Actual source code: mpiaij.c

      1: #include <../src/mat/impls/aij/mpi/mpiaij.h>
      2: #include <petsc/private/vecimpl.h>
      3: #include <petsc/private/sfimpl.h>
      4: #include <petsc/private/isimpl.h>
      5: #include <petscblaslapack.h>
      6: #include <petscsf.h>
      7: #include <petsc/private/hashmapi.h>

      9: /* defines MatSetValues_MPI_Hash(), MatAssemblyBegin_MPI_Hash(), and MatAssemblyEnd_MPI_Hash() */
     10: #define TYPE AIJ
     11: #define TYPE_AIJ
     12: #include "../src/mat/impls/aij/mpi/mpihashmat.h"
     13: #undef TYPE
     14: #undef TYPE_AIJ

     16: static PetscErrorCode MatReset_MPIAIJ(Mat mat)
     17: {
     18:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

     20:   PetscFunctionBegin;
     21:   PetscCall(PetscLogObjectState((PetscObject)mat, "Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT, mat->rmap->N, mat->cmap->N));
     22:   PetscCall(MatStashDestroy_Private(&mat->stash));
     23:   PetscCall(VecDestroy(&aij->diag));
     24:   PetscCall(MatDestroy(&aij->A));
     25:   PetscCall(MatDestroy(&aij->B));
     26: #if defined(PETSC_USE_CTABLE)
     27:   PetscCall(PetscHMapIDestroy(&aij->colmap));
     28: #else
     29:   PetscCall(PetscFree(aij->colmap));
     30: #endif
     31:   PetscCall(PetscFree(aij->garray));
     32:   PetscCall(VecDestroy(&aij->lvec));
     33:   PetscCall(VecScatterDestroy(&aij->Mvctx));
     34:   PetscCall(PetscFree2(aij->rowvalues, aij->rowindices));
     35:   PetscCall(PetscFree(aij->ld));
     36:   PetscFunctionReturn(PETSC_SUCCESS);
     37: }

     39: static PetscErrorCode MatResetHash_MPIAIJ(Mat mat)
     40: {
     41:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
     42:   /* Save the nonzero states of the component matrices because those are what are used to determine
     43:     the nonzero state of mat */
     44:   PetscObjectState Astate = aij->A->nonzerostate, Bstate = aij->B->nonzerostate;

     46:   PetscFunctionBegin;
     47:   PetscCall(MatReset_MPIAIJ(mat));
     48:   PetscCall(MatSetUp_MPI_Hash(mat));
     49:   aij->A->nonzerostate = ++Astate, aij->B->nonzerostate = ++Bstate;
     50:   PetscFunctionReturn(PETSC_SUCCESS);
     51: }

     53: PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
     54: {
     55:   PetscFunctionBegin;
     56:   PetscCall(MatReset_MPIAIJ(mat));

     58:   PetscCall(PetscFree(mat->data));

     60:   /* may be created by MatCreateMPIAIJSumSeqAIJSymbolic */
     61:   PetscCall(PetscObjectCompose((PetscObject)mat, "MatMergeSeqsToMPI", NULL));

     63:   PetscCall(PetscObjectChangeTypeName((PetscObject)mat, NULL));
     64:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatStoreValues_C", NULL));
     65:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatRetrieveValues_C", NULL));
     66:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatIsTranspose_C", NULL));
     67:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetPreallocation_C", NULL));
     68:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatResetPreallocation_C", NULL));
     69:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatResetHash_C", NULL));
     70:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetPreallocationCSR_C", NULL));
     71:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDiagonalScaleLocal_C", NULL));
     72:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpibaij_C", NULL));
     73:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpisbaij_C", NULL));
     74: #if defined(PETSC_HAVE_CUDA)
     75:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijcusparse_C", NULL));
     76: #endif
     77: #if defined(PETSC_HAVE_HIP)
     78:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijhipsparse_C", NULL));
     79: #endif
     80: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
     81:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijkokkos_C", NULL));
     82: #endif
     83:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpidense_C", NULL));
     84: #if defined(PETSC_HAVE_ELEMENTAL)
     85:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_elemental_C", NULL));
     86: #endif
     87: #if defined(PETSC_HAVE_SCALAPACK)
     88:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_scalapack_C", NULL));
     89: #endif
     90: #if defined(PETSC_HAVE_HYPRE)
     91:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_hypre_C", NULL));
     92:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", NULL));
     93: #endif
     94:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_is_C", NULL));
     95:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_is_mpiaij_C", NULL));
     96:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaij_mpiaij_C", NULL));
     97:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetUseScalableIncreaseOverlap_C", NULL));
     98:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijperm_C", NULL));
     99:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijsell_C", NULL));
    100: #if defined(PETSC_HAVE_MKL_SPARSE)
    101:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijmkl_C", NULL));
    102: #endif
    103:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijcrl_C", NULL));
    104:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_is_C", NULL));
    105:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpisell_C", NULL));
    106:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetPreallocationCOO_C", NULL));
    107:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetValuesCOO_C", NULL));
    108:   PetscFunctionReturn(PETSC_SUCCESS);
    109: }

    111: static PetscErrorCode MatGetRowIJ_MPIAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *m, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    112: {
    113:   Mat B;

    115:   PetscFunctionBegin;
    116:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &B));
    117:   PetscCall(PetscObjectCompose((PetscObject)A, "MatGetRowIJ_MPIAIJ", (PetscObject)B));
    118:   PetscCall(MatGetRowIJ(B, oshift, symmetric, inodecompressed, m, ia, ja, done));
    119:   PetscCall(MatDestroy(&B));
    120:   PetscFunctionReturn(PETSC_SUCCESS);
    121: }

    123: static PetscErrorCode MatRestoreRowIJ_MPIAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *m, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    124: {
    125:   Mat B;

    127:   PetscFunctionBegin;
    128:   PetscCall(PetscObjectQuery((PetscObject)A, "MatGetRowIJ_MPIAIJ", (PetscObject *)&B));
    129:   PetscCall(MatRestoreRowIJ(B, oshift, symmetric, inodecompressed, m, ia, ja, done));
    130:   PetscCall(PetscObjectCompose((PetscObject)A, "MatGetRowIJ_MPIAIJ", NULL));
    131:   PetscFunctionReturn(PETSC_SUCCESS);
    132: }

    134: /*MC
    135:    MATAIJ - MATAIJ = "aij" - A matrix type to be used for sparse matrices.

    137:    This matrix type is identical to` MATSEQAIJ` when constructed with a single process communicator,
    138:    and `MATMPIAIJ` otherwise.  As a result, for single process communicators,
    139:   `MatSeqAIJSetPreallocation()` is supported, and similarly `MatMPIAIJSetPreallocation()` is supported
    140:   for communicators controlling multiple processes.  It is recommended that you call both of
    141:   the above preallocation routines for simplicity.

    143:    Options Database Key:
    144: . -mat_type aij - sets the matrix type to `MATAIJ` during a call to `MatSetFromOptions()`

    146:   Developer Note:
    147:   Level: beginner

    149:     Subclasses include `MATAIJCUSPARSE`, `MATAIJPERM`, `MATAIJSELL`, `MATAIJMKL`, `MATAIJCRL`, `MATAIJKOKKOS`,and also automatically switches over to use inodes when
    150:    enough exist.

    152: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MATSEQAIJ`, `MatCreateAIJ()`, `MatCreateSeqAIJ()`, `MATSEQAIJ`, `MATMPIAIJ`
    153: M*/

    155: /*MC
    156:    MATAIJCRL - MATAIJCRL = "aijcrl" - A matrix type to be used for sparse matrices.

    158:    This matrix type is identical to `MATSEQAIJCRL` when constructed with a single process communicator,
    159:    and `MATMPIAIJCRL` otherwise.  As a result, for single process communicators,
    160:    `MatSeqAIJSetPreallocation()` is supported, and similarly `MatMPIAIJSetPreallocation()` is supported
    161:   for communicators controlling multiple processes.  It is recommended that you call both of
    162:   the above preallocation routines for simplicity.

    164:    Options Database Key:
    165: . -mat_type aijcrl - sets the matrix type to `MATMPIAIJCRL` during a call to `MatSetFromOptions()`

    167:   Level: beginner

    169: .seealso: [](ch_matrices), `Mat`, `MatCreateMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`, `MATSEQAIJCRL`, `MATMPIAIJCRL`
    170: M*/

    172: static PetscErrorCode MatBindToCPU_MPIAIJ(Mat A, PetscBool flg)
    173: {
    174:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    176:   PetscFunctionBegin;
    177: #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP) || defined(PETSC_HAVE_VIENNACL)
    178:   A->boundtocpu = flg;
    179: #endif
    180:   if (a->A) PetscCall(MatBindToCPU(a->A, flg));
    181:   if (a->B) PetscCall(MatBindToCPU(a->B, flg));

    183:   /* In addition to binding the diagonal and off-diagonal matrices, bind the local vectors used for matrix-vector products.
    184:    * This maybe seems a little odd for a MatBindToCPU() call to do, but it makes no sense for the binding of these vectors
    185:    * to differ from the parent matrix. */
    186:   if (a->lvec) PetscCall(VecBindToCPU(a->lvec, flg));
    187:   if (a->diag) PetscCall(VecBindToCPU(a->diag, flg));
    188:   PetscFunctionReturn(PETSC_SUCCESS);
    189: }

    191: static PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
    192: {
    193:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)M->data;

    195:   PetscFunctionBegin;
    196:   if (mat->A) {
    197:     PetscCall(MatSetBlockSizes(mat->A, rbs, cbs));
    198:     PetscCall(MatSetBlockSizes(mat->B, rbs, 1));
    199:   }
    200:   PetscFunctionReturn(PETSC_SUCCESS);
    201: }

    203: static PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M, IS *keptrows)
    204: {
    205:   Mat_MPIAIJ      *mat = (Mat_MPIAIJ *)M->data;
    206:   Mat_SeqAIJ      *a   = (Mat_SeqAIJ *)mat->A->data;
    207:   Mat_SeqAIJ      *b   = (Mat_SeqAIJ *)mat->B->data;
    208:   const PetscInt  *ia, *ib;
    209:   const MatScalar *aa, *bb, *aav, *bav;
    210:   PetscInt         na, nb, i, j, *rows, cnt = 0, n0rows;
    211:   PetscInt         m = M->rmap->n, rstart = M->rmap->rstart;

    213:   PetscFunctionBegin;
    214:   *keptrows = NULL;

    216:   ia = a->i;
    217:   ib = b->i;
    218:   PetscCall(MatSeqAIJGetArrayRead(mat->A, &aav));
    219:   PetscCall(MatSeqAIJGetArrayRead(mat->B, &bav));
    220:   for (i = 0; i < m; i++) {
    221:     na = ia[i + 1] - ia[i];
    222:     nb = ib[i + 1] - ib[i];
    223:     if (!na && !nb) {
    224:       cnt++;
    225:       goto ok1;
    226:     }
    227:     aa = aav + ia[i];
    228:     for (j = 0; j < na; j++) {
    229:       if (aa[j] != 0.0) goto ok1;
    230:     }
    231:     bb = PetscSafePointerPlusOffset(bav, ib[i]);
    232:     for (j = 0; j < nb; j++) {
    233:       if (bb[j] != 0.0) goto ok1;
    234:     }
    235:     cnt++;
    236:   ok1:;
    237:   }
    238:   PetscCallMPI(MPIU_Allreduce(&cnt, &n0rows, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)M)));
    239:   if (!n0rows) {
    240:     PetscCall(MatSeqAIJRestoreArrayRead(mat->A, &aav));
    241:     PetscCall(MatSeqAIJRestoreArrayRead(mat->B, &bav));
    242:     PetscFunctionReturn(PETSC_SUCCESS);
    243:   }
    244:   PetscCall(PetscMalloc1(M->rmap->n - cnt, &rows));
    245:   cnt = 0;
    246:   for (i = 0; i < m; i++) {
    247:     na = ia[i + 1] - ia[i];
    248:     nb = ib[i + 1] - ib[i];
    249:     if (!na && !nb) continue;
    250:     aa = aav + ia[i];
    251:     for (j = 0; j < na; j++) {
    252:       if (aa[j] != 0.0) {
    253:         rows[cnt++] = rstart + i;
    254:         goto ok2;
    255:       }
    256:     }
    257:     bb = PetscSafePointerPlusOffset(bav, ib[i]);
    258:     for (j = 0; j < nb; j++) {
    259:       if (bb[j] != 0.0) {
    260:         rows[cnt++] = rstart + i;
    261:         goto ok2;
    262:       }
    263:     }
    264:   ok2:;
    265:   }
    266:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)M), cnt, rows, PETSC_OWN_POINTER, keptrows));
    267:   PetscCall(MatSeqAIJRestoreArrayRead(mat->A, &aav));
    268:   PetscCall(MatSeqAIJRestoreArrayRead(mat->B, &bav));
    269:   PetscFunctionReturn(PETSC_SUCCESS);
    270: }

    272: static PetscErrorCode MatDiagonalSet_MPIAIJ(Mat Y, Vec D, InsertMode is)
    273: {
    274:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)Y->data;
    275:   PetscBool   cong;

    277:   PetscFunctionBegin;
    278:   PetscCall(MatHasCongruentLayouts(Y, &cong));
    279:   if (Y->assembled && cong) {
    280:     PetscCall(MatDiagonalSet(aij->A, D, is));
    281:   } else {
    282:     PetscCall(MatDiagonalSet_Default(Y, D, is));
    283:   }
    284:   PetscFunctionReturn(PETSC_SUCCESS);
    285: }

    287: static PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M, IS *zrows)
    288: {
    289:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)M->data;
    290:   PetscInt    i, rstart, nrows, *rows;

    292:   PetscFunctionBegin;
    293:   *zrows = NULL;
    294:   PetscCall(MatFindZeroDiagonals_SeqAIJ_Private(aij->A, &nrows, &rows));
    295:   PetscCall(MatGetOwnershipRange(M, &rstart, NULL));
    296:   for (i = 0; i < nrows; i++) rows[i] += rstart;
    297:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)M), nrows, rows, PETSC_OWN_POINTER, zrows));
    298:   PetscFunctionReturn(PETSC_SUCCESS);
    299: }

    301: static PetscErrorCode MatGetColumnReductions_MPIAIJ(Mat A, PetscInt type, PetscReal *reductions)
    302: {
    303:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)A->data;
    304:   PetscInt           i, m, n, *garray = aij->garray;
    305:   Mat_SeqAIJ        *a_aij = (Mat_SeqAIJ *)aij->A->data;
    306:   Mat_SeqAIJ        *b_aij = (Mat_SeqAIJ *)aij->B->data;
    307:   PetscReal         *work;
    308:   const PetscScalar *dummy;

    310:   PetscFunctionBegin;
    311:   PetscCall(MatGetSize(A, &m, &n));
    312:   PetscCall(PetscCalloc1(n, &work));
    313:   PetscCall(MatSeqAIJGetArrayRead(aij->A, &dummy));
    314:   PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &dummy));
    315:   PetscCall(MatSeqAIJGetArrayRead(aij->B, &dummy));
    316:   PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &dummy));
    317:   if (type == NORM_2) {
    318:     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i] * a_aij->a[i]);
    319:     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i] * b_aij->a[i]);
    320:   } else if (type == NORM_1) {
    321:     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] += PetscAbsScalar(a_aij->a[i]);
    322:     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
    323:   } else if (type == NORM_INFINITY) {
    324:     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] = PetscMax(PetscAbsScalar(a_aij->a[i]), work[A->cmap->rstart + a_aij->j[i]]);
    325:     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] = PetscMax(PetscAbsScalar(b_aij->a[i]), work[garray[b_aij->j[i]]]);
    326:   } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
    327:     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] += PetscRealPart(a_aij->a[i]);
    328:     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscRealPart(b_aij->a[i]);
    329:   } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    330:     for (i = 0; i < a_aij->i[aij->A->rmap->n]; i++) work[A->cmap->rstart + a_aij->j[i]] += PetscImaginaryPart(a_aij->a[i]);
    331:     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscImaginaryPart(b_aij->a[i]);
    332:   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unknown reduction type");
    333:   if (type == NORM_INFINITY) {
    334:     PetscCallMPI(MPIU_Allreduce(work, reductions, n, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)A)));
    335:   } else {
    336:     PetscCallMPI(MPIU_Allreduce(work, reductions, n, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)A)));
    337:   }
    338:   PetscCall(PetscFree(work));
    339:   if (type == NORM_2) {
    340:     for (i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
    341:   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    342:     for (i = 0; i < n; i++) reductions[i] /= m;
    343:   }
    344:   PetscFunctionReturn(PETSC_SUCCESS);
    345: }

    347: static PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A, IS *is)
    348: {
    349:   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)A->data;
    350:   IS              sis, gis;
    351:   const PetscInt *isis, *igis;
    352:   PetscInt        n, *iis, nsis, ngis, rstart, i;

    354:   PetscFunctionBegin;
    355:   PetscCall(MatFindOffBlockDiagonalEntries(a->A, &sis));
    356:   PetscCall(MatFindNonzeroRows(a->B, &gis));
    357:   PetscCall(ISGetSize(gis, &ngis));
    358:   PetscCall(ISGetSize(sis, &nsis));
    359:   PetscCall(ISGetIndices(sis, &isis));
    360:   PetscCall(ISGetIndices(gis, &igis));

    362:   PetscCall(PetscMalloc1(ngis + nsis, &iis));
    363:   PetscCall(PetscArraycpy(iis, igis, ngis));
    364:   PetscCall(PetscArraycpy(iis + ngis, isis, nsis));
    365:   n = ngis + nsis;
    366:   PetscCall(PetscSortRemoveDupsInt(&n, iis));
    367:   PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
    368:   for (i = 0; i < n; i++) iis[i] += rstart;
    369:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), n, iis, PETSC_OWN_POINTER, is));

    371:   PetscCall(ISRestoreIndices(sis, &isis));
    372:   PetscCall(ISRestoreIndices(gis, &igis));
    373:   PetscCall(ISDestroy(&sis));
    374:   PetscCall(ISDestroy(&gis));
    375:   PetscFunctionReturn(PETSC_SUCCESS);
    376: }

    378: /*
    379:   Local utility routine that creates a mapping from the global column
    380: number to the local number in the off-diagonal part of the local
    381: storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
    382: a slightly higher hash table cost; without it it is not scalable (each processor
    383: has an order N integer array but is fast to access.
    384: */
    385: PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
    386: {
    387:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    388:   PetscInt    n   = aij->B->cmap->n, i;

    390:   PetscFunctionBegin;
    391:   PetscCheck(!n || aij->garray, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MPIAIJ Matrix was assembled but is missing garray");
    392: #if defined(PETSC_USE_CTABLE)
    393:   PetscCall(PetscHMapICreateWithSize(n, &aij->colmap));
    394:   for (i = 0; i < n; i++) PetscCall(PetscHMapISet(aij->colmap, aij->garray[i] + 1, i + 1));
    395: #else
    396:   PetscCall(PetscCalloc1(mat->cmap->N + 1, &aij->colmap));
    397:   for (i = 0; i < n; i++) aij->colmap[aij->garray[i]] = i + 1;
    398: #endif
    399:   PetscFunctionReturn(PETSC_SUCCESS);
    400: }

    402: #define MatSetValues_SeqAIJ_A_Private(row, col, value, addv, orow, ocol) \
    403:   do { \
    404:     if (col <= lastcol1) low1 = 0; \
    405:     else high1 = nrow1; \
    406:     lastcol1 = col; \
    407:     while (high1 - low1 > 5) { \
    408:       t = (low1 + high1) / 2; \
    409:       if (rp1[t] > col) high1 = t; \
    410:       else low1 = t; \
    411:     } \
    412:     for (_i = low1; _i < high1; _i++) { \
    413:       if (rp1[_i] > col) break; \
    414:       if (rp1[_i] == col) { \
    415:         if (addv == ADD_VALUES) { \
    416:           ap1[_i] += value; \
    417:           /* Not sure LogFlops will slow down the code or not */ \
    418:           (void)PetscLogFlops(1.0); \
    419:         } else ap1[_i] = value; \
    420:         goto a_noinsert; \
    421:       } \
    422:     } \
    423:     if (value == 0.0 && ignorezeroentries && row != col) { \
    424:       low1  = 0; \
    425:       high1 = nrow1; \
    426:       goto a_noinsert; \
    427:     } \
    428:     if (nonew == 1) { \
    429:       low1  = 0; \
    430:       high1 = nrow1; \
    431:       goto a_noinsert; \
    432:     } \
    433:     PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", orow, ocol); \
    434:     MatSeqXAIJReallocateAIJ(A, am, 1, nrow1, row, col, rmax1, aa, ai, aj, rp1, ap1, aimax, nonew, MatScalar); \
    435:     N = nrow1++ - 1; \
    436:     a->nz++; \
    437:     high1++; \
    438:     /* shift up all the later entries in this row */ \
    439:     PetscCall(PetscArraymove(rp1 + _i + 1, rp1 + _i, N - _i + 1)); \
    440:     PetscCall(PetscArraymove(ap1 + _i + 1, ap1 + _i, N - _i + 1)); \
    441:     rp1[_i] = col; \
    442:     ap1[_i] = value; \
    443:   a_noinsert:; \
    444:     ailen[row] = nrow1; \
    445:   } while (0)

    447: #define MatSetValues_SeqAIJ_B_Private(row, col, value, addv, orow, ocol) \
    448:   do { \
    449:     if (col <= lastcol2) low2 = 0; \
    450:     else high2 = nrow2; \
    451:     lastcol2 = col; \
    452:     while (high2 - low2 > 5) { \
    453:       t = (low2 + high2) / 2; \
    454:       if (rp2[t] > col) high2 = t; \
    455:       else low2 = t; \
    456:     } \
    457:     for (_i = low2; _i < high2; _i++) { \
    458:       if (rp2[_i] > col) break; \
    459:       if (rp2[_i] == col) { \
    460:         if (addv == ADD_VALUES) { \
    461:           ap2[_i] += value; \
    462:           (void)PetscLogFlops(1.0); \
    463:         } else ap2[_i] = value; \
    464:         goto b_noinsert; \
    465:       } \
    466:     } \
    467:     if (value == 0.0 && ignorezeroentries) { \
    468:       low2  = 0; \
    469:       high2 = nrow2; \
    470:       goto b_noinsert; \
    471:     } \
    472:     if (nonew == 1) { \
    473:       low2  = 0; \
    474:       high2 = nrow2; \
    475:       goto b_noinsert; \
    476:     } \
    477:     PetscCheck(nonew != -1, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", orow, ocol); \
    478:     MatSeqXAIJReallocateAIJ(B, bm, 1, nrow2, row, col, rmax2, ba, bi, bj, rp2, ap2, bimax, nonew, MatScalar); \
    479:     N = nrow2++ - 1; \
    480:     b->nz++; \
    481:     high2++; \
    482:     /* shift up all the later entries in this row */ \
    483:     PetscCall(PetscArraymove(rp2 + _i + 1, rp2 + _i, N - _i + 1)); \
    484:     PetscCall(PetscArraymove(ap2 + _i + 1, ap2 + _i, N - _i + 1)); \
    485:     rp2[_i] = col; \
    486:     ap2[_i] = value; \
    487:   b_noinsert:; \
    488:     bilen[row] = nrow2; \
    489:   } while (0)

    491: static PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A, PetscInt row, const PetscScalar v[])
    492: {
    493:   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)A->data;
    494:   Mat_SeqAIJ  *a = (Mat_SeqAIJ *)mat->A->data, *b = (Mat_SeqAIJ *)mat->B->data;
    495:   PetscInt     l, *garray                         = mat->garray, diag;
    496:   PetscScalar *aa, *ba;

    498:   PetscFunctionBegin;
    499:   /* code only works for square matrices A */

    501:   /* find size of row to the left of the diagonal part */
    502:   PetscCall(MatGetOwnershipRange(A, &diag, NULL));
    503:   row = row - diag;
    504:   for (l = 0; l < b->i[row + 1] - b->i[row]; l++) {
    505:     if (garray[b->j[b->i[row] + l]] > diag) break;
    506:   }
    507:   if (l) {
    508:     PetscCall(MatSeqAIJGetArray(mat->B, &ba));
    509:     PetscCall(PetscArraycpy(ba + b->i[row], v, l));
    510:     PetscCall(MatSeqAIJRestoreArray(mat->B, &ba));
    511:   }

    513:   /* diagonal part */
    514:   if (a->i[row + 1] - a->i[row]) {
    515:     PetscCall(MatSeqAIJGetArray(mat->A, &aa));
    516:     PetscCall(PetscArraycpy(aa + a->i[row], v + l, a->i[row + 1] - a->i[row]));
    517:     PetscCall(MatSeqAIJRestoreArray(mat->A, &aa));
    518:   }

    520:   /* right of diagonal part */
    521:   if (b->i[row + 1] - b->i[row] - l) {
    522:     PetscCall(MatSeqAIJGetArray(mat->B, &ba));
    523:     PetscCall(PetscArraycpy(ba + b->i[row] + l, v + l + a->i[row + 1] - a->i[row], b->i[row + 1] - b->i[row] - l));
    524:     PetscCall(MatSeqAIJRestoreArray(mat->B, &ba));
    525:   }
    526:   PetscFunctionReturn(PETSC_SUCCESS);
    527: }

    529: PetscErrorCode MatSetValues_MPIAIJ(Mat mat, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode addv)
    530: {
    531:   Mat_MPIAIJ *aij   = (Mat_MPIAIJ *)mat->data;
    532:   PetscScalar value = 0.0;
    533:   PetscInt    i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    534:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
    535:   PetscBool   roworiented = aij->roworiented;

    537:   /* Some Variables required in the macro */
    538:   Mat         A     = aij->A;
    539:   Mat_SeqAIJ *a     = (Mat_SeqAIJ *)A->data;
    540:   PetscInt   *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
    541:   PetscBool   ignorezeroentries = a->ignorezeroentries;
    542:   Mat         B                 = aij->B;
    543:   Mat_SeqAIJ *b                 = (Mat_SeqAIJ *)B->data;
    544:   PetscInt   *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j, bm = aij->B->rmap->n, am = aij->A->rmap->n;
    545:   MatScalar  *aa, *ba;
    546:   PetscInt   *rp1, *rp2, ii, nrow1, nrow2, _i, rmax1, rmax2, N, low1, high1, low2, high2, t, lastcol1, lastcol2;
    547:   PetscInt    nonew;
    548:   MatScalar  *ap1, *ap2;

    550:   PetscFunctionBegin;
    551:   PetscCall(MatSeqAIJGetArray(A, &aa));
    552:   PetscCall(MatSeqAIJGetArray(B, &ba));
    553:   for (i = 0; i < m; i++) {
    554:     if (im[i] < 0) continue;
    555:     PetscCheck(im[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, im[i], mat->rmap->N - 1);
    556:     if (im[i] >= rstart && im[i] < rend) {
    557:       row      = im[i] - rstart;
    558:       lastcol1 = -1;
    559:       rp1      = PetscSafePointerPlusOffset(aj, ai[row]);
    560:       ap1      = PetscSafePointerPlusOffset(aa, ai[row]);
    561:       rmax1    = aimax[row];
    562:       nrow1    = ailen[row];
    563:       low1     = 0;
    564:       high1    = nrow1;
    565:       lastcol2 = -1;
    566:       rp2      = PetscSafePointerPlusOffset(bj, bi[row]);
    567:       ap2      = PetscSafePointerPlusOffset(ba, bi[row]);
    568:       rmax2    = bimax[row];
    569:       nrow2    = bilen[row];
    570:       low2     = 0;
    571:       high2    = nrow2;

    573:       for (j = 0; j < n; j++) {
    574:         if (v) value = roworiented ? v[i * n + j] : v[i + j * m];
    575:         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
    576:         if (in[j] >= cstart && in[j] < cend) {
    577:           col   = in[j] - cstart;
    578:           nonew = a->nonew;
    579:           MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
    580:         } else if (in[j] < 0) {
    581:           continue;
    582:         } else {
    583:           PetscCheck(in[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
    584:           if (mat->was_assembled) {
    585:             if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    586: #if defined(PETSC_USE_CTABLE)
    587:             PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col)); /* map global col ids to local ones */
    588:             col--;
    589: #else
    590:             col = aij->colmap[in[j]] - 1;
    591: #endif
    592:             if (col < 0 && !((Mat_SeqAIJ *)aij->B->data)->nonew) { /* col < 0 means in[j] is a new col for B */
    593:               PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));  /* Change aij->B from reduced/local format to expanded/global format */
    594:               col = in[j];
    595:               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
    596:               B     = aij->B;
    597:               b     = (Mat_SeqAIJ *)B->data;
    598:               bimax = b->imax;
    599:               bi    = b->i;
    600:               bilen = b->ilen;
    601:               bj    = b->j;
    602:               ba    = b->a;
    603:               rp2   = PetscSafePointerPlusOffset(bj, bi[row]);
    604:               ap2   = PetscSafePointerPlusOffset(ba, bi[row]);
    605:               rmax2 = bimax[row];
    606:               nrow2 = bilen[row];
    607:               low2  = 0;
    608:               high2 = nrow2;
    609:               bm    = aij->B->rmap->n;
    610:               ba    = b->a;
    611:             } else if (col < 0 && !(ignorezeroentries && value == 0.0)) {
    612:               PetscCheck(1 == ((Mat_SeqAIJ *)aij->B->data)->nonew, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Inserting a new nonzero at global row/column (%" PetscInt_FMT ", %" PetscInt_FMT ") into matrix", im[i], in[j]);
    613:               PetscCall(PetscInfo(mat, "Skipping of insertion of new nonzero location in off-diagonal portion of matrix %g(%" PetscInt_FMT ",%" PetscInt_FMT ")\n", (double)PetscRealPart(value), im[i], in[j]));
    614:             }
    615:           } else col = in[j];
    616:           nonew = b->nonew;
    617:           MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
    618:         }
    619:       }
    620:     } else {
    621:       PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Setting off process row %" PetscInt_FMT " even though MatSetOption(,MAT_NO_OFF_PROC_ENTRIES,PETSC_TRUE) was set", im[i]);
    622:       if (!aij->donotstash) {
    623:         mat->assembled = PETSC_FALSE;
    624:         if (roworiented) {
    625:           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, PetscSafePointerPlusOffset(v, i * n), (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    626:         } else {
    627:           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, PetscSafePointerPlusOffset(v, i), m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    628:         }
    629:       }
    630:     }
    631:   }
    632:   PetscCall(MatSeqAIJRestoreArray(A, &aa)); /* aa, bb might have been free'd due to reallocation above. But we don't access them here */
    633:   PetscCall(MatSeqAIJRestoreArray(B, &ba));
    634:   PetscFunctionReturn(PETSC_SUCCESS);
    635: }

    637: /*
    638:     This function sets the j and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
    639:     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
    640:     No off-processor parts off the matrix are allowed here and mat->was_assembled has to be PETSC_FALSE.
    641: */
    642: PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Mat mat, const PetscInt mat_j[], const PetscInt mat_i[])
    643: {
    644:   Mat_MPIAIJ *aij    = (Mat_MPIAIJ *)mat->data;
    645:   Mat         A      = aij->A; /* diagonal part of the matrix */
    646:   Mat         B      = aij->B; /* off-diagonal part of the matrix */
    647:   Mat_SeqAIJ *a      = (Mat_SeqAIJ *)A->data;
    648:   Mat_SeqAIJ *b      = (Mat_SeqAIJ *)B->data;
    649:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, col;
    650:   PetscInt   *ailen = a->ilen, *aj = a->j;
    651:   PetscInt   *bilen = b->ilen, *bj = b->j;
    652:   PetscInt    am          = aij->A->rmap->n, j;
    653:   PetscInt    diag_so_far = 0, dnz;
    654:   PetscInt    offd_so_far = 0, onz;

    656:   PetscFunctionBegin;
    657:   /* Iterate over all rows of the matrix */
    658:   for (j = 0; j < am; j++) {
    659:     dnz = onz = 0;
    660:     /*  Iterate over all non-zero columns of the current row */
    661:     for (col = mat_i[j]; col < mat_i[j + 1]; col++) {
    662:       /* If column is in the diagonal */
    663:       if (mat_j[col] >= cstart && mat_j[col] < cend) {
    664:         aj[diag_so_far++] = mat_j[col] - cstart;
    665:         dnz++;
    666:       } else { /* off-diagonal entries */
    667:         bj[offd_so_far++] = mat_j[col];
    668:         onz++;
    669:       }
    670:     }
    671:     ailen[j] = dnz;
    672:     bilen[j] = onz;
    673:   }
    674:   PetscFunctionReturn(PETSC_SUCCESS);
    675: }

    677: /*
    678:     This function sets the local j, a and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
    679:     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
    680:     No off-processor parts off the matrix are allowed here, they are set at a later point by MatSetValues_MPIAIJ.
    681:     Also, mat->was_assembled has to be false, otherwise the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart;
    682:     would not be true and the more complex MatSetValues_MPIAIJ has to be used.
    683: */
    684: PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat(Mat mat, const PetscInt mat_j[], const PetscInt mat_i[], const PetscScalar mat_a[])
    685: {
    686:   Mat_MPIAIJ  *aij  = (Mat_MPIAIJ *)mat->data;
    687:   Mat          A    = aij->A; /* diagonal part of the matrix */
    688:   Mat          B    = aij->B; /* off-diagonal part of the matrix */
    689:   Mat_SeqAIJ  *aijd = (Mat_SeqAIJ *)aij->A->data, *aijo = (Mat_SeqAIJ *)aij->B->data;
    690:   Mat_SeqAIJ  *a      = (Mat_SeqAIJ *)A->data;
    691:   Mat_SeqAIJ  *b      = (Mat_SeqAIJ *)B->data;
    692:   PetscInt     cstart = mat->cmap->rstart, cend = mat->cmap->rend;
    693:   PetscInt    *ailen = a->ilen, *aj = a->j;
    694:   PetscInt    *bilen = b->ilen, *bj = b->j;
    695:   PetscInt     am          = aij->A->rmap->n, j;
    696:   PetscInt    *full_diag_i = aijd->i, *full_offd_i = aijo->i; /* These variables can also include non-local elements, which are set at a later point. */
    697:   PetscInt     col, dnz_row, onz_row, rowstart_diag, rowstart_offd;
    698:   PetscScalar *aa = a->a, *ba = b->a;

    700:   PetscFunctionBegin;
    701:   /* Iterate over all rows of the matrix */
    702:   for (j = 0; j < am; j++) {
    703:     dnz_row = onz_row = 0;
    704:     rowstart_offd     = full_offd_i[j];
    705:     rowstart_diag     = full_diag_i[j];
    706:     /*  Iterate over all non-zero columns of the current row */
    707:     for (col = mat_i[j]; col < mat_i[j + 1]; col++) {
    708:       /* If column is in the diagonal */
    709:       if (mat_j[col] >= cstart && mat_j[col] < cend) {
    710:         aj[rowstart_diag + dnz_row] = mat_j[col] - cstart;
    711:         aa[rowstart_diag + dnz_row] = mat_a[col];
    712:         dnz_row++;
    713:       } else { /* off-diagonal entries */
    714:         bj[rowstart_offd + onz_row] = mat_j[col];
    715:         ba[rowstart_offd + onz_row] = mat_a[col];
    716:         onz_row++;
    717:       }
    718:     }
    719:     ailen[j] = dnz_row;
    720:     bilen[j] = onz_row;
    721:   }
    722:   PetscFunctionReturn(PETSC_SUCCESS);
    723: }

    725: static PetscErrorCode MatGetValues_MPIAIJ(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], PetscScalar v[])
    726: {
    727:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    728:   PetscInt    i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    729:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;

    731:   PetscFunctionBegin;
    732:   for (i = 0; i < m; i++) {
    733:     if (idxm[i] < 0) continue; /* negative row */
    734:     PetscCheck(idxm[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, idxm[i], mat->rmap->N - 1);
    735:     PetscCheck(idxm[i] >= rstart && idxm[i] < rend, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only local values currently supported, row requested %" PetscInt_FMT " range [%" PetscInt_FMT " %" PetscInt_FMT ")", idxm[i], rstart, rend);
    736:     row = idxm[i] - rstart;
    737:     for (j = 0; j < n; j++) {
    738:       if (idxn[j] < 0) continue; /* negative column */
    739:       PetscCheck(idxn[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, idxn[j], mat->cmap->N - 1);
    740:       if (idxn[j] >= cstart && idxn[j] < cend) {
    741:         col = idxn[j] - cstart;
    742:         PetscCall(MatGetValues(aij->A, 1, &row, 1, &col, v + i * n + j));
    743:       } else {
    744:         if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    745: #if defined(PETSC_USE_CTABLE)
    746:         PetscCall(PetscHMapIGetWithDefault(aij->colmap, idxn[j] + 1, 0, &col));
    747:         col--;
    748: #else
    749:         col = aij->colmap[idxn[j]] - 1;
    750: #endif
    751:         if ((col < 0) || (aij->garray[col] != idxn[j])) *(v + i * n + j) = 0.0;
    752:         else PetscCall(MatGetValues(aij->B, 1, &row, 1, &col, v + i * n + j));
    753:       }
    754:     }
    755:   }
    756:   PetscFunctionReturn(PETSC_SUCCESS);
    757: }

    759: static PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat, MatAssemblyType mode)
    760: {
    761:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    762:   PetscInt    nstash, reallocs;

    764:   PetscFunctionBegin;
    765:   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(PETSC_SUCCESS);

    767:   PetscCall(MatStashScatterBegin_Private(mat, &mat->stash, mat->rmap->range));
    768:   PetscCall(MatStashGetInfo_Private(&mat->stash, &nstash, &reallocs));
    769:   PetscCall(PetscInfo(aij->A, "Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
    770:   PetscFunctionReturn(PETSC_SUCCESS);
    771: }

    773: PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat, MatAssemblyType mode)
    774: {
    775:   Mat_MPIAIJ  *aij = (Mat_MPIAIJ *)mat->data;
    776:   PetscMPIInt  n;
    777:   PetscInt     i, j, rstart, ncols, flg;
    778:   PetscInt    *row, *col;
    779:   PetscBool    all_assembled;
    780:   PetscScalar *val;

    782:   /* do not use 'b = (Mat_SeqAIJ*)aij->B->data' as B can be reset in disassembly */

    784:   PetscFunctionBegin;
    785:   if (!aij->donotstash && !mat->nooffprocentries) {
    786:     while (1) {
    787:       PetscCall(MatStashScatterGetMesg_Private(&mat->stash, &n, &row, &col, &val, &flg));
    788:       if (!flg) break;

    790:       for (i = 0; i < n;) {
    791:         /* Now identify the consecutive vals belonging to the same row */
    792:         for (j = i, rstart = row[j]; j < n; j++) {
    793:           if (row[j] != rstart) break;
    794:         }
    795:         if (j < n) ncols = j - i;
    796:         else ncols = n - i;
    797:         /* Now assemble all these values with a single function call */
    798:         PetscCall(MatSetValues_MPIAIJ(mat, 1, row + i, ncols, col + i, val + i, mat->insertmode));
    799:         i = j;
    800:       }
    801:     }
    802:     PetscCall(MatStashScatterEnd_Private(&mat->stash));
    803:   }
    804: #if defined(PETSC_HAVE_DEVICE)
    805:   if (mat->offloadmask == PETSC_OFFLOAD_CPU) aij->A->offloadmask = PETSC_OFFLOAD_CPU;
    806:   /* We call MatBindToCPU() on aij->A and aij->B here, because if MatBindToCPU_MPIAIJ() is called before assembly, it cannot bind these. */
    807:   if (mat->boundtocpu) {
    808:     PetscCall(MatBindToCPU(aij->A, PETSC_TRUE));
    809:     PetscCall(MatBindToCPU(aij->B, PETSC_TRUE));
    810:   }
    811: #endif
    812:   PetscCall(MatAssemblyBegin(aij->A, mode));
    813:   PetscCall(MatAssemblyEnd(aij->A, mode));

    815:   /* determine if any process has disassembled, if so we must
    816:      also disassemble ourself, in order that we may reassemble. */
    817:   /*
    818:      if nonzero structure of submatrix B cannot change then we know that
    819:      no process disassembled thus we can skip this stuff
    820:   */
    821:   if (!((Mat_SeqAIJ *)aij->B->data)->nonew) {
    822:     PetscCallMPI(MPIU_Allreduce(&mat->was_assembled, &all_assembled, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    823:     if (mat->was_assembled && !all_assembled) { /* mat on this rank has reduced off-diag B with local col ids, but globally it does not */
    824:       PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));
    825:     }
    826:   }
    827:   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) PetscCall(MatSetUpMultiply_MPIAIJ(mat));
    828:   PetscCall(MatSetOption(aij->B, MAT_USE_INODES, PETSC_FALSE));
    829: #if defined(PETSC_HAVE_DEVICE)
    830:   if (mat->offloadmask == PETSC_OFFLOAD_CPU && aij->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) aij->B->offloadmask = PETSC_OFFLOAD_CPU;
    831: #endif
    832:   PetscCall(MatAssemblyBegin(aij->B, mode));
    833:   PetscCall(MatAssemblyEnd(aij->B, mode));

    835:   PetscCall(PetscFree2(aij->rowvalues, aij->rowindices));

    837:   aij->rowvalues = NULL;

    839:   PetscCall(VecDestroy(&aij->diag));

    841:   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
    842:   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ *)aij->A->data)->nonew) {
    843:     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
    844:     PetscCallMPI(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));
    845:   }
    846: #if defined(PETSC_HAVE_DEVICE)
    847:   mat->offloadmask = PETSC_OFFLOAD_BOTH;
    848: #endif
    849:   PetscFunctionReturn(PETSC_SUCCESS);
    850: }

    852: static PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
    853: {
    854:   Mat_MPIAIJ *l = (Mat_MPIAIJ *)A->data;

    856:   PetscFunctionBegin;
    857:   PetscCall(MatZeroEntries(l->A));
    858:   PetscCall(MatZeroEntries(l->B));
    859:   PetscFunctionReturn(PETSC_SUCCESS);
    860: }

    862: static PetscErrorCode MatZeroRows_MPIAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    863: {
    864:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)A->data;
    865:   PetscInt   *lrows;
    866:   PetscInt    r, len;
    867:   PetscBool   cong;

    869:   PetscFunctionBegin;
    870:   /* get locally owned rows */
    871:   PetscCall(MatZeroRowsMapLocal_Private(A, N, rows, &len, &lrows));
    872:   PetscCall(MatHasCongruentLayouts(A, &cong));
    873:   /* fix right-hand side if needed */
    874:   if (x && b) {
    875:     const PetscScalar *xx;
    876:     PetscScalar       *bb;

    878:     PetscCheck(cong, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Need matching row/col layout");
    879:     PetscCall(VecGetArrayRead(x, &xx));
    880:     PetscCall(VecGetArray(b, &bb));
    881:     for (r = 0; r < len; ++r) bb[lrows[r]] = diag * xx[lrows[r]];
    882:     PetscCall(VecRestoreArrayRead(x, &xx));
    883:     PetscCall(VecRestoreArray(b, &bb));
    884:   }

    886:   if (diag != 0.0 && cong) {
    887:     PetscCall(MatZeroRows(mat->A, len, lrows, diag, NULL, NULL));
    888:     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
    889:   } else if (diag != 0.0) { /* non-square or non congruent layouts -> if keepnonzeropattern is false, we allow for new insertion */
    890:     Mat_SeqAIJ *aijA = (Mat_SeqAIJ *)mat->A->data;
    891:     Mat_SeqAIJ *aijB = (Mat_SeqAIJ *)mat->B->data;
    892:     PetscInt    nnwA, nnwB;
    893:     PetscBool   nnzA, nnzB;

    895:     nnwA = aijA->nonew;
    896:     nnwB = aijB->nonew;
    897:     nnzA = aijA->keepnonzeropattern;
    898:     nnzB = aijB->keepnonzeropattern;
    899:     if (!nnzA) {
    900:       PetscCall(PetscInfo(mat->A, "Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on diagonal block.\n"));
    901:       aijA->nonew = 0;
    902:     }
    903:     if (!nnzB) {
    904:       PetscCall(PetscInfo(mat->B, "Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on off-diagonal block.\n"));
    905:       aijB->nonew = 0;
    906:     }
    907:     /* Must zero here before the next loop */
    908:     PetscCall(MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL));
    909:     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
    910:     for (r = 0; r < len; ++r) {
    911:       const PetscInt row = lrows[r] + A->rmap->rstart;
    912:       if (row >= A->cmap->N) continue;
    913:       PetscCall(MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES));
    914:     }
    915:     aijA->nonew = nnwA;
    916:     aijB->nonew = nnwB;
    917:   } else {
    918:     PetscCall(MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL));
    919:     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
    920:   }
    921:   PetscCall(PetscFree(lrows));
    922:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    923:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

    925:   /* only change matrix nonzero state if pattern was allowed to be changed */
    926:   if (!((Mat_SeqAIJ *)mat->A->data)->keepnonzeropattern || !((Mat_SeqAIJ *)mat->A->data)->nonew) {
    927:     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
    928:     PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
    929:   }
    930:   PetscFunctionReturn(PETSC_SUCCESS);
    931: }

    933: static PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    934: {
    935:   Mat_MPIAIJ        *l = (Mat_MPIAIJ *)A->data;
    936:   PetscInt           n = A->rmap->n;
    937:   PetscInt           i, j, r, m, len = 0;
    938:   PetscInt          *lrows, *owners = A->rmap->range;
    939:   PetscMPIInt        p = 0;
    940:   PetscSFNode       *rrows;
    941:   PetscSF            sf;
    942:   const PetscScalar *xx;
    943:   PetscScalar       *bb, *mask, *aij_a;
    944:   Vec                xmask, lmask;
    945:   Mat_SeqAIJ        *aij = (Mat_SeqAIJ *)l->B->data;
    946:   const PetscInt    *aj, *ii, *ridx;
    947:   PetscScalar       *aa;

    949:   PetscFunctionBegin;
    950:   /* Create SF where leaves are input rows and roots are owned rows */
    951:   PetscCall(PetscMalloc1(n, &lrows));
    952:   for (r = 0; r < n; ++r) lrows[r] = -1;
    953:   PetscCall(PetscMalloc1(N, &rrows));
    954:   for (r = 0; r < N; ++r) {
    955:     const PetscInt idx = rows[r];
    956:     PetscCheck(idx >= 0 && A->rmap->N > idx, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row %" PetscInt_FMT " out of range [0,%" PetscInt_FMT ")", idx, A->rmap->N);
    957:     if (idx < owners[p] || owners[p + 1] <= idx) { /* short-circuit the search if the last p owns this row too */
    958:       PetscCall(PetscLayoutFindOwner(A->rmap, idx, &p));
    959:     }
    960:     rrows[r].rank  = p;
    961:     rrows[r].index = rows[r] - owners[p];
    962:   }
    963:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    964:   PetscCall(PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER));
    965:   /* Collect flags for rows to be zeroed */
    966:   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *)rows, lrows, MPI_LOR));
    967:   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *)rows, lrows, MPI_LOR));
    968:   PetscCall(PetscSFDestroy(&sf));
    969:   /* Compress and put in row numbers */
    970:   for (r = 0; r < n; ++r)
    971:     if (lrows[r] >= 0) lrows[len++] = r;
    972:   /* zero diagonal part of matrix */
    973:   PetscCall(MatZeroRowsColumns(l->A, len, lrows, diag, x, b));
    974:   /* handle off-diagonal part of matrix */
    975:   PetscCall(MatCreateVecs(A, &xmask, NULL));
    976:   PetscCall(VecDuplicate(l->lvec, &lmask));
    977:   PetscCall(VecGetArray(xmask, &bb));
    978:   for (i = 0; i < len; i++) bb[lrows[i]] = 1;
    979:   PetscCall(VecRestoreArray(xmask, &bb));
    980:   PetscCall(VecScatterBegin(l->Mvctx, xmask, lmask, ADD_VALUES, SCATTER_FORWARD));
    981:   PetscCall(VecScatterEnd(l->Mvctx, xmask, lmask, ADD_VALUES, SCATTER_FORWARD));
    982:   PetscCall(VecDestroy(&xmask));
    983:   if (x && b) { /* this code is buggy when the row and column layout don't match */
    984:     PetscBool cong;

    986:     PetscCall(MatHasCongruentLayouts(A, &cong));
    987:     PetscCheck(cong, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Need matching row/col layout");
    988:     PetscCall(VecScatterBegin(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
    989:     PetscCall(VecScatterEnd(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
    990:     PetscCall(VecGetArrayRead(l->lvec, &xx));
    991:     PetscCall(VecGetArray(b, &bb));
    992:   }
    993:   PetscCall(VecGetArray(lmask, &mask));
    994:   /* remove zeroed rows of off-diagonal matrix */
    995:   PetscCall(MatSeqAIJGetArray(l->B, &aij_a));
    996:   ii = aij->i;
    997:   for (i = 0; i < len; i++) PetscCall(PetscArrayzero(PetscSafePointerPlusOffset(aij_a, ii[lrows[i]]), ii[lrows[i] + 1] - ii[lrows[i]]));
    998:   /* loop over all elements of off process part of matrix zeroing removed columns*/
    999:   if (aij->compressedrow.use) {
    1000:     m    = aij->compressedrow.nrows;
    1001:     ii   = aij->compressedrow.i;
    1002:     ridx = aij->compressedrow.rindex;
    1003:     for (i = 0; i < m; i++) {
    1004:       n  = ii[i + 1] - ii[i];
    1005:       aj = aij->j + ii[i];
    1006:       aa = aij_a + ii[i];

