Actual source code: mpimatmatmult.c

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

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

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

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

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

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

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

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

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

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

 76: PetscErrorCode MatDestroy_MPIAIJ_MatMatMult(void *data)
 77: {
 78:   Mat_APMPI *ptap = (Mat_APMPI *)data;

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

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

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

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

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

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

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

139:   api = ptap->api;
140:   apj = ptap->apj;
141:   /* trigger copy to CPU */
142:   PetscCall(MatSeqAIJGetArrayRead(a->A, &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:   Mat_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 Mat_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(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
312:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
313:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

747:     /* 1st off-diagonal part of C */
748:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
749:     k  = 0;
750:     for (k0 = 0; k0 < conz; k0++) {
751:       if (apJ[k] >= cstart) break;
752:       ca[k0]        = apa_sparse[k];
753:       apa_sparse[k] = 0.0;
754:       k++;
755:     }

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

765:     /* 2nd off-diagonal part of C */
766:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
767:     for (; k0 < conz; k0++) {
768:       ca[k0]        = apa_sparse[k];
769:       apa_sparse[k] = 0.0;
770:       k++;
771:     }
772:   }
773:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
774:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
775:   PetscFunctionReturn(PETSC_SUCCESS);
776: }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

917:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
918:   C->ops->productnumeric = MatProductNumeric_AB;

920:   /* attach the supporting struct to C for reuse */
921:   C->product->data    = ptap;
922:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

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

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

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

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

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

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

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

1006:   /* Traverse one remaining array */
1007:   while (i < size1) out[l++] = in1[i++];
1008:   while (j < size2) out[l++] = in2[j++];
1009:   while (k < size3) out[l++] = in3[k++];

1011:   *size4 = l;
1012: }

1014: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
1015: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
1016: /* matrix-matrix multiplications.  */
1017: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
1018: {
1019:   MPI_Comm           comm;
1020:   PetscMPIInt        size;
1021:   Mat_APMPI         *ptap;
1022:   PetscFreeSpaceList free_space_diag = NULL, current_space = NULL;
1023:   Mat_MPIAIJ        *a  = (Mat_MPIAIJ *)A->data;
1024:   Mat_SeqAIJ        *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
1025:   Mat_MPIAIJ        *p = (Mat_MPIAIJ *)P->data;
1026:   Mat_SeqAIJ        *adpd_seq, *p_off, *aopoth_seq;
1027:   PetscInt           adponz, adpdnz;
1028:   PetscInt          *pi_loc, *dnz, *onz;
1029:   PetscInt          *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
1030:   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;
1031:   PetscInt           am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
1032:   PetscBT            lnkbt;
1033:   PetscReal          afill;
1034:   PetscMPIInt        rank;
1035:   Mat                adpd, aopoth;
1036:   MatType            mtype;
1037:   const char        *prefix;

1039:   PetscFunctionBegin;
1040:   MatCheckProduct(C, 4);
1041:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
1042:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1043:   PetscCallMPI(MPI_Comm_size(comm, &size));
1044:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
1045:   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));

1047:   /* create struct Mat_APMPI and attached it to C later */
1048:   PetscCall(PetscNew(&ptap));

1050:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
1051:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));

1053:   /* get P_loc by taking all local rows of P */
1054:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));

1056:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
1057:   pi_loc = p_loc->i;

1059:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
1060:   PetscCall(PetscMalloc1(am + 1, &api));
1061:   PetscCall(PetscMalloc1(am + 1, &adpoi));

1063:   adpoi[0]  = 0;
1064:   ptap->api = api;
1065:   api[0]    = 0;

1067:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
1068:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
1069:   MatPreallocateBegin(comm, am, pn, dnz, onz);

1071:   /* Symbolic calc of A_loc_diag * P_loc_diag */
1072:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1073:   PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
1074:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1075:   PetscCall(MatSetOptionsPrefix(adpd, prefix));
1076:   PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));

1078:   PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
1079:   PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
1080:   PetscCall(MatProductSetFill(adpd, fill));
1081:   PetscCall(MatProductSetFromOptions(adpd));

1083:   adpd->force_diagonals = C->force_diagonals;
1084:   PetscCall(MatProductSymbolic(adpd));

1086:   adpd_seq = (Mat_SeqAIJ *)((adpd)->data);
1087:   adpdi    = adpd_seq->i;
1088:   adpdj    = adpd_seq->j;
1089:   p_off    = (Mat_SeqAIJ *)p->B->data;
1090:   poff_i   = p_off->i;
1091:   poff_j   = p_off->j;

1093:   /* j_temp stores indices of a result row before they are added to the linked list */
1094:   PetscCall(PetscMalloc1(pN, &j_temp));

1096:   /* Symbolic calc of the A_diag * p_loc_off */
1097:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
1098:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
1099:   current_space = free_space_diag;

1101:   for (i = 0; i < am; i++) {
1102:     /* A_diag * P_loc_off */
1103:     nzi = adi[i + 1] - adi[i];
1104:     for (j = 0; j < nzi; j++) {
1105:       row  = *adj++;
1106:       pnz  = poff_i[row + 1] - poff_i[row];
1107:       Jptr = poff_j + poff_i[row];
1108:       for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
1109:       /* add non-zero cols of P into the sorted linked list lnk */
1110:       PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
1111:     }

1113:     adponz       = lnk[0];
1114:     adpoi[i + 1] = adpoi[i] + adponz;

1116:     /* if free space is not available, double the total space in the list */
1117:     if (current_space->local_remaining < adponz) {
1118:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), &current_space));
1119:       nspacedouble++;
1120:     }

1122:     /* Copy data into free space, then initialize lnk */
1123:     PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));

1125:     current_space->array += adponz;
1126:     current_space->local_used += adponz;
1127:     current_space->local_remaining -= adponz;
1128:   }

