Date: 2026-07-30T21:14:12+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 MatProductCtxDestroy_MPIAIJ_MatMatMult(PetscCtxRt data)
     77: {
     78:   MatProductCtx_APMPI *ptap = *(MatProductCtx_APMPI **)data;

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

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

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

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

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

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

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

    139:   api = ptap->api;
    140:   apj = ptap->apj;
    141:   /* trigger copy to CPU */
    142:   PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy1));
    143:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy2));
    144:   PetscCall(MatSeqAIJGetArrayRead(ptap->P_loc, &dummy3));
    145:   if (ptap->P_oth) PetscCall(MatSeqAIJGetArrayRead(ptap->P_oth, &dummy4));
    146:   PetscCall(MatSeqAIJGetArrayWrite(c->A, &cda));
    147:   PetscCall(MatSeqAIJGetArrayWrite(c->B, &coa));
    148:   for (i = 0; i < cm; i++) {
    149:     /* compute apa = A[i,:]*P */
    150:     AProw_nonscalable(i, ad, ao, p_loc, p_oth, apa);

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    349:   PetscFunctionBegin;
    350:   if (A->cmap->rstart != B->rmap->rstart || A->cmap->rend != B->rmap->rend)
    351:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);

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

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

    363:   PetscFunctionBegin;
    364:   if (A->rmap->rstart != B->rmap->rstart || A->rmap->rend != B->rmap->rend)
    365:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")", A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

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

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

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

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

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

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

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

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

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

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

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

    455:   /* Enable runtime option for Bbn */
    456:   PetscOptionsBegin(comm, ((PetscObject)C)->prefix, "MatProduct", "Mat");
    457:   PetscCall(PetscOptionsDeprecated("-matmatmult_Bbn", "-matproduct_batch_size", "3.25", NULL));
    458:   PetscCall(PetscOptionsInt("-matproduct_batch_size", "Number of columns in Bb", "MatProduct", Bbn, &Bbn, NULL));
    459:   PetscOptionsEnd();
    460:   Bbn = PetscMin(Bbn, BN);

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

    467:   if (numBb) {
    468:     PetscCall(PetscInfo(C, "use Bb, BN=%" PetscInt_FMT ", Bbn=%" PetscInt_FMT "; numBb=%" PetscInt_FMT "\n", BN, Bbn, numBb));
    469:     if (Bbn1) { /* Create workB1 for the remaining columns */
    470:       PetscCall(PetscInfo(C, "use Bb1, BN=%" PetscInt_FMT ", Bbn1=%" PetscInt_FMT "\n", BN, Bbn1));
    471:       /* Create work matrix used to store off processor rows of B needed for local product */
    472:       PetscCall(MatCreateSeqDense(PETSC_COMM_SELF, nz, Bbn1, NULL, &contents->workB1));
    473:     } else contents->workB1 = NULL;
    474:   }

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

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

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

    488:   PetscCall(PetscMalloc1(Bm, &disp));
    489:   for (PetscMPIInt i = 0; i < nsends; i++) {
    490:     PetscCall(PetscMPIIntCast(sstarts[i + 1] - sstarts[i], &nrows_to));
    491:     for (PetscInt j = 0; j < nrows_to; j++) PetscCall(PetscMPIIntCast(sindices[sstarts[i] + j], &disp[j])); /* rowB to be sent */
    492:     PetscCallMPI(MPI_Type_create_indexed_block(nrows_to, 1, disp, MPIU_SCALAR, &type1));
    493:     PetscCallMPI(MPI_Type_create_resized(type1, 0, blda * sizeof(PetscScalar), &stype[i]));
    494:     PetscCallMPI(MPI_Type_commit(&stype[i]));
    495:     PetscCallMPI(MPI_Type_free(&type1));
    496:   }

    498:   for (PetscMPIInt i = 0; i < nrecvs; i++) {
    499:     /* received values from a process form a (nrows_from x Bbn) row block in workB (column-wise) */
    500:     PetscCall(PetscMPIIntCast(rstarts[i + 1] - rstarts[i], &nrows_from));
    501:     disp[0] = 0;
    502:     PetscCallMPI(MPI_Type_create_indexed_block(1, nrows_from, disp, MPIU_SCALAR, &type1));
    503:     PetscCallMPI(MPI_Type_create_resized(type1, 0, nz * sizeof(PetscScalar), &rtype[i]));
    504:     PetscCallMPI(MPI_Type_commit(&rtype[i]));
    505:     PetscCallMPI(MPI_Type_free(&type1));
    506:   }

    508:   PetscCall(PetscFree(disp));
    509:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, NULL, NULL));
    510:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, NULL, NULL));
    511:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    512:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    513:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    514:   PetscCall(MatProductClear(aij->A));
    515:   PetscCall(MatProductClear(((Mat_MPIDense *)B->data)->A));
    516:   PetscCall(MatProductClear(((Mat_MPIDense *)C->data)->A));
    517:   PetscCall(MatProductCreateWithMat(aij->A, ((Mat_MPIDense *)B->data)->A, NULL, ((Mat_MPIDense *)C->data)->A));
    518:   PetscCall(MatProductSetType(((Mat_MPIDense *)C->data)->A, MATPRODUCT_AB));
    519:   PetscCall(MatProductSetFromOptions(((Mat_MPIDense *)C->data)->A));
    520:   PetscCall(MatProductSymbolic(((Mat_MPIDense *)C->data)->A));
    521:   C->product->data       = contents;
    522:   C->product->destroy    = MatMPIAIJ_MPIDenseDestroy;
    523:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIDense;
    524:   PetscFunctionReturn(PETSC_SUCCESS);
    525: }

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

    529: /*
    530:     Performs an efficient scatter on the rows of B needed by this process; this is
    531:     a modification of the VecScatterBegin_() routines.

    533:     Input: If Bbidx = 0, uses B = Bb, else B = Bb1, see MatMatMultSymbolic_MPIAIJ_MPIDense()
    534: */

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

    553:   PetscFunctionBegin;
    554:   MatCheckProduct(C, 4);
    555:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
    556:   PetscCall(PetscMPIIntCast(B->cmap->N, &ncols));
    557:   PetscCall(PetscMPIIntCast(aij->B->cmap->n, &nrows));
    558:   contents = (MPIAIJ_MPIDense *)C->product->data;
    559:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL /*bs*/));
    560:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL /*bs*/));
    561:   PetscCall(PetscMPIIntCast(nsends, &nsends_mpi));
    562:   PetscCall(PetscMPIIntCast(nrecvs, &nrecvs_mpi));
    563:   if (Bbidx == 0) workB = *outworkB = contents->workB;
    564:   else workB = *outworkB = contents->workB1;
    565:   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);
    566:   swaits = contents->swaits;
    567:   rwaits = contents->rwaits;

    569:   PetscCall(MatDenseGetArrayRead(B, &b));
    570:   PetscCall(MatDenseGetLDA(B, &blda));
    571:   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);
    572:   PetscCall(MatDenseGetArray(workB, &rvalues));

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

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

    582:   if (nrecvs) PetscCallMPI(MPI_Waitall(nrecvs_mpi, rwaits, MPI_STATUSES_IGNORE));
    583:   if (nsends) PetscCallMPI(MPI_Waitall(nsends_mpi, swaits, MPI_STATUSES_IGNORE));

    585:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &sindices, &sprocs, NULL));
    586:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL, &rprocs, NULL));
    587:   PetscCall(MatDenseRestoreArrayRead(B, &b));
    588:   PetscCall(MatDenseRestoreArray(workB, &rvalues));
    589:   PetscFunctionReturn(PETSC_SUCCESS);
    590: }

    592: static PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIDense(Mat A, Mat B, Mat C)
    593: {
    594:   Mat_MPIAIJ      *aij    = (Mat_MPIAIJ *)A->data;
    595:   Mat_MPIDense    *bdense = (Mat_MPIDense *)B->data;
    596:   Mat_MPIDense    *cdense = (Mat_MPIDense *)C->data;
    597:   Mat              workB;
    598:   MPIAIJ_MPIDense *contents;

    600:   PetscFunctionBegin;
    601:   MatCheckProduct(C, 3);
    602:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
    603:   contents = (MPIAIJ_MPIDense *)C->product->data;
    604:   /* diagonal block of A times all local rows of B, first make sure that everything is up-to-date */
    605:   if (!cdense->A->product) {
    606:     PetscCall(MatProductCreateWithMat(aij->A, bdense->A, NULL, cdense->A));
    607:     PetscCall(MatProductSetType(cdense->A, MATPRODUCT_AB));
    608:     PetscCall(MatProductSetFromOptions(cdense->A));
    609:     PetscCall(MatProductSymbolic(cdense->A));
    610:   } else PetscCall(MatProductReplaceMats(aij->A, bdense->A, NULL, cdense->A));
    611:   if (PetscDefined(HAVE_CUPM) && !cdense->A->product->clear) {
    612:     PetscBool flg;

    614:     PetscCall(PetscObjectTypeCompare((PetscObject)C, MATMPIDENSE, &flg));
    615:     if (flg) PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &flg));
    616:     if (!flg) cdense->A->product->clear = PETSC_TRUE; /* if either A or C is a device Mat, make sure MatProductClear() is called */
    617:   }
    618:   PetscCall(MatProductNumeric(cdense->A));
    619:   if (contents->workB->cmap->n == B->cmap->N) {
    620:     /* get off processor parts of B needed to complete C=A*B */
    621:     PetscCall(MatMPIDenseScatter(A, B, 0, C, &workB));

    623:     /* off-diagonal block of A times nonlocal rows of B */
    624:     PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
    625:   } else {
    626:     Mat       Bb, Cb;
    627:     PetscInt  BN = B->cmap->N, n = contents->workB->cmap->n;
    628:     PetscBool ccpu;

    630:     PetscCheck(n > 0, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Column block size %" PetscInt_FMT " must be positive", n);
    631:     /* Prevent from unneeded copies back and forth from the GPU
    632:        when getting and restoring the submatrix
    633:        We need a proper GPU code for AIJ * dense in parallel */
    634:     PetscCall(MatBoundToCPU(C, &ccpu));
    635:     PetscCall(MatBindToCPU(C, PETSC_TRUE));
    636:     for (PetscInt i = 0; i < BN; i += n) {
    637:       PetscCall(MatDenseGetSubMatrix(B, PETSC_DECIDE, PETSC_DECIDE, i, PetscMin(i + n, BN), &Bb));
    638:       PetscCall(MatDenseGetSubMatrix(C, PETSC_DECIDE, PETSC_DECIDE, i, PetscMin(i + n, BN), &Cb));

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

    643:       /* off-diagonal block of A times nonlocal rows of B */
    644:       cdense = (Mat_MPIDense *)Cb->data;
    645:       PetscCall(MatMatMultNumericAdd_SeqAIJ_SeqDense(aij->B, workB, cdense->A, PETSC_TRUE));
    646:       PetscCall(MatDenseRestoreSubMatrix(B, &Bb));
    647:       PetscCall(MatDenseRestoreSubMatrix(C, &Cb));
    648:     }
    649:     PetscCall(MatBindToCPU(C, ccpu));
    650:   }
    651:   PetscFunctionReturn(PETSC_SUCCESS);
    652: }