    1008:       for (j = 0; j < n; j++) {
    1009:         if (PetscAbsScalar(mask[*aj])) {
    1010:           if (b) bb[*ridx] -= *aa * xx[*aj];
    1011:           *aa = 0.0;
    1012:         }
    1013:         aa++;
    1014:         aj++;
    1015:       }
    1016:       ridx++;
    1017:     }
    1018:   } else { /* do not use compressed row format */
    1019:     m = l->B->rmap->n;
    1020:     for (i = 0; i < m; i++) {
    1021:       n  = ii[i + 1] - ii[i];
    1022:       aj = aij->j + ii[i];
    1023:       aa = aij_a + ii[i];
    1024:       for (j = 0; j < n; j++) {
    1025:         if (PetscAbsScalar(mask[*aj])) {
    1026:           if (b) bb[i] -= *aa * xx[*aj];
    1027:           *aa = 0.0;
    1028:         }
    1029:         aa++;
    1030:         aj++;
    1031:       }
    1032:     }
    1033:   }
    1034:   if (x && b) {
    1035:     PetscCall(VecRestoreArray(b, &bb));
    1036:     PetscCall(VecRestoreArrayRead(l->lvec, &xx));
    1037:   }
    1038:   PetscCall(MatSeqAIJRestoreArray(l->B, &aij_a));
    1039:   PetscCall(VecRestoreArray(lmask, &mask));
    1040:   PetscCall(VecDestroy(&lmask));
    1041:   PetscCall(PetscFree(lrows));

    1043:   /* only change matrix nonzero state if pattern was allowed to be changed */
    1044:   if (!((Mat_SeqAIJ *)l->A->data)->nonew) {
    1045:     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
    1046:     PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
    1047:   }
    1048:   PetscFunctionReturn(PETSC_SUCCESS);
    1049: }

    1051: static PetscErrorCode MatMult_MPIAIJ(Mat A, Vec xx, Vec yy)
    1052: {
    1053:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    1054:   PetscInt    nt;
    1055:   VecScatter  Mvctx = a->Mvctx;

    1057:   PetscFunctionBegin;
    1058:   PetscCall(VecGetLocalSize(xx, &nt));
    1059:   PetscCheck(nt == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Incompatible partition of A (%" PetscInt_FMT ") and xx (%" PetscInt_FMT ")", A->cmap->n, nt);
    1060:   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1061:   PetscUseTypeMethod(a->A, mult, xx, yy);
    1062:   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1063:   PetscUseTypeMethod(a->B, multadd, a->lvec, yy, yy);
    1064:   PetscFunctionReturn(PETSC_SUCCESS);
    1065: }

    1067: static PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A, Vec bb, Vec xx)
    1068: {
    1069:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1071:   PetscFunctionBegin;
    1072:   PetscCall(MatMultDiagonalBlock(a->A, bb, xx));
    1073:   PetscFunctionReturn(PETSC_SUCCESS);
    1074: }

    1076: static PetscErrorCode MatMultAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
    1077: {
    1078:   Mat_MPIAIJ *a     = (Mat_MPIAIJ *)A->data;
    1079:   VecScatter  Mvctx = a->Mvctx;

    1081:   PetscFunctionBegin;
    1082:   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1083:   PetscCall((*a->A->ops->multadd)(a->A, xx, yy, zz));
    1084:   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1085:   PetscCall((*a->B->ops->multadd)(a->B, a->lvec, zz, zz));
    1086:   PetscFunctionReturn(PETSC_SUCCESS);
    1087: }

    1089: static PetscErrorCode MatMultTranspose_MPIAIJ(Mat A, Vec xx, Vec yy)
    1090: {
    1091:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1093:   PetscFunctionBegin;
    1094:   /* do nondiagonal part */
    1095:   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
    1096:   /* do local part */
    1097:   PetscCall((*a->A->ops->multtranspose)(a->A, xx, yy));
    1098:   /* add partial results together */
    1099:   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
    1100:   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
    1101:   PetscFunctionReturn(PETSC_SUCCESS);
    1102: }

    1104: static PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat, Mat Bmat, PetscReal tol, PetscBool *f)
    1105: {
    1106:   MPI_Comm    comm;
    1107:   Mat_MPIAIJ *Aij = (Mat_MPIAIJ *)Amat->data, *Bij = (Mat_MPIAIJ *)Bmat->data;
    1108:   Mat         Adia = Aij->A, Bdia = Bij->A, Aoff, Boff, *Aoffs, *Boffs;
    1109:   IS          Me, Notme;
    1110:   PetscInt    M, N, first, last, *notme, i;
    1111:   PetscBool   lf;
    1112:   PetscMPIInt size;

    1114:   PetscFunctionBegin;
    1115:   /* Easy test: symmetric diagonal block */
    1116:   PetscCall(MatIsTranspose(Adia, Bdia, tol, &lf));
    1117:   PetscCallMPI(MPIU_Allreduce(&lf, f, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)Amat)));
    1118:   if (!*f) PetscFunctionReturn(PETSC_SUCCESS);
    1119:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
    1120:   PetscCallMPI(MPI_Comm_size(comm, &size));
    1121:   if (size == 1) PetscFunctionReturn(PETSC_SUCCESS);

    1123:   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
    1124:   PetscCall(MatGetSize(Amat, &M, &N));
    1125:   PetscCall(MatGetOwnershipRange(Amat, &first, &last));
    1126:   PetscCall(PetscMalloc1(N - last + first, &notme));
    1127:   for (i = 0; i < first; i++) notme[i] = i;
    1128:   for (i = last; i < M; i++) notme[i - last + first] = i;
    1129:   PetscCall(ISCreateGeneral(MPI_COMM_SELF, N - last + first, notme, PETSC_COPY_VALUES, &Notme));
    1130:   PetscCall(ISCreateStride(MPI_COMM_SELF, last - first, first, 1, &Me));
    1131:   PetscCall(MatCreateSubMatrices(Amat, 1, &Me, &Notme, MAT_INITIAL_MATRIX, &Aoffs));
    1132:   Aoff = Aoffs[0];
    1133:   PetscCall(MatCreateSubMatrices(Bmat, 1, &Notme, &Me, MAT_INITIAL_MATRIX, &Boffs));
    1134:   Boff = Boffs[0];
    1135:   PetscCall(MatIsTranspose(Aoff, Boff, tol, f));
    1136:   PetscCall(MatDestroyMatrices(1, &Aoffs));
    1137:   PetscCall(MatDestroyMatrices(1, &Boffs));
    1138:   PetscCall(ISDestroy(&Me));
    1139:   PetscCall(ISDestroy(&Notme));
    1140:   PetscCall(PetscFree(notme));
    1141:   PetscFunctionReturn(PETSC_SUCCESS);
    1142: }

    1144: static PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
    1145: {
    1146:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1148:   PetscFunctionBegin;
    1149:   /* do nondiagonal part */
    1150:   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
    1151:   /* do local part */
    1152:   PetscCall((*a->A->ops->multtransposeadd)(a->A, xx, yy, zz));
    1153:   /* add partial results together */
    1154:   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
    1155:   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
    1156:   PetscFunctionReturn(PETSC_SUCCESS);
    1157: }

    1159: /*
    1160:   This only works correctly for square matrices where the subblock A->A is the
    1161:    diagonal block
    1162: */
    1163: static PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A, Vec v)
    1164: {
    1165:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1167:   PetscFunctionBegin;
    1168:   PetscCheck(A->rmap->N == A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Supports only square matrix where A->A is diag block");
    1169:   PetscCheck(A->rmap->rstart == A->cmap->rstart && A->rmap->rend == A->cmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "row partition must equal col partition");
    1170:   PetscCall(MatGetDiagonal(a->A, v));
    1171:   PetscFunctionReturn(PETSC_SUCCESS);
    1172: }

    1174: static PetscErrorCode MatScale_MPIAIJ(Mat A, PetscScalar aa)
    1175: {
    1176:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1178:   PetscFunctionBegin;
    1179:   PetscCall(MatScale(a->A, aa));
    1180:   PetscCall(MatScale(a->B, aa));
    1181:   PetscFunctionReturn(PETSC_SUCCESS);
    1182: }

    1184: static PetscErrorCode MatView_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
    1185: {
    1186:   Mat_MPIAIJ        *aij    = (Mat_MPIAIJ *)mat->data;
    1187:   Mat_SeqAIJ        *A      = (Mat_SeqAIJ *)aij->A->data;
    1188:   Mat_SeqAIJ        *B      = (Mat_SeqAIJ *)aij->B->data;
    1189:   const PetscInt    *garray = aij->garray;
    1190:   const PetscScalar *aa, *ba;
    1191:   PetscInt           header[4], M, N, m, rs, cs, cnt, i, ja, jb;
    1192:   PetscInt64         nz, hnz;
    1193:   PetscInt          *rowlens;
    1194:   PetscInt          *colidxs;
    1195:   PetscScalar       *matvals;
    1196:   PetscMPIInt        rank;

    1198:   PetscFunctionBegin;
    1199:   PetscCall(PetscViewerSetUp(viewer));

    1201:   M  = mat->rmap->N;
    1202:   N  = mat->cmap->N;
    1203:   m  = mat->rmap->n;
    1204:   rs = mat->rmap->rstart;
    1205:   cs = mat->cmap->rstart;
    1206:   nz = A->nz + B->nz;

    1208:   /* write matrix header */
    1209:   header[0] = MAT_FILE_CLASSID;
    1210:   header[1] = M;
    1211:   header[2] = N;
    1212:   PetscCallMPI(MPI_Reduce(&nz, &hnz, 1, MPIU_INT64, MPI_SUM, 0, PetscObjectComm((PetscObject)mat)));
    1213:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
    1214:   if (rank == 0) PetscCall(PetscIntCast(hnz, &header[3]));
    1215:   PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));

    1217:   /* fill in and store row lengths  */
    1218:   PetscCall(PetscMalloc1(m, &rowlens));
    1219:   for (i = 0; i < m; i++) rowlens[i] = A->i[i + 1] - A->i[i] + B->i[i + 1] - B->i[i];
    1220:   PetscCall(PetscViewerBinaryWriteAll(viewer, rowlens, m, rs, M, PETSC_INT));
    1221:   PetscCall(PetscFree(rowlens));

    1223:   /* fill in and store column indices */
    1224:   PetscCall(PetscMalloc1(nz, &colidxs));
    1225:   for (cnt = 0, i = 0; i < m; i++) {
    1226:     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
    1227:       if (garray[B->j[jb]] > cs) break;
    1228:       colidxs[cnt++] = garray[B->j[jb]];
    1229:     }
    1230:     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) colidxs[cnt++] = A->j[ja] + cs;
    1231:     for (; jb < B->i[i + 1]; jb++) colidxs[cnt++] = garray[B->j[jb]];
    1232:   }
    1233:   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
    1234:   PetscCall(PetscViewerBinaryWriteAll(viewer, colidxs, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
    1235:   PetscCall(PetscFree(colidxs));

    1237:   /* fill in and store nonzero values */
    1238:   PetscCall(MatSeqAIJGetArrayRead(aij->A, &aa));
    1239:   PetscCall(MatSeqAIJGetArrayRead(aij->B, &ba));
    1240:   PetscCall(PetscMalloc1(nz, &matvals));
    1241:   for (cnt = 0, i = 0; i < m; i++) {
    1242:     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
    1243:       if (garray[B->j[jb]] > cs) break;
    1244:       matvals[cnt++] = ba[jb];
    1245:     }
    1246:     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) matvals[cnt++] = aa[ja];
    1247:     for (; jb < B->i[i + 1]; jb++) matvals[cnt++] = ba[jb];
    1248:   }
    1249:   PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &aa));
    1250:   PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &ba));
    1251:   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_LIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
    1252:   PetscCall(PetscViewerBinaryWriteAll(viewer, matvals, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
    1253:   PetscCall(PetscFree(matvals));

    1255:   /* write block size option to the viewer's .info file */
    1256:   PetscCall(MatView_Binary_BlockSizes(mat, viewer));
    1257:   PetscFunctionReturn(PETSC_SUCCESS);
    1258: }

    1260: #include <petscdraw.h>
    1261: static PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat, PetscViewer viewer)
    1262: {
    1263:   Mat_MPIAIJ       *aij  = (Mat_MPIAIJ *)mat->data;
    1264:   PetscMPIInt       rank = aij->rank, size = aij->size;
    1265:   PetscBool         isdraw, isascii, isbinary;
    1266:   PetscViewer       sviewer;
    1267:   PetscViewerFormat format;

    1269:   PetscFunctionBegin;
    1270:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
    1271:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    1272:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    1273:   if (isascii) {
    1274:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1275:     if (format == PETSC_VIEWER_LOAD_BALANCE) {
    1276:       PetscInt i, nmax = 0, nmin = PETSC_INT_MAX, navg = 0, *nz, nzlocal = ((Mat_SeqAIJ *)aij->A->data)->nz + ((Mat_SeqAIJ *)aij->B->data)->nz;
    1277:       PetscCall(PetscMalloc1(size, &nz));
    1278:       PetscCallMPI(MPI_Allgather(&nzlocal, 1, MPIU_INT, nz, 1, MPIU_INT, PetscObjectComm((PetscObject)mat)));
    1279:       for (i = 0; i < size; i++) {
    1280:         nmax = PetscMax(nmax, nz[i]);
    1281:         nmin = PetscMin(nmin, nz[i]);
    1282:         navg += nz[i];
    1283:       }
    1284:       PetscCall(PetscFree(nz));
    1285:       navg = navg / size;
    1286:       PetscCall(PetscViewerASCIIPrintf(viewer, "Load Balance - Nonzeros: Min %" PetscInt_FMT "  avg %" PetscInt_FMT "  max %" PetscInt_FMT "\n", nmin, navg, nmax));
    1287:       PetscFunctionReturn(PETSC_SUCCESS);
    1288:     }
    1289:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1290:     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1291:       MatInfo   info;
    1292:       PetscInt *inodes = NULL;

    1294:       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
    1295:       PetscCall(MatGetInfo(mat, MAT_LOCAL, &info));
    1296:       PetscCall(MatInodeGetInodeSizes(aij->A, NULL, &inodes, NULL));
    1297:       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    1298:       if (!inodes) {
    1299:         PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] Local rows %" PetscInt_FMT " nz %" PetscInt_FMT " nz alloced %" PetscInt_FMT " mem %g, not using I-node routines\n", rank, mat->rmap->n, (PetscInt)info.nz_used, (PetscInt)info.nz_allocated,
    1300:                                                      info.memory));
    1301:       } else {
    1302:         PetscCall(
    1303:           PetscViewerASCIISynchronizedPrintf(viewer, "[%d] Local rows %" PetscInt_FMT " nz %" PetscInt_FMT " nz alloced %" PetscInt_FMT " mem %g, using I-node routines\n", rank, mat->rmap->n, (PetscInt)info.nz_used, (PetscInt)info.nz_allocated, info.memory));
    1304:       }
    1305:       PetscCall(MatGetInfo(aij->A, MAT_LOCAL, &info));
    1306:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] on-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
    1307:       PetscCall(MatGetInfo(aij->B, MAT_LOCAL, &info));
    1308:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] off-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
    1309:       PetscCall(PetscViewerFlush(viewer));
    1310:       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    1311:       PetscCall(PetscViewerASCIIPrintf(viewer, "Information on VecScatter used in matrix-vector product: \n"));
    1312:       PetscCall(VecScatterView(aij->Mvctx, viewer));
    1313:       PetscFunctionReturn(PETSC_SUCCESS);
    1314:     } else if (format == PETSC_VIEWER_ASCII_INFO) {
    1315:       PetscInt inodecount, inodelimit, *inodes;
    1316:       PetscCall(MatInodeGetInodeSizes(aij->A, &inodecount, &inodes, &inodelimit));
    1317:       if (inodes) {
    1318:         PetscCall(PetscViewerASCIIPrintf(viewer, "using I-node (on process 0) routines: found %" PetscInt_FMT " nodes, limit used is %" PetscInt_FMT "\n", inodecount, inodelimit));
    1319:       } else {
    1320:         PetscCall(PetscViewerASCIIPrintf(viewer, "not using I-node (on process 0) routines\n"));
    1321:       }
    1322:       PetscFunctionReturn(PETSC_SUCCESS);
    1323:     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
    1324:       PetscFunctionReturn(PETSC_SUCCESS);
    1325:     }
    1326:   } else if (isbinary) {
    1327:     if (size == 1) {
    1328:       PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
    1329:       PetscCall(MatView(aij->A, viewer));
    1330:     } else {
    1331:       PetscCall(MatView_MPIAIJ_Binary(mat, viewer));
    1332:     }
    1333:     PetscFunctionReturn(PETSC_SUCCESS);
    1334:   } else if (isascii && size == 1) {
    1335:     PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
    1336:     PetscCall(MatView(aij->A, viewer));
    1337:     PetscFunctionReturn(PETSC_SUCCESS);
    1338:   } else if (isdraw) {
    1339:     PetscDraw draw;
    1340:     PetscBool isnull;
    1341:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
    1342:     PetscCall(PetscDrawIsNull(draw, &isnull));
    1343:     if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
    1344:   }

    1346:   { /* assemble the entire matrix onto first processor */
    1347:     Mat A = NULL, Av;
    1348:     IS  isrow, iscol;

    1350:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->rmap->N : 0, 0, 1, &isrow));
    1351:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->cmap->N : 0, 0, 1, &iscol));
    1352:     PetscCall(MatCreateSubMatrix(mat, isrow, iscol, MAT_INITIAL_MATRIX, &A));
    1353:     PetscCall(MatMPIAIJGetSeqAIJ(A, &Av, NULL, NULL));
    1354:     /*  The commented code uses MatCreateSubMatrices instead */
    1355:     /*
    1356:     Mat *AA, A = NULL, Av;
    1357:     IS  isrow,iscol;

    1359:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->rmap->N : 0,0,1,&isrow));
    1360:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->cmap->N : 0,0,1,&iscol));
    1361:     PetscCall(MatCreateSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&AA));
    1362:     if (rank == 0) {
    1363:        PetscCall(PetscObjectReference((PetscObject)AA[0]));
    1364:        A    = AA[0];
    1365:        Av   = AA[0];
    1366:     }
    1367:     PetscCall(MatDestroySubMatrices(1,&AA));
    1368: */
    1369:     PetscCall(ISDestroy(&iscol));
    1370:     PetscCall(ISDestroy(&isrow));
    1371:     /*
    1372:        Everyone has to call to draw the matrix since the graphics waits are
    1373:        synchronized across all processors that share the PetscDraw object
    1374:     */
    1375:     PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    1376:     if (rank == 0) {
    1377:       if (((PetscObject)mat)->name) PetscCall(PetscObjectSetName((PetscObject)Av, ((PetscObject)mat)->name));
    1378:       PetscCall(MatView_SeqAIJ(Av, sviewer));
    1379:     }
    1380:     PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    1381:     PetscCall(MatDestroy(&A));
    1382:   }
    1383:   PetscFunctionReturn(PETSC_SUCCESS);
    1384: }

    1386: PetscErrorCode MatView_MPIAIJ(Mat mat, PetscViewer viewer)
    1387: {
    1388:   PetscBool isascii, isdraw, issocket, isbinary;

    1390:   PetscFunctionBegin;
    1391:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    1392:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
    1393:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    1394:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSOCKET, &issocket));
    1395:   if (isascii || isdraw || isbinary || issocket) PetscCall(MatView_MPIAIJ_ASCIIorDraworSocket(mat, viewer));
    1396:   PetscFunctionReturn(PETSC_SUCCESS);
    1397: }

    1399: static PetscErrorCode MatSOR_MPIAIJ(Mat matin, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
    1400: {
    1401:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)matin->data;
    1402:   Vec         bb1 = NULL;
    1403:   PetscBool   hasop;

    1405:   PetscFunctionBegin;
    1406:   if (flag == SOR_APPLY_UPPER) {
    1407:     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1408:     PetscFunctionReturn(PETSC_SUCCESS);
    1409:   }

    1411:   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) PetscCall(VecDuplicate(bb, &bb1));

    1413:   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
    1414:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1415:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1416:       its--;
    1417:     }

    1419:     while (its--) {
    1420:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1421:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1423:       /* update rhs: bb1 = bb - B*x */
    1424:       PetscCall(VecScale(mat->lvec, -1.0));
    1425:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1427:       /* local sweep */
    1428:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_SYMMETRIC_SWEEP, fshift, lits, 1, xx));
    1429:     }
    1430:   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
    1431:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1432:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1433:       its--;
    1434:     }
    1435:     while (its--) {
    1436:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1437:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1439:       /* update rhs: bb1 = bb - B*x */
    1440:       PetscCall(VecScale(mat->lvec, -1.0));
    1441:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1443:       /* local sweep */
    1444:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_FORWARD_SWEEP, fshift, lits, 1, xx));
    1445:     }
    1446:   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
    1447:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1448:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1449:       its--;
    1450:     }
    1451:     while (its--) {
    1452:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1453:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1455:       /* update rhs: bb1 = bb - B*x */
    1456:       PetscCall(VecScale(mat->lvec, -1.0));
    1457:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1459:       /* local sweep */
    1460:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_BACKWARD_SWEEP, fshift, lits, 1, xx));
    1461:     }
    1462:   } else if (flag & SOR_EISENSTAT) {
    1463:     Vec xx1;

    1465:     PetscCall(VecDuplicate(bb, &xx1));
    1466:     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP), fshift, lits, 1, xx));

    1468:     PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1469:     PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1470:     if (!mat->diag) {
    1471:       PetscCall(MatCreateVecs(matin, &mat->diag, NULL));
    1472:       PetscCall(MatGetDiagonal(matin, mat->diag));
    1473:     }
    1474:     PetscCall(MatHasOperation(matin, MATOP_MULT_DIAGONAL_BLOCK, &hasop));
    1475:     if (hasop) {
    1476:       PetscCall(MatMultDiagonalBlock(matin, xx, bb1));
    1477:     } else {
    1478:       PetscCall(VecPointwiseMult(bb1, mat->diag, xx));
    1479:     }
    1480:     PetscCall(VecAYPX(bb1, (omega - 2.0) / omega, bb));

    1482:     PetscCall(MatMultAdd(mat->B, mat->lvec, bb1, bb1));

    1484:     /* local sweep */
    1485:     PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP), fshift, lits, 1, xx1));
    1486:     PetscCall(VecAXPY(xx, 1.0, xx1));
    1487:     PetscCall(VecDestroy(&xx1));
    1488:   } else SETERRQ(PetscObjectComm((PetscObject)matin), PETSC_ERR_SUP, "Parallel SOR not supported");

    1490:   PetscCall(VecDestroy(&bb1));

    1492:   matin->factorerrortype = mat->A->factorerrortype;
    1493:   PetscFunctionReturn(PETSC_SUCCESS);
    1494: }

    1496: static PetscErrorCode MatPermute_MPIAIJ(Mat A, IS rowp, IS colp, Mat *B)
    1497: {
    1498:   Mat             aA, aB, Aperm;
    1499:   const PetscInt *rwant, *cwant, *gcols, *ai, *bi, *aj, *bj;
    1500:   PetscScalar    *aa, *ba;
    1501:   PetscInt        i, j, m, n, ng, anz, bnz, *dnnz, *onnz, *tdnnz, *tonnz, *rdest, *cdest, *work, *gcdest;
    1502:   PetscSF         rowsf, sf;
    1503:   IS              parcolp = NULL;
    1504:   PetscBool       done;

    1506:   PetscFunctionBegin;
    1507:   PetscCall(MatGetLocalSize(A, &m, &n));
    1508:   PetscCall(ISGetIndices(rowp, &rwant));
    1509:   PetscCall(ISGetIndices(colp, &cwant));
    1510:   PetscCall(PetscMalloc3(PetscMax(m, n), &work, m, &rdest, n, &cdest));

    1512:   /* Invert row permutation to find out where my rows should go */
    1513:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &rowsf));
    1514:   PetscCall(PetscSFSetGraphLayout(rowsf, A->rmap, A->rmap->n, NULL, PETSC_OWN_POINTER, rwant));
    1515:   PetscCall(PetscSFSetFromOptions(rowsf));
    1516:   for (i = 0; i < m; i++) work[i] = A->rmap->rstart + i;
    1517:   PetscCall(PetscSFReduceBegin(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));
    1518:   PetscCall(PetscSFReduceEnd(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));

    1520:   /* Invert column permutation to find out where my columns should go */
    1521:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1522:   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, A->cmap->n, NULL, PETSC_OWN_POINTER, cwant));
    1523:   PetscCall(PetscSFSetFromOptions(sf));
    1524:   for (i = 0; i < n; i++) work[i] = A->cmap->rstart + i;
    1525:   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, work, cdest, MPI_REPLACE));
    1526:   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, work, cdest, MPI_REPLACE));
    1527:   PetscCall(PetscSFDestroy(&sf));

    1529:   PetscCall(ISRestoreIndices(rowp, &rwant));
    1530:   PetscCall(ISRestoreIndices(colp, &cwant));
    1531:   PetscCall(MatMPIAIJGetSeqAIJ(A, &aA, &aB, &gcols));

    1533:   /* Find out where my gcols should go */
    1534:   PetscCall(MatGetSize(aB, NULL, &ng));
    1535:   PetscCall(PetscMalloc1(ng, &gcdest));
    1536:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1537:   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, ng, NULL, PETSC_OWN_POINTER, gcols));
    1538:   PetscCall(PetscSFSetFromOptions(sf));
    1539:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
    1540:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
    1541:   PetscCall(PetscSFDestroy(&sf));

    1543:   PetscCall(PetscCalloc4(m, &dnnz, m, &onnz, m, &tdnnz, m, &tonnz));
    1544:   PetscCall(MatGetRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
    1545:   PetscCall(MatGetRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
    1546:   for (i = 0; i < m; i++) {
    1547:     PetscInt    row = rdest[i];
    1548:     PetscMPIInt rowner;
    1549:     PetscCall(PetscLayoutFindOwner(A->rmap, row, &rowner));
    1550:     for (j = ai[i]; j < ai[i + 1]; j++) {
    1551:       PetscInt    col = cdest[aj[j]];
    1552:       PetscMPIInt cowner;
    1553:       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner)); /* Could build an index for the columns to eliminate this search */
    1554:       if (rowner == cowner) dnnz[i]++;
    1555:       else onnz[i]++;
    1556:     }
    1557:     for (j = bi[i]; j < bi[i + 1]; j++) {
    1558:       PetscInt    col = gcdest[bj[j]];
    1559:       PetscMPIInt cowner;
    1560:       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner));
    1561:       if (rowner == cowner) dnnz[i]++;
    1562:       else onnz[i]++;
    1563:     }
    1564:   }
    1565:   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
    1566:   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
    1567:   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
    1568:   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
    1569:   PetscCall(PetscSFDestroy(&rowsf));

    1571:   PetscCall(MatCreateAIJ(PetscObjectComm((PetscObject)A), A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N, 0, tdnnz, 0, tonnz, &Aperm));
    1572:   PetscCall(MatSeqAIJGetArray(aA, &aa));
    1573:   PetscCall(MatSeqAIJGetArray(aB, &ba));
    1574:   for (i = 0; i < m; i++) {
    1575:     PetscInt *acols = dnnz, *bcols = onnz; /* Repurpose now-unneeded arrays */
    1576:     PetscInt  j0, rowlen;
    1577:     rowlen = ai[i + 1] - ai[i];
    1578:     for (j0 = j = 0; j < rowlen; j0 = j) { /* rowlen could be larger than number of rows m, so sum in batches */
    1579:       for (; j < PetscMin(rowlen, j0 + m); j++) acols[j - j0] = cdest[aj[ai[i] + j]];
    1580:       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, acols, aa + ai[i] + j0, INSERT_VALUES));
    1581:     }
    1582:     rowlen = bi[i + 1] - bi[i];
    1583:     for (j0 = j = 0; j < rowlen; j0 = j) {
    1584:       for (; j < PetscMin(rowlen, j0 + m); j++) bcols[j - j0] = gcdest[bj[bi[i] + j]];
    1585:       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, bcols, ba + bi[i] + j0, INSERT_VALUES));
    1586:     }
    1587:   }
    1588:   PetscCall(MatAssemblyBegin(Aperm, MAT_FINAL_ASSEMBLY));
    1589:   PetscCall(MatAssemblyEnd(Aperm, MAT_FINAL_ASSEMBLY));
    1590:   PetscCall(MatRestoreRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
    1591:   PetscCall(MatRestoreRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
    1592:   PetscCall(MatSeqAIJRestoreArray(aA, &aa));
    1593:   PetscCall(MatSeqAIJRestoreArray(aB, &ba));
    1594:   PetscCall(PetscFree4(dnnz, onnz, tdnnz, tonnz));
    1595:   PetscCall(PetscFree3(work, rdest, cdest));
    1596:   PetscCall(PetscFree(gcdest));
    1597:   if (parcolp) PetscCall(ISDestroy(&colp));
    1598:   *B = Aperm;
    1599:   PetscFunctionReturn(PETSC_SUCCESS);
    1600: }

    1602: static PetscErrorCode MatGetGhosts_MPIAIJ(Mat mat, PetscInt *nghosts, const PetscInt *ghosts[])
    1603: {
    1604:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    1606:   PetscFunctionBegin;
    1607:   PetscCall(MatGetSize(aij->B, NULL, nghosts));
    1608:   if (ghosts) *ghosts = aij->garray;
    1609:   PetscFunctionReturn(PETSC_SUCCESS);
    1610: }

    1612: static PetscErrorCode MatGetInfo_MPIAIJ(Mat matin, MatInfoType flag, MatInfo *info)
    1613: {
    1614:   Mat_MPIAIJ    *mat = (Mat_MPIAIJ *)matin->data;
    1615:   Mat            A = mat->A, B = mat->B;
    1616:   PetscLogDouble isend[5], irecv[5];

    1618:   PetscFunctionBegin;
    1619:   info->block_size = 1.0;
    1620:   PetscCall(MatGetInfo(A, MAT_LOCAL, info));

    1622:   isend[0] = info->nz_used;
    1623:   isend[1] = info->nz_allocated;
    1624:   isend[2] = info->nz_unneeded;
    1625:   isend[3] = info->memory;
    1626:   isend[4] = info->mallocs;

    1628:   PetscCall(MatGetInfo(B, MAT_LOCAL, info));

    1630:   isend[0] += info->nz_used;
    1631:   isend[1] += info->nz_allocated;
    1632:   isend[2] += info->nz_unneeded;
    1633:   isend[3] += info->memory;
    1634:   isend[4] += info->mallocs;
    1635:   if (flag == MAT_LOCAL) {
    1636:     info->nz_used      = isend[0];
    1637:     info->nz_allocated = isend[1];
    1638:     info->nz_unneeded  = isend[2];
    1639:     info->memory       = isend[3];
    1640:     info->mallocs      = isend[4];
    1641:   } else if (flag == MAT_GLOBAL_MAX) {
    1642:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)matin)));

    1644:     info->nz_used      = irecv[0];
    1645:     info->nz_allocated = irecv[1];
    1646:     info->nz_unneeded  = irecv[2];
    1647:     info->memory       = irecv[3];
    1648:     info->mallocs      = irecv[4];
    1649:   } else if (flag == MAT_GLOBAL_SUM) {
    1650:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)matin)));

    1652:     info->nz_used      = irecv[0];
    1653:     info->nz_allocated = irecv[1];
    1654:     info->nz_unneeded  = irecv[2];
    1655:     info->memory       = irecv[3];
    1656:     info->mallocs      = irecv[4];
    1657:   }
    1658:   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
    1659:   info->fill_ratio_needed = 0;
    1660:   info->factor_mallocs    = 0;
    1661:   PetscFunctionReturn(PETSC_SUCCESS);
    1662: }

    1664: PetscErrorCode MatSetOption_MPIAIJ(Mat A, MatOption op, PetscBool flg)
    1665: {
    1666:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1668:   PetscFunctionBegin;
    1669:   switch (op) {
    1670:   case MAT_NEW_NONZERO_LOCATIONS:
    1671:   case MAT_NEW_NONZERO_ALLOCATION_ERR:
    1672:   case MAT_UNUSED_NONZERO_LOCATION_ERR:
    1673:   case MAT_KEEP_NONZERO_PATTERN:
    1674:   case MAT_NEW_NONZERO_LOCATION_ERR:
    1675:   case MAT_USE_INODES:
    1676:   case MAT_IGNORE_ZERO_ENTRIES:
    1677:   case MAT_FORM_EXPLICIT_TRANSPOSE:
    1678:     MatCheckPreallocated(A, 1);
    1679:     PetscCall(MatSetOption(a->A, op, flg));
    1680:     PetscCall(MatSetOption(a->B, op, flg));
    1681:     break;
    1682:   case MAT_ROW_ORIENTED:
    1683:     MatCheckPreallocated(A, 1);
    1684:     a->roworiented = flg;

    1686:     PetscCall(MatSetOption(a->A, op, flg));
    1687:     PetscCall(MatSetOption(a->B, op, flg));
    1688:     break;
    1689:   case MAT_IGNORE_OFF_PROC_ENTRIES:
    1690:     a->donotstash = flg;
    1691:     break;
    1692:   /* Symmetry flags are handled directly by MatSetOption() and they don't affect preallocation */
    1693:   case MAT_SPD:
    1694:   case MAT_SYMMETRIC:
    1695:   case MAT_STRUCTURALLY_SYMMETRIC:
    1696:   case MAT_HERMITIAN:
    1697:   case MAT_SYMMETRY_ETERNAL:
    1698:   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
    1699:   case MAT_SPD_ETERNAL:
    1700:     /* if the diagonal matrix is square it inherits some of the properties above */
    1701:     if (a->A && A->rmap->n == A->cmap->n) PetscCall(MatSetOption(a->A, op, flg));
    1702:     break;
    1703:   case MAT_SUBMAT_SINGLEIS:
    1704:     A->submat_singleis = flg;
    1705:     break;
    1706:   default:
    1707:     break;
    1708:   }
    1709:   PetscFunctionReturn(PETSC_SUCCESS);
    1710: }

    1712: PetscErrorCode MatGetRow_MPIAIJ(Mat matin, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    1713: {
    1714:   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)matin->data;
    1715:   PetscScalar *vworkA, *vworkB, **pvA, **pvB, *v_p;
    1716:   PetscInt     i, *cworkA, *cworkB, **pcA, **pcB, cstart = matin->cmap->rstart;
    1717:   PetscInt     nztot, nzA, nzB, lrow, rstart = matin->rmap->rstart, rend = matin->rmap->rend;
    1718:   PetscInt    *cmap, *idx_p;

    1720:   PetscFunctionBegin;
    1721:   PetscCheck(!mat->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Already active");
    1722:   mat->getrowactive = PETSC_TRUE;

    1724:   if (!mat->rowvalues && (idx || v)) {
    1725:     /*
    1726:         allocate enough space to hold information from the longest row.
    1727:     */
    1728:     Mat_SeqAIJ *Aa = (Mat_SeqAIJ *)mat->A->data, *Ba = (Mat_SeqAIJ *)mat->B->data;
    1729:     PetscInt    max = 1, tmp;
    1730:     for (i = 0; i < matin->rmap->n; i++) {
    1731:       tmp = Aa->i[i + 1] - Aa->i[i] + Ba->i[i + 1] - Ba->i[i];
    1732:       if (max < tmp) max = tmp;
    1733:     }
    1734:     PetscCall(PetscMalloc2(max, &mat->rowvalues, max, &mat->rowindices));
    1735:   }

    1737:   PetscCheck(row >= rstart && row < rend, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Only local rows");
    1738:   lrow = row - rstart;

    1740:   pvA = &vworkA;
    1741:   pcA = &cworkA;
    1742:   pvB = &vworkB;
    1743:   pcB = &cworkB;
    1744:   if (!v) {
    1745:     pvA = NULL;
    1746:     pvB = NULL;
    1747:   }
    1748:   if (!idx) {
    1749:     pcA = NULL;
    1750:     if (!v) pcB = NULL;
    1751:   }
    1752:   PetscCall((*mat->A->ops->getrow)(mat->A, lrow, &nzA, pcA, pvA));
    1753:   PetscCall((*mat->B->ops->getrow)(mat->B, lrow, &nzB, pcB, pvB));
    1754:   nztot = nzA + nzB;

    1756:   cmap = mat->garray;
    1757:   if (v || idx) {
    1758:     if (nztot) {
    1759:       /* Sort by increasing column numbers, assuming A and B already sorted */
    1760:       PetscInt imark = -1;
    1761:       if (v) {
    1762:         *v = v_p = mat->rowvalues;
    1763:         for (i = 0; i < nzB; i++) {
    1764:           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
    1765:           else break;
    1766:         }
    1767:         imark = i;
    1768:         for (i = 0; i < nzA; i++) v_p[imark + i] = vworkA[i];
    1769:         for (i = imark; i < nzB; i++) v_p[nzA + i] = vworkB[i];
    1770:       }
    1771:       if (idx) {
    1772:         *idx = idx_p = mat->rowindices;
    1773:         if (imark > -1) {
    1774:           for (i = 0; i < imark; i++) idx_p[i] = cmap[cworkB[i]];
    1775:         } else {
    1776:           for (i = 0; i < nzB; i++) {
    1777:             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
    1778:             else break;
    1779:           }
    1780:           imark = i;
    1781:         }
    1782:         for (i = 0; i < nzA; i++) idx_p[imark + i] = cstart + cworkA[i];
    1783:         for (i = imark; i < nzB; i++) idx_p[nzA + i] = cmap[cworkB[i]];
    1784:       }
    1785:     } else {
    1786:       if (idx) *idx = NULL;
    1787:       if (v) *v = NULL;
    1788:     }
    1789:   }
    1790:   *nz = nztot;
    1791:   PetscCall((*mat->A->ops->restorerow)(mat->A, lrow, &nzA, pcA, pvA));
    1792:   PetscCall((*mat->B->ops->restorerow)(mat->B, lrow, &nzB, pcB, pvB));
    1793:   PetscFunctionReturn(PETSC_SUCCESS);
    1794: }

    1796: PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    1797: {
    1798:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    1800:   PetscFunctionBegin;
    1801:   PetscCheck(aij->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "MatGetRow() must be called first");
    1802:   aij->getrowactive = PETSC_FALSE;
    1803:   PetscFunctionReturn(PETSC_SUCCESS);
    1804: }

    1806: static PetscErrorCode MatNorm_MPIAIJ(Mat mat, NormType type, PetscReal *norm)
    1807: {
    1808:   Mat_MPIAIJ      *aij  = (Mat_MPIAIJ *)mat->data;
    1809:   Mat_SeqAIJ      *amat = (Mat_SeqAIJ *)aij->A->data, *bmat = (Mat_SeqAIJ *)aij->B->data;
    1810:   PetscInt         i, j, cstart = mat->cmap->rstart;
    1811:   PetscReal        sum = 0.0;
    1812:   const MatScalar *v, *amata, *bmata;

    1814:   PetscFunctionBegin;
    1815:   if (aij->size == 1) {
    1816:     PetscCall(MatNorm(aij->A, type, norm));
    1817:   } else {
    1818:     PetscCall(MatSeqAIJGetArrayRead(aij->A, &amata));
    1819:     PetscCall(MatSeqAIJGetArrayRead(aij->B, &bmata));
    1820:     if (type == NORM_FROBENIUS) {
    1821:       v = amata;
    1822:       for (i = 0; i < amat->nz; i++) {
    1823:         sum += PetscRealPart(PetscConj(*v) * (*v));
    1824:         v++;
    1825:       }
    1826:       v = bmata;
    1827:       for (i = 0; i < bmat->nz; i++) {
    1828:         sum += PetscRealPart(PetscConj(*v) * (*v));
    1829:         v++;
    1830:       }
    1831:       PetscCallMPI(MPIU_Allreduce(&sum, norm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
    1832:       *norm = PetscSqrtReal(*norm);
    1833:       PetscCall(PetscLogFlops(2.0 * amat->nz + 2.0 * bmat->nz));
    1834:     } else if (type == NORM_1) { /* max column norm */
    1835:       PetscReal *tmp;
    1836:       PetscInt  *jj, *garray = aij->garray;
    1837:       PetscCall(PetscCalloc1(mat->cmap->N + 1, &tmp));
    1838:       *norm = 0.0;
    1839:       v     = amata;
    1840:       jj    = amat->j;
    1841:       for (j = 0; j < amat->nz; j++) {
    1842:         tmp[cstart + *jj++] += PetscAbsScalar(*v);
    1843:         v++;
    1844:       }
    1845:       v  = bmata;
    1846:       jj = bmat->j;
    1847:       for (j = 0; j < bmat->nz; j++) {
    1848:         tmp[garray[*jj++]] += PetscAbsScalar(*v);
    1849:         v++;
    1850:       }
    1851:       PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, tmp, mat->cmap->N, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
    1852:       for (j = 0; j < mat->cmap->N; j++) {
    1853:         if (tmp[j] > *norm) *norm = tmp[j];
    1854:       }
    1855:       PetscCall(PetscFree(tmp));
    1856:       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
    1857:     } else if (type == NORM_INFINITY) { /* max row norm */
    1858:       PetscReal ntemp = 0.0;
    1859:       for (j = 0; j < aij->A->rmap->n; j++) {
    1860:         v   = PetscSafePointerPlusOffset(amata, amat->i[j]);
    1861:         sum = 0.0;
    1862:         for (i = 0; i < amat->i[j + 1] - amat->i[j]; i++) {
    1863:           sum += PetscAbsScalar(*v);
    1864:           v++;
    1865:         }
    1866:         v = PetscSafePointerPlusOffset(bmata, bmat->i[j]);
    1867:         for (i = 0; i < bmat->i[j + 1] - bmat->i[j]; i++) {
    1868:           sum += PetscAbsScalar(*v);
    1869:           v++;
    1870:         }
    1871:         if (sum > ntemp) ntemp = sum;
    1872:       }
    1873:       PetscCallMPI(MPIU_Allreduce(&ntemp, norm, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)mat)));
    1874:       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
    1875:     } else SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "No support for two norm");
    1876:     PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &amata));
    1877:     PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &bmata));
    1878:   }
    1879:   PetscFunctionReturn(PETSC_SUCCESS);
    1880: }

    1882: static PetscErrorCode MatTranspose_MPIAIJ(Mat A, MatReuse reuse, Mat *matout)
    1883: {
    1884:   Mat_MPIAIJ      *a    = (Mat_MPIAIJ *)A->data, *b;
    1885:   Mat_SeqAIJ      *Aloc = (Mat_SeqAIJ *)a->A->data, *Bloc = (Mat_SeqAIJ *)a->B->data, *sub_B_diag;
    1886:   PetscInt         M = A->rmap->N, N = A->cmap->N, ma, na, mb, nb, row, *cols, *cols_tmp, *B_diag_ilen, i, ncol, A_diag_ncol;
    1887:   const PetscInt  *ai, *aj, *bi, *bj, *B_diag_i;
    1888:   Mat              B, A_diag, *B_diag;
    1889:   const MatScalar *pbv, *bv;

    1891:   PetscFunctionBegin;
    1892:   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *matout));
    1893:   ma = A->rmap->n;
    1894:   na = A->cmap->n;
    1895:   mb = a->B->rmap->n;
    1896:   nb = a->B->cmap->n;
    1897:   ai = Aloc->i;
    1898:   aj = Aloc->j;
    1899:   bi = Bloc->i;
    1900:   bj = Bloc->j;
    1901:   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
    1902:     PetscInt            *d_nnz, *g_nnz, *o_nnz;
    1903:     PetscSFNode         *oloc;
    1904:     PETSC_UNUSED PetscSF sf;

    1906:     PetscCall(PetscMalloc4(na, &d_nnz, na, &o_nnz, nb, &g_nnz, nb, &oloc));
    1907:     /* compute d_nnz for preallocation */
    1908:     PetscCall(PetscArrayzero(d_nnz, na));
    1909:     for (i = 0; i < ai[ma]; i++) d_nnz[aj[i]]++;
    1910:     /* compute local off-diagonal contributions */
    1911:     PetscCall(PetscArrayzero(g_nnz, nb));
    1912:     for (i = 0; i < bi[ma]; i++) g_nnz[bj[i]]++;
    1913:     /* map those to global */
    1914:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1915:     PetscCall(PetscSFSetGraphLayout(sf, A->cmap, nb, NULL, PETSC_USE_POINTER, a->garray));
    1916:     PetscCall(PetscSFSetFromOptions(sf));
    1917:     PetscCall(PetscArrayzero(o_nnz, na));
    1918:     PetscCall(PetscSFReduceBegin(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
    1919:     PetscCall(PetscSFReduceEnd(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
    1920:     PetscCall(PetscSFDestroy(&sf));

    1922:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    1923:     PetscCall(MatSetSizes(B, A->cmap->n, A->rmap->n, N, M));
    1924:     PetscCall(MatSetBlockSizes(B, A->cmap->bs, A->rmap->bs));
    1925:     PetscCall(MatSetType(B, ((PetscObject)A)->type_name));
    1926:     PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
    1927:     PetscCall(PetscFree4(d_nnz, o_nnz, g_nnz, oloc));
    1928:   } else {
    1929:     B = *matout;
    1930:     PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
    1931:   }

    1933:   b           = (Mat_MPIAIJ *)B->data;
    1934:   A_diag      = a->A;
    1935:   B_diag      = &b->A;
    1936:   sub_B_diag  = (Mat_SeqAIJ *)(*B_diag)->data;
    1937:   A_diag_ncol = A_diag->cmap->N;
    1938:   B_diag_ilen = sub_B_diag->ilen;
    1939:   B_diag_i    = sub_B_diag->i;

    1941:   /* Set ilen for diagonal of B */
    1942:   for (i = 0; i < A_diag_ncol; i++) B_diag_ilen[i] = B_diag_i[i + 1] - B_diag_i[i];

    1944:   /* Transpose the diagonal part of the matrix. In contrast to the off-diagonal part, this can be done
    1945:   very quickly (=without using MatSetValues), because all writes are local. */
    1946:   PetscCall(MatTransposeSetPrecursor(A_diag, *B_diag));
    1947:   PetscCall(MatTranspose(A_diag, MAT_REUSE_MATRIX, B_diag));

    1949:   /* copy over the B part */
    1950:   PetscCall(PetscMalloc1(bi[mb], &cols));
    1951:   PetscCall(MatSeqAIJGetArrayRead(a->B, &bv));
    1952:   pbv = bv;
    1953:   row = A->rmap->rstart;
    1954:   for (i = 0; i < bi[mb]; i++) cols[i] = a->garray[bj[i]];
    1955:   cols_tmp = cols;
    1956:   for (i = 0; i < mb; i++) {
    1957:     ncol = bi[i + 1] - bi[i];
    1958:     PetscCall(MatSetValues(B, ncol, cols_tmp, 1, &row, pbv, INSERT_VALUES));
    1959:     row++;
    1960:     if (pbv) pbv += ncol;
    1961:     if (cols_tmp) cols_tmp += ncol;
    1962:   }
    1963:   PetscCall(PetscFree(cols));
    1964:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &bv));

    1966:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    1967:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    1968:   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
    1969:     *matout = B;
    1970:   } else {
    1971:     PetscCall(MatHeaderMerge(A, &B));
    1972:   }
    1973:   PetscFunctionReturn(PETSC_SUCCESS);
    1974: }

    1976: static PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat, Vec ll, Vec rr)
    1977: {
    1978:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    1979:   Mat         a = aij->A, b = aij->B;
    1980:   PetscInt    s1, s2, s3;

    1982:   PetscFunctionBegin;
    1983:   PetscCall(MatGetLocalSize(mat, &s2, &s3));
    1984:   if (rr) {
    1985:     PetscCall(VecGetLocalSize(rr, &s1));
    1986:     PetscCheck(s1 == s3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "right vector non-conforming local size");
    1987:     /* Overlap communication with computation. */
    1988:     PetscCall(VecScatterBegin(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1989:   }
    1990:   if (ll) {
    1991:     PetscCall(VecGetLocalSize(ll, &s1));
    1992:     PetscCheck(s1 == s2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "left vector non-conforming local size");
    1993:     PetscUseTypeMethod(b, diagonalscale, ll, NULL);
    1994:   }
    1995:   /* scale  the diagonal block */
    1996:   PetscUseTypeMethod(a, diagonalscale, ll, rr);

    1998:   if (rr) {
    1999:     /* Do a scatter end and then right scale the off-diagonal block */
    2000:     PetscCall(VecScatterEnd(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    2001:     PetscUseTypeMethod(b, diagonalscale, NULL, aij->lvec);
    2002:   }
    2003:   PetscFunctionReturn(PETSC_SUCCESS);
    2004: }

    2006: static PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
    2007: {
    2008:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2010:   PetscFunctionBegin;
    2011:   PetscCall(MatSetUnfactored(a->A));
    2012:   PetscFunctionReturn(PETSC_SUCCESS);
    2013: }

    2015: static PetscErrorCode MatEqual_MPIAIJ(Mat A, Mat B, PetscBool *flag)
    2016: {
    2017:   Mat_MPIAIJ *matB = (Mat_MPIAIJ *)B->data, *matA = (Mat_MPIAIJ *)A->data;
    2018:   Mat         a, b, c, d;
    2019:   PetscBool   flg;

    2021:   PetscFunctionBegin;
    2022:   a = matA->A;
    2023:   b = matA->B;
    2024:   c = matB->A;
    2025:   d = matB->B;

    2027:   PetscCall(MatEqual(a, c, &flg));
    2028:   if (flg) PetscCall(MatEqual(b, d, &flg));
    2029:   PetscCallMPI(MPIU_Allreduce(&flg, flag, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
    2030:   PetscFunctionReturn(PETSC_SUCCESS);
    2031: }