1130:   /* Symbolic calc of A_off * P_oth */
1131:   PetscCall(MatSetOptionsPrefix(a->B, prefix));
1132:   PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
1133:   PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
1134:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
1135:   aopoth_seq = (Mat_SeqAIJ *)((aopoth)->data);
1136:   aopothi    = aopoth_seq->i;
1137:   aopothj    = aopoth_seq->j;

1139:   /* Allocate space for apj, adpj, aopj, ... */
1140:   /* destroy lists of free space and other temporary array(s) */

1142:   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am], &ptap->apj));
1143:   PetscCall(PetscMalloc1(adpoi[am], &adpoj));

1145:   /* Copy from linked list to j-array */
1146:   PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
1147:   PetscCall(PetscLLDestroy(lnk, lnkbt));

1149:   adpoJ = adpoj;
1150:   adpdJ = adpdj;
1151:   aopJ  = aopothj;
1152:   apj   = ptap->apj;
1153:   apJ   = apj; /* still empty */

1155:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
1156:   /* A_diag * P_loc_diag to get A*P */
1157:   for (i = 0; i < am; i++) {
1158:     aopnz  = aopothi[i + 1] - aopothi[i];
1159:     adponz = adpoi[i + 1] - adpoi[i];
1160:     adpdnz = adpdi[i + 1] - adpdi[i];

1162:     /* Correct indices from A_diag*P_diag */
1163:     for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
1164:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
1165:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
1166:     PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));

1168:     aopJ += aopnz;
1169:     adpoJ += adponz;
1170:     adpdJ += adpdnz;
1171:     apJ += apnz;
1172:     api[i + 1] = api[i] + apnz;
1173:   }

1175:   /* malloc apa to store dense row A[i,:]*P */
1176:   PetscCall(PetscCalloc1(pN, &ptap->apa));

1178:   /* create and assemble symbolic parallel matrix C */
1179:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
1180:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
1181:   PetscCall(MatGetType(A, &mtype));
1182:   PetscCall(MatSetType(C, mtype));
1183:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1184:   MatPreallocateEnd(dnz, onz);

1186:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
1187:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1188:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1189:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1191:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
1192:   C->ops->productnumeric = MatProductNumeric_AB;

1194:   /* attach the supporting struct to C for reuse */
1195:   C->product->data    = ptap;
1196:   C->product->destroy = MatDestroy_MPIAIJ_MatMatMult;

1198:   /* set MatInfo */
1199:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
1200:   if (afill < 1.0) afill = 1.0;
1201:   C->info.mallocs           = nspacedouble;
1202:   C->info.fill_ratio_given  = fill;
1203:   C->info.fill_ratio_needed = afill;

1205: #if defined(PETSC_USE_INFO)
1206:   if (api[am]) {
1207:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
1208:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
1209:   } else {
1210:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
1211:   }
1212: #endif

1214:   PetscCall(MatDestroy(&aopoth));
1215:   PetscCall(MatDestroy(&adpd));
1216:   PetscCall(PetscFree(j_temp));
1217:   PetscCall(PetscFree(adpoj));
1218:   PetscCall(PetscFree(adpoi));
1219:   PetscFunctionReturn(PETSC_SUCCESS);
1220: }

1222: /* This routine only works when scall=MAT_REUSE_MATRIX! */
1223: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
1224: {
1225:   Mat_APMPI *ptap;
1226:   Mat        Pt;

1228:   PetscFunctionBegin;
1229:   MatCheckProduct(C, 3);
1230:   ptap = (Mat_APMPI *)C->product->data;
1231:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1232:   PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");

1234:   Pt = ptap->Pt;
1235:   PetscCall(MatTransposeSetPrecursor(P, Pt));
1236:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
1237:   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
1238:   PetscFunctionReturn(PETSC_SUCCESS);
1239: }

1241: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
1242: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, PetscReal fill, Mat C)
1243: {
1244:   Mat_APMPI               *ptap;
1245:   Mat_MPIAIJ              *p = (Mat_MPIAIJ *)P->data;
1246:   MPI_Comm                 comm;
1247:   PetscMPIInt              size, rank;
1248:   PetscFreeSpaceList       free_space = NULL, current_space = NULL;
1249:   PetscInt                 pn = P->cmap->n, aN = A->cmap->N, an = A->cmap->n;
1250:   PetscInt                *lnk, i, k, rstart;
1251:   PetscBT                  lnkbt;
1252:   PetscMPIInt              tagi, tagj, *len_si, *len_s, *len_ri, nrecv, proc, nsend;
1253:   PETSC_UNUSED PetscMPIInt icompleted = 0;
1254:   PetscInt               **buf_rj, **buf_ri, **buf_ri_k, row, ncols, *cols;
1255:   PetscInt                 len, *dnz, *onz, *owners, nzi;
1256:   PetscInt                 nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1257:   MPI_Request             *swaits, *rwaits;
1258:   MPI_Status              *sstatus, rstatus;
1259:   PetscLayout              rowmap;
1260:   PetscInt                *owners_co, *coi, *coj; /* i and j array of (p->B)^T*A*P - used in the communication */
1261:   PetscMPIInt             *len_r, *id_r;          /* array of length of comm->size, store send/recv matrix values */
1262:   PetscInt                *Jptr, *prmap = p->garray, con, j, Crmax;
1263:   Mat_SeqAIJ              *a_loc, *c_loc, *c_oth;
1264:   PetscHMapI               ta;
1265:   MatType                  mtype;
1266:   const char              *prefix;

1268:   PetscFunctionBegin;
1269:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1270:   PetscCallMPI(MPI_Comm_size(comm, &size));
1271:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1273:   /* create symbolic parallel matrix C */
1274:   PetscCall(MatGetType(A, &mtype));
1275:   PetscCall(MatSetType(C, mtype));

1277:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

1279:   /* create struct Mat_APMPI and attached it to C later */
1280:   PetscCall(PetscNew(&ptap));

