Date: 2026-03-31T05:46:18+00:00

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) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
     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()`, `MATBAIJ`
    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`, `MATSEQAIJ`, `MATMPIAIJ`, `MATAIJ`
    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) PetscCall(MatDiagonalSet(aij->A, D, is));
    280:   else PetscCall(MatDiagonalSet_Default(Y, D, is));
    281:   PetscFunctionReturn(PETSC_SUCCESS);
    282: }

    284: static PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M, IS *zrows)
    285: {
    286:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)M->data;
    287:   PetscInt    i, rstart, nrows, *rows;

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

    298: static PetscErrorCode MatGetColumnReductions_MPIAIJ(Mat A, PetscInt type, PetscReal *reductions)
    299: {
    300:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)A->data;
    301:   PetscInt           i, m, n, *garray = aij->garray;
    302:   Mat_SeqAIJ        *a_aij = (Mat_SeqAIJ *)aij->A->data;
    303:   Mat_SeqAIJ        *b_aij = (Mat_SeqAIJ *)aij->B->data;
    304:   PetscReal         *work;
    305:   const PetscScalar *dummy;

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

    344: static PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A, IS *is)
    345: {
    346:   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)A->data;
    347:   IS              sis, gis;
    348:   const PetscInt *isis, *igis;
    349:   PetscInt        n, *iis, nsis, ngis, rstart, i;

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

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

    368:   PetscCall(ISRestoreIndices(sis, &isis));
    369:   PetscCall(ISRestoreIndices(gis, &igis));
    370:   PetscCall(ISDestroy(&sis));
    371:   PetscCall(ISDestroy(&gis));
    372:   PetscFunctionReturn(PETSC_SUCCESS);
    373: }

    375: /*
    376:   Local utility routine that creates a mapping from the global column
    377: number to the local number in the off-diagonal part of the local
    378: storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
    379: a slightly higher hash table cost; without it it is not scalable (each processor
    380: has an order N integer array but is fast to access.
    381: */
    382: PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
    383: {
    384:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    385:   PetscInt    n   = aij->B->cmap->n, i;

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

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

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

    488: static PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A, PetscInt row, const PetscScalar v[])
    489: {
    490:   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)A->data;
    491:   Mat_SeqAIJ  *a = (Mat_SeqAIJ *)mat->A->data, *b = (Mat_SeqAIJ *)mat->B->data;
    492:   PetscInt     l, *garray                         = mat->garray, diag;
    493:   PetscScalar *aa, *ba;

    495:   PetscFunctionBegin;
    496:   /* code only works for square matrices A */

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

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

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

    526: PetscErrorCode MatSetValues_MPIAIJ(Mat mat, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode addv)
    527: {
    528:   Mat_MPIAIJ *aij   = (Mat_MPIAIJ *)mat->data;
    529:   PetscScalar value = 0.0;
    530:   PetscInt    i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    531:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
    532:   PetscBool   roworiented = aij->roworiented;

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

    547:   PetscFunctionBegin;
    548:   PetscCall(MatSeqAIJGetArray(A, &aa));
    549:   PetscCall(MatSeqAIJGetArray(B, &ba));
    550:   for (i = 0; i < m; i++) {
    551:     if (im[i] < 0) continue;
    552:     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);
    553:     if (im[i] >= rstart && im[i] < rend) {
    554:       row      = im[i] - rstart;
    555:       lastcol1 = -1;
    556:       rp1      = PetscSafePointerPlusOffset(aj, ai[row]);
    557:       ap1      = PetscSafePointerPlusOffset(aa, ai[row]);
    558:       rmax1    = aimax[row];
    559:       nrow1    = ailen[row];
    560:       low1     = 0;
    561:       high1    = nrow1;
    562:       lastcol2 = -1;
    563:       rp2      = PetscSafePointerPlusOffset(bj, bi[row]);
    564:       ap2      = PetscSafePointerPlusOffset(ba, bi[row]);
    565:       rmax2    = bimax[row];
    566:       nrow2    = bilen[row];
    567:       low2     = 0;
    568:       high2    = nrow2;

    570:       for (j = 0; j < n; j++) {
    571:         if (v) value = roworiented ? v[i * n + j] : v[i + j * m];
    572:         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
    573:         if (in[j] >= cstart && in[j] < cend) {
    574:           col   = in[j] - cstart;
    575:           nonew = a->nonew;
    576:           MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
    577:         } else if (in[j] < 0) {
    578:           continue;
    579:         } else {
    580:           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);
    581:           if (mat->was_assembled) {
    582:             if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    583: #if defined(PETSC_USE_CTABLE)
    584:             PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col)); /* map global col ids to local ones */
    585:             col--;
    586: #else
    587:             col = aij->colmap[in[j]] - 1;
    588: #endif
    589:             if (col < 0 && !((Mat_SeqAIJ *)aij->B->data)->nonew) { /* col < 0 means in[j] is a new col for B */
    590:               PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));  /* Change aij->B from reduced/local format to expanded/global format */
    591:               col = in[j];
    592:               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
    593:               B     = aij->B;
    594:               b     = (Mat_SeqAIJ *)B->data;
    595:               bimax = b->imax;
    596:               bi    = b->i;
    597:               bilen = b->ilen;
    598:               bj    = b->j;
    599:               ba    = b->a;
    600:               rp2   = PetscSafePointerPlusOffset(bj, bi[row]);
    601:               ap2   = PetscSafePointerPlusOffset(ba, bi[row]);
    602:               rmax2 = bimax[row];
    603:               nrow2 = bilen[row];
    604:               low2  = 0;
    605:               high2 = nrow2;
    606:               bm    = aij->B->rmap->n;
    607:               ba    = b->a;
    608:             } else if (col < 0 && !(ignorezeroentries && value == 0.0)) {
    609:               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]);
    610:               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]));
    611:             }
    612:           } else col = in[j];
    613:           nonew = b->nonew;
    614:           MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
    615:         }
    616:       }
    617:     } else {
    618:       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]);
    619:       if (!aij->donotstash) {
    620:         mat->assembled = PETSC_FALSE;
    621:         if (roworiented) {
    622:           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, PetscSafePointerPlusOffset(v, i * n), (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    623:         } else {
    624:           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, PetscSafePointerPlusOffset(v, i), m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    625:         }
    626:       }
    627:     }
    628:   }
    629:   PetscCall(MatSeqAIJRestoreArray(A, &aa)); /* aa, bb might have been free'd due to reallocation above. But we don't access them here */
    630:   PetscCall(MatSeqAIJRestoreArray(B, &ba));
    631:   PetscFunctionReturn(PETSC_SUCCESS);
    632: }

    634: /*
    635:     This function sets the j and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
    636:     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
    637:     No off-processor parts off the matrix are allowed here and mat->was_assembled has to be PETSC_FALSE.
    638: */
    639: PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Mat mat, const PetscInt mat_j[], const PetscInt mat_i[])
    640: {
    641:   Mat_MPIAIJ *aij    = (Mat_MPIAIJ *)mat->data;
    642:   Mat         A      = aij->A; /* diagonal part of the matrix */
    643:   Mat         B      = aij->B; /* off-diagonal part of the matrix */
    644:   Mat_SeqAIJ *a      = (Mat_SeqAIJ *)A->data;
    645:   Mat_SeqAIJ *b      = (Mat_SeqAIJ *)B->data;
    646:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, col;
    647:   PetscInt   *ailen = a->ilen, *aj = a->j;
    648:   PetscInt   *bilen = b->ilen, *bj = b->j;
    649:   PetscInt    am          = aij->A->rmap->n, j;
    650:   PetscInt    diag_so_far = 0, dnz;
    651:   PetscInt    offd_so_far = 0, onz;

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

    674: /*
    675:     This function sets the local j, a and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
    676:     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
    677:     No off-processor parts off the matrix are allowed here, they are set at a later point by MatSetValues_MPIAIJ.
    678:     Also, mat->was_assembled has to be false, otherwise the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart;
    679:     would not be true and the more complex MatSetValues_MPIAIJ has to be used.
    680: */
    681: PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat(Mat mat, const PetscInt mat_j[], const PetscInt mat_i[], const PetscScalar mat_a[])
    682: {
    683:   Mat_MPIAIJ  *aij  = (Mat_MPIAIJ *)mat->data;
    684:   Mat          A    = aij->A; /* diagonal part of the matrix */
    685:   Mat          B    = aij->B; /* off-diagonal part of the matrix */
    686:   Mat_SeqAIJ  *aijd = (Mat_SeqAIJ *)aij->A->data, *aijo = (Mat_SeqAIJ *)aij->B->data;
    687:   Mat_SeqAIJ  *a      = (Mat_SeqAIJ *)A->data;
    688:   Mat_SeqAIJ  *b      = (Mat_SeqAIJ *)B->data;
    689:   PetscInt     cstart = mat->cmap->rstart, cend = mat->cmap->rend;
    690:   PetscInt    *ailen = a->ilen, *aj = a->j;
    691:   PetscInt    *bilen = b->ilen, *bj = b->j;
    692:   PetscInt     am          = aij->A->rmap->n, j;
    693:   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. */
    694:   PetscInt     col, dnz_row, onz_row, rowstart_diag, rowstart_offd;
    695:   PetscScalar *aa = a->a, *ba = b->a;

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

    722: static PetscErrorCode MatGetValues_MPIAIJ(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], PetscScalar v[])
    723: {
    724:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    725:   PetscInt    i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    726:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;

    728:   PetscFunctionBegin;
    729:   for (i = 0; i < m; i++) {
    730:     if (idxm[i] < 0) continue; /* negative row */
    731:     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);
    732:     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);
    733:     row = idxm[i] - rstart;
    734:     for (j = 0; j < n; j++) {
    735:       if (idxn[j] < 0) continue; /* negative column */
    736:       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);
    737:       if (idxn[j] >= cstart && idxn[j] < cend) {
    738:         col = idxn[j] - cstart;
    739:         PetscCall(MatGetValues(aij->A, 1, &row, 1, &col, v + i * n + j));
    740:       } else {
    741:         if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    742: #if defined(PETSC_USE_CTABLE)
    743:         PetscCall(PetscHMapIGetWithDefault(aij->colmap, idxn[j] + 1, 0, &col));
    744:         col--;
    745: #else
    746:         col = aij->colmap[idxn[j]] - 1;
    747: #endif
    748:         if ((col < 0) || (aij->garray[col] != idxn[j])) *(v + i * n + j) = 0.0;
    749:         else PetscCall(MatGetValues(aij->B, 1, &row, 1, &col, v + i * n + j));
    750:       }
    751:     }
    752:   }
    753:   PetscFunctionReturn(PETSC_SUCCESS);
    754: }

