
1636:     for (j = 0; j < pnz; j++) {
1637:       row = poJ[j];
1638:       cj  = coj + coi[row];
1639:       ca  = coa + coi[row];
1640:       /* perform sparse axpy */
1641:       nexta  = 0;
1642:       valtmp = pA[j];
1643:       for (k = 0; nexta < anz; k++) {
1644:         if (cj[k] == adj[nexta]) {
1645:           ca[k] += valtmp * ada[nexta];
1646:           nexta++;
1647:         }
1648:       }
1649:       PetscCall(PetscLogFlops(2.0 * anz));
1650:     }

1652:     /* put the value into Cd (diagonal part) */
1653:     pnz = pd->i[i + 1] - pd->i[i];
1654:     pdJ = pd->j + pd->i[i];
1655:     pA  = pd->a + pd->i[i];
1656:     for (j = 0; j < pnz; j++) {
1657:       row = pdJ[j];
1658:       cj  = bj + bi[row];
1659:       ca  = ba + bi[row];
1660:       /* perform sparse axpy */
1661:       nexta  = 0;
1662:       valtmp = pA[j];
1663:       for (k = 0; nexta < anz; k++) {
1664:         if (cj[k] == adj[nexta]) {
1665:           ca[k] += valtmp * ada[nexta];
1666:           nexta++;
1667:         }
1668:       }
1669:       PetscCall(PetscLogFlops(2.0 * anz));
1670:     }
1671:   }

1673:   /* 3) send and recv matrix values coa */
1674:   buf_ri = merge->buf_ri;
1675:   buf_rj = merge->buf_rj;
1676:   len_s  = merge->len_s;
1677:   PetscCall(PetscCommGetNewTag(comm, &taga));
1678:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

1680:   PetscCall(PetscMalloc2(merge->nsend, &s_waits, size, &status));
1681:   for (proc = 0, k = 0; proc < size; proc++) {
1682:     if (!len_s[proc]) continue;
1683:     i = merge->owners_co[proc];
1684:     PetscCallMPI(MPIU_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
1685:     k++;
1686:   }
1687:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
1688:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));

1690:   PetscCall(PetscFree2(s_waits, status));
1691:   PetscCall(PetscFree(r_waits));
1692:   PetscCall(PetscFree(coa));

1694:   /* 4) insert local Cseq and received values into Cmpi */
1695:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1696:   for (k = 0; k < merge->nrecv; k++) {
1697:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1698:     nrows       = *buf_ri_k[k];
1699:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1700:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1701:   }

1703:   for (i = 0; i < cm; i++) {
1704:     row  = owners[rank] + i; /* global row index of C_seq */
1705:     bj_i = bj + bi[i];       /* col indices of the i-th row of C */
1706:     ba_i = ba + bi[i];
1707:     bnz  = bi[i + 1] - bi[i];
1708:     /* add received vals into ba */
1709:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1710:       /* i-th row */
1711:       if (i == *nextrow[k]) {
1712:         cnz    = *(nextci[k] + 1) - *nextci[k];
1713:         cj     = buf_rj[k] + *nextci[k];
1714:         ca     = abuf_r[k] + *nextci[k];
1715:         nextcj = 0;
1716:         for (j = 0; nextcj < cnz; j++) {
1717:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1718:             ba_i[j] += ca[nextcj++];
1719:           }
1720:         }
1721:         nextrow[k]++;
1722:         nextci[k]++;
1723:         PetscCall(PetscLogFlops(2.0 * cnz));
1724:       }
1725:     }
1726:     PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
1727:   }
1728:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1729:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

1731:   PetscCall(PetscFree(ba));
1732:   PetscCall(PetscFree(abuf_r[0]));
1733:   PetscCall(PetscFree(abuf_r));
1734:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1735:   PetscFunctionReturn(PETSC_SUCCESS);
1736: }

1738: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
1739: {
1740:   Mat                  A_loc;
1741:   MatProductCtx_APMPI *ap;
1742:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
1743:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
1744:   PetscInt            *pdti, *pdtj, *poti, *potj, *ptJ;
1745:   PetscInt             nnz;
1746:   PetscInt            *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
1747:   PetscInt             am = A->rmap->n, pn = P->cmap->n;
1748:   MPI_Comm             comm;
1749:   PetscMPIInt          size, rank, tagi, tagj, *len_si, *len_s, *len_ri, proc;
1750:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
1751:   PetscInt             len, *dnz, *onz, *owners;
1752:   PetscInt             nzi, *bi, *bj;
1753:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1754:   MPI_Request         *swaits, *rwaits;
1755:   MPI_Status          *sstatus, rstatus;
1756:   MatMergeSeqsToMPI   *merge;
1757:   PetscInt            *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
1758:   PetscReal            afill  = 1.0, afill_tmp;
1759:   PetscInt             rstart = P->cmap->rstart, rmax, Armax;
1760:   Mat_SeqAIJ          *a_loc;
1761:   PetscHMapI           ta;
1762:   MatType              mtype;