1282:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
1283:   PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
1284:   PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));

1286:   /* (1) compute symbolic A_loc */
1287:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));

1289:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
1290:   PetscCall(MatGetOptionsPrefix(A, &prefix));
1291:   PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
1292:   PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
1293:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
1294:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));

1296:   /* (3) send coj of C_oth to other processors  */
1297:   /* determine row ownership */
1298:   PetscCall(PetscLayoutCreate(comm, &rowmap));
1299:   rowmap->n  = pn;
1300:   rowmap->bs = 1;
1301:   PetscCall(PetscLayoutSetUp(rowmap));
1302:   owners = rowmap->range;

1304:   /* determine the number of messages to send, their lengths */
1305:   PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 1, &owners_co));
1306:   PetscCall(PetscArrayzero(len_s, size));
1307:   PetscCall(PetscArrayzero(len_si, size));

1309:   c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
1310:   coi   = c_oth->i;
1311:   coj   = c_oth->j;
1312:   con   = ptap->C_oth->rmap->n;
1313:   proc  = 0;
1314:   for (i = 0; i < con; i++) {
1315:     while (prmap[i] >= owners[proc + 1]) proc++;
1316:     len_si[proc]++;                     /* num of rows in Co(=Pt*A) to be sent to [proc] */
1317:     len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
1318:   }

1320:   len          = 0; /* max length of buf_si[], see (4) */
1321:   owners_co[0] = 0;
1322:   nsend        = 0;
1323:   for (proc = 0; proc < size; proc++) {
1324:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1325:     if (len_s[proc]) {
1326:       nsend++;
1327:       len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
1328:       len += len_si[proc];
1329:     }
1330:   }

1332:   /* determine the number and length of messages to receive for coi and coj  */
1333:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
1334:   PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));

1336:   /* post the Irecv and Isend of coj */
1337:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1338:   PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
1339:   PetscCall(PetscMalloc1(nsend, &swaits));
1340:   for (proc = 0, k = 0; proc < size; proc++) {
1341:     if (!len_s[proc]) continue;
1342:     i = owners_co[proc];
1343:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1344:     k++;
1345:   }

1347:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
1348:   PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
1349:   PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
1350:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
1351:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
1352:   c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;

1354:   /* receives coj are complete */
1355:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1356:   PetscCall(PetscFree(rwaits));
1357:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1359:   /* add received column indices into ta to update Crmax */
1360:   a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;

1362:   /* create and initialize a linked list */
1363:   PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
1364:   MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);

1366:   for (k = 0; k < nrecv; k++) { /* k-th received message */
1367:     Jptr = buf_rj[k];
1368:     for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1369:   }
1370:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
1371:   PetscCall(PetscHMapIDestroy(&ta));

1373:   /* (4) send and recv coi */
1374:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1375:   PetscCall(PetscPostIrecvInt(comm, tagi, nrecv, id_r, len_ri, &buf_ri, &rwaits));
1376:   PetscCall(PetscMalloc1(len, &buf_s));
1377:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1378:   for (proc = 0, k = 0; proc < size; proc++) {
1379:     if (!len_s[proc]) continue;
1380:     /* form outgoing message for i-structure:
1381:          buf_si[0]:                 nrows to be sent
1382:                [1:nrows]:           row index (global)
1383:                [nrows+1:2*nrows+1]: i-structure index
1384:     */
1385:     nrows       = len_si[proc] / 2 - 1; /* num of rows in Co to be sent to [proc] */
1386:     buf_si_i    = buf_si + nrows + 1;
1387:     buf_si[0]   = nrows;
1388:     buf_si_i[0] = 0;
1389:     nrows       = 0;
1390:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1391:       nzi                 = coi[i + 1] - coi[i];
1392:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1393:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1394:       nrows++;
1395:     }
1396:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1397:     k++;
1398:     buf_si += len_si[proc];
1399:   }
1400:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
1401:   PetscCall(PetscFree(rwaits));
1402:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

1404:   PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
1405:   PetscCall(PetscFree(len_ri));
1406:   PetscCall(PetscFree(swaits));
1407:   PetscCall(PetscFree(buf_s));

1409:   /* (5) compute the local portion of C      */
1410:   /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
1411:   PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
1412:   current_space = free_space;

1414:   PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
1415:   for (k = 0; k < nrecv; k++) {
1416:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1417:     nrows       = *buf_ri_k[k];
1418:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1419:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1420:   }

1422:   MatPreallocateBegin(comm, pn, an, dnz, onz);
1423:   PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
1424:   for (i = 0; i < pn; i++) { /* for each local row of C */
1425:     /* add C_loc into C */
1426:     nzi  = c_loc->i[i + 1] - c_loc->i[i];
1427:     Jptr = c_loc->j + c_loc->i[i];
1428:     PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));

1430:     /* add received col data into lnk */
1431:     for (k = 0; k < nrecv; k++) { /* k-th received message */
1432:       if (i == *nextrow[k]) {     /* i-th row */
1433:         nzi  = *(nextci[k] + 1) - *nextci[k];
1434:         Jptr = buf_rj[k] + *nextci[k];
1435:         PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
1436:         nextrow[k]++;
1437:         nextci[k]++;
1438:       }
1439:     }

1441:     /* add missing diagonal entry */
1442:     if (C->force_diagonals) {
1443:       k = i + owners[rank]; /* column index */
1444:       PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
1445:     }

1447:     nzi = lnk[0];

1449:     /* copy data into free space, then initialize lnk */
1450:     PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
1451:     PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
1452:   }
1453:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1454:   PetscCall(PetscLLDestroy(lnk, lnkbt));
1455:   PetscCall(PetscFreeSpaceDestroy(free_space));

1457:   /* local sizes and preallocation */
1458:   PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
1459:   PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
1460:   PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
1461:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
1462:   MatPreallocateEnd(dnz, onz);