    756: static PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat, MatAssemblyType mode)
    757: {
    758:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    759:   PetscInt    nstash, reallocs;

    761:   PetscFunctionBegin;
    762:   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(PETSC_SUCCESS);

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

    770: PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat, MatAssemblyType mode)
    771: {
    772:   Mat_MPIAIJ  *aij = (Mat_MPIAIJ *)mat->data;
    773:   PetscMPIInt  n;
    774:   PetscInt     i, j, rstart, ncols, flg;
    775:   PetscInt    *row, *col;
    776:   PetscBool    all_assembled;
    777:   PetscScalar *val;

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

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

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

    812:   /* determine if any process has disassembled, if so we must
    813:      also disassemble ourself, in order that we may reassemble. */
    814:   /*
    815:      if nonzero structure of submatrix B cannot change then we know that
    816:      no process disassembled thus we can skip this stuff
    817:   */
    818:   if (!((Mat_SeqAIJ *)aij->B->data)->nonew) {
    819:     PetscCallMPI(MPIU_Allreduce(&mat->was_assembled, &all_assembled, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    820:     if (mat->was_assembled && !all_assembled) { /* mat on this rank has reduced off-diag B with local col ids, but globally it does not */
    821:       PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));
    822:     }
    823:   }
    824:   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) PetscCall(MatSetUpMultiply_MPIAIJ(mat));
    825:   PetscCall(MatSetOption(aij->B, MAT_USE_INODES, PETSC_FALSE));
    826: #if defined(PETSC_HAVE_DEVICE)
    827:   if (mat->offloadmask == PETSC_OFFLOAD_CPU && aij->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) aij->B->offloadmask = PETSC_OFFLOAD_CPU;
    828: #endif
    829:   PetscCall(MatAssemblyBegin(aij->B, mode));
    830:   PetscCall(MatAssemblyEnd(aij->B, mode));

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

    834:   aij->rowvalues = NULL;

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

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

    849: static PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
    850: {
    851:   Mat_MPIAIJ *l = (Mat_MPIAIJ *)A->data;

    853:   PetscFunctionBegin;
    854:   PetscCall(MatZeroEntries(l->A));
    855:   PetscCall(MatZeroEntries(l->B));
    856:   PetscFunctionReturn(PETSC_SUCCESS);
    857: }

    859: static PetscErrorCode MatZeroRows_MPIAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    860: {
    861:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)A->data;
    862:   PetscInt   *lrows;
    863:   PetscInt    r, len;
    864:   PetscBool   cong;

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

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

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

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

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

    930: static PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    931: {
    932:   Mat_MPIAIJ        *l = (Mat_MPIAIJ *)A->data;
    933:   PetscInt           n = A->rmap->n;
    934:   PetscInt           i, j, r, m, len = 0;
    935:   PetscInt          *lrows, *owners = A->rmap->range;
    936:   PetscMPIInt        p = 0;
    937:   PetscSFNode       *rrows;
    938:   PetscSF            sf;
    939:   const PetscScalar *xx;
    940:   PetscScalar       *bb, *mask, *aij_a;
    941:   Vec                xmask, lmask;
    942:   Mat_SeqAIJ        *aij = (Mat_SeqAIJ *)l->B->data;
    943:   const PetscInt    *aj, *ii, *ridx;
    944:   PetscScalar       *aa;

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

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

    1005:       for (j = 0; j < n; j++) {
    1006:         if (PetscAbsScalar(mask[*aj])) {
    1007:           if (b) bb[*ridx] -= *aa * xx[*aj];
    1008:           *aa = 0.0;
    1009:         }
    1010:         aa++;
    1011:         aj++;
    1012:       }
    1013:       ridx++;
    1014:     }
    1015:   } else { /* do not use compressed row format */
    1016:     m = l->B->rmap->n;
    1017:     for (i = 0; i < m; i++) {
    1018:       n  = ii[i + 1] - ii[i];
    1019:       aj = aij->j + ii[i];
    1020:       aa = aij_a + ii[i];
    1021:       for (j = 0; j < n; j++) {
    1022:         if (PetscAbsScalar(mask[*aj])) {
    1023:           if (b) bb[i] -= *aa * xx[*aj];
    1024:           *aa = 0.0;
    1025:         }
    1026:         aa++;
    1027:         aj++;
    1028:       }
    1029:     }
    1030:   }
    1031:   if (x && b) {
    1032:     PetscCall(VecRestoreArray(b, &bb));
    1033:     PetscCall(VecRestoreArrayRead(l->lvec, &xx));
    1034:   }
    1035:   PetscCall(MatSeqAIJRestoreArray(l->B, &aij_a));
    1036:   PetscCall(VecRestoreArray(lmask, &mask));
    1037:   PetscCall(VecDestroy(&lmask));
    1038:   PetscCall(PetscFree(lrows));

    1040:   /* only change matrix nonzero state if pattern was allowed to be changed */
    1041:   if (!((Mat_SeqAIJ *)l->A->data)->nonew) {
    1042:     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
    1043:     PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
    1044:   }
    1045:   PetscFunctionReturn(PETSC_SUCCESS);
    1046: }

    1048: static PetscErrorCode MatMult_MPIAIJ(Mat A, Vec xx, Vec yy)
    1049: {
    1050:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    1051:   PetscInt    nt;
    1052:   VecScatter  Mvctx = a->Mvctx;

    1054:   PetscFunctionBegin;
    1055:   PetscCall(VecGetLocalSize(xx, &nt));
    1056:   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);
    1057:   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1058:   PetscUseTypeMethod(a->A, mult, xx, yy);
    1059:   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1060:   PetscUseTypeMethod(a->B, multadd, a->lvec, yy, yy);
    1061:   PetscFunctionReturn(PETSC_SUCCESS);
    1062: }

    1064: static PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A, Vec bb, Vec xx)
    1065: {
    1066:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1068:   PetscFunctionBegin;
    1069:   PetscCall(MatMultDiagonalBlock(a->A, bb, xx));
    1070:   PetscFunctionReturn(PETSC_SUCCESS);
    1071: }

    1073: static PetscErrorCode MatMultAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
    1074: {
    1075:   Mat_MPIAIJ *a     = (Mat_MPIAIJ *)A->data;
    1076:   VecScatter  Mvctx = a->Mvctx;

    1078:   PetscFunctionBegin;
    1079:   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1080:   PetscCall((*a->A->ops->multadd)(a->A, xx, yy, zz));
    1081:   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1082:   PetscCall((*a->B->ops->multadd)(a->B, a->lvec, zz, zz));
    1083:   PetscFunctionReturn(PETSC_SUCCESS);
    1084: }

    1086: static PetscErrorCode MatMultTranspose_MPIAIJ(Mat A, Vec xx, Vec yy)
    1087: {
    1088:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1090:   PetscFunctionBegin;
    1091:   /* do nondiagonal part */
    1092:   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
    1093:   /* do local part */
    1094:   PetscCall((*a->A->ops->multtranspose)(a->A, xx, yy));
    1095:   /* add partial results together */
    1096:   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
    1097:   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
    1098:   PetscFunctionReturn(PETSC_SUCCESS);
    1099: }

    1101: static PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat, Mat Bmat, PetscReal tol, PetscBool *f)
    1102: {
    1103:   MPI_Comm    comm;
    1104:   Mat_MPIAIJ *Aij = (Mat_MPIAIJ *)Amat->data, *Bij = (Mat_MPIAIJ *)Bmat->data;
    1105:   Mat         Adia = Aij->A, Bdia = Bij->A, Aoff, Boff, *Aoffs, *Boffs;
    1106:   IS          Me, Notme;
    1107:   PetscInt    M, N, first, last, *notme, i;
    1108:   PetscBool   lf;
    1109:   PetscMPIInt size;

    1111:   PetscFunctionBegin;
    1112:   /* Easy test: symmetric diagonal block */
    1113:   PetscCall(MatIsTranspose(Adia, Bdia, tol, &lf));
    1114:   PetscCallMPI(MPIU_Allreduce(&lf, f, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)Amat)));
    1115:   if (!*f) PetscFunctionReturn(PETSC_SUCCESS);
    1116:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
    1117:   PetscCallMPI(MPI_Comm_size(comm, &size));
    1118:   if (size == 1) PetscFunctionReturn(PETSC_SUCCESS);

    1120:   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
    1121:   PetscCall(MatGetSize(Amat, &M, &N));
    1122:   PetscCall(MatGetOwnershipRange(Amat, &first, &last));
    1123:   PetscCall(PetscMalloc1(N - last + first, &notme));
    1124:   for (i = 0; i < first; i++) notme[i] = i;
    1125:   for (i = last; i < M; i++) notme[i - last + first] = i;
    1126:   PetscCall(ISCreateGeneral(MPI_COMM_SELF, N - last + first, notme, PETSC_COPY_VALUES, &Notme));
    1127:   PetscCall(ISCreateStride(MPI_COMM_SELF, last - first, first, 1, &Me));
    1128:   PetscCall(MatCreateSubMatrices(Amat, 1, &Me, &Notme, MAT_INITIAL_MATRIX, &Aoffs));
    1129:   Aoff = Aoffs[0];
    1130:   PetscCall(MatCreateSubMatrices(Bmat, 1, &Notme, &Me, MAT_INITIAL_MATRIX, &Boffs));
    1131:   Boff = Boffs[0];
    1132:   PetscCall(MatIsTranspose(Aoff, Boff, tol, f));
    1133:   PetscCall(MatDestroyMatrices(1, &Aoffs));
    1134:   PetscCall(MatDestroyMatrices(1, &Boffs));
    1135:   PetscCall(ISDestroy(&Me));
    1136:   PetscCall(ISDestroy(&Notme));
    1137:   PetscCall(PetscFree(notme));
    1138:   PetscFunctionReturn(PETSC_SUCCESS);
    1139: }