1764:   PetscFunctionBegin;
1765:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1766:   /* check if matrix local sizes are compatible */
1767:   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,
1768:              A->rmap->rend, P->rmap->rstart, P->rmap->rend);

1770:   PetscCallMPI(MPI_Comm_size(comm, &size));
1771:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1773:   /* create struct MatProductCtx_APMPI and attached it to C later */
1774:   PetscCall(PetscNew(&ap));

1776:   /* get A_loc by taking all local rows of A */
1777:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));

1779:   ap->A_loc = A_loc;
1780:   a_loc     = (Mat_SeqAIJ *)A_loc->data;
1781:   ai        = a_loc->i;
1782:   aj        = a_loc->j;

1784:   /* determine symbolic Co=(p->B)^T*A - send to others */
1785:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
1786:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
1787:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1788:                          >= (num of nonzero rows of C_seq) - pn */
1789:   PetscCall(PetscMalloc1(pon + 1, &coi));
1790:   coi[0] = 0;

1792:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1793:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
1794:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1795:   current_space = free_space;

1797:   /* create and initialize a linked list */
1798:   PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
1799:   MatRowMergeMax_SeqAIJ(a_loc, am, ta);
1800:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1802:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));

1804:   for (i = 0; i < pon; i++) {
1805:     pnz = poti[i + 1] - poti[i];
1806:     ptJ = potj + poti[i];
1807:     for (j = 0; j < pnz; j++) {
1808:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1809:       anz  = ai[row + 1] - ai[row];
1810:       Jptr = aj + ai[row];
1811:       /* add non-zero cols of AP into the sorted linked list lnk */
1812:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1813:     }
1814:     nnz = lnk[0];

1816:     /* If free space is not available, double the total space in the list */
1817:     if (current_space->local_remaining < nnz) {
1818:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1819:       nspacedouble++;
1820:     }

1822:     /* Copy data into free space, and zero out denserows */
1823:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));

1825:     current_space->array += nnz;
1826:     current_space->local_used += nnz;
1827:     current_space->local_remaining -= nnz;

1829:     coi[i + 1] = coi[i] + nnz;
1830:   }

1832:   PetscCall(PetscMalloc1(coi[pon], &coj));
1833:   PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
1834:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */

1836:   afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
1837:   if (afill_tmp > afill) afill = afill_tmp;

1839:   /* send j-array (coj) of Co to other processors */
1840:   /* determine row ownership */
1841:   PetscCall(PetscNew(&merge));
1842:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));

1844:   merge->rowmap->n  = pn;
1845:   merge->rowmap->bs = 1;

1847:   PetscCall(PetscLayoutSetUp(merge->rowmap));
1848:   owners = merge->rowmap->range;

1850:   /* determine the number of messages to send, their lengths */
1851:   PetscCall(PetscCalloc1(size, &len_si));
1852:   PetscCall(PetscCalloc1(size, &merge->len_s));

1854:   len_s        = merge->len_s;
1855:   merge->nsend = 0;

1857:   PetscCall(PetscMalloc1(size + 1, &owners_co));

1859:   proc = 0;
1860:   for (i = 0; i < pon; i++) {
1861:     while (prmap[i] >= owners[proc + 1]) proc++;
1862:     len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1863:     len_s[proc] += coi[i + 1] - coi[i];
1864:   }

1866:   len          = 0; /* max length of buf_si[] */
1867:   owners_co[0] = 0;
1868:   for (proc = 0; proc < size; proc++) {
1869:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1870:     if (len_s[proc]) {
1871:       merge->nsend++;
1872:       len_si[proc] = 2 * (len_si[proc] + 1);
1873:       len += len_si[proc];
1874:     }
1875:   }

1877:   /* determine the number and length of messages to receive for coi and coj  */
1878:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
1879:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