1464:   /* add C_loc and C_oth to C */
1465:   PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
1466:   for (i = 0; i < pn; i++) {
1467:     ncols = c_loc->i[i + 1] - c_loc->i[i];
1468:     cols  = c_loc->j + c_loc->i[i];
1469:     row   = rstart + i;
1470:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));

1472:     if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
1473:   }
1474:   for (i = 0; i < con; i++) {
1475:     ncols = c_oth->i[i + 1] - c_oth->i[i];
1476:     cols  = c_oth->j + c_oth->i[i];
1477:     row   = prmap[i];
1478:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
1479:   }
1480:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1481:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1482:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

1484:   /* members in merge */
1485:   PetscCall(PetscFree(id_r));
1486:   PetscCall(PetscFree(len_r));
1487:   PetscCall(PetscFree(buf_ri[0]));
1488:   PetscCall(PetscFree(buf_ri));
1489:   PetscCall(PetscFree(buf_rj[0]));
1490:   PetscCall(PetscFree(buf_rj));
1491:   PetscCall(PetscLayoutDestroy(&rowmap));

1493:   /* attach the supporting struct to C for reuse */
1494:   C->product->data    = ptap;
1495:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
1496:   PetscFunctionReturn(PETSC_SUCCESS);
1497: }

1499: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
1500: {
1501:   Mat_MPIAIJ        *p = (Mat_MPIAIJ *)P->data;
1502:   Mat_SeqAIJ        *c_seq;
1503:   Mat_APMPI         *ptap;
1504:   Mat                A_loc, C_loc, C_oth;
1505:   PetscInt           i, rstart, rend, cm, ncols, row;
1506:   const PetscInt    *cols;
1507:   const PetscScalar *vals;

1509:   PetscFunctionBegin;
1510:   MatCheckProduct(C, 3);
1511:   ptap = (Mat_APMPI *)C->product->data;
1512:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
1513:   PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1514:   PetscCall(MatZeroEntries(C));

1516:   /* These matrices are obtained in MatTransposeMatMultSymbolic() */
1517:   /* 1) get R = Pd^T, Ro = Po^T */
1518:   PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
1519:   PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
1520:   PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
1521:   PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));

1523:   /* 2) compute numeric A_loc */
1524:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));

1526:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
1527:   A_loc = ptap->A_loc;
1528:   PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
1529:   PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
1530:   C_loc = ptap->C_loc;
1531:   C_oth = ptap->C_oth;

1533:   /* add C_loc and C_oth to C */
1534:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));

1536:   /* C_loc -> C */
1537:   cm    = C_loc->rmap->N;
1538:   c_seq = (Mat_SeqAIJ *)C_loc->data;
1539:   cols  = c_seq->j;
1540:   vals  = c_seq->a;
1541:   for (i = 0; i < cm; i++) {
1542:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1543:     row   = rstart + i;
1544:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1545:     cols += ncols;
1546:     vals += ncols;
1547:   }

1549:   /* Co -> C, off-processor part */
1550:   cm    = C_oth->rmap->N;
1551:   c_seq = (Mat_SeqAIJ *)C_oth->data;
1552:   cols  = c_seq->j;
1553:   vals  = c_seq->a;
1554:   for (i = 0; i < cm; i++) {
1555:     ncols = c_seq->i[i + 1] - c_seq->i[i];
1556:     row   = p->garray[i];
1557:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
1558:     cols += ncols;
1559:     vals += ncols;
1560:   }
1561:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1562:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
1563:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
1564:   PetscFunctionReturn(PETSC_SUCCESS);
1565: }

1567: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
1568: {
1569:   Mat_Merge_SeqsToMPI *merge;
1570:   Mat_MPIAIJ          *p  = (Mat_MPIAIJ *)P->data;
1571:   Mat_SeqAIJ          *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
1572:   Mat_APMPI           *ap;
1573:   PetscInt            *adj;
1574:   PetscInt             i, j, k, anz, pnz, row, *cj, nexta;
1575:   MatScalar           *ada, *ca, valtmp;
1576:   PetscInt             am = A->rmap->n, cm = C->rmap->n, pon = (p->B)->cmap->n;
1577:   MPI_Comm             comm;
1578:   PetscMPIInt          size, rank, taga, *len_s, proc;
1579:   PetscInt            *owners, nrows, **buf_ri_k, **nextrow, **nextci;
1580:   PetscInt           **buf_ri, **buf_rj;
1581:   PetscInt             cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
1582:   MPI_Request         *s_waits, *r_waits;
1583:   MPI_Status          *status;
1584:   MatScalar          **abuf_r, *ba_i, *pA, *coa, *ba;
1585:   const PetscScalar   *dummy;
1586:   PetscInt            *ai, *aj, *coi, *coj, *poJ, *pdJ;
1587:   Mat                  A_loc;
1588:   Mat_SeqAIJ          *a_loc;

1590:   PetscFunctionBegin;
1591:   MatCheckProduct(C, 3);
1592:   ap = (Mat_APMPI *)C->product->data;
1593:   PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
1594:   PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
1595:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
1596:   PetscCallMPI(MPI_Comm_size(comm, &size));
1597:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1599:   merge = ap->merge;

1601:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
1602:   /* get data from symbolic products */
1603:   coi = merge->coi;
1604:   coj = merge->coj;
1605:   PetscCall(PetscCalloc1(coi[pon], &coa));
1606:   bi     = merge->bi;
1607:   bj     = merge->bj;
1608:   owners = merge->rowmap->range;
1609:   PetscCall(PetscCalloc1(bi[cm], &ba));

1611:   /* get A_loc by taking all local rows of A */
1612:   A_loc = ap->A_loc;
1613:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
1614:   a_loc = (Mat_SeqAIJ *)A_loc->data;
1615:   ai    = a_loc->i;
1616:   aj    = a_loc->j;