    2033: static PetscErrorCode MatCopy_MPIAIJ(Mat A, Mat B, MatStructure str)
    2034: {
    2035:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    2036:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;

    2038:   PetscFunctionBegin;
    2039:   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
    2040:   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
    2041:     /* because of the column compression in the off-processor part of the matrix a->B,
    2042:        the number of columns in a->B and b->B may be different, hence we cannot call
    2043:        the MatCopy() directly on the two parts. If need be, we can provide a more
    2044:        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
    2045:        then copying the submatrices */
    2046:     PetscCall(MatCopy_Basic(A, B, str));
    2047:   } else {
    2048:     PetscCall(MatCopy(a->A, b->A, str));
    2049:     PetscCall(MatCopy(a->B, b->B, str));
    2050:   }
    2051:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    2052:   PetscFunctionReturn(PETSC_SUCCESS);
    2053: }

    2055: /*
    2056:    Computes the number of nonzeros per row needed for preallocation when X and Y
    2057:    have different nonzero structure.
    2058: */
    2059: PetscErrorCode MatAXPYGetPreallocation_MPIX_private(PetscInt m, const PetscInt *xi, const PetscInt *xj, const PetscInt *xltog, const PetscInt *yi, const PetscInt *yj, const PetscInt *yltog, PetscInt *nnz)
    2060: {
    2061:   PetscInt i, j, k, nzx, nzy;

    2063:   PetscFunctionBegin;
    2064:   /* Set the number of nonzeros in the new matrix */
    2065:   for (i = 0; i < m; i++) {
    2066:     const PetscInt *xjj = PetscSafePointerPlusOffset(xj, xi[i]), *yjj = PetscSafePointerPlusOffset(yj, yi[i]);
    2067:     nzx    = xi[i + 1] - xi[i];
    2068:     nzy    = yi[i + 1] - yi[i];
    2069:     nnz[i] = 0;
    2070:     for (j = 0, k = 0; j < nzx; j++) {                                /* Point in X */
    2071:       for (; k < nzy && yltog[yjj[k]] < xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
    2072:       if (k < nzy && yltog[yjj[k]] == xltog[xjj[j]]) k++;             /* Skip duplicate */
    2073:       nnz[i]++;
    2074:     }
    2075:     for (; k < nzy; k++) nnz[i]++;
    2076:   }
    2077:   PetscFunctionReturn(PETSC_SUCCESS);
    2078: }

    2080: /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
    2081: static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y, const PetscInt *yltog, Mat X, const PetscInt *xltog, PetscInt *nnz)
    2082: {
    2083:   PetscInt    m = Y->rmap->N;
    2084:   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data;
    2085:   Mat_SeqAIJ *y = (Mat_SeqAIJ *)Y->data;

    2087:   PetscFunctionBegin;
    2088:   PetscCall(MatAXPYGetPreallocation_MPIX_private(m, x->i, x->j, xltog, y->i, y->j, yltog, nnz));
    2089:   PetscFunctionReturn(PETSC_SUCCESS);
    2090: }

    2092: static PetscErrorCode MatAXPY_MPIAIJ(Mat Y, PetscScalar a, Mat X, MatStructure str)
    2093: {
    2094:   Mat_MPIAIJ *xx = (Mat_MPIAIJ *)X->data, *yy = (Mat_MPIAIJ *)Y->data;

    2096:   PetscFunctionBegin;
    2097:   if (str == SAME_NONZERO_PATTERN) {
    2098:     PetscCall(MatAXPY(yy->A, a, xx->A, str));
    2099:     PetscCall(MatAXPY(yy->B, a, xx->B, str));
    2100:   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
    2101:     PetscCall(MatAXPY_Basic(Y, a, X, str));
    2102:   } else {
    2103:     Mat       B;
    2104:     PetscInt *nnz_d, *nnz_o;

    2106:     PetscCall(PetscMalloc1(yy->A->rmap->N, &nnz_d));
    2107:     PetscCall(PetscMalloc1(yy->B->rmap->N, &nnz_o));
    2108:     PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
    2109:     PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
    2110:     PetscCall(MatSetLayouts(B, Y->rmap, Y->cmap));
    2111:     PetscCall(MatSetType(B, ((PetscObject)Y)->type_name));
    2112:     PetscCall(MatAXPYGetPreallocation_SeqAIJ(yy->A, xx->A, nnz_d));
    2113:     PetscCall(MatAXPYGetPreallocation_MPIAIJ(yy->B, yy->garray, xx->B, xx->garray, nnz_o));
    2114:     PetscCall(MatMPIAIJSetPreallocation(B, 0, nnz_d, 0, nnz_o));
    2115:     PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
    2116:     PetscCall(MatHeaderMerge(Y, &B));
    2117:     PetscCall(PetscFree(nnz_d));
    2118:     PetscCall(PetscFree(nnz_o));
    2119:   }
    2120:   PetscFunctionReturn(PETSC_SUCCESS);
    2121: }

    2123: PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat);

    2125: static PetscErrorCode MatConjugate_MPIAIJ(Mat mat)
    2126: {
    2127:   PetscFunctionBegin;
    2128:   if (PetscDefined(USE_COMPLEX)) {
    2129:     Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2131:     PetscCall(MatConjugate_SeqAIJ(aij->A));
    2132:     PetscCall(MatConjugate_SeqAIJ(aij->B));
    2133:   }
    2134:   PetscFunctionReturn(PETSC_SUCCESS);
    2135: }

    2137: static PetscErrorCode MatRealPart_MPIAIJ(Mat A)
    2138: {
    2139:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2141:   PetscFunctionBegin;
    2142:   PetscCall(MatRealPart(a->A));
    2143:   PetscCall(MatRealPart(a->B));
    2144:   PetscFunctionReturn(PETSC_SUCCESS);
    2145: }

    2147: static PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
    2148: {
    2149:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2151:   PetscFunctionBegin;
    2152:   PetscCall(MatImaginaryPart(a->A));
    2153:   PetscCall(MatImaginaryPart(a->B));
    2154:   PetscFunctionReturn(PETSC_SUCCESS);
    2155: }

    2157: static PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2158: {
    2159:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
    2160:   PetscInt           i, *idxb = NULL, m = A->rmap->n;
    2161:   PetscScalar       *vv;
    2162:   Vec                vB, vA;
    2163:   const PetscScalar *va, *vb;

    2165:   PetscFunctionBegin;
    2166:   PetscCall(MatCreateVecs(a->A, NULL, &vA));
    2167:   PetscCall(MatGetRowMaxAbs(a->A, vA, idx));

    2169:   PetscCall(VecGetArrayRead(vA, &va));
    2170:   if (idx) {
    2171:     for (i = 0; i < m; i++) {
    2172:       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
    2173:     }
    2174:   }

    2176:   PetscCall(MatCreateVecs(a->B, NULL, &vB));
    2177:   PetscCall(PetscMalloc1(m, &idxb));
    2178:   PetscCall(MatGetRowMaxAbs(a->B, vB, idxb));

    2180:   PetscCall(VecGetArrayWrite(v, &vv));
    2181:   PetscCall(VecGetArrayRead(vB, &vb));
    2182:   for (i = 0; i < m; i++) {
    2183:     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
    2184:       vv[i] = vb[i];
    2185:       if (idx) idx[i] = a->garray[idxb[i]];
    2186:     } else {
    2187:       vv[i] = va[i];
    2188:       if (idx && PetscAbsScalar(va[i]) == PetscAbsScalar(vb[i]) && idxb[i] != -1 && idx[i] > a->garray[idxb[i]]) idx[i] = a->garray[idxb[i]];
    2189:     }
    2190:   }
    2191:   PetscCall(VecRestoreArrayWrite(v, &vv));
    2192:   PetscCall(VecRestoreArrayRead(vA, &va));
    2193:   PetscCall(VecRestoreArrayRead(vB, &vb));
    2194:   PetscCall(PetscFree(idxb));
    2195:   PetscCall(VecDestroy(&vA));
    2196:   PetscCall(VecDestroy(&vB));
    2197:   PetscFunctionReturn(PETSC_SUCCESS);
    2198: }

    2200: static PetscErrorCode MatGetRowSumAbs_MPIAIJ(Mat A, Vec v)
    2201: {
    2202:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    2203:   Vec         vB, vA;

    2205:   PetscFunctionBegin;
    2206:   PetscCall(MatCreateVecs(a->A, NULL, &vA));
    2207:   PetscCall(MatGetRowSumAbs(a->A, vA));
    2208:   PetscCall(MatCreateVecs(a->B, NULL, &vB));
    2209:   PetscCall(MatGetRowSumAbs(a->B, vB));
    2210:   PetscCall(VecAXPY(vA, 1.0, vB));
    2211:   PetscCall(VecDestroy(&vB));
    2212:   PetscCall(VecCopy(vA, v));
    2213:   PetscCall(VecDestroy(&vA));
    2214:   PetscFunctionReturn(PETSC_SUCCESS);
    2215: }

    2217: static PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2218: {
    2219:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2220:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2221:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2222:   PetscInt          *cmap = mat->garray;
    2223:   PetscInt          *diagIdx, *offdiagIdx;
    2224:   Vec                diagV, offdiagV;
    2225:   PetscScalar       *a, *diagA, *offdiagA;
    2226:   const PetscScalar *ba, *bav;
    2227:   PetscInt           r, j, col, ncols, *bi, *bj;
    2228:   Mat                B = mat->B;
    2229:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2231:   PetscFunctionBegin;
    2232:   /* When a process holds entire A and other processes have no entry */
    2233:   if (A->cmap->N == n) {
    2234:     PetscCall(VecGetArrayWrite(v, &diagA));
    2235:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2236:     PetscCall(MatGetRowMinAbs(mat->A, diagV, idx));
    2237:     PetscCall(VecDestroy(&diagV));
    2238:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2239:     PetscFunctionReturn(PETSC_SUCCESS);
    2240:   } else if (n == 0) {
    2241:     if (m) {
    2242:       PetscCall(VecGetArrayWrite(v, &a));
    2243:       for (r = 0; r < m; r++) {
    2244:         a[r] = 0.0;
    2245:         if (idx) idx[r] = -1;
    2246:       }
    2247:       PetscCall(VecRestoreArrayWrite(v, &a));
    2248:     }
    2249:     PetscFunctionReturn(PETSC_SUCCESS);
    2250:   }

    2252:   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
    2253:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2254:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2255:   PetscCall(MatGetRowMinAbs(mat->A, diagV, diagIdx));

    2257:   /* Get offdiagIdx[] for implicit 0.0 */
    2258:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2259:   ba = bav;
    2260:   bi = b->i;
    2261:   bj = b->j;
    2262:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2263:   for (r = 0; r < m; r++) {
    2264:     ncols = bi[r + 1] - bi[r];
    2265:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2266:       offdiagA[r]   = *ba;
    2267:       offdiagIdx[r] = cmap[0];
    2268:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2269:       offdiagA[r] = 0.0;

    2271:       /* Find first hole in the cmap */
    2272:       for (j = 0; j < ncols; j++) {
    2273:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2274:         if (col > j && j < cstart) {
    2275:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2276:           break;
    2277:         } else if (col > j + n && j >= cstart) {
    2278:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2279:           break;
    2280:         }
    2281:       }
    2282:       if (j == ncols && ncols < A->cmap->N - n) {
    2283:         /* a hole is outside compressed Bcols */
    2284:         if (ncols == 0) {
    2285:           if (cstart) {
    2286:             offdiagIdx[r] = 0;
    2287:           } else offdiagIdx[r] = cend;
    2288:         } else { /* ncols > 0 */
    2289:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2290:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2291:         }
    2292:       }
    2293:     }

    2295:     for (j = 0; j < ncols; j++) {
    2296:       if (PetscAbsScalar(offdiagA[r]) > PetscAbsScalar(*ba)) {
    2297:         offdiagA[r]   = *ba;
    2298:         offdiagIdx[r] = cmap[*bj];
    2299:       }
    2300:       ba++;
    2301:       bj++;
    2302:     }
    2303:   }

    2305:   PetscCall(VecGetArrayWrite(v, &a));
    2306:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2307:   for (r = 0; r < m; ++r) {
    2308:     if (PetscAbsScalar(diagA[r]) < PetscAbsScalar(offdiagA[r])) {
    2309:       a[r] = diagA[r];
    2310:       if (idx) idx[r] = cstart + diagIdx[r];
    2311:     } else if (PetscAbsScalar(diagA[r]) == PetscAbsScalar(offdiagA[r])) {
    2312:       a[r] = diagA[r];
    2313:       if (idx) {
    2314:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2315:           idx[r] = cstart + diagIdx[r];
    2316:         } else idx[r] = offdiagIdx[r];
    2317:       }
    2318:     } else {
    2319:       a[r] = offdiagA[r];
    2320:       if (idx) idx[r] = offdiagIdx[r];
    2321:     }
    2322:   }
    2323:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2324:   PetscCall(VecRestoreArrayWrite(v, &a));
    2325:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2326:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2327:   PetscCall(VecDestroy(&diagV));
    2328:   PetscCall(VecDestroy(&offdiagV));
    2329:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2330:   PetscFunctionReturn(PETSC_SUCCESS);
    2331: }

    2333: static PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2334: {
    2335:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2336:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2337:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2338:   PetscInt          *cmap = mat->garray;
    2339:   PetscInt          *diagIdx, *offdiagIdx;
    2340:   Vec                diagV, offdiagV;
    2341:   PetscScalar       *a, *diagA, *offdiagA;
    2342:   const PetscScalar *ba, *bav;
    2343:   PetscInt           r, j, col, ncols, *bi, *bj;
    2344:   Mat                B = mat->B;
    2345:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2347:   PetscFunctionBegin;
    2348:   /* When a process holds entire A and other processes have no entry */
    2349:   if (A->cmap->N == n) {
    2350:     PetscCall(VecGetArrayWrite(v, &diagA));
    2351:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2352:     PetscCall(MatGetRowMin(mat->A, diagV, idx));
    2353:     PetscCall(VecDestroy(&diagV));
    2354:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2355:     PetscFunctionReturn(PETSC_SUCCESS);
    2356:   } else if (n == 0) {
    2357:     if (m) {
    2358:       PetscCall(VecGetArrayWrite(v, &a));
    2359:       for (r = 0; r < m; r++) {
    2360:         a[r] = PETSC_MAX_REAL;
    2361:         if (idx) idx[r] = -1;
    2362:       }
    2363:       PetscCall(VecRestoreArrayWrite(v, &a));
    2364:     }
    2365:     PetscFunctionReturn(PETSC_SUCCESS);
    2366:   }

    2368:   PetscCall(PetscCalloc2(m, &diagIdx, m, &offdiagIdx));
    2369:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2370:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2371:   PetscCall(MatGetRowMin(mat->A, diagV, diagIdx));

    2373:   /* Get offdiagIdx[] for implicit 0.0 */
    2374:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2375:   ba = bav;
    2376:   bi = b->i;
    2377:   bj = b->j;
    2378:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2379:   for (r = 0; r < m; r++) {
    2380:     ncols = bi[r + 1] - bi[r];
    2381:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2382:       offdiagA[r]   = *ba;
    2383:       offdiagIdx[r] = cmap[0];
    2384:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2385:       offdiagA[r] = 0.0;

    2387:       /* Find first hole in the cmap */
    2388:       for (j = 0; j < ncols; j++) {
    2389:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2390:         if (col > j && j < cstart) {
    2391:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2392:           break;
    2393:         } else if (col > j + n && j >= cstart) {
    2394:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2395:           break;
    2396:         }
    2397:       }
    2398:       if (j == ncols && ncols < A->cmap->N - n) {
    2399:         /* a hole is outside compressed Bcols */
    2400:         if (ncols == 0) {
    2401:           if (cstart) {
    2402:             offdiagIdx[r] = 0;
    2403:           } else offdiagIdx[r] = cend;
    2404:         } else { /* ncols > 0 */
    2405:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2406:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2407:         }
    2408:       }
    2409:     }

    2411:     for (j = 0; j < ncols; j++) {
    2412:       if (PetscRealPart(offdiagA[r]) > PetscRealPart(*ba)) {
    2413:         offdiagA[r]   = *ba;
    2414:         offdiagIdx[r] = cmap[*bj];
    2415:       }
    2416:       ba++;
    2417:       bj++;
    2418:     }
    2419:   }

    2421:   PetscCall(VecGetArrayWrite(v, &a));
    2422:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2423:   for (r = 0; r < m; ++r) {
    2424:     if (PetscRealPart(diagA[r]) < PetscRealPart(offdiagA[r])) {
    2425:       a[r] = diagA[r];
    2426:       if (idx) idx[r] = cstart + diagIdx[r];
    2427:     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
    2428:       a[r] = diagA[r];
    2429:       if (idx) {
    2430:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2431:           idx[r] = cstart + diagIdx[r];
    2432:         } else idx[r] = offdiagIdx[r];
    2433:       }
    2434:     } else {
    2435:       a[r] = offdiagA[r];
    2436:       if (idx) idx[r] = offdiagIdx[r];
    2437:     }
    2438:   }
    2439:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2440:   PetscCall(VecRestoreArrayWrite(v, &a));
    2441:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2442:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2443:   PetscCall(VecDestroy(&diagV));
    2444:   PetscCall(VecDestroy(&offdiagV));
    2445:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2446:   PetscFunctionReturn(PETSC_SUCCESS);
    2447: }

    2449: static PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2450: {
    2451:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2452:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2453:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2454:   PetscInt          *cmap = mat->garray;
    2455:   PetscInt          *diagIdx, *offdiagIdx;
    2456:   Vec                diagV, offdiagV;
    2457:   PetscScalar       *a, *diagA, *offdiagA;
    2458:   const PetscScalar *ba, *bav;
    2459:   PetscInt           r, j, col, ncols, *bi, *bj;
    2460:   Mat                B = mat->B;
    2461:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2463:   PetscFunctionBegin;
    2464:   /* When a process holds entire A and other processes have no entry */
    2465:   if (A->cmap->N == n) {
    2466:     PetscCall(VecGetArrayWrite(v, &diagA));
    2467:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2468:     PetscCall(MatGetRowMax(mat->A, diagV, idx));
    2469:     PetscCall(VecDestroy(&diagV));
    2470:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2471:     PetscFunctionReturn(PETSC_SUCCESS);
    2472:   } else if (n == 0) {
    2473:     if (m) {
    2474:       PetscCall(VecGetArrayWrite(v, &a));
    2475:       for (r = 0; r < m; r++) {
    2476:         a[r] = PETSC_MIN_REAL;
    2477:         if (idx) idx[r] = -1;
    2478:       }
    2479:       PetscCall(VecRestoreArrayWrite(v, &a));
    2480:     }
    2481:     PetscFunctionReturn(PETSC_SUCCESS);
    2482:   }

    2484:   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
    2485:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2486:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2487:   PetscCall(MatGetRowMax(mat->A, diagV, diagIdx));

    2489:   /* Get offdiagIdx[] for implicit 0.0 */
    2490:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2491:   ba = bav;
    2492:   bi = b->i;
    2493:   bj = b->j;
    2494:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2495:   for (r = 0; r < m; r++) {
    2496:     ncols = bi[r + 1] - bi[r];
    2497:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2498:       offdiagA[r]   = *ba;
    2499:       offdiagIdx[r] = cmap[0];
    2500:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2501:       offdiagA[r] = 0.0;

    2503:       /* Find first hole in the cmap */
    2504:       for (j = 0; j < ncols; j++) {
    2505:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2506:         if (col > j && j < cstart) {
    2507:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2508:           break;
    2509:         } else if (col > j + n && j >= cstart) {
    2510:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2511:           break;
    2512:         }
    2513:       }
    2514:       if (j == ncols && ncols < A->cmap->N - n) {
    2515:         /* a hole is outside compressed Bcols */
    2516:         if (ncols == 0) {
    2517:           if (cstart) {
    2518:             offdiagIdx[r] = 0;
    2519:           } else offdiagIdx[r] = cend;
    2520:         } else { /* ncols > 0 */
    2521:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2522:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2523:         }
    2524:       }
    2525:     }

    2527:     for (j = 0; j < ncols; j++) {
    2528:       if (PetscRealPart(offdiagA[r]) < PetscRealPart(*ba)) {
    2529:         offdiagA[r]   = *ba;
    2530:         offdiagIdx[r] = cmap[*bj];
    2531:       }
    2532:       ba++;
    2533:       bj++;
    2534:     }
    2535:   }

    2537:   PetscCall(VecGetArrayWrite(v, &a));
    2538:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2539:   for (r = 0; r < m; ++r) {
    2540:     if (PetscRealPart(diagA[r]) > PetscRealPart(offdiagA[r])) {
    2541:       a[r] = diagA[r];
    2542:       if (idx) idx[r] = cstart + diagIdx[r];
    2543:     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
    2544:       a[r] = diagA[r];
    2545:       if (idx) {
    2546:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2547:           idx[r] = cstart + diagIdx[r];
    2548:         } else idx[r] = offdiagIdx[r];
    2549:       }
    2550:     } else {
    2551:       a[r] = offdiagA[r];
    2552:       if (idx) idx[r] = offdiagIdx[r];
    2553:     }
    2554:   }
    2555:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2556:   PetscCall(VecRestoreArrayWrite(v, &a));
    2557:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2558:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2559:   PetscCall(VecDestroy(&diagV));
    2560:   PetscCall(VecDestroy(&offdiagV));
    2561:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2562:   PetscFunctionReturn(PETSC_SUCCESS);
    2563: }

    2565: PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat, Mat *newmat)
    2566: {
    2567:   Mat *dummy;

    2569:   PetscFunctionBegin;
    2570:   PetscCall(MatCreateSubMatrix_MPIAIJ_All(mat, MAT_DO_NOT_GET_VALUES, MAT_INITIAL_MATRIX, &dummy));
    2571:   *newmat = *dummy;
    2572:   PetscCall(PetscFree(dummy));
    2573:   PetscFunctionReturn(PETSC_SUCCESS);
    2574: }

    2576: static PetscErrorCode MatInvertBlockDiagonal_MPIAIJ(Mat A, const PetscScalar **values)
    2577: {
    2578:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2580:   PetscFunctionBegin;
    2581:   PetscCall(MatInvertBlockDiagonal(a->A, values));
    2582:   A->factorerrortype = a->A->factorerrortype;
    2583:   PetscFunctionReturn(PETSC_SUCCESS);
    2584: }

    2586: static PetscErrorCode MatSetRandom_MPIAIJ(Mat x, PetscRandom rctx)
    2587: {
    2588:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)x->data;

    2590:   PetscFunctionBegin;
    2591:   PetscCheck(x->assembled || x->preallocated, PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_WRONGSTATE, "MatSetRandom on an unassembled and unpreallocated MATMPIAIJ is not allowed");
    2592:   PetscCall(MatSetRandom(aij->A, rctx));
    2593:   if (x->assembled) {
    2594:     PetscCall(MatSetRandom(aij->B, rctx));
    2595:   } else {
    2596:     PetscCall(MatSetRandomSkipColumnRange_SeqAIJ_Private(aij->B, x->cmap->rstart, x->cmap->rend, rctx));
    2597:   }
    2598:   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
    2599:   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
    2600:   PetscFunctionReturn(PETSC_SUCCESS);
    2601: }

    2603: static PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A, PetscBool sc)
    2604: {
    2605:   PetscFunctionBegin;
    2606:   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
    2607:   else A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ;
    2608:   PetscFunctionReturn(PETSC_SUCCESS);
    2609: }

    2611: /*@
    2612:   MatMPIAIJGetNumberNonzeros - gets the number of nonzeros in the matrix on this MPI rank

    2614:   Not Collective

    2616:   Input Parameter:
    2617: . A - the matrix

    2619:   Output Parameter:
    2620: . nz - the number of nonzeros

    2622:   Level: advanced

    2624: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
    2625: @*/
    2626: PetscErrorCode MatMPIAIJGetNumberNonzeros(Mat A, PetscCount *nz)
    2627: {
    2628:   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)A->data;
    2629:   Mat_SeqAIJ *aaij = (Mat_SeqAIJ *)maij->A->data, *baij = (Mat_SeqAIJ *)maij->B->data;
    2630:   PetscBool   isaij;

    2632:   PetscFunctionBegin;
    2633:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIAIJ, &isaij));
    2634:   PetscCheck(isaij, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for type %s", ((PetscObject)A)->type_name);
    2635:   *nz = aaij->i[A->rmap->n] + baij->i[A->rmap->n];
    2636:   PetscFunctionReturn(PETSC_SUCCESS);
    2637: }

    2639: /*@
    2640:   MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap

    2642:   Collective

    2644:   Input Parameters:
    2645: + A  - the matrix
    2646: - sc - `PETSC_TRUE` indicates use the scalable algorithm (default is not to use the scalable algorithm)

    2648:   Level: advanced

    2650: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
    2651: @*/
    2652: PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A, PetscBool sc)
    2653: {
    2654:   PetscFunctionBegin;
    2655:   PetscTryMethod(A, "MatMPIAIJSetUseScalableIncreaseOverlap_C", (Mat, PetscBool), (A, sc));
    2656:   PetscFunctionReturn(PETSC_SUCCESS);
    2657: }

    2659: PetscErrorCode MatSetFromOptions_MPIAIJ(Mat A, PetscOptionItems PetscOptionsObject)
    2660: {
    2661:   PetscBool sc = PETSC_FALSE, flg;

    2663:   PetscFunctionBegin;
    2664:   PetscOptionsHeadBegin(PetscOptionsObject, "MPIAIJ options");
    2665:   if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
    2666:   PetscCall(PetscOptionsBool("-mat_increase_overlap_scalable", "Use a scalable algorithm to compute the overlap", "MatIncreaseOverlap", sc, &sc, &flg));
    2667:   if (flg) PetscCall(MatMPIAIJSetUseScalableIncreaseOverlap(A, sc));
    2668:   PetscOptionsHeadEnd();
    2669:   PetscFunctionReturn(PETSC_SUCCESS);
    2670: }

    2672: static PetscErrorCode MatShift_MPIAIJ(Mat Y, PetscScalar a)
    2673: {
    2674:   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)Y->data;
    2675:   Mat_SeqAIJ *aij  = (Mat_SeqAIJ *)maij->A->data;

    2677:   PetscFunctionBegin;
    2678:   if (!Y->preallocated) {
    2679:     PetscCall(MatMPIAIJSetPreallocation(Y, 1, NULL, 0, NULL));
    2680:   } else if (!aij->nz) { /* It does not matter if diagonals of Y only partially lie in maij->A. We just need an estimated preallocation. */
    2681:     PetscInt nonew = aij->nonew;
    2682:     PetscCall(MatSeqAIJSetPreallocation(maij->A, 1, NULL));
    2683:     aij->nonew = nonew;
    2684:   }
    2685:   PetscCall(MatShift_Basic(Y, a));
    2686:   PetscFunctionReturn(PETSC_SUCCESS);
    2687: }

    2689: static PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A, PetscBool *missing, PetscInt *d)
    2690: {
    2691:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2693:   PetscFunctionBegin;
    2694:   PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only works for square matrices");
    2695:   PetscCall(MatMissingDiagonal(a->A, missing, d));
    2696:   if (d) {
    2697:     PetscInt rstart;
    2698:     PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
    2699:     *d += rstart;
    2700:   }
    2701:   PetscFunctionReturn(PETSC_SUCCESS);
    2702: }

    2704: static PetscErrorCode MatInvertVariableBlockDiagonal_MPIAIJ(Mat A, PetscInt nblocks, const PetscInt *bsizes, PetscScalar *diag)
    2705: {
    2706:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2708:   PetscFunctionBegin;
    2709:   PetscCall(MatInvertVariableBlockDiagonal(a->A, nblocks, bsizes, diag));
    2710:   PetscFunctionReturn(PETSC_SUCCESS);
    2711: }

    2713: static PetscErrorCode MatEliminateZeros_MPIAIJ(Mat A, PetscBool keep)
    2714: {
    2715:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2717:   PetscFunctionBegin;
    2718:   PetscCall(MatEliminateZeros_SeqAIJ(a->A, keep));        // possibly keep zero diagonal coefficients
    2719:   PetscCall(MatEliminateZeros_SeqAIJ(a->B, PETSC_FALSE)); // never keep zero diagonal coefficients
    2720:   PetscFunctionReturn(PETSC_SUCCESS);
    2721: }

    2723: static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
    2724:                                        MatGetRow_MPIAIJ,
    2725:                                        MatRestoreRow_MPIAIJ,
    2726:                                        MatMult_MPIAIJ,
    2727:                                        /* 4*/ MatMultAdd_MPIAIJ,
    2728:                                        MatMultTranspose_MPIAIJ,
    2729:                                        MatMultTransposeAdd_MPIAIJ,
    2730:                                        NULL,
    2731:                                        NULL,
    2732:                                        NULL,
    2733:                                        /*10*/ NULL,
    2734:                                        NULL,
    2735:                                        NULL,
    2736:                                        MatSOR_MPIAIJ,
    2737:                                        MatTranspose_MPIAIJ,
    2738:                                        /*15*/ MatGetInfo_MPIAIJ,
    2739:                                        MatEqual_MPIAIJ,
    2740:                                        MatGetDiagonal_MPIAIJ,
    2741:                                        MatDiagonalScale_MPIAIJ,
    2742:                                        MatNorm_MPIAIJ,
    2743:                                        /*20*/ MatAssemblyBegin_MPIAIJ,
    2744:                                        MatAssemblyEnd_MPIAIJ,
    2745:                                        MatSetOption_MPIAIJ,
    2746:                                        MatZeroEntries_MPIAIJ,
    2747:                                        /*24*/ MatZeroRows_MPIAIJ,
    2748:                                        NULL,
    2749:                                        NULL,
    2750:                                        NULL,
    2751:                                        NULL,
    2752:                                        /*29*/ MatSetUp_MPI_Hash,
    2753:                                        NULL,
    2754:                                        NULL,
    2755:                                        MatGetDiagonalBlock_MPIAIJ,
    2756:                                        NULL,
    2757:                                        /*34*/ MatDuplicate_MPIAIJ,
    2758:                                        NULL,
    2759:                                        NULL,
    2760:                                        NULL,
    2761:                                        NULL,
    2762:                                        /*39*/ MatAXPY_MPIAIJ,
    2763:                                        MatCreateSubMatrices_MPIAIJ,
    2764:                                        MatIncreaseOverlap_MPIAIJ,
    2765:                                        MatGetValues_MPIAIJ,
    2766:                                        MatCopy_MPIAIJ,
    2767:                                        /*44*/ MatGetRowMax_MPIAIJ,
    2768:                                        MatScale_MPIAIJ,
    2769:                                        MatShift_MPIAIJ,
    2770:                                        MatDiagonalSet_MPIAIJ,
    2771:                                        MatZeroRowsColumns_MPIAIJ,
    2772:                                        /*49*/ MatSetRandom_MPIAIJ,
    2773:                                        MatGetRowIJ_MPIAIJ,
    2774:                                        MatRestoreRowIJ_MPIAIJ,
    2775:                                        NULL,
    2776:                                        NULL,
    2777:                                        /*54*/ MatFDColoringCreate_MPIXAIJ,
    2778:                                        NULL,
    2779:                                        MatSetUnfactored_MPIAIJ,
    2780:                                        MatPermute_MPIAIJ,
    2781:                                        NULL,
    2782:                                        /*59*/ MatCreateSubMatrix_MPIAIJ,
    2783:                                        MatDestroy_MPIAIJ,
    2784:                                        MatView_MPIAIJ,
    2785:                                        NULL,
    2786:                                        NULL,
    2787:                                        /*64*/ MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
    2788:                                        NULL,
    2789:                                        NULL,
    2790:                                        NULL,
    2791:                                        MatGetRowMaxAbs_MPIAIJ,
    2792:                                        /*69*/ MatGetRowMinAbs_MPIAIJ,
    2793:                                        NULL,
    2794:                                        NULL,
    2795:                                        MatFDColoringApply_AIJ,
    2796:                                        MatSetFromOptions_MPIAIJ,
    2797:                                        MatFindZeroDiagonals_MPIAIJ,
    2798:                                        /*75*/ NULL,
    2799:                                        NULL,
    2800:                                        NULL,
    2801:                                        MatLoad_MPIAIJ,
    2802:                                        NULL,
    2803:                                        /*80*/ NULL,
    2804:                                        NULL,
    2805:                                        NULL,
    2806:                                        /*83*/ NULL,
    2807:                                        NULL,
    2808:                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
    2809:                                        MatPtAPNumeric_MPIAIJ_MPIAIJ,
    2810:                                        NULL,
    2811:                                        NULL,
    2812:                                        /*89*/ MatBindToCPU_MPIAIJ,
    2813:                                        MatProductSetFromOptions_MPIAIJ,
    2814:                                        NULL,
    2815:                                        NULL,
    2816:                                        MatConjugate_MPIAIJ,
    2817:                                        /*94*/ NULL,
    2818:                                        MatSetValuesRow_MPIAIJ,
    2819:                                        MatRealPart_MPIAIJ,
    2820:                                        MatImaginaryPart_MPIAIJ,
    2821:                                        NULL,
    2822:                                        /*99*/ NULL,
    2823:                                        NULL,
    2824:                                        NULL,
    2825:                                        MatGetRowMin_MPIAIJ,
    2826:                                        NULL,
    2827:                                        /*104*/ MatMissingDiagonal_MPIAIJ,
    2828:                                        MatGetSeqNonzeroStructure_MPIAIJ,
    2829:                                        NULL,
    2830:                                        MatGetGhosts_MPIAIJ,
    2831:                                        NULL,
    2832:                                        /*109*/ NULL,
    2833:                                        MatMultDiagonalBlock_MPIAIJ,
    2834:                                        NULL,
    2835:                                        NULL,
    2836:                                        NULL,
    2837:                                        /*114*/ MatGetMultiProcBlock_MPIAIJ,
    2838:                                        MatFindNonzeroRows_MPIAIJ,
    2839:                                        MatGetColumnReductions_MPIAIJ,
    2840:                                        MatInvertBlockDiagonal_MPIAIJ,
    2841:                                        MatInvertVariableBlockDiagonal_MPIAIJ,
    2842:                                        /*119*/ MatCreateSubMatricesMPI_MPIAIJ,
    2843:                                        NULL,
    2844:                                        NULL,
    2845:                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
    2846:                                        NULL,
    2847:                                        /*124*/ NULL,
    2848:                                        NULL,
    2849:                                        NULL,
    2850:                                        MatSetBlockSizes_MPIAIJ,
    2851:                                        NULL,
    2852:                                        /*129*/ MatFDColoringSetUp_MPIXAIJ,
    2853:                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
    2854:                                        MatCreateMPIMatConcatenateSeqMat_MPIAIJ,
    2855:                                        NULL,
    2856:                                        NULL,
    2857:                                        /*134*/ NULL,
    2858:                                        MatCreateGraph_Simple_AIJ,
    2859:                                        NULL,
    2860:                                        MatEliminateZeros_MPIAIJ,
    2861:                                        MatGetRowSumAbs_MPIAIJ,
    2862:                                        /*139*/ NULL,
    2863:                                        NULL,
    2864:                                        NULL,
    2865:                                        MatCopyHashToXAIJ_MPI_Hash,
    2866:                                        MatGetCurrentMemType_MPIAIJ,
    2867:                                        NULL};

    2869: static PetscErrorCode MatStoreValues_MPIAIJ(Mat mat)
    2870: {
    2871:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2873:   PetscFunctionBegin;
    2874:   PetscCall(MatStoreValues(aij->A));
    2875:   PetscCall(MatStoreValues(aij->B));
    2876:   PetscFunctionReturn(PETSC_SUCCESS);
    2877: }

    2879: static PetscErrorCode MatRetrieveValues_MPIAIJ(Mat mat)
    2880: {
    2881:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2883:   PetscFunctionBegin;
    2884:   PetscCall(MatRetrieveValues(aij->A));
    2885:   PetscCall(MatRetrieveValues(aij->B));
    2886:   PetscFunctionReturn(PETSC_SUCCESS);
    2887: }

    2889: PetscErrorCode MatMPIAIJSetPreallocation_MPIAIJ(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
    2890: {
    2891:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
    2892:   PetscMPIInt size;

    2894:   PetscFunctionBegin;
    2895:   if (B->hash_active) {
    2896:     B->ops[0]      = b->cops;
    2897:     B->hash_active = PETSC_FALSE;
    2898:   }
    2899:   PetscCall(PetscLayoutSetUp(B->rmap));
    2900:   PetscCall(PetscLayoutSetUp(B->cmap));

    2902: #if defined(PETSC_USE_CTABLE)
    2903:   PetscCall(PetscHMapIDestroy(&b->colmap));
    2904: #else
    2905:   PetscCall(PetscFree(b->colmap));
    2906: #endif
    2907:   PetscCall(PetscFree(b->garray));
    2908:   PetscCall(VecDestroy(&b->lvec));
    2909:   PetscCall(VecScatterDestroy(&b->Mvctx));

    2911:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

    2913:   MatSeqXAIJGetOptions_Private(b->B);
    2914:   PetscCall(MatDestroy(&b->B));
    2915:   PetscCall(MatCreate(PETSC_COMM_SELF, &b->B));
    2916:   PetscCall(MatSetSizes(b->B, B->rmap->n, size > 1 ? B->cmap->N : 0, B->rmap->n, size > 1 ? B->cmap->N : 0));
    2917:   PetscCall(MatSetBlockSizesFromMats(b->B, B, B));
    2918:   PetscCall(MatSetType(b->B, MATSEQAIJ));
    2919:   MatSeqXAIJRestoreOptions_Private(b->B);

    2921:   MatSeqXAIJGetOptions_Private(b->A);
    2922:   PetscCall(MatDestroy(&b->A));
    2923:   PetscCall(MatCreate(PETSC_COMM_SELF, &b->A));
    2924:   PetscCall(MatSetSizes(b->A, B->rmap->n, B->cmap->n, B->rmap->n, B->cmap->n));
    2925:   PetscCall(MatSetBlockSizesFromMats(b->A, B, B));
    2926:   PetscCall(MatSetType(b->A, MATSEQAIJ));
    2927:   MatSeqXAIJRestoreOptions_Private(b->A);

    2929:   PetscCall(MatSeqAIJSetPreallocation(b->A, d_nz, d_nnz));
    2930:   PetscCall(MatSeqAIJSetPreallocation(b->B, o_nz, o_nnz));
    2931:   B->preallocated  = PETSC_TRUE;
    2932:   B->was_assembled = PETSC_FALSE;
    2933:   B->assembled     = PETSC_FALSE;
    2934:   PetscFunctionReturn(PETSC_SUCCESS);
    2935: }

    2937: static PetscErrorCode MatResetPreallocation_MPIAIJ(Mat B)
    2938: {
    2939:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
    2940:   PetscBool   ondiagreset, offdiagreset, memoryreset;

    2942:   PetscFunctionBegin;
    2944:   PetscCheck(B->insertmode == NOT_SET_VALUES, PETSC_COMM_SELF, PETSC_ERR_SUP, "Cannot reset preallocation after setting some values but not yet calling MatAssemblyBegin()/MatAssemblyEnd()");
    2945:   if (B->num_ass == 0) PetscFunctionReturn(PETSC_SUCCESS);

    2947:   PetscCall(MatResetPreallocation_SeqAIJ_Private(b->A, &ondiagreset));
    2948:   PetscCall(MatResetPreallocation_SeqAIJ_Private(b->B, &offdiagreset));
    2949:   memoryreset = (PetscBool)(ondiagreset || offdiagreset);
    2950:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &memoryreset, 1, MPI_C_BOOL, MPI_LOR, PetscObjectComm((PetscObject)B)));
    2951:   if (!memoryreset) PetscFunctionReturn(PETSC_SUCCESS);

    2953:   PetscCall(PetscLayoutSetUp(B->rmap));
    2954:   PetscCall(PetscLayoutSetUp(B->cmap));
    2955:   PetscCheck(B->assembled || B->was_assembled, PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONGSTATE, "Should not need to reset preallocation if the matrix was never assembled");
    2956:   PetscCall(MatDisAssemble_MPIAIJ(B, PETSC_TRUE));
    2957:   PetscCall(VecScatterDestroy(&b->Mvctx));

    2959:   B->preallocated  = PETSC_TRUE;
    2960:   B->was_assembled = PETSC_FALSE;
    2961:   B->assembled     = PETSC_FALSE;
    2962:   /* Log that the state of this object has changed; this will help guarantee that preconditioners get re-setup */
    2963:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    2964:   PetscFunctionReturn(PETSC_SUCCESS);
    2965: }

    2967: PetscErrorCode MatDuplicate_MPIAIJ(Mat matin, MatDuplicateOption cpvalues, Mat *newmat)
    2968: {
    2969:   Mat         mat;
    2970:   Mat_MPIAIJ *a, *oldmat = (Mat_MPIAIJ *)matin->data;

    2972:   PetscFunctionBegin;
    2973:   *newmat = NULL;
    2974:   PetscCall(MatCreate(PetscObjectComm((PetscObject)matin), &mat));
    2975:   PetscCall(MatSetSizes(mat, matin->rmap->n, matin->cmap->n, matin->rmap->N, matin->cmap->N));
    2976:   PetscCall(MatSetBlockSizesFromMats(mat, matin, matin));
    2977:   PetscCall(MatSetType(mat, ((PetscObject)matin)->type_name));
    2978:   a = (Mat_MPIAIJ *)mat->data;

    2980:   mat->factortype = matin->factortype;
    2981:   mat->assembled  = matin->assembled;
    2982:   mat->insertmode = NOT_SET_VALUES;

    2984:   a->size         = oldmat->size;
    2985:   a->rank         = oldmat->rank;
    2986:   a->donotstash   = oldmat->donotstash;
    2987:   a->roworiented  = oldmat->roworiented;
    2988:   a->rowindices   = NULL;
    2989:   a->rowvalues    = NULL;
    2990:   a->getrowactive = PETSC_FALSE;

    2992:   PetscCall(PetscLayoutReference(matin->rmap, &mat->rmap));
    2993:   PetscCall(PetscLayoutReference(matin->cmap, &mat->cmap));
    2994:   if (matin->hash_active) {
    2995:     PetscCall(MatSetUp(mat));
    2996:   } else {
    2997:     mat->preallocated = matin->preallocated;
    2998:     if (oldmat->colmap) {
    2999: #if defined(PETSC_USE_CTABLE)
    3000:       PetscCall(PetscHMapIDuplicate(oldmat->colmap, &a->colmap));
    3001: #else
    3002:       PetscCall(PetscMalloc1(mat->cmap->N, &a->colmap));
    3003:       PetscCall(PetscArraycpy(a->colmap, oldmat->colmap, mat->cmap->N));
    3004: #endif
    3005:     } else a->colmap = NULL;
    3006:     if (oldmat->garray) {
    3007:       PetscInt len;
    3008:       len = oldmat->B->cmap->n;
    3009:       PetscCall(PetscMalloc1(len, &a->garray));
    3010:       if (len) PetscCall(PetscArraycpy(a->garray, oldmat->garray, len));
    3011:     } else a->garray = NULL;

    3013:     /* It may happen MatDuplicate is called with a non-assembled matrix
    3014:       In fact, MatDuplicate only requires the matrix to be preallocated
    3015:       This may happen inside a DMCreateMatrix_Shell */
    3016:     if (oldmat->lvec) PetscCall(VecDuplicate(oldmat->lvec, &a->lvec));
    3017:     if (oldmat->Mvctx) {
    3018:       a->Mvctx = oldmat->Mvctx;
    3019:       PetscCall(PetscObjectReference((PetscObject)oldmat->Mvctx));
    3020:     }
    3021:     PetscCall(MatDuplicate(oldmat->A, cpvalues, &a->A));
    3022:     PetscCall(MatDuplicate(oldmat->B, cpvalues, &a->B));
    3023:   }
    3024:   PetscCall(PetscFunctionListDuplicate(((PetscObject)matin)->qlist, &((PetscObject)mat)->qlist));
    3025:   *newmat = mat;
    3026:   PetscFunctionReturn(PETSC_SUCCESS);
    3027: }

    3029: PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
    3030: {
    3031:   PetscBool isbinary, ishdf5;

    3033:   PetscFunctionBegin;
    3036:   /* force binary viewer to load .info file if it has not yet done so */
    3037:   PetscCall(PetscViewerSetUp(viewer));
    3038:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    3039:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
    3040:   if (isbinary) {
    3041:     PetscCall(MatLoad_MPIAIJ_Binary(newMat, viewer));
    3042:   } else if (ishdf5) {
    3043: #if defined(PETSC_HAVE_HDF5)
    3044:     PetscCall(MatLoad_AIJ_HDF5(newMat, viewer));
    3045: #else
    3046:     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
    3047: #endif
    3048:   } else {
    3049:     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "Viewer type %s not yet supported for reading %s matrices", ((PetscObject)viewer)->type_name, ((PetscObject)newMat)->type_name);
    3050:   }
    3051:   PetscFunctionReturn(PETSC_SUCCESS);
    3052: }

    3054: PetscErrorCode MatLoad_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
    3055: {
    3056:   PetscInt     header[4], M, N, m, nz, rows, cols, sum, i;
    3057:   PetscInt    *rowidxs, *colidxs;
    3058:   PetscScalar *matvals;

    3060:   PetscFunctionBegin;
    3061:   PetscCall(PetscViewerSetUp(viewer));

    3063:   /* read in matrix header */
    3064:   PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
    3065:   PetscCheck(header[0] == MAT_FILE_CLASSID, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Not a matrix object in file");
    3066:   M  = header[1];
    3067:   N  = header[2];
    3068:   nz = header[3];
    3069:   PetscCheck(M >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix row size (%" PetscInt_FMT ") in file is negative", M);
    3070:   PetscCheck(N >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix column size (%" PetscInt_FMT ") in file is negative", N);
    3071:   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix stored in special format on disk, cannot load as MPIAIJ");

    3073:   /* set block sizes from the viewer's .info file */
    3074:   PetscCall(MatLoad_Binary_BlockSizes(mat, viewer));
    3075:   /* set global sizes if not set already */
    3076:   if (mat->rmap->N < 0) mat->rmap->N = M;
    3077:   if (mat->cmap->N < 0) mat->cmap->N = N;
    3078:   PetscCall(PetscLayoutSetUp(mat->rmap));
    3079:   PetscCall(PetscLayoutSetUp(mat->cmap));

    3081:   /* check if the matrix sizes are correct */
    3082:   PetscCall(MatGetSize(mat, &rows, &cols));
    3083:   PetscCheck(M == rows && N == cols, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix in file of different sizes (%" PetscInt_FMT ", %" PetscInt_FMT ") than the input matrix (%" PetscInt_FMT ", %" PetscInt_FMT ")", M, N, rows, cols);

    3085:   /* read in row lengths and build row indices */
    3086:   PetscCall(MatGetLocalSize(mat, &m, NULL));
    3087:   PetscCall(PetscMalloc1(m + 1, &rowidxs));
    3088:   PetscCall(PetscViewerBinaryReadAll(viewer, rowidxs + 1, m, PETSC_DECIDE, M, PETSC_INT));
    3089:   rowidxs[0] = 0;
    3090:   for (i = 0; i < m; i++) rowidxs[i + 1] += rowidxs[i];
    3091:   if (nz != PETSC_INT_MAX) {
    3092:     PetscCallMPI(MPIU_Allreduce(&rowidxs[m], &sum, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)viewer)));
    3093:     PetscCheck(sum == nz, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Inconsistent matrix data in file: nonzeros = %" PetscInt_FMT ", sum-row-lengths = %" PetscInt_FMT, nz, sum);
    3094:   }

    3096:   /* read in column indices and matrix values */
    3097:   PetscCall(PetscMalloc2(rowidxs[m], &colidxs, rowidxs[m], &matvals));
    3098:   PetscCall(PetscViewerBinaryReadAll(viewer, colidxs, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
    3099:   PetscCall(PetscViewerBinaryReadAll(viewer, matvals, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
    3100:   /* store matrix indices and values */
    3101:   PetscCall(MatMPIAIJSetPreallocationCSR(mat, rowidxs, colidxs, matvals));
    3102:   PetscCall(PetscFree(rowidxs));
    3103:   PetscCall(PetscFree2(colidxs, matvals));
    3104:   PetscFunctionReturn(PETSC_SUCCESS);
    3105: }

    3107: /* Not scalable because of ISAllGather() unless getting all columns. */
    3108: static PetscErrorCode ISGetSeqIS_Private(Mat mat, IS iscol, IS *isseq)
    3109: {
    3110:   IS          iscol_local;
    3111:   PetscBool   isstride;
    3112:   PetscMPIInt gisstride = 0;

    3114:   PetscFunctionBegin;
    3115:   /* check if we are grabbing all columns*/
    3116:   PetscCall(PetscObjectTypeCompare((PetscObject)iscol, ISSTRIDE, &isstride));

    3118:   if (isstride) {
    3119:     PetscInt start, len, mstart, mlen;
    3120:     PetscCall(ISStrideGetInfo(iscol, &start, NULL));
    3121:     PetscCall(ISGetLocalSize(iscol, &len));
    3122:     PetscCall(MatGetOwnershipRangeColumn(mat, &mstart, &mlen));
    3123:     if (mstart == start && mlen - mstart == len) gisstride = 1;
    3124:   }