1881:   /* post the Irecv and Isend of coj */
1882:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1883:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
1884:   PetscCall(PetscMalloc1(merge->nsend, &swaits));
1885:   for (proc = 0, k = 0; proc < size; proc++) {
1886:     if (!len_s[proc]) continue;
1887:     i = owners_co[proc];
1888:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1889:     k++;
1890:   }

1892:   /* receives and sends of coj are complete */
1893:   PetscCall(PetscMalloc1(size, &sstatus));
1894:   for (i = 0; i < merge->nrecv; i++) {
1895:     PETSC_UNUSED PetscMPIInt icompleted;
1896:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1897:   }
1898:   PetscCall(PetscFree(rwaits));
1899:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));

1901:   /* add received column indices into table to update Armax */
1902:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1903:   for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1904:     Jptr = buf_rj[k];
1905:     for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1906:   }
1907:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1909:   /* send and recv coi */
1910:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1911:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &rwaits));
1912:   PetscCall(PetscMalloc1(len, &buf_s));
1913:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1914:   for (proc = 0, k = 0; proc < size; proc++) {
1915:     if (!len_s[proc]) continue;
1916:     /* form outgoing message for i-structure:
1917:          buf_si[0]:                 nrows to be sent
1918:                [1:nrows]:           row index (global)
1919:                [nrows+1:2*nrows+1]: i-structure index
1920:     */
1921:     nrows       = len_si[proc] / 2 - 1;
1922:     buf_si_i    = buf_si + nrows + 1;
1923:     buf_si[0]   = nrows;
1924:     buf_si_i[0] = 0;
1925:     nrows       = 0;
1926:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1927:       nzi                 = coi[i + 1] - coi[i];
1928:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1929:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1930:       nrows++;
1931:     }
1932:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1933:     k++;
1934:     buf_si += len_si[proc];
1935:   }
1936:   i = merge->nrecv;
1937:   while (i--) {
1938:     PETSC_UNUSED PetscMPIInt icompleted;
1939:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1940:   }
1941:   PetscCall(PetscFree(rwaits));
1942:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
1943:   PetscCall(PetscFree(len_si));
1944:   PetscCall(PetscFree(len_ri));
1945:   PetscCall(PetscFree(swaits));
1946:   PetscCall(PetscFree(sstatus));
1947:   PetscCall(PetscFree(buf_s));

1949:   /* compute the local portion of C (mpi mat) */
1950:   /* allocate bi array and free space for accumulating nonzero column info */
1951:   PetscCall(PetscMalloc1(pn + 1, &bi));
1952:   bi[0] = 0;

1954:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1955:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
1956:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1957:   current_space = free_space;

1959:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1960:   for (k = 0; k < merge->nrecv; k++) {
1961:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1962:     nrows       = *buf_ri_k[k];
1963:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1964:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1965:   }

1967:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
1968:   MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
1969:   rmax = 0;
1970:   for (i = 0; i < pn; i++) {
1971:     /* add pdt[i,:]*AP into lnk */
1972:     pnz = pdti[i + 1] - pdti[i];
1973:     ptJ = pdtj + pdti[i];
1974:     for (j = 0; j < pnz; j++) {
1975:       row  = ptJ[j]; /* row of AP == col of Pt */
1976:       anz  = ai[row + 1] - ai[row];
1977:       Jptr = aj + ai[row];
1978:       /* add non-zero cols of AP into the sorted linked list lnk */
1979:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1980:     }

1982:     /* add received col data into lnk */
1983:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1984:       if (i == *nextrow[k]) {            /* i-th row */
1985:         nzi  = *(nextci[k] + 1) - *nextci[k];
1986:         Jptr = buf_rj[k] + *nextci[k];
1987:         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
1988:         nextrow[k]++;
1989:         nextci[k]++;
1990:       }
1991:     }

1993:     /* add missing diagonal entry */
1994:     if (C->force_diagonals) {
1995:       k = i + owners[rank]; /* column index */
1996:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
1997:     }

1999:     nnz = lnk[0];

2001:     /* if free space is not available, make more free space */
2002:     if (current_space->local_remaining < nnz) {
2003:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
2004:       nspacedouble++;
2005:     }
2006:     /* copy data into free space, then initialize lnk */
2007:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
2008:     PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));

2010:     current_space->array += nnz;
2011:     current_space->local_used += nnz;
2012:     current_space->local_remaining -= nnz;

2014:     bi[i + 1] = bi[i] + nnz;
2015:     if (nnz > rmax) rmax = nnz;
2016:   }
2017:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));