1618:   /* trigger copy to CPU */
1619:   PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
1620:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
1621:   PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
1622:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
1623:   for (i = 0; i < am; i++) {
1624:     anz = ai[i + 1] - ai[i];
1625:     adj = aj + ai[i];
1626:     ada = a_loc->a + ai[i];

1628:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
1629:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
1630:     pnz = po->i[i + 1] - po->i[i];
1631:     poJ = po->j + po->i[i];
1632:     pA  = po->a + po->i[i];
1633:     for (j = 0; j < pnz; j++) {
1634:       row = poJ[j];
1635:       cj  = coj + coi[row];
1636:       ca  = coa + coi[row];
1637:       /* perform sparse axpy */
1638:       nexta  = 0;
1639:       valtmp = pA[j];
1640:       for (k = 0; nexta < anz; k++) {
1641:         if (cj[k] == adj[nexta]) {
1642:           ca[k] += valtmp * ada[nexta];
1643:           nexta++;
1644:         }
1645:       }
1646:       PetscCall(PetscLogFlops(2.0 * anz));
1647:     }

1649:     /* put the value into Cd (diagonal part) */
1650:     pnz = pd->i[i + 1] - pd->i[i];
1651:     pdJ = pd->j + pd->i[i];
1652:     pA  = pd->a + pd->i[i];
1653:     for (j = 0; j < pnz; j++) {
1654:       row = pdJ[j];
1655:       cj  = bj + bi[row];
1656:       ca  = ba + bi[row];
1657:       /* perform sparse axpy */
1658:       nexta  = 0;
1659:       valtmp = pA[j];
1660:       for (k = 0; nexta < anz; k++) {
1661:         if (cj[k] == adj[nexta]) {
1662:           ca[k] += valtmp * ada[nexta];
1663:           nexta++;
1664:         }
1665:       }
1666:       PetscCall(PetscLogFlops(2.0 * anz));
1667:     }
1668:   }

1670:   /* 3) send and recv matrix values coa */
1671:   buf_ri = merge->buf_ri;
1672:   buf_rj = merge->buf_rj;
1673:   len_s  = merge->len_s;
1674:   PetscCall(PetscCommGetNewTag(comm, &taga));
1675:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

1677:   PetscCall(PetscMalloc2(merge->nsend, &s_waits, size, &status));
1678:   for (proc = 0, k = 0; proc < size; proc++) {
1679:     if (!len_s[proc]) continue;
1680:     i = merge->owners_co[proc];
1681:     PetscCallMPI(MPIU_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
1682:     k++;
1683:   }
1684:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
1685:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));

1687:   PetscCall(PetscFree2(s_waits, status));
1688:   PetscCall(PetscFree(r_waits));
1689:   PetscCall(PetscFree(coa));

1691:   /* 4) insert local Cseq and received values into Cmpi */
1692:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1693:   for (k = 0; k < merge->nrecv; k++) {
1694:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1695:     nrows       = *buf_ri_k[k];
1696:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1697:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
1698:   }

1700:   for (i = 0; i < cm; i++) {
1701:     row  = owners[rank] + i; /* global row index of C_seq */
1702:     bj_i = bj + bi[i];       /* col indices of the i-th row of C */
1703:     ba_i = ba + bi[i];
1704:     bnz  = bi[i + 1] - bi[i];
1705:     /* add received vals into ba */
1706:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1707:       /* i-th row */
1708:       if (i == *nextrow[k]) {
1709:         cnz    = *(nextci[k] + 1) - *nextci[k];
1710:         cj     = buf_rj[k] + *nextci[k];
1711:         ca     = abuf_r[k] + *nextci[k];
1712:         nextcj = 0;
1713:         for (j = 0; nextcj < cnz; j++) {
1714:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
1715:             ba_i[j] += ca[nextcj++];
1716:           }
1717:         }
1718:         nextrow[k]++;
1719:         nextci[k]++;
1720:         PetscCall(PetscLogFlops(2.0 * cnz));
1721:       }
1722:     }
1723:     PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
1724:   }
1725:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
1726:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

1728:   PetscCall(PetscFree(ba));
1729:   PetscCall(PetscFree(abuf_r[0]));
1730:   PetscCall(PetscFree(abuf_r));
1731:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
1732:   PetscFunctionReturn(PETSC_SUCCESS);
1733: }

1735: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
1736: {
1737:   Mat                  A_loc;
1738:   Mat_APMPI           *ap;
1739:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
1740:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
1741:   PetscInt            *pdti, *pdtj, *poti, *potj, *ptJ;
1742:   PetscInt             nnz;
1743:   PetscInt            *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
1744:   PetscInt             am = A->rmap->n, pn = P->cmap->n;
1745:   MPI_Comm             comm;
1746:   PetscMPIInt          size, rank, tagi, tagj, *len_si, *len_s, *len_ri, proc;
1747:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
1748:   PetscInt             len, *dnz, *onz, *owners;
1749:   PetscInt             nzi, *bi, *bj;
1750:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
1751:   MPI_Request         *swaits, *rwaits;
1752:   MPI_Status          *sstatus, rstatus;
1753:   Mat_Merge_SeqsToMPI *merge;
1754:   PetscInt            *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
1755:   PetscReal            afill  = 1.0, afill_tmp;
1756:   PetscInt             rstart = P->cmap->rstart, rmax, Armax;
1757:   Mat_SeqAIJ          *a_loc;
1758:   PetscHMapI           ta;
1759:   MatType              mtype;

1761:   PetscFunctionBegin;
1762:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
1763:   /* check if matrix local sizes are compatible */
1764:   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,
1765:              A->rmap->rend, P->rmap->rstart, P->rmap->rend);

1767:   PetscCallMPI(MPI_Comm_size(comm, &size));
1768:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

1770:   /* create struct Mat_APMPI and attached it to C later */
1771:   PetscCall(PetscNew(&ap));