    1141: static PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
    1142: {
    1143:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1145:   PetscFunctionBegin;
    1146:   /* do nondiagonal part */
    1147:   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
    1148:   /* do local part */
    1149:   PetscCall((*a->A->ops->multtransposeadd)(a->A, xx, yy, zz));
    1150:   /* add partial results together */
    1151:   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
    1152:   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
    1153:   PetscFunctionReturn(PETSC_SUCCESS);
    1154: }

    1156: /*
    1157:   This only works correctly for square matrices where the subblock A->A is the
    1158:    diagonal block
    1159: */
    1160: static PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A, Vec v)
    1161: {
    1162:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1164:   PetscFunctionBegin;
    1165:   PetscCheck(A->rmap->N == A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Supports only square matrix where A->A is diag block");
    1166:   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");
    1167:   PetscCall(MatGetDiagonal(a->A, v));
    1168:   PetscFunctionReturn(PETSC_SUCCESS);
    1169: }

    1171: static PetscErrorCode MatScale_MPIAIJ(Mat A, PetscScalar aa)
    1172: {
    1173:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1175:   PetscFunctionBegin;
    1176:   PetscCall(MatScale(a->A, aa));
    1177:   PetscCall(MatScale(a->B, aa));
    1178:   PetscFunctionReturn(PETSC_SUCCESS);
    1179: }

    1181: static PetscErrorCode MatView_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
    1182: {
    1183:   Mat_MPIAIJ        *aij    = (Mat_MPIAIJ *)mat->data;
    1184:   Mat_SeqAIJ        *A      = (Mat_SeqAIJ *)aij->A->data;
    1185:   Mat_SeqAIJ        *B      = (Mat_SeqAIJ *)aij->B->data;
    1186:   const PetscInt    *garray = aij->garray;
    1187:   const PetscScalar *aa, *ba;
    1188:   PetscInt           header[4], M, N, m, rs, cs, cnt, i, ja, jb;
    1189:   PetscInt64         nz, hnz;
    1190:   PetscInt          *rowlens;
    1191:   PetscInt          *colidxs;
    1192:   PetscScalar       *matvals;
    1193:   PetscMPIInt        rank;

    1195:   PetscFunctionBegin;
    1196:   PetscCall(PetscViewerSetUp(viewer));

    1198:   M  = mat->rmap->N;
    1199:   N  = mat->cmap->N;
    1200:   m  = mat->rmap->n;
    1201:   rs = mat->rmap->rstart;
    1202:   cs = mat->cmap->rstart;
    1203:   nz = A->nz + B->nz;

    1205:   /* write matrix header */
    1206:   header[0] = MAT_FILE_CLASSID;
    1207:   header[1] = M;
    1208:   header[2] = N;
    1209:   PetscCallMPI(MPI_Reduce(&nz, &hnz, 1, MPIU_INT64, MPI_SUM, 0, PetscObjectComm((PetscObject)mat)));
    1210:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
    1211:   if (rank == 0) PetscCall(PetscIntCast(hnz, &header[3]));
    1212:   PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));

    1214:   /* fill in and store row lengths  */
    1215:   PetscCall(PetscMalloc1(m, &rowlens));
    1216:   for (i = 0; i < m; i++) rowlens[i] = A->i[i + 1] - A->i[i] + B->i[i + 1] - B->i[i];
    1217:   PetscCall(PetscViewerBinaryWriteAll(viewer, rowlens, m, rs, M, PETSC_INT));
    1218:   PetscCall(PetscFree(rowlens));

    1220:   /* fill in and store column indices */
    1221:   PetscCall(PetscMalloc1(nz, &colidxs));
    1222:   for (cnt = 0, i = 0; i < m; i++) {
    1223:     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
    1224:       if (garray[B->j[jb]] > cs) break;
    1225:       colidxs[cnt++] = garray[B->j[jb]];
    1226:     }
    1227:     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) colidxs[cnt++] = A->j[ja] + cs;
    1228:     for (; jb < B->i[i + 1]; jb++) colidxs[cnt++] = garray[B->j[jb]];
    1229:   }
    1230:   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
    1231:   PetscCall(PetscViewerBinaryWriteAll(viewer, colidxs, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
    1232:   PetscCall(PetscFree(colidxs));

    1234:   /* fill in and store nonzero values */
    1235:   PetscCall(MatSeqAIJGetArrayRead(aij->A, &aa));
    1236:   PetscCall(MatSeqAIJGetArrayRead(aij->B, &ba));
    1237:   PetscCall(PetscMalloc1(nz, &matvals));
    1238:   for (cnt = 0, i = 0; i < m; i++) {
    1239:     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
    1240:       if (garray[B->j[jb]] > cs) break;
    1241:       matvals[cnt++] = ba[jb];
    1242:     }
    1243:     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) matvals[cnt++] = aa[ja];
    1244:     for (; jb < B->i[i + 1]; jb++) matvals[cnt++] = ba[jb];
    1245:   }
    1246:   PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &aa));
    1247:   PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &ba));
    1248:   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_LIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
    1249:   PetscCall(PetscViewerBinaryWriteAll(viewer, matvals, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
    1250:   PetscCall(PetscFree(matvals));

    1252:   /* write block size option to the viewer's .info file */
    1253:   PetscCall(MatView_Binary_BlockSizes(mat, viewer));
    1254:   PetscFunctionReturn(PETSC_SUCCESS);
    1255: }

    1257: #include <petscdraw.h>
    1258: static PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat, PetscViewer viewer)
    1259: {
    1260:   Mat_MPIAIJ       *aij  = (Mat_MPIAIJ *)mat->data;
    1261:   PetscMPIInt       rank = aij->rank, size = aij->size;
    1262:   PetscBool         isdraw, isascii, isbinary;
    1263:   PetscViewer       sviewer;
    1264:   PetscViewerFormat format;

    1266:   PetscFunctionBegin;
    1267:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
    1268:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    1269:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    1270:   if (isascii) {
    1271:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1272:     if (format == PETSC_VIEWER_LOAD_BALANCE) {
    1273:       PetscInt i, nmax = 0, nmin = PETSC_INT_MAX, navg = 0, *nz, nzlocal = ((Mat_SeqAIJ *)aij->A->data)->nz + ((Mat_SeqAIJ *)aij->B->data)->nz;
    1274:       PetscCall(PetscMalloc1(size, &nz));
    1275:       PetscCallMPI(MPI_Allgather(&nzlocal, 1, MPIU_INT, nz, 1, MPIU_INT, PetscObjectComm((PetscObject)mat)));
    1276:       for (i = 0; i < size; i++) {
    1277:         nmax = PetscMax(nmax, nz[i]);
    1278:         nmin = PetscMin(nmin, nz[i]);
    1279:         navg += nz[i];
    1280:       }
    1281:       PetscCall(PetscFree(nz));
    1282:       navg = navg / size;
    1283:       PetscCall(PetscViewerASCIIPrintf(viewer, "Load Balance - Nonzeros: Min %" PetscInt_FMT "  avg %" PetscInt_FMT "  max %" PetscInt_FMT "\n", nmin, navg, nmax));
    1284:       PetscFunctionReturn(PETSC_SUCCESS);
    1285:     }
    1286:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1287:     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1288:       MatInfo   info;
    1289:       PetscInt *inodes = NULL;

    1291:       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
    1292:       PetscCall(MatGetInfo(mat, MAT_LOCAL, &info));
    1293:       PetscCall(MatInodeGetInodeSizes(aij->A, NULL, &inodes, NULL));
    1294:       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    1295:       if (!inodes) {
    1296:         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,
    1297:                                                      info.memory));
    1298:       } else {
    1299:         PetscCall(
    1300:           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));
    1301:       }
    1302:       PetscCall(MatGetInfo(aij->A, MAT_LOCAL, &info));
    1303:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] on-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
    1304:       PetscCall(MatGetInfo(aij->B, MAT_LOCAL, &info));
    1305:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] off-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
    1306:       PetscCall(PetscViewerFlush(viewer));
    1307:       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    1308:       PetscCall(PetscViewerASCIIPrintf(viewer, "Information on VecScatter used in matrix-vector product: \n"));
    1309:       PetscCall(VecScatterView(aij->Mvctx, viewer));
    1310:       PetscFunctionReturn(PETSC_SUCCESS);
    1311:     } else if (format == PETSC_VIEWER_ASCII_INFO) {
    1312:       PetscInt inodecount, inodelimit, *inodes;
    1313:       PetscCall(MatInodeGetInodeSizes(aij->A, &inodecount, &inodes, &inodelimit));
    1314:       if (inodes) {
    1315:         PetscCall(PetscViewerASCIIPrintf(viewer, "using I-node (on process 0) routines: found %" PetscInt_FMT " nodes, limit used is %" PetscInt_FMT "\n", inodecount, inodelimit));
    1316:       } else {
    1317:         PetscCall(PetscViewerASCIIPrintf(viewer, "not using I-node (on process 0) routines\n"));
    1318:       }
    1319:       PetscFunctionReturn(PETSC_SUCCESS);
    1320:     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
    1321:       PetscFunctionReturn(PETSC_SUCCESS);
    1322:     }
    1323:   } else if (isbinary) {
    1324:     if (size == 1) {
    1325:       PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
    1326:       PetscCall(MatView(aij->A, viewer));
    1327:     } else {
    1328:       PetscCall(MatView_MPIAIJ_Binary(mat, viewer));
    1329:     }
    1330:     PetscFunctionReturn(PETSC_SUCCESS);
    1331:   } else if (isascii && size == 1) {
    1332:     PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
    1333:     PetscCall(MatView(aij->A, viewer));
    1334:     PetscFunctionReturn(PETSC_SUCCESS);
    1335:   } else if (isdraw) {
    1336:     PetscDraw draw;
    1337:     PetscBool isnull;
    1338:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
    1339:     PetscCall(PetscDrawIsNull(draw, &isnull));
    1340:     if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
    1341:   }