2019:   PetscCall(PetscMalloc1(bi[pn], &bj));
2020:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
2021:   afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
2022:   if (afill_tmp > afill) afill = afill_tmp;
2023:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2024:   PetscCall(PetscHMapIDestroy(&ta));
2025:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
2026:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));

2028:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2029:   PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
2030:   PetscCall(MatSetBlockSizes(C, P->cmap->bs, A->cmap->bs));
2031:   PetscCall(MatGetType(A, &mtype));
2032:   PetscCall(MatSetType(C, mtype));
2033:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
2034:   MatPreallocateEnd(dnz, onz);
2035:   PetscCall(MatSetBlockSize(C, 1));
2036:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2037:   for (i = 0; i < pn; i++) {
2038:     row  = i + rstart;
2039:     nnz  = bi[i + 1] - bi[i];
2040:     Jptr = bj + bi[i];
2041:     PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
2042:   }
2043:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2044:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2045:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
2046:   merge->bi        = bi;
2047:   merge->bj        = bj;
2048:   merge->coi       = coi;
2049:   merge->coj       = coj;
2050:   merge->buf_ri    = buf_ri;
2051:   merge->buf_rj    = buf_rj;
2052:   merge->owners_co = owners_co;

2054:   /* attach the supporting struct to C for reuse */
2055:   C->product->data    = ap;
2056:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2057:   ap->merge           = merge;

2059:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2061: #if defined(PETSC_USE_INFO)
2062:   if (bi[pn] != 0) {
2063:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
2064:     PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
2065:   } else {
2066:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
2067:   }
2068: #endif
2069:   PetscFunctionReturn(PETSC_SUCCESS);
2070: }

2072: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2073: {
2074:   Mat_Product *product = C->product;
2075:   Mat          A = product->A, B = product->B;
2076:   PetscReal    fill = product->fill;
2077:   PetscBool    flg;

2079:   PetscFunctionBegin;
2080:   /* scalable */
2081:   PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
2082:   if (flg) {
2083:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
2084:     goto next;
2085:   }

2087:   /* nonscalable */
2088:   PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
2089:   if (flg) {
2090:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
2091:     goto next;
2092:   }

2094:   /* matmatmult */
2095:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
2096:   if (flg) {
2097:     Mat                  At;
2098:     MatProductCtx_APMPI *ptap;

2100:     PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
2101:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
2102:     ptap = (MatProductCtx_APMPI *)C->product->data;
2103:     if (ptap) {
2104:       ptap->Pt            = At;
2105:       C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
2106:     }
2107:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2108:     goto next;
2109:   }

2111:   /* backend general code */
2112:   PetscCall(PetscStrcmp(product->alg, "backend", &flg));
2113:   if (flg) {
2114:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2115:     PetscFunctionReturn(PETSC_SUCCESS);
2116:   }

2118:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");

2120: next:
2121:   C->ops->productnumeric = MatProductNumeric_AtB;
2122:   PetscFunctionReturn(PETSC_SUCCESS);
2123: }

2125: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2126: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2127: {
2128:   Mat_Product *product = C->product;
2129:   Mat          A = product->A, B = product->B;
2130: #if defined(PETSC_HAVE_HYPRE)
2131:   const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
2132:   PetscInt    nalg        = 5;
2133: #else
2134:   const char *algTypes[4] = {
2135:     "scalable",
2136:     "nonscalable",
2137:     "seqmpi",
2138:     "backend",
2139:   };
2140:   PetscInt nalg = 4;
2141: #endif
2142:   PetscInt  alg = 1; /* set nonscalable algorithm as default */
2143:   PetscBool flg;
2144:   MPI_Comm  comm;

2146:   PetscFunctionBegin;
2147:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));

2149:   /* Set "nonscalable" as default algorithm */
2150:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2151:   if (flg) {
2152:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2154:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2155:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2156:       MatInfo   Ainfo, Binfo;
2157:       PetscInt  nz_local;
2158:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2160:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2161:       PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2162:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2164:       if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2165:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2167:       if (alg_scalable) {
2168:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2169:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2170:         PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2171:       }
2172:     }
2173:   }

2175:   /* Get runtime option */
2176:   if (product->api_user) {
2177:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2178:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2179:     PetscOptionsEnd();
2180:   } else {
2181:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2182:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2183:     PetscOptionsEnd();
2184:   }
2185:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2187:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2188:   PetscFunctionReturn(PETSC_SUCCESS);
2189: }

2191: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2192: {
2193:   PetscFunctionBegin;
2194:   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2195:   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2196:   PetscFunctionReturn(PETSC_SUCCESS);
2197: }