    654: PetscErrorCode MatMatMultNumeric_MPIAIJ_MPIAIJ(Mat A, Mat P, Mat C)
    655: {
    656:   Mat_MPIAIJ          *a = (Mat_MPIAIJ *)A->data, *c = (Mat_MPIAIJ *)C->data;
    657:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data;
    658:   Mat_SeqAIJ          *cd = (Mat_SeqAIJ *)c->A->data, *co = (Mat_SeqAIJ *)c->B->data;
    659:   PetscInt            *adi = ad->i, *adj, *aoi = ao->i, *aoj;
    660:   PetscScalar         *ada, *aoa, *cda = cd->a, *coa = co->a;
    661:   Mat_SeqAIJ          *p_loc, *p_oth;
    662:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *pj;
    663:   PetscScalar         *pa_loc, *pa_oth, *pa, valtmp, *ca;
    664:   PetscInt             cm = C->rmap->n, anz, pnz;
    665:   MatProductCtx_APMPI *ptap;
    666:   PetscScalar         *apa_sparse;
    667:   const PetscScalar   *dummy;
    668:   PetscInt            *api, *apj, *apJ, i, j, k, row;
    669:   PetscInt             cstart = C->cmap->rstart;
    670:   PetscInt             cdnz, conz, k0, k1, nextp;
    671:   MPI_Comm             comm;
    672:   PetscMPIInt          size;

    674:   PetscFunctionBegin;
    675:   MatCheckProduct(C, 3);
    676:   ptap = (MatProductCtx_APMPI *)C->product->data;
    677:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
    678:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
    679:   PetscCallMPI(MPI_Comm_size(comm, &size));
    680:   PetscCheck(ptap->P_oth || size <= 1, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "AP cannot be reused. Do not call MatProductClear()");

    682:   /* flag CPU mask for C */
    683: #if defined(PETSC_HAVE_DEVICE)
    684:   if (C->offloadmask != PETSC_OFFLOAD_UNALLOCATED) C->offloadmask = PETSC_OFFLOAD_CPU;
    685:   if (c->A->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->A->offloadmask = PETSC_OFFLOAD_CPU;
    686:   if (c->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) c->B->offloadmask = PETSC_OFFLOAD_CPU;
    687: #endif
    688:   apa_sparse = ptap->apa;

    690:   /* 1) get P_oth = ptap->P_oth  and P_loc = ptap->P_loc */
    691:   /* update numerical values of P_oth and P_loc */
    692:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_REUSE_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));
    693:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_REUSE_MATRIX, &ptap->P_loc));

    695:   /* 2) compute numeric C_loc = A_loc*P = Ad*P_loc + Ao*P_oth */
    696:   /* get data from symbolic products */
    697:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
    698:   pi_loc = p_loc->i;
    699:   pj_loc = p_loc->j;
    700:   pa_loc = p_loc->a;
    701:   if (size > 1) {
    702:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
    703:     pi_oth = p_oth->i;
    704:     pj_oth = p_oth->j;
    705:     pa_oth = p_oth->a;
    706:   } else {
    707:     p_oth  = NULL;
    708:     pi_oth = NULL;
    709:     pj_oth = NULL;
    710:     pa_oth = NULL;
    711:   }

    713:   /* trigger copy to CPU */
    714:   PetscCall(MatSeqAIJGetArrayRead(a->A, &dummy));
    715:   PetscCall(MatSeqAIJRestoreArrayRead(a->A, &dummy));
    716:   PetscCall(MatSeqAIJGetArrayRead(a->B, &dummy));
    717:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &dummy));
    718:   api = ptap->api;
    719:   apj = ptap->apj;
    720:   for (i = 0; i < cm; i++) {
    721:     apJ = apj + api[i];

    723:     /* diagonal portion of A */
    724:     anz = adi[i + 1] - adi[i];
    725:     adj = ad->j + adi[i];
    726:     ada = ad->a + adi[i];
    727:     for (j = 0; j < anz; j++) {
    728:       row = adj[j];
    729:       pnz = pi_loc[row + 1] - pi_loc[row];
    730:       pj  = pj_loc + pi_loc[row];
    731:       pa  = pa_loc + pi_loc[row];
    732:       /* perform sparse axpy */
    733:       valtmp = ada[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:     /* off-diagonal portion of A */
    744:     anz = aoi[i + 1] - aoi[i];
    745:     aoj = PetscSafePointerPlusOffset(ao->j, aoi[i]);
    746:     aoa = PetscSafePointerPlusOffset(ao->a, aoi[i]);
    747:     for (j = 0; j < anz; j++) {
    748:       row = aoj[j];
    749:       pnz = pi_oth[row + 1] - pi_oth[row];
    750:       pj  = pj_oth + pi_oth[row];
    751:       pa  = pa_oth + pi_oth[row];
    752:       /* perform sparse axpy */
    753:       valtmp = aoa[j];
    754:       nextp  = 0;
    755:       for (k = 0; nextp < pnz; k++) {
    756:         if (apJ[k] == pj[nextp]) { /* column of AP == column of P */
    757:           apa_sparse[k] += valtmp * pa[nextp++];
    758:         }
    759:       }
    760:       PetscCall(PetscLogFlops(2.0 * pnz));
    761:     }

    763:     /* set values in C */
    764:     cdnz = cd->i[i + 1] - cd->i[i];
    765:     conz = co->i[i + 1] - co->i[i];

    767:     /* 1st off-diagonal part of C */
    768:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
    769:     k  = 0;
    770:     for (k0 = 0; k0 < conz; k0++) {
    771:       if (apJ[k] >= cstart) break;
    772:       ca[k0]        = apa_sparse[k];
    773:       apa_sparse[k] = 0.0;
    774:       k++;
    775:     }

    777:     /* diagonal part of C */
    778:     ca = cda + cd->i[i];
    779:     for (k1 = 0; k1 < cdnz; k1++) {
    780:       ca[k1]        = apa_sparse[k];
    781:       apa_sparse[k] = 0.0;
    782:       k++;
    783:     }

    785:     /* 2nd off-diagonal part of C */
    786:     ca = PetscSafePointerPlusOffset(coa, co->i[i]);
    787:     for (; k0 < conz; k0++) {
    788:       ca[k0]        = apa_sparse[k];
    789:       apa_sparse[k] = 0.0;
    790:       k++;
    791:     }
    792:   }
    793:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    794:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    795:   PetscFunctionReturn(PETSC_SUCCESS);
    796: }

    798: /* same as MatMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(), except using LLCondensed to avoid O(BN) memory requirement */
    799: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ(Mat A, Mat P, PetscReal fill, Mat C)
    800: {
    801:   MPI_Comm             comm;
    802:   PetscMPIInt          size;
    803:   MatProductCtx_APMPI *ptap;
    804:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
    805:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
    806:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc, *p_oth;
    807:   PetscInt            *pi_loc, *pj_loc, *pi_oth, *pj_oth, *dnz, *onz;
    808:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, *aoj = ao->j, rstart = A->rmap->rstart;
    809:   PetscInt             i, pnz, row, *api, *apj, *Jptr, apnz, nspacedouble = 0, j, nzi, *lnk, apnz_max = 1;
    810:   PetscInt             am = A->rmap->n, pn = P->cmap->n, pm = P->rmap->n, lsize = pn + 20;
    811:   PetscReal            afill;
    812:   MatType              mtype;

    814:   PetscFunctionBegin;
    815:   MatCheckProduct(C, 4);
    816:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
    817:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    818:   PetscCallMPI(MPI_Comm_size(comm, &size));

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

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

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

    829:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
    830:   pi_loc = p_loc->i;
    831:   pj_loc = p_loc->j;
    832:   if (size > 1) {
    833:     p_oth  = (Mat_SeqAIJ *)ptap->P_oth->data;
    834:     pi_oth = p_oth->i;
    835:     pj_oth = p_oth->j;
    836:   } else {
    837:     p_oth  = NULL;
    838:     pi_oth = NULL;
    839:     pj_oth = NULL;
    840:   }

    842:   /* first, compute symbolic AP = A_loc*P = A_diag*P_loc + A_off*P_oth */
    843:   PetscCall(PetscMalloc1(am + 1, &api));
    844:   ptap->api = api;
    845:   api[0]    = 0;

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

    849:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    850:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space));
    851:   current_space = free_space;
    852:   MatPreallocateBegin(comm, am, pn, dnz, onz);
    853:   for (i = 0; i < am; i++) {
    854:     /* diagonal portion of A */
    855:     nzi = adi[i + 1] - adi[i];
    856:     for (j = 0; j < nzi; j++) {
    857:       row  = *adj++;
    858:       pnz  = pi_loc[row + 1] - pi_loc[row];
    859:       Jptr = pj_loc + pi_loc[row];
    860:       /* Expand list if it is not long enough */
    861:       if (pnz + apnz_max > lsize) {
    862:         lsize = pnz + apnz_max;
    863:         PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
    864:       }
    865:       /* add non-zero cols of P into the sorted linked list lnk */
    866:       PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
    867:       apnz       = *lnk; /* The first element in the list is the number of items in the list */
    868:       api[i + 1] = api[i] + apnz;
    869:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
    870:     }
    871:     /* off-diagonal portion of A */
    872:     nzi = aoi[i + 1] - aoi[i];
    873:     for (j = 0; j < nzi; j++) {
    874:       row  = *aoj++;
    875:       pnz  = pi_oth[row + 1] - pi_oth[row];
    876:       Jptr = pj_oth + pi_oth[row];
    877:       /* Expand list if it is not long enough */
    878:       if (pnz + apnz_max > lsize) {
    879:         lsize = pnz + apnz_max;
    880:         PetscCall(PetscLLCondensedExpand_Scalable(lsize, &lnk));
    881:       }
    882:       /* add non-zero cols of P into the sorted linked list lnk */
    883:       PetscCall(PetscLLCondensedAddSorted_Scalable(pnz, Jptr, lnk));
    884:       apnz       = *lnk; /* The first element in the list is the number of items in the list */
    885:       api[i + 1] = api[i] + apnz;
    886:       if (apnz > apnz_max) apnz_max = apnz + 1; /* '1' for diagonal entry */
    887:     }

    889:     /* add missing diagonal entry */
    890:     if (C->force_diagonals) {
    891:       j = i + rstart; /* column index */
    892:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &j, lnk));
    893:     }

    895:     apnz       = *lnk;
    896:     api[i + 1] = api[i] + apnz;
    897:     if (apnz > apnz_max) apnz_max = apnz;

    899:     /* if free space is not available, double the total space in the list */
    900:     if (current_space->local_remaining < apnz) {
    901:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(apnz, current_space->total_array_size), &current_space));
    902:       nspacedouble++;
    903:     }

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

    909:     current_space->array += apnz;
    910:     current_space->local_used += apnz;
    911:     current_space->local_remaining -= apnz;
    912:   }

    914:   /* Allocate space for apj, initialize apj, and */
    915:   /* destroy list of free space and other temporary array(s) */
    916:   PetscCall(PetscMalloc1(api[am], &ptap->apj));
    917:   apj = ptap->apj;
    918:   PetscCall(PetscFreeSpaceContiguous(&free_space, ptap->apj));
    919:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));

    921:   /* create and assemble symbolic parallel matrix C */
    922:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
    923:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
    924:   PetscCall(MatGetType(A, &mtype));
    925:   PetscCall(MatSetType(C, mtype));
    926:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
    927:   MatPreallocateEnd(dnz, onz);

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

    932:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
    933:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    934:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    935:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    936:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

    938:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ;
    939:   C->ops->productnumeric = MatProductNumeric_AB;

    941:   /* attach the supporting struct to C for reuse */
    942:   C->product->data    = ptap;
    943:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

    945:   /* set MatInfo */
    946:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
    947:   if (afill < 1.0) afill = 1.0;
    948:   C->info.mallocs           = nspacedouble;
    949:   C->info.fill_ratio_given  = fill;
    950:   C->info.fill_ratio_needed = afill;