    1343:   { /* assemble the entire matrix onto first processor */
    1344:     Mat A = NULL, Av;
    1345:     IS  isrow, iscol;

    1347:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->rmap->N : 0, 0, 1, &isrow));
    1348:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->cmap->N : 0, 0, 1, &iscol));
    1349:     PetscCall(MatCreateSubMatrix(mat, isrow, iscol, MAT_INITIAL_MATRIX, &A));
    1350:     PetscCall(MatMPIAIJGetSeqAIJ(A, &Av, NULL, NULL));
    1351:     /*  The commented code uses MatCreateSubMatrices instead */
    1352:     /*
    1353:     Mat *AA, A = NULL, Av;
    1354:     IS  isrow,iscol;

    1356:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->rmap->N : 0,0,1,&isrow));
    1357:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->cmap->N : 0,0,1,&iscol));
    1358:     PetscCall(MatCreateSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&AA));
    1359:     if (rank == 0) {
    1360:        PetscCall(PetscObjectReference((PetscObject)AA[0]));
    1361:        A    = AA[0];
    1362:        Av   = AA[0];
    1363:     }
    1364:     PetscCall(MatDestroySubMatrices(1,&AA));
    1365: */
    1366:     PetscCall(ISDestroy(&iscol));
    1367:     PetscCall(ISDestroy(&isrow));
    1368:     /*
    1369:        Everyone has to call to draw the matrix since the graphics waits are
    1370:        synchronized across all processors that share the PetscDraw object
    1371:     */
    1372:     PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    1373:     if (rank == 0) {
    1374:       if (((PetscObject)mat)->name) PetscCall(PetscObjectSetName((PetscObject)Av, ((PetscObject)mat)->name));
    1375:       PetscCall(MatView_SeqAIJ(Av, sviewer));
    1376:     }
    1377:     PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    1378:     PetscCall(MatDestroy(&A));
    1379:   }
    1380:   PetscFunctionReturn(PETSC_SUCCESS);
    1381: }

    1383: PetscErrorCode MatView_MPIAIJ(Mat mat, PetscViewer viewer)
    1384: {
    1385:   PetscBool isascii, isdraw, issocket, isbinary;

    1387:   PetscFunctionBegin;
    1388:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &isascii));
    1389:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
    1390:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    1391:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSOCKET, &issocket));
    1392:   if (isascii || isdraw || isbinary || issocket) PetscCall(MatView_MPIAIJ_ASCIIorDraworSocket(mat, viewer));
    1393:   PetscFunctionReturn(PETSC_SUCCESS);
    1394: }

    1396: static PetscErrorCode MatSOR_MPIAIJ(Mat matin, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
    1397: {
    1398:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)matin->data;
    1399:   Vec         bb1 = NULL;
    1400:   PetscBool   hasop;

    1402:   PetscFunctionBegin;
    1403:   if (flag == SOR_APPLY_UPPER) {
    1404:     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1405:     PetscFunctionReturn(PETSC_SUCCESS);
    1406:   }

    1408:   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) PetscCall(VecDuplicate(bb, &bb1));

    1410:   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
    1411:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1412:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1413:       its--;
    1414:     }

    1416:     while (its--) {
    1417:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1418:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1420:       /* update rhs: bb1 = bb - B*x */
    1421:       PetscCall(VecScale(mat->lvec, -1.0));
    1422:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1424:       /* local sweep */
    1425:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_SYMMETRIC_SWEEP, fshift, lits, 1, xx));
    1426:     }
    1427:   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
    1428:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1429:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1430:       its--;
    1431:     }
    1432:     while (its--) {
    1433:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1434:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1436:       /* update rhs: bb1 = bb - B*x */
    1437:       PetscCall(VecScale(mat->lvec, -1.0));
    1438:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1440:       /* local sweep */
    1441:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_FORWARD_SWEEP, fshift, lits, 1, xx));
    1442:     }
    1443:   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
    1444:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1445:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1446:       its--;
    1447:     }
    1448:     while (its--) {
    1449:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1450:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1452:       /* update rhs: bb1 = bb - B*x */
    1453:       PetscCall(VecScale(mat->lvec, -1.0));
    1454:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1456:       /* local sweep */
    1457:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_BACKWARD_SWEEP, fshift, lits, 1, xx));
    1458:     }
    1459:   } else if (flag & SOR_EISENSTAT) {
    1460:     Vec xx1;

    1462:     PetscCall(VecDuplicate(bb, &xx1));
    1463:     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP), fshift, lits, 1, xx));

    1465:     PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1466:     PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1467:     if (!mat->diag) {
    1468:       PetscCall(MatCreateVecs(matin, &mat->diag, NULL));
    1469:       PetscCall(MatGetDiagonal(matin, mat->diag));
    1470:     }
    1471:     PetscCall(MatHasOperation(matin, MATOP_MULT_DIAGONAL_BLOCK, &hasop));
    1472:     if (hasop) PetscCall(MatMultDiagonalBlock(matin, xx, bb1));
    1473:     else PetscCall(VecPointwiseMult(bb1, mat->diag, xx));
    1474:     PetscCall(VecAYPX(bb1, (omega - 2.0) / omega, bb));

    1476:     PetscCall(MatMultAdd(mat->B, mat->lvec, bb1, bb1));

    1478:     /* local sweep */
    1479:     PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP), fshift, lits, 1, xx1));
    1480:     PetscCall(VecAXPY(xx, 1.0, xx1));
    1481:     PetscCall(VecDestroy(&xx1));
    1482:   } else SETERRQ(PetscObjectComm((PetscObject)matin), PETSC_ERR_SUP, "Parallel SOR not supported");

    1484:   PetscCall(VecDestroy(&bb1));

    1486:   matin->factorerrortype = mat->A->factorerrortype;
    1487:   PetscFunctionReturn(PETSC_SUCCESS);
    1488: }

    1490: static PetscErrorCode MatPermute_MPIAIJ(Mat A, IS rowp, IS colp, Mat *B)
    1491: {
    1492:   Mat             aA, aB, Aperm;
    1493:   const PetscInt *rwant, *cwant, *gcols, *ai, *bi, *aj, *bj;
    1494:   PetscScalar    *aa, *ba;
    1495:   PetscInt        i, j, m, n, ng, anz, bnz, *dnnz, *onnz, *tdnnz, *tonnz, *rdest, *cdest, *work, *gcdest;
    1496:   PetscSF         rowsf, sf;
    1497:   IS              parcolp = NULL;
    1498:   PetscBool       done;

    1500:   PetscFunctionBegin;
    1501:   PetscCall(MatGetLocalSize(A, &m, &n));
    1502:   PetscCall(ISGetIndices(rowp, &rwant));
    1503:   PetscCall(ISGetIndices(colp, &cwant));
    1504:   PetscCall(PetscMalloc3(PetscMax(m, n), &work, m, &rdest, n, &cdest));

    1506:   /* Invert row permutation to find out where my rows should go */
    1507:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &rowsf));
    1508:   PetscCall(PetscSFSetGraphLayout(rowsf, A->rmap, A->rmap->n, NULL, PETSC_OWN_POINTER, rwant));
    1509:   PetscCall(PetscSFSetFromOptions(rowsf));
    1510:   for (i = 0; i < m; i++) work[i] = A->rmap->rstart + i;
    1511:   PetscCall(PetscSFReduceBegin(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));
    1512:   PetscCall(PetscSFReduceEnd(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));

    1514:   /* Invert column permutation to find out where my columns should go */
    1515:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1516:   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, A->cmap->n, NULL, PETSC_OWN_POINTER, cwant));
    1517:   PetscCall(PetscSFSetFromOptions(sf));
    1518:   for (i = 0; i < n; i++) work[i] = A->cmap->rstart + i;
    1519:   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, work, cdest, MPI_REPLACE));
    1520:   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, work, cdest, MPI_REPLACE));
    1521:   PetscCall(PetscSFDestroy(&sf));

    1523:   PetscCall(ISRestoreIndices(rowp, &rwant));
    1524:   PetscCall(ISRestoreIndices(colp, &cwant));
    1525:   PetscCall(MatMPIAIJGetSeqAIJ(A, &aA, &aB, &gcols));

    1527:   /* Find out where my gcols should go */
    1528:   PetscCall(MatGetSize(aB, NULL, &ng));
    1529:   PetscCall(PetscMalloc1(ng, &gcdest));
    1530:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1531:   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, ng, NULL, PETSC_OWN_POINTER, gcols));
    1532:   PetscCall(PetscSFSetFromOptions(sf));
    1533:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
    1534:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
    1535:   PetscCall(PetscSFDestroy(&sf));

    1537:   PetscCall(PetscCalloc4(m, &dnnz, m, &onnz, m, &tdnnz, m, &tonnz));
    1538:   PetscCall(MatGetRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
    1539:   PetscCall(MatGetRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
    1540:   for (i = 0; i < m; i++) {
    1541:     PetscInt    row = rdest[i];
    1542:     PetscMPIInt rowner;
    1543:     PetscCall(PetscLayoutFindOwner(A->rmap, row, &rowner));
    1544:     for (j = ai[i]; j < ai[i + 1]; j++) {
    1545:       PetscInt    col = cdest[aj[j]];
    1546:       PetscMPIInt cowner;
    1547:       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner)); /* Could build an index for the columns to eliminate this search */
    1548:       if (rowner == cowner) dnnz[i]++;
    1549:       else onnz[i]++;
    1550:     }
    1551:     for (j = bi[i]; j < bi[i + 1]; j++) {
    1552:       PetscInt    col = gcdest[bj[j]];
    1553:       PetscMPIInt cowner;
    1554:       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner));
    1555:       if (rowner == cowner) dnnz[i]++;
    1556:       else onnz[i]++;
    1557:     }
    1558:   }
    1559:   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
    1560:   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
    1561:   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
    1562:   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
    1563:   PetscCall(PetscSFDestroy(&rowsf));

