Date: 2026-03-01T05:24:56+00:00

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: }