    952: #if defined(PETSC_USE_INFO)
    953:   if (api[am]) {
    954:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
    955:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
    956:   } else {
    957:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
    958:   }
    959: #endif
    960:   PetscFunctionReturn(PETSC_SUCCESS);
    961: }

    963: /* This function is needed for the seqMPI matrix-matrix multiplication.  */
    964: /* Three input arrays are merged to one output array. The size of the    */
    965: /* output array is also output. Duplicate entries only show up once.     */
    966: static void Merge3SortedArrays(PetscInt size1, PetscInt *in1, PetscInt size2, PetscInt *in2, PetscInt size3, PetscInt *in3, PetscInt *size4, PetscInt *out)
    967: {
    968:   int i = 0, j = 0, k = 0, l = 0;

    970:   /* Traverse all three arrays */
    971:   while (i < size1 && j < size2 && k < size3) {
    972:     if (in1[i] < in2[j] && in1[i] < in3[k]) {
    973:       out[l++] = in1[i++];
    974:     } else if (in2[j] < in1[i] && in2[j] < in3[k]) {
    975:       out[l++] = in2[j++];
    976:     } else if (in3[k] < in1[i] && in3[k] < in2[j]) {
    977:       out[l++] = in3[k++];
    978:     } else if (in1[i] == in2[j] && in1[i] < in3[k]) {
    979:       out[l++] = in1[i];
    980:       i++, j++;
    981:     } else if (in1[i] == in3[k] && in1[i] < in2[j]) {
    982:       out[l++] = in1[i];
    983:       i++, k++;
    984:     } else if (in3[k] == in2[j] && in2[j] < in1[i]) {
    985:       out[l++] = in2[j];
    986:       k++, j++;
    987:     } else if (in1[i] == in2[j] && in1[i] == in3[k]) {
    988:       out[l++] = in1[i];
    989:       i++, j++, k++;
    990:     }
    991:   }

    993:   /* Traverse two remaining arrays */
    994:   while (i < size1 && j < size2) {
    995:     if (in1[i] < in2[j]) {
    996:       out[l++] = in1[i++];
    997:     } else if (in1[i] > in2[j]) {
    998:       out[l++] = in2[j++];
    999:     } else {
    1000:       out[l++] = in1[i];
    1001:       i++, j++;
    1002:     }
    1003:   }

    1005:   while (i < size1 && k < size3) {
    1006:     if (in1[i] < in3[k]) {
    1007:       out[l++] = in1[i++];
    1008:     } else if (in1[i] > in3[k]) {
    1009:       out[l++] = in3[k++];
    1010:     } else {
    1011:       out[l++] = in1[i];
    1012:       i++, k++;
    1013:     }
    1014:   }

    1016:   while (k < size3 && j < size2) {
    1017:     if (in3[k] < in2[j]) {
    1018:       out[l++] = in3[k++];
    1019:     } else if (in3[k] > in2[j]) {
    1020:       out[l++] = in2[j++];
    1021:     } else {
    1022:       out[l++] = in3[k];
    1023:       k++, j++;
    1024:     }
    1025:   }

    1027:   /* Traverse one remaining array */
    1028:   while (i < size1) out[l++] = in1[i++];
    1029:   while (j < size2) out[l++] = in2[j++];
    1030:   while (k < size3) out[l++] = in3[k++];

    1032:   *size4 = l;
    1033: }

    1035: /* This matrix-matrix multiplication algorithm divides the multiplication into three multiplications and  */
    1036: /* adds up the products. Two of these three multiplications are performed with existing (sequential)      */
    1037: /* matrix-matrix multiplications.  */
    1038: PetscErrorCode MatMatMultSymbolic_MPIAIJ_MPIAIJ_seqMPI(Mat A, Mat P, PetscReal fill, Mat C)
    1039: {
    1040:   MPI_Comm             comm;
    1041:   PetscMPIInt          size;
    1042:   MatProductCtx_APMPI *ptap;
    1043:   PetscFreeSpaceList   free_space_diag = NULL, current_space = NULL;
    1044:   Mat_MPIAIJ          *a  = (Mat_MPIAIJ *)A->data;
    1045:   Mat_SeqAIJ          *ad = (Mat_SeqAIJ *)a->A->data, *ao = (Mat_SeqAIJ *)a->B->data, *p_loc;
    1046:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
    1047:   Mat_SeqAIJ          *adpd_seq, *p_off, *aopoth_seq;
    1048:   PetscInt             adponz, adpdnz;
    1049:   PetscInt            *pi_loc, *dnz, *onz;
    1050:   PetscInt            *adi = ad->i, *adj = ad->j, *aoi = ao->i, rstart = A->rmap->rstart;
    1051:   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;
    1052:   PetscInt             am = A->rmap->n, pN = P->cmap->N, pn = P->cmap->n, pm = P->rmap->n, p_colstart, p_colend;
    1053:   PetscBT              lnkbt;
    1054:   PetscReal            afill;
    1055:   PetscMPIInt          rank;
    1056:   Mat                  adpd, aopoth;
    1057:   MatType              mtype;
    1058:   const char          *prefix;

    1060:   PetscFunctionBegin;
    1061:   MatCheckProduct(C, 4);
    1062:   PetscCheck(!C->product->data, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Extra product struct not empty");
    1063:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    1064:   PetscCallMPI(MPI_Comm_size(comm, &size));
    1065:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    1066:   PetscCall(MatGetOwnershipRangeColumn(P, &p_colstart, &p_colend));

    1068:   /* create struct MatProductCtx_APMPI and attached it to C later */
    1069:   PetscCall(PetscNew(&ptap));

    1071:   /* get P_oth by taking rows of P (= non-zero cols of local A) from other processors */
    1072:   PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &ptap->startsj_s, &ptap->startsj_r, &ptap->bufa, &ptap->P_oth));

    1074:   /* get P_loc by taking all local rows of P */
    1075:   PetscCall(MatMPIAIJGetLocalMat(P, MAT_INITIAL_MATRIX, &ptap->P_loc));

    1077:   p_loc  = (Mat_SeqAIJ *)ptap->P_loc->data;
    1078:   pi_loc = p_loc->i;

    1080:   /* Allocate memory for the i arrays of the matrices A*P, A_diag*P_off and A_offd * P */
    1081:   PetscCall(PetscMalloc1(am + 1, &api));
    1082:   PetscCall(PetscMalloc1(am + 1, &adpoi));

    1084:   adpoi[0]  = 0;
    1085:   ptap->api = api;
    1086:   api[0]    = 0;

    1088:   /* create and initialize a linked list, will be used for both A_diag * P_loc_off and A_offd * P_oth */
    1089:   PetscCall(PetscLLCondensedCreate(pN, pN, &lnk, &lnkbt));
    1090:   MatPreallocateBegin(comm, am, pn, dnz, onz);

    1092:   /* Symbolic calc of A_loc_diag * P_loc_diag */
    1093:   PetscCall(MatGetOptionsPrefix(A, &prefix));
    1094:   PetscCall(MatProductCreate(a->A, p->A, NULL, &adpd));
    1095:   PetscCall(MatGetOptionsPrefix(A, &prefix));
    1096:   PetscCall(MatSetOptionsPrefix(adpd, prefix));
    1097:   PetscCall(MatAppendOptionsPrefix(adpd, "inner_diag_"));

    1099:   PetscCall(MatProductSetType(adpd, MATPRODUCT_AB));
    1100:   PetscCall(MatProductSetAlgorithm(adpd, "sorted"));
    1101:   PetscCall(MatProductSetFill(adpd, fill));
    1102:   PetscCall(MatProductSetFromOptions(adpd));

    1104:   adpd->force_diagonals = C->force_diagonals;
    1105:   PetscCall(MatProductSymbolic(adpd));

    1107:   adpd_seq = (Mat_SeqAIJ *)((adpd)->data);
    1108:   adpdi    = adpd_seq->i;
    1109:   adpdj    = adpd_seq->j;
    1110:   p_off    = (Mat_SeqAIJ *)p->B->data;
    1111:   poff_i   = p_off->i;
    1112:   poff_j   = p_off->j;

    1114:   /* j_temp stores indices of a result row before they are added to the linked list */
    1115:   PetscCall(PetscMalloc1(pN, &j_temp));

    1117:   /* Symbolic calc of the A_diag * p_loc_off */
    1118:   /* Initial FreeSpace size is fill*(nnz(A)+nnz(P)) */
    1119:   PetscCall(PetscFreeSpaceGet(PetscRealIntMultTruncate(fill, PetscIntSumTruncate(adi[am], PetscIntSumTruncate(aoi[am], pi_loc[pm]))), &free_space_diag));
    1120:   current_space = free_space_diag;

    1122:   for (i = 0; i < am; i++) {
    1123:     /* A_diag * P_loc_off */
    1124:     nzi = adi[i + 1] - adi[i];
    1125:     for (j = 0; j < nzi; j++) {
    1126:       row  = *adj++;
    1127:       pnz  = poff_i[row + 1] - poff_i[row];
    1128:       Jptr = poff_j + poff_i[row];
    1129:       for (i1 = 0; i1 < pnz; i1++) j_temp[i1] = p->garray[Jptr[i1]];
    1130:       /* add non-zero cols of P into the sorted linked list lnk */
    1131:       PetscCall(PetscLLCondensedAddSorted(pnz, j_temp, lnk, lnkbt));
    1132:     }

    1134:     adponz       = lnk[0];
    1135:     adpoi[i + 1] = adpoi[i] + adponz;

    1137:     /* if free space is not available, double the total space in the list */
    1138:     if (current_space->local_remaining < adponz) {
    1139:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(adponz, current_space->total_array_size), &current_space));
    1140:       nspacedouble++;
    1141:     }

    1143:     /* Copy data into free space, then initialize lnk */
    1144:     PetscCall(PetscLLCondensedClean(pN, adponz, current_space->array, lnk, lnkbt));

    1146:     current_space->array += adponz;
    1147:     current_space->local_used += adponz;
    1148:     current_space->local_remaining -= adponz;
    1149:   }

    1151:   /* Symbolic calc of A_off * P_oth */
    1152:   PetscCall(MatSetOptionsPrefix(a->B, prefix));
    1153:   PetscCall(MatAppendOptionsPrefix(a->B, "inner_offdiag_"));
    1154:   PetscCall(MatCreate(PETSC_COMM_SELF, &aopoth));
    1155:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(a->B, ptap->P_oth, fill, aopoth));
    1156:   aopoth_seq = (Mat_SeqAIJ *)((aopoth)->data);
    1157:   aopothi    = aopoth_seq->i;
    1158:   aopothj    = aopoth_seq->j;

    1160:   /* Allocate space for apj, adpj, aopj, ... */
    1161:   /* destroy lists of free space and other temporary array(s) */

    1163:   PetscCall(PetscMalloc1(aopothi[am] + adpoi[am] + adpdi[am], &ptap->apj));
    1164:   PetscCall(PetscMalloc1(adpoi[am], &adpoj));

    1166:   /* Copy from linked list to j-array */
    1167:   PetscCall(PetscFreeSpaceContiguous(&free_space_diag, adpoj));
    1168:   PetscCall(PetscLLDestroy(lnk, lnkbt));

    1170:   adpoJ = adpoj;
    1171:   adpdJ = adpdj;
    1172:   aopJ  = aopothj;
    1173:   apj   = ptap->apj;
    1174:   apJ   = apj; /* still empty */

    1176:   /* Merge j-arrays of A_off * P, A_diag * P_loc_off, and */
    1177:   /* A_diag * P_loc_diag to get A*P */
    1178:   for (i = 0; i < am; i++) {
    1179:     aopnz  = aopothi[i + 1] - aopothi[i];
    1180:     adponz = adpoi[i + 1] - adpoi[i];
    1181:     adpdnz = adpdi[i + 1] - adpdi[i];