1773:   /* get A_loc by taking all local rows of A */
1774:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));

1776:   ap->A_loc = A_loc;
1777:   a_loc     = (Mat_SeqAIJ *)A_loc->data;
1778:   ai        = a_loc->i;
1779:   aj        = a_loc->j;

1781:   /* determine symbolic Co=(p->B)^T*A - send to others */
1782:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
1783:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
1784:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
1785:                          >= (num of nonzero rows of C_seq) - pn */
1786:   PetscCall(PetscMalloc1(pon + 1, &coi));
1787:   coi[0] = 0;

1789:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
1790:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
1791:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1792:   current_space = free_space;

1794:   /* create and initialize a linked list */
1795:   PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
1796:   MatRowMergeMax_SeqAIJ(a_loc, am, ta);
1797:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1799:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));

1801:   for (i = 0; i < pon; i++) {
1802:     pnz = poti[i + 1] - poti[i];
1803:     ptJ = potj + poti[i];
1804:     for (j = 0; j < pnz; j++) {
1805:       row  = ptJ[j]; /* row of A_loc == col of Pot */
1806:       anz  = ai[row + 1] - ai[row];
1807:       Jptr = aj + ai[row];
1808:       /* add non-zero cols of AP into the sorted linked list lnk */
1809:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1810:     }
1811:     nnz = lnk[0];

1813:     /* If free space is not available, double the total space in the list */
1814:     if (current_space->local_remaining < nnz) {
1815:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
1816:       nspacedouble++;
1817:     }

1819:     /* Copy data into free space, and zero out denserows */
1820:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));

1822:     current_space->array += nnz;
1823:     current_space->local_used += nnz;
1824:     current_space->local_remaining -= nnz;

1826:     coi[i + 1] = coi[i] + nnz;
1827:   }

1829:   PetscCall(PetscMalloc1(coi[pon], &coj));
1830:   PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
1831:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */

1833:   afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
1834:   if (afill_tmp > afill) afill = afill_tmp;

1836:   /* send j-array (coj) of Co to other processors */
1837:   /* determine row ownership */
1838:   PetscCall(PetscNew(&merge));
1839:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));

1841:   merge->rowmap->n  = pn;
1842:   merge->rowmap->bs = 1;

1844:   PetscCall(PetscLayoutSetUp(merge->rowmap));
1845:   owners = merge->rowmap->range;

1847:   /* determine the number of messages to send, their lengths */
1848:   PetscCall(PetscCalloc1(size, &len_si));
1849:   PetscCall(PetscCalloc1(size, &merge->len_s));

1851:   len_s        = merge->len_s;
1852:   merge->nsend = 0;

1854:   PetscCall(PetscMalloc1(size + 1, &owners_co));

1856:   proc = 0;
1857:   for (i = 0; i < pon; i++) {
1858:     while (prmap[i] >= owners[proc + 1]) proc++;
1859:     len_si[proc]++; /* num of rows in Co to be sent to [proc] */
1860:     len_s[proc] += coi[i + 1] - coi[i];
1861:   }

1863:   len          = 0; /* max length of buf_si[] */
1864:   owners_co[0] = 0;
1865:   for (proc = 0; proc < size; proc++) {
1866:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
1867:     if (len_s[proc]) {
1868:       merge->nsend++;
1869:       len_si[proc] = 2 * (len_si[proc] + 1);
1870:       len += len_si[proc];
1871:     }
1872:   }

1874:   /* determine the number and length of messages to receive for coi and coj  */
1875:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
1876:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

1878:   /* post the Irecv and Isend of coj */
1879:   PetscCall(PetscCommGetNewTag(comm, &tagj));
1880:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
1881:   PetscCall(PetscMalloc1(merge->nsend, &swaits));
1882:   for (proc = 0, k = 0; proc < size; proc++) {
1883:     if (!len_s[proc]) continue;
1884:     i = owners_co[proc];
1885:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
1886:     k++;
1887:   }

1889:   /* receives and sends of coj are complete */
1890:   PetscCall(PetscMalloc1(size, &sstatus));
1891:   for (i = 0; i < merge->nrecv; i++) {
1892:     PETSC_UNUSED PetscMPIInt icompleted;
1893:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1894:   }
1895:   PetscCall(PetscFree(rwaits));
1896:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));

1898:   /* add received column indices into table to update Armax */
1899:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
1900:   for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1901:     Jptr = buf_rj[k];
1902:     for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
1903:   }
1904:   PetscCall(PetscHMapIGetSize(ta, &Armax));

1906:   /* send and recv coi */
1907:   PetscCall(PetscCommGetNewTag(comm, &tagi));
1908:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &rwaits));
1909:   PetscCall(PetscMalloc1(len, &buf_s));
1910:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
1911:   for (proc = 0, k = 0; proc < size; proc++) {
1912:     if (!len_s[proc]) continue;
1913:     /* form outgoing message for i-structure:
1914:          buf_si[0]:                 nrows to be sent
1915:                [1:nrows]:           row index (global)
1916:                [nrows+1:2*nrows+1]: i-structure index
1917:     */
1918:     nrows       = len_si[proc] / 2 - 1;
1919:     buf_si_i    = buf_si + nrows + 1;
1920:     buf_si[0]   = nrows;
1921:     buf_si_i[0] = 0;
1922:     nrows       = 0;
1923:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
1924:       nzi                 = coi[i + 1] - coi[i];
1925:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
1926:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
1927:       nrows++;
1928:     }
1929:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
1930:     k++;
1931:     buf_si += len_si[proc];
1932:   }
1933:   i = merge->nrecv;
1934:   while (i--) {
1935:     PETSC_UNUSED PetscMPIInt icompleted;
1936:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
1937:   }
1938:   PetscCall(PetscFree(rwaits));
1939:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
1940:   PetscCall(PetscFree(len_si));
1941:   PetscCall(PetscFree(len_ri));
1942:   PetscCall(PetscFree(swaits));
1943:   PetscCall(PetscFree(sstatus));
1944:   PetscCall(PetscFree(buf_s));