    1565:   PetscCall(MatCreateAIJ(PetscObjectComm((PetscObject)A), A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N, 0, tdnnz, 0, tonnz, &Aperm));
    1566:   PetscCall(MatSeqAIJGetArray(aA, &aa));
    1567:   PetscCall(MatSeqAIJGetArray(aB, &ba));
    1568:   for (i = 0; i < m; i++) {
    1569:     PetscInt *acols = dnnz, *bcols = onnz; /* Repurpose now-unneeded arrays */
    1570:     PetscInt  j0, rowlen;
    1571:     rowlen = ai[i + 1] - ai[i];
    1572:     for (j0 = j = 0; j < rowlen; j0 = j) { /* rowlen could be larger than number of rows m, so sum in batches */
    1573:       for (; j < PetscMin(rowlen, j0 + m); j++) acols[j - j0] = cdest[aj[ai[i] + j]];
    1574:       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, acols, aa + ai[i] + j0, INSERT_VALUES));
    1575:     }
    1576:     rowlen = bi[i + 1] - bi[i];
    1577:     for (j0 = j = 0; j < rowlen; j0 = j) {
    1578:       for (; j < PetscMin(rowlen, j0 + m); j++) bcols[j - j0] = gcdest[bj[bi[i] + j]];
    1579:       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, bcols, ba + bi[i] + j0, INSERT_VALUES));
    1580:     }
    1581:   }
    1582:   PetscCall(MatAssemblyBegin(Aperm, MAT_FINAL_ASSEMBLY));
    1583:   PetscCall(MatAssemblyEnd(Aperm, MAT_FINAL_ASSEMBLY));
    1584:   PetscCall(MatRestoreRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
    1585:   PetscCall(MatRestoreRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
    1586:   PetscCall(MatSeqAIJRestoreArray(aA, &aa));
    1587:   PetscCall(MatSeqAIJRestoreArray(aB, &ba));
    1588:   PetscCall(PetscFree4(dnnz, onnz, tdnnz, tonnz));
    1589:   PetscCall(PetscFree3(work, rdest, cdest));
    1590:   PetscCall(PetscFree(gcdest));
    1591:   if (parcolp) PetscCall(ISDestroy(&colp));
    1592:   *B = Aperm;
    1593:   PetscFunctionReturn(PETSC_SUCCESS);
    1594: }

    1596: static PetscErrorCode MatGetGhosts_MPIAIJ(Mat mat, PetscInt *nghosts, const PetscInt *ghosts[])
    1597: {
    1598:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    1600:   PetscFunctionBegin;
    1601:   PetscCall(MatGetSize(aij->B, NULL, nghosts));
    1602:   if (ghosts) *ghosts = aij->garray;
    1603:   PetscFunctionReturn(PETSC_SUCCESS);
    1604: }

    1606: static PetscErrorCode MatGetInfo_MPIAIJ(Mat matin, MatInfoType flag, MatInfo *info)
    1607: {
    1608:   Mat_MPIAIJ    *mat = (Mat_MPIAIJ *)matin->data;
    1609:   Mat            A = mat->A, B = mat->B;
    1610:   PetscLogDouble isend[5], irecv[5];

    1612:   PetscFunctionBegin;
    1613:   info->block_size = 1.0;
    1614:   PetscCall(MatGetInfo(A, MAT_LOCAL, info));

    1616:   isend[0] = info->nz_used;
    1617:   isend[1] = info->nz_allocated;
    1618:   isend[2] = info->nz_unneeded;
    1619:   isend[3] = info->memory;
    1620:   isend[4] = info->mallocs;

    1622:   PetscCall(MatGetInfo(B, MAT_LOCAL, info));

    1624:   isend[0] += info->nz_used;
    1625:   isend[1] += info->nz_allocated;
    1626:   isend[2] += info->nz_unneeded;
    1627:   isend[3] += info->memory;
    1628:   isend[4] += info->mallocs;
    1629:   if (flag == MAT_LOCAL) {
    1630:     info->nz_used      = isend[0];
    1631:     info->nz_allocated = isend[1];
    1632:     info->nz_unneeded  = isend[2];
    1633:     info->memory       = isend[3];
    1634:     info->mallocs      = isend[4];
    1635:   } else if (flag == MAT_GLOBAL_MAX) {
    1636:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)matin)));

    1638:     info->nz_used      = irecv[0];
    1639:     info->nz_allocated = irecv[1];
    1640:     info->nz_unneeded  = irecv[2];
    1641:     info->memory       = irecv[3];
    1642:     info->mallocs      = irecv[4];
    1643:   } else if (flag == MAT_GLOBAL_SUM) {
    1644:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)matin)));

    1646:     info->nz_used      = irecv[0];
    1647:     info->nz_allocated = irecv[1];
    1648:     info->nz_unneeded  = irecv[2];
    1649:     info->memory       = irecv[3];
    1650:     info->mallocs      = irecv[4];
    1651:   }
    1652:   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
    1653:   info->fill_ratio_needed = 0;
    1654:   info->factor_mallocs    = 0;
    1655:   PetscFunctionReturn(PETSC_SUCCESS);
    1656: }

    1658: PetscErrorCode MatSetOption_MPIAIJ(Mat A, MatOption op, PetscBool flg)
    1659: {
    1660:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1662:   PetscFunctionBegin;
    1663:   switch (op) {
    1664:   case MAT_NEW_NONZERO_LOCATIONS:
    1665:   case MAT_NEW_NONZERO_ALLOCATION_ERR:
    1666:   case MAT_UNUSED_NONZERO_LOCATION_ERR:
    1667:   case MAT_KEEP_NONZERO_PATTERN:
    1668:   case MAT_NEW_NONZERO_LOCATION_ERR:
    1669:   case MAT_USE_INODES:
    1670:   case MAT_IGNORE_ZERO_ENTRIES:
    1671:   case MAT_FORM_EXPLICIT_TRANSPOSE:
    1672:     MatCheckPreallocated(A, 1);
    1673:     PetscCall(MatSetOption(a->A, op, flg));
    1674:     PetscCall(MatSetOption(a->B, op, flg));
    1675:     break;
    1676:   case MAT_ROW_ORIENTED:
    1677:     MatCheckPreallocated(A, 1);
    1678:     a->roworiented = flg;

    1680:     PetscCall(MatSetOption(a->A, op, flg));
    1681:     PetscCall(MatSetOption(a->B, op, flg));
    1682:     break;
    1683:   case MAT_IGNORE_OFF_PROC_ENTRIES:
    1684:     a->donotstash = flg;
    1685:     break;
    1686:   /* Symmetry flags are handled directly by MatSetOption() and they don't affect preallocation */
    1687:   case MAT_SPD:
    1688:   case MAT_SYMMETRIC:
    1689:   case MAT_STRUCTURALLY_SYMMETRIC:
    1690:   case MAT_HERMITIAN:
    1691:   case MAT_SYMMETRY_ETERNAL:
    1692:   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
    1693:   case MAT_SPD_ETERNAL:
    1694:     /* if the diagonal matrix is square it inherits some of the properties above */
    1695:     if (a->A && A->rmap->n == A->cmap->n) PetscCall(MatSetOption(a->A, op, flg));
    1696:     break;
    1697:   case MAT_SUBMAT_SINGLEIS:
    1698:     A->submat_singleis = flg;
    1699:     break;
    1700:   default:
    1701:     break;
    1702:   }
    1703:   PetscFunctionReturn(PETSC_SUCCESS);
    1704: }

    1706: PetscErrorCode MatGetRow_MPIAIJ(Mat matin, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    1707: {
    1708:   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)matin->data;
    1709:   PetscScalar *vworkA, *vworkB, **pvA, **pvB, *v_p;
    1710:   PetscInt     i, *cworkA, *cworkB, **pcA, **pcB, cstart = matin->cmap->rstart;
    1711:   PetscInt     nztot, nzA, nzB, lrow, rstart = matin->rmap->rstart, rend = matin->rmap->rend;
    1712:   PetscInt    *cmap, *idx_p;

    1714:   PetscFunctionBegin;
    1715:   PetscCheck(!mat->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Already active");
    1716:   mat->getrowactive = PETSC_TRUE;

    1718:   if (!mat->rowvalues && (idx || v)) {
    1719:     /*
    1720:         allocate enough space to hold information from the longest row.
    1721:     */
    1722:     Mat_SeqAIJ *Aa = (Mat_SeqAIJ *)mat->A->data, *Ba = (Mat_SeqAIJ *)mat->B->data;
    1723:     PetscInt    max = 1, tmp;
    1724:     for (i = 0; i < matin->rmap->n; i++) {
    1725:       tmp = Aa->i[i + 1] - Aa->i[i] + Ba->i[i + 1] - Ba->i[i];
    1726:       if (max < tmp) max = tmp;
    1727:     }
    1728:     PetscCall(PetscMalloc2(max, &mat->rowvalues, max, &mat->rowindices));
    1729:   }

    1731:   PetscCheck(row >= rstart && row < rend, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Only local rows");
    1732:   lrow = row - rstart;

    1734:   pvA = &vworkA;
    1735:   pcA = &cworkA;
    1736:   pvB = &vworkB;
    1737:   pcB = &cworkB;
    1738:   if (!v) {
    1739:     pvA = NULL;
    1740:     pvB = NULL;
    1741:   }
    1742:   if (!idx) {
    1743:     pcA = NULL;
    1744:     if (!v) pcB = NULL;
    1745:   }
    1746:   PetscCall((*mat->A->ops->getrow)(mat->A, lrow, &nzA, pcA, pvA));
    1747:   PetscCall((*mat->B->ops->getrow)(mat->B, lrow, &nzB, pcB, pvB));
    1748:   nztot = nzA + nzB;