    1183:     /* Correct indices from A_diag*P_diag */
    1184:     for (i1 = 0; i1 < adpdnz; i1++) adpdJ[i1] += p_colstart;
    1185:     /* Merge j-arrays of A_diag * P_loc_off and A_diag * P_loc_diag and A_off * P_oth */
    1186:     Merge3SortedArrays(adponz, adpoJ, adpdnz, adpdJ, aopnz, aopJ, &apnz, apJ);
    1187:     PetscCall(MatPreallocateSet(i + rstart, apnz, apJ, dnz, onz));

    1189:     aopJ += aopnz;
    1190:     adpoJ += adponz;
    1191:     adpdJ += adpdnz;
    1192:     apJ += apnz;
    1193:     api[i + 1] = api[i] + apnz;
    1194:   }

    1196:   /* malloc apa to store dense row A[i,:]*P */
    1197:   PetscCall(PetscCalloc1(pN, &ptap->apa));

    1199:   /* create and assemble symbolic parallel matrix C */
    1200:   PetscCall(MatSetSizes(C, am, pn, PETSC_DETERMINE, PETSC_DETERMINE));
    1201:   PetscCall(MatSetBlockSizesFromMats(C, A, P));
    1202:   PetscCall(MatGetType(A, &mtype));
    1203:   PetscCall(MatSetType(C, mtype));
    1204:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
    1205:   MatPreallocateEnd(dnz, onz);

    1207:   PetscCall(MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(C, apj, api));
    1208:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    1209:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    1210:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    1211:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

    1213:   C->ops->matmultnumeric = MatMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;
    1214:   C->ops->productnumeric = MatProductNumeric_AB;

    1216:   /* attach the supporting struct to C for reuse */
    1217:   C->product->data    = ptap;
    1218:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_MatMatMult;

    1220:   /* set MatInfo */
    1221:   afill = (PetscReal)api[am] / (adi[am] + aoi[am] + pi_loc[pm] + 1) + 1.e-5;
    1222:   if (afill < 1.0) afill = 1.0;
    1223:   C->info.mallocs           = nspacedouble;
    1224:   C->info.fill_ratio_given  = fill;
    1225:   C->info.fill_ratio_needed = afill;

    1227: #if defined(PETSC_USE_INFO)
    1228:   if (api[am]) {
    1229:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
    1230:     PetscCall(PetscInfo(C, "Use MatMatMult(A,B,MatReuse,%g,&C) for best performance.;\n", (double)afill));
    1231:   } else {
    1232:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
    1233:   }
    1234: #endif

    1236:   PetscCall(MatDestroy(&aopoth));
    1237:   PetscCall(MatDestroy(&adpd));
    1238:   PetscCall(PetscFree(j_temp));
    1239:   PetscCall(PetscFree(adpoj));
    1240:   PetscCall(PetscFree(adpoi));
    1241:   PetscFunctionReturn(PETSC_SUCCESS);
    1242: }

    1244: /* This routine only works when scall=MAT_REUSE_MATRIX! */
    1245: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult(Mat P, Mat A, Mat C)
    1246: {
    1247:   MatProductCtx_APMPI *ptap;
    1248:   Mat                  Pt;

    1250:   PetscFunctionBegin;
    1251:   MatCheckProduct(C, 3);
    1252:   ptap = (MatProductCtx_APMPI *)C->product->data;
    1253:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
    1254:   PetscCheck(ptap->Pt, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");

    1256:   Pt = ptap->Pt;
    1257:   PetscCall(MatTransposeSetPrecursor(P, Pt));
    1258:   PetscCall(MatTranspose(P, MAT_REUSE_MATRIX, &Pt));
    1259:   PetscCall(MatMatMultNumeric_MPIAIJ_MPIAIJ(Pt, A, C));
    1260:   PetscFunctionReturn(PETSC_SUCCESS);
    1261: }

    1263: /* This routine is modified from MatPtAPSymbolic_MPIAIJ_MPIAIJ() */
    1264: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, PetscReal fill, Mat C)
    1265: {
    1266:   MatProductCtx_APMPI     *ptap;
    1267:   Mat_MPIAIJ              *p = (Mat_MPIAIJ *)P->data;
    1268:   MPI_Comm                 comm;
    1269:   PetscMPIInt              size, rank;
    1270:   PetscFreeSpaceList       free_space = NULL, current_space = NULL;
    1271:   PetscInt                 pn = P->cmap->n, aN = A->cmap->N, an = A->cmap->n;
    1272:   PetscInt                *lnk, i, k, rstart;
    1273:   PetscBT                  lnkbt;
    1274:   PetscMPIInt              tagi, tagj, *len_si, *len_s, *len_ri, nrecv, proc, nsend;
    1275:   PETSC_UNUSED PetscMPIInt icompleted = 0;
    1276:   PetscInt               **buf_rj, **buf_ri, **buf_ri_k, row, ncols, *cols;
    1277:   PetscInt                 len, *dnz, *onz, *owners, nzi;
    1278:   PetscInt                 nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
    1279:   MPI_Request             *swaits, *rwaits;
    1280:   MPI_Status              *sstatus, rstatus;
    1281:   PetscLayout              rowmap;
    1282:   PetscInt                *owners_co, *coi, *coj; /* i and j array of (p->B)^T*A*P - used in the communication */
    1283:   PetscMPIInt             *len_r, *id_r;          /* array of length of comm->size, store send/recv matrix values */
    1284:   PetscInt                *Jptr, *prmap = p->garray, con, j, Crmax;
    1285:   Mat_SeqAIJ              *a_loc, *c_loc, *c_oth;
    1286:   PetscHMapI               ta;
    1287:   MatType                  mtype;
    1288:   const char              *prefix;

    1290:   PetscFunctionBegin;
    1291:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    1292:   PetscCallMPI(MPI_Comm_size(comm, &size));
    1293:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    1295:   /* create symbolic parallel matrix C */
    1296:   PetscCall(MatGetType(A, &mtype));
    1297:   PetscCall(MatSetType(C, mtype));

    1299:   C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable;

    1301:   /* create struct MatProductCtx_APMPI and attached it to C later */
    1302:   PetscCall(PetscNew(&ptap));

    1304:   /* (0) compute Rd = Pd^T, Ro = Po^T  */
    1305:   PetscCall(MatTranspose(p->A, MAT_INITIAL_MATRIX, &ptap->Rd));
    1306:   PetscCall(MatTranspose(p->B, MAT_INITIAL_MATRIX, &ptap->Ro));

    1308:   /* (1) compute symbolic A_loc */
    1309:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &ptap->A_loc));

    1311:   /* (2-1) compute symbolic C_oth = Ro*A_loc  */
    1312:   PetscCall(MatGetOptionsPrefix(A, &prefix));
    1313:   PetscCall(MatSetOptionsPrefix(ptap->Ro, prefix));
    1314:   PetscCall(MatAppendOptionsPrefix(ptap->Ro, "inner_offdiag_"));
    1315:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_oth));
    1316:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Ro, ptap->A_loc, fill, ptap->C_oth));

    1318:   /* (3) send coj of C_oth to other processors  */
    1319:   /* determine row ownership */
    1320:   PetscCall(PetscLayoutCreate(comm, &rowmap));
    1321:   rowmap->n  = pn;
    1322:   rowmap->bs = 1;
    1323:   PetscCall(PetscLayoutSetUp(rowmap));
    1324:   owners = rowmap->range;

    1326:   /* determine the number of messages to send, their lengths */
    1327:   PetscCall(PetscMalloc4(size, &len_s, size, &len_si, size, &sstatus, size + 1, &owners_co));
    1328:   PetscCall(PetscArrayzero(len_s, size));
    1329:   PetscCall(PetscArrayzero(len_si, size));

    1331:   c_oth = (Mat_SeqAIJ *)ptap->C_oth->data;
    1332:   coi   = c_oth->i;
    1333:   coj   = c_oth->j;
    1334:   con   = ptap->C_oth->rmap->n;
    1335:   proc  = 0;
    1336:   for (i = 0; i < con; i++) {
    1337:     while (prmap[i] >= owners[proc + 1]) proc++;
    1338:     len_si[proc]++;                     /* num of rows in Co(=Pt*A) to be sent to [proc] */
    1339:     len_s[proc] += coi[i + 1] - coi[i]; /* num of nonzeros in Co to be sent to [proc] */
    1340:   }

    1342:   len          = 0; /* max length of buf_si[], see (4) */
    1343:   owners_co[0] = 0;
    1344:   nsend        = 0;
    1345:   for (proc = 0; proc < size; proc++) {
    1346:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
    1347:     if (len_s[proc]) {
    1348:       nsend++;
    1349:       len_si[proc] = 2 * (len_si[proc] + 1); /* length of buf_si to be sent to [proc] */
    1350:       len += len_si[proc];
    1351:     }
    1352:   }

    1354:   /* determine the number and length of messages to receive for coi and coj  */
    1355:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &nrecv));
    1356:   PetscCall(PetscGatherMessageLengths2(comm, nsend, nrecv, len_s, len_si, &id_r, &len_r, &len_ri));

    1358:   /* post the Irecv and Isend of coj */
    1359:   PetscCall(PetscCommGetNewTag(comm, &tagj));
    1360:   PetscCall(PetscPostIrecvInt(comm, tagj, nrecv, id_r, len_r, &buf_rj, &rwaits));
    1361:   PetscCall(PetscMalloc1(nsend, &swaits));
    1362:   for (proc = 0, k = 0; proc < size; proc++) {
    1363:     if (!len_s[proc]) continue;
    1364:     i = owners_co[proc];
    1365:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
    1366:     k++;
    1367:   }

    1369:   /* (2-2) compute symbolic C_loc = Rd*A_loc */
    1370:   PetscCall(MatSetOptionsPrefix(ptap->Rd, prefix));
    1371:   PetscCall(MatAppendOptionsPrefix(ptap->Rd, "inner_diag_"));
    1372:   PetscCall(MatCreate(PETSC_COMM_SELF, &ptap->C_loc));
    1373:   PetscCall(MatMatMultSymbolic_SeqAIJ_SeqAIJ(ptap->Rd, ptap->A_loc, fill, ptap->C_loc));
    1374:   c_loc = (Mat_SeqAIJ *)ptap->C_loc->data;

    1376:   /* receives coj are complete */
    1377:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
    1378:   PetscCall(PetscFree(rwaits));
    1379:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

    1381:   /* add received column indices into ta to update Crmax */
    1382:   a_loc = (Mat_SeqAIJ *)ptap->A_loc->data;

    1384:   /* create and initialize a linked list */
    1385:   PetscCall(PetscHMapICreateWithSize(an, &ta)); /* for compute Crmax */
    1386:   MatRowMergeMax_SeqAIJ(a_loc, ptap->A_loc->rmap->N, ta);

    1388:   for (k = 0; k < nrecv; k++) { /* k-th received message */
    1389:     Jptr = buf_rj[k];
    1390:     for (j = 0; j < len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
    1391:   }
    1392:   PetscCall(PetscHMapIGetSize(ta, &Crmax));
    1393:   PetscCall(PetscHMapIDestroy(&ta));