2199: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2200: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2201: {
2202:   Mat_Product *product = C->product;
2203:   Mat          A = product->A, B = product->B;
2204:   const char  *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
2205:   PetscInt     nalg        = 4;
2206:   PetscInt     alg         = 1; /* set default algorithm  */
2207:   PetscBool    flg;
2208:   MPI_Comm     comm;

2210:   PetscFunctionBegin;
2211:   /* Check matrix local sizes */
2212:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2213:   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 ")",
2214:              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

2216:   /* Set default algorithm */
2217:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2218:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2220:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2221:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2222:     MatInfo   Ainfo, Binfo;
2223:     PetscInt  nz_local;
2224:     PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2226:     PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2227:     PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2228:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2230:     if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2231:     PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2233:     if (alg_scalable) {
2234:       alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2235:       PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2236:       PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2237:     }
2238:   }

2240:   /* Get runtime option */
2241:   if (product->api_user) {
2242:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2243:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2244:     PetscOptionsEnd();
2245:   } else {
2246:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2247:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2248:     PetscOptionsEnd();
2249:   }
2250:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2252:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2253:   PetscFunctionReturn(PETSC_SUCCESS);
2254: }

2256: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2257: {
2258:   Mat_Product *product = C->product;
2259:   Mat          A = product->A, P = product->B;
2260:   MPI_Comm     comm;
2261:   PetscBool    flg;
2262:   PetscInt     alg = 1; /* set default algorithm */
2263: #if !defined(PETSC_HAVE_HYPRE)
2264:   const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
2265:   PetscInt    nalg        = 5;
2266: #else
2267:   const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
2268:   PetscInt    nalg        = 6;
2269: #endif
2270:   PetscInt pN = P->cmap->N;

2272:   PetscFunctionBegin;
2273:   /* Check matrix local sizes */
2274:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2275:   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 ")",
2276:              A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
2277:   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 ")",
2278:              A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);

2280:   /* Set "nonscalable" as default algorithm */
2281:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2282:   if (flg) {
2283:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2285:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2286:     if (pN > 100000) {
2287:       MatInfo   Ainfo, Pinfo;
2288:       PetscInt  nz_local;
2289:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2291:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2292:       PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
2293:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2295:       if (pN > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2296:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2298:       if (alg_scalable) {
2299:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2300:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2301:       }
2302:     }
2303:   }

2305:   /* Get runtime option */
2306:   if (product->api_user) {
2307:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2308:     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2309:     PetscOptionsEnd();
2310:   } else {
2311:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2312:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2313:     PetscOptionsEnd();
2314:   }
2315:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

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

2321: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2322: {
2323:   Mat_Product *product = C->product;
2324:   Mat          A = product->A, R = product->B;

2326:   PetscFunctionBegin;
2327:   /* Check matrix local sizes */
2328:   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,
2329:              A->rmap->n, R->rmap->n, R->cmap->n);

2331:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2332:   PetscFunctionReturn(PETSC_SUCCESS);
2333: }

2335: /*
2336:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2337: */
2338: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2339: {
2340:   Mat_Product *product     = C->product;
2341:   PetscBool    flg         = PETSC_FALSE;
2342:   PetscInt     alg         = 1; /* default algorithm */
2343:   const char  *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
2344:   PetscInt     nalg        = 3;

2346:   PetscFunctionBegin;
2347:   /* Set default algorithm */
2348:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2349:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2351:   /* Get runtime option */
2352:   if (product->api_user) {
2353:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2354:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2355:     PetscOptionsEnd();
2356:   } else {
2357:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2358:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2359:     PetscOptionsEnd();
2360:   }
2361:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2363:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2364:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2365:   PetscFunctionReturn(PETSC_SUCCESS);
2366: }

2368: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2369: {
2370:   Mat_Product *product = C->product;

2372:   PetscFunctionBegin;
2373:   switch (product->type) {
2374:   case MATPRODUCT_AB:
2375:     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2376:     break;
2377:   case MATPRODUCT_ABt:
2378:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2379:     break;
2380:   case MATPRODUCT_AtB:
2381:     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2382:     break;
2383:   case MATPRODUCT_PtAP:
2384:     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2385:     break;
2386:   case MATPRODUCT_RARt:
2387:     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2388:     break;
2389:   case MATPRODUCT_ABC:
2390:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2391:     break;
2392:   default:
2393:     break;
2394:   }
2395:   PetscFunctionReturn(PETSC_SUCCESS);
2396: }