1946:   /* compute the local portion of C (mpi mat) */
1947:   /* allocate bi array and free space for accumulating nonzero column info */
1948:   PetscCall(PetscMalloc1(pn + 1, &bi));
1949:   bi[0] = 0;

1951:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
1952:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
1953:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
1954:   current_space = free_space;

1956:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
1957:   for (k = 0; k < merge->nrecv; k++) {
1958:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
1959:     nrows       = *buf_ri_k[k];
1960:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
1961:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
1962:   }

1964:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
1965:   MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
1966:   rmax = 0;
1967:   for (i = 0; i < pn; i++) {
1968:     /* add pdt[i,:]*AP into lnk */
1969:     pnz = pdti[i + 1] - pdti[i];
1970:     ptJ = pdtj + pdti[i];
1971:     for (j = 0; j < pnz; j++) {
1972:       row  = ptJ[j]; /* row of AP == col of Pt */
1973:       anz  = ai[row + 1] - ai[row];
1974:       Jptr = aj + ai[row];
1975:       /* add non-zero cols of AP into the sorted linked list lnk */
1976:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
1977:     }

1979:     /* add received col data into lnk */
1980:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
1981:       if (i == *nextrow[k]) {            /* i-th row */
1982:         nzi  = *(nextci[k] + 1) - *nextci[k];
1983:         Jptr = buf_rj[k] + *nextci[k];
1984:         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
1985:         nextrow[k]++;
1986:         nextci[k]++;
1987:       }
1988:     }

1990:     /* add missing diagonal entry */
1991:     if (C->force_diagonals) {
1992:       k = i + owners[rank]; /* column index */
1993:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
1994:     }

1996:     nnz = lnk[0];

1998:     /* if free space is not available, make more free space */
1999:     if (current_space->local_remaining < nnz) {
2000:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
2001:       nspacedouble++;
2002:     }
2003:     /* copy data into free space, then initialize lnk */
2004:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
2005:     PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));

2007:     current_space->array += nnz;
2008:     current_space->local_used += nnz;
2009:     current_space->local_remaining -= nnz;

2011:     bi[i + 1] = bi[i] + nnz;
2012:     if (nnz > rmax) rmax = nnz;
2013:   }
2014:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));

2016:   PetscCall(PetscMalloc1(bi[pn], &bj));
2017:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
2018:   afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
2019:   if (afill_tmp > afill) afill = afill_tmp;
2020:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
2021:   PetscCall(PetscHMapIDestroy(&ta));
2022:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
2023:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));

2025:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
2026:   PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
2027:   PetscCall(MatSetBlockSizes(C, P->cmap->bs, A->cmap->bs));
2028:   PetscCall(MatGetType(A, &mtype));
2029:   PetscCall(MatSetType(C, mtype));
2030:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
2031:   MatPreallocateEnd(dnz, onz);
2032:   PetscCall(MatSetBlockSize(C, 1));
2033:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
2034:   for (i = 0; i < pn; i++) {
2035:     row  = i + rstart;
2036:     nnz  = bi[i + 1] - bi[i];
2037:     Jptr = bj + bi[i];
2038:     PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
2039:   }
2040:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
2041:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
2042:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
2043:   merge->bi        = bi;
2044:   merge->bj        = bj;
2045:   merge->coi       = coi;
2046:   merge->coj       = coj;
2047:   merge->buf_ri    = buf_ri;
2048:   merge->buf_rj    = buf_rj;
2049:   merge->owners_co = owners_co;

2051:   /* attach the supporting struct to C for reuse */
2052:   C->product->data    = ap;
2053:   C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2054:   ap->merge           = merge;

2056:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

2058: #if defined(PETSC_USE_INFO)
2059:   if (bi[pn] != 0) {
2060:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
2061:     PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
2062:   } else {
2063:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
2064:   }
2065: #endif
2066:   PetscFunctionReturn(PETSC_SUCCESS);
2067: }

2069: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
2070: {
2071:   Mat_Product *product = C->product;
2072:   Mat          A = product->A, B = product->B;
2073:   PetscReal    fill = product->fill;
2074:   PetscBool    flg;

2076:   PetscFunctionBegin;
2077:   /* scalable */
2078:   PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
2079:   if (flg) {
2080:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
2081:     goto next;
2082:   }

2084:   /* nonscalable */
2085:   PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
2086:   if (flg) {
2087:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
2088:     goto next;
2089:   }

2091:   /* matmatmult */
2092:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
2093:   if (flg) {
2094:     Mat        At;
2095:     Mat_APMPI *ptap;

2097:     PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
2098:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
2099:     ptap = (Mat_APMPI *)C->product->data;
2100:     if (ptap) {
2101:       ptap->Pt            = At;
2102:       C->product->destroy = MatDestroy_MPIAIJ_PtAP;
2103:     }
2104:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
2105:     goto next;
2106:   }

2108:   /* backend general code */
2109:   PetscCall(PetscStrcmp(product->alg, "backend", &flg));
2110:   if (flg) {
2111:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
2112:     PetscFunctionReturn(PETSC_SUCCESS);
2113:   }

2115:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");

2117: next:
2118:   C->ops->productnumeric = MatProductNumeric_AtB;
2119:   PetscFunctionReturn(PETSC_SUCCESS);
2120: }

2122: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
2123: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
2124: {
2125:   Mat_Product *product = C->product;
2126:   Mat          A = product->A, B = product->B;
2127: #if defined(PETSC_HAVE_HYPRE)
2128:   const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
2129:   PetscInt    nalg        = 5;
2130: #else
2131:   const char *algTypes[4] = {
2132:     "scalable",
2133:     "nonscalable",
2134:     "seqmpi",
2135:     "backend",
2136:   };
2137:   PetscInt nalg = 4;
2138: #endif
2139:   PetscInt  alg = 1; /* set nonscalable algorithm as default */
2140:   PetscBool flg;
2141:   MPI_Comm  comm;