    1395:   /* (4) send and recv coi */
    1396:   PetscCall(PetscCommGetNewTag(comm, &tagi));
    1397:   PetscCall(PetscPostIrecvInt(comm, tagi, nrecv, id_r, len_ri, &buf_ri, &rwaits));
    1398:   PetscCall(PetscMalloc1(len, &buf_s));
    1399:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
    1400:   for (proc = 0, k = 0; proc < size; proc++) {
    1401:     if (!len_s[proc]) continue;
    1402:     /* form outgoing message for i-structure:
    1403:          buf_si[0]:                 nrows to be sent
    1404:                [1:nrows]:           row index (global)
    1405:                [nrows+1:2*nrows+1]: i-structure index
    1406:     */
    1407:     nrows       = len_si[proc] / 2 - 1; /* num of rows in Co to be sent to [proc] */
    1408:     buf_si_i    = buf_si + nrows + 1;
    1409:     buf_si[0]   = nrows;
    1410:     buf_si_i[0] = 0;
    1411:     nrows       = 0;
    1412:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
    1413:       nzi                 = coi[i + 1] - coi[i];
    1414:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
    1415:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
    1416:       nrows++;
    1417:     }
    1418:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
    1419:     k++;
    1420:     buf_si += len_si[proc];
    1421:   }
    1422:   for (i = 0; i < nrecv; i++) PetscCallMPI(MPI_Waitany(nrecv, rwaits, &icompleted, &rstatus));
    1423:   PetscCall(PetscFree(rwaits));
    1424:   if (nsend) PetscCallMPI(MPI_Waitall(nsend, swaits, sstatus));

    1426:   PetscCall(PetscFree4(len_s, len_si, sstatus, owners_co));
    1427:   PetscCall(PetscFree(len_ri));
    1428:   PetscCall(PetscFree(swaits));
    1429:   PetscCall(PetscFree(buf_s));

    1431:   /* (5) compute the local portion of C      */
    1432:   /* set initial free space to be Crmax, sufficient for holding nonzeros in each row of C */
    1433:   PetscCall(PetscFreeSpaceGet(Crmax, &free_space));
    1434:   current_space = free_space;

    1436:   PetscCall(PetscMalloc3(nrecv, &buf_ri_k, nrecv, &nextrow, nrecv, &nextci));
    1437:   for (k = 0; k < nrecv; k++) {
    1438:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1439:     nrows       = *buf_ri_k[k];
    1440:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    1441:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    1442:   }

    1444:   MatPreallocateBegin(comm, pn, an, dnz, onz);
    1445:   PetscCall(PetscLLCondensedCreate(Crmax, aN, &lnk, &lnkbt));
    1446:   for (i = 0; i < pn; i++) { /* for each local row of C */
    1447:     /* add C_loc into C */
    1448:     nzi  = c_loc->i[i + 1] - c_loc->i[i];
    1449:     Jptr = c_loc->j + c_loc->i[i];
    1450:     PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));

    1452:     /* add received col data into lnk */
    1453:     for (k = 0; k < nrecv; k++) { /* k-th received message */
    1454:       if (i == *nextrow[k]) {     /* i-th row */
    1455:         nzi  = *(nextci[k] + 1) - *nextci[k];
    1456:         Jptr = buf_rj[k] + *nextci[k];
    1457:         PetscCall(PetscLLCondensedAddSorted(nzi, Jptr, lnk, lnkbt));
    1458:         nextrow[k]++;
    1459:         nextci[k]++;
    1460:       }
    1461:     }

    1463:     /* add missing diagonal entry */
    1464:     if (C->force_diagonals) {
    1465:       k = i + owners[rank]; /* column index */
    1466:       PetscCall(PetscLLCondensedAddSorted(1, &k, lnk, lnkbt));
    1467:     }

    1469:     nzi = lnk[0];

    1471:     /* copy data into free space, then initialize lnk */
    1472:     PetscCall(PetscLLCondensedClean(aN, nzi, current_space->array, lnk, lnkbt));
    1473:     PetscCall(MatPreallocateSet(i + owners[rank], nzi, current_space->array, dnz, onz));
    1474:   }
    1475:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
    1476:   PetscCall(PetscLLDestroy(lnk, lnkbt));
    1477:   PetscCall(PetscFreeSpaceDestroy(free_space));

    1479:   /* local sizes and preallocation */
    1480:   PetscCall(MatSetSizes(C, pn, an, PETSC_DETERMINE, PETSC_DETERMINE));
    1481:   PetscCall(PetscLayoutSetBlockSize(C->rmap, P->cmap->bs));
    1482:   PetscCall(PetscLayoutSetBlockSize(C->cmap, A->cmap->bs));
    1483:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
    1484:   MatPreallocateEnd(dnz, onz);

    1486:   /* add C_loc and C_oth to C */
    1487:   PetscCall(MatGetOwnershipRange(C, &rstart, NULL));
    1488:   for (i = 0; i < pn; i++) {
    1489:     ncols = c_loc->i[i + 1] - c_loc->i[i];
    1490:     cols  = c_loc->j + c_loc->i[i];
    1491:     row   = rstart + i;
    1492:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));

    1494:     if (C->force_diagonals) PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, 1, (const PetscInt *)&row, NULL, INSERT_VALUES));
    1495:   }
    1496:   for (i = 0; i < con; i++) {
    1497:     ncols = c_oth->i[i + 1] - c_oth->i[i];
    1498:     cols  = c_oth->j + c_oth->i[i];
    1499:     row   = prmap[i];
    1500:     PetscCall(MatSetValues(C, 1, (const PetscInt *)&row, ncols, (const PetscInt *)cols, NULL, INSERT_VALUES));
    1501:   }
    1502:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    1503:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    1504:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));

    1506:   /* members in merge */
    1507:   PetscCall(PetscFree(id_r));
    1508:   PetscCall(PetscFree(len_r));
    1509:   PetscCall(PetscFree(buf_ri[0]));
    1510:   PetscCall(PetscFree(buf_ri));
    1511:   PetscCall(PetscFree(buf_rj[0]));
    1512:   PetscCall(PetscFree(buf_rj));
    1513:   PetscCall(PetscLayoutDestroy(&rowmap));

    1515:   /* attach the supporting struct to C for reuse */
    1516:   C->product->data    = ptap;
    1517:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
    1518:   PetscFunctionReturn(PETSC_SUCCESS);
    1519: }

    1521: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_nonscalable(Mat P, Mat A, Mat C)
    1522: {
    1523:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data;
    1524:   Mat_SeqAIJ          *c_seq;
    1525:   MatProductCtx_APMPI *ptap;
    1526:   Mat                  A_loc, C_loc, C_oth;
    1527:   PetscInt             i, rstart, rend, cm, ncols, row;
    1528:   const PetscInt      *cols;
    1529:   const PetscScalar   *vals;

    1531:   PetscFunctionBegin;
    1532:   MatCheckProduct(C, 3);
    1533:   ptap = (MatProductCtx_APMPI *)C->product->data;
    1534:   PetscCheck(ptap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtAP cannot be computed. Missing data");
    1535:   PetscCheck(ptap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
    1536:   PetscCall(MatZeroEntries(C));

    1538:   /* These matrices are obtained in MatTransposeMatMultSymbolic() */
    1539:   /* 1) get R = Pd^T, Ro = Po^T */
    1540:   PetscCall(MatTransposeSetPrecursor(p->A, ptap->Rd));
    1541:   PetscCall(MatTranspose(p->A, MAT_REUSE_MATRIX, &ptap->Rd));
    1542:   PetscCall(MatTransposeSetPrecursor(p->B, ptap->Ro));
    1543:   PetscCall(MatTranspose(p->B, MAT_REUSE_MATRIX, &ptap->Ro));

    1545:   /* 2) compute numeric A_loc */
    1546:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &ptap->A_loc));

    1548:   /* 3) C_loc = Rd*A_loc, C_oth = Ro*A_loc */
    1549:   A_loc = ptap->A_loc;
    1550:   PetscCall(ptap->C_loc->ops->matmultnumeric(ptap->Rd, A_loc, ptap->C_loc));
    1551:   PetscCall(ptap->C_oth->ops->matmultnumeric(ptap->Ro, A_loc, ptap->C_oth));
    1552:   C_loc = ptap->C_loc;
    1553:   C_oth = ptap->C_oth;

    1555:   /* add C_loc and C_oth to C */
    1556:   PetscCall(MatGetOwnershipRange(C, &rstart, &rend));

    1558:   /* C_loc -> C */
    1559:   cm    = C_loc->rmap->N;
    1560:   c_seq = (Mat_SeqAIJ *)C_loc->data;
    1561:   cols  = c_seq->j;
    1562:   vals  = c_seq->a;
    1563:   for (i = 0; i < cm; i++) {
    1564:     ncols = c_seq->i[i + 1] - c_seq->i[i];
    1565:     row   = rstart + i;
    1566:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
    1567:     cols += ncols;
    1568:     vals += ncols;
    1569:   }

    1571:   /* Co -> C, off-processor part */
    1572:   cm    = C_oth->rmap->N;
    1573:   c_seq = (Mat_SeqAIJ *)C_oth->data;
    1574:   cols  = c_seq->j;
    1575:   vals  = c_seq->a;
    1576:   for (i = 0; i < cm; i++) {
    1577:     ncols = c_seq->i[i + 1] - c_seq->i[i];
    1578:     row   = p->garray[i];
    1579:     PetscCall(MatSetValues(C, 1, &row, ncols, cols, vals, ADD_VALUES));
    1580:     cols += ncols;
    1581:     vals += ncols;
    1582:   }
    1583:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    1584:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    1585:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    1586:   PetscFunctionReturn(PETSC_SUCCESS);
    1587: }

    1589: PetscErrorCode MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ(Mat P, Mat A, Mat C)
    1590: {
    1591:   MatMergeSeqsToMPI   *merge;
    1592:   Mat_MPIAIJ          *p  = (Mat_MPIAIJ *)P->data;
    1593:   Mat_SeqAIJ          *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data;
    1594:   MatProductCtx_APMPI *ap;
    1595:   PetscInt            *adj;
    1596:   PetscInt             i, j, k, anz, pnz, row, *cj, nexta;
    1597:   MatScalar           *ada, *ca, valtmp;
    1598:   PetscInt             am = A->rmap->n, cm = C->rmap->n, pon = (p->B)->cmap->n;
    1599:   MPI_Comm             comm;
    1600:   PetscMPIInt          size, rank, taga, *len_s, proc;
    1601:   PetscInt            *owners, nrows, **buf_ri_k, **nextrow, **nextci;
    1602:   PetscInt           **buf_ri, **buf_rj;
    1603:   PetscInt             cnz = 0, *bj_i, *bi, *bj, bnz, nextcj; /* bi,bj,ba: local array of C(mpi mat) */
    1604:   MPI_Request         *s_waits, *r_waits;
    1605:   MPI_Status          *status;
    1606:   MatScalar          **abuf_r, *ba_i, *pA, *coa, *ba;
    1607:   const PetscScalar   *dummy;
    1608:   PetscInt            *ai, *aj, *coi, *coj, *poJ, *pdJ;
    1609:   Mat                  A_loc;
    1610:   Mat_SeqAIJ          *a_loc;

    1612:   PetscFunctionBegin;
    1613:   MatCheckProduct(C, 3);
    1614:   ap = (MatProductCtx_APMPI *)C->product->data;
    1615:   PetscCheck(ap, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be computed. Missing data");
    1616:   PetscCheck(ap->A_loc, PetscObjectComm((PetscObject)C), PETSC_ERR_ARG_WRONGSTATE, "PtA cannot be reused. Do not call MatProductClear()");
    1617:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
    1618:   PetscCallMPI(MPI_Comm_size(comm, &size));
    1619:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    1621:   merge = ap->merge;

    1623:   /* 2) compute numeric C_seq = P_loc^T*A_loc */
    1624:   /* get data from symbolic products */
    1625:   coi = merge->coi;
    1626:   coj = merge->coj;
    1627:   PetscCall(PetscCalloc1(coi[pon], &coa));
    1628:   bi     = merge->bi;
    1629:   bj     = merge->bj;
    1630:   owners = merge->rowmap->range;
    1631:   PetscCall(PetscCalloc1(bi[cm], &ba));