    1750:   cmap = mat->garray;
    1751:   if (v || idx) {
    1752:     if (nztot) {
    1753:       /* Sort by increasing column numbers, assuming A and B already sorted */
    1754:       PetscInt imark = -1;
    1755:       if (v) {
    1756:         *v = v_p = mat->rowvalues;
    1757:         for (i = 0; i < nzB; i++) {
    1758:           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
    1759:           else break;
    1760:         }
    1761:         imark = i;
    1762:         for (i = 0; i < nzA; i++) v_p[imark + i] = vworkA[i];
    1763:         for (i = imark; i < nzB; i++) v_p[nzA + i] = vworkB[i];
    1764:       }
    1765:       if (idx) {
    1766:         *idx = idx_p = mat->rowindices;
    1767:         if (imark > -1) {
    1768:           for (i = 0; i < imark; i++) idx_p[i] = cmap[cworkB[i]];
    1769:         } else {
    1770:           for (i = 0; i < nzB; i++) {
    1771:             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
    1772:             else break;
    1773:           }
    1774:           imark = i;
    1775:         }
    1776:         for (i = 0; i < nzA; i++) idx_p[imark + i] = cstart + cworkA[i];
    1777:         for (i = imark; i < nzB; i++) idx_p[nzA + i] = cmap[cworkB[i]];
    1778:       }
    1779:     } else {
    1780:       if (idx) *idx = NULL;
    1781:       if (v) *v = NULL;
    1782:     }
    1783:   }
    1784:   *nz = nztot;
    1785:   PetscCall((*mat->A->ops->restorerow)(mat->A, lrow, &nzA, pcA, pvA));
    1786:   PetscCall((*mat->B->ops->restorerow)(mat->B, lrow, &nzB, pcB, pvB));
    1787:   PetscFunctionReturn(PETSC_SUCCESS);
    1788: }

    1790: PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    1791: {
    1792:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    1794:   PetscFunctionBegin;
    1795:   PetscCheck(aij->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "MatGetRow() must be called first");
    1796:   aij->getrowactive = PETSC_FALSE;
    1797:   PetscFunctionReturn(PETSC_SUCCESS);
    1798: }

    1800: static PetscErrorCode MatNorm_MPIAIJ(Mat mat, NormType type, PetscReal *norm)
    1801: {
    1802:   Mat_MPIAIJ      *aij  = (Mat_MPIAIJ *)mat->data;
    1803:   Mat_SeqAIJ      *amat = (Mat_SeqAIJ *)aij->A->data, *bmat = (Mat_SeqAIJ *)aij->B->data;
    1804:   PetscInt         i, j;
    1805:   PetscReal        sum = 0.0;
    1806:   const MatScalar *v, *amata, *bmata;

    1808:   PetscFunctionBegin;
    1809:   if (aij->size == 1) {
    1810:     PetscCall(MatNorm(aij->A, type, norm));
    1811:   } else {
    1812:     PetscCall(MatSeqAIJGetArrayRead(aij->A, &amata));
    1813:     PetscCall(MatSeqAIJGetArrayRead(aij->B, &bmata));
    1814:     if (type == NORM_FROBENIUS) {
    1815:       v = amata;
    1816:       for (i = 0; i < amat->nz; i++) {
    1817:         sum += PetscRealPart(PetscConj(*v) * (*v));
    1818:         v++;
    1819:       }
    1820:       v = bmata;
    1821:       for (i = 0; i < bmat->nz; i++) {
    1822:         sum += PetscRealPart(PetscConj(*v) * (*v));
    1823:         v++;
    1824:       }
    1825:       PetscCallMPI(MPIU_Allreduce(&sum, norm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
    1826:       *norm = PetscSqrtReal(*norm);
    1827:       PetscCall(PetscLogFlops(2.0 * amat->nz + 2.0 * bmat->nz));
    1828:     } else if (type == NORM_1) { /* max column norm */
    1829:       Vec          col, bcol;
    1830:       PetscScalar *array;
    1831:       PetscInt    *jj, *garray = aij->garray;

    1833:       PetscCall(MatCreateVecs(mat, &col, NULL));
    1834:       PetscCall(VecSet(col, 0.0));
    1835:       PetscCall(VecGetArrayWrite(col, &array));
    1836:       v  = amata;
    1837:       jj = amat->j;
    1838:       for (j = 0; j < amat->nz; j++) array[*jj++] += PetscAbsScalar(*v++);
    1839:       PetscCall(VecRestoreArrayWrite(col, &array));
    1840:       PetscCall(MatCreateVecs(aij->B, &bcol, NULL));
    1841:       PetscCall(VecSet(bcol, 0.0));
    1842:       PetscCall(VecGetArrayWrite(bcol, &array));
    1843:       v  = bmata;
    1844:       jj = bmat->j;
    1845:       for (j = 0; j < bmat->nz; j++) array[*jj++] += PetscAbsScalar(*v++);
    1846:       PetscCall(VecSetValues(col, aij->B->cmap->n, garray, array, ADD_VALUES));
    1847:       PetscCall(VecRestoreArrayWrite(bcol, &array));
    1848:       PetscCall(VecDestroy(&bcol));
    1849:       PetscCall(VecAssemblyBegin(col));
    1850:       PetscCall(VecAssemblyEnd(col));
    1851:       PetscCall(VecNorm(col, NORM_INFINITY, norm));
    1852:       PetscCall(VecDestroy(&col));
    1853:     } else if (type == NORM_INFINITY) { /* max row norm */
    1854:       PetscReal ntemp = 0.0;
    1855:       for (j = 0; j < aij->A->rmap->n; j++) {
    1856:         v   = PetscSafePointerPlusOffset(amata, amat->i[j]);
    1857:         sum = 0.0;
    1858:         for (i = 0; i < amat->i[j + 1] - amat->i[j]; i++) {
    1859:           sum += PetscAbsScalar(*v);
    1860:           v++;
    1861:         }
    1862:         v = PetscSafePointerPlusOffset(bmata, bmat->i[j]);
    1863:         for (i = 0; i < bmat->i[j + 1] - bmat->i[j]; i++) {
    1864:           sum += PetscAbsScalar(*v);
    1865:           v++;
    1866:         }
    1867:         if (sum > ntemp) ntemp = sum;
    1868:       }
    1869:       PetscCallMPI(MPIU_Allreduce(&ntemp, norm, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)mat)));
    1870:       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
    1871:     } else SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "No support for two norm");
    1872:     PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &amata));
    1873:     PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &bmata));
    1874:   }
    1875:   PetscFunctionReturn(PETSC_SUCCESS);
    1876: }

    1878: static PetscErrorCode MatTranspose_MPIAIJ(Mat A, MatReuse reuse, Mat *matout)
    1879: {
    1880:   Mat_MPIAIJ      *a    = (Mat_MPIAIJ *)A->data, *b;
    1881:   Mat_SeqAIJ      *Aloc = (Mat_SeqAIJ *)a->A->data, *Bloc = (Mat_SeqAIJ *)a->B->data, *sub_B_diag;
    1882:   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;
    1883:   const PetscInt  *ai, *aj, *bi, *bj, *B_diag_i;
    1884:   Mat              B, A_diag, *B_diag;
    1885:   const MatScalar *pbv, *bv;

    1887:   PetscFunctionBegin;
    1888:   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *matout));
    1889:   ma = A->rmap->n;
    1890:   na = A->cmap->n;
    1891:   mb = a->B->rmap->n;
    1892:   nb = a->B->cmap->n;
    1893:   ai = Aloc->i;
    1894:   aj = Aloc->j;
    1895:   bi = Bloc->i;
    1896:   bj = Bloc->j;
    1897:   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
    1898:     PetscInt            *d_nnz, *g_nnz, *o_nnz;
    1899:     PetscSFNode         *oloc;
    1900:     PETSC_UNUSED PetscSF sf;

    1902:     PetscCall(PetscMalloc4(na, &d_nnz, na, &o_nnz, nb, &g_nnz, nb, &oloc));
    1903:     /* compute d_nnz for preallocation */
    1904:     PetscCall(PetscArrayzero(d_nnz, na));
    1905:     for (i = 0; i < ai[ma]; i++) d_nnz[aj[i]]++;
    1906:     /* compute local off-diagonal contributions */
    1907:     PetscCall(PetscArrayzero(g_nnz, nb));
    1908:     for (i = 0; i < bi[ma]; i++) g_nnz[bj[i]]++;
    1909:     /* map those to global */
    1910:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1911:     PetscCall(PetscSFSetGraphLayout(sf, A->cmap, nb, NULL, PETSC_USE_POINTER, a->garray));
    1912:     PetscCall(PetscSFSetFromOptions(sf));
    1913:     PetscCall(PetscArrayzero(o_nnz, na));
    1914:     PetscCall(PetscSFReduceBegin(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
    1915:     PetscCall(PetscSFReduceEnd(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
    1916:     PetscCall(PetscSFDestroy(&sf));

    1918:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    1919:     PetscCall(MatSetSizes(B, A->cmap->n, A->rmap->n, N, M));
    1920:     PetscCall(MatSetBlockSizes(B, A->cmap->bs, A->rmap->bs));
    1921:     PetscCall(MatSetType(B, ((PetscObject)A)->type_name));
    1922:     PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
    1923:     PetscCall(PetscFree4(d_nnz, o_nnz, g_nnz, oloc));
    1924:   } else {
    1925:     B = *matout;
    1926:     PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
    1927:   }

    1929:   b           = (Mat_MPIAIJ *)B->data;
    1930:   A_diag      = a->A;
    1931:   B_diag      = &b->A;
    1932:   sub_B_diag  = (Mat_SeqAIJ *)(*B_diag)->data;
    1933:   A_diag_ncol = A_diag->cmap->N;
    1934:   B_diag_ilen = sub_B_diag->ilen;
    1935:   B_diag_i    = sub_B_diag->i;

    1937:   /* Set ilen for diagonal of B */
    1938:   for (i = 0; i < A_diag_ncol; i++) B_diag_ilen[i] = B_diag_i[i + 1] - B_diag_i[i];

    1940:   /* Transpose the diagonal part of the matrix. In contrast to the off-diagonal part, this can be done
    1941:   very quickly (=without using MatSetValues), because all writes are local. */
    1942:   PetscCall(MatTransposeSetPrecursor(A_diag, *B_diag));
    1943:   PetscCall(MatTranspose(A_diag, MAT_REUSE_MATRIX, B_diag));