    3126:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &gisstride, 1, MPI_INT, MPI_MIN, PetscObjectComm((PetscObject)mat)));
    3127:   if (gisstride) {
    3128:     PetscInt N;
    3129:     PetscCall(MatGetSize(mat, NULL, &N));
    3130:     PetscCall(ISCreateStride(PETSC_COMM_SELF, N, 0, 1, &iscol_local));
    3131:     PetscCall(ISSetIdentity(iscol_local));
    3132:     PetscCall(PetscInfo(mat, "Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n"));
    3133:   } else {
    3134:     PetscInt cbs;
    3135:     PetscCall(ISGetBlockSize(iscol, &cbs));
    3136:     PetscCall(ISAllGather(iscol, &iscol_local));
    3137:     PetscCall(ISSetBlockSize(iscol_local, cbs));
    3138:   }

    3140:   *isseq = iscol_local;
    3141:   PetscFunctionReturn(PETSC_SUCCESS);
    3142: }

    3144: /*
    3145:  Used by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
    3146:  (see MatCreateSubMatrix_MPIAIJ_nonscalable)

    3148:  Input Parameters:
    3149: +   mat - matrix
    3150: .   isrow - parallel row index set; its local indices are a subset of local columns of `mat`,
    3151:            i.e., mat->rstart <= isrow[i] < mat->rend
    3152: -   iscol - parallel column index set; its local indices are a subset of local columns of `mat`,
    3153:            i.e., mat->cstart <= iscol[i] < mat->cend

    3155:  Output Parameters:
    3156: +   isrow_d - sequential row index set for retrieving mat->A
    3157: .   iscol_d - sequential  column index set for retrieving mat->A
    3158: .   iscol_o - sequential column index set for retrieving mat->B
    3159: -   garray - column map; garray[i] indicates global location of iscol_o[i] in `iscol`
    3160:  */
    3161: static PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat, IS isrow, IS iscol, IS *isrow_d, IS *iscol_d, IS *iscol_o, PetscInt *garray[])
    3162: {
    3163:   Vec             x, cmap;
    3164:   const PetscInt *is_idx;
    3165:   PetscScalar    *xarray, *cmaparray;
    3166:   PetscInt        ncols, isstart, *idx, m, rstart, *cmap1, count;
    3167:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ *)mat->data;
    3168:   Mat             B    = a->B;
    3169:   Vec             lvec = a->lvec, lcmap;
    3170:   PetscInt        i, cstart, cend, Bn = B->cmap->N;
    3171:   MPI_Comm        comm;
    3172:   VecScatter      Mvctx = a->Mvctx;

    3174:   PetscFunctionBegin;
    3175:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3176:   PetscCall(ISGetLocalSize(iscol, &ncols));

    3178:   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
    3179:   PetscCall(MatCreateVecs(mat, &x, NULL));
    3180:   PetscCall(VecSet(x, -1.0));
    3181:   PetscCall(VecDuplicate(x, &cmap));
    3182:   PetscCall(VecSet(cmap, -1.0));

    3184:   /* Get start indices */
    3185:   PetscCallMPI(MPI_Scan(&ncols, &isstart, 1, MPIU_INT, MPI_SUM, comm));
    3186:   isstart -= ncols;
    3187:   PetscCall(MatGetOwnershipRangeColumn(mat, &cstart, &cend));

    3189:   PetscCall(ISGetIndices(iscol, &is_idx));
    3190:   PetscCall(VecGetArray(x, &xarray));
    3191:   PetscCall(VecGetArray(cmap, &cmaparray));
    3192:   PetscCall(PetscMalloc1(ncols, &idx));
    3193:   for (i = 0; i < ncols; i++) {
    3194:     xarray[is_idx[i] - cstart]    = (PetscScalar)is_idx[i];
    3195:     cmaparray[is_idx[i] - cstart] = i + isstart;        /* global index of iscol[i] */
    3196:     idx[i]                        = is_idx[i] - cstart; /* local index of iscol[i]  */
    3197:   }
    3198:   PetscCall(VecRestoreArray(x, &xarray));
    3199:   PetscCall(VecRestoreArray(cmap, &cmaparray));
    3200:   PetscCall(ISRestoreIndices(iscol, &is_idx));

    3202:   /* Get iscol_d */
    3203:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, iscol_d));
    3204:   PetscCall(ISGetBlockSize(iscol, &i));
    3205:   PetscCall(ISSetBlockSize(*iscol_d, i));

    3207:   /* Get isrow_d */
    3208:   PetscCall(ISGetLocalSize(isrow, &m));
    3209:   rstart = mat->rmap->rstart;
    3210:   PetscCall(PetscMalloc1(m, &idx));
    3211:   PetscCall(ISGetIndices(isrow, &is_idx));
    3212:   for (i = 0; i < m; i++) idx[i] = is_idx[i] - rstart;
    3213:   PetscCall(ISRestoreIndices(isrow, &is_idx));

    3215:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, idx, PETSC_OWN_POINTER, isrow_d));
    3216:   PetscCall(ISGetBlockSize(isrow, &i));
    3217:   PetscCall(ISSetBlockSize(*isrow_d, i));

    3219:   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
    3220:   PetscCall(VecScatterBegin(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));
    3221:   PetscCall(VecScatterEnd(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));

    3223:   PetscCall(VecDuplicate(lvec, &lcmap));

    3225:   PetscCall(VecScatterBegin(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));
    3226:   PetscCall(VecScatterEnd(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));

    3228:   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
    3229:   /* off-process column indices */
    3230:   count = 0;
    3231:   PetscCall(PetscMalloc1(Bn, &idx));
    3232:   PetscCall(PetscMalloc1(Bn, &cmap1));

    3234:   PetscCall(VecGetArray(lvec, &xarray));
    3235:   PetscCall(VecGetArray(lcmap, &cmaparray));
    3236:   for (i = 0; i < Bn; i++) {
    3237:     if (PetscRealPart(xarray[i]) > -1.0) {
    3238:       idx[count]   = i;                                     /* local column index in off-diagonal part B */
    3239:       cmap1[count] = (PetscInt)PetscRealPart(cmaparray[i]); /* column index in submat */
    3240:       count++;
    3241:     }
    3242:   }
    3243:   PetscCall(VecRestoreArray(lvec, &xarray));
    3244:   PetscCall(VecRestoreArray(lcmap, &cmaparray));

    3246:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_COPY_VALUES, iscol_o));
    3247:   /* cannot ensure iscol_o has same blocksize as iscol! */

    3249:   PetscCall(PetscFree(idx));
    3250:   *garray = cmap1;

    3252:   PetscCall(VecDestroy(&x));
    3253:   PetscCall(VecDestroy(&cmap));
    3254:   PetscCall(VecDestroy(&lcmap));
    3255:   PetscFunctionReturn(PETSC_SUCCESS);
    3256: }

    3258: /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
    3259: PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *submat)
    3260: {
    3261:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)mat->data, *asub;
    3262:   Mat         M = NULL;
    3263:   MPI_Comm    comm;
    3264:   IS          iscol_d, isrow_d, iscol_o;
    3265:   Mat         Asub = NULL, Bsub = NULL;
    3266:   PetscInt    n, count, M_size, N_size;

    3268:   PetscFunctionBegin;
    3269:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));

    3271:   if (call == MAT_REUSE_MATRIX) {
    3272:     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
    3273:     PetscCall(PetscObjectQuery((PetscObject)*submat, "isrow_d", (PetscObject *)&isrow_d));
    3274:     PetscCheck(isrow_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "isrow_d passed in was not used before, cannot reuse");

    3276:     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_d", (PetscObject *)&iscol_d));
    3277:     PetscCheck(iscol_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_d passed in was not used before, cannot reuse");

    3279:     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_o", (PetscObject *)&iscol_o));
    3280:     PetscCheck(iscol_o, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_o passed in was not used before, cannot reuse");

    3282:     /* Update diagonal and off-diagonal portions of submat */
    3283:     asub = (Mat_MPIAIJ *)(*submat)->data;
    3284:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->A));
    3285:     PetscCall(ISGetLocalSize(iscol_o, &n));
    3286:     if (n) PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->B));
    3287:     PetscCall(MatAssemblyBegin(*submat, MAT_FINAL_ASSEMBLY));
    3288:     PetscCall(MatAssemblyEnd(*submat, MAT_FINAL_ASSEMBLY));

    3290:   } else { /* call == MAT_INITIAL_MATRIX) */
    3291:     PetscInt *garray, *garray_compact;
    3292:     PetscInt  BsubN;

    3294:     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
    3295:     PetscCall(ISGetSeqIS_SameColDist_Private(mat, isrow, iscol, &isrow_d, &iscol_d, &iscol_o, &garray));

    3297:     /* Create local submatrices Asub and Bsub */
    3298:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Asub));
    3299:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Bsub));

    3301:     // Compact garray so its not of size Bn
    3302:     PetscCall(ISGetSize(iscol_o, &count));
    3303:     PetscCall(PetscMalloc1(count, &garray_compact));
    3304:     PetscCall(PetscArraycpy(garray_compact, garray, count));

    3306:     /* Create submatrix M */
    3307:     PetscCall(ISGetSize(isrow, &M_size));
    3308:     PetscCall(ISGetSize(iscol, &N_size));
    3309:     PetscCall(MatCreateMPIAIJWithSeqAIJ(comm, M_size, N_size, Asub, Bsub, garray_compact, &M));

    3311:     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
    3312:     asub = (Mat_MPIAIJ *)M->data;

    3314:     PetscCall(ISGetLocalSize(iscol_o, &BsubN));
    3315:     n = asub->B->cmap->N;
    3316:     if (BsubN > n) {
    3317:       /* This case can be tested using ~petsc/src/tao/bound/tutorials/runplate2_3 */
    3318:       const PetscInt *idx;
    3319:       PetscInt        i, j, *idx_new, *subgarray = asub->garray;
    3320:       PetscCall(PetscInfo(M, "submatrix Bn %" PetscInt_FMT " != BsubN %" PetscInt_FMT ", update iscol_o\n", n, BsubN));

    3322:       PetscCall(PetscMalloc1(n, &idx_new));
    3323:       j = 0;
    3324:       PetscCall(ISGetIndices(iscol_o, &idx));
    3325:       for (i = 0; i < n; i++) {
    3326:         if (j >= BsubN) break;
    3327:         while (subgarray[i] > garray[j]) j++;

    3329:         PetscCheck(subgarray[i] == garray[j], PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "subgarray[%" PetscInt_FMT "]=%" PetscInt_FMT " cannot < garray[%" PetscInt_FMT "]=%" PetscInt_FMT, i, subgarray[i], j, garray[j]);
    3330:         idx_new[i] = idx[j++];
    3331:       }
    3332:       PetscCall(ISRestoreIndices(iscol_o, &idx));

    3334:       PetscCall(ISDestroy(&iscol_o));
    3335:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, idx_new, PETSC_OWN_POINTER, &iscol_o));

    3337:     } else PetscCheck(BsubN >= n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Columns of Bsub (%" PetscInt_FMT ") cannot be smaller than B's (%" PetscInt_FMT ")", BsubN, asub->B->cmap->N);

    3339:     PetscCall(PetscFree(garray));
    3340:     *submat = M;

    3342:     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
    3343:     PetscCall(PetscObjectCompose((PetscObject)M, "isrow_d", (PetscObject)isrow_d));
    3344:     PetscCall(ISDestroy(&isrow_d));

    3346:     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_d", (PetscObject)iscol_d));
    3347:     PetscCall(ISDestroy(&iscol_d));

    3349:     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_o", (PetscObject)iscol_o));
    3350:     PetscCall(ISDestroy(&iscol_o));
    3351:   }
    3352:   PetscFunctionReturn(PETSC_SUCCESS);
    3353: }

    3355: PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *newmat)
    3356: {
    3357:   IS        iscol_local = NULL, isrow_d;
    3358:   PetscInt  csize;
    3359:   PetscInt  n, i, j, start, end;
    3360:   PetscBool sameRowDist = PETSC_FALSE, sameDist[2], tsameDist[2];
    3361:   MPI_Comm  comm;

    3363:   PetscFunctionBegin;
    3364:   /* If isrow has same processor distribution as mat,
    3365:      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
    3366:   if (call == MAT_REUSE_MATRIX) {
    3367:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "isrow_d", (PetscObject *)&isrow_d));
    3368:     if (isrow_d) {
    3369:       sameRowDist  = PETSC_TRUE;
    3370:       tsameDist[1] = PETSC_TRUE; /* sameColDist */
    3371:     } else {
    3372:       PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_local));
    3373:       if (iscol_local) {
    3374:         sameRowDist  = PETSC_TRUE;
    3375:         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
    3376:       }
    3377:     }
    3378:   } else {
    3379:     /* Check if isrow has same processor distribution as mat */
    3380:     sameDist[0] = PETSC_FALSE;
    3381:     PetscCall(ISGetLocalSize(isrow, &n));
    3382:     if (!n) {
    3383:       sameDist[0] = PETSC_TRUE;
    3384:     } else {
    3385:       PetscCall(ISGetMinMax(isrow, &i, &j));
    3386:       PetscCall(MatGetOwnershipRange(mat, &start, &end));
    3387:       if (i >= start && j < end) sameDist[0] = PETSC_TRUE;
    3388:     }

    3390:     /* Check if iscol has same processor distribution as mat */
    3391:     sameDist[1] = PETSC_FALSE;
    3392:     PetscCall(ISGetLocalSize(iscol, &n));
    3393:     if (!n) {
    3394:       sameDist[1] = PETSC_TRUE;
    3395:     } else {
    3396:       PetscCall(ISGetMinMax(iscol, &i, &j));
    3397:       PetscCall(MatGetOwnershipRangeColumn(mat, &start, &end));
    3398:       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
    3399:     }

    3401:     PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3402:     PetscCallMPI(MPIU_Allreduce(&sameDist, &tsameDist, 2, MPI_C_BOOL, MPI_LAND, comm));
    3403:     sameRowDist = tsameDist[0];
    3404:   }

    3406:   if (sameRowDist) {
    3407:     if (tsameDist[1]) { /* sameRowDist & sameColDist */
    3408:       /* isrow and iscol have same processor distribution as mat */
    3409:       PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat, isrow, iscol, call, newmat));
    3410:       PetscFunctionReturn(PETSC_SUCCESS);
    3411:     } else { /* sameRowDist */
    3412:       /* isrow has same processor distribution as mat */
    3413:       if (call == MAT_INITIAL_MATRIX) {
    3414:         PetscBool sorted;
    3415:         PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
    3416:         PetscCall(ISGetLocalSize(iscol_local, &n)); /* local size of iscol_local = global columns of newmat */
    3417:         PetscCall(ISGetSize(iscol, &i));
    3418:         PetscCheck(n == i, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "n %" PetscInt_FMT " != size of iscol %" PetscInt_FMT, n, i);

    3420:         PetscCall(ISSorted(iscol_local, &sorted));
    3421:         if (sorted) {
    3422:           /* MatCreateSubMatrix_MPIAIJ_SameRowDist() requires iscol_local be sorted; it can have duplicate indices */
    3423:           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, iscol_local, MAT_INITIAL_MATRIX, newmat));
    3424:           PetscFunctionReturn(PETSC_SUCCESS);
    3425:         }
    3426:       } else { /* call == MAT_REUSE_MATRIX */
    3427:         IS iscol_sub;
    3428:         PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
    3429:         if (iscol_sub) {
    3430:           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, NULL, call, newmat));
    3431:           PetscFunctionReturn(PETSC_SUCCESS);
    3432:         }
    3433:       }
    3434:     }
    3435:   }

    3437:   /* General case: iscol -> iscol_local which has global size of iscol */
    3438:   if (call == MAT_REUSE_MATRIX) {
    3439:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "ISAllGather", (PetscObject *)&iscol_local));
    3440:     PetscCheck(iscol_local, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    3441:   } else {
    3442:     if (!iscol_local) PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
    3443:   }

    3445:   PetscCall(ISGetLocalSize(iscol, &csize));
    3446:   PetscCall(MatCreateSubMatrix_MPIAIJ_nonscalable(mat, isrow, iscol_local, csize, call, newmat));

    3448:   if (call == MAT_INITIAL_MATRIX) {
    3449:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    3450:     PetscCall(ISDestroy(&iscol_local));
    3451:   }
    3452:   PetscFunctionReturn(PETSC_SUCCESS);
    3453: }

    3455: /*@C
    3456:   MatCreateMPIAIJWithSeqAIJ - creates a `MATMPIAIJ` matrix using `MATSEQAIJ` matrices that contain the "diagonal"
    3457:   and "off-diagonal" part of the matrix in CSR format.

    3459:   Collective

    3461:   Input Parameters:
    3462: + comm   - MPI communicator
    3463: . M      - the global row size
    3464: . N      - the global column size
    3465: . A      - "diagonal" portion of matrix
    3466: . B      - if garray is `NULL`, B should be the offdiag matrix using global col ids and of size N - if garray is not `NULL`, B should be the offdiag matrix using local col ids and of size garray
    3467: - garray - either `NULL` or the global index of `B` columns. If not `NULL`, it should be allocated by `PetscMalloc1()` and will be owned by `mat` thereafter.

    3469:   Output Parameter:
    3470: . mat - the matrix, with input `A` as its local diagonal matrix

    3472:   Level: advanced

    3474:   Notes:
    3475:   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix.

    3477:   `A` and `B` becomes part of output mat. The user cannot use `A` and `B` anymore.

    3479:   If `garray` is `NULL`, `B` will be compacted to use local indices. In this sense, `B`'s sparsity pattern (nonzerostate) will be changed. If `B` is a device matrix, we need to somehow also update
    3480:   `B`'s copy on device.  We do so by increasing `B`'s nonzerostate. In use of `B` on device, device matrix types should detect this change (ref. internal routines `MatSeqAIJCUSPARSECopyToGPU()` or
    3481:   `MatAssemblyEnd_SeqAIJKokkos()`) and will just destroy and then recreate the device copy of `B`. It is not optimal, but is easy to implement and less hacky. To avoid this overhead, try to compute `garray`
    3482:   yourself, see algorithms in the private function `MatSetUpMultiply_MPIAIJ()`.

    3484:   The `NULL`-ness of `garray` doesn't need to be collective, in other words, `garray` can be `NULL` on some processes while not on others.

    3486: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MATSEQAIJ`, `MatCreateMPIAIJWithSplitArrays()`
    3487: @*/
    3488: PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm, PetscInt M, PetscInt N, Mat A, Mat B, PetscInt *garray, Mat *mat)
    3489: {
    3490:   PetscInt    m, n;
    3491:   MatType     mpi_mat_type;
    3492:   Mat_MPIAIJ *mpiaij;
    3493:   Mat         C;

    3495:   PetscFunctionBegin;
    3496:   PetscCall(MatCreate(comm, &C));
    3497:   PetscCall(MatGetSize(A, &m, &n));
    3498:   PetscCheck(m == B->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Am %" PetscInt_FMT " != Bm %" PetscInt_FMT, m, B->rmap->N);
    3499:   PetscCheck(A->rmap->bs == B->rmap->bs, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "A row bs %" PetscInt_FMT " != B row bs %" PetscInt_FMT, A->rmap->bs, B->rmap->bs);

    3501:   PetscCall(MatSetSizes(C, m, n, M, N));
    3502:   /* Determine the type of MPI matrix that should be created from the type of matrix A, which holds the "diagonal" portion. */
    3503:   PetscCall(MatGetMPIMatType_Private(A, &mpi_mat_type));
    3504:   PetscCall(MatSetType(C, mpi_mat_type));
    3505:   if (!garray) {
    3506:     const PetscScalar *ba;

    3508:     B->nonzerostate++;
    3509:     PetscCall(MatSeqAIJGetArrayRead(B, &ba)); /* Since we will destroy B's device copy, we need to make sure the host copy is up to date */
    3510:     PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
    3511:   }

    3513:   PetscCall(MatSetBlockSizes(C, A->rmap->bs, A->cmap->bs));
    3514:   PetscCall(PetscLayoutSetUp(C->rmap));
    3515:   PetscCall(PetscLayoutSetUp(C->cmap));

    3517:   mpiaij              = (Mat_MPIAIJ *)C->data;
    3518:   mpiaij->A           = A;
    3519:   mpiaij->B           = B;
    3520:   mpiaij->garray      = garray;
    3521:   C->preallocated     = PETSC_TRUE;
    3522:   C->nooffprocentries = PETSC_TRUE; /* See MatAssemblyBegin_MPIAIJ. In effect, making MatAssemblyBegin a nop */

    3524:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    3525:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    3526:   /* MatAssemblyEnd is critical here. It sets mat->offloadmask according to A and B's, and
    3527:    also gets mpiaij->B compacted (if garray is NULL), with its col ids and size reduced
    3528:    */
    3529:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    3530:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    3531:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    3532:   *mat = C;
    3533:   PetscFunctionReturn(PETSC_SUCCESS);
    3534: }

    3536: extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat, PetscInt, const IS[], const IS[], MatReuse, PetscBool, Mat *);

    3538: PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat, IS isrow, IS iscol, IS iscol_local, MatReuse call, Mat *newmat)
    3539: {
    3540:   PetscInt        i, m, n, rstart, row, rend, nz, j, bs, cbs;
    3541:   PetscInt       *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
    3542:   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)mat->data;
    3543:   Mat             M, Msub, B = a->B;
    3544:   MatScalar      *aa;
    3545:   Mat_SeqAIJ     *aij;
    3546:   PetscInt       *garray = a->garray, *colsub, Ncols;
    3547:   PetscInt        count, Bn = B->cmap->N, cstart = mat->cmap->rstart, cend = mat->cmap->rend;
    3548:   IS              iscol_sub, iscmap;
    3549:   const PetscInt *is_idx, *cmap;
    3550:   PetscBool       allcolumns = PETSC_FALSE;
    3551:   MPI_Comm        comm;

    3553:   PetscFunctionBegin;
    3554:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3555:   if (call == MAT_REUSE_MATRIX) {
    3556:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
    3557:     PetscCheck(iscol_sub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "SubIScol passed in was not used before, cannot reuse");
    3558:     PetscCall(ISGetLocalSize(iscol_sub, &count));

    3560:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "Subcmap", (PetscObject *)&iscmap));
    3561:     PetscCheck(iscmap, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Subcmap passed in was not used before, cannot reuse");

    3563:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Msub));
    3564:     PetscCheck(Msub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");

    3566:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_REUSE_MATRIX, PETSC_FALSE, &Msub));

    3568:   } else { /* call == MAT_INITIAL_MATRIX) */
    3569:     PetscBool flg;

    3571:     PetscCall(ISGetLocalSize(iscol, &n));
    3572:     PetscCall(ISGetSize(iscol, &Ncols));

    3574:     /* (1) iscol -> nonscalable iscol_local */
    3575:     /* Check for special case: each processor gets entire matrix columns */
    3576:     PetscCall(ISIdentity(iscol_local, &flg));
    3577:     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
    3578:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    3579:     if (allcolumns) {
    3580:       iscol_sub = iscol_local;
    3581:       PetscCall(PetscObjectReference((PetscObject)iscol_local));
    3582:       PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &iscmap));

    3584:     } else {
    3585:       /* (2) iscol_local -> iscol_sub and iscmap. Implementation below requires iscol_local be sorted, it can have duplicate indices */
    3586:       PetscInt *idx, *cmap1, k;
    3587:       PetscCall(PetscMalloc1(Ncols, &idx));
    3588:       PetscCall(PetscMalloc1(Ncols, &cmap1));
    3589:       PetscCall(ISGetIndices(iscol_local, &is_idx));
    3590:       count = 0;
    3591:       k     = 0;
    3592:       for (i = 0; i < Ncols; i++) {
    3593:         j = is_idx[i];
    3594:         if (j >= cstart && j < cend) {
    3595:           /* diagonal part of mat */
    3596:           idx[count]     = j;
    3597:           cmap1[count++] = i; /* column index in submat */
    3598:         } else if (Bn) {
    3599:           /* off-diagonal part of mat */
    3600:           if (j == garray[k]) {
    3601:             idx[count]     = j;
    3602:             cmap1[count++] = i; /* column index in submat */
    3603:           } else if (j > garray[k]) {
    3604:             while (j > garray[k] && k < Bn - 1) k++;
    3605:             if (j == garray[k]) {
    3606:               idx[count]     = j;
    3607:               cmap1[count++] = i; /* column index in submat */
    3608:             }
    3609:           }
    3610:         }
    3611:       }
    3612:       PetscCall(ISRestoreIndices(iscol_local, &is_idx));

    3614:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_OWN_POINTER, &iscol_sub));
    3615:       PetscCall(ISGetBlockSize(iscol, &cbs));
    3616:       PetscCall(ISSetBlockSize(iscol_sub, cbs));

    3618:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local), count, cmap1, PETSC_OWN_POINTER, &iscmap));
    3619:     }

    3621:     /* (3) Create sequential Msub */
    3622:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_INITIAL_MATRIX, allcolumns, &Msub));
    3623:   }

    3625:   PetscCall(ISGetLocalSize(iscol_sub, &count));
    3626:   aij = (Mat_SeqAIJ *)Msub->data;
    3627:   ii  = aij->i;
    3628:   PetscCall(ISGetIndices(iscmap, &cmap));

    3630:   /*
    3631:       m - number of local rows
    3632:       Ncols - number of columns (same on all processors)
    3633:       rstart - first row in new global matrix generated
    3634:   */
    3635:   PetscCall(MatGetSize(Msub, &m, NULL));

    3637:   if (call == MAT_INITIAL_MATRIX) {
    3638:     /* (4) Create parallel newmat */
    3639:     PetscMPIInt rank, size;
    3640:     PetscInt    csize;

    3642:     PetscCallMPI(MPI_Comm_size(comm, &size));
    3643:     PetscCallMPI(MPI_Comm_rank(comm, &rank));

    3645:     /*
    3646:         Determine the number of non-zeros in the diagonal and off-diagonal
    3647:         portions of the matrix in order to do correct preallocation
    3648:     */

    3650:     /* first get start and end of "diagonal" columns */
    3651:     PetscCall(ISGetLocalSize(iscol, &csize));
    3652:     if (csize == PETSC_DECIDE) {
    3653:       PetscCall(ISGetSize(isrow, &mglobal));
    3654:       if (mglobal == Ncols) { /* square matrix */
    3655:         nlocal = m;
    3656:       } else {
    3657:         nlocal = Ncols / size + ((Ncols % size) > rank);
    3658:       }
    3659:     } else {
    3660:       nlocal = csize;
    3661:     }
    3662:     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    3663:     rstart = rend - nlocal;
    3664:     PetscCheck(rank != size - 1 || rend == Ncols, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local column sizes %" PetscInt_FMT " do not add up to total number of columns %" PetscInt_FMT, rend, Ncols);

    3666:     /* next, compute all the lengths */
    3667:     jj = aij->j;
    3668:     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
    3669:     olens = dlens + m;
    3670:     for (i = 0; i < m; i++) {
    3671:       jend = ii[i + 1] - ii[i];
    3672:       olen = 0;
    3673:       dlen = 0;
    3674:       for (j = 0; j < jend; j++) {
    3675:         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
    3676:         else dlen++;
    3677:         jj++;
    3678:       }
    3679:       olens[i] = olen;
    3680:       dlens[i] = dlen;
    3681:     }

    3683:     PetscCall(ISGetBlockSize(isrow, &bs));
    3684:     PetscCall(ISGetBlockSize(iscol, &cbs));

    3686:     PetscCall(MatCreate(comm, &M));
    3687:     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, Ncols));
    3688:     PetscCall(MatSetBlockSizes(M, bs, cbs));
    3689:     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
    3690:     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
    3691:     PetscCall(PetscFree(dlens));

    3693:   } else { /* call == MAT_REUSE_MATRIX */
    3694:     M = *newmat;
    3695:     PetscCall(MatGetLocalSize(M, &i, NULL));
    3696:     PetscCheck(i == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    3697:     PetscCall(MatZeroEntries(M));
    3698:     /*
    3699:          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
    3700:        rather than the slower MatSetValues().
    3701:     */
    3702:     M->was_assembled = PETSC_TRUE;
    3703:     M->assembled     = PETSC_FALSE;
    3704:   }

    3706:   /* (5) Set values of Msub to *newmat */
    3707:   PetscCall(PetscMalloc1(count, &colsub));
    3708:   PetscCall(MatGetOwnershipRange(M, &rstart, NULL));

    3710:   jj = aij->j;
    3711:   PetscCall(MatSeqAIJGetArrayRead(Msub, (const PetscScalar **)&aa));
    3712:   for (i = 0; i < m; i++) {
    3713:     row = rstart + i;
    3714:     nz  = ii[i + 1] - ii[i];
    3715:     for (j = 0; j < nz; j++) colsub[j] = cmap[jj[j]];
    3716:     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, colsub, aa, INSERT_VALUES));
    3717:     jj += nz;
    3718:     aa += nz;
    3719:   }
    3720:   PetscCall(MatSeqAIJRestoreArrayRead(Msub, (const PetscScalar **)&aa));
    3721:   PetscCall(ISRestoreIndices(iscmap, &cmap));

    3723:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
    3724:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));

    3726:   PetscCall(PetscFree(colsub));

    3728:   /* save Msub, iscol_sub and iscmap used in processor for next request */
    3729:   if (call == MAT_INITIAL_MATRIX) {
    3730:     *newmat = M;
    3731:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "SubMatrix", (PetscObject)Msub));
    3732:     PetscCall(MatDestroy(&Msub));

    3734:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "SubIScol", (PetscObject)iscol_sub));
    3735:     PetscCall(ISDestroy(&iscol_sub));

    3737:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "Subcmap", (PetscObject)iscmap));
    3738:     PetscCall(ISDestroy(&iscmap));

    3740:     if (iscol_local) {
    3741:       PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    3742:       PetscCall(ISDestroy(&iscol_local));
    3743:     }
    3744:   }
    3745:   PetscFunctionReturn(PETSC_SUCCESS);
    3746: }

    3748: /*
    3749:     Not great since it makes two copies of the submatrix, first an SeqAIJ
    3750:   in local and then by concatenating the local matrices the end result.
    3751:   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()

    3753:   This requires a sequential iscol with all indices.
    3754: */
    3755: PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat, IS isrow, IS iscol, PetscInt csize, MatReuse call, Mat *newmat)
    3756: {
    3757:   PetscMPIInt rank, size;
    3758:   PetscInt    i, m, n, rstart, row, rend, nz, *cwork, j, bs, cbs;
    3759:   PetscInt   *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
    3760:   Mat         M, Mreuse;
    3761:   MatScalar  *aa, *vwork;
    3762:   MPI_Comm    comm;
    3763:   Mat_SeqAIJ *aij;
    3764:   PetscBool   colflag, allcolumns = PETSC_FALSE;

    3766:   PetscFunctionBegin;
    3767:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3768:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    3769:   PetscCallMPI(MPI_Comm_size(comm, &size));

    3771:   /* Check for special case: each processor gets entire matrix columns */
    3772:   PetscCall(ISIdentity(iscol, &colflag));
    3773:   PetscCall(ISGetLocalSize(iscol, &n));
    3774:   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
    3775:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));

    3777:   if (call == MAT_REUSE_MATRIX) {
    3778:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Mreuse));
    3779:     PetscCheck(Mreuse, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    3780:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_REUSE_MATRIX, allcolumns, &Mreuse));
    3781:   } else {
    3782:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_INITIAL_MATRIX, allcolumns, &Mreuse));
    3783:   }

    3785:   /*
    3786:       m - number of local rows
    3787:       n - number of columns (same on all processors)
    3788:       rstart - first row in new global matrix generated
    3789:   */
    3790:   PetscCall(MatGetSize(Mreuse, &m, &n));
    3791:   PetscCall(MatGetBlockSizes(Mreuse, &bs, &cbs));
    3792:   if (call == MAT_INITIAL_MATRIX) {
    3793:     aij = (Mat_SeqAIJ *)Mreuse->data;
    3794:     ii  = aij->i;
    3795:     jj  = aij->j;

    3797:     /*
    3798:         Determine the number of non-zeros in the diagonal and off-diagonal
    3799:         portions of the matrix in order to do correct preallocation
    3800:     */

    3802:     /* first get start and end of "diagonal" columns */
    3803:     if (csize == PETSC_DECIDE) {
    3804:       PetscCall(ISGetSize(isrow, &mglobal));
    3805:       if (mglobal == n) { /* square matrix */
    3806:         nlocal = m;
    3807:       } else {
    3808:         nlocal = n / size + ((n % size) > rank);
    3809:       }
    3810:     } else {
    3811:       nlocal = csize;
    3812:     }
    3813:     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    3814:     rstart = rend - nlocal;
    3815:     PetscCheck(rank != size - 1 || rend == n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Local column sizes %" PetscInt_FMT " do not add up to total number of columns %" PetscInt_FMT, rend, n);

    3817:     /* next, compute all the lengths */
    3818:     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
    3819:     olens = dlens + m;
    3820:     for (i = 0; i < m; i++) {
    3821:       jend = ii[i + 1] - ii[i];
    3822:       olen = 0;
    3823:       dlen = 0;
    3824:       for (j = 0; j < jend; j++) {
    3825:         if (*jj < rstart || *jj >= rend) olen++;
    3826:         else dlen++;
    3827:         jj++;
    3828:       }
    3829:       olens[i] = olen;
    3830:       dlens[i] = dlen;
    3831:     }
    3832:     PetscCall(MatCreate(comm, &M));
    3833:     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, n));
    3834:     PetscCall(MatSetBlockSizes(M, bs, cbs));
    3835:     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
    3836:     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
    3837:     PetscCall(PetscFree(dlens));
    3838:   } else {
    3839:     PetscInt ml, nl;

    3841:     M = *newmat;
    3842:     PetscCall(MatGetLocalSize(M, &ml, &nl));
    3843:     PetscCheck(ml == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    3844:     PetscCall(MatZeroEntries(M));
    3845:     /*
    3846:          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
    3847:        rather than the slower MatSetValues().
    3848:     */
    3849:     M->was_assembled = PETSC_TRUE;
    3850:     M->assembled     = PETSC_FALSE;
    3851:   }
    3852:   PetscCall(MatGetOwnershipRange(M, &rstart, &rend));
    3853:   aij = (Mat_SeqAIJ *)Mreuse->data;
    3854:   ii  = aij->i;
    3855:   jj  = aij->j;

    3857:   /* trigger copy to CPU if needed */
    3858:   PetscCall(MatSeqAIJGetArrayRead(Mreuse, (const PetscScalar **)&aa));
    3859:   for (i = 0; i < m; i++) {
    3860:     row   = rstart + i;
    3861:     nz    = ii[i + 1] - ii[i];
    3862:     cwork = jj;
    3863:     jj    = PetscSafePointerPlusOffset(jj, nz);
    3864:     vwork = aa;
    3865:     aa    = PetscSafePointerPlusOffset(aa, nz);
    3866:     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, cwork, vwork, INSERT_VALUES));
    3867:   }
    3868:   PetscCall(MatSeqAIJRestoreArrayRead(Mreuse, (const PetscScalar **)&aa));

    3870:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
    3871:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
    3872:   *newmat = M;

    3874:   /* save submatrix used in processor for next request */
    3875:   if (call == MAT_INITIAL_MATRIX) {
    3876:     PetscCall(PetscObjectCompose((PetscObject)M, "SubMatrix", (PetscObject)Mreuse));
    3877:     PetscCall(MatDestroy(&Mreuse));
    3878:   }
    3879:   PetscFunctionReturn(PETSC_SUCCESS);
    3880: }

    3882: static PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
    3883: {
    3884:   PetscInt        m, cstart, cend, j, nnz, i, d, *ld;
    3885:   PetscInt       *d_nnz, *o_nnz, nnz_max = 0, rstart, ii, irstart;
    3886:   const PetscInt *JJ;
    3887:   PetscBool       nooffprocentries;
    3888:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)B->data;

    3890:   PetscFunctionBegin;
    3891:   PetscCall(PetscLayoutSetUp(B->rmap));
    3892:   PetscCall(PetscLayoutSetUp(B->cmap));
    3893:   m       = B->rmap->n;
    3894:   cstart  = B->cmap->rstart;
    3895:   cend    = B->cmap->rend;
    3896:   rstart  = B->rmap->rstart;
    3897:   irstart = Ii[0];

    3899:   PetscCall(PetscCalloc2(m, &d_nnz, m, &o_nnz));

    3901:   if (PetscDefined(USE_DEBUG)) {
    3902:     for (i = 0; i < m; i++) {
    3903:       nnz = Ii[i + 1] - Ii[i];
    3904:       JJ  = PetscSafePointerPlusOffset(J, Ii[i] - irstart);
    3905:       PetscCheck(nnz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative %" PetscInt_FMT " number of columns", i, nnz);
    3906:       PetscCheck(!nnz || !(JJ[0] < 0), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Row %" PetscInt_FMT " starts with negative column index %" PetscInt_FMT, i, JJ[0]);
    3907:       PetscCheck(!nnz || !(JJ[nnz - 1] >= B->cmap->N), PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Row %" PetscInt_FMT " ends with too large a column index %" PetscInt_FMT " (max allowed %" PetscInt_FMT ")", i, JJ[nnz - 1], B->cmap->N);
    3908:     }
    3909:   }

    3911:   for (i = 0; i < m; i++) {
    3912:     nnz     = Ii[i + 1] - Ii[i];
    3913:     JJ      = PetscSafePointerPlusOffset(J, Ii[i] - irstart);
    3914:     nnz_max = PetscMax(nnz_max, nnz);
    3915:     d       = 0;
    3916:     for (j = 0; j < nnz; j++) {
    3917:       if (cstart <= JJ[j] && JJ[j] < cend) d++;
    3918:     }
    3919:     d_nnz[i] = d;
    3920:     o_nnz[i] = nnz - d;
    3921:   }
    3922:   PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
    3923:   PetscCall(PetscFree2(d_nnz, o_nnz));

    3925:   for (i = 0; i < m; i++) {
    3926:     ii = i + rstart;
    3927:     PetscCall(MatSetValues_MPIAIJ(B, 1, &ii, Ii[i + 1] - Ii[i], PetscSafePointerPlusOffset(J, Ii[i] - irstart), PetscSafePointerPlusOffset(v, Ii[i] - irstart), INSERT_VALUES));
    3928:   }
    3929:   nooffprocentries    = B->nooffprocentries;
    3930:   B->nooffprocentries = PETSC_TRUE;
    3931:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    3932:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    3933:   B->nooffprocentries = nooffprocentries;

    3935:   /* count number of entries below block diagonal */
    3936:   PetscCall(PetscFree(Aij->ld));
    3937:   PetscCall(PetscCalloc1(m, &ld));
    3938:   Aij->ld = ld;
    3939:   for (i = 0; i < m; i++) {
    3940:     nnz = Ii[i + 1] - Ii[i];
    3941:     j   = 0;
    3942:     while (j < nnz && J[j] < cstart) j++;
    3943:     ld[i] = j;
    3944:     if (J) J += nnz;
    3945:   }

    3947:   PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    3948:   PetscFunctionReturn(PETSC_SUCCESS);
    3949: }

    3951: /*@
    3952:   MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in `MATAIJ` format
    3953:   (the default parallel PETSc format).

    3955:   Collective

    3957:   Input Parameters:
    3958: + B - the matrix
    3959: . i - the indices into `j` for the start of each local row (indices start with zero)
    3960: . j - the column indices for each local row (indices start with zero)
    3961: - v - optional values in the matrix

    3963:   Level: developer

    3965:   Notes:
    3966:   The `i`, `j`, and `v` arrays ARE copied by this routine into the internal format used by PETSc;
    3967:   thus you CANNOT change the matrix entries by changing the values of `v` after you have
    3968:   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

    3970:   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

    3972:   A convenience routine for this functionality is `MatCreateMPIAIJWithArrays()`.

    3974:   You can update the matrix with new numerical values using `MatUpdateMPIAIJWithArrays()` after this call if the column indices in `j` are sorted.

    3976:   If you do **not** use `MatUpdateMPIAIJWithArrays()`, the column indices in `j` do not need to be sorted. If you will use
    3977:   `MatUpdateMPIAIJWithArrays()`, the column indices **must** be sorted.

    3979:   The format which is used for the sparse matrix input, is equivalent to a
    3980:   row-major ordering.. i.e for the following matrix, the input data expected is
    3981:   as shown
    3982: .vb
    3983:         1 0 0
    3984:         2 0 3     P0
    3985:        -------
    3986:         4 5 6     P1

    3988:      Process0 [P0] rows_owned=[0,1]
    3989:         i =  {0,1,3}  [size = nrow+1  = 2+1]
    3990:         j =  {0,0,2}  [size = 3]
    3991:         v =  {1,2,3}  [size = 3]

    3993:      Process1 [P1] rows_owned=[2]
    3994:         i =  {0,3}    [size = nrow+1  = 1+1]
    3995:         j =  {0,1,2}  [size = 3]
    3996:         v =  {4,5,6}  [size = 3]
    3997: .ve

    3999: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatCreateAIJ()`,
    4000:           `MatCreateSeqAIJWithArrays()`, `MatCreateMPIAIJWithSplitArrays()`, `MatCreateMPIAIJWithArrays()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4001: @*/
    4002: PetscErrorCode MatMPIAIJSetPreallocationCSR(Mat B, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
    4003: {
    4004:   PetscFunctionBegin;
    4005:   PetscTryMethod(B, "MatMPIAIJSetPreallocationCSR_C", (Mat, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, i, j, v));
    4006:   PetscFunctionReturn(PETSC_SUCCESS);
    4007: }

    4009: /*@
    4010:   MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in `MATMPIAIJ` format
    4011:   (the default parallel PETSc format).  For good matrix assembly performance
    4012:   the user should preallocate the matrix storage by setting the parameters
    4013:   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).

    4015:   Collective

    4017:   Input Parameters:
    4018: + B     - the matrix
    4019: . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
    4020:            (same value is used for all local rows)
    4021: . d_nnz - array containing the number of nonzeros in the various rows of the
    4022:            DIAGONAL portion of the local submatrix (possibly different for each row)
    4023:            or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `d_nz` is used to specify the nonzero structure.
    4024:            The size of this array is equal to the number of local rows, i.e 'm'.
    4025:            For matrices that will be factored, you must leave room for (and set)
    4026:            the diagonal entry even if it is zero.
    4027: . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
    4028:            submatrix (same value is used for all local rows).
    4029: - o_nnz - array containing the number of nonzeros in the various rows of the
    4030:            OFF-DIAGONAL portion of the local submatrix (possibly different for
    4031:            each row) or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `o_nz` is used to specify the nonzero
    4032:            structure. The size of this array is equal to the number
    4033:            of local rows, i.e 'm'.

    4035:   Example Usage:
    4036:   Consider the following 8x8 matrix with 34 non-zero values, that is
    4037:   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
    4038:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    4039:   as follows

    4041: .vb
    4042:             1  2  0  |  0  3  0  |  0  4
    4043:     Proc0   0  5  6  |  7  0  0  |  8  0
    4044:             9  0 10  | 11  0  0  | 12  0
    4045:     -------------------------------------
    4046:            13  0 14  | 15 16 17  |  0  0
    4047:     Proc1   0 18  0  | 19 20 21  |  0  0
    4048:             0  0  0  | 22 23  0  | 24  0
    4049:     -------------------------------------
    4050:     Proc2  25 26 27  |  0  0 28  | 29  0
    4051:            30  0  0  | 31 32 33  |  0 34
    4052: .ve

    4054:   This can be represented as a collection of submatrices as
    4055: .vb
    4056:       A B C
    4057:       D E F
    4058:       G H I
    4059: .ve

    4061:   Where the submatrices A,B,C are owned by proc0, D,E,F are
    4062:   owned by proc1, G,H,I are owned by proc2.

    4064:   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4065:   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4066:   The 'M','N' parameters are 8,8, and have the same values on all procs.

    4068:   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
    4069:   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
    4070:   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
    4071:   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
    4072:   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
    4073:   matrix, and [DF] as another `MATSEQAIJ` matrix.

    4075:   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
    4076:   allocated for every row of the local DIAGONAL submatrix, and `o_nz`
    4077:   storage locations are allocated for every row of the OFF-DIAGONAL submatrix.
    4078:   One way to choose `d_nz` and `o_nz` is to use the maximum number of nonzeros over
    4079:   the local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
    4080:   In this case, the values of `d_nz`, `o_nz` are
    4081: .vb
    4082:      proc0  dnz = 2, o_nz = 2
    4083:      proc1  dnz = 3, o_nz = 2
    4084:      proc2  dnz = 1, o_nz = 4
    4085: .ve
    4086:   We are allocating `m`*(`d_nz`+`o_nz`) storage locations for every proc. This
    4087:   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
    4088:   for proc3. i.e we are using 12+15+10=37 storage locations to store
    4089:   34 values.

    4091:   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
    4092:   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
    4093:   In the above case the values for `d_nnz`, `o_nnz` are
    4094: .vb
    4095:      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
    4096:      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
    4097:      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
    4098: .ve
    4099:   Here the space allocated is sum of all the above values i.e 34, and
    4100:   hence pre-allocation is perfect.

    4102:   Level: intermediate

    4104:   Notes:
    4105:   If the *_nnz parameter is given then the *_nz parameter is ignored

    4107:   The `MATAIJ` format, also called compressed row storage (CSR), is compatible with standard Fortran
    4108:   storage.  The stored row and column indices begin with zero.
    4109:   See [Sparse Matrices](sec_matsparse) for details.

    4111:   The parallel matrix is partitioned such that the first m0 rows belong to
    4112:   process 0, the next m1 rows belong to process 1, the next m2 rows belong
    4113:   to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.

    4115:   The DIAGONAL portion of the local submatrix of a processor can be defined
    4116:   as the submatrix which is obtained by extraction the part corresponding to
    4117:   the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
    4118:   first row that belongs to the processor, r2 is the last row belonging to
    4119:   the this processor, and c1-c2 is range of indices of the local part of a
    4120:   vector suitable for applying the matrix to.  This is an mxn matrix.  In the
    4121:   common case of a square matrix, the row and column ranges are the same and
    4122:   the DIAGONAL part is also square. The remaining portion of the local
    4123:   submatrix (mxN) constitute the OFF-DIAGONAL portion.

    4125:   If `o_nnz` and `d_nnz` are specified, then `o_nz` and `d_nz` are ignored.

    4127:   You can call `MatGetInfo()` to get information on how effective the preallocation was;
    4128:   for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
    4129:   You can also run with the option `-info` and look for messages with the string
    4130:   malloc in them to see if additional memory allocation was needed.

    4132: .seealso: [](ch_matrices), `Mat`, [Sparse Matrices](sec_matsparse), `MATMPIAIJ`, `MATAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatCreateAIJ()`, `MatMPIAIJSetPreallocationCSR()`,
    4133:           `MatGetInfo()`, `PetscSplitOwnership()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4134: @*/
    4135: PetscErrorCode MatMPIAIJSetPreallocation(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
    4136: {
    4137:   PetscFunctionBegin;
    4140:   PetscTryMethod(B, "MatMPIAIJSetPreallocation_C", (Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]), (B, d_nz, d_nnz, o_nz, o_nnz));
    4141:   PetscFunctionReturn(PETSC_SUCCESS);
    4142: }

    4144: /*@
    4145:   MatCreateMPIAIJWithArrays - creates a `MATMPIAIJ` matrix using arrays that contain in standard
    4146:   CSR format for the local rows.

    4148:   Collective

    4150:   Input Parameters:
    4151: + comm - MPI communicator
    4152: . m    - number of local rows (Cannot be `PETSC_DECIDE`)
    4153: . n    - This value should be the same as the local size used in creating the
    4154:          x vector for the matrix-vector product $ y = Ax$. (or `PETSC_DECIDE` to have
    4155:          calculated if `N` is given) For square matrices n is almost always `m`.
    4156: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    4157: . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    4158: . i    - row indices (of length m+1); that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
    4159: . j    - global column indices
    4160: - a    - optional matrix values

    4162:   Output Parameter:
    4163: . mat - the matrix

    4165:   Level: intermediate

    4167:   Notes:
    4168:   The `i`, `j`, and `a` arrays ARE copied by this routine into the internal format used by PETSc;
    4169:   thus you CANNOT change the matrix entries by changing the values of `a[]` after you have
    4170:   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

    4172:   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

    4174:   Once you have created the matrix you can update it with new numerical values using `MatUpdateMPIAIJWithArray()`

    4176:   If you do **not** use `MatUpdateMPIAIJWithArray()`, the column indices in `j` do not need to be sorted. If you will use
    4177:   `MatUpdateMPIAIJWithArrays()`, the column indices **must** be sorted.