    1633:   /* get A_loc by taking all local rows of A */
    1634:   A_loc = ap->A_loc;
    1635:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_REUSE_MATRIX, &A_loc));
    1636:   a_loc = (Mat_SeqAIJ *)A_loc->data;
    1637:   ai    = a_loc->i;
    1638:   aj    = a_loc->j;

    1640:   /* trigger copy to CPU */
    1641:   PetscCall(MatSeqAIJGetArrayRead(p->A, &dummy));
    1642:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &dummy));
    1643:   PetscCall(MatSeqAIJGetArrayRead(p->B, &dummy));
    1644:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &dummy));
    1645:   for (i = 0; i < am; i++) {
    1646:     anz = ai[i + 1] - ai[i];
    1647:     adj = aj + ai[i];
    1648:     ada = a_loc->a + ai[i];

    1650:     /* 2-b) Compute Cseq = P_loc[i,:]^T*A[i,:] using outer product */
    1651:     /* put the value into Co=(p->B)^T*A (off-diagonal part, send to others) */
    1652:     pnz = po->i[i + 1] - po->i[i];
    1653:     poJ = po->j + po->i[i];
    1654:     pA  = po->a + po->i[i];
    1655:     for (j = 0; j < pnz; j++) {
    1656:       row = poJ[j];
    1657:       cj  = coj + coi[row];
    1658:       ca  = coa + coi[row];
    1659:       /* perform sparse axpy */
    1660:       nexta  = 0;
    1661:       valtmp = pA[j];
    1662:       for (k = 0; nexta < anz; k++) {
    1663:         if (cj[k] == adj[nexta]) {
    1664:           ca[k] += valtmp * ada[nexta];
    1665:           nexta++;
    1666:         }
    1667:       }
    1668:       PetscCall(PetscLogFlops(2.0 * anz));
    1669:     }

    1671:     /* put the value into Cd (diagonal part) */
    1672:     pnz = pd->i[i + 1] - pd->i[i];
    1673:     pdJ = pd->j + pd->i[i];
    1674:     pA  = pd->a + pd->i[i];
    1675:     for (j = 0; j < pnz; j++) {
    1676:       row = pdJ[j];
    1677:       cj  = bj + bi[row];
    1678:       ca  = ba + bi[row];
    1679:       /* perform sparse axpy */
    1680:       nexta  = 0;
    1681:       valtmp = pA[j];
    1682:       for (k = 0; nexta < anz; k++) {
    1683:         if (cj[k] == adj[nexta]) {
    1684:           ca[k] += valtmp * ada[nexta];
    1685:           nexta++;
    1686:         }
    1687:       }
    1688:       PetscCall(PetscLogFlops(2.0 * anz));
    1689:     }
    1690:   }

    1692:   /* 3) send and recv matrix values coa */
    1693:   buf_ri = merge->buf_ri;
    1694:   buf_rj = merge->buf_rj;
    1695:   len_s  = merge->len_s;
    1696:   PetscCall(PetscCommGetNewTag(comm, &taga));
    1697:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

    1699:   PetscCall(PetscMalloc2(merge->nsend, &s_waits, size, &status));
    1700:   for (proc = 0, k = 0; proc < size; proc++) {
    1701:     if (!len_s[proc]) continue;
    1702:     i = merge->owners_co[proc];
    1703:     PetscCallMPI(MPIU_Isend(coa + coi[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
    1704:     k++;
    1705:   }
    1706:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
    1707:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));

    1709:   PetscCall(PetscFree2(s_waits, status));
    1710:   PetscCall(PetscFree(r_waits));
    1711:   PetscCall(PetscFree(coa));

    1713:   /* 4) insert local Cseq and received values into Cmpi */
    1714:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
    1715:   for (k = 0; k < merge->nrecv; k++) {
    1716:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1717:     nrows       = *buf_ri_k[k];
    1718:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    1719:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    1720:   }

    1722:   for (i = 0; i < cm; i++) {
    1723:     row  = owners[rank] + i; /* global row index of C_seq */
    1724:     bj_i = bj + bi[i];       /* col indices of the i-th row of C */
    1725:     ba_i = ba + bi[i];
    1726:     bnz  = bi[i + 1] - bi[i];
    1727:     /* add received vals into ba */
    1728:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    1729:       /* i-th row */
    1730:       if (i == *nextrow[k]) {
    1731:         cnz    = *(nextci[k] + 1) - *nextci[k];
    1732:         cj     = buf_rj[k] + *nextci[k];
    1733:         ca     = abuf_r[k] + *nextci[k];
    1734:         nextcj = 0;
    1735:         for (j = 0; nextcj < cnz; j++) {
    1736:           if (bj_i[j] == cj[nextcj]) { /* bcol == ccol */
    1737:             ba_i[j] += ca[nextcj++];
    1738:           }
    1739:         }
    1740:         nextrow[k]++;
    1741:         nextci[k]++;
    1742:         PetscCall(PetscLogFlops(2.0 * cnz));
    1743:       }
    1744:     }
    1745:     PetscCall(MatSetValues(C, 1, &row, bnz, bj_i, ba_i, INSERT_VALUES));
    1746:   }
    1747:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    1748:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));

    1750:   PetscCall(PetscFree(ba));
    1751:   PetscCall(PetscFree(abuf_r[0]));
    1752:   PetscCall(PetscFree(abuf_r));
    1753:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));
    1754:   PetscFunctionReturn(PETSC_SUCCESS);
    1755: }

    1757: PetscErrorCode MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(Mat P, Mat A, PetscReal fill, Mat C)
    1758: {
    1759:   Mat                  A_loc;
    1760:   MatProductCtx_APMPI *ap;
    1761:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
    1762:   Mat_MPIAIJ          *p = (Mat_MPIAIJ *)P->data, *a = (Mat_MPIAIJ *)A->data;
    1763:   PetscInt            *pdti, *pdtj, *poti, *potj, *ptJ;
    1764:   PetscInt             nnz;
    1765:   PetscInt            *lnk, *owners_co, *coi, *coj, i, k, pnz, row;
    1766:   PetscInt             am = A->rmap->n, pn = P->cmap->n;
    1767:   MPI_Comm             comm;
    1768:   PetscMPIInt          size, rank, tagi, tagj, *len_si, *len_s, *len_ri, proc;
    1769:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
    1770:   PetscInt             len, *dnz, *onz, *owners;
    1771:   PetscInt             nzi, *bi, *bj;
    1772:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextci;
    1773:   MPI_Request         *swaits, *rwaits;
    1774:   MPI_Status          *sstatus, rstatus;
    1775:   MatMergeSeqsToMPI   *merge;
    1776:   PetscInt            *ai, *aj, *Jptr, anz, *prmap = p->garray, pon, nspacedouble = 0, j;
    1777:   PetscReal            afill  = 1.0, afill_tmp;
    1778:   PetscInt             rstart = P->cmap->rstart, rmax, Armax;
    1779:   Mat_SeqAIJ          *a_loc;
    1780:   PetscHMapI           ta;
    1781:   MatType              mtype;

    1783:   PetscFunctionBegin;
    1784:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    1785:   /* check if matrix local sizes are compatible */
    1786:   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,
    1787:              A->rmap->rend, P->rmap->rstart, P->rmap->rend);

    1789:   PetscCallMPI(MPI_Comm_size(comm, &size));
    1790:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    1792:   /* create struct MatProductCtx_APMPI and attached it to C later */
    1793:   PetscCall(PetscNew(&ap));

    1795:   /* get A_loc by taking all local rows of A */
    1796:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &A_loc));

    1798:   ap->A_loc = A_loc;
    1799:   a_loc     = (Mat_SeqAIJ *)A_loc->data;
    1800:   ai        = a_loc->i;
    1801:   aj        = a_loc->j;

    1803:   /* determine symbolic Co=(p->B)^T*A - send to others */
    1804:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
    1805:   PetscCall(MatGetSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));
    1806:   pon = (p->B)->cmap->n; /* total num of rows to be sent to other processors
    1807:                          >= (num of nonzero rows of C_seq) - pn */
    1808:   PetscCall(PetscMalloc1(pon + 1, &coi));
    1809:   coi[0] = 0;

    1811:   /* set initial free space to be fill*(nnz(p->B) + nnz(A)) */
    1812:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(poti[pon], ai[am]));
    1813:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
    1814:   current_space = free_space;

    1816:   /* create and initialize a linked list */
    1817:   PetscCall(PetscHMapICreateWithSize(A->cmap->n + a->B->cmap->N, &ta));
    1818:   MatRowMergeMax_SeqAIJ(a_loc, am, ta);
    1819:   PetscCall(PetscHMapIGetSize(ta, &Armax));

    1821:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));

    1823:   for (i = 0; i < pon; i++) {
    1824:     pnz = poti[i + 1] - poti[i];
    1825:     ptJ = potj + poti[i];
    1826:     for (j = 0; j < pnz; j++) {
    1827:       row  = ptJ[j]; /* row of A_loc == col of Pot */
    1828:       anz  = ai[row + 1] - ai[row];
    1829:       Jptr = aj + ai[row];
    1830:       /* add non-zero cols of AP into the sorted linked list lnk */
    1831:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
    1832:     }
    1833:     nnz = lnk[0];

    1835:     /* If free space is not available, double the total space in the list */
    1836:     if (current_space->local_remaining < nnz) {
    1837:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
    1838:       nspacedouble++;
    1839:     }

    1841:     /* Copy data into free space, and zero out denserows */
    1842:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));

    1844:     current_space->array += nnz;
    1845:     current_space->local_used += nnz;
    1846:     current_space->local_remaining -= nnz;

    1848:     coi[i + 1] = coi[i] + nnz;
    1849:   }

    1851:   PetscCall(PetscMalloc1(coi[pon], &coj));
    1852:   PetscCall(PetscFreeSpaceContiguous(&free_space, coj));
    1853:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk)); /* must destroy to get a new one for C */

    1855:   afill_tmp = (PetscReal)coi[pon] / (poti[pon] + ai[am] + 1);
    1856:   if (afill_tmp > afill) afill = afill_tmp;

    1858:   /* send j-array (coj) of Co to other processors */
    1859:   /* determine row ownership */
    1860:   PetscCall(PetscNew(&merge));
    1861:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));

    1863:   merge->rowmap->n  = pn;
    1864:   merge->rowmap->bs = 1;

    1866:   PetscCall(PetscLayoutSetUp(merge->rowmap));
    1867:   owners = merge->rowmap->range;

    1869:   /* determine the number of messages to send, their lengths */
    1870:   PetscCall(PetscCalloc1(size, &len_si));
    1871:   PetscCall(PetscCalloc1(size, &merge->len_s));

    1873:   len_s        = merge->len_s;
    1874:   merge->nsend = 0;

    1876:   PetscCall(PetscMalloc1(size + 1, &owners_co));

    1878:   proc = 0;
    1879:   for (i = 0; i < pon; i++) {
    1880:     while (prmap[i] >= owners[proc + 1]) proc++;
    1881:     len_si[proc]++; /* num of rows in Co to be sent to [proc] */
    1882:     len_s[proc] += coi[i + 1] - coi[i];
    1883:   }

    1885:   len          = 0; /* max length of buf_si[] */
    1886:   owners_co[0] = 0;
    1887:   for (proc = 0; proc < size; proc++) {
    1888:     owners_co[proc + 1] = owners_co[proc] + len_si[proc];
    1889:     if (len_s[proc]) {
    1890:       merge->nsend++;
    1891:       len_si[proc] = 2 * (len_si[proc] + 1);
    1892:       len += len_si[proc];
    1893:     }
    1894:   }