2143:   PetscFunctionBegin;
2144:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));

2146:   /* Set "nonscalable" as default algorithm */
2147:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2148:   if (flg) {
2149:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2151:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2152:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2153:       MatInfo   Ainfo, Binfo;
2154:       PetscInt  nz_local;
2155:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2157:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2158:       PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2159:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2161:       if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2162:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2164:       if (alg_scalable) {
2165:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2166:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2167:         PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2168:       }
2169:     }
2170:   }

2172:   /* Get runtime option */
2173:   if (product->api_user) {
2174:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
2175:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2176:     PetscOptionsEnd();
2177:   } else {
2178:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
2179:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2180:     PetscOptionsEnd();
2181:   }
2182:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2184:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
2185:   PetscFunctionReturn(PETSC_SUCCESS);
2186: }

2188: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
2189: {
2190:   PetscFunctionBegin;
2191:   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2192:   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
2193:   PetscFunctionReturn(PETSC_SUCCESS);
2194: }

2196: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
2197: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
2198: {
2199:   Mat_Product *product = C->product;
2200:   Mat          A = product->A, B = product->B;
2201:   const char  *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
2202:   PetscInt     nalg        = 4;
2203:   PetscInt     alg         = 1; /* set default algorithm  */
2204:   PetscBool    flg;
2205:   MPI_Comm     comm;

2207:   PetscFunctionBegin;
2208:   /* Check matrix local sizes */
2209:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2210:   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 ")",
2211:              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

2213:   /* Set default algorithm */
2214:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2215:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2217:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2218:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
2219:     MatInfo   Ainfo, Binfo;
2220:     PetscInt  nz_local;
2221:     PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2223:     PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2224:     PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
2225:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

2227:     if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2228:     PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2230:     if (alg_scalable) {
2231:       alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2232:       PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2233:       PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
2234:     }
2235:   }

2237:   /* Get runtime option */
2238:   if (product->api_user) {
2239:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
2240:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2241:     PetscOptionsEnd();
2242:   } else {
2243:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
2244:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2245:     PetscOptionsEnd();
2246:   }
2247:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2249:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
2250:   PetscFunctionReturn(PETSC_SUCCESS);
2251: }

2253: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
2254: {
2255:   Mat_Product *product = C->product;
2256:   Mat          A = product->A, P = product->B;
2257:   MPI_Comm     comm;
2258:   PetscBool    flg;
2259:   PetscInt     alg = 1; /* set default algorithm */
2260: #if !defined(PETSC_HAVE_HYPRE)
2261:   const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
2262:   PetscInt    nalg        = 5;
2263: #else
2264:   const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
2265:   PetscInt    nalg        = 6;
2266: #endif
2267:   PetscInt pN = P->cmap->N;

2269:   PetscFunctionBegin;
2270:   /* Check matrix local sizes */
2271:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
2272:   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 ")",
2273:              A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
2274:   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 ")",
2275:              A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);

2277:   /* Set "nonscalable" as default algorithm */
2278:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2279:   if (flg) {
2280:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2282:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
2283:     if (pN > 100000) {
2284:       MatInfo   Ainfo, Pinfo;
2285:       PetscInt  nz_local;
2286:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

2288:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
2289:       PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
2290:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

2292:       if (pN > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
2293:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

2295:       if (alg_scalable) {
2296:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
2297:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
2298:       }
2299:     }
2300:   }

2302:   /* Get runtime option */
2303:   if (product->api_user) {
2304:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
2305:     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2306:     PetscOptionsEnd();
2307:   } else {
2308:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
2309:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
2310:     PetscOptionsEnd();
2311:   }
2312:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2314:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
2315:   PetscFunctionReturn(PETSC_SUCCESS);
2316: }

2318: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
2319: {
2320:   Mat_Product *product = C->product;
2321:   Mat          A = product->A, R = product->B;

2323:   PetscFunctionBegin;
2324:   /* Check matrix local sizes */
2325:   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,
2326:              A->rmap->n, R->rmap->n, R->cmap->n);

2328:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
2329:   PetscFunctionReturn(PETSC_SUCCESS);
2330: }

2332: /*
2333:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
2334: */
2335: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
2336: {
2337:   Mat_Product *product     = C->product;
2338:   PetscBool    flg         = PETSC_FALSE;
2339:   PetscInt     alg         = 1; /* default algorithm */
2340:   const char  *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
2341:   PetscInt     nalg        = 3;

2343:   PetscFunctionBegin;
2344:   /* Set default algorithm */
2345:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
2346:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2348:   /* Get runtime option */
2349:   if (product->api_user) {
2350:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
2351:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
2352:     PetscOptionsEnd();
2353:   } else {
2354:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
2355:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
2356:     PetscOptionsEnd();
2357:   }
2358:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

2360:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
2361:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
2362:   PetscFunctionReturn(PETSC_SUCCESS);
2363: }

2365: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
2366: {
2367:   Mat_Product *product = C->product;

2369:   PetscFunctionBegin;
2370:   switch (product->type) {
2371:   case MATPRODUCT_AB:
2372:     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
2373:     break;
2374:   case MATPRODUCT_ABt:
2375:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
2376:     break;
2377:   case MATPRODUCT_AtB:
2378:     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
2379:     break;
2380:   case MATPRODUCT_PtAP:
2381:     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
2382:     break;
2383:   case MATPRODUCT_RARt:
2384:     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
2385:     break;
2386:   case MATPRODUCT_ABC:
2387:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
2388:     break;
2389:   default:
2390:     break;
2391:   }
2392:   PetscFunctionReturn(PETSC_SUCCESS);
2393: }