    4179:   The format which is used for the sparse matrix input, is equivalent to a
    4180:   row-major ordering, i.e., for the following matrix, the input data expected is
    4181:   as shown
    4182: .vb
    4183:         1 0 0
    4184:         2 0 3     P0
    4185:        -------
    4186:         4 5 6     P1

    4188:      Process0 [P0] rows_owned=[0,1]
    4189:         i =  {0,1,3}  [size = nrow+1  = 2+1]
    4190:         j =  {0,0,2}  [size = 3]
    4191:         v =  {1,2,3}  [size = 3]

    4193:      Process1 [P1] rows_owned=[2]
    4194:         i =  {0,3}    [size = nrow+1  = 1+1]
    4195:         j =  {0,1,2}  [size = 3]
    4196:         v =  {4,5,6}  [size = 3]
    4197: .ve

    4199: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4200:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4201: @*/
    4202: PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt i[], const PetscInt j[], const PetscScalar a[], Mat *mat)
    4203: {
    4204:   PetscFunctionBegin;
    4205:   PetscCheck(!i || !i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    4206:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    4207:   PetscCall(MatCreate(comm, mat));
    4208:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    4209:   /* PetscCall(MatSetBlockSizes(M,bs,cbs)); */
    4210:   PetscCall(MatSetType(*mat, MATMPIAIJ));
    4211:   PetscCall(MatMPIAIJSetPreallocationCSR(*mat, i, j, a));
    4212:   PetscFunctionReturn(PETSC_SUCCESS);
    4213: }

    4215: /*@
    4216:   MatUpdateMPIAIJWithArrays - updates a `MATMPIAIJ` matrix using arrays that contain in standard
    4217:   CSR format for the local rows. Only the numerical values are updated the other arrays must be identical to what was passed
    4218:   from `MatCreateMPIAIJWithArrays()`

    4220:   Deprecated: Use `MatUpdateMPIAIJWithArray()`

    4222:   Collective

    4224:   Input Parameters:
    4225: + mat - the matrix
    4226: . m   - number of local rows (Cannot be `PETSC_DECIDE`)
    4227: . n   - This value should be the same as the local size used in creating the
    4228:        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
    4229:        calculated if N is given) For square matrices n is almost always m.
    4230: . M   - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
    4231: . N   - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
    4232: . Ii  - row indices; that is Ii[0] = 0, Ii[row] = Ii[row-1] + number of elements in that row of the matrix
    4233: . J   - column indices
    4234: - v   - matrix values

    4236:   Level: deprecated

    4238: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4239:           `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4240: @*/
    4241: PetscErrorCode MatUpdateMPIAIJWithArrays(Mat mat, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
    4242: {
    4243:   PetscInt        nnz, i;
    4244:   PetscBool       nooffprocentries;
    4245:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
    4246:   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
    4247:   PetscScalar    *ad, *ao;
    4248:   PetscInt        ldi, Iii, md;
    4249:   const PetscInt *Adi = Ad->i;
    4250:   PetscInt       *ld  = Aij->ld;

    4252:   PetscFunctionBegin;
    4253:   PetscCheck(Ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    4254:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    4255:   PetscCheck(m == mat->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of rows cannot change from call to MatUpdateMPIAIJWithArrays()");
    4256:   PetscCheck(n == mat->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of columns cannot change from call to MatUpdateMPIAIJWithArrays()");

    4258:   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
    4259:   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));

    4261:   for (i = 0; i < m; i++) {
    4262:     if (PetscDefined(USE_DEBUG)) {
    4263:       for (PetscInt j = Ii[i] + 1; j < Ii[i + 1]; ++j) {
    4264:         PetscCheck(J[j] >= J[j - 1], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column entry number %" PetscInt_FMT " (actual column %" PetscInt_FMT ") in row %" PetscInt_FMT " is not sorted", j - Ii[i], J[j], i);
    4265:         PetscCheck(J[j] != J[j - 1], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column entry number %" PetscInt_FMT " (actual column %" PetscInt_FMT ") in row %" PetscInt_FMT " is identical to previous entry", j - Ii[i], J[j], i);
    4266:       }
    4267:     }
    4268:     nnz = Ii[i + 1] - Ii[i];
    4269:     Iii = Ii[i];
    4270:     ldi = ld[i];
    4271:     md  = Adi[i + 1] - Adi[i];
    4272:     PetscCall(PetscArraycpy(ao, v + Iii, ldi));
    4273:     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
    4274:     PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
    4275:     ad += md;
    4276:     ao += nnz - md;
    4277:   }
    4278:   nooffprocentries      = mat->nooffprocentries;
    4279:   mat->nooffprocentries = PETSC_TRUE;
    4280:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
    4281:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
    4282:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
    4283:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
    4284:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    4285:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    4286:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    4287:   mat->nooffprocentries = nooffprocentries;
    4288:   PetscFunctionReturn(PETSC_SUCCESS);
    4289: }

    4291: /*@
    4292:   MatUpdateMPIAIJWithArray - updates an `MATMPIAIJ` matrix using an array that contains the nonzero values

    4294:   Collective

    4296:   Input Parameters:
    4297: + mat - the matrix
    4298: - v   - matrix values, stored by row

    4300:   Level: intermediate

    4302:   Notes:
    4303:   The matrix must have been obtained with `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()`

    4305:   The column indices in the call to `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()` must have been sorted for this call to work correctly

    4307: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4308:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArrays()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4309: @*/
    4310: PetscErrorCode MatUpdateMPIAIJWithArray(Mat mat, const PetscScalar v[])
    4311: {
    4312:   PetscInt        nnz, i, m;
    4313:   PetscBool       nooffprocentries;
    4314:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
    4315:   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
    4316:   Mat_SeqAIJ     *Ao  = (Mat_SeqAIJ *)Aij->B->data;
    4317:   PetscScalar    *ad, *ao;
    4318:   const PetscInt *Adi = Ad->i, *Adj = Ao->i;
    4319:   PetscInt        ldi, Iii, md;
    4320:   PetscInt       *ld = Aij->ld;

    4322:   PetscFunctionBegin;
    4323:   m = mat->rmap->n;

    4325:   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
    4326:   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));
    4327:   Iii = 0;
    4328:   for (i = 0; i < m; i++) {
    4329:     nnz = Adi[i + 1] - Adi[i] + Adj[i + 1] - Adj[i];
    4330:     ldi = ld[i];
    4331:     md  = Adi[i + 1] - Adi[i];
    4332:     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
    4333:     ad += md;
    4334:     if (ao) {
    4335:       PetscCall(PetscArraycpy(ao, v + Iii, ldi));
    4336:       PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
    4337:       ao += nnz - md;
    4338:     }
    4339:     Iii += nnz;
    4340:   }
    4341:   nooffprocentries      = mat->nooffprocentries;
    4342:   mat->nooffprocentries = PETSC_TRUE;
    4343:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
    4344:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
    4345:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
    4346:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
    4347:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    4348:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    4349:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    4350:   mat->nooffprocentries = nooffprocentries;
    4351:   PetscFunctionReturn(PETSC_SUCCESS);
    4352: }

    4354: /*@
    4355:   MatCreateAIJ - Creates a sparse parallel matrix in `MATAIJ` format
    4356:   (the default parallel PETSc format).  For good matrix assembly performance
    4357:   the user should preallocate the matrix storage by setting the parameters
    4358:   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).

    4360:   Collective

    4362:   Input Parameters:
    4363: + comm  - MPI communicator
    4364: . m     - number of local rows (or `PETSC_DECIDE` to have calculated if M is given)
    4365:           This value should be the same as the local size used in creating the
    4366:           y vector for the matrix-vector product y = Ax.
    4367: . n     - This value should be the same as the local size used in creating the
    4368:           x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
    4369:           calculated if N is given) For square matrices n is almost always m.
    4370: . M     - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
    4371: . N     - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
    4372: . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
    4373:           (same value is used for all local rows)
    4374: . d_nnz - array containing the number of nonzeros in the various rows of the
    4375:           DIAGONAL portion of the local submatrix (possibly different for each row)
    4376:           or `NULL`, if `d_nz` is used to specify the nonzero structure.
    4377:           The size of this array is equal to the number of local rows, i.e 'm'.
    4378: . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
    4379:           submatrix (same value is used for all local rows).
    4380: - o_nnz - array containing the number of nonzeros in the various rows of the
    4381:           OFF-DIAGONAL portion of the local submatrix (possibly different for
    4382:           each row) or `NULL`, if `o_nz` is used to specify the nonzero
    4383:           structure. The size of this array is equal to the number
    4384:           of local rows, i.e 'm'.

    4386:   Output Parameter:
    4387: . A - the matrix

    4389:   Options Database Keys:
    4390: + -mat_no_inode                     - Do not use inodes
    4391: . -mat_inode_limit <limit>          - Sets inode limit (max limit=5)
    4392: - -matmult_vecscatter_view <viewer> - View the vecscatter (i.e., communication pattern) used in `MatMult()` of sparse parallel matrices.
    4393:                                       See viewer types in manual of `MatView()`. Of them, ascii_matlab, draw or binary cause the `VecScatter`
    4394:                                       to be viewed as a matrix. Entry (i,j) is the size of message (in bytes) rank i sends to rank j in one `MatMult()` call.

    4396:   Level: intermediate

    4398:   Notes:
    4399:   It is recommended that one use `MatCreateFromOptions()` or the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
    4400:   MatXXXXSetPreallocation() paradigm instead of this routine directly.
    4401:   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]

    4403:   If the *_nnz parameter is given then the *_nz parameter is ignored

    4405:   The `m`,`n`,`M`,`N` parameters specify the size of the matrix, and its partitioning across
    4406:   processors, while `d_nz`,`d_nnz`,`o_nz`,`o_nnz` parameters specify the approximate
    4407:   storage requirements for this matrix.

    4409:   If `PETSC_DECIDE` or  `PETSC_DETERMINE` is used for a particular argument on one
    4410:   processor than it must be used on all processors that share the object for
    4411:   that argument.

    4413:   If `m` and `n` are not `PETSC_DECIDE`, then the values determine the `PetscLayout` of the matrix and the ranges returned by
    4414:   `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`, and `MatGetOwnershipRangesColumn()`.

    4416:   The user MUST specify either the local or global matrix dimensions
    4417:   (possibly both).

    4419:   The parallel matrix is partitioned across processors such that the
    4420:   first `m0` rows belong to process 0, the next `m1` rows belong to
    4421:   process 1, the next `m2` rows belong to process 2, etc., where
    4422:   `m0`, `m1`, `m2`... are the input parameter `m` on each MPI process. I.e., each MPI process stores
    4423:   values corresponding to [m x N] submatrix.

    4425:   The columns are logically partitioned with the n0 columns belonging
    4426:   to 0th partition, the next n1 columns belonging to the next
    4427:   partition etc.. where n0,n1,n2... are the input parameter 'n'.

    4429:   The DIAGONAL portion of the local submatrix on any given processor
    4430:   is the submatrix corresponding to the rows and columns m,n
    4431:   corresponding to the given processor. i.e diagonal matrix on
    4432:   process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
    4433:   etc. The remaining portion of the local submatrix [m x (N-n)]
    4434:   constitute the OFF-DIAGONAL portion. The example below better
    4435:   illustrates this concept. The two matrices, the DIAGONAL portion and
    4436:   the OFF-DIAGONAL portion are each stored as `MATSEQAIJ` matrices.

    4438:   For a square global matrix we define each processor's diagonal portion
    4439:   to be its local rows and the corresponding columns (a square submatrix);
    4440:   each processor's off-diagonal portion encompasses the remainder of the
    4441:   local matrix (a rectangular submatrix).

    4443:   If `o_nnz`, `d_nnz` are specified, then `o_nz`, and `d_nz` are ignored.

    4445:   When calling this routine with a single process communicator, a matrix of
    4446:   type `MATSEQAIJ` is returned.  If a matrix of type `MATMPIAIJ` is desired for this
    4447:   type of communicator, use the construction mechanism
    4448: .vb
    4449:   MatCreate(..., &A);
    4450:   MatSetType(A, MATMPIAIJ);
    4451:   MatSetSizes(A, m, n, M, N);
    4452:   MatMPIAIJSetPreallocation(A, ...);
    4453: .ve

    4455:   By default, this format uses inodes (identical nodes) when possible.
    4456:   We search for consecutive rows with the same nonzero structure, thereby
    4457:   reusing matrix information to achieve increased efficiency.

    4459:   Example Usage:
    4460:   Consider the following 8x8 matrix with 34 non-zero values, that is
    4461:   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
    4462:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    4463:   as follows

    4465: .vb
    4466:             1  2  0  |  0  3  0  |  0  4
    4467:     Proc0   0  5  6  |  7  0  0  |  8  0
    4468:             9  0 10  | 11  0  0  | 12  0
    4469:     -------------------------------------
    4470:            13  0 14  | 15 16 17  |  0  0
    4471:     Proc1   0 18  0  | 19 20 21  |  0  0
    4472:             0  0  0  | 22 23  0  | 24  0
    4473:     -------------------------------------
    4474:     Proc2  25 26 27  |  0  0 28  | 29  0
    4475:            30  0  0  | 31 32 33  |  0 34
    4476: .ve

    4478:   This can be represented as a collection of submatrices as

    4480: .vb
    4481:       A B C
    4482:       D E F
    4483:       G H I
    4484: .ve

    4486:   Where the submatrices A,B,C are owned by proc0, D,E,F are
    4487:   owned by proc1, G,H,I are owned by proc2.

    4489:   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4490:   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4491:   The 'M','N' parameters are 8,8, and have the same values on all procs.

    4493:   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
    4494:   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
    4495:   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
    4496:   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
    4497:   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
    4498:   matrix, and [DF] as another SeqAIJ matrix.

    4500:   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
    4501:   allocated for every row of the local DIAGONAL submatrix, and `o_nz`
    4502:   storage locations are allocated for every row of the OFF-DIAGONAL submatrix.
    4503:   One way to choose `d_nz` and `o_nz` is to use the maximum number of nonzeros over
    4504:   the local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
    4505:   In this case, the values of `d_nz`,`o_nz` are
    4506: .vb
    4507:      proc0  dnz = 2, o_nz = 2
    4508:      proc1  dnz = 3, o_nz = 2
    4509:      proc2  dnz = 1, o_nz = 4
    4510: .ve
    4511:   We are allocating m*(`d_nz`+`o_nz`) storage locations for every proc. This
    4512:   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
    4513:   for proc3. i.e we are using 12+15+10=37 storage locations to store
    4514:   34 values.

    4516:   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
    4517:   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
    4518:   In the above case the values for d_nnz,o_nnz are
    4519: .vb
    4520:      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
    4521:      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
    4522:      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
    4523: .ve
    4524:   Here the space allocated is sum of all the above values i.e 34, and
    4525:   hence pre-allocation is perfect.

    4527: .seealso: [](ch_matrices), `Mat`, [Sparse Matrix Creation](sec_matsparse), `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4528:           `MATMPIAIJ`, `MatCreateMPIAIJWithArrays()`, `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`,
    4529:           `MatGetOwnershipRangesColumn()`, `PetscLayout`
    4530: @*/
    4531: PetscErrorCode MatCreateAIJ(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[], Mat *A)
    4532: {
    4533:   PetscMPIInt size;

    4535:   PetscFunctionBegin;
    4536:   PetscCall(MatCreate(comm, A));
    4537:   PetscCall(MatSetSizes(*A, m, n, M, N));
    4538:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4539:   if (size > 1) {
    4540:     PetscCall(MatSetType(*A, MATMPIAIJ));
    4541:     PetscCall(MatMPIAIJSetPreallocation(*A, d_nz, d_nnz, o_nz, o_nnz));
    4542:   } else {
    4543:     PetscCall(MatSetType(*A, MATSEQAIJ));
    4544:     PetscCall(MatSeqAIJSetPreallocation(*A, d_nz, d_nnz));
    4545:   }
    4546:   PetscFunctionReturn(PETSC_SUCCESS);
    4547: }

    4549: /*@C
    4550:   MatMPIAIJGetSeqAIJ - Returns the local pieces of this distributed matrix

    4552:   Not Collective

    4554:   Input Parameter:
    4555: . A - The `MATMPIAIJ` matrix

    4557:   Output Parameters:
    4558: + Ad     - The local diagonal block as a `MATSEQAIJ` matrix
    4559: . Ao     - The local off-diagonal block as a `MATSEQAIJ` matrix
    4560: - colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix

    4562:   Level: intermediate

    4564:   Note:
    4565:   The rows in `Ad` and `Ao` are in [0, Nr), where Nr is the number of local rows on this process. The columns
    4566:   in `Ad` are in [0, Nc) where Nc is the number of local columns. The columns are `Ao` are in [0, Nco), where Nco is
    4567:   the number of nonzero columns in the local off-diagonal piece of the matrix `A`. The array colmap maps these
    4568:   local column numbers to global column numbers in the original matrix.

    4570: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`, `MatCreateAIJ()`, `MATSEQAIJ`
    4571: @*/
    4572: PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A, Mat *Ad, Mat *Ao, const PetscInt *colmap[])
    4573: {
    4574:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    4575:   PetscBool   flg;

    4577:   PetscFunctionBegin;
    4578:   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &flg));
    4579:   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "This function requires a MATMPIAIJ matrix as input");
    4580:   if (Ad) *Ad = a->A;
    4581:   if (Ao) *Ao = a->B;
    4582:   if (colmap) *colmap = a->garray;
    4583:   PetscFunctionReturn(PETSC_SUCCESS);
    4584: }

    4586: PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
    4587: {
    4588:   PetscInt     m, N, i, rstart, nnz, Ii;
    4589:   PetscInt    *indx;
    4590:   PetscScalar *values;
    4591:   MatType      rootType;

    4593:   PetscFunctionBegin;
    4594:   PetscCall(MatGetSize(inmat, &m, &N));
    4595:   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
    4596:     PetscInt *dnz, *onz, sum, bs, cbs;

    4598:     if (n == PETSC_DECIDE) PetscCall(PetscSplitOwnership(comm, &n, &N));
    4599:     /* Check sum(n) = N */
    4600:     PetscCallMPI(MPIU_Allreduce(&n, &sum, 1, MPIU_INT, MPI_SUM, comm));
    4601:     PetscCheck(sum == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Sum of local columns %" PetscInt_FMT " != global columns %" PetscInt_FMT, sum, N);

    4603:     PetscCallMPI(MPI_Scan(&m, &rstart, 1, MPIU_INT, MPI_SUM, comm));
    4604:     rstart -= m;

    4606:     MatPreallocateBegin(comm, m, n, dnz, onz);
    4607:     for (i = 0; i < m; i++) {
    4608:       PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
    4609:       PetscCall(MatPreallocateSet(i + rstart, nnz, indx, dnz, onz));
    4610:       PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
    4611:     }

    4613:     PetscCall(MatCreate(comm, outmat));
    4614:     PetscCall(MatSetSizes(*outmat, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    4615:     PetscCall(MatGetBlockSizes(inmat, &bs, &cbs));
    4616:     PetscCall(MatSetBlockSizes(*outmat, bs, cbs));
    4617:     PetscCall(MatGetRootType_Private(inmat, &rootType));
    4618:     PetscCall(MatSetType(*outmat, rootType));
    4619:     PetscCall(MatSeqAIJSetPreallocation(*outmat, 0, dnz));
    4620:     PetscCall(MatMPIAIJSetPreallocation(*outmat, 0, dnz, 0, onz));
    4621:     MatPreallocateEnd(dnz, onz);
    4622:     PetscCall(MatSetOption(*outmat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    4623:   }

    4625:   /* numeric phase */
    4626:   PetscCall(MatGetOwnershipRange(*outmat, &rstart, NULL));
    4627:   for (i = 0; i < m; i++) {
    4628:     PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
    4629:     Ii = i + rstart;
    4630:     PetscCall(MatSetValues(*outmat, 1, &Ii, nnz, indx, values, INSERT_VALUES));
    4631:     PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
    4632:   }
    4633:   PetscCall(MatAssemblyBegin(*outmat, MAT_FINAL_ASSEMBLY));
    4634:   PetscCall(MatAssemblyEnd(*outmat, MAT_FINAL_ASSEMBLY));
    4635:   PetscFunctionReturn(PETSC_SUCCESS);
    4636: }

    4638: static PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(void **data)
    4639: {
    4640:   Mat_Merge_SeqsToMPI *merge = (Mat_Merge_SeqsToMPI *)*data;

    4642:   PetscFunctionBegin;
    4643:   if (!merge) PetscFunctionReturn(PETSC_SUCCESS);
    4644:   PetscCall(PetscFree(merge->id_r));
    4645:   PetscCall(PetscFree(merge->len_s));
    4646:   PetscCall(PetscFree(merge->len_r));
    4647:   PetscCall(PetscFree(merge->bi));
    4648:   PetscCall(PetscFree(merge->bj));
    4649:   PetscCall(PetscFree(merge->buf_ri[0]));
    4650:   PetscCall(PetscFree(merge->buf_ri));
    4651:   PetscCall(PetscFree(merge->buf_rj[0]));
    4652:   PetscCall(PetscFree(merge->buf_rj));
    4653:   PetscCall(PetscFree(merge->coi));
    4654:   PetscCall(PetscFree(merge->coj));
    4655:   PetscCall(PetscFree(merge->owners_co));
    4656:   PetscCall(PetscLayoutDestroy(&merge->rowmap));
    4657:   PetscCall(PetscFree(merge));
    4658:   PetscFunctionReturn(PETSC_SUCCESS);
    4659: }

    4661: #include <../src/mat/utils/freespace.h>
    4662: #include <petscbt.h>

    4664: PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat, Mat mpimat)
    4665: {
    4666:   MPI_Comm             comm;
    4667:   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)seqmat->data;
    4668:   PetscMPIInt          size, rank, taga, *len_s;
    4669:   PetscInt             N = mpimat->cmap->N, i, j, *owners, *ai = a->i, *aj, m;
    4670:   PetscMPIInt          proc, k;
    4671:   PetscInt           **buf_ri, **buf_rj;
    4672:   PetscInt             anzi, *bj_i, *bi, *bj, arow, bnzi, nextaj;
    4673:   PetscInt             nrows, **buf_ri_k, **nextrow, **nextai;
    4674:   MPI_Request         *s_waits, *r_waits;
    4675:   MPI_Status          *status;
    4676:   const MatScalar     *aa, *a_a;
    4677:   MatScalar          **abuf_r, *ba_i;
    4678:   Mat_Merge_SeqsToMPI *merge;
    4679:   PetscContainer       container;

    4681:   PetscFunctionBegin;
    4682:   PetscCall(PetscObjectGetComm((PetscObject)mpimat, &comm));
    4683:   PetscCall(PetscLogEventBegin(MAT_Seqstompinum, seqmat, 0, 0, 0));

    4685:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4686:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    4688:   PetscCall(PetscObjectQuery((PetscObject)mpimat, "MatMergeSeqsToMPI", (PetscObject *)&container));
    4689:   PetscCheck(container, PetscObjectComm((PetscObject)mpimat), PETSC_ERR_PLIB, "Mat not created from MatCreateMPIAIJSumSeqAIJSymbolic");
    4690:   PetscCall(PetscContainerGetPointer(container, (void **)&merge));
    4691:   PetscCall(MatSeqAIJGetArrayRead(seqmat, &a_a));
    4692:   aa = a_a;

    4694:   bi     = merge->bi;
    4695:   bj     = merge->bj;
    4696:   buf_ri = merge->buf_ri;
    4697:   buf_rj = merge->buf_rj;

    4699:   PetscCall(PetscMalloc1(size, &status));
    4700:   owners = merge->rowmap->range;
    4701:   len_s  = merge->len_s;

    4703:   /* send and recv matrix values */
    4704:   PetscCall(PetscObjectGetNewTag((PetscObject)mpimat, &taga));
    4705:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

    4707:   PetscCall(PetscMalloc1(merge->nsend + 1, &s_waits));
    4708:   for (proc = 0, k = 0; proc < size; proc++) {
    4709:     if (!len_s[proc]) continue;
    4710:     i = owners[proc];
    4711:     PetscCallMPI(MPIU_Isend(aa + ai[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
    4712:     k++;
    4713:   }

    4715:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
    4716:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));
    4717:   PetscCall(PetscFree(status));

    4719:   PetscCall(PetscFree(s_waits));
    4720:   PetscCall(PetscFree(r_waits));

    4722:   /* insert mat values of mpimat */
    4723:   PetscCall(PetscMalloc1(N, &ba_i));
    4724:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));

    4726:   for (k = 0; k < merge->nrecv; k++) {
    4727:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    4728:     nrows       = *buf_ri_k[k];
    4729:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    4730:     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    4731:   }

    4733:   /* set values of ba */
    4734:   m = merge->rowmap->n;
    4735:   for (i = 0; i < m; i++) {
    4736:     arow = owners[rank] + i;
    4737:     bj_i = bj + bi[i]; /* col indices of the i-th row of mpimat */
    4738:     bnzi = bi[i + 1] - bi[i];
    4739:     PetscCall(PetscArrayzero(ba_i, bnzi));

    4741:     /* add local non-zero vals of this proc's seqmat into ba */
    4742:     anzi   = ai[arow + 1] - ai[arow];
    4743:     aj     = a->j + ai[arow];
    4744:     aa     = a_a + ai[arow];
    4745:     nextaj = 0;
    4746:     for (j = 0; nextaj < anzi; j++) {
    4747:       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
    4748:         ba_i[j] += aa[nextaj++];
    4749:       }
    4750:     }

    4752:     /* add received vals into ba */
    4753:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    4754:       /* i-th row */
    4755:       if (i == *nextrow[k]) {
    4756:         anzi   = *(nextai[k] + 1) - *nextai[k];
    4757:         aj     = buf_rj[k] + *nextai[k];
    4758:         aa     = abuf_r[k] + *nextai[k];
    4759:         nextaj = 0;
    4760:         for (j = 0; nextaj < anzi; j++) {
    4761:           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
    4762:             ba_i[j] += aa[nextaj++];
    4763:           }
    4764:         }
    4765:         nextrow[k]++;
    4766:         nextai[k]++;
    4767:       }
    4768:     }
    4769:     PetscCall(MatSetValues(mpimat, 1, &arow, bnzi, bj_i, ba_i, INSERT_VALUES));
    4770:   }
    4771:   PetscCall(MatSeqAIJRestoreArrayRead(seqmat, &a_a));
    4772:   PetscCall(MatAssemblyBegin(mpimat, MAT_FINAL_ASSEMBLY));
    4773:   PetscCall(MatAssemblyEnd(mpimat, MAT_FINAL_ASSEMBLY));

    4775:   PetscCall(PetscFree(abuf_r[0]));
    4776:   PetscCall(PetscFree(abuf_r));
    4777:   PetscCall(PetscFree(ba_i));
    4778:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));
    4779:   PetscCall(PetscLogEventEnd(MAT_Seqstompinum, seqmat, 0, 0, 0));
    4780:   PetscFunctionReturn(PETSC_SUCCESS);
    4781: }

    4783: PetscErrorCode MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, Mat *mpimat)
    4784: {
    4785:   Mat                  B_mpi;
    4786:   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)seqmat->data;
    4787:   PetscMPIInt          size, rank, tagi, tagj, *len_s, *len_si, *len_ri;
    4788:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
    4789:   PetscInt             M = seqmat->rmap->n, N = seqmat->cmap->n, i, *owners, *ai = a->i, *aj = a->j;
    4790:   PetscInt             len, *dnz, *onz, bs, cbs;
    4791:   PetscInt             k, anzi, *bi, *bj, *lnk, nlnk, arow, bnzi;
    4792:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextai;
    4793:   MPI_Request         *si_waits, *sj_waits, *ri_waits, *rj_waits;
    4794:   MPI_Status          *status;
    4795:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
    4796:   PetscBT              lnkbt;
    4797:   Mat_Merge_SeqsToMPI *merge;
    4798:   PetscContainer       container;

    4800:   PetscFunctionBegin;
    4801:   PetscCall(PetscLogEventBegin(MAT_Seqstompisym, seqmat, 0, 0, 0));

    4803:   /* make sure it is a PETSc comm */
    4804:   PetscCall(PetscCommDuplicate(comm, &comm, NULL));
    4805:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4806:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    4808:   PetscCall(PetscNew(&merge));
    4809:   PetscCall(PetscMalloc1(size, &status));

    4811:   /* determine row ownership */
    4812:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));
    4813:   PetscCall(PetscLayoutSetLocalSize(merge->rowmap, m));
    4814:   PetscCall(PetscLayoutSetSize(merge->rowmap, M));
    4815:   PetscCall(PetscLayoutSetBlockSize(merge->rowmap, 1));
    4816:   PetscCall(PetscLayoutSetUp(merge->rowmap));
    4817:   PetscCall(PetscMalloc1(size, &len_si));
    4818:   PetscCall(PetscMalloc1(size, &merge->len_s));

    4820:   m      = merge->rowmap->n;
    4821:   owners = merge->rowmap->range;

    4823:   /* determine the number of messages to send, their lengths */
    4824:   len_s = merge->len_s;

    4826:   len          = 0; /* length of buf_si[] */
    4827:   merge->nsend = 0;
    4828:   for (PetscMPIInt proc = 0; proc < size; proc++) {
    4829:     len_si[proc] = 0;
    4830:     if (proc == rank) {
    4831:       len_s[proc] = 0;
    4832:     } else {
    4833:       PetscCall(PetscMPIIntCast(owners[proc + 1] - owners[proc] + 1, &len_si[proc]));
    4834:       PetscCall(PetscMPIIntCast(ai[owners[proc + 1]] - ai[owners[proc]], &len_s[proc])); /* num of rows to be sent to [proc] */
    4835:     }
    4836:     if (len_s[proc]) {
    4837:       merge->nsend++;
    4838:       nrows = 0;
    4839:       for (i = owners[proc]; i < owners[proc + 1]; i++) {
    4840:         if (ai[i + 1] > ai[i]) nrows++;
    4841:       }
    4842:       PetscCall(PetscMPIIntCast(2 * (nrows + 1), &len_si[proc]));
    4843:       len += len_si[proc];
    4844:     }
    4845:   }

    4847:   /* determine the number and length of messages to receive for ij-structure */
    4848:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
    4849:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

    4851:   /* post the Irecv of j-structure */
    4852:   PetscCall(PetscCommGetNewTag(comm, &tagj));
    4853:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rj_waits));

    4855:   /* post the Isend of j-structure */
    4856:   PetscCall(PetscMalloc2(merge->nsend, &si_waits, merge->nsend, &sj_waits));

    4858:   for (PetscMPIInt proc = 0, k = 0; proc < size; proc++) {
    4859:     if (!len_s[proc]) continue;
    4860:     i = owners[proc];
    4861:     PetscCallMPI(MPIU_Isend(aj + ai[i], len_s[proc], MPIU_INT, proc, tagj, comm, sj_waits + k));
    4862:     k++;
    4863:   }

    4865:   /* receives and sends of j-structure are complete */
    4866:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, rj_waits, status));
    4867:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, sj_waits, status));

    4869:   /* send and recv i-structure */
    4870:   PetscCall(PetscCommGetNewTag(comm, &tagi));
    4871:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &ri_waits));

    4873:   PetscCall(PetscMalloc1(len + 1, &buf_s));
    4874:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
    4875:   for (PetscMPIInt proc = 0, k = 0; proc < size; proc++) {
    4876:     if (!len_s[proc]) continue;
    4877:     /* form outgoing message for i-structure:
    4878:          buf_si[0]:                 nrows to be sent
    4879:                [1:nrows]:           row index (global)
    4880:                [nrows+1:2*nrows+1]: i-structure index
    4881:     */
    4882:     nrows       = len_si[proc] / 2 - 1;
    4883:     buf_si_i    = buf_si + nrows + 1;
    4884:     buf_si[0]   = nrows;
    4885:     buf_si_i[0] = 0;
    4886:     nrows       = 0;
    4887:     for (i = owners[proc]; i < owners[proc + 1]; i++) {
    4888:       anzi = ai[i + 1] - ai[i];
    4889:       if (anzi) {
    4890:         buf_si_i[nrows + 1] = buf_si_i[nrows] + anzi; /* i-structure */
    4891:         buf_si[nrows + 1]   = i - owners[proc];       /* local row index */
    4892:         nrows++;
    4893:       }
    4894:     }
    4895:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, si_waits + k));
    4896:     k++;
    4897:     buf_si += len_si[proc];
    4898:   }

    4900:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, ri_waits, status));
    4901:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, si_waits, status));

    4903:   PetscCall(PetscInfo(seqmat, "nsend: %d, nrecv: %d\n", merge->nsend, merge->nrecv));
    4904:   for (i = 0; i < merge->nrecv; i++) PetscCall(PetscInfo(seqmat, "recv len_ri=%d, len_rj=%d from [%d]\n", len_ri[i], merge->len_r[i], merge->id_r[i]));

    4906:   PetscCall(PetscFree(len_si));
    4907:   PetscCall(PetscFree(len_ri));
    4908:   PetscCall(PetscFree(rj_waits));
    4909:   PetscCall(PetscFree2(si_waits, sj_waits));
    4910:   PetscCall(PetscFree(ri_waits));
    4911:   PetscCall(PetscFree(buf_s));
    4912:   PetscCall(PetscFree(status));

    4914:   /* compute a local seq matrix in each processor */
    4915:   /* allocate bi array and free space for accumulating nonzero column info */
    4916:   PetscCall(PetscMalloc1(m + 1, &bi));
    4917:   bi[0] = 0;

    4919:   /* create and initialize a linked list */
    4920:   nlnk = N + 1;
    4921:   PetscCall(PetscLLCreate(N, N, nlnk, lnk, lnkbt));

    4923:   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
    4924:   len = ai[owners[rank + 1]] - ai[owners[rank]];
    4925:   PetscCall(PetscFreeSpaceGet(PetscIntMultTruncate(2, len) + 1, &free_space));

    4927:   current_space = free_space;

    4929:   /* determine symbolic info for each local row */
    4930:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));

    4932:   for (k = 0; k < merge->nrecv; k++) {
    4933:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    4934:     nrows       = *buf_ri_k[k];
    4935:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    4936:     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    4937:   }

    4939:   MatPreallocateBegin(comm, m, n, dnz, onz);
    4940:   len = 0;
    4941:   for (i = 0; i < m; i++) {
    4942:     bnzi = 0;
    4943:     /* add local non-zero cols of this proc's seqmat into lnk */
    4944:     arow = owners[rank] + i;
    4945:     anzi = ai[arow + 1] - ai[arow];
    4946:     aj   = a->j + ai[arow];
    4947:     PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
    4948:     bnzi += nlnk;
    4949:     /* add received col data into lnk */
    4950:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    4951:       if (i == *nextrow[k]) {            /* i-th row */
    4952:         anzi = *(nextai[k] + 1) - *nextai[k];
    4953:         aj   = buf_rj[k] + *nextai[k];
    4954:         PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
    4955:         bnzi += nlnk;
    4956:         nextrow[k]++;
    4957:         nextai[k]++;
    4958:       }
    4959:     }
    4960:     if (len < bnzi) len = bnzi; /* =max(bnzi) */

    4962:     /* if free space is not available, make more free space */
    4963:     if (current_space->local_remaining < bnzi) PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(bnzi, current_space->total_array_size), &current_space));
    4964:     /* copy data into free space, then initialize lnk */
    4965:     PetscCall(PetscLLClean(N, N, bnzi, lnk, current_space->array, lnkbt));
    4966:     PetscCall(MatPreallocateSet(i + owners[rank], bnzi, current_space->array, dnz, onz));

    4968:     current_space->array += bnzi;
    4969:     current_space->local_used += bnzi;
    4970:     current_space->local_remaining -= bnzi;

    4972:     bi[i + 1] = bi[i] + bnzi;
    4973:   }

    4975:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));

    4977:   PetscCall(PetscMalloc1(bi[m], &bj));
    4978:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
    4979:   PetscCall(PetscLLDestroy(lnk, lnkbt));

    4981:   /* create symbolic parallel matrix B_mpi */
    4982:   PetscCall(MatGetBlockSizes(seqmat, &bs, &cbs));
    4983:   PetscCall(MatCreate(comm, &B_mpi));
    4984:   if (n == PETSC_DECIDE) {
    4985:     PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, N));
    4986:   } else {
    4987:     PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    4988:   }
    4989:   PetscCall(MatSetBlockSizes(B_mpi, bs, cbs));
    4990:   PetscCall(MatSetType(B_mpi, MATMPIAIJ));
    4991:   PetscCall(MatMPIAIJSetPreallocation(B_mpi, 0, dnz, 0, onz));
    4992:   MatPreallocateEnd(dnz, onz);
    4993:   PetscCall(MatSetOption(B_mpi, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));

    4995:   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
    4996:   B_mpi->assembled = PETSC_FALSE;
    4997:   merge->bi        = bi;
    4998:   merge->bj        = bj;
    4999:   merge->buf_ri    = buf_ri;
    5000:   merge->buf_rj    = buf_rj;
    5001:   merge->coi       = NULL;
    5002:   merge->coj       = NULL;
    5003:   merge->owners_co = NULL;

    5005:   PetscCall(PetscCommDestroy(&comm));

    5007:   /* attach the supporting struct to B_mpi for reuse */
    5008:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    5009:   PetscCall(PetscContainerSetPointer(container, merge));
    5010:   PetscCall(PetscContainerSetCtxDestroy(container, MatDestroy_MPIAIJ_SeqsToMPI));
    5011:   PetscCall(PetscObjectCompose((PetscObject)B_mpi, "MatMergeSeqsToMPI", (PetscObject)container));
    5012:   PetscCall(PetscContainerDestroy(&container));
    5013:   *mpimat = B_mpi;

    5015:   PetscCall(PetscLogEventEnd(MAT_Seqstompisym, seqmat, 0, 0, 0));
    5016:   PetscFunctionReturn(PETSC_SUCCESS);
    5017: }

    5019: /*@
    5020:   MatCreateMPIAIJSumSeqAIJ - Creates a `MATMPIAIJ` matrix by adding sequential
    5021:   matrices from each processor

    5023:   Collective

    5025:   Input Parameters:
    5026: + comm   - the communicators the parallel matrix will live on
    5027: . seqmat - the input sequential matrices
    5028: . m      - number of local rows (or `PETSC_DECIDE`)
    5029: . n      - number of local columns (or `PETSC_DECIDE`)
    5030: - scall  - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5032:   Output Parameter:
    5033: . mpimat - the parallel matrix generated

    5035:   Level: advanced

    5037:   Note:
    5038:   The dimensions of the sequential matrix in each processor MUST be the same.
    5039:   The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
    5040:   destroyed when `mpimat` is destroyed. Call `PetscObjectQuery()` to access `seqmat`.

    5042: .seealso: [](ch_matrices), `Mat`, `MatCreateAIJ()`
    5043: @*/
    5044: PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, MatReuse scall, Mat *mpimat)
    5045: {
    5046:   PetscMPIInt size;

    5048:   PetscFunctionBegin;
    5049:   PetscCallMPI(MPI_Comm_size(comm, &size));
    5050:   if (size == 1) {
    5051:     PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
    5052:     if (scall == MAT_INITIAL_MATRIX) {
    5053:       PetscCall(MatDuplicate(seqmat, MAT_COPY_VALUES, mpimat));
    5054:     } else {
    5055:       PetscCall(MatCopy(seqmat, *mpimat, SAME_NONZERO_PATTERN));
    5056:     }
    5057:     PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
    5058:     PetscFunctionReturn(PETSC_SUCCESS);
    5059:   }
    5060:   PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
    5061:   if (scall == MAT_INITIAL_MATRIX) PetscCall(MatCreateMPIAIJSumSeqAIJSymbolic(comm, seqmat, m, n, mpimat));
    5062:   PetscCall(MatCreateMPIAIJSumSeqAIJNumeric(seqmat, *mpimat));
    5063:   PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
    5064:   PetscFunctionReturn(PETSC_SUCCESS);
    5065: }

    5067: /*@
    5068:   MatAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATAIJ` matrix.

    5070:   Not Collective

    5072:   Input Parameter:
    5073: . A - the matrix

    5075:   Output Parameter:
    5076: . A_loc - the local sequential matrix generated

    5078:   Level: developer

    5080:   Notes:
    5081:   The matrix is created by taking `A`'s local rows and putting them into a sequential matrix
    5082:   with `mlocal` rows and `n` columns. Where `mlocal` is obtained with `MatGetLocalSize()` and
    5083:   `n` is the global column count obtained with `MatGetSize()`

    5085:   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.

    5087:   For parallel matrices this creates an entirely new matrix. If the matrix is sequential it merely increases the reference count.

    5089:   Destroy the matrix with `MatDestroy()`

    5091: .seealso: [](ch_matrices), `Mat`, `MatMPIAIJGetLocalMat()`
    5092: @*/
    5093: PetscErrorCode MatAIJGetLocalMat(Mat A, Mat *A_loc)
    5094: {
    5095:   PetscBool mpi;

    5097:   PetscFunctionBegin;
    5098:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &mpi));
    5099:   if (mpi) {
    5100:     PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, A_loc));
    5101:   } else {
    5102:     *A_loc = A;
    5103:     PetscCall(PetscObjectReference((PetscObject)*A_loc));
    5104:   }
    5105:   PetscFunctionReturn(PETSC_SUCCESS);
    5106: }

    5108: /*@
    5109:   MatMPIAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix.

    5111:   Not Collective

    5113:   Input Parameters:
    5114: + A     - the matrix
    5115: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5117:   Output Parameter:
    5118: . A_loc - the local sequential matrix generated

    5120:   Level: developer

    5122:   Notes:
    5123:   The matrix is created by taking all `A`'s local rows and putting them into a sequential
    5124:   matrix with `mlocal` rows and `n` columns.`mlocal` is the row count obtained with
    5125:   `MatGetLocalSize()` and `n` is the global column count obtained with `MatGetSize()`.

    5127:   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.

    5129:   When `A` is sequential and `MAT_INITIAL_MATRIX` is requested, the matrix returned is the diagonal part of `A` (which contains the entire matrix),
    5130:   with its reference count increased by one. Hence changing values of `A_loc` changes `A`. If `MAT_REUSE_MATRIX` is requested on a sequential matrix
    5131:   then `MatCopy`(Adiag,*`A_loc`,`SAME_NONZERO_PATTERN`) is called to fill `A_loc`. Thus one can preallocate the appropriate sequential matrix `A_loc`
    5132:   and then call this routine with `MAT_REUSE_MATRIX`. In this case, one can modify the values of `A_loc` without affecting the original sequential matrix.

    5134: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMatCondensed()`, `MatMPIAIJGetLocalMatMerge()`
    5135: @*/
    5136: PetscErrorCode MatMPIAIJGetLocalMat(Mat A, MatReuse scall, Mat *A_loc)
    5137: {
    5138:   Mat_MPIAIJ        *mpimat = (Mat_MPIAIJ *)A->data;
    5139:   Mat_SeqAIJ        *mat, *a, *b;
    5140:   PetscInt          *ai, *aj, *bi, *bj, *cmap = mpimat->garray;
    5141:   const PetscScalar *aa, *ba, *aav, *bav;
    5142:   PetscScalar       *ca, *cam;
    5143:   PetscMPIInt        size;
    5144:   PetscInt           am = A->rmap->n, i, j, k, cstart = A->cmap->rstart;
    5145:   PetscInt          *ci, *cj, col, ncols_d, ncols_o, jo;
    5146:   PetscBool          match;

    5148:   PetscFunctionBegin;
    5149:   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &match));
    5150:   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
    5151:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    5152:   if (size == 1) {
    5153:     if (scall == MAT_INITIAL_MATRIX) {
    5154:       PetscCall(PetscObjectReference((PetscObject)mpimat->A));
    5155:       *A_loc = mpimat->A;
    5156:     } else if (scall == MAT_REUSE_MATRIX) {
    5157:       PetscCall(MatCopy(mpimat->A, *A_loc, SAME_NONZERO_PATTERN));
    5158:     }
    5159:     PetscFunctionReturn(PETSC_SUCCESS);
    5160:   }

    5162:   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
    5163:   a  = (Mat_SeqAIJ *)mpimat->A->data;
    5164:   b  = (Mat_SeqAIJ *)mpimat->B->data;
    5165:   ai = a->i;
    5166:   aj = a->j;
    5167:   bi = b->i;
    5168:   bj = b->j;
    5169:   PetscCall(MatSeqAIJGetArrayRead(mpimat->A, &aav));
    5170:   PetscCall(MatSeqAIJGetArrayRead(mpimat->B, &bav));
    5171:   aa = aav;
    5172:   ba = bav;
    5173:   if (scall == MAT_INITIAL_MATRIX) {
    5174:     PetscCall(PetscMalloc1(1 + am, &ci));
    5175:     ci[0] = 0;
    5176:     for (i = 0; i < am; i++) ci[i + 1] = ci[i] + (ai[i + 1] - ai[i]) + (bi[i + 1] - bi[i]);
    5177:     PetscCall(PetscMalloc1(1 + ci[am], &cj));
    5178:     PetscCall(PetscMalloc1(1 + ci[am], &ca));
    5179:     k = 0;
    5180:     for (i = 0; i < am; i++) {
    5181:       ncols_o = bi[i + 1] - bi[i];
    5182:       ncols_d = ai[i + 1] - ai[i];
    5183:       /* off-diagonal portion of A */
    5184:       for (jo = 0; jo < ncols_o; jo++) {
    5185:         col = cmap[*bj];
    5186:         if (col >= cstart) break;
    5187:         cj[k] = col;
    5188:         bj++;
    5189:         ca[k++] = *ba++;
    5190:       }
    5191:       /* diagonal portion of A */
    5192:       for (j = 0; j < ncols_d; j++) {
    5193:         cj[k]   = cstart + *aj++;
    5194:         ca[k++] = *aa++;
    5195:       }
    5196:       /* off-diagonal portion of A */
    5197:       for (j = jo; j < ncols_o; j++) {
    5198:         cj[k]   = cmap[*bj++];
    5199:         ca[k++] = *ba++;
    5200:       }
    5201:     }
    5202:     /* put together the new matrix */
    5203:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, A->cmap->N, ci, cj, ca, A_loc));
    5204:     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5205:     /* Since these are PETSc arrays, change flags to free them as necessary. */
    5206:     mat          = (Mat_SeqAIJ *)(*A_loc)->data;
    5207:     mat->free_a  = PETSC_TRUE;
    5208:     mat->free_ij = PETSC_TRUE;
    5209:     mat->nonew   = 0;
    5210:   } else if (scall == MAT_REUSE_MATRIX) {
    5211:     mat = (Mat_SeqAIJ *)(*A_loc)->data;
    5212:     ci  = mat->i;
    5213:     cj  = mat->j;
    5214:     PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &cam));
    5215:     for (i = 0; i < am; i++) {
    5216:       /* off-diagonal portion of A */
    5217:       ncols_o = bi[i + 1] - bi[i];
    5218:       for (jo = 0; jo < ncols_o; jo++) {
    5219:         col = cmap[*bj];
    5220:         if (col >= cstart) break;
    5221:         *cam++ = *ba++;
    5222:         bj++;
    5223:       }
    5224:       /* diagonal portion of A */
    5225:       ncols_d = ai[i + 1] - ai[i];
    5226:       for (j = 0; j < ncols_d; j++) *cam++ = *aa++;
    5227:       /* off-diagonal portion of A */
    5228:       for (j = jo; j < ncols_o; j++) {
    5229:         *cam++ = *ba++;
    5230:         bj++;
    5231:       }
    5232:     }
    5233:     PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &cam));
    5234:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
    5235:   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->A, &aav));
    5236:   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->B, &bav));
    5237:   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
    5238:   PetscFunctionReturn(PETSC_SUCCESS);
    5239: }

    5241: /*@
    5242:   MatMPIAIJGetLocalMatMerge - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix by taking all its local rows and putting them into a sequential matrix with
    5243:   mlocal rows and n columns. Where n is the sum of the number of columns of the diagonal and off-diagonal part

    5245:   Not Collective

    5247:   Input Parameters:
    5248: + A     - the matrix
    5249: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5251:   Output Parameters:
    5252: + glob  - sequential `IS` with global indices associated with the columns of the local sequential matrix generated (can be `NULL`)
    5253: - A_loc - the local sequential matrix generated

    5255:   Level: developer

    5257:   Note:
    5258:   This is different from `MatMPIAIJGetLocalMat()` since the first columns in the returning matrix are those associated with the diagonal
    5259:   part, then those associated with the off-diagonal part (in its local ordering)

    5261: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`
    5262: @*/
    5263: PetscErrorCode MatMPIAIJGetLocalMatMerge(Mat A, MatReuse scall, IS *glob, Mat *A_loc)
    5264: {
    5265:   Mat             Ao, Ad;
    5266:   const PetscInt *cmap;
    5267:   PetscMPIInt     size;
    5268:   PetscErrorCode (*f)(Mat, MatReuse, IS *, Mat *);

    5270:   PetscFunctionBegin;
    5271:   PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &cmap));
    5272:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    5273:   if (size == 1) {
    5274:     if (scall == MAT_INITIAL_MATRIX) {
    5275:       PetscCall(PetscObjectReference((PetscObject)Ad));
    5276:       *A_loc = Ad;
    5277:     } else if (scall == MAT_REUSE_MATRIX) {
    5278:       PetscCall(MatCopy(Ad, *A_loc, SAME_NONZERO_PATTERN));
    5279:     }
    5280:     if (glob) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)Ad), Ad->cmap->n, Ad->cmap->rstart, 1, glob));
    5281:     PetscFunctionReturn(PETSC_SUCCESS);
    5282:   }
    5283:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatMPIAIJGetLocalMatMerge_C", &f));
    5284:   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
    5285:   if (f) {
    5286:     PetscCall((*f)(A, scall, glob, A_loc));
    5287:   } else {
    5288:     Mat_SeqAIJ        *a = (Mat_SeqAIJ *)Ad->data;
    5289:     Mat_SeqAIJ        *b = (Mat_SeqAIJ *)Ao->data;
    5290:     Mat_SeqAIJ        *c;
    5291:     PetscInt          *ai = a->i, *aj = a->j;
    5292:     PetscInt          *bi = b->i, *bj = b->j;
    5293:     PetscInt          *ci, *cj;
    5294:     const PetscScalar *aa, *ba;
    5295:     PetscScalar       *ca;
    5296:     PetscInt           i, j, am, dn, on;

    5298:     PetscCall(MatGetLocalSize(Ad, &am, &dn));
    5299:     PetscCall(MatGetLocalSize(Ao, NULL, &on));
    5300:     PetscCall(MatSeqAIJGetArrayRead(Ad, &aa));
    5301:     PetscCall(MatSeqAIJGetArrayRead(Ao, &ba));
    5302:     if (scall == MAT_INITIAL_MATRIX) {
    5303:       PetscInt k;
    5304:       PetscCall(PetscMalloc1(1 + am, &ci));
    5305:       PetscCall(PetscMalloc1(ai[am] + bi[am], &cj));
    5306:       PetscCall(PetscMalloc1(ai[am] + bi[am], &ca));
    5307:       ci[0] = 0;
    5308:       for (i = 0, k = 0; i < am; i++) {
    5309:         const PetscInt ncols_o = bi[i + 1] - bi[i];
    5310:         const PetscInt ncols_d = ai[i + 1] - ai[i];
    5311:         ci[i + 1]              = ci[i] + ncols_o + ncols_d;
    5312:         /* diagonal portion of A */
    5313:         for (j = 0; j < ncols_d; j++, k++) {
    5314:           cj[k] = *aj++;
    5315:           ca[k] = *aa++;
    5316:         }
    5317:         /* off-diagonal portion of A */
    5318:         for (j = 0; j < ncols_o; j++, k++) {
    5319:           cj[k] = dn + *bj++;
    5320:           ca[k] = *ba++;
    5321:         }
    5322:       }
    5323:       /* put together the new matrix */
    5324:       PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, dn + on, ci, cj, ca, A_loc));
    5325:       /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5326:       /* Since these are PETSc arrays, change flags to free them as necessary. */
    5327:       c          = (Mat_SeqAIJ *)(*A_loc)->data;
    5328:       c->free_a  = PETSC_TRUE;
    5329:       c->free_ij = PETSC_TRUE;
    5330:       c->nonew   = 0;
    5331:       PetscCall(MatSetType(*A_loc, ((PetscObject)Ad)->type_name));
    5332:     } else if (scall == MAT_REUSE_MATRIX) {
    5333:       PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &ca));
    5334:       for (i = 0; i < am; i++) {
    5335:         const PetscInt ncols_d = ai[i + 1] - ai[i];
    5336:         const PetscInt ncols_o = bi[i + 1] - bi[i];
    5337:         /* diagonal portion of A */
    5338:         for (j = 0; j < ncols_d; j++) *ca++ = *aa++;
    5339:         /* off-diagonal portion of A */
    5340:         for (j = 0; j < ncols_o; j++) *ca++ = *ba++;
    5341:       }
    5342:       PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &ca));
    5343:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
    5344:     PetscCall(MatSeqAIJRestoreArrayRead(Ad, &aa));
    5345:     PetscCall(MatSeqAIJRestoreArrayRead(Ao, &aa));
    5346:     if (glob) {
    5347:       PetscInt cst, *gidx;

    5349:       PetscCall(MatGetOwnershipRangeColumn(A, &cst, NULL));
    5350:       PetscCall(PetscMalloc1(dn + on, &gidx));
    5351:       for (i = 0; i < dn; i++) gidx[i] = cst + i;
    5352:       for (i = 0; i < on; i++) gidx[i + dn] = cmap[i];
    5353:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)Ad), dn + on, gidx, PETSC_OWN_POINTER, glob));
    5354:     }
    5355:   }
    5356:   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
    5357:   PetscFunctionReturn(PETSC_SUCCESS);
    5358: }

    5360: /*@C
    5361:   MatMPIAIJGetLocalMatCondensed - Creates a `MATSEQAIJ` matrix from an `MATMPIAIJ` matrix by taking all its local rows and NON-ZERO columns

    5363:   Not Collective

    5365:   Input Parameters:
    5366: + A     - the matrix
    5367: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    5368: . row   - index set of rows to extract (or `NULL`)
    5369: - col   - index set of columns to extract (or `NULL`)

    5371:   Output Parameter:
    5372: . A_loc - the local sequential matrix generated

    5374:   Level: developer

    5376: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`
    5377: @*/
    5378: PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A, MatReuse scall, IS *row, IS *col, Mat *A_loc)
    5379: {
    5380:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    5381:   PetscInt    i, start, end, ncols, nzA, nzB, *cmap, imark, *idx;
    5382:   IS          isrowa, iscola;
    5383:   Mat        *aloc;
    5384:   PetscBool   match;

    5386:   PetscFunctionBegin;
    5387:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &match));
    5388:   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
    5389:   PetscCall(PetscLogEventBegin(MAT_Getlocalmatcondensed, A, 0, 0, 0));
    5390:   if (!row) {
    5391:     start = A->rmap->rstart;
    5392:     end   = A->rmap->rend;
    5393:     PetscCall(ISCreateStride(PETSC_COMM_SELF, end - start, start, 1, &isrowa));
    5394:   } else {
    5395:     isrowa = *row;
    5396:   }
    5397:   if (!col) {
    5398:     start = A->cmap->rstart;
    5399:     cmap  = a->garray;
    5400:     nzA   = a->A->cmap->n;
    5401:     nzB   = a->B->cmap->n;
    5402:     PetscCall(PetscMalloc1(nzA + nzB, &idx));
    5403:     ncols = 0;
    5404:     for (i = 0; i < nzB; i++) {
    5405:       if (cmap[i] < start) idx[ncols++] = cmap[i];
    5406:       else break;
    5407:     }
    5408:     imark = i;
    5409:     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;
    5410:     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i];
    5411:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &iscola));
    5412:   } else {
    5413:     iscola = *col;
    5414:   }
    5415:   if (scall != MAT_INITIAL_MATRIX) {
    5416:     PetscCall(PetscMalloc1(1, &aloc));
    5417:     aloc[0] = *A_loc;
    5418:   }
    5419:   PetscCall(MatCreateSubMatrices(A, 1, &isrowa, &iscola, scall, &aloc));
    5420:   if (!col) { /* attach global id of condensed columns */
    5421:     PetscCall(PetscObjectCompose((PetscObject)aloc[0], "_petsc_GetLocalMatCondensed_iscol", (PetscObject)iscola));
    5422:   }
    5423:   *A_loc = aloc[0];
    5424:   PetscCall(PetscFree(aloc));
    5425:   if (!row) PetscCall(ISDestroy(&isrowa));
    5426:   if (!col) PetscCall(ISDestroy(&iscola));
    5427:   PetscCall(PetscLogEventEnd(MAT_Getlocalmatcondensed, A, 0, 0, 0));
    5428:   PetscFunctionReturn(PETSC_SUCCESS);
    5429: }

    5431: /*
    5432:  * Create a sequential AIJ matrix based on row indices. a whole column is extracted once a row is matched.
    5433:  * Row could be local or remote.The routine is designed to be scalable in memory so that nothing is based
    5434:  * on a global size.
    5435:  * */
    5436: static PetscErrorCode MatCreateSeqSubMatrixWithRows_Private(Mat P, IS rows, Mat *P_oth)
    5437: {
    5438:   Mat_MPIAIJ            *p  = (Mat_MPIAIJ *)P->data;
    5439:   Mat_SeqAIJ            *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data, *p_oth;
    5440:   PetscInt               plocalsize, nrows, *ilocal, *oilocal, i, lidx, *nrcols, *nlcols, ncol;
    5441:   PetscMPIInt            owner;
    5442:   PetscSFNode           *iremote, *oiremote;
    5443:   const PetscInt        *lrowindices;
    5444:   PetscSF                sf, osf;
    5445:   PetscInt               pcstart, *roffsets, *loffsets, *pnnz, j;
    5446:   PetscInt               ontotalcols, dntotalcols, ntotalcols, nout;
    5447:   MPI_Comm               comm;
    5448:   ISLocalToGlobalMapping mapping;
    5449:   const PetscScalar     *pd_a, *po_a;

    5451:   PetscFunctionBegin;
    5452:   PetscCall(PetscObjectGetComm((PetscObject)P, &comm));
    5453:   /* plocalsize is the number of roots
    5454:    * nrows is the number of leaves
    5455:    * */
    5456:   PetscCall(MatGetLocalSize(P, &plocalsize, NULL));
    5457:   PetscCall(ISGetLocalSize(rows, &nrows));
    5458:   PetscCall(PetscCalloc1(nrows, &iremote));
    5459:   PetscCall(ISGetIndices(rows, &lrowindices));
    5460:   for (i = 0; i < nrows; i++) {
    5461:     /* Find a remote index and an owner for a row
    5462:      * The row could be local or remote
    5463:      * */
    5464:     owner = 0;
    5465:     lidx  = 0;
    5466:     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, &lidx));
    5467:     iremote[i].index = lidx;
    5468:     iremote[i].rank  = owner;
    5469:   }
    5470:   /* Create SF to communicate how many nonzero columns for each row */
    5471:   PetscCall(PetscSFCreate(comm, &sf));
    5472:   /* SF will figure out the number of nonzero columns for each row, and their
    5473:    * offsets
    5474:    * */
    5475:   PetscCall(PetscSFSetGraph(sf, plocalsize, nrows, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    5476:   PetscCall(PetscSFSetFromOptions(sf));
    5477:   PetscCall(PetscSFSetUp(sf));

    5479:   PetscCall(PetscCalloc1(2 * (plocalsize + 1), &roffsets));
    5480:   PetscCall(PetscCalloc1(2 * plocalsize, &nrcols));
    5481:   PetscCall(PetscCalloc1(nrows, &pnnz));
    5482:   roffsets[0] = 0;
    5483:   roffsets[1] = 0;
    5484:   for (i = 0; i < plocalsize; i++) {
    5485:     /* diagonal */
    5486:     nrcols[i * 2 + 0] = pd->i[i + 1] - pd->i[i];
    5487:     /* off-diagonal */
    5488:     nrcols[i * 2 + 1] = po->i[i + 1] - po->i[i];
    5489:     /* compute offsets so that we relative location for each row */
    5490:     roffsets[(i + 1) * 2 + 0] = roffsets[i * 2 + 0] + nrcols[i * 2 + 0];
    5491:     roffsets[(i + 1) * 2 + 1] = roffsets[i * 2 + 1] + nrcols[i * 2 + 1];
    5492:   }
    5493:   PetscCall(PetscCalloc1(2 * nrows, &nlcols));
    5494:   PetscCall(PetscCalloc1(2 * nrows, &loffsets));
    5495:   /* 'r' means root, and 'l' means leaf */
    5496:   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
    5497:   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
    5498:   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
    5499:   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
    5500:   PetscCall(PetscSFDestroy(&sf));
    5501:   PetscCall(PetscFree(roffsets));
    5502:   PetscCall(PetscFree(nrcols));
    5503:   dntotalcols = 0;
    5504:   ontotalcols = 0;
    5505:   ncol        = 0;
    5506:   for (i = 0; i < nrows; i++) {
    5507:     pnnz[i] = nlcols[i * 2 + 0] + nlcols[i * 2 + 1];
    5508:     ncol    = PetscMax(pnnz[i], ncol);
    5509:     /* diagonal */
    5510:     dntotalcols += nlcols[i * 2 + 0];
    5511:     /* off-diagonal */
    5512:     ontotalcols += nlcols[i * 2 + 1];
    5513:   }
    5514:   /* We do not need to figure the right number of columns
    5515:    * since all the calculations will be done by going through the raw data
    5516:    * */
    5517:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nrows, ncol, 0, pnnz, P_oth));
    5518:   PetscCall(MatSetUp(*P_oth));
    5519:   PetscCall(PetscFree(pnnz));
    5520:   p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
    5521:   /* diagonal */
    5522:   PetscCall(PetscCalloc1(dntotalcols, &iremote));
    5523:   /* off-diagonal */
    5524:   PetscCall(PetscCalloc1(ontotalcols, &oiremote));
    5525:   /* diagonal */
    5526:   PetscCall(PetscCalloc1(dntotalcols, &ilocal));
    5527:   /* off-diagonal */
    5528:   PetscCall(PetscCalloc1(ontotalcols, &oilocal));
    5529:   dntotalcols = 0;
    5530:   ontotalcols = 0;
    5531:   ntotalcols  = 0;
    5532:   for (i = 0; i < nrows; i++) {
    5533:     owner = 0;
    5534:     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, NULL));
    5535:     /* Set iremote for diag matrix */
    5536:     for (j = 0; j < nlcols[i * 2 + 0]; j++) {
    5537:       iremote[dntotalcols].index = loffsets[i * 2 + 0] + j;
    5538:       iremote[dntotalcols].rank  = owner;
    5539:       /* P_oth is seqAIJ so that ilocal need to point to the first part of memory */
    5540:       ilocal[dntotalcols++] = ntotalcols++;
    5541:     }
    5542:     /* off-diagonal */
    5543:     for (j = 0; j < nlcols[i * 2 + 1]; j++) {
    5544:       oiremote[ontotalcols].index = loffsets[i * 2 + 1] + j;
    5545:       oiremote[ontotalcols].rank  = owner;
    5546:       oilocal[ontotalcols++]      = ntotalcols++;
    5547:     }
    5548:   }
    5549:   PetscCall(ISRestoreIndices(rows, &lrowindices));
    5550:   PetscCall(PetscFree(loffsets));
    5551:   PetscCall(PetscFree(nlcols));
    5552:   PetscCall(PetscSFCreate(comm, &sf));
    5553:   /* P serves as roots and P_oth is leaves
    5554:    * Diag matrix
    5555:    * */
    5556:   PetscCall(PetscSFSetGraph(sf, pd->i[plocalsize], dntotalcols, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    5557:   PetscCall(PetscSFSetFromOptions(sf));
    5558:   PetscCall(PetscSFSetUp(sf));

    5560:   PetscCall(PetscSFCreate(comm, &osf));
    5561:   /* off-diagonal */
    5562:   PetscCall(PetscSFSetGraph(osf, po->i[plocalsize], ontotalcols, oilocal, PETSC_OWN_POINTER, oiremote, PETSC_OWN_POINTER));
    5563:   PetscCall(PetscSFSetFromOptions(osf));
    5564:   PetscCall(PetscSFSetUp(osf));
    5565:   PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
    5566:   PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
    5567:   /* operate on the matrix internal data to save memory */
    5568:   PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5569:   PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5570:   PetscCall(MatGetOwnershipRangeColumn(P, &pcstart, NULL));
    5571:   /* Convert to global indices for diag matrix */
    5572:   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] += pcstart;
    5573:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
    5574:   /* We want P_oth store global indices */
    5575:   PetscCall(ISLocalToGlobalMappingCreate(comm, 1, p->B->cmap->n, p->garray, PETSC_COPY_VALUES, &mapping));
    5576:   /* Use memory scalable approach */
    5577:   PetscCall(ISLocalToGlobalMappingSetType(mapping, ISLOCALTOGLOBALMAPPINGHASH));
    5578:   PetscCall(ISLocalToGlobalMappingApply(mapping, po->i[plocalsize], po->j, po->j));
    5579:   PetscCall(PetscSFBcastBegin(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
    5580:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
    5581:   /* Convert back to local indices */
    5582:   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] -= pcstart;
    5583:   PetscCall(PetscSFBcastEnd(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
    5584:   nout = 0;
    5585:   PetscCall(ISGlobalToLocalMappingApply(mapping, IS_GTOLM_DROP, po->i[plocalsize], po->j, &nout, po->j));
    5586:   PetscCheck(nout == po->i[plocalsize], comm, PETSC_ERR_ARG_INCOMP, "n %" PetscInt_FMT " does not equal to nout %" PetscInt_FMT " ", po->i[plocalsize], nout);
    5587:   PetscCall(ISLocalToGlobalMappingDestroy(&mapping));
    5588:   /* Exchange values */
    5589:   PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5590:   PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5591:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
    5592:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
    5593:   /* Stop PETSc from shrinking memory */
    5594:   for (i = 0; i < nrows; i++) p_oth->ilen[i] = p_oth->imax[i];
    5595:   PetscCall(MatAssemblyBegin(*P_oth, MAT_FINAL_ASSEMBLY));
    5596:   PetscCall(MatAssemblyEnd(*P_oth, MAT_FINAL_ASSEMBLY));
    5597:   /* Attach PetscSF objects to P_oth so that we can reuse it later */
    5598:   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "diagsf", (PetscObject)sf));
    5599:   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "offdiagsf", (PetscObject)osf));
    5600:   PetscCall(PetscSFDestroy(&sf));
    5601:   PetscCall(PetscSFDestroy(&osf));
    5602:   PetscFunctionReturn(PETSC_SUCCESS);
    5603: }

    5605: /*
    5606:  * Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
    5607:  * This supports MPIAIJ and MAIJ
    5608:  * */
    5609: PetscErrorCode MatGetBrowsOfAcols_MPIXAIJ(Mat A, Mat P, PetscInt dof, MatReuse reuse, Mat *P_oth)
    5610: {
    5611:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data, *p = (Mat_MPIAIJ *)P->data;
    5612:   Mat_SeqAIJ *p_oth;
    5613:   IS          rows, map;
    5614:   PetscHMapI  hamp;
    5615:   PetscInt    i, htsize, *rowindices, off, *mapping, key, count;
    5616:   MPI_Comm    comm;
    5617:   PetscSF     sf, osf;
    5618:   PetscBool   has;

    5620:   PetscFunctionBegin;
    5621:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    5622:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, P, 0, 0));
    5623:   /* If it is the first time, create an index set of off-diag nonzero columns of A,
    5624:    *  and then create a submatrix (that often is an overlapping matrix)
    5625:    * */
    5626:   if (reuse == MAT_INITIAL_MATRIX) {
    5627:     /* Use a hash table to figure out unique keys */
    5628:     PetscCall(PetscHMapICreateWithSize(a->B->cmap->n, &hamp));
    5629:     PetscCall(PetscCalloc1(a->B->cmap->n, &mapping));
    5630:     count = 0;
    5631:     /* Assume that  a->g is sorted, otherwise the following does not make sense */
    5632:     for (i = 0; i < a->B->cmap->n; i++) {
    5633:       key = a->garray[i] / dof;
    5634:       PetscCall(PetscHMapIHas(hamp, key, &has));
    5635:       if (!has) {
    5636:         mapping[i] = count;
    5637:         PetscCall(PetscHMapISet(hamp, key, count++));
    5638:       } else {
    5639:         /* Current 'i' has the same value the previous step */
    5640:         mapping[i] = count - 1;
    5641:       }
    5642:     }
    5643:     PetscCall(ISCreateGeneral(comm, a->B->cmap->n, mapping, PETSC_OWN_POINTER, &map));
    5644:     PetscCall(PetscHMapIGetSize(hamp, &htsize));
    5645:     PetscCheck(htsize == count, comm, PETSC_ERR_ARG_INCOMP, " Size of hash map %" PetscInt_FMT " is inconsistent with count %" PetscInt_FMT, htsize, count);
    5646:     PetscCall(PetscCalloc1(htsize, &rowindices));
    5647:     off = 0;
    5648:     PetscCall(PetscHMapIGetKeys(hamp, &off, rowindices));
    5649:     PetscCall(PetscHMapIDestroy(&hamp));
    5650:     PetscCall(PetscSortInt(htsize, rowindices));
    5651:     PetscCall(ISCreateGeneral(comm, htsize, rowindices, PETSC_OWN_POINTER, &rows));
    5652:     /* In case, the matrix was already created but users want to recreate the matrix */
    5653:     PetscCall(MatDestroy(P_oth));
    5654:     PetscCall(MatCreateSeqSubMatrixWithRows_Private(P, rows, P_oth));
    5655:     PetscCall(PetscObjectCompose((PetscObject)*P_oth, "aoffdiagtopothmapping", (PetscObject)map));
    5656:     PetscCall(ISDestroy(&map));
    5657:     PetscCall(ISDestroy(&rows));
    5658:   } else if (reuse == MAT_REUSE_MATRIX) {
    5659:     /* If matrix was already created, we simply update values using SF objects
    5660:      * that as attached to the matrix earlier.
    5661:      */
    5662:     const PetscScalar *pd_a, *po_a;

    5664:     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "diagsf", (PetscObject *)&sf));
    5665:     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "offdiagsf", (PetscObject *)&osf));
    5666:     PetscCheck(sf && osf, comm, PETSC_ERR_ARG_NULL, "Matrix is not initialized yet");
    5667:     p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
    5668:     /* Update values in place */
    5669:     PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
    5670:     PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
    5671:     PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5672:     PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5673:     PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5674:     PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5675:     PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
    5676:     PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
    5677:   } else SETERRQ(comm, PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown reuse type");
    5678:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, P, 0, 0));
    5679:   PetscFunctionReturn(PETSC_SUCCESS);
    5680: }

    5682: /*@C
    5683:   MatGetBrowsOfAcols - Returns `IS` that contain rows of `B` that equal to nonzero columns of local `A`

    5685:   Collective

    5687:   Input Parameters:
    5688: + A     - the first matrix in `MATMPIAIJ` format
    5689: . B     - the second matrix in `MATMPIAIJ` format
    5690: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5692:   Output Parameters:
    5693: + rowb  - On input index sets of rows of B to extract (or `NULL`), modified on output
    5694: . colb  - On input index sets of columns of B to extract (or `NULL`), modified on output
    5695: - B_seq - the sequential matrix generated

    5697:   Level: developer

    5699: .seealso: `Mat`, `MATMPIAIJ`, `IS`, `MatReuse`
    5700: @*/
    5701: PetscErrorCode MatGetBrowsOfAcols(Mat A, Mat B, MatReuse scall, IS *rowb, IS *colb, Mat *B_seq)
    5702: {
    5703:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    5704:   PetscInt   *idx, i, start, ncols, nzA, nzB, *cmap, imark;
    5705:   IS          isrowb, iscolb;
    5706:   Mat        *bseq = NULL;

    5708:   PetscFunctionBegin;
    5709:   PetscCheck(A->cmap->rstart == B->rmap->rstart && A->cmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",
    5710:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    5711:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAcols, A, B, 0, 0));

    5713:   if (scall == MAT_INITIAL_MATRIX) {
    5714:     start = A->cmap->rstart;
    5715:     cmap  = a->garray;
    5716:     nzA   = a->A->cmap->n;
    5717:     nzB   = a->B->cmap->n;
    5718:     PetscCall(PetscMalloc1(nzA + nzB, &idx));
    5719:     ncols = 0;
    5720:     for (i = 0; i < nzB; i++) { /* row < local row index */
    5721:       if (cmap[i] < start) idx[ncols++] = cmap[i];
    5722:       else break;
    5723:     }
    5724:     imark = i;
    5725:     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;   /* local rows */
    5726:     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
    5727:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &isrowb));
    5728:     PetscCall(ISCreateStride(PETSC_COMM_SELF, B->cmap->N, 0, 1, &iscolb));
    5729:   } else {
    5730:     PetscCheck(rowb && colb, PETSC_COMM_SELF, PETSC_ERR_SUP, "IS rowb and colb must be provided for MAT_REUSE_MATRIX");
    5731:     isrowb = *rowb;
    5732:     iscolb = *colb;
    5733:     PetscCall(PetscMalloc1(1, &bseq));
    5734:     bseq[0] = *B_seq;
    5735:   }
    5736:   PetscCall(MatCreateSubMatrices(B, 1, &isrowb, &iscolb, scall, &bseq));
    5737:   *B_seq = bseq[0];
    5738:   PetscCall(PetscFree(bseq));
    5739:   if (!rowb) {
    5740:     PetscCall(ISDestroy(&isrowb));
    5741:   } else {
    5742:     *rowb = isrowb;
    5743:   }
    5744:   if (!colb) {
    5745:     PetscCall(ISDestroy(&iscolb));
    5746:   } else {
    5747:     *colb = iscolb;
    5748:   }
    5749:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAcols, A, B, 0, 0));
    5750:   PetscFunctionReturn(PETSC_SUCCESS);
    5751: }

    5753: /*
    5754:     MatGetBrowsOfAoCols_MPIAIJ - Creates a `MATSEQAIJ` matrix by taking rows of B that equal to nonzero columns
    5755:     of the OFF-DIAGONAL portion of local A

    5757:     Collective

    5759:    Input Parameters:
    5760: +    A,B - the matrices in `MATMPIAIJ` format
    5761: -    scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5763:    Output Parameter:
    5764: +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
    5765: .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
    5766: .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
    5767: -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N

    5769:     Developer Note:
    5770:     This directly accesses information inside the VecScatter associated with the matrix-vector product
    5771:      for this matrix. This is not desirable..

    5773:     Level: developer

    5775: */

    5777: PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A, Mat B, MatReuse scall, PetscInt **startsj_s, PetscInt **startsj_r, MatScalar **bufa_ptr, Mat *B_oth)
    5778: {
    5779:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
    5780:   VecScatter         ctx;
    5781:   MPI_Comm           comm;
    5782:   const PetscMPIInt *rprocs, *sprocs;
    5783:   PetscMPIInt        nrecvs, nsends;
    5784:   const PetscInt    *srow, *rstarts, *sstarts;
    5785:   PetscInt          *rowlen, *bufj, *bufJ, ncols = 0, aBn = a->B->cmap->n, row, *b_othi, *b_othj, *rvalues = NULL, *svalues = NULL, *cols, sbs, rbs;
    5786:   PetscInt           i, j, k = 0, l, ll, nrows, *rstartsj = NULL, *sstartsj, len;
    5787:   PetscScalar       *b_otha, *bufa, *bufA, *vals = NULL;
    5788:   MPI_Request       *reqs = NULL, *rwaits = NULL, *swaits = NULL;
    5789:   PetscMPIInt        size, tag, rank, nreqs;

    5791:   PetscFunctionBegin;
    5792:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    5793:   PetscCallMPI(MPI_Comm_size(comm, &size));

    5795:   PetscCheck(A->cmap->rstart == B->rmap->rstart && A->cmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",
    5796:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    5797:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, B, 0, 0));
    5798:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    5800:   if (size == 1) {
    5801:     startsj_s = NULL;
    5802:     bufa_ptr  = NULL;
    5803:     *B_oth    = NULL;
    5804:     PetscFunctionReturn(PETSC_SUCCESS);
    5805:   }

    5807:   ctx = a->Mvctx;
    5808:   tag = ((PetscObject)ctx)->tag;

    5810:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &srow, &sprocs, &sbs));
    5811:   /* rprocs[] must be ordered so that indices received from them are ordered in rvalues[], which is key to algorithms used in this subroutine */
    5812:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL /*indices not needed*/, &rprocs, &rbs));
    5813:   PetscCall(PetscMPIIntCast(nsends + nrecvs, &nreqs));
    5814:   PetscCall(PetscMalloc1(nreqs, &reqs));
    5815:   rwaits = reqs;
    5816:   swaits = PetscSafePointerPlusOffset(reqs, nrecvs);

    5818:   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
    5819:   if (scall == MAT_INITIAL_MATRIX) {
    5820:     /* i-array */
    5821:     /*  post receives */
    5822:     if (nrecvs) PetscCall(PetscMalloc1(rbs * (rstarts[nrecvs] - rstarts[0]), &rvalues)); /* rstarts can be NULL when nrecvs=0 */
    5823:     for (i = 0; i < nrecvs; i++) {
    5824:       rowlen = rvalues + rstarts[i] * rbs;
    5825:       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of indices to be received */
    5826:       PetscCallMPI(MPIU_Irecv(rowlen, nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
    5827:     }

    5829:     /* pack the outgoing message */
    5830:     PetscCall(PetscMalloc2(nsends + 1, &sstartsj, nrecvs + 1, &rstartsj));

    5832:     sstartsj[0] = 0;
    5833:     rstartsj[0] = 0;
    5834:     len         = 0; /* total length of j or a array to be sent */
    5835:     if (nsends) {
    5836:       k = sstarts[0]; /* ATTENTION: sstarts[0] and rstarts[0] are not necessarily zero */
    5837:       PetscCall(PetscMalloc1(sbs * (sstarts[nsends] - sstarts[0]), &svalues));
    5838:     }
    5839:     for (i = 0; i < nsends; i++) {
    5840:       rowlen = svalues + (sstarts[i] - sstarts[0]) * sbs;
    5841:       nrows  = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5842:       for (j = 0; j < nrows; j++) {
    5843:         row = srow[k] + B->rmap->range[rank]; /* global row idx */
    5844:         for (l = 0; l < sbs; l++) {
    5845:           PetscCall(MatGetRow_MPIAIJ(B, row + l, &ncols, NULL, NULL)); /* rowlength */

    5847:           rowlen[j * sbs + l] = ncols;

    5849:           len += ncols;
    5850:           PetscCall(MatRestoreRow_MPIAIJ(B, row + l, &ncols, NULL, NULL));
    5851:         }
    5852:         k++;
    5853:       }
    5854:       PetscCallMPI(MPIU_Isend(rowlen, nrows * sbs, MPIU_INT, sprocs[i], tag, comm, swaits + i));

    5856:       sstartsj[i + 1] = len; /* starting point of (i+1)-th outgoing msg in bufj and bufa */
    5857:     }
    5858:     /* recvs and sends of i-array are completed */
    5859:     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5860:     PetscCall(PetscFree(svalues));

    5862:     /* allocate buffers for sending j and a arrays */
    5863:     PetscCall(PetscMalloc1(len, &bufj));
    5864:     PetscCall(PetscMalloc1(len, &bufa));

    5866:     /* create i-array of B_oth */
    5867:     PetscCall(PetscMalloc1(aBn + 1, &b_othi));

    5869:     b_othi[0] = 0;
    5870:     len       = 0; /* total length of j or a array to be received */
    5871:     k         = 0;
    5872:     for (i = 0; i < nrecvs; i++) {
    5873:       rowlen = rvalues + (rstarts[i] - rstarts[0]) * rbs;
    5874:       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of rows to be received */
    5875:       for (j = 0; j < nrows; j++) {
    5876:         b_othi[k + 1] = b_othi[k] + rowlen[j];
    5877:         PetscCall(PetscIntSumError(rowlen[j], len, &len));
    5878:         k++;
    5879:       }
    5880:       rstartsj[i + 1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
    5881:     }
    5882:     PetscCall(PetscFree(rvalues));

    5884:     /* allocate space for j and a arrays of B_oth */
    5885:     PetscCall(PetscMalloc1(b_othi[aBn], &b_othj));
    5886:     PetscCall(PetscMalloc1(b_othi[aBn], &b_otha));

    5888:     /* j-array */
    5889:     /*  post receives of j-array */
    5890:     for (i = 0; i < nrecvs; i++) {
    5891:       nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
    5892:       PetscCallMPI(MPIU_Irecv(PetscSafePointerPlusOffset(b_othj, rstartsj[i]), nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
    5893:     }

    5895:     /* pack the outgoing message j-array */
    5896:     if (nsends) k = sstarts[0];
    5897:     for (i = 0; i < nsends; i++) {
    5898:       nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5899:       bufJ  = PetscSafePointerPlusOffset(bufj, sstartsj[i]);
    5900:       for (j = 0; j < nrows; j++) {
    5901:         row = srow[k++] + B->rmap->range[rank]; /* global row idx */
    5902:         for (ll = 0; ll < sbs; ll++) {
    5903:           PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
    5904:           for (l = 0; l < ncols; l++) *bufJ++ = cols[l];
    5905:           PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
    5906:         }
    5907:       }
    5908:       PetscCallMPI(MPIU_Isend(PetscSafePointerPlusOffset(bufj, sstartsj[i]), sstartsj[i + 1] - sstartsj[i], MPIU_INT, sprocs[i], tag, comm, swaits + i));
    5909:     }

    5911:     /* recvs and sends of j-array are completed */
    5912:     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5913:   } else if (scall == MAT_REUSE_MATRIX) {
    5914:     sstartsj = *startsj_s;
    5915:     rstartsj = *startsj_r;
    5916:     bufa     = *bufa_ptr;
    5917:     PetscCall(MatSeqAIJGetArrayWrite(*B_oth, &b_otha));
    5918:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not possess an object container");

    5920:   /* a-array */
    5921:   /*  post receives of a-array */
    5922:   for (i = 0; i < nrecvs; i++) {
    5923:     nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
    5924:     PetscCallMPI(MPIU_Irecv(PetscSafePointerPlusOffset(b_otha, rstartsj[i]), nrows, MPIU_SCALAR, rprocs[i], tag, comm, rwaits + i));
    5925:   }

    5927:   /* pack the outgoing message a-array */
    5928:   if (nsends) k = sstarts[0];
    5929:   for (i = 0; i < nsends; i++) {
    5930:     nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5931:     bufA  = PetscSafePointerPlusOffset(bufa, sstartsj[i]);
    5932:     for (j = 0; j < nrows; j++) {
    5933:       row = srow[k++] + B->rmap->range[rank]; /* global row idx */
    5934:       for (ll = 0; ll < sbs; ll++) {
    5935:         PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
    5936:         for (l = 0; l < ncols; l++) *bufA++ = vals[l];
    5937:         PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
    5938:       }
    5939:     }
    5940:     PetscCallMPI(MPIU_Isend(PetscSafePointerPlusOffset(bufa, sstartsj[i]), sstartsj[i + 1] - sstartsj[i], MPIU_SCALAR, sprocs[i], tag, comm, swaits + i));
    5941:   }
    5942:   /* recvs and sends of a-array are completed */
    5943:   if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5944:   PetscCall(PetscFree(reqs));

    5946:   if (scall == MAT_INITIAL_MATRIX) {
    5947:     Mat_SeqAIJ *b_oth;

    5949:     /* put together the new matrix */
    5950:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, aBn, B->cmap->N, b_othi, b_othj, b_otha, B_oth));

    5952:     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5953:     /* Since these are PETSc arrays, change flags to free them as necessary. */
    5954:     b_oth          = (Mat_SeqAIJ *)(*B_oth)->data;
    5955:     b_oth->free_a  = PETSC_TRUE;
    5956:     b_oth->free_ij = PETSC_TRUE;
    5957:     b_oth->nonew   = 0;

    5959:     PetscCall(PetscFree(bufj));
    5960:     if (!startsj_s || !bufa_ptr) {
    5961:       PetscCall(PetscFree2(sstartsj, rstartsj));
    5962:       PetscCall(PetscFree(bufa_ptr));
    5963:     } else {
    5964:       *startsj_s = sstartsj;
    5965:       *startsj_r = rstartsj;
    5966:       *bufa_ptr  = bufa;
    5967:     }
    5968:   } else if (scall == MAT_REUSE_MATRIX) {
    5969:     PetscCall(MatSeqAIJRestoreArrayWrite(*B_oth, &b_otha));
    5970:   }

    5972:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE, &nsends, &sstarts, &srow, &sprocs, &sbs));
    5973:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE, &nrecvs, &rstarts, NULL, &rprocs, &rbs));
    5974:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, B, 0, 0));
    5975:   PetscFunctionReturn(PETSC_SUCCESS);
    5976: }

    5978: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat, MatType, MatReuse, Mat *);
    5979: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat, MatType, MatReuse, Mat *);
    5980: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJSELL(Mat, MatType, MatReuse, Mat *);
    5981: #if defined(PETSC_HAVE_MKL_SPARSE)
    5982: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJMKL(Mat, MatType, MatReuse, Mat *);
    5983: #endif
    5984: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIBAIJ(Mat, MatType, MatReuse, Mat *);
    5985: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat, MatType, MatReuse, Mat *);
    5986: #if defined(PETSC_HAVE_ELEMENTAL)
    5987: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
    5988: #endif
    5989: #if defined(PETSC_HAVE_SCALAPACK)
    5990: PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
    5991: #endif
    5992: #if defined(PETSC_HAVE_HYPRE)
    5993: PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat, MatType, MatReuse, Mat *);
    5994: #endif
    5995: #if defined(PETSC_HAVE_CUDA)
    5996: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
    5997: #endif
    5998: #if defined(PETSC_HAVE_HIP)
    5999: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJHIPSPARSE(Mat, MatType, MatReuse, Mat *);
    6000: #endif
    6001: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    6002: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJKokkos(Mat, MatType, MatReuse, Mat *);
    6003: #endif
    6004: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISELL(Mat, MatType, MatReuse, Mat *);
    6005: PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);
    6006: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);

    6008: /*
    6009:     Computes (B'*A')' since computing B*A directly is untenable

    6011:                n                       p                          p
    6012:         [             ]       [             ]         [                 ]
    6013:       m [      A      ]  *  n [       B     ]   =   m [         C       ]
    6014:         [             ]       [             ]         [                 ]

    6016: */
    6017: static PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A, Mat B, Mat C)
    6018: {
    6019:   Mat At, Bt, Ct;

    6021:   PetscFunctionBegin;
    6022:   PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
    6023:   PetscCall(MatTranspose(B, MAT_INITIAL_MATRIX, &Bt));
    6024:   PetscCall(MatMatMult(Bt, At, MAT_INITIAL_MATRIX, PETSC_CURRENT, &Ct));
    6025:   PetscCall(MatDestroy(&At));
    6026:   PetscCall(MatDestroy(&Bt));
    6027:   PetscCall(MatTransposeSetPrecursor(Ct, C));
    6028:   PetscCall(MatTranspose(Ct, MAT_REUSE_MATRIX, &C));
    6029:   PetscCall(MatDestroy(&Ct));
    6030:   PetscFunctionReturn(PETSC_SUCCESS);
    6031: }

    6033: static PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A, Mat B, PetscReal fill, Mat C)
    6034: {
    6035:   PetscBool cisdense;

    6037:   PetscFunctionBegin;
    6038:   PetscCheck(A->cmap->n == B->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "A->cmap->n %" PetscInt_FMT " != B->rmap->n %" PetscInt_FMT, A->cmap->n, B->rmap->n);
    6039:   PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
    6040:   PetscCall(MatSetBlockSizesFromMats(C, A, B));
    6041:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATMPIDENSE, MATMPIDENSECUDA, MATMPIDENSEHIP, ""));
    6042:   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    6043:   PetscCall(MatSetUp(C));

    6045:   C->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
    6046:   PetscFunctionReturn(PETSC_SUCCESS);
    6047: }

    6049: static PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ_AB(Mat C)
    6050: {
    6051:   Mat_Product *product = C->product;
    6052:   Mat          A = product->A, B = product->B;

    6054:   PetscFunctionBegin;
    6055:   PetscCheck(A->cmap->rstart == B->rmap->rstart && A->cmap->rend == B->rmap->rend, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Matrix local dimensions are incompatible, (%" PetscInt_FMT ", %" PetscInt_FMT ") != (%" PetscInt_FMT ",%" PetscInt_FMT ")",
    6056:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    6057:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIDense_MPIAIJ;
    6058:   C->ops->productsymbolic = MatProductSymbolic_AB;
    6059:   PetscFunctionReturn(PETSC_SUCCESS);
    6060: }

    6062: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ(Mat C)
    6063: {
    6064:   Mat_Product *product = C->product;

    6066:   PetscFunctionBegin;
    6067:   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_MPIDense_MPIAIJ_AB(C));
    6068:   PetscFunctionReturn(PETSC_SUCCESS);
    6069: }

    6071: /*
    6072:    Merge two sets of sorted nonzeros and return a CSR for the merged (sequential) matrix

    6074:   Input Parameters:

    6076:     j1,rowBegin1,rowEnd1,jmap1: describe the first set of nonzeros (Set1)
    6077:     j2,rowBegin2,rowEnd2,jmap2: describe the second set of nonzeros (Set2)

    6079:     mat: both sets' nonzeros are on m rows, where m is the number of local rows of the matrix mat

    6081:     For Set1, j1[] contains column indices of the nonzeros.
    6082:     For the k-th row (0<=k<m), [rowBegin1[k],rowEnd1[k]) index into j1[] and point to the begin/end nonzero in row k
    6083:     respectively (note rowEnd1[k] is not necessarily equal to rwoBegin1[k+1]). Indices in this range of j1[] are sorted,
    6084:     but might have repeats. jmap1[t+1] - jmap1[t] is the number of repeats for the t-th unique nonzero in Set1.

    6086:     Similar for Set2.

    6088:     This routine merges the two sets of nonzeros row by row and removes repeats.

    6090:   Output Parameters: (memory is allocated by the caller)

    6092:     i[],j[]: the CSR of the merged matrix, which has m rows.
    6093:     imap1[]: the k-th unique nonzero in Set1 (k=0,1,...) corresponds to imap1[k]-th unique nonzero in the merged matrix.
    6094:     imap2[]: similar to imap1[], but for Set2.
    6095:     Note we order nonzeros row-by-row and from left to right.
    6096: */
    6097: static PetscErrorCode MatMergeEntries_Internal(Mat mat, const PetscInt j1[], const PetscInt j2[], const PetscCount rowBegin1[], const PetscCount rowEnd1[], const PetscCount rowBegin2[], const PetscCount rowEnd2[], const PetscCount jmap1[], const PetscCount jmap2[], PetscCount imap1[], PetscCount imap2[], PetscInt i[], PetscInt j[])
    6098: {
    6099:   PetscInt   r, m; /* Row index of mat */
    6100:   PetscCount t, t1, t2, b1, e1, b2, e2;

    6102:   PetscFunctionBegin;
    6103:   PetscCall(MatGetLocalSize(mat, &m, NULL));
    6104:   t1 = t2 = t = 0; /* Count unique nonzeros of in Set1, Set1 and the merged respectively */
    6105:   i[0]        = 0;
    6106:   for (r = 0; r < m; r++) { /* Do row by row merging */
    6107:     b1 = rowBegin1[r];
    6108:     e1 = rowEnd1[r];
    6109:     b2 = rowBegin2[r];
    6110:     e2 = rowEnd2[r];
    6111:     while (b1 < e1 && b2 < e2) {
    6112:       if (j1[b1] == j2[b2]) { /* Same column index and hence same nonzero */
    6113:         j[t]      = j1[b1];
    6114:         imap1[t1] = t;
    6115:         imap2[t2] = t;
    6116:         b1 += jmap1[t1 + 1] - jmap1[t1]; /* Jump to next unique local nonzero */
    6117:         b2 += jmap2[t2 + 1] - jmap2[t2]; /* Jump to next unique remote nonzero */
    6118:         t1++;
    6119:         t2++;
    6120:         t++;
    6121:       } else if (j1[b1] < j2[b2]) {
    6122:         j[t]      = j1[b1];
    6123:         imap1[t1] = t;
    6124:         b1 += jmap1[t1 + 1] - jmap1[t1];
    6125:         t1++;
    6126:         t++;
    6127:       } else {
    6128:         j[t]      = j2[b2];
    6129:         imap2[t2] = t;
    6130:         b2 += jmap2[t2 + 1] - jmap2[t2];
    6131:         t2++;
    6132:         t++;
    6133:       }
    6134:     }
    6135:     /* Merge the remaining in either j1[] or j2[] */
    6136:     while (b1 < e1) {
    6137:       j[t]      = j1[b1];
    6138:       imap1[t1] = t;
    6139:       b1 += jmap1[t1 + 1] - jmap1[t1];
    6140:       t1++;
    6141:       t++;
    6142:     }
    6143:     while (b2 < e2) {
    6144:       j[t]      = j2[b2];
    6145:       imap2[t2] = t;
    6146:       b2 += jmap2[t2 + 1] - jmap2[t2];
    6147:       t2++;
    6148:       t++;
    6149:     }
    6150:     PetscCall(PetscIntCast(t, i + r + 1));
    6151:   }
    6152:   PetscFunctionReturn(PETSC_SUCCESS);
    6153: }

    6155: /*
    6156:   Split nonzeros in a block of local rows into two subsets: those in the diagonal block and those in the off-diagonal block

    6158:   Input Parameters:
    6159:     mat: an MPI matrix that provides row and column layout information for splitting. Let's say its number of local rows is m.
    6160:     n,i[],j[],perm[]: there are n input entries, belonging to m rows. Row/col indices of the entries are stored in i[] and j[]
    6161:       respectively, along with a permutation array perm[]. Length of the i[],j[],perm[] arrays is n.

    6163:       i[] is already sorted, but within a row, j[] is not sorted and might have repeats.
    6164:       i[] might contain negative indices at the beginning, which means the corresponding entries should be ignored in the splitting.

    6166:   Output Parameters:
    6167:     j[],perm[]: the routine needs to sort j[] within each row along with perm[].
    6168:     rowBegin[],rowMid[],rowEnd[]: of length m, and the memory is preallocated and zeroed by the caller.
    6169:       They contain indices pointing to j[]. For 0<=r<m, [rowBegin[r],rowMid[r]) point to begin/end entries of row r of the diagonal block,
    6170:       and [rowMid[r],rowEnd[r]) point to begin/end entries of row r of the off-diagonal block.

    6172:     Aperm[],Ajmap[],Atot,Annz: Arrays are allocated by this routine.
    6173:       Atot: number of entries belonging to the diagonal block.
    6174:       Annz: number of unique nonzeros belonging to the diagonal block.
    6175:       Aperm[Atot] stores values from perm[] for entries belonging to the diagonal block. Length of Aperm[] is Atot, though it may also count
    6176:         repeats (i.e., same 'i,j' pair).
    6177:       Ajmap[Annz+1] stores the number of repeats of each unique entry belonging to the diagonal block. More precisely, Ajmap[t+1] - Ajmap[t]
    6178:         is the number of repeats for the t-th unique entry in the diagonal block. Ajmap[0] is always 0.

    6180:       Atot: number of entries belonging to the diagonal block
    6181:       Annz: number of unique nonzeros belonging to the diagonal block.

    6183:     Bperm[], Bjmap[], Btot, Bnnz are similar but for the off-diagonal block.

    6185:     Aperm[],Bperm[],Ajmap[] and Bjmap[] are allocated separately by this routine with PetscMalloc1().
    6186: */
    6187: static PetscErrorCode MatSplitEntries_Internal(Mat mat, PetscCount n, const PetscInt i[], PetscInt j[], PetscCount perm[], PetscCount rowBegin[], PetscCount rowMid[], PetscCount rowEnd[], PetscCount *Atot_, PetscCount **Aperm_, PetscCount *Annz_, PetscCount **Ajmap_, PetscCount *Btot_, PetscCount **Bperm_, PetscCount *Bnnz_, PetscCount **Bjmap_)
    6188: {
    6189:   PetscInt    cstart, cend, rstart, rend, row, col;
    6190:   PetscCount  Atot = 0, Btot = 0; /* Total number of nonzeros in the diagonal and off-diagonal blocks */
    6191:   PetscCount  Annz = 0, Bnnz = 0; /* Number of unique nonzeros in the diagonal and off-diagonal blocks */
    6192:   PetscCount  k, m, p, q, r, s, mid;
    6193:   PetscCount *Aperm, *Bperm, *Ajmap, *Bjmap;

    6195:   PetscFunctionBegin;
    6196:   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
    6197:   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
    6198:   m = rend - rstart;

    6200:   /* Skip negative rows */
    6201:   for (k = 0; k < n; k++)
    6202:     if (i[k] >= 0) break;

    6204:   /* Process [k,n): sort and partition each local row into diag and offdiag portions,
    6205:      fill rowBegin[], rowMid[], rowEnd[], and count Atot, Btot, Annz, Bnnz.
    6206:   */
    6207:   while (k < n) {
    6208:     row = i[k];
    6209:     /* Entries in [k,s) are in one row. Shift diagonal block col indices so that diag is ahead of offdiag after sorting the row */
    6210:     for (s = k; s < n; s++)
    6211:       if (i[s] != row) break;

    6213:     /* Shift diag columns to range of [-PETSC_INT_MAX, -1] */
    6214:     for (p = k; p < s; p++) {
    6215:       if (j[p] >= cstart && j[p] < cend) j[p] -= PETSC_INT_MAX;
    6216:     }
    6217:     PetscCall(PetscSortIntWithCountArray(s - k, j + k, perm + k));
    6218:     PetscCall(PetscSortedIntUpperBound(j, k, s, -1, &mid)); /* Separate [k,s) into [k,mid) for diag and [mid,s) for offdiag */
    6219:     rowBegin[row - rstart] = k;
    6220:     rowMid[row - rstart]   = mid;
    6221:     rowEnd[row - rstart]   = s;
    6222:     PetscCheck(k == s || j[s - 1] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column index %" PetscInt_FMT " is >= matrix column size %" PetscInt_FMT, j[s - 1], mat->cmap->N);

    6224:     /* Count nonzeros of this diag/offdiag row, which might have repeats */
    6225:     Atot += mid - k;
    6226:     Btot += s - mid;

    6228:     /* Count unique nonzeros of this diag row */
    6229:     for (p = k; p < mid;) {
    6230:       col = j[p];
    6231:       do {
    6232:         j[p] += PETSC_INT_MAX; /* Revert the modified diagonal indices */
    6233:         p++;
    6234:       } while (p < mid && j[p] == col);
    6235:       Annz++;
    6236:     }

    6238:     /* Count unique nonzeros of this offdiag row */
    6239:     for (p = mid; p < s;) {
    6240:       col = j[p];
    6241:       do {
    6242:         p++;
    6243:       } while (p < s && j[p] == col);
    6244:       Bnnz++;
    6245:     }
    6246:     k = s;
    6247:   }

    6249:   /* Allocation according to Atot, Btot, Annz, Bnnz */
    6250:   PetscCall(PetscMalloc1(Atot, &Aperm));
    6251:   PetscCall(PetscMalloc1(Btot, &Bperm));
    6252:   PetscCall(PetscMalloc1(Annz + 1, &Ajmap));
    6253:   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap));

    6255:   /* Re-scan indices and copy diag/offdiag permutation indices to Aperm, Bperm and also fill Ajmap and Bjmap */
    6256:   Ajmap[0] = Bjmap[0] = Atot = Btot = Annz = Bnnz = 0;
    6257:   for (r = 0; r < m; r++) {
    6258:     k   = rowBegin[r];
    6259:     mid = rowMid[r];
    6260:     s   = rowEnd[r];
    6261:     PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(Aperm, Atot), PetscSafePointerPlusOffset(perm, k), mid - k));
    6262:     PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(Bperm, Btot), PetscSafePointerPlusOffset(perm, mid), s - mid));
    6263:     Atot += mid - k;
    6264:     Btot += s - mid;

    6266:     /* Scan column indices in this row and find out how many repeats each unique nonzero has */
    6267:     for (p = k; p < mid;) {
    6268:       col = j[p];
    6269:       q   = p;
    6270:       do {
    6271:         p++;
    6272:       } while (p < mid && j[p] == col);
    6273:       Ajmap[Annz + 1] = Ajmap[Annz] + (p - q);
    6274:       Annz++;
    6275:     }

    6277:     for (p = mid; p < s;) {
    6278:       col = j[p];
    6279:       q   = p;
    6280:       do {
    6281:         p++;
    6282:       } while (p < s && j[p] == col);
    6283:       Bjmap[Bnnz + 1] = Bjmap[Bnnz] + (p - q);
    6284:       Bnnz++;
    6285:     }
    6286:   }
    6287:   /* Output */
    6288:   *Aperm_ = Aperm;
    6289:   *Annz_  = Annz;
    6290:   *Atot_  = Atot;
    6291:   *Ajmap_ = Ajmap;
    6292:   *Bperm_ = Bperm;
    6293:   *Bnnz_  = Bnnz;
    6294:   *Btot_  = Btot;
    6295:   *Bjmap_ = Bjmap;
    6296:   PetscFunctionReturn(PETSC_SUCCESS);
    6297: }

    6299: /*
    6300:   Expand the jmap[] array to make a new one in view of nonzeros in the merged matrix

    6302:   Input Parameters:
    6303:     nnz1: number of unique nonzeros in a set that was used to produce imap[], jmap[]
    6304:     nnz:  number of unique nonzeros in the merged matrix
    6305:     imap[nnz1]: i-th nonzero in the set is the imap[i]-th nonzero in the merged matrix
    6306:     jmap[nnz1+1]: i-th nonzero in the set has jmap[i+1] - jmap[i] repeats in the set

    6308:   Output Parameter: (memory is allocated by the caller)
    6309:     jmap_new[nnz+1]: i-th nonzero in the merged matrix has jmap_new[i+1] - jmap_new[i] repeats in the set

    6311:   Example:
    6312:     nnz1 = 4
    6313:     nnz  = 6
    6314:     imap = [1,3,4,5]
    6315:     jmap = [0,3,5,6,7]
    6316:    then,
    6317:     jmap_new = [0,0,3,3,5,6,7]
    6318: */
    6319: static PetscErrorCode ExpandJmap_Internal(PetscCount nnz1, PetscCount nnz, const PetscCount imap[], const PetscCount jmap[], PetscCount jmap_new[])
    6320: {
    6321:   PetscCount k, p;

    6323:   PetscFunctionBegin;
    6324:   jmap_new[0] = 0;
    6325:   p           = nnz;                /* p loops over jmap_new[] backwards */
    6326:   for (k = nnz1 - 1; k >= 0; k--) { /* k loops over imap[] */
    6327:     for (; p > imap[k]; p--) jmap_new[p] = jmap[k + 1];
    6328:   }
    6329:   for (; p >= 0; p--) jmap_new[p] = jmap[0];
    6330:   PetscFunctionReturn(PETSC_SUCCESS);
    6331: }

    6333: static PetscErrorCode MatCOOStructDestroy_MPIAIJ(void **data)
    6334: {
    6335:   MatCOOStruct_MPIAIJ *coo = (MatCOOStruct_MPIAIJ *)*data;

    6337:   PetscFunctionBegin;
    6338:   PetscCall(PetscSFDestroy(&coo->sf));
    6339:   PetscCall(PetscFree(coo->Aperm1));
    6340:   PetscCall(PetscFree(coo->Bperm1));
    6341:   PetscCall(PetscFree(coo->Ajmap1));
    6342:   PetscCall(PetscFree(coo->Bjmap1));
    6343:   PetscCall(PetscFree(coo->Aimap2));
    6344:   PetscCall(PetscFree(coo->Bimap2));
    6345:   PetscCall(PetscFree(coo->Aperm2));
    6346:   PetscCall(PetscFree(coo->Bperm2));
    6347:   PetscCall(PetscFree(coo->Ajmap2));
    6348:   PetscCall(PetscFree(coo->Bjmap2));
    6349:   PetscCall(PetscFree(coo->Cperm1));
    6350:   PetscCall(PetscFree2(coo->sendbuf, coo->recvbuf));
    6351:   PetscCall(PetscFree(coo));
    6352:   PetscFunctionReturn(PETSC_SUCCESS);
    6353: }

    6355: PetscErrorCode MatSetPreallocationCOO_MPIAIJ(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
    6356: {
    6357:   MPI_Comm             comm;
    6358:   PetscMPIInt          rank, size;
    6359:   PetscInt             m, n, M, N, rstart, rend, cstart, cend; /* Sizes, indices of row/col, therefore with type PetscInt */
    6360:   PetscCount           k, p, q, rem;                           /* Loop variables over coo arrays */
    6361:   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
    6362:   PetscContainer       container;
    6363:   MatCOOStruct_MPIAIJ *coo;

    6365:   PetscFunctionBegin;
    6366:   PetscCall(PetscFree(mpiaij->garray));
    6367:   PetscCall(VecDestroy(&mpiaij->lvec));
    6368: #if defined(PETSC_USE_CTABLE)
    6369:   PetscCall(PetscHMapIDestroy(&mpiaij->colmap));
    6370: #else
    6371:   PetscCall(PetscFree(mpiaij->colmap));
    6372: #endif
    6373:   PetscCall(VecScatterDestroy(&mpiaij->Mvctx));
    6374:   mat->assembled     = PETSC_FALSE;
    6375:   mat->was_assembled = PETSC_FALSE;

    6377:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    6378:   PetscCallMPI(MPI_Comm_size(comm, &size));
    6379:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    6380:   PetscCall(PetscLayoutSetUp(mat->rmap));
    6381:   PetscCall(PetscLayoutSetUp(mat->cmap));
    6382:   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
    6383:   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
    6384:   PetscCall(MatGetLocalSize(mat, &m, &n));
    6385:   PetscCall(MatGetSize(mat, &M, &N));

    6387:   /* Sort (i,j) by row along with a permutation array, so that the to-be-ignored */
    6388:   /* entries come first, then local rows, then remote rows.                     */
    6389:   PetscCount n1 = coo_n, *perm1;
    6390:   PetscInt  *i1 = coo_i, *j1 = coo_j;

    6392:   PetscCall(PetscMalloc1(n1, &perm1));
    6393:   for (k = 0; k < n1; k++) perm1[k] = k;

    6395:   /* Manipulate indices so that entries with negative row or col indices will have smallest
    6396:      row indices, local entries will have greater but negative row indices, and remote entries
    6397:      will have positive row indices.
    6398:   */
    6399:   for (k = 0; k < n1; k++) {
    6400:     if (i1[k] < 0 || j1[k] < 0) i1[k] = PETSC_INT_MIN;                /* e.g., -2^31, minimal to move them ahead */
    6401:     else if (i1[k] >= rstart && i1[k] < rend) i1[k] -= PETSC_INT_MAX; /* e.g., minus 2^31-1 to shift local rows to range of [-PETSC_INT_MAX, -1] */
    6402:     else {
    6403:       PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "MAT_NO_OFF_PROC_ENTRIES is set but insert to remote rows");
    6404:       if (mpiaij->donotstash) i1[k] = PETSC_INT_MIN; /* Ignore offproc entries as if they had negative indices */
    6405:     }
    6406:   }

    6408:   /* Sort by row; after that, [0,k) have ignored entries, [k,rem) have local rows and [rem,n1) have remote rows */
    6409:   PetscCall(PetscSortIntWithIntCountArrayPair(n1, i1, j1, perm1));

    6411:   /* Advance k to the first entry we need to take care of */
    6412:   for (k = 0; k < n1; k++)
    6413:     if (i1[k] > PETSC_INT_MIN) break;
    6414:   PetscCount i1start = k;

    6416:   PetscCall(PetscSortedIntUpperBound(i1, k, n1, rend - 1 - PETSC_INT_MAX, &rem)); /* rem is upper bound of the last local row */
    6417:   for (; k < rem; k++) i1[k] += PETSC_INT_MAX;                                    /* Revert row indices of local rows*/

    6419:   PetscCheck(n1 == 0 || i1[n1 - 1] < M, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "COO row index %" PetscInt_FMT " is >= the matrix row size %" PetscInt_FMT, i1[n1 - 1], M);

    6421:   /*           Send remote rows to their owner                                  */
    6422:   /* Find which rows should be sent to which remote ranks*/
    6423:   PetscInt        nsend = 0; /* Number of MPI ranks to send data to */
    6424:   PetscMPIInt    *sendto;    /* [nsend], storing remote ranks */
    6425:   PetscInt       *nentries;  /* [nsend], storing number of entries sent to remote ranks; Assume PetscInt is big enough for this count, and error if not */
    6426:   const PetscInt *ranges;
    6427:   PetscInt        maxNsend = size >= 128 ? 128 : size; /* Assume max 128 neighbors; realloc when needed */

    6429:   PetscCall(PetscLayoutGetRanges(mat->rmap, &ranges));
    6430:   PetscCall(PetscMalloc2(maxNsend, &sendto, maxNsend, &nentries));
    6431:   for (k = rem; k < n1;) {
    6432:     PetscMPIInt owner;
    6433:     PetscInt    firstRow, lastRow;

    6435:     /* Locate a row range */
    6436:     firstRow = i1[k]; /* first row of this owner */
    6437:     PetscCall(PetscLayoutFindOwner(mat->rmap, firstRow, &owner));
    6438:     lastRow = ranges[owner + 1] - 1; /* last row of this owner */

    6440:     /* Find the first index 'p' in [k,n) with i1[p] belonging to next owner */
    6441:     PetscCall(PetscSortedIntUpperBound(i1, k, n1, lastRow, &p));

    6443:     /* All entries in [k,p) belong to this remote owner */
    6444:     if (nsend >= maxNsend) { /* Double the remote ranks arrays if not long enough */
    6445:       PetscMPIInt *sendto2;
    6446:       PetscInt    *nentries2;
    6447:       PetscInt     maxNsend2 = (maxNsend <= size / 2) ? maxNsend * 2 : size;

    6449:       PetscCall(PetscMalloc2(maxNsend2, &sendto2, maxNsend2, &nentries2));
    6450:       PetscCall(PetscArraycpy(sendto2, sendto, maxNsend));
    6451:       PetscCall(PetscArraycpy(nentries2, nentries2, maxNsend + 1));
    6452:       PetscCall(PetscFree2(sendto, nentries2));
    6453:       sendto   = sendto2;
    6454:       nentries = nentries2;
    6455:       maxNsend = maxNsend2;
    6456:     }
    6457:     sendto[nsend] = owner;
    6458:     PetscCall(PetscIntCast(p - k, &nentries[nsend]));
    6459:     nsend++;
    6460:     k = p;
    6461:   }

    6463:   /* Build 1st SF to know offsets on remote to send data */
    6464:   PetscSF      sf1;
    6465:   PetscInt     nroots = 1, nroots2 = 0;
    6466:   PetscInt     nleaves = nsend, nleaves2 = 0;
    6467:   PetscInt    *offsets;
    6468:   PetscSFNode *iremote;

    6470:   PetscCall(PetscSFCreate(comm, &sf1));
    6471:   PetscCall(PetscMalloc1(nsend, &iremote));
    6472:   PetscCall(PetscMalloc1(nsend, &offsets));
    6473:   for (k = 0; k < nsend; k++) {
    6474:     iremote[k].rank  = sendto[k];
    6475:     iremote[k].index = 0;
    6476:     nleaves2 += nentries[k];
    6477:     PetscCheck(nleaves2 >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF leaves is too large for PetscInt");
    6478:   }
    6479:   PetscCall(PetscSFSetGraph(sf1, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    6480:   PetscCall(PetscSFFetchAndOpWithMemTypeBegin(sf1, MPIU_INT, PETSC_MEMTYPE_HOST, &nroots2 /*rootdata*/, PETSC_MEMTYPE_HOST, nentries /*leafdata*/, PETSC_MEMTYPE_HOST, offsets /*leafupdate*/, MPI_SUM));
    6481:   PetscCall(PetscSFFetchAndOpEnd(sf1, MPIU_INT, &nroots2, nentries, offsets, MPI_SUM)); /* Would nroots2 overflow, we check offsets[] below */
    6482:   PetscCall(PetscSFDestroy(&sf1));
    6483:   PetscAssert(nleaves2 == n1 - rem, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nleaves2 %" PetscInt_FMT " != number of remote entries %" PetscCount_FMT, nleaves2, n1 - rem);

    6485:   /* Build 2nd SF to send remote COOs to their owner */
    6486:   PetscSF sf2;
    6487:   nroots  = nroots2;
    6488:   nleaves = nleaves2;
    6489:   PetscCall(PetscSFCreate(comm, &sf2));
    6490:   PetscCall(PetscSFSetFromOptions(sf2));
    6491:   PetscCall(PetscMalloc1(nleaves, &iremote));
    6492:   p = 0;
    6493:   for (k = 0; k < nsend; k++) {
    6494:     PetscCheck(offsets[k] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF roots is too large for PetscInt");
    6495:     for (q = 0; q < nentries[k]; q++, p++) {
    6496:       iremote[p].rank = sendto[k];
    6497:       PetscCall(PetscIntCast(offsets[k] + q, &iremote[p].index));
    6498:     }
    6499:   }
    6500:   PetscCall(PetscSFSetGraph(sf2, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));

    6502:   /* Send the remote COOs to their owner */
    6503:   PetscInt    n2 = nroots, *i2, *j2; /* Buffers for received COOs from other ranks, along with a permutation array */
    6504:   PetscCount *perm2;                 /* Though PetscInt is enough for remote entries, we use PetscCount here as we want to reuse MatSplitEntries_Internal() */
    6505:   PetscCall(PetscMalloc3(n2, &i2, n2, &j2, n2, &perm2));
    6506:   PetscAssert(rem == 0 || i1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6507:   PetscAssert(rem == 0 || j1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6508:   PetscInt *i1prem = PetscSafePointerPlusOffset(i1, rem);
    6509:   PetscInt *j1prem = PetscSafePointerPlusOffset(j1, rem);
    6510:   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, i1prem, PETSC_MEMTYPE_HOST, i2, MPI_REPLACE));
    6511:   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, i1prem, i2, MPI_REPLACE));
    6512:   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, j1prem, PETSC_MEMTYPE_HOST, j2, MPI_REPLACE));
    6513:   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, j1prem, j2, MPI_REPLACE));

    6515:   PetscCall(PetscFree(offsets));
    6516:   PetscCall(PetscFree2(sendto, nentries));

    6518:   /* Sort received COOs by row along with the permutation array     */
    6519:   for (k = 0; k < n2; k++) perm2[k] = k;
    6520:   PetscCall(PetscSortIntWithIntCountArrayPair(n2, i2, j2, perm2));

    6522:   /* sf2 only sends contiguous leafdata to contiguous rootdata. We record the permutation which will be used to fill leafdata */
    6523:   PetscCount *Cperm1;
    6524:   PetscAssert(rem == 0 || perm1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6525:   PetscCount *perm1prem = PetscSafePointerPlusOffset(perm1, rem);
    6526:   PetscCall(PetscMalloc1(nleaves, &Cperm1));
    6527:   PetscCall(PetscArraycpy(Cperm1, perm1prem, nleaves));

    6529:   /* Support for HYPRE matrices, kind of a hack.
    6530:      Swap min column with diagonal so that diagonal values will go first */
    6531:   PetscBool hypre;
    6532:   PetscCall(PetscStrcmp("_internal_COO_mat_for_hypre", ((PetscObject)mat)->name, &hypre));
    6533:   if (hypre) {
    6534:     PetscInt *minj;
    6535:     PetscBT   hasdiag;

    6537:     PetscCall(PetscBTCreate(m, &hasdiag));
    6538:     PetscCall(PetscMalloc1(m, &minj));
    6539:     for (k = 0; k < m; k++) minj[k] = PETSC_INT_MAX;
    6540:     for (k = i1start; k < rem; k++) {
    6541:       if (j1[k] < cstart || j1[k] >= cend) continue;
    6542:       const PetscInt rindex = i1[k] - rstart;
    6543:       if ((j1[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
    6544:       minj[rindex] = PetscMin(minj[rindex], j1[k]);
    6545:     }
    6546:     for (k = 0; k < n2; k++) {
    6547:       if (j2[k] < cstart || j2[k] >= cend) continue;
    6548:       const PetscInt rindex = i2[k] - rstart;
    6549:       if ((j2[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
    6550:       minj[rindex] = PetscMin(minj[rindex], j2[k]);
    6551:     }
    6552:     for (k = i1start; k < rem; k++) {
    6553:       const PetscInt rindex = i1[k] - rstart;
    6554:       if (j1[k] < cstart || j1[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
    6555:       if (j1[k] == minj[rindex]) j1[k] = i1[k] + (cstart - rstart);
    6556:       else if ((j1[k] - cstart) == rindex) j1[k] = minj[rindex];
    6557:     }
    6558:     for (k = 0; k < n2; k++) {
    6559:       const PetscInt rindex = i2[k] - rstart;
    6560:       if (j2[k] < cstart || j2[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
    6561:       if (j2[k] == minj[rindex]) j2[k] = i2[k] + (cstart - rstart);
    6562:       else if ((j2[k] - cstart) == rindex) j2[k] = minj[rindex];
    6563:     }
    6564:     PetscCall(PetscBTDestroy(&hasdiag));
    6565:     PetscCall(PetscFree(minj));
    6566:   }

    6568:   /* Split local COOs and received COOs into diag/offdiag portions */
    6569:   PetscCount *rowBegin1, *rowMid1, *rowEnd1;
    6570:   PetscCount *Ajmap1, *Aperm1, *Bjmap1, *Bperm1;
    6571:   PetscCount  Annz1, Bnnz1, Atot1, Btot1;
    6572:   PetscCount *rowBegin2, *rowMid2, *rowEnd2;
    6573:   PetscCount *Ajmap2, *Aperm2, *Bjmap2, *Bperm2;
    6574:   PetscCount  Annz2, Bnnz2, Atot2, Btot2;

    6576:   PetscCall(PetscCalloc3(m, &rowBegin1, m, &rowMid1, m, &rowEnd1));
    6577:   PetscCall(PetscCalloc3(m, &rowBegin2, m, &rowMid2, m, &rowEnd2));
    6578:   PetscCall(MatSplitEntries_Internal(mat, rem, i1, j1, perm1, rowBegin1, rowMid1, rowEnd1, &Atot1, &Aperm1, &Annz1, &Ajmap1, &Btot1, &Bperm1, &Bnnz1, &Bjmap1));
    6579:   PetscCall(MatSplitEntries_Internal(mat, n2, i2, j2, perm2, rowBegin2, rowMid2, rowEnd2, &Atot2, &Aperm2, &Annz2, &Ajmap2, &Btot2, &Bperm2, &Bnnz2, &Bjmap2));

    6581:   /* Merge local COOs with received COOs: diag with diag, offdiag with offdiag */
    6582:   PetscInt *Ai, *Bi;
    6583:   PetscInt *Aj, *Bj;

    6585:   PetscCall(PetscMalloc1(m + 1, &Ai));
    6586:   PetscCall(PetscMalloc1(m + 1, &Bi));
    6587:   PetscCall(PetscMalloc1(Annz1 + Annz2, &Aj)); /* Since local and remote entries might have dups, we might allocate excess memory */
    6588:   PetscCall(PetscMalloc1(Bnnz1 + Bnnz2, &Bj));

    6590:   PetscCount *Aimap1, *Bimap1, *Aimap2, *Bimap2;
    6591:   PetscCall(PetscMalloc1(Annz1, &Aimap1));
    6592:   PetscCall(PetscMalloc1(Bnnz1, &Bimap1));
    6593:   PetscCall(PetscMalloc1(Annz2, &Aimap2));
    6594:   PetscCall(PetscMalloc1(Bnnz2, &Bimap2));

    6596:   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowBegin1, rowMid1, rowBegin2, rowMid2, Ajmap1, Ajmap2, Aimap1, Aimap2, Ai, Aj));
    6597:   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowMid1, rowEnd1, rowMid2, rowEnd2, Bjmap1, Bjmap2, Bimap1, Bimap2, Bi, Bj));

    6599:   /* Expand Ajmap1/Bjmap1 to make them based off nonzeros in A/B, since we     */
    6600:   /* expect nonzeros in A/B most likely have local contributing entries        */
    6601:   PetscInt    Annz = Ai[m];
    6602:   PetscInt    Bnnz = Bi[m];
    6603:   PetscCount *Ajmap1_new, *Bjmap1_new;

    6605:   PetscCall(PetscMalloc1(Annz + 1, &Ajmap1_new));
    6606:   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap1_new));

    6608:   PetscCall(ExpandJmap_Internal(Annz1, Annz, Aimap1, Ajmap1, Ajmap1_new));
    6609:   PetscCall(ExpandJmap_Internal(Bnnz1, Bnnz, Bimap1, Bjmap1, Bjmap1_new));

    6611:   PetscCall(PetscFree(Aimap1));
    6612:   PetscCall(PetscFree(Ajmap1));
    6613:   PetscCall(PetscFree(Bimap1));
    6614:   PetscCall(PetscFree(Bjmap1));
    6615:   PetscCall(PetscFree3(rowBegin1, rowMid1, rowEnd1));
    6616:   PetscCall(PetscFree3(rowBegin2, rowMid2, rowEnd2));
    6617:   PetscCall(PetscFree(perm1));
    6618:   PetscCall(PetscFree3(i2, j2, perm2));

    6620:   Ajmap1 = Ajmap1_new;
    6621:   Bjmap1 = Bjmap1_new;

    6623:   /* Reallocate Aj, Bj once we know actual numbers of unique nonzeros in A and B */
    6624:   if (Annz < Annz1 + Annz2) {
    6625:     PetscInt *Aj_new;
    6626:     PetscCall(PetscMalloc1(Annz, &Aj_new));
    6627:     PetscCall(PetscArraycpy(Aj_new, Aj, Annz));
    6628:     PetscCall(PetscFree(Aj));
    6629:     Aj = Aj_new;
    6630:   }

    6632:   if (Bnnz < Bnnz1 + Bnnz2) {
    6633:     PetscInt *Bj_new;
    6634:     PetscCall(PetscMalloc1(Bnnz, &Bj_new));
    6635:     PetscCall(PetscArraycpy(Bj_new, Bj, Bnnz));
    6636:     PetscCall(PetscFree(Bj));
    6637:     Bj = Bj_new;
    6638:   }

    6640:   /* Create new submatrices for on-process and off-process coupling                  */
    6641:   PetscScalar     *Aa, *Ba;
    6642:   MatType          rtype;
    6643:   Mat_SeqAIJ      *a, *b;
    6644:   PetscObjectState state;
    6645:   PetscCall(PetscCalloc1(Annz, &Aa)); /* Zero matrix on device */
    6646:   PetscCall(PetscCalloc1(Bnnz, &Ba));
    6647:   /* make Aj[] local, i.e, based off the start column of the diagonal portion */
    6648:   if (cstart) {
    6649:     for (k = 0; k < Annz; k++) Aj[k] -= cstart;
    6650:   }

    6652:   PetscCall(MatGetRootType_Private(mat, &rtype));

    6654:   MatSeqXAIJGetOptions_Private(mpiaij->A);
    6655:   PetscCall(MatDestroy(&mpiaij->A));
    6656:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, Ai, Aj, Aa, &mpiaij->A));
    6657:   PetscCall(MatSetBlockSizesFromMats(mpiaij->A, mat, mat));
    6658:   MatSeqXAIJRestoreOptions_Private(mpiaij->A);

    6660:   MatSeqXAIJGetOptions_Private(mpiaij->B);
    6661:   PetscCall(MatDestroy(&mpiaij->B));
    6662:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, mat->cmap->N, Bi, Bj, Ba, &mpiaij->B));
    6663:   PetscCall(MatSetBlockSizesFromMats(mpiaij->B, mat, mat));
    6664:   MatSeqXAIJRestoreOptions_Private(mpiaij->B);

    6666:   PetscCall(MatSetUpMultiply_MPIAIJ(mat));
    6667:   mat->was_assembled = PETSC_TRUE; // was_assembled in effect means the Mvctx is built; doing so avoids redundant MatSetUpMultiply_MPIAIJ
    6668:   state              = mpiaij->A->nonzerostate + mpiaij->B->nonzerostate;
    6669:   PetscCallMPI(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));

    6671:   a          = (Mat_SeqAIJ *)mpiaij->A->data;
    6672:   b          = (Mat_SeqAIJ *)mpiaij->B->data;
    6673:   a->free_a  = PETSC_TRUE;
    6674:   a->free_ij = PETSC_TRUE;
    6675:   b->free_a  = PETSC_TRUE;
    6676:   b->free_ij = PETSC_TRUE;
    6677:   a->maxnz   = a->nz;
    6678:   b->maxnz   = b->nz;

    6680:   /* conversion must happen AFTER multiply setup */
    6681:   PetscCall(MatConvert(mpiaij->A, rtype, MAT_INPLACE_MATRIX, &mpiaij->A));
    6682:   PetscCall(MatConvert(mpiaij->B, rtype, MAT_INPLACE_MATRIX, &mpiaij->B));
    6683:   PetscCall(VecDestroy(&mpiaij->lvec));
    6684:   PetscCall(MatCreateVecs(mpiaij->B, &mpiaij->lvec, NULL));

    6686:   // Put the COO struct in a container and then attach that to the matrix
    6687:   PetscCall(PetscMalloc1(1, &coo));
    6688:   coo->n       = coo_n;
    6689:   coo->sf      = sf2;
    6690:   coo->sendlen = nleaves;
    6691:   coo->recvlen = nroots;
    6692:   coo->Annz    = Annz;
    6693:   coo->Bnnz    = Bnnz;
    6694:   coo->Annz2   = Annz2;
    6695:   coo->Bnnz2   = Bnnz2;
    6696:   coo->Atot1   = Atot1;
    6697:   coo->Atot2   = Atot2;
    6698:   coo->Btot1   = Btot1;
    6699:   coo->Btot2   = Btot2;
    6700:   coo->Ajmap1  = Ajmap1;
    6701:   coo->Aperm1  = Aperm1;
    6702:   coo->Bjmap1  = Bjmap1;
    6703:   coo->Bperm1  = Bperm1;
    6704:   coo->Aimap2  = Aimap2;
    6705:   coo->Ajmap2  = Ajmap2;
    6706:   coo->Aperm2  = Aperm2;
    6707:   coo->Bimap2  = Bimap2;
    6708:   coo->Bjmap2  = Bjmap2;
    6709:   coo->Bperm2  = Bperm2;
    6710:   coo->Cperm1  = Cperm1;
    6711:   // Allocate in preallocation. If not used, it has zero cost on host
    6712:   PetscCall(PetscMalloc2(coo->sendlen, &coo->sendbuf, coo->recvlen, &coo->recvbuf));
    6713:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    6714:   PetscCall(PetscContainerSetPointer(container, coo));
    6715:   PetscCall(PetscContainerSetCtxDestroy(container, MatCOOStructDestroy_MPIAIJ));
    6716:   PetscCall(PetscObjectCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject)container));
    6717:   PetscCall(PetscContainerDestroy(&container));
    6718:   PetscFunctionReturn(PETSC_SUCCESS);
    6719: }

    6721: static PetscErrorCode MatSetValuesCOO_MPIAIJ(Mat mat, const PetscScalar v[], InsertMode imode)
    6722: {
    6723:   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
    6724:   Mat                  A = mpiaij->A, B = mpiaij->B;
    6725:   PetscScalar         *Aa, *Ba;
    6726:   PetscScalar         *sendbuf, *recvbuf;
    6727:   const PetscCount    *Ajmap1, *Ajmap2, *Aimap2;
    6728:   const PetscCount    *Bjmap1, *Bjmap2, *Bimap2;
    6729:   const PetscCount    *Aperm1, *Aperm2, *Bperm1, *Bperm2;
    6730:   const PetscCount    *Cperm1;
    6731:   PetscContainer       container;
    6732:   MatCOOStruct_MPIAIJ *coo;

    6734:   PetscFunctionBegin;
    6735:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container));
    6736:   PetscCheck(container, PetscObjectComm((PetscObject)mat), PETSC_ERR_PLIB, "Not found MatCOOStruct on this matrix");
    6737:   PetscCall(PetscContainerGetPointer(container, (void **)&coo));
    6738:   sendbuf = coo->sendbuf;
    6739:   recvbuf = coo->recvbuf;
    6740:   Ajmap1  = coo->Ajmap1;
    6741:   Ajmap2  = coo->Ajmap2;
    6742:   Aimap2  = coo->Aimap2;
    6743:   Bjmap1  = coo->Bjmap1;
    6744:   Bjmap2  = coo->Bjmap2;
    6745:   Bimap2  = coo->Bimap2;
    6746:   Aperm1  = coo->Aperm1;
    6747:   Aperm2  = coo->Aperm2;
    6748:   Bperm1  = coo->Bperm1;
    6749:   Bperm2  = coo->Bperm2;
    6750:   Cperm1  = coo->Cperm1;

    6752:   PetscCall(MatSeqAIJGetArray(A, &Aa)); /* Might read and write matrix values */
    6753:   PetscCall(MatSeqAIJGetArray(B, &Ba));

    6755:   /* Pack entries to be sent to remote */
    6756:   for (PetscCount i = 0; i < coo->sendlen; i++) sendbuf[i] = v[Cperm1[i]];

    6758:   /* Send remote entries to their owner and overlap the communication with local computation */
    6759:   PetscCall(PetscSFReduceWithMemTypeBegin(coo->sf, MPIU_SCALAR, PETSC_MEMTYPE_HOST, sendbuf, PETSC_MEMTYPE_HOST, recvbuf, MPI_REPLACE));
    6760:   /* Add local entries to A and B */
    6761:   for (PetscCount i = 0; i < coo->Annz; i++) { /* All nonzeros in A are either zero'ed or added with a value (i.e., initialized) */
    6762:     PetscScalar sum = 0.0;                     /* Do partial summation first to improve numerical stability */
    6763:     for (PetscCount k = Ajmap1[i]; k < Ajmap1[i + 1]; k++) sum += v[Aperm1[k]];
    6764:     Aa[i] = (imode == INSERT_VALUES ? 0.0 : Aa[i]) + sum;
    6765:   }
    6766:   for (PetscCount i = 0; i < coo->Bnnz; i++) {
    6767:     PetscScalar sum = 0.0;
    6768:     for (PetscCount k = Bjmap1[i]; k < Bjmap1[i + 1]; k++) sum += v[Bperm1[k]];
    6769:     Ba[i] = (imode == INSERT_VALUES ? 0.0 : Ba[i]) + sum;
    6770:   }
    6771:   PetscCall(PetscSFReduceEnd(coo->sf, MPIU_SCALAR, sendbuf, recvbuf, MPI_REPLACE));

    6773:   /* Add received remote entries to A and B */
    6774:   for (PetscCount i = 0; i < coo->Annz2; i++) {
    6775:     for (PetscCount k = Ajmap2[i]; k < Ajmap2[i + 1]; k++) Aa[Aimap2[i]] += recvbuf[Aperm2[k]];
    6776:   }
    6777:   for (PetscCount i = 0; i < coo->Bnnz2; i++) {
    6778:     for (PetscCount k = Bjmap2[i]; k < Bjmap2[i + 1]; k++) Ba[Bimap2[i]] += recvbuf[Bperm2[k]];
    6779:   }
    6780:   PetscCall(MatSeqAIJRestoreArray(A, &Aa));
    6781:   PetscCall(MatSeqAIJRestoreArray(B, &Ba));
    6782:   PetscFunctionReturn(PETSC_SUCCESS);
    6783: }

    6785: /*MC
    6786:    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.

    6788:    Options Database Keys:
    6789: . -mat_type mpiaij - sets the matrix type to `MATMPIAIJ` during a call to `MatSetFromOptions()`

    6791:    Level: beginner

    6793:    Notes:
    6794:    `MatSetValues()` may be called for this matrix type with a `NULL` argument for the numerical values,
    6795:     in this case the values associated with the rows and columns one passes in are set to zero
    6796:     in the matrix

    6798:     `MatSetOptions`(,`MAT_STRUCTURE_ONLY`,`PETSC_TRUE`) may be called for this matrix type. In this no
    6799:     space is allocated for the nonzero entries and any entries passed with `MatSetValues()` are ignored

    6801: .seealso: [](ch_matrices), `Mat`, `MATSEQAIJ`, `MATAIJ`, `MatCreateAIJ()`
    6802: M*/
    6803: PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
    6804: {
    6805:   Mat_MPIAIJ *b;
    6806:   PetscMPIInt size;

    6808:   PetscFunctionBegin;
    6809:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

    6811:   PetscCall(PetscNew(&b));
    6812:   B->data       = (void *)b;
    6813:   B->ops[0]     = MatOps_Values;
    6814:   B->assembled  = PETSC_FALSE;
    6815:   B->insertmode = NOT_SET_VALUES;
    6816:   b->size       = size;

    6818:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)B), &b->rank));

    6820:   /* build cache for off array entries formed */
    6821:   PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)B), 1, &B->stash));

    6823:   b->donotstash  = PETSC_FALSE;
    6824:   b->colmap      = NULL;
    6825:   b->garray      = NULL;
    6826:   b->roworiented = PETSC_TRUE;

    6828:   /* stuff used for matrix vector multiply */
    6829:   b->lvec  = NULL;
    6830:   b->Mvctx = NULL;

    6832:   /* stuff for MatGetRow() */
    6833:   b->rowindices   = NULL;
    6834:   b->rowvalues    = NULL;
    6835:   b->getrowactive = PETSC_FALSE;

    6837:   /* flexible pointer used in CUSPARSE classes */
    6838:   b->spptr = NULL;

    6840:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetUseScalableIncreaseOverlap_C", MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ));
    6841:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_MPIAIJ));
    6842:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_MPIAIJ));
    6843:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsTranspose_C", MatIsTranspose_MPIAIJ));
    6844:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocation_C", MatMPIAIJSetPreallocation_MPIAIJ));
    6845:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetPreallocation_C", MatResetPreallocation_MPIAIJ));
    6846:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetHash_C", MatResetHash_MPIAIJ));
    6847:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocationCSR_C", MatMPIAIJSetPreallocationCSR_MPIAIJ));
    6848:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDiagonalScaleLocal_C", MatDiagonalScaleLocal_MPIAIJ));
    6849:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijperm_C", MatConvert_MPIAIJ_MPIAIJPERM));
    6850:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijsell_C", MatConvert_MPIAIJ_MPIAIJSELL));
    6851: #if defined(PETSC_HAVE_CUDA)
    6852:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcusparse_C", MatConvert_MPIAIJ_MPIAIJCUSPARSE));
    6853: #endif
    6854: #if defined(PETSC_HAVE_HIP)
    6855:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijhipsparse_C", MatConvert_MPIAIJ_MPIAIJHIPSPARSE));
    6856: #endif
    6857: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    6858:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijkokkos_C", MatConvert_MPIAIJ_MPIAIJKokkos));
    6859: #endif
    6860: #if defined(PETSC_HAVE_MKL_SPARSE)
    6861:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijmkl_C", MatConvert_MPIAIJ_MPIAIJMKL));
    6862: #endif
    6863:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcrl_C", MatConvert_MPIAIJ_MPIAIJCRL));
    6864:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpibaij_C", MatConvert_MPIAIJ_MPIBAIJ));
    6865:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisbaij_C", MatConvert_MPIAIJ_MPISBAIJ));
    6866:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpidense_C", MatConvert_MPIAIJ_MPIDense));
    6867: #if defined(PETSC_HAVE_ELEMENTAL)
    6868:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_elemental_C", MatConvert_MPIAIJ_Elemental));
    6869: #endif
    6870: #if defined(PETSC_HAVE_SCALAPACK)
    6871:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_scalapack_C", MatConvert_AIJ_ScaLAPACK));
    6872: #endif
    6873:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_is_C", MatConvert_XAIJ_IS));
    6874:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisell_C", MatConvert_MPIAIJ_MPISELL));
    6875: #if defined(PETSC_HAVE_HYPRE)
    6876:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_hypre_C", MatConvert_AIJ_HYPRE));
    6877:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", MatProductSetFromOptions_Transpose_AIJ_AIJ));
    6878: #endif
    6879:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_is_mpiaij_C", MatProductSetFromOptions_IS_XAIJ));
    6880:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_mpiaij_mpiaij_C", MatProductSetFromOptions_MPIAIJ));
    6881:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_MPIAIJ));
    6882:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetValuesCOO_C", MatSetValuesCOO_MPIAIJ));
    6883:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATMPIAIJ));
    6884:   PetscFunctionReturn(PETSC_SUCCESS);
    6885: }

    6887: /*@
    6888:   MatCreateMPIAIJWithSplitArrays - creates a `MATMPIAIJ` matrix using arrays that contain the "diagonal"
    6889:   and "off-diagonal" part of the matrix in CSR format.

    6891:   Collective

    6893:   Input Parameters:
    6894: + comm - MPI communicator
    6895: . m    - number of local rows (Cannot be `PETSC_DECIDE`)
    6896: . n    - This value should be the same as the local size used in creating the
    6897:          x vector for the matrix-vector product $y = Ax$. (or `PETSC_DECIDE` to have
    6898:          calculated if `N` is given) For square matrices `n` is almost always `m`.
    6899: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    6900: . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    6901: . i    - row indices for "diagonal" portion of matrix; that is i[0] = 0, i[row] = i[row-1] + number of elements in that row of the matrix
    6902: . j    - column indices, which must be local, i.e., based off the start column of the diagonal portion
    6903: . a    - matrix values
    6904: . oi   - row indices for "off-diagonal" portion of matrix; that is oi[0] = 0, oi[row] = oi[row-1] + number of elements in that row of the matrix
    6905: . oj   - column indices, which must be global, representing global columns in the `MATMPIAIJ` matrix
    6906: - oa   - matrix values

    6908:   Output Parameter:
    6909: . mat - the matrix

    6911:   Level: advanced

    6913:   Notes:
    6914:   The `i`, `j`, and `a` arrays ARE NOT copied by this routine into the internal format used by PETSc (even in Fortran). The user
    6915:   must free the arrays once the matrix has been destroyed and not before.

    6917:   The `i` and `j` indices are 0 based

    6919:   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix

    6921:   This sets local rows and cannot be used to set off-processor values.

    6923:   Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
    6924:   legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
    6925:   not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
    6926:   the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
    6927:   keep track of the underlying array. Use `MatSetOption`(A,`MAT_NO_OFF_PROC_ENTRIES`,`PETSC_TRUE`) to disable all
    6928:   communication if it is known that only local entries will be set.

    6930: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    6931:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithArrays()`
    6932: @*/
    6933: PetscErrorCode MatCreateMPIAIJWithSplitArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, PetscInt i[], PetscInt j[], PetscScalar a[], PetscInt oi[], PetscInt oj[], PetscScalar oa[], Mat *mat)
    6934: {
    6935:   Mat_MPIAIJ *maij;

    6937:   PetscFunctionBegin;
    6938:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    6939:   PetscCheck(i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    6940:   PetscCheck(oi[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "oi (row indices) must start with 0");
    6941:   PetscCall(MatCreate(comm, mat));
    6942:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    6943:   PetscCall(MatSetType(*mat, MATMPIAIJ));
    6944:   maij = (Mat_MPIAIJ *)(*mat)->data;

    6946:   (*mat)->preallocated = PETSC_TRUE;

    6948:   PetscCall(PetscLayoutSetUp((*mat)->rmap));
    6949:   PetscCall(PetscLayoutSetUp((*mat)->cmap));

    6951:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, i, j, a, &maij->A));
    6952:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, (*mat)->cmap->N, oi, oj, oa, &maij->B));

    6954:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    6955:   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
    6956:   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
    6957:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    6958:   PetscCall(MatSetOption(*mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    6959:   PetscFunctionReturn(PETSC_SUCCESS);
    6960: }

    6962: typedef struct {
    6963:   Mat       *mp;    /* intermediate products */
    6964:   PetscBool *mptmp; /* is the intermediate product temporary ? */
    6965:   PetscInt   cp;    /* number of intermediate products */

    6967:   /* support for MatGetBrowsOfAoCols_MPIAIJ for P_oth */
    6968:   PetscInt    *startsj_s, *startsj_r;
    6969:   PetscScalar *bufa;
    6970:   Mat          P_oth;

    6972:   /* may take advantage of merging product->B */
    6973:   Mat Bloc; /* B-local by merging diag and off-diag */

    6975:   /* cusparse does not have support to split between symbolic and numeric phases.
    6976:      When api_user is true, we don't need to update the numerical values
    6977:      of the temporary storage */
    6978:   PetscBool reusesym;

    6980:   /* support for COO values insertion */
    6981:   PetscScalar *coo_v, *coo_w; /* store on-process and off-process COO scalars, and used as MPI recv/send buffers respectively */
    6982:   PetscInt   **own;           /* own[i] points to address of on-process COO indices for Mat mp[i] */
    6983:   PetscInt   **off;           /* off[i] points to address of off-process COO indices for Mat mp[i] */
    6984:   PetscBool    hasoffproc;    /* if true, have off-process values insertion (i.e. AtB or PtAP) */
    6985:   PetscSF      sf;            /* used for non-local values insertion and memory malloc */
    6986:   PetscMemType mtype;

    6988:   /* customization */
    6989:   PetscBool abmerge;
    6990:   PetscBool P_oth_bind;
    6991: } MatMatMPIAIJBACKEND;

    6993: static PetscErrorCode MatDestroy_MatMatMPIAIJBACKEND(void *data)
    6994: {
    6995:   MatMatMPIAIJBACKEND *mmdata = (MatMatMPIAIJBACKEND *)data;
    6996:   PetscInt             i;

    6998:   PetscFunctionBegin;
    6999:   PetscCall(PetscFree2(mmdata->startsj_s, mmdata->startsj_r));
    7000:   PetscCall(PetscFree(mmdata->bufa));
    7001:   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_v));
    7002:   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_w));
    7003:   PetscCall(MatDestroy(&mmdata->P_oth));
    7004:   PetscCall(MatDestroy(&mmdata->Bloc));
    7005:   PetscCall(PetscSFDestroy(&mmdata->sf));
    7006:   for (i = 0; i < mmdata->cp; i++) PetscCall(MatDestroy(&mmdata->mp[i]));
    7007:   PetscCall(PetscFree2(mmdata->mp, mmdata->mptmp));
    7008:   PetscCall(PetscFree(mmdata->own[0]));
    7009:   PetscCall(PetscFree(mmdata->own));
    7010:   PetscCall(PetscFree(mmdata->off[0]));
    7011:   PetscCall(PetscFree(mmdata->off));
    7012:   PetscCall(PetscFree(mmdata));
    7013:   PetscFunctionReturn(PETSC_SUCCESS);
    7014: }

    7016: /* Copy selected n entries with indices in idx[] of A to v[].
    7017:    If idx is NULL, copy the whole data array of A to v[]
    7018:  */
    7019: static PetscErrorCode MatSeqAIJCopySubArray(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
    7020: {
    7021:   PetscErrorCode (*f)(Mat, PetscInt, const PetscInt[], PetscScalar[]);

    7023:   PetscFunctionBegin;
    7024:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", &f));
    7025:   if (f) {
    7026:     PetscCall((*f)(A, n, idx, v));
    7027:   } else {
    7028:     const PetscScalar *vv;

    7030:     PetscCall(MatSeqAIJGetArrayRead(A, &vv));
    7031:     if (n && idx) {
    7032:       PetscScalar    *w  = v;
    7033:       const PetscInt *oi = idx;
    7034:       PetscInt        j;

    7036:       for (j = 0; j < n; j++) *w++ = vv[*oi++];
    7037:     } else {
    7038:       PetscCall(PetscArraycpy(v, vv, n));
    7039:     }
    7040:     PetscCall(MatSeqAIJRestoreArrayRead(A, &vv));
    7041:   }
    7042:   PetscFunctionReturn(PETSC_SUCCESS);
    7043: }

    7045: static PetscErrorCode MatProductNumeric_MPIAIJBACKEND(Mat C)
    7046: {
    7047:   MatMatMPIAIJBACKEND *mmdata;
    7048:   PetscInt             i, n_d, n_o;

    7050:   PetscFunctionBegin;
    7051:   MatCheckProduct(C, 1);
    7052:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
    7053:   mmdata = (MatMatMPIAIJBACKEND *)C->product->data;
    7054:   if (!mmdata->reusesym) { /* update temporary matrices */
    7055:     if (mmdata->P_oth) PetscCall(MatGetBrowsOfAoCols_MPIAIJ(C->product->A, C->product->B, MAT_REUSE_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));
    7056:     if (mmdata->Bloc) PetscCall(MatMPIAIJGetLocalMatMerge(C->product->B, MAT_REUSE_MATRIX, NULL, &mmdata->Bloc));
    7057:   }
    7058:   mmdata->reusesym = PETSC_FALSE;

    7060:   for (i = 0; i < mmdata->cp; i++) {
    7061:     PetscCheck(mmdata->mp[i]->ops->productnumeric, PetscObjectComm((PetscObject)mmdata->mp[i]), PETSC_ERR_PLIB, "Missing numeric op for %s", MatProductTypes[mmdata->mp[i]->product->type]);
    7062:     PetscCall((*mmdata->mp[i]->ops->productnumeric)(mmdata->mp[i]));
    7063:   }
    7064:   for (i = 0, n_d = 0, n_o = 0; i < mmdata->cp; i++) {
    7065:     PetscInt noff;

    7067:     PetscCall(PetscIntCast(mmdata->off[i + 1] - mmdata->off[i], &noff));
    7068:     if (mmdata->mptmp[i]) continue;
    7069:     if (noff) {
    7070:       PetscInt nown;

    7072:       PetscCall(PetscIntCast(mmdata->own[i + 1] - mmdata->own[i], &nown));
    7073:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], noff, mmdata->off[i], mmdata->coo_w + n_o));
    7074:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], nown, mmdata->own[i], mmdata->coo_v + n_d));
    7075:       n_o += noff;
    7076:       n_d += nown;
    7077:     } else {
    7078:       Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mmdata->mp[i]->data;

    7080:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], mm->nz, NULL, mmdata->coo_v + n_d));
    7081:       n_d += mm->nz;
    7082:     }
    7083:   }
    7084:   if (mmdata->hasoffproc) { /* offprocess insertion */
    7085:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
    7086:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
    7087:   }
    7088:   PetscCall(MatSetValuesCOO(C, mmdata->coo_v, INSERT_VALUES));
    7089:   PetscFunctionReturn(PETSC_SUCCESS);
    7090: }

    7092: /* Support for Pt * A, A * P, or Pt * A * P */
    7093: #define MAX_NUMBER_INTERMEDIATE 4
    7094: PetscErrorCode MatProductSymbolic_MPIAIJBACKEND(Mat C)
    7095: {
    7096:   Mat_Product           *product = C->product;
    7097:   Mat                    A, P, mp[MAX_NUMBER_INTERMEDIATE]; /* A, P and a series of intermediate matrices */
    7098:   Mat_MPIAIJ            *a, *p;
    7099:   MatMatMPIAIJBACKEND   *mmdata;
    7100:   ISLocalToGlobalMapping P_oth_l2g = NULL;
    7101:   IS                     glob      = NULL;
    7102:   const char            *prefix;
    7103:   char                   pprefix[256];
    7104:   const PetscInt        *globidx, *P_oth_idx;
    7105:   PetscInt               i, j, cp, m, n, M, N, *coo_i, *coo_j;
    7106:   PetscCount             ncoo, ncoo_d, ncoo_o, ncoo_oown;
    7107:   PetscInt               cmapt[MAX_NUMBER_INTERMEDIATE], rmapt[MAX_NUMBER_INTERMEDIATE]; /* col/row map type for each Mat in mp[]. */
    7108:                                                                                          /* type-0: consecutive, start from 0; type-1: consecutive with */
    7109:                                                                                          /* a base offset; type-2: sparse with a local to global map table */
    7110:   const PetscInt *cmapa[MAX_NUMBER_INTERMEDIATE], *rmapa[MAX_NUMBER_INTERMEDIATE];       /* col/row local to global map array (table) for type-2 map type */

    7112:   MatProductType ptype;
    7113:   PetscBool      mptmp[MAX_NUMBER_INTERMEDIATE], hasoffproc = PETSC_FALSE, iscuda, iship, iskokk;
    7114:   PetscMPIInt    size;

    7116:   PetscFunctionBegin;
    7117:   MatCheckProduct(C, 1);
    7118:   PetscCheck(!product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
    7119:   ptype = product->type;
    7120:   if (product->A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
    7121:     ptype                                          = MATPRODUCT_AB;
    7122:     product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
    7123:   }
    7124:   switch (ptype) {
    7125:   case MATPRODUCT_AB:
    7126:     A          = product->A;
    7127:     P          = product->B;
    7128:     m          = A->rmap->n;
    7129:     n          = P->cmap->n;
    7130:     M          = A->rmap->N;
    7131:     N          = P->cmap->N;
    7132:     hasoffproc = PETSC_FALSE; /* will not scatter mat product values to other processes */
    7133:     break;
    7134:   case MATPRODUCT_AtB:
    7135:     P          = product->A;
    7136:     A          = product->B;
    7137:     m          = P->cmap->n;
    7138:     n          = A->cmap->n;
    7139:     M          = P->cmap->N;
    7140:     N          = A->cmap->N;
    7141:     hasoffproc = PETSC_TRUE;
    7142:     break;
    7143:   case MATPRODUCT_PtAP:
    7144:     A          = product->A;
    7145:     P          = product->B;
    7146:     m          = P->cmap->n;
    7147:     n          = P->cmap->n;
    7148:     M          = P->cmap->N;
    7149:     N          = P->cmap->N;
    7150:     hasoffproc = PETSC_TRUE;
    7151:     break;
    7152:   default:
    7153:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
    7154:   }
    7155:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)C), &size));
    7156:   if (size == 1) hasoffproc = PETSC_FALSE;