    1896:   /* determine the number and length of messages to receive for coi and coj  */
    1897:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
    1898:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

    1900:   /* post the Irecv and Isend of coj */
    1901:   PetscCall(PetscCommGetNewTag(comm, &tagj));
    1902:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rwaits));
    1903:   PetscCall(PetscMalloc1(merge->nsend, &swaits));
    1904:   for (proc = 0, k = 0; proc < size; proc++) {
    1905:     if (!len_s[proc]) continue;
    1906:     i = owners_co[proc];
    1907:     PetscCallMPI(MPIU_Isend(coj + coi[i], len_s[proc], MPIU_INT, proc, tagj, comm, swaits + k));
    1908:     k++;
    1909:   }

    1911:   /* receives and sends of coj are complete */
    1912:   PetscCall(PetscMalloc1(size, &sstatus));
    1913:   for (i = 0; i < merge->nrecv; i++) {
    1914:     PETSC_UNUSED PetscMPIInt icompleted;
    1915:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
    1916:   }
    1917:   PetscCall(PetscFree(rwaits));
    1918:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));

    1920:   /* add received column indices into table to update Armax */
    1921:   /* Armax can be as large as aN if a P[row,:] is dense, see src/ksp/ksp/tutorials/ex56.c! */
    1922:   for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    1923:     Jptr = buf_rj[k];
    1924:     for (j = 0; j < merge->len_r[k]; j++) PetscCall(PetscHMapISet(ta, *(Jptr + j) + 1, 1));
    1925:   }
    1926:   PetscCall(PetscHMapIGetSize(ta, &Armax));

    1928:   /* send and recv coi */
    1929:   PetscCall(PetscCommGetNewTag(comm, &tagi));
    1930:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &rwaits));
    1931:   PetscCall(PetscMalloc1(len, &buf_s));
    1932:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
    1933:   for (proc = 0, k = 0; proc < size; proc++) {
    1934:     if (!len_s[proc]) continue;
    1935:     /* form outgoing message for i-structure:
    1936:          buf_si[0]:                 nrows to be sent
    1937:                [1:nrows]:           row index (global)
    1938:                [nrows+1:2*nrows+1]: i-structure index
    1939:     */
    1940:     nrows       = len_si[proc] / 2 - 1;
    1941:     buf_si_i    = buf_si + nrows + 1;
    1942:     buf_si[0]   = nrows;
    1943:     buf_si_i[0] = 0;
    1944:     nrows       = 0;
    1945:     for (i = owners_co[proc]; i < owners_co[proc + 1]; i++) {
    1946:       nzi                 = coi[i + 1] - coi[i];
    1947:       buf_si_i[nrows + 1] = buf_si_i[nrows] + nzi;   /* i-structure */
    1948:       buf_si[nrows + 1]   = prmap[i] - owners[proc]; /* local row index */
    1949:       nrows++;
    1950:     }
    1951:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, swaits + k));
    1952:     k++;
    1953:     buf_si += len_si[proc];
    1954:   }
    1955:   i = merge->nrecv;
    1956:   while (i--) {
    1957:     PETSC_UNUSED PetscMPIInt icompleted;
    1958:     PetscCallMPI(MPI_Waitany(merge->nrecv, rwaits, &icompleted, &rstatus));
    1959:   }
    1960:   PetscCall(PetscFree(rwaits));
    1961:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, swaits, sstatus));
    1962:   PetscCall(PetscFree(len_si));
    1963:   PetscCall(PetscFree(len_ri));
    1964:   PetscCall(PetscFree(swaits));
    1965:   PetscCall(PetscFree(sstatus));
    1966:   PetscCall(PetscFree(buf_s));

    1968:   /* compute the local portion of C (mpi mat) */
    1969:   /* allocate bi array and free space for accumulating nonzero column info */
    1970:   PetscCall(PetscMalloc1(pn + 1, &bi));
    1971:   bi[0] = 0;

    1973:   /* set initial free space to be fill*(nnz(P) + nnz(AP)) */
    1974:   nnz = PetscRealIntMultTruncate(fill, PetscIntSumTruncate(pdti[pn], PetscIntSumTruncate(poti[pon], ai[am])));
    1975:   PetscCall(PetscFreeSpaceGet(nnz, &free_space));
    1976:   current_space = free_space;

    1978:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextci));
    1979:   for (k = 0; k < merge->nrecv; k++) {
    1980:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    1981:     nrows       = *buf_ri_k[k];
    1982:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    1983:     nextci[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th received i-structure  */
    1984:   }

    1986:   PetscCall(PetscLLCondensedCreate_Scalable(Armax, &lnk));
    1987:   MatPreallocateBegin(comm, pn, A->cmap->n, dnz, onz);
    1988:   rmax = 0;
    1989:   for (i = 0; i < pn; i++) {
    1990:     /* add pdt[i,:]*AP into lnk */
    1991:     pnz = pdti[i + 1] - pdti[i];
    1992:     ptJ = pdtj + pdti[i];
    1993:     for (j = 0; j < pnz; j++) {
    1994:       row  = ptJ[j]; /* row of AP == col of Pt */
    1995:       anz  = ai[row + 1] - ai[row];
    1996:       Jptr = aj + ai[row];
    1997:       /* add non-zero cols of AP into the sorted linked list lnk */
    1998:       PetscCall(PetscLLCondensedAddSorted_Scalable(anz, Jptr, lnk));
    1999:     }

    2001:     /* add received col data into lnk */
    2002:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    2003:       if (i == *nextrow[k]) {            /* i-th row */
    2004:         nzi  = *(nextci[k] + 1) - *nextci[k];
    2005:         Jptr = buf_rj[k] + *nextci[k];
    2006:         PetscCall(PetscLLCondensedAddSorted_Scalable(nzi, Jptr, lnk));
    2007:         nextrow[k]++;
    2008:         nextci[k]++;
    2009:       }
    2010:     }

    2012:     /* add missing diagonal entry */
    2013:     if (C->force_diagonals) {
    2014:       k = i + owners[rank]; /* column index */
    2015:       PetscCall(PetscLLCondensedAddSorted_Scalable(1, &k, lnk));
    2016:     }

    2018:     nnz = lnk[0];

    2020:     /* if free space is not available, make more free space */
    2021:     if (current_space->local_remaining < nnz) {
    2022:       PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(nnz, current_space->total_array_size), &current_space));
    2023:       nspacedouble++;
    2024:     }
    2025:     /* copy data into free space, then initialize lnk */
    2026:     PetscCall(PetscLLCondensedClean_Scalable(nnz, current_space->array, lnk));
    2027:     PetscCall(MatPreallocateSet(i + owners[rank], nnz, current_space->array, dnz, onz));

    2029:     current_space->array += nnz;
    2030:     current_space->local_used += nnz;
    2031:     current_space->local_remaining -= nnz;

    2033:     bi[i + 1] = bi[i] + nnz;
    2034:     if (nnz > rmax) rmax = nnz;
    2035:   }
    2036:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextci));

    2038:   PetscCall(PetscMalloc1(bi[pn], &bj));
    2039:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
    2040:   afill_tmp = (PetscReal)bi[pn] / (pdti[pn] + poti[pon] + ai[am] + 1);
    2041:   if (afill_tmp > afill) afill = afill_tmp;
    2042:   PetscCall(PetscLLCondensedDestroy_Scalable(lnk));
    2043:   PetscCall(PetscHMapIDestroy(&ta));
    2044:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->A, &pdti, &pdtj));
    2045:   PetscCall(MatRestoreSymbolicTranspose_SeqAIJ(p->B, &poti, &potj));

    2047:   /* create symbolic parallel matrix C - why cannot be assembled in Numeric part   */
    2048:   PetscCall(MatSetSizes(C, pn, A->cmap->n, PETSC_DETERMINE, PETSC_DETERMINE));
    2049:   PetscCall(MatSetBlockSizes(C, P->cmap->bs, A->cmap->bs));
    2050:   PetscCall(MatGetType(A, &mtype));
    2051:   PetscCall(MatSetType(C, mtype));
    2052:   PetscCall(MatMPIAIJSetPreallocation(C, 0, dnz, 0, onz));
    2053:   MatPreallocateEnd(dnz, onz);
    2054:   PetscCall(MatSetBlockSize(C, 1));
    2055:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    2056:   for (i = 0; i < pn; i++) {
    2057:     row  = i + rstart;
    2058:     nnz  = bi[i + 1] - bi[i];
    2059:     Jptr = bj + bi[i];
    2060:     PetscCall(MatSetValues(C, 1, &row, nnz, Jptr, NULL, INSERT_VALUES));
    2061:   }
    2062:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    2063:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    2064:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    2065:   merge->bi        = bi;
    2066:   merge->bj        = bj;
    2067:   merge->coi       = coi;
    2068:   merge->coj       = coj;
    2069:   merge->buf_ri    = buf_ri;
    2070:   merge->buf_rj    = buf_rj;
    2071:   merge->owners_co = owners_co;

    2073:   /* attach the supporting struct to C for reuse */
    2074:   C->product->data    = ap;
    2075:   C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
    2076:   ap->merge           = merge;

    2078:   C->ops->mattransposemultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ;

    2080: #if defined(PETSC_USE_INFO)
    2081:   if (bi[pn] != 0) {
    2082:     PetscCall(PetscInfo(C, "Reallocs %" PetscInt_FMT "; Fill ratio: given %g needed %g.\n", nspacedouble, (double)fill, (double)afill));
    2083:     PetscCall(PetscInfo(C, "Use MatTransposeMatMult(A,B,MatReuse,%g,&C) for best performance.\n", (double)afill));
    2084:   } else {
    2085:     PetscCall(PetscInfo(C, "Empty matrix product\n"));
    2086:   }
    2087: #endif
    2088:   PetscFunctionReturn(PETSC_SUCCESS);
    2089: }

    2091: static PetscErrorCode MatProductSymbolic_AtB_MPIAIJ_MPIAIJ(Mat C)
    2092: {
    2093:   Mat_Product *product = C->product;
    2094:   Mat          A = product->A, B = product->B;
    2095:   PetscReal    fill = product->fill;
    2096:   PetscBool    flg;

    2098:   PetscFunctionBegin;
    2099:   /* scalable */
    2100:   PetscCall(PetscStrcmp(product->alg, "scalable", &flg));
    2101:   if (flg) {
    2102:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ(A, B, fill, C));
    2103:     goto next;
    2104:   }

    2106:   /* nonscalable */
    2107:   PetscCall(PetscStrcmp(product->alg, "nonscalable", &flg));
    2108:   if (flg) {
    2109:     PetscCall(MatTransposeMatMultSymbolic_MPIAIJ_MPIAIJ_nonscalable(A, B, fill, C));
    2110:     goto next;
    2111:   }

    2113:   /* matmatmult */
    2114:   PetscCall(PetscStrcmp(product->alg, "at*b", &flg));
    2115:   if (flg) {
    2116:     Mat                  At;
    2117:     MatProductCtx_APMPI *ptap;

    2119:     PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
    2120:     PetscCall(MatMatMultSymbolic_MPIAIJ_MPIAIJ(At, B, fill, C));
    2121:     ptap = (MatProductCtx_APMPI *)C->product->data;
    2122:     if (ptap) {
    2123:       ptap->Pt            = At;
    2124:       C->product->destroy = MatProductCtxDestroy_MPIAIJ_PtAP;
    2125:     }
    2126:     C->ops->transposematmultnumeric = MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ_matmatmult;
    2127:     goto next;
    2128:   }