    1945:   /* copy over the B part */
    1946:   PetscCall(PetscMalloc1(bi[mb], &cols));
    1947:   PetscCall(MatSeqAIJGetArrayRead(a->B, &bv));
    1948:   pbv = bv;
    1949:   row = A->rmap->rstart;
    1950:   for (i = 0; i < bi[mb]; i++) cols[i] = a->garray[bj[i]];
    1951:   cols_tmp = cols;
    1952:   for (i = 0; i < mb; i++) {
    1953:     ncol = bi[i + 1] - bi[i];
    1954:     PetscCall(MatSetValues(B, ncol, cols_tmp, 1, &row, pbv, INSERT_VALUES));
    1955:     row++;
    1956:     if (pbv) pbv += ncol;
    1957:     if (cols_tmp) cols_tmp += ncol;
    1958:   }
    1959:   PetscCall(PetscFree(cols));
    1960:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &bv));

    1962:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    1963:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    1964:   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
    1965:     *matout = B;
    1966:   } else {
    1967:     PetscCall(MatHeaderMerge(A, &B));
    1968:   }
    1969:   PetscFunctionReturn(PETSC_SUCCESS);
    1970: }

    1972: static PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat, Vec ll, Vec rr)
    1973: {
    1974:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    1975:   Mat         a = aij->A, b = aij->B;
    1976:   PetscInt    s1, s2, s3;

    1978:   PetscFunctionBegin;
    1979:   PetscCall(MatGetLocalSize(mat, &s2, &s3));
    1980:   if (rr) {
    1981:     PetscCall(VecGetLocalSize(rr, &s1));
    1982:     PetscCheck(s1 == s3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "right vector non-conforming local size");
    1983:     /* Overlap communication with computation. */
    1984:     PetscCall(VecScatterBegin(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1985:   }
    1986:   if (ll) {
    1987:     PetscCall(VecGetLocalSize(ll, &s1));
    1988:     PetscCheck(s1 == s2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "left vector non-conforming local size");
    1989:     PetscUseTypeMethod(b, diagonalscale, ll, NULL);
    1990:   }
    1991:   /* scale  the diagonal block */
    1992:   PetscUseTypeMethod(a, diagonalscale, ll, rr);

    1994:   if (rr) {
    1995:     /* Do a scatter end and then right scale the off-diagonal block */
    1996:     PetscCall(VecScatterEnd(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1997:     PetscUseTypeMethod(b, diagonalscale, NULL, aij->lvec);
    1998:   }
    1999:   PetscFunctionReturn(PETSC_SUCCESS);
    2000: }

    2002: static PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
    2003: {
    2004:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2006:   PetscFunctionBegin;
    2007:   PetscCall(MatSetUnfactored(a->A));
    2008:   PetscFunctionReturn(PETSC_SUCCESS);
    2009: }

    2011: static PetscErrorCode MatEqual_MPIAIJ(Mat A, Mat B, PetscBool *flag)
    2012: {
    2013:   Mat_MPIAIJ *matB = (Mat_MPIAIJ *)B->data, *matA = (Mat_MPIAIJ *)A->data;
    2014:   Mat         a, b, c, d;
    2015:   PetscBool   flg;

    2017:   PetscFunctionBegin;
    2018:   a = matA->A;
    2019:   b = matA->B;
    2020:   c = matB->A;
    2021:   d = matB->B;

    2023:   PetscCall(MatEqual(a, c, &flg));
    2024:   if (flg) PetscCall(MatEqual(b, d, &flg));
    2025:   PetscCallMPI(MPIU_Allreduce(&flg, flag, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
    2026:   PetscFunctionReturn(PETSC_SUCCESS);
    2027: }

    2029: static PetscErrorCode MatCopy_MPIAIJ(Mat A, Mat B, MatStructure str)
    2030: {
    2031:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    2032:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;

    2034:   PetscFunctionBegin;
    2035:   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
    2036:   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
    2037:     /* because of the column compression in the off-processor part of the matrix a->B,
    2038:        the number of columns in a->B and b->B may be different, hence we cannot call
    2039:        the MatCopy() directly on the two parts. If need be, we can provide a more
    2040:        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
    2041:        then copying the submatrices */
    2042:     PetscCall(MatCopy_Basic(A, B, str));
    2043:   } else {
    2044:     PetscCall(MatCopy(a->A, b->A, str));
    2045:     PetscCall(MatCopy(a->B, b->B, str));
    2046:   }
    2047:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    2048:   PetscFunctionReturn(PETSC_SUCCESS);
    2049: }

    2051: /*
    2052:    Computes the number of nonzeros per row needed for preallocation when X and Y
    2053:    have different nonzero structure.
    2054: */
    2055: 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)
    2056: {
    2057:   PetscInt i, j, k, nzx, nzy;

    2059:   PetscFunctionBegin;
    2060:   /* Set the number of nonzeros in the new matrix */
    2061:   for (i = 0; i < m; i++) {
    2062:     const PetscInt *xjj = PetscSafePointerPlusOffset(xj, xi[i]), *yjj = PetscSafePointerPlusOffset(yj, yi[i]);
    2063:     nzx    = xi[i + 1] - xi[i];
    2064:     nzy    = yi[i + 1] - yi[i];
    2065:     nnz[i] = 0;
    2066:     for (j = 0, k = 0; j < nzx; j++) {                                /* Point in X */
    2067:       for (; k < nzy && yltog[yjj[k]] < xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
    2068:       if (k < nzy && yltog[yjj[k]] == xltog[xjj[j]]) k++;             /* Skip duplicate */
    2069:       nnz[i]++;
    2070:     }
    2071:     for (; k < nzy; k++) nnz[i]++;
    2072:   }
    2073:   PetscFunctionReturn(PETSC_SUCCESS);
    2074: }

    2076: /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
    2077: static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y, const PetscInt *yltog, Mat X, const PetscInt *xltog, PetscInt *nnz)
    2078: {
    2079:   PetscInt    m = Y->rmap->N;
    2080:   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data;
    2081:   Mat_SeqAIJ *y = (Mat_SeqAIJ *)Y->data;

    2083:   PetscFunctionBegin;
    2084:   PetscCall(MatAXPYGetPreallocation_MPIX_private(m, x->i, x->j, xltog, y->i, y->j, yltog, nnz));
    2085:   PetscFunctionReturn(PETSC_SUCCESS);
    2086: }

    2088: static PetscErrorCode MatAXPY_MPIAIJ(Mat Y, PetscScalar a, Mat X, MatStructure str)
    2089: {
    2090:   Mat_MPIAIJ *xx = (Mat_MPIAIJ *)X->data, *yy = (Mat_MPIAIJ *)Y->data;

    2092:   PetscFunctionBegin;
    2093:   if (str == SAME_NONZERO_PATTERN) {
    2094:     PetscCall(MatAXPY(yy->A, a, xx->A, str));
    2095:     PetscCall(MatAXPY(yy->B, a, xx->B, str));
    2096:   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
    2097:     PetscCall(MatAXPY_Basic(Y, a, X, str));
    2098:   } else {
    2099:     Mat       B;
    2100:     PetscInt *nnz_d, *nnz_o;

    2102:     PetscCall(PetscMalloc1(yy->A->rmap->N, &nnz_d));
    2103:     PetscCall(PetscMalloc1(yy->B->rmap->N, &nnz_o));
    2104:     PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
    2105:     PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
    2106:     PetscCall(MatSetLayouts(B, Y->rmap, Y->cmap));
    2107:     PetscCall(MatSetType(B, ((PetscObject)Y)->type_name));
    2108:     PetscCall(MatAXPYGetPreallocation_SeqAIJ(yy->A, xx->A, nnz_d));
    2109:     PetscCall(MatAXPYGetPreallocation_MPIAIJ(yy->B, yy->garray, xx->B, xx->garray, nnz_o));
    2110:     PetscCall(MatMPIAIJSetPreallocation(B, 0, nnz_d, 0, nnz_o));
    2111:     PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
    2112:     PetscCall(MatHeaderMerge(Y, &B));
    2113:     PetscCall(PetscFree(nnz_d));
    2114:     PetscCall(PetscFree(nnz_o));
    2115:   }
    2116:   PetscFunctionReturn(PETSC_SUCCESS);
    2117: }

    2119: PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat);

    2121: static PetscErrorCode MatConjugate_MPIAIJ(Mat mat)
    2122: {
    2123:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2125:   PetscFunctionBegin;
    2126:   PetscCall(MatConjugate_SeqAIJ(aij->A));
    2127:   PetscCall(MatConjugate_SeqAIJ(aij->B));
    2128:   PetscFunctionReturn(PETSC_SUCCESS);
    2129: }

    2131: static PetscErrorCode MatRealPart_MPIAIJ(Mat A)
    2132: {
    2133:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2135:   PetscFunctionBegin;
    2136:   PetscCall(MatRealPart(a->A));
    2137:   PetscCall(MatRealPart(a->B));
    2138:   PetscFunctionReturn(PETSC_SUCCESS);
    2139: }

    2141: static PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
    2142: {
    2143:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2145:   PetscFunctionBegin;
    2146:   PetscCall(MatImaginaryPart(a->A));
    2147:   PetscCall(MatImaginaryPart(a->B));
    2148:   PetscFunctionReturn(PETSC_SUCCESS);
    2149: }

    2151: static PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2152: {
    2153:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
    2154:   PetscInt           i, *idxb = NULL, m = A->rmap->n;
    2155:   PetscScalar       *vv;
    2156:   Vec                vB, vA;
    2157:   const PetscScalar *va, *vb;

    2159:   PetscFunctionBegin;
    2160:   PetscCall(MatCreateVecs(a->A, NULL, &vA));
    2161:   PetscCall(MatGetRowMaxAbs(a->A, vA, idx));

    2163:   PetscCall(VecGetArrayRead(vA, &va));
    2164:   if (idx) {
    2165:     for (i = 0; i < m; i++) {
    2166:       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
    2167:     }
    2168:   }

    2170:   PetscCall(MatCreateVecs(a->B, NULL, &vB));
    2171:   PetscCall(PetscMalloc1(m, &idxb));
    2172:   PetscCall(MatGetRowMaxAbs(a->B, vB, idxb));

    2174:   PetscCall(VecGetArrayWrite(v, &vv));
    2175:   PetscCall(VecGetArrayRead(vB, &vb));
    2176:   for (i = 0; i < m; i++) {
    2177:     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
    2178:       vv[i] = vb[i];
    2179:       if (idx) idx[i] = a->garray[idxb[i]];
    2180:     } else {
    2181:       vv[i] = va[i];
    2182:       if (idx && PetscAbsScalar(va[i]) == PetscAbsScalar(vb[i]) && idxb[i] != -1 && idx[i] > a->garray[idxb[i]]) idx[i] = a->garray[idxb[i]];
    2183:     }
    2184:   }
    2185:   PetscCall(VecRestoreArrayWrite(v, &vv));
    2186:   PetscCall(VecRestoreArrayRead(vA, &va));
    2187:   PetscCall(VecRestoreArrayRead(vB, &vb));
    2188:   PetscCall(PetscFree(idxb));
    2189:   PetscCall(VecDestroy(&vA));
    2190:   PetscCall(VecDestroy(&vB));
    2191:   PetscFunctionReturn(PETSC_SUCCESS);
    2192: }

    2194: static PetscErrorCode MatGetRowSumAbs_MPIAIJ(Mat A, Vec v)
    2195: {
    2196:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    2197:   Vec         vB, vA;

    2199:   PetscFunctionBegin;
    2200:   PetscCall(MatCreateVecs(a->A, NULL, &vA));
    2201:   PetscCall(MatGetRowSumAbs(a->A, vA));
    2202:   PetscCall(MatCreateVecs(a->B, NULL, &vB));
    2203:   PetscCall(MatGetRowSumAbs(a->B, vB));
    2204:   PetscCall(VecAXPY(vA, 1.0, vB));
    2205:   PetscCall(VecDestroy(&vB));
    2206:   PetscCall(VecCopy(vA, v));
    2207:   PetscCall(VecDestroy(&vA));
    2208:   PetscFunctionReturn(PETSC_SUCCESS);
    2209: }

    2211: static PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2212: {
    2213:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2214:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2215:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2216:   PetscInt          *cmap = mat->garray;
    2217:   PetscInt          *diagIdx, *offdiagIdx;
    2218:   Vec                diagV, offdiagV;
    2219:   PetscScalar       *a, *diagA, *offdiagA;
    2220:   const PetscScalar *ba, *bav;
    2221:   PetscInt           r, j, col, ncols, *bi, *bj;
    2222:   Mat                B = mat->B;
    2223:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2225:   PetscFunctionBegin;
    2226:   /* When a process holds entire A and other processes have no entry */
    2227:   if (A->cmap->N == n) {
    2228:     PetscCall(VecGetArrayWrite(v, &diagA));
    2229:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2230:     PetscCall(MatGetRowMinAbs(mat->A, diagV, idx));
    2231:     PetscCall(VecDestroy(&diagV));
    2232:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2233:     PetscFunctionReturn(PETSC_SUCCESS);
    2234:   } else if (n == 0) {
    2235:     if (m) {
    2236:       PetscCall(VecGetArrayWrite(v, &a));
    2237:       for (r = 0; r < m; r++) {
    2238:         a[r] = 0.0;
    2239:         if (idx) idx[r] = -1;
    2240:       }
    2241:       PetscCall(VecRestoreArrayWrite(v, &a));
    2242:     }
    2243:     PetscFunctionReturn(PETSC_SUCCESS);
    2244:   }

    2246:   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
    2247:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2248:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2249:   PetscCall(MatGetRowMinAbs(mat->A, diagV, diagIdx));

    2251:   /* Get offdiagIdx[] for implicit 0.0 */
    2252:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2253:   ba = bav;
    2254:   bi = b->i;
    2255:   bj = b->j;
    2256:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2257:   for (r = 0; r < m; r++) {
    2258:     ncols = bi[r + 1] - bi[r];
    2259:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2260:       offdiagA[r]   = *ba;
    2261:       offdiagIdx[r] = cmap[0];
    2262:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2263:       offdiagA[r] = 0.0;

    2265:       /* Find first hole in the cmap */
    2266:       for (j = 0; j < ncols; j++) {
    2267:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2268:         if (col > j && j < cstart) {
    2269:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2270:           break;
    2271:         } else if (col > j + n && j >= cstart) {
    2272:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2273:           break;
    2274:         }
    2275:       }
    2276:       if (j == ncols && ncols < A->cmap->N - n) {
    2277:         /* a hole is outside compressed Bcols */
    2278:         if (ncols == 0) {
    2279:           if (cstart) {
    2280:             offdiagIdx[r] = 0;
    2281:           } else offdiagIdx[r] = cend;
    2282:         } else { /* ncols > 0 */
    2283:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2284:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2285:         }
    2286:       }
    2287:     }

    2289:     for (j = 0; j < ncols; j++) {
    2290:       if (PetscAbsScalar(offdiagA[r]) > PetscAbsScalar(*ba)) {
    2291:         offdiagA[r]   = *ba;
    2292:         offdiagIdx[r] = cmap[*bj];
    2293:       }
    2294:       ba++;
    2295:       bj++;
    2296:     }
    2297:   }

    2299:   PetscCall(VecGetArrayWrite(v, &a));
    2300:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2301:   for (r = 0; r < m; ++r) {
    2302:     if (PetscAbsScalar(diagA[r]) < PetscAbsScalar(offdiagA[r])) {
    2303:       a[r] = diagA[r];
    2304:       if (idx) idx[r] = cstart + diagIdx[r];
    2305:     } else if (PetscAbsScalar(diagA[r]) == PetscAbsScalar(offdiagA[r])) {
    2306:       a[r] = diagA[r];
    2307:       if (idx) {
    2308:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2309:           idx[r] = cstart + diagIdx[r];
    2310:         } else idx[r] = offdiagIdx[r];
    2311:       }
    2312:     } else {
    2313:       a[r] = offdiagA[r];
    2314:       if (idx) idx[r] = offdiagIdx[r];
    2315:     }
    2316:   }
    2317:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2318:   PetscCall(VecRestoreArrayWrite(v, &a));
    2319:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2320:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2321:   PetscCall(VecDestroy(&diagV));
    2322:   PetscCall(VecDestroy(&offdiagV));
    2323:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2324:   PetscFunctionReturn(PETSC_SUCCESS);
    2325: }

    2327: static PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2328: {
    2329:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2330:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2331:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2332:   PetscInt          *cmap = mat->garray;
    2333:   PetscInt          *diagIdx, *offdiagIdx;
    2334:   Vec                diagV, offdiagV;
    2335:   PetscScalar       *a, *diagA, *offdiagA;
    2336:   const PetscScalar *ba, *bav;
    2337:   PetscInt           r, j, col, ncols, *bi, *bj;
    2338:   Mat                B = mat->B;
    2339:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2341:   PetscFunctionBegin;
    2342:   /* When a process holds entire A and other processes have no entry */
    2343:   if (A->cmap->N == n) {
    2344:     PetscCall(VecGetArrayWrite(v, &diagA));
    2345:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2346:     PetscCall(MatGetRowMin(mat->A, diagV, idx));
    2347:     PetscCall(VecDestroy(&diagV));
    2348:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2349:     PetscFunctionReturn(PETSC_SUCCESS);
    2350:   } else if (n == 0) {
    2351:     if (m) {
    2352:       PetscCall(VecGetArrayWrite(v, &a));
    2353:       for (r = 0; r < m; r++) {
    2354:         a[r] = PETSC_MAX_REAL;
    2355:         if (idx) idx[r] = -1;
    2356:       }
    2357:       PetscCall(VecRestoreArrayWrite(v, &a));
    2358:     }
    2359:     PetscFunctionReturn(PETSC_SUCCESS);
    2360:   }

    2362:   PetscCall(PetscCalloc2(m, &diagIdx, m, &offdiagIdx));
    2363:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2364:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2365:   PetscCall(MatGetRowMin(mat->A, diagV, diagIdx));

    2367:   /* Get offdiagIdx[] for implicit 0.0 */
    2368:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2369:   ba = bav;
    2370:   bi = b->i;
    2371:   bj = b->j;
    2372:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2373:   for (r = 0; r < m; r++) {
    2374:     ncols = bi[r + 1] - bi[r];
    2375:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2376:       offdiagA[r]   = *ba;
    2377:       offdiagIdx[r] = cmap[0];
    2378:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2379:       offdiagA[r] = 0.0;

    2381:       /* Find first hole in the cmap */
    2382:       for (j = 0; j < ncols; j++) {
    2383:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2384:         if (col > j && j < cstart) {
    2385:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2386:           break;
    2387:         } else if (col > j + n && j >= cstart) {
    2388:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2389:           break;
    2390:         }
    2391:       }
    2392:       if (j == ncols && ncols < A->cmap->N - n) {
    2393:         /* a hole is outside compressed Bcols */
    2394:         if (ncols == 0) {
    2395:           if (cstart) {
    2396:             offdiagIdx[r] = 0;
    2397:           } else offdiagIdx[r] = cend;
    2398:         } else { /* ncols > 0 */
    2399:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2400:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2401:         }
    2402:       }
    2403:     }

    2405:     for (j = 0; j < ncols; j++) {
    2406:       if (PetscRealPart(offdiagA[r]) > PetscRealPart(*ba)) {
    2407:         offdiagA[r]   = *ba;
    2408:         offdiagIdx[r] = cmap[*bj];
    2409:       }
    2410:       ba++;
    2411:       bj++;
    2412:     }
    2413:   }

    2415:   PetscCall(VecGetArrayWrite(v, &a));
    2416:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2417:   for (r = 0; r < m; ++r) {
    2418:     if (PetscRealPart(diagA[r]) < PetscRealPart(offdiagA[r])) {
    2419:       a[r] = diagA[r];
    2420:       if (idx) idx[r] = cstart + diagIdx[r];
    2421:     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
    2422:       a[r] = diagA[r];
    2423:       if (idx) {
    2424:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2425:           idx[r] = cstart + diagIdx[r];
    2426:         } else idx[r] = offdiagIdx[r];
    2427:       }
    2428:     } else {