    7158:   /* defaults */
    7159:   for (i = 0; i < MAX_NUMBER_INTERMEDIATE; i++) {
    7160:     mp[i]    = NULL;
    7161:     mptmp[i] = PETSC_FALSE;
    7162:     rmapt[i] = -1;
    7163:     cmapt[i] = -1;
    7164:     rmapa[i] = NULL;
    7165:     cmapa[i] = NULL;
    7166:   }

    7168:   /* customization */
    7169:   PetscCall(PetscNew(&mmdata));
    7170:   mmdata->reusesym = product->api_user;
    7171:   if (ptype == MATPRODUCT_AB) {
    7172:     if (product->api_user) {
    7173:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
    7174:       PetscCall(PetscOptionsBool("-matmatmult_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
    7175:       PetscCall(PetscOptionsBool("-matmatmult_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7176:       PetscOptionsEnd();
    7177:     } else {
    7178:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
    7179:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
    7180:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7181:       PetscOptionsEnd();
    7182:     }
    7183:   } else if (ptype == MATPRODUCT_PtAP) {
    7184:     if (product->api_user) {
    7185:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
    7186:       PetscCall(PetscOptionsBool("-matptap_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7187:       PetscOptionsEnd();
    7188:     } else {
    7189:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
    7190:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7191:       PetscOptionsEnd();
    7192:     }
    7193:   }
    7194:   a = (Mat_MPIAIJ *)A->data;
    7195:   p = (Mat_MPIAIJ *)P->data;
    7196:   PetscCall(MatSetSizes(C, m, n, M, N));
    7197:   PetscCall(PetscLayoutSetUp(C->rmap));
    7198:   PetscCall(PetscLayoutSetUp(C->cmap));
    7199:   PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    7200:   PetscCall(MatGetOptionsPrefix(C, &prefix));

    7202:   cp = 0;
    7203:   switch (ptype) {
    7204:   case MATPRODUCT_AB: /* A * P */
    7205:     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));

    7207:     /* A_diag * P_local (merged or not) */
    7208:     if (mmdata->abmerge) { /* P's diagonal and off-diag blocks are merged to one matrix, then multiplied by A_diag */
    7209:       /* P is product->B */
    7210:       PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7211:       PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
    7212:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7213:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7214:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7215:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7216:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7217:       mp[cp]->product->api_user = product->api_user;
    7218:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7219:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7220:       PetscCall(ISGetIndices(glob, &globidx));
    7221:       rmapt[cp] = 1;
    7222:       cmapt[cp] = 2;
    7223:       cmapa[cp] = globidx;
    7224:       mptmp[cp] = PETSC_FALSE;
    7225:       cp++;
    7226:     } else { /* A_diag * P_diag and A_diag * P_off */
    7227:       PetscCall(MatProductCreate(a->A, p->A, NULL, &mp[cp]));
    7228:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7229:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7230:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7231:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7232:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7233:       mp[cp]->product->api_user = product->api_user;
    7234:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7235:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7236:       rmapt[cp] = 1;
    7237:       cmapt[cp] = 1;
    7238:       mptmp[cp] = PETSC_FALSE;
    7239:       cp++;
    7240:       PetscCall(MatProductCreate(a->A, p->B, NULL, &mp[cp]));
    7241:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7242:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7243:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7244:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7245:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7246:       mp[cp]->product->api_user = product->api_user;
    7247:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7248:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7249:       rmapt[cp] = 1;
    7250:       cmapt[cp] = 2;
    7251:       cmapa[cp] = p->garray;
    7252:       mptmp[cp] = PETSC_FALSE;
    7253:       cp++;
    7254:     }

    7256:     /* A_off * P_other */
    7257:     if (mmdata->P_oth) {
    7258:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g)); /* make P_oth use local col ids */
    7259:       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
    7260:       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)a->B)->type_name));
    7261:       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
    7262:       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
    7263:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7264:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7265:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7266:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7267:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7268:       mp[cp]->product->api_user = product->api_user;
    7269:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7270:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7271:       rmapt[cp] = 1;
    7272:       cmapt[cp] = 2;
    7273:       cmapa[cp] = P_oth_idx;
    7274:       mptmp[cp] = PETSC_FALSE;
    7275:       cp++;
    7276:     }
    7277:     break;

    7279:   case MATPRODUCT_AtB: /* (P^t * A): P_diag * A_loc + P_off * A_loc */
    7280:     /* A is product->B */
    7281:     PetscCall(MatMPIAIJGetLocalMatMerge(A, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7282:     if (A == P) { /* when A==P, we can take advantage of the already merged mmdata->Bloc */
    7283:       PetscCall(MatProductCreate(mmdata->Bloc, mmdata->Bloc, NULL, &mp[cp]));
    7284:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7285:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7286:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7287:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7288:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7289:       mp[cp]->product->api_user = product->api_user;
    7290:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7291:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7292:       PetscCall(ISGetIndices(glob, &globidx));
    7293:       rmapt[cp] = 2;
    7294:       rmapa[cp] = globidx;
    7295:       cmapt[cp] = 2;
    7296:       cmapa[cp] = globidx;
    7297:       mptmp[cp] = PETSC_FALSE;
    7298:       cp++;
    7299:     } else {
    7300:       PetscCall(MatProductCreate(p->A, mmdata->Bloc, NULL, &mp[cp]));
    7301:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7302:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7303:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7304:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7305:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7306:       mp[cp]->product->api_user = product->api_user;
    7307:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7308:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7309:       PetscCall(ISGetIndices(glob, &globidx));
    7310:       rmapt[cp] = 1;
    7311:       cmapt[cp] = 2;
    7312:       cmapa[cp] = globidx;
    7313:       mptmp[cp] = PETSC_FALSE;
    7314:       cp++;
    7315:       PetscCall(MatProductCreate(p->B, mmdata->Bloc, NULL, &mp[cp]));
    7316:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7317:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7318:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7319:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7320:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7321:       mp[cp]->product->api_user = product->api_user;
    7322:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7323:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7324:       rmapt[cp] = 2;
    7325:       rmapa[cp] = p->garray;
    7326:       cmapt[cp] = 2;
    7327:       cmapa[cp] = globidx;
    7328:       mptmp[cp] = PETSC_FALSE;
    7329:       cp++;
    7330:     }
    7331:     break;
    7332:   case MATPRODUCT_PtAP:
    7333:     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));
    7334:     /* P is product->B */
    7335:     PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7336:     PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
    7337:     PetscCall(MatProductSetType(mp[cp], MATPRODUCT_PtAP));
    7338:     PetscCall(MatProductSetFill(mp[cp], product->fill));
    7339:     PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7340:     PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7341:     PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7342:     mp[cp]->product->api_user = product->api_user;
    7343:     PetscCall(MatProductSetFromOptions(mp[cp]));
    7344:     PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7345:     PetscCall(ISGetIndices(glob, &globidx));
    7346:     rmapt[cp] = 2;
    7347:     rmapa[cp] = globidx;
    7348:     cmapt[cp] = 2;
    7349:     cmapa[cp] = globidx;
    7350:     mptmp[cp] = PETSC_FALSE;
    7351:     cp++;
    7352:     if (mmdata->P_oth) {
    7353:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g));
    7354:       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
    7355:       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)a->B)->type_name));
    7356:       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
    7357:       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
    7358:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7359:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7360:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7361:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7362:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7363:       mp[cp]->product->api_user = product->api_user;
    7364:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7365:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7366:       mptmp[cp] = PETSC_TRUE;
    7367:       cp++;
    7368:       PetscCall(MatProductCreate(mmdata->Bloc, mp[1], NULL, &mp[cp]));
    7369:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7370:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7371:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7372:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7373:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7374:       mp[cp]->product->api_user = product->api_user;
    7375:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7376:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7377:       rmapt[cp] = 2;
    7378:       rmapa[cp] = globidx;
    7379:       cmapt[cp] = 2;
    7380:       cmapa[cp] = P_oth_idx;
    7381:       mptmp[cp] = PETSC_FALSE;
    7382:       cp++;
    7383:     }
    7384:     break;
    7385:   default:
    7386:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
    7387:   }
    7388:   /* sanity check */
    7389:   if (size > 1)
    7390:     for (i = 0; i < cp; i++) PetscCheck(rmapt[i] != 2 || hasoffproc, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Unexpected offproc map type for product %" PetscInt_FMT, i);

    7392:   PetscCall(PetscMalloc2(cp, &mmdata->mp, cp, &mmdata->mptmp));
    7393:   for (i = 0; i < cp; i++) {
    7394:     mmdata->mp[i]    = mp[i];
    7395:     mmdata->mptmp[i] = mptmp[i];
    7396:   }
    7397:   mmdata->cp             = cp;
    7398:   C->product->data       = mmdata;
    7399:   C->product->destroy    = MatDestroy_MatMatMPIAIJBACKEND;
    7400:   C->ops->productnumeric = MatProductNumeric_MPIAIJBACKEND;

    7402:   /* memory type */
    7403:   mmdata->mtype = PETSC_MEMTYPE_HOST;
    7404:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iscuda, MATSEQAIJCUSPARSE, MATMPIAIJCUSPARSE, ""));
    7405:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iship, MATSEQAIJHIPSPARSE, MATMPIAIJHIPSPARSE, ""));
    7406:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iskokk, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, ""));
    7407:   if (iscuda) mmdata->mtype = PETSC_MEMTYPE_CUDA;
    7408:   else if (iship) mmdata->mtype = PETSC_MEMTYPE_HIP;
    7409:   else if (iskokk) mmdata->mtype = PETSC_MEMTYPE_KOKKOS;

    7411:   /* prepare coo coordinates for values insertion */

    7413:   /* count total nonzeros of those intermediate seqaij Mats
    7414:     ncoo_d:    # of nonzeros of matrices that do not have offproc entries
    7415:     ncoo_o:    # of nonzeros (of matrices that might have offproc entries) that will be inserted to remote procs
    7416:     ncoo_oown: # of nonzeros (of matrices that might have offproc entries) that will be inserted locally
    7417:   */
    7418:   for (cp = 0, ncoo_d = 0, ncoo_o = 0, ncoo_oown = 0; cp < mmdata->cp; cp++) {
    7419:     Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mp[cp]->data;
    7420:     if (mptmp[cp]) continue;
    7421:     if (rmapt[cp] == 2 && hasoffproc) { /* the rows need to be scatter to all processes (might include self) */
    7422:       const PetscInt *rmap = rmapa[cp];
    7423:       const PetscInt  mr   = mp[cp]->rmap->n;
    7424:       const PetscInt  rs   = C->rmap->rstart;
    7425:       const PetscInt  re   = C->rmap->rend;
    7426:       const PetscInt *ii   = mm->i;
    7427:       for (i = 0; i < mr; i++) {
    7428:         const PetscInt gr = rmap[i];
    7429:         const PetscInt nz = ii[i + 1] - ii[i];
    7430:         if (gr < rs || gr >= re) ncoo_o += nz; /* this row is offproc */
    7431:         else ncoo_oown += nz;                  /* this row is local */
    7432:       }
    7433:     } else ncoo_d += mm->nz;
    7434:   }

    7436:   /*
    7437:     ncoo: total number of nonzeros (including those inserted by remote procs) belonging to this proc

    7439:     ncoo = ncoo_d + ncoo_oown + ncoo2, which ncoo2 is number of nonzeros inserted to me by other procs.

    7441:     off[0] points to a big index array, which is shared by off[1,2,...]. Similarly, for own[0].

    7443:     off[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert to others
    7444:     own[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert locally
    7445:     so, off[p+1]-off[p] is the number of nonzeros that mp[p] will send to others.

    7447:     coo_i/j/v[]: [ncoo] row/col/val of nonzeros belonging to this proc.
    7448:     Ex. coo_i[]: the beginning part (of size ncoo_d + ncoo_oown) stores i of local nonzeros, and the remaining part stores i of nonzeros I will receive.
    7449:   */
    7450:   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->off)); /* +1 to make a csr-like data structure */
    7451:   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->own));

    7453:   /* gather (i,j) of nonzeros inserted by remote procs */
    7454:   if (hasoffproc) {
    7455:     PetscSF  msf;
    7456:     PetscInt ncoo2, *coo_i2, *coo_j2;

    7458:     PetscCall(PetscMalloc1(ncoo_o, &mmdata->off[0]));
    7459:     PetscCall(PetscMalloc1(ncoo_oown, &mmdata->own[0]));
    7460:     PetscCall(PetscMalloc2(ncoo_o, &coo_i, ncoo_o, &coo_j)); /* to collect (i,j) of entries to be sent to others */

    7462:     for (cp = 0, ncoo_o = 0; cp < mmdata->cp; cp++) {
    7463:       Mat_SeqAIJ *mm     = (Mat_SeqAIJ *)mp[cp]->data;
    7464:       PetscInt   *idxoff = mmdata->off[cp];
    7465:       PetscInt   *idxown = mmdata->own[cp];
    7466:       if (!mptmp[cp] && rmapt[cp] == 2) { /* row map is sparse */
    7467:         const PetscInt *rmap = rmapa[cp];
    7468:         const PetscInt *cmap = cmapa[cp];
    7469:         const PetscInt *ii   = mm->i;
    7470:         PetscInt       *coi  = coo_i + ncoo_o;
    7471:         PetscInt       *coj  = coo_j + ncoo_o;
    7472:         const PetscInt  mr   = mp[cp]->rmap->n;
    7473:         const PetscInt  rs   = C->rmap->rstart;
    7474:         const PetscInt  re   = C->rmap->rend;
    7475:         const PetscInt  cs   = C->cmap->rstart;
    7476:         for (i = 0; i < mr; i++) {
    7477:           const PetscInt *jj = mm->j + ii[i];
    7478:           const PetscInt  gr = rmap[i];
    7479:           const PetscInt  nz = ii[i + 1] - ii[i];
    7480:           if (gr < rs || gr >= re) { /* this is an offproc row */
    7481:             for (j = ii[i]; j < ii[i + 1]; j++) {
    7482:               *coi++    = gr;
    7483:               *idxoff++ = j;
    7484:             }
    7485:             if (!cmapt[cp]) { /* already global */
    7486:               for (j = 0; j < nz; j++) *coj++ = jj[j];
    7487:             } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
    7488:               for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
    7489:             } else { /* offdiag */
    7490:               for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
    7491:             }
    7492:             ncoo_o += nz;
    7493:           } else { /* this is a local row */
    7494:             for (j = ii[i]; j < ii[i + 1]; j++) *idxown++ = j;
    7495:           }
    7496:         }
    7497:       }
    7498:       mmdata->off[cp + 1] = idxoff;
    7499:       mmdata->own[cp + 1] = idxown;
    7500:     }

    7502:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
    7503:     PetscInt incoo_o;
    7504:     PetscCall(PetscIntCast(ncoo_o, &incoo_o));
    7505:     PetscCall(PetscSFSetGraphLayout(mmdata->sf, C->rmap, incoo_o /*nleaves*/, NULL /*ilocal*/, PETSC_OWN_POINTER, coo_i));
    7506:     PetscCall(PetscSFGetMultiSF(mmdata->sf, &msf));
    7507:     PetscCall(PetscSFGetGraph(msf, &ncoo2 /*nroots*/, NULL, NULL, NULL));
    7508:     ncoo = ncoo_d + ncoo_oown + ncoo2;
    7509:     PetscCall(PetscMalloc2(ncoo, &coo_i2, ncoo, &coo_j2));
    7510:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown)); /* put (i,j) of remote nonzeros at back */
    7511:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown));
    7512:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
    7513:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
    7514:     PetscCall(PetscFree2(coo_i, coo_j));
    7515:     /* allocate MPI send buffer to collect nonzero values to be sent to remote procs */
    7516:     PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo_o * sizeof(PetscScalar), (void **)&mmdata->coo_w));
    7517:     coo_i = coo_i2;
    7518:     coo_j = coo_j2;
    7519:   } else { /* no offproc values insertion */
    7520:     ncoo = ncoo_d;
    7521:     PetscCall(PetscMalloc2(ncoo, &coo_i, ncoo, &coo_j));

    7523:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
    7524:     PetscCall(PetscSFSetGraph(mmdata->sf, 0, 0, NULL, PETSC_OWN_POINTER, NULL, PETSC_OWN_POINTER));
    7525:     PetscCall(PetscSFSetUp(mmdata->sf));
    7526:   }
    7527:   mmdata->hasoffproc = hasoffproc;

    7529:   /* gather (i,j) of nonzeros inserted locally */
    7530:   for (cp = 0, ncoo_d = 0; cp < mmdata->cp; cp++) {
    7531:     Mat_SeqAIJ     *mm   = (Mat_SeqAIJ *)mp[cp]->data;
    7532:     PetscInt       *coi  = coo_i + ncoo_d;
    7533:     PetscInt       *coj  = coo_j + ncoo_d;
    7534:     const PetscInt *jj   = mm->j;
    7535:     const PetscInt *ii   = mm->i;
    7536:     const PetscInt *cmap = cmapa[cp];
    7537:     const PetscInt *rmap = rmapa[cp];
    7538:     const PetscInt  mr   = mp[cp]->rmap->n;
    7539:     const PetscInt  rs   = C->rmap->rstart;
    7540:     const PetscInt  re   = C->rmap->rend;
    7541:     const PetscInt  cs   = C->cmap->rstart;

    7543:     if (mptmp[cp]) continue;
    7544:     if (rmapt[cp] == 1) { /* consecutive rows */
    7545:       /* fill coo_i */
    7546:       for (i = 0; i < mr; i++) {
    7547:         const PetscInt gr = i + rs;
    7548:         for (j = ii[i]; j < ii[i + 1]; j++) coi[j] = gr;
    7549:       }
    7550:       /* fill coo_j */
    7551:       if (!cmapt[cp]) { /* type-0, already global */
    7552:         PetscCall(PetscArraycpy(coj, jj, mm->nz));
    7553:       } else if (cmapt[cp] == 1) {                        /* type-1, local to global for consecutive columns of C */
    7554:         for (j = 0; j < mm->nz; j++) coj[j] = jj[j] + cs; /* lid + col start */
    7555:       } else {                                            /* type-2, local to global for sparse columns */
    7556:         for (j = 0; j < mm->nz; j++) coj[j] = cmap[jj[j]];
    7557:       }
    7558:       ncoo_d += mm->nz;
    7559:     } else if (rmapt[cp] == 2) { /* sparse rows */
    7560:       for (i = 0; i < mr; i++) {
    7561:         const PetscInt *jj = mm->j + ii[i];
    7562:         const PetscInt  gr = rmap[i];
    7563:         const PetscInt  nz = ii[i + 1] - ii[i];
    7564:         if (gr >= rs && gr < re) { /* local rows */
    7565:           for (j = ii[i]; j < ii[i + 1]; j++) *coi++ = gr;
    7566:           if (!cmapt[cp]) { /* type-0, already global */
    7567:             for (j = 0; j < nz; j++) *coj++ = jj[j];
    7568:           } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
    7569:             for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
    7570:           } else { /* type-2, local to global for sparse columns */
    7571:             for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
    7572:           }
    7573:           ncoo_d += nz;
    7574:         }
    7575:       }
    7576:     }
    7577:   }
    7578:   if (glob) PetscCall(ISRestoreIndices(glob, &globidx));
    7579:   PetscCall(ISDestroy(&glob));
    7580:   if (P_oth_l2g) PetscCall(ISLocalToGlobalMappingRestoreIndices(P_oth_l2g, &P_oth_idx));
    7581:   PetscCall(ISLocalToGlobalMappingDestroy(&P_oth_l2g));
    7582:   /* allocate an array to store all nonzeros (inserted locally or remotely) belonging to this proc */
    7583:   PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo * sizeof(PetscScalar), (void **)&mmdata->coo_v));

    7585:   /* set block sizes */
    7586:   A = product->A;
    7587:   P = product->B;
    7588:   switch (ptype) {
    7589:   case MATPRODUCT_PtAP:
    7590:     PetscCall(MatSetBlockSizes(C, P->cmap->bs, P->cmap->bs));
    7591:     break;
    7592:   case MATPRODUCT_RARt:
    7593:     PetscCall(MatSetBlockSizes(C, P->rmap->bs, P->rmap->bs));
    7594:     break;
    7595:   case MATPRODUCT_ABC:
    7596:     PetscCall(MatSetBlockSizesFromMats(C, A, product->C));
    7597:     break;
    7598:   case MATPRODUCT_AB:
    7599:     PetscCall(MatSetBlockSizesFromMats(C, A, P));
    7600:     break;
    7601:   case MATPRODUCT_AtB:
    7602:     PetscCall(MatSetBlockSizes(C, A->cmap->bs, P->cmap->bs));
    7603:     break;
    7604:   case MATPRODUCT_ABt:
    7605:     PetscCall(MatSetBlockSizes(C, A->rmap->bs, P->rmap->bs));
    7606:     break;
    7607:   default:
    7608:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for ProductType %s", MatProductTypes[ptype]);
    7609:   }

    7611:   /* preallocate with COO data */
    7612:   PetscCall(MatSetPreallocationCOO(C, ncoo, coo_i, coo_j));
    7613:   PetscCall(PetscFree2(coo_i, coo_j));
    7614:   PetscFunctionReturn(PETSC_SUCCESS);
    7615: }

    7617: PetscErrorCode MatProductSetFromOptions_MPIAIJBACKEND(Mat mat)
    7618: {
    7619:   Mat_Product *product = mat->product;
    7620: #if defined(PETSC_HAVE_DEVICE)
    7621:   PetscBool match  = PETSC_FALSE;
    7622:   PetscBool usecpu = PETSC_FALSE;
    7623: #else
    7624:   PetscBool match = PETSC_TRUE;
    7625: #endif

    7627:   PetscFunctionBegin;
    7628:   MatCheckProduct(mat, 1);
    7629: #if defined(PETSC_HAVE_DEVICE)
    7630:   if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, ((PetscObject)product->A)->type_name, &match));
    7631:   if (match) { /* we can always fallback to the CPU if requested */
    7632:     switch (product->type) {
    7633:     case MATPRODUCT_AB:
    7634:       if (product->api_user) {
    7635:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
    7636:         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
    7637:         PetscOptionsEnd();
    7638:       } else {
    7639:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
    7640:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
    7641:         PetscOptionsEnd();
    7642:       }
    7643:       break;
    7644:     case MATPRODUCT_AtB:
    7645:       if (product->api_user) {
    7646:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
    7647:         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
    7648:         PetscOptionsEnd();
    7649:       } else {
    7650:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
    7651:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
    7652:         PetscOptionsEnd();
    7653:       }
    7654:       break;
    7655:     case MATPRODUCT_PtAP:
    7656:       if (product->api_user) {
    7657:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
    7658:         PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
    7659:         PetscOptionsEnd();
    7660:       } else {
    7661:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
    7662:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
    7663:         PetscOptionsEnd();
    7664:       }
    7665:       break;
    7666:     default:
    7667:       break;
    7668:     }
    7669:     match = (PetscBool)!usecpu;
    7670:   }
    7671: #endif
    7672:   if (match) {
    7673:     switch (product->type) {
    7674:     case MATPRODUCT_AB:
    7675:     case MATPRODUCT_AtB:
    7676:     case MATPRODUCT_PtAP:
    7677:       mat->ops->productsymbolic = MatProductSymbolic_MPIAIJBACKEND;
    7678:       break;
    7679:     default:
    7680:       break;
    7681:     }
    7682:   }
    7683:   /* fallback to MPIAIJ ops */
    7684:   if (!mat->ops->productsymbolic) PetscCall(MatProductSetFromOptions_MPIAIJ(mat));
    7685:   PetscFunctionReturn(PETSC_SUCCESS);
    7686: }

    7688: /*
    7689:    Produces a set of block column indices of the matrix row, one for each block represented in the original row

    7691:    n - the number of block indices in cc[]
    7692:    cc - the block indices (must be large enough to contain the indices)
    7693: */
    7694: static inline PetscErrorCode MatCollapseRow(Mat Amat, PetscInt row, PetscInt bs, PetscInt *n, PetscInt *cc)
    7695: {
    7696:   PetscInt        cnt = -1, nidx, j;
    7697:   const PetscInt *idx;

    7699:   PetscFunctionBegin;
    7700:   PetscCall(MatGetRow(Amat, row, &nidx, &idx, NULL));
    7701:   if (nidx) {
    7702:     cnt     = 0;
    7703:     cc[cnt] = idx[0] / bs;
    7704:     for (j = 1; j < nidx; j++) {
    7705:       if (cc[cnt] < idx[j] / bs) cc[++cnt] = idx[j] / bs;
    7706:     }
    7707:   }
    7708:   PetscCall(MatRestoreRow(Amat, row, &nidx, &idx, NULL));
    7709:   *n = cnt + 1;
    7710:   PetscFunctionReturn(PETSC_SUCCESS);
    7711: }

    7713: /*
    7714:     Produces a set of block column indices of the matrix block row, one for each block represented in the original set of rows

    7716:     ncollapsed - the number of block indices
    7717:     collapsed - the block indices (must be large enough to contain the indices)
    7718: */
    7719: static inline PetscErrorCode MatCollapseRows(Mat Amat, PetscInt start, PetscInt bs, PetscInt *w0, PetscInt *w1, PetscInt *w2, PetscInt *ncollapsed, PetscInt **collapsed)
    7720: {
    7721:   PetscInt i, nprev, *cprev = w0, ncur = 0, *ccur = w1, *merged = w2, *cprevtmp;

    7723:   PetscFunctionBegin;
    7724:   PetscCall(MatCollapseRow(Amat, start, bs, &nprev, cprev));
    7725:   for (i = start + 1; i < start + bs; i++) {
    7726:     PetscCall(MatCollapseRow(Amat, i, bs, &ncur, ccur));
    7727:     PetscCall(PetscMergeIntArray(nprev, cprev, ncur, ccur, &nprev, &merged));
    7728:     cprevtmp = cprev;
    7729:     cprev    = merged;
    7730:     merged   = cprevtmp;
    7731:   }
    7732:   *ncollapsed = nprev;
    7733:   if (collapsed) *collapsed = cprev;
    7734:   PetscFunctionReturn(PETSC_SUCCESS);
    7735: }

    7737: /*
    7738:  MatCreateGraph_Simple_AIJ - create simple scalar matrix (graph) from potentially blocked matrix

    7740:  Input Parameter:
    7741:  . Amat - matrix
    7742:  - symmetrize - make the result symmetric
    7743:  + scale - scale with diagonal

    7745:  Output Parameter:
    7746:  . a_Gmat - output scalar graph >= 0

    7748: */
    7749: PETSC_INTERN PetscErrorCode MatCreateGraph_Simple_AIJ(Mat Amat, PetscBool symmetrize, PetscBool scale, PetscReal filter, PetscInt index_size, PetscInt index[], Mat *a_Gmat)
    7750: {
    7751:   PetscInt  Istart, Iend, Ii, jj, kk, ncols, nloc, NN, MM, bs;
    7752:   MPI_Comm  comm;
    7753:   Mat       Gmat;
    7754:   PetscBool ismpiaij, isseqaij;
    7755:   Mat       a, b, c;
    7756:   MatType   jtype;

    7758:   PetscFunctionBegin;
    7759:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
    7760:   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
    7761:   PetscCall(MatGetSize(Amat, &MM, &NN));
    7762:   PetscCall(MatGetBlockSize(Amat, &bs));
    7763:   nloc = (Iend - Istart) / bs;

    7765:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATSEQAIJ, &isseqaij));
    7766:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATMPIAIJ, &ismpiaij));
    7767:   PetscCheck(isseqaij || ismpiaij, comm, PETSC_ERR_USER, "Require (MPI)AIJ matrix type");

    7769:   /* TODO GPU: these calls are potentially expensive if matrices are large and we want to use the GPU */
    7770:   /* A solution consists in providing a new API, MatAIJGetCollapsedAIJ, and each class can provide a fast
    7771:      implementation */
    7772:   if (bs > 1) {
    7773:     PetscCall(MatGetType(Amat, &jtype));
    7774:     PetscCall(MatCreate(comm, &Gmat));
    7775:     PetscCall(MatSetType(Gmat, jtype));
    7776:     PetscCall(MatSetSizes(Gmat, nloc, nloc, PETSC_DETERMINE, PETSC_DETERMINE));
    7777:     PetscCall(MatSetBlockSizes(Gmat, 1, 1));
    7778:     if (isseqaij || ((Mat_MPIAIJ *)Amat->data)->garray) {
    7779:       PetscInt  *d_nnz, *o_nnz;
    7780:       MatScalar *aa, val, *AA;
    7781:       PetscInt  *aj, *ai, *AJ, nc, nmax = 0;

    7783:       if (isseqaij) {
    7784:         a = Amat;
    7785:         b = NULL;
    7786:       } else {
    7787:         Mat_MPIAIJ *d = (Mat_MPIAIJ *)Amat->data;
    7788:         a             = d->A;
    7789:         b             = d->B;
    7790:       }
    7791:       PetscCall(PetscInfo(Amat, "New bs>1 Graph. nloc=%" PetscInt_FMT "\n", nloc));
    7792:       PetscCall(PetscMalloc2(nloc, &d_nnz, (isseqaij ? 0 : nloc), &o_nnz));
    7793:       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
    7794:         PetscInt       *nnz = (c == a) ? d_nnz : o_nnz;
    7795:         const PetscInt *cols1, *cols2;

    7797:         for (PetscInt brow = 0, nc1, nc2, ok = 1; brow < nloc * bs; brow += bs) { // block rows
    7798:           PetscCall(MatGetRow(c, brow, &nc2, &cols2, NULL));
    7799:           nnz[brow / bs] = nc2 / bs;
    7800:           if (nc2 % bs) ok = 0;
    7801:           if (nnz[brow / bs] > nmax) nmax = nnz[brow / bs];
    7802:           for (PetscInt ii = 1; ii < bs; ii++) { // check for non-dense blocks
    7803:             PetscCall(MatGetRow(c, brow + ii, &nc1, &cols1, NULL));
    7804:             if (nc1 != nc2) ok = 0;
    7805:             else {
    7806:               for (PetscInt jj = 0; jj < nc1 && ok == 1; jj++) {
    7807:                 if (cols1[jj] != cols2[jj]) ok = 0;
    7808:                 if (cols1[jj] % bs != jj % bs) ok = 0;
    7809:               }
    7810:             }
    7811:             PetscCall(MatRestoreRow(c, brow + ii, &nc1, &cols1, NULL));
    7812:           }
    7813:           PetscCall(MatRestoreRow(c, brow, &nc2, &cols2, NULL));
    7814:           if (!ok) {
    7815:             PetscCall(PetscFree2(d_nnz, o_nnz));
    7816:             PetscCall(PetscInfo(Amat, "Found sparse blocks - revert to slow method\n"));
    7817:             goto old_bs;
    7818:           }
    7819:         }
    7820:       }
    7821:       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
    7822:       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
    7823:       PetscCall(PetscFree2(d_nnz, o_nnz));
    7824:       PetscCall(PetscMalloc2(nmax, &AA, nmax, &AJ));
    7825:       // diag
    7826:       for (PetscInt brow = 0, n, grow; brow < nloc * bs; brow += bs) { // block rows
    7827:         Mat_SeqAIJ *aseq = (Mat_SeqAIJ *)a->data;

    7829:         ai = aseq->i;
    7830:         n  = ai[brow + 1] - ai[brow];
    7831:         aj = aseq->j + ai[brow];
    7832:         for (PetscInt k = 0; k < n; k += bs) {   // block columns
    7833:           AJ[k / bs] = aj[k] / bs + Istart / bs; // diag starts at (Istart,Istart)
    7834:           val        = 0;
    7835:           if (index_size == 0) {
    7836:             for (PetscInt ii = 0; ii < bs; ii++) { // rows in block
    7837:               aa = aseq->a + ai[brow + ii] + k;
    7838:               for (PetscInt jj = 0; jj < bs; jj++) {    // columns in block
    7839:                 val += PetscAbs(PetscRealPart(aa[jj])); // a sort of norm
    7840:               }
    7841:             }
    7842:           } else {                                            // use (index,index) value if provided
    7843:             for (PetscInt iii = 0; iii < index_size; iii++) { // rows in block
    7844:               PetscInt ii = index[iii];
    7845:               aa          = aseq->a + ai[brow + ii] + k;
    7846:               for (PetscInt jjj = 0; jjj < index_size; jjj++) { // columns in block
    7847:                 PetscInt jj = index[jjj];
    7848:                 val += PetscAbs(PetscRealPart(aa[jj]));
    7849:               }
    7850:             }
    7851:           }
    7852:           PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%" PetscInt_FMT ") >= nmax (%" PetscInt_FMT ")", k / bs, nmax);
    7853:           AA[k / bs] = val;
    7854:         }
    7855:         grow = Istart / bs + brow / bs;
    7856:         PetscCall(MatSetValues(Gmat, 1, &grow, n / bs, AJ, AA, ADD_VALUES));
    7857:       }
    7858:       // off-diag
    7859:       if (ismpiaij) {
    7860:         Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)Amat->data;
    7861:         const PetscScalar *vals;
    7862:         const PetscInt    *cols, *garray = aij->garray;

    7864:         PetscCheck(garray, PETSC_COMM_SELF, PETSC_ERR_USER, "No garray ?");
    7865:         for (PetscInt brow = 0, grow; brow < nloc * bs; brow += bs) { // block rows
    7866:           PetscCall(MatGetRow(b, brow, &ncols, &cols, NULL));
    7867:           for (PetscInt k = 0, cidx = 0; k < ncols; k += bs, cidx++) {
    7868:             PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs >= nmax");
    7869:             AA[k / bs] = 0;
    7870:             AJ[cidx]   = garray[cols[k]] / bs;
    7871:           }
    7872:           nc = ncols / bs;
    7873:           PetscCall(MatRestoreRow(b, brow, &ncols, &cols, NULL));
    7874:           if (index_size == 0) {
    7875:             for (PetscInt ii = 0; ii < bs; ii++) { // rows in block
    7876:               PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
    7877:               for (PetscInt k = 0; k < ncols; k += bs) {
    7878:                 for (PetscInt jj = 0; jj < bs; jj++) { // cols in block
    7879:                   PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%" PetscInt_FMT ") >= nmax (%" PetscInt_FMT ")", k / bs, nmax);
    7880:                   AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
    7881:                 }
    7882:               }
    7883:               PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
    7884:             }
    7885:           } else {                                            // use (index,index) value if provided
    7886:             for (PetscInt iii = 0; iii < index_size; iii++) { // rows in block
    7887:               PetscInt ii = index[iii];
    7888:               PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
    7889:               for (PetscInt k = 0; k < ncols; k += bs) {
    7890:                 for (PetscInt jjj = 0; jjj < index_size; jjj++) { // cols in block
    7891:                   PetscInt jj = index[jjj];
    7892:                   AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
    7893:                 }
    7894:               }
    7895:               PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
    7896:             }
    7897:           }
    7898:           grow = Istart / bs + brow / bs;
    7899:           PetscCall(MatSetValues(Gmat, 1, &grow, nc, AJ, AA, ADD_VALUES));
    7900:         }
    7901:       }
    7902:       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
    7903:       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
    7904:       PetscCall(PetscFree2(AA, AJ));
    7905:     } else {
    7906:       const PetscScalar *vals;
    7907:       const PetscInt    *idx;
    7908:       PetscInt          *d_nnz, *o_nnz, *w0, *w1, *w2;
    7909:     old_bs:
    7910:       /*
    7911:        Determine the preallocation needed for the scalar matrix derived from the vector matrix.
    7912:        */
    7913:       PetscCall(PetscInfo(Amat, "OLD bs>1 CreateGraph\n"));
    7914:       PetscCall(PetscMalloc2(nloc, &d_nnz, (isseqaij ? 0 : nloc), &o_nnz));
    7915:       if (isseqaij) {
    7916:         PetscInt max_d_nnz;

    7918:         /*
    7919:          Determine exact preallocation count for (sequential) scalar matrix
    7920:          */
    7921:         PetscCall(MatSeqAIJGetMaxRowNonzeros(Amat, &max_d_nnz));
    7922:         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
    7923:         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
    7924:         for (Ii = 0, jj = 0; Ii < Iend; Ii += bs, jj++) PetscCall(MatCollapseRows(Amat, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
    7925:         PetscCall(PetscFree3(w0, w1, w2));
    7926:       } else if (ismpiaij) {
    7927:         Mat             Daij, Oaij;
    7928:         const PetscInt *garray;
    7929:         PetscInt        max_d_nnz;

    7931:         PetscCall(MatMPIAIJGetSeqAIJ(Amat, &Daij, &Oaij, &garray));
    7932:         /*
    7933:          Determine exact preallocation count for diagonal block portion of scalar matrix
    7934:          */
    7935:         PetscCall(MatSeqAIJGetMaxRowNonzeros(Daij, &max_d_nnz));
    7936:         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
    7937:         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
    7938:         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) PetscCall(MatCollapseRows(Daij, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
    7939:         PetscCall(PetscFree3(w0, w1, w2));
    7940:         /*
    7941:          Over estimate (usually grossly over), preallocation count for off-diagonal portion of scalar matrix
    7942:          */
    7943:         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
    7944:           o_nnz[jj] = 0;
    7945:           for (kk = 0; kk < bs; kk++) { /* rows that get collapsed to a single row */
    7946:             PetscCall(MatGetRow(Oaij, Ii + kk, &ncols, NULL, NULL));
    7947:             o_nnz[jj] += ncols;
    7948:             PetscCall(MatRestoreRow(Oaij, Ii + kk, &ncols, NULL, NULL));
    7949:           }
    7950:           if (o_nnz[jj] > (NN / bs - nloc)) o_nnz[jj] = NN / bs - nloc;
    7951:         }
    7952:       } else SETERRQ(comm, PETSC_ERR_USER, "Require AIJ matrix type");
    7953:       /* get scalar copy (norms) of matrix */
    7954:       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
    7955:       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
    7956:       PetscCall(PetscFree2(d_nnz, o_nnz));
    7957:       for (Ii = Istart; Ii < Iend; Ii++) {
    7958:         PetscInt dest_row = Ii / bs;

    7960:         PetscCall(MatGetRow(Amat, Ii, &ncols, &idx, &vals));
    7961:         for (jj = 0; jj < ncols; jj++) {
    7962:           PetscInt    dest_col = idx[jj] / bs;
    7963:           PetscScalar sv       = PetscAbs(PetscRealPart(vals[jj]));

    7965:           PetscCall(MatSetValues(Gmat, 1, &dest_row, 1, &dest_col, &sv, ADD_VALUES));
    7966:         }
    7967:         PetscCall(MatRestoreRow(Amat, Ii, &ncols, &idx, &vals));
    7968:       }
    7969:       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
    7970:       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
    7971:     }
    7972:   } else {
    7973:     if (symmetrize || filter >= 0 || scale) PetscCall(MatDuplicate(Amat, MAT_COPY_VALUES, &Gmat));
    7974:     else {
    7975:       Gmat = Amat;
    7976:       PetscCall(PetscObjectReference((PetscObject)Gmat));
    7977:     }
    7978:     if (isseqaij) {
    7979:       a = Gmat;
    7980:       b = NULL;
    7981:     } else {
    7982:       Mat_MPIAIJ *d = (Mat_MPIAIJ *)Gmat->data;
    7983:       a             = d->A;
    7984:       b             = d->B;
    7985:     }
    7986:     if (filter >= 0 || scale) {
    7987:       /* take absolute value of each entry */
    7988:       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
    7989:         MatInfo      info;
    7990:         PetscScalar *avals;

    7992:         PetscCall(MatGetInfo(c, MAT_LOCAL, &info));
    7993:         PetscCall(MatSeqAIJGetArray(c, &avals));
    7994:         for (int jj = 0; jj < info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    7995:         PetscCall(MatSeqAIJRestoreArray(c, &avals));
    7996:       }
    7997:     }
    7998:   }
    7999:   if (symmetrize) {
    8000:     PetscBool isset, issym;

    8002:     PetscCall(MatIsSymmetricKnown(Amat, &isset, &issym));
    8003:     if (!isset || !issym) {
    8004:       Mat matTrans;

    8006:       PetscCall(MatTranspose(Gmat, MAT_INITIAL_MATRIX, &matTrans));
    8007:       PetscCall(MatAXPY(Gmat, 1.0, matTrans, Gmat->structurally_symmetric == PETSC_BOOL3_TRUE ? SAME_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN));
    8008:       PetscCall(MatDestroy(&matTrans));
    8009:     }
    8010:     PetscCall(MatSetOption(Gmat, MAT_SYMMETRIC, PETSC_TRUE));
    8011:   } else if (Amat != Gmat) PetscCall(MatPropagateSymmetryOptions(Amat, Gmat));
    8012:   if (scale) {
    8013:     /* scale c for all diagonal values = 1 or -1 */
    8014:     Vec diag;

    8016:     PetscCall(MatCreateVecs(Gmat, &diag, NULL));
    8017:     PetscCall(MatGetDiagonal(Gmat, diag));
    8018:     PetscCall(VecReciprocal(diag));
    8019:     PetscCall(VecSqrtAbs(diag));
    8020:     PetscCall(MatDiagonalScale(Gmat, diag, diag));
    8021:     PetscCall(VecDestroy(&diag));
    8022:   }
    8023:   PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_graph_view"));
    8024:   if (filter >= 0) {
    8025:     PetscCall(MatFilter(Gmat, filter, PETSC_TRUE, PETSC_TRUE));
    8026:     PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_filter_graph_view"));
    8027:   }
    8028:   *a_Gmat = Gmat;
    8029:   PetscFunctionReturn(PETSC_SUCCESS);
    8030: }

    8032: PETSC_INTERN PetscErrorCode MatGetCurrentMemType_MPIAIJ(Mat A, PetscMemType *memtype)
    8033: {
    8034:   Mat_MPIAIJ  *mpiaij = (Mat_MPIAIJ *)A->data;
    8035:   PetscMemType mD = PETSC_MEMTYPE_HOST, mO = PETSC_MEMTYPE_HOST;

    8037:   PetscFunctionBegin;
    8038:   if (mpiaij->A) PetscCall(MatGetCurrentMemType(mpiaij->A, &mD));
    8039:   if (mpiaij->B) PetscCall(MatGetCurrentMemType(mpiaij->B, &mO));
    8040:   *memtype = (mD == mO) ? mD : PETSC_MEMTYPE_HOST;
    8041:   PetscFunctionReturn(PETSC_SUCCESS);
    8042: }

    8044: /*
    8045:     Special version for direct calls from Fortran
    8046: */

    8048: /* Change these macros so can be used in void function */
    8049: /* Identical to PetscCallVoid, except it assigns to *_ierr */
    8050: #undef PetscCall
    8051: #define PetscCall(...) \
    8052:   do { \
    8053:     PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__; \
    8054:     if (PetscUnlikely(ierr_msv_mpiaij)) { \
    8055:       *_ierr = PetscError(PETSC_COMM_SELF, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr_msv_mpiaij, PETSC_ERROR_REPEAT, " "); \
    8056:       return; \
    8057:     } \
    8058:   } while (0)

    8060: #undef SETERRQ
    8061: #define SETERRQ(comm, ierr, ...) \
    8062:   do { \
    8063:     *_ierr = PetscError(comm, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr, PETSC_ERROR_INITIAL, __VA_ARGS__); \
    8064:     return; \
    8065:   } while (0)

    8067: #if defined(PETSC_HAVE_FORTRAN_CAPS)
    8068:   #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
    8069: #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
    8070:   #define matsetvaluesmpiaij_ matsetvaluesmpiaij
    8071: #else
    8072: #endif
    8073: PETSC_EXTERN void matsetvaluesmpiaij_(Mat *mmat, PetscInt *mm, const PetscInt im[], PetscInt *mn, const PetscInt in[], const PetscScalar v[], InsertMode *maddv, PetscErrorCode *_ierr)
    8074: {
    8075:   Mat         mat = *mmat;
    8076:   PetscInt    m = *mm, n = *mn;
    8077:   InsertMode  addv = *maddv;
    8078:   Mat_MPIAIJ *aij  = (Mat_MPIAIJ *)mat->data;
    8079:   PetscScalar value;

    8081:   MatCheckPreallocated(mat, 1);
    8082:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    8083:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    8084:   {
    8085:     PetscInt  i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    8086:     PetscInt  cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
    8087:     PetscBool roworiented = aij->roworiented;

    8089:     /* Some Variables required in the macro */
    8090:     Mat         A     = aij->A;
    8091:     Mat_SeqAIJ *a     = (Mat_SeqAIJ *)A->data;
    8092:     PetscInt   *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
    8093:     MatScalar  *aa;
    8094:     PetscBool   ignorezeroentries = ((a->ignorezeroentries && (addv == ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
    8095:     Mat         B                 = aij->B;
    8096:     Mat_SeqAIJ *b                 = (Mat_SeqAIJ *)B->data;
    8097:     PetscInt   *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j, bm = aij->B->rmap->n, am = aij->A->rmap->n;
    8098:     MatScalar  *ba;
    8099:     /* This variable below is only for the PETSC_HAVE_VIENNACL or PETSC_HAVE_CUDA cases, but we define it in all cases because we
    8100:      * cannot use "#if defined" inside a macro. */
    8101:     PETSC_UNUSED PetscBool inserted = PETSC_FALSE;

    8103:     PetscInt  *rp1, *rp2, ii, nrow1, nrow2, _i, rmax1, rmax2, N, low1, high1, low2, high2, t, lastcol1, lastcol2;
    8104:     PetscInt   nonew = a->nonew;
    8105:     MatScalar *ap1, *ap2;

    8107:     PetscFunctionBegin;
    8108:     PetscCall(MatSeqAIJGetArray(A, &aa));
    8109:     PetscCall(MatSeqAIJGetArray(B, &ba));
    8110:     for (i = 0; i < m; i++) {
    8111:       if (im[i] < 0) continue;
    8112:       PetscCheck(im[i] < mat->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Row too large: row %" PetscInt_FMT " max %" PetscInt_FMT, im[i], mat->rmap->N - 1);
    8113:       if (im[i] >= rstart && im[i] < rend) {
    8114:         row      = im[i] - rstart;
    8115:         lastcol1 = -1;
    8116:         rp1      = aj + ai[row];
    8117:         ap1      = aa + ai[row];
    8118:         rmax1    = aimax[row];
    8119:         nrow1    = ailen[row];
    8120:         low1     = 0;
    8121:         high1    = nrow1;
    8122:         lastcol2 = -1;
    8123:         rp2      = bj + bi[row];
    8124:         ap2      = ba + bi[row];
    8125:         rmax2    = bimax[row];
    8126:         nrow2    = bilen[row];
    8127:         low2     = 0;
    8128:         high2    = nrow2;

    8130:         for (j = 0; j < n; j++) {
    8131:           if (roworiented) value = v[i * n + j];
    8132:           else value = v[i + j * m];
    8133:           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
    8134:           if (in[j] >= cstart && in[j] < cend) {
    8135:             col = in[j] - cstart;
    8136:             MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
    8137:           } else if (in[j] < 0) continue;
    8138:           else if (PetscUnlikelyDebug(in[j] >= mat->cmap->N)) {
    8139:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
    8140:           } else {
    8141:             if (mat->was_assembled) {
    8142:               if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    8143: #if defined(PETSC_USE_CTABLE)
    8144:               PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col));
    8145:               col--;
    8146: #else
    8147:               col = aij->colmap[in[j]] - 1;
    8148: #endif
    8149:               if (col < 0 && !((Mat_SeqAIJ *)aij->A->data)->nonew) {
    8150:                 PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));
    8151:                 col = in[j];
    8152:                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
    8153:                 B        = aij->B;
    8154:                 b        = (Mat_SeqAIJ *)B->data;
    8155:                 bimax    = b->imax;
    8156:                 bi       = b->i;
    8157:                 bilen    = b->ilen;
    8158:                 bj       = b->j;
    8159:                 rp2      = bj + bi[row];
    8160:                 ap2      = ba + bi[row];
    8161:                 rmax2    = bimax[row];
    8162:                 nrow2    = bilen[row];
    8163:                 low2     = 0;
    8164:                 high2    = nrow2;
    8165:                 bm       = aij->B->rmap->n;
    8166:                 ba       = b->a;
    8167:                 inserted = PETSC_FALSE;
    8168:               }
    8169:             } else col = in[j];
    8170:             MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
    8171:           }
    8172:         }
    8173:       } else if (!aij->donotstash) {
    8174:         if (roworiented) {
    8175:           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, v + i * n, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    8176:         } else {
    8177:           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, v + i, m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    8178:         }
    8179:       }
    8180:     }
    8181:     PetscCall(MatSeqAIJRestoreArray(A, &aa));
    8182:     PetscCall(MatSeqAIJRestoreArray(B, &ba));
    8183:   }
    8184:   PetscFunctionReturnVoid();
    8185: }

    8187: /* Undefining these here since they were redefined from their original definition above! No
    8188:  * other PETSc functions should be defined past this point, as it is impossible to recover the
    8189:  * original definitions */
    8190: #undef PetscCall
    8191: #undef SETERRQ