    2130:   /* backend general code */
    2131:   PetscCall(PetscStrcmp(product->alg, "backend", &flg));
    2132:   if (flg) {
    2133:     PetscCall(MatProductSymbolic_MPIAIJBACKEND(C));
    2134:     PetscFunctionReturn(PETSC_SUCCESS);
    2135:   }

    2137:   SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "MatProduct type is not supported");

    2139: next:
    2140:   C->ops->productnumeric = MatProductNumeric_AtB;
    2141:   PetscFunctionReturn(PETSC_SUCCESS);
    2142: }

    2144: /* Set options for MatMatMultxxx_MPIAIJ_MPIAIJ */
    2145: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AB(Mat C)
    2146: {
    2147:   Mat_Product *product = C->product;
    2148:   Mat          A = product->A, B = product->B;
    2149: #if defined(PETSC_HAVE_HYPRE)
    2150:   const char *algTypes[5] = {"scalable", "nonscalable", "seqmpi", "backend", "hypre"};
    2151:   PetscInt    nalg        = 5;
    2152: #else
    2153:   const char *algTypes[4] = {
    2154:     "scalable",
    2155:     "nonscalable",
    2156:     "seqmpi",
    2157:     "backend",
    2158:   };
    2159:   PetscInt nalg = 4;
    2160: #endif
    2161:   PetscInt  alg = 1; /* set nonscalable algorithm as default */
    2162:   PetscBool flg;
    2163:   MPI_Comm  comm;

    2165:   PetscFunctionBegin;
    2166:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));

    2168:   /* Set "nonscalable" as default algorithm */
    2169:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
    2170:   if (flg) {
    2171:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

    2173:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2174:     if (B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2175:       MatInfo   Ainfo, Binfo;
    2176:       PetscInt  nz_local;
    2177:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

    2179:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
    2180:       PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
    2181:       nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2183:       if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
    2184:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

    2186:       if (alg_scalable) {
    2187:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2188:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
    2189:         PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
    2190:       }
    2191:     }
    2192:   }

    2194:   /* Get runtime option */
    2195:   if (product->api_user) {
    2196:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
    2197:     PetscCall(PetscOptionsEList("-matmatmult_via", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
    2198:     PetscOptionsEnd();
    2199:   } else {
    2200:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
    2201:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
    2202:     PetscOptionsEnd();
    2203:   }
    2204:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

    2206:   C->ops->productsymbolic = MatProductSymbolic_AB_MPIAIJ_MPIAIJ;
    2207:   PetscFunctionReturn(PETSC_SUCCESS);
    2208: }

    2210: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABt(Mat C)
    2211: {
    2212:   PetscFunctionBegin;
    2213:   PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
    2214:   C->ops->productsymbolic = MatProductSymbolic_ABt_MPIAIJ_MPIAIJ;
    2215:   PetscFunctionReturn(PETSC_SUCCESS);
    2216: }

    2218: /* Set options for MatTransposeMatMultXXX_MPIAIJ_MPIAIJ */
    2219: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_AtB(Mat C)
    2220: {
    2221:   Mat_Product *product = C->product;
    2222:   Mat          A = product->A, B = product->B;
    2223:   const char  *algTypes[4] = {"scalable", "nonscalable", "at*b", "backend"};
    2224:   PetscInt     nalg        = 4;
    2225:   PetscInt     alg         = 1; /* set default algorithm  */
    2226:   PetscBool    flg;
    2227:   MPI_Comm     comm;

    2229:   PetscFunctionBegin;
    2230:   /* Check matrix local sizes */
    2231:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
    2232:   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 ")",
    2233:              A->rmap->rstart, A->rmap->rend, B->rmap->rstart, B->rmap->rend);

    2235:   /* Set default algorithm */
    2236:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
    2237:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

    2239:   /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2240:   if (alg && B->cmap->N > 100000) { /* may switch to scalable algorithm as default */
    2241:     MatInfo   Ainfo, Binfo;
    2242:     PetscInt  nz_local;
    2243:     PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

    2245:     PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
    2246:     PetscCall(MatGetInfo(B, MAT_LOCAL, &Binfo));
    2247:     nz_local = (PetscInt)(Ainfo.nz_allocated + Binfo.nz_allocated);

    2249:     if (B->cmap->N > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
    2250:     PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

    2252:     if (alg_scalable) {
    2253:       alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2254:       PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
    2255:       PetscCall(PetscInfo(B, "Use scalable algorithm, BN %" PetscInt_FMT ", fill*nz_allocated %g\n", B->cmap->N, (double)(product->fill * nz_local)));
    2256:     }
    2257:   }

    2259:   /* Get runtime option */
    2260:   if (product->api_user) {
    2261:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatTransposeMatMult", "Mat");
    2262:     PetscCall(PetscOptionsEList("-mattransposematmult_via", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
    2263:     PetscOptionsEnd();
    2264:   } else {
    2265:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AtB", "Mat");
    2266:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatTransposeMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
    2267:     PetscOptionsEnd();
    2268:   }
    2269:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

    2271:   C->ops->productsymbolic = MatProductSymbolic_AtB_MPIAIJ_MPIAIJ;
    2272:   PetscFunctionReturn(PETSC_SUCCESS);
    2273: }

    2275: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_PtAP(Mat C)
    2276: {
    2277:   Mat_Product *product = C->product;
    2278:   Mat          A = product->A, P = product->B;
    2279:   MPI_Comm     comm;
    2280:   PetscBool    flg;
    2281:   PetscInt     alg = 1; /* set default algorithm */
    2282: #if !defined(PETSC_HAVE_HYPRE)
    2283:   const char *algTypes[5] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend"};
    2284:   PetscInt    nalg        = 5;
    2285: #else
    2286:   const char *algTypes[6] = {"scalable", "nonscalable", "allatonce", "allatonce_merged", "backend", "hypre"};
    2287:   PetscInt    nalg        = 6;
    2288: #endif
    2289:   PetscInt pN = P->cmap->N;

    2291:   PetscFunctionBegin;
    2292:   /* Check matrix local sizes */
    2293:   PetscCall(PetscObjectGetComm((PetscObject)C, &comm));
    2294:   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 ")",
    2295:              A->rmap->rstart, A->rmap->rend, P->rmap->rstart, P->rmap->rend);
    2296:   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 ")",
    2297:              A->cmap->rstart, A->cmap->rend, P->rmap->rstart, P->rmap->rend);

    2299:   /* Set "nonscalable" as default algorithm */
    2300:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
    2301:   if (flg) {
    2302:     PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

    2304:     /* Set "scalable" as default if BN and local nonzeros of A and B are large */
    2305:     if (pN > 100000) {
    2306:       MatInfo   Ainfo, Pinfo;
    2307:       PetscInt  nz_local;
    2308:       PetscBool alg_scalable_loc = PETSC_FALSE, alg_scalable;

    2310:       PetscCall(MatGetInfo(A, MAT_LOCAL, &Ainfo));
    2311:       PetscCall(MatGetInfo(P, MAT_LOCAL, &Pinfo));
    2312:       nz_local = (PetscInt)(Ainfo.nz_allocated + Pinfo.nz_allocated);

    2314:       if (pN > product->fill * nz_local) alg_scalable_loc = PETSC_TRUE;
    2315:       PetscCallMPI(MPIU_Allreduce(&alg_scalable_loc, &alg_scalable, 1, MPI_C_BOOL, MPI_LOR, comm));

    2317:       if (alg_scalable) {
    2318:         alg = 0; /* scalable algorithm would 50% slower than nonscalable algorithm */
    2319:         PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));
    2320:       }
    2321:     }
    2322:   }

    2324:   /* Get runtime option */
    2325:   if (product->api_user) {
    2326:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
    2327:     PetscCall(PetscOptionsEList("-matptap_via", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
    2328:     PetscOptionsEnd();
    2329:   } else {
    2330:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
    2331:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatPtAP", algTypes, nalg, algTypes[alg], &alg, &flg));
    2332:     PetscOptionsEnd();
    2333:   }
    2334:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

    2336:   C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIAIJ;
    2337:   PetscFunctionReturn(PETSC_SUCCESS);
    2338: }

    2340: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_RARt(Mat C)
    2341: {
    2342:   Mat_Product *product = C->product;
    2343:   Mat          A = product->A, R = product->B;

    2345:   PetscFunctionBegin;
    2346:   /* Check matrix local sizes */
    2347:   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,
    2348:              A->rmap->n, R->rmap->n, R->cmap->n);

    2350:   C->ops->productsymbolic = MatProductSymbolic_RARt_MPIAIJ_MPIAIJ;
    2351:   PetscFunctionReturn(PETSC_SUCCESS);
    2352: }

    2354: /*
    2355:  Set options for ABC = A*B*C = A*(B*C); ABC's algorithm must be chosen from AB's algorithm
    2356: */
    2357: static PetscErrorCode MatProductSetFromOptions_MPIAIJ_ABC(Mat C)
    2358: {
    2359:   Mat_Product *product     = C->product;
    2360:   PetscBool    flg         = PETSC_FALSE;
    2361:   PetscInt     alg         = 1; /* default algorithm */
    2362:   const char  *algTypes[3] = {"scalable", "nonscalable", "seqmpi"};
    2363:   PetscInt     nalg        = 3;

    2365:   PetscFunctionBegin;
    2366:   /* Set default algorithm */
    2367:   PetscCall(PetscStrcmp(C->product->alg, "default", &flg));
    2368:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

    2370:   /* Get runtime option */
    2371:   if (product->api_user) {
    2372:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMatMult", "Mat");
    2373:     PetscCall(PetscOptionsEList("-matmatmatmult_via", "Algorithmic approach", "MatMatMatMult", algTypes, nalg, algTypes[alg], &alg, &flg));
    2374:     PetscOptionsEnd();
    2375:   } else {
    2376:     PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_ABC", "Mat");
    2377:     PetscCall(PetscOptionsEList("-mat_product_algorithm", "Algorithmic approach", "MatProduct_ABC", algTypes, nalg, algTypes[alg], &alg, &flg));
    2378:     PetscOptionsEnd();
    2379:   }
    2380:   if (flg) PetscCall(MatProductSetAlgorithm(C, algTypes[alg]));

    2382:   C->ops->matmatmultsymbolic = MatMatMatMultSymbolic_MPIAIJ_MPIAIJ_MPIAIJ;
    2383:   C->ops->productsymbolic    = MatProductSymbolic_ABC;
    2384:   PetscFunctionReturn(PETSC_SUCCESS);
    2385: }

    2387: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIAIJ(Mat C)
    2388: {
    2389:   Mat_Product *product = C->product;

    2391:   PetscFunctionBegin;
    2392:   switch (product->type) {
    2393:   case MATPRODUCT_AB:
    2394:     PetscCall(MatProductSetFromOptions_MPIAIJ_AB(C));
    2395:     break;
    2396:   case MATPRODUCT_ABt:
    2397:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABt(C));
    2398:     break;
    2399:   case MATPRODUCT_AtB:
    2400:     PetscCall(MatProductSetFromOptions_MPIAIJ_AtB(C));
    2401:     break;
    2402:   case MATPRODUCT_PtAP:
    2403:     PetscCall(MatProductSetFromOptions_MPIAIJ_PtAP(C));
    2404:     break;
    2405:   case MATPRODUCT_RARt:
    2406:     PetscCall(MatProductSetFromOptions_MPIAIJ_RARt(C));
    2407:     break;
    2408:   case MATPRODUCT_ABC:
    2409:     PetscCall(MatProductSetFromOptions_MPIAIJ_ABC(C));
    2410:     break;
    2411:   default:
    2412:     break;
    2413:   }
    2414:   PetscFunctionReturn(PETSC_SUCCESS);
    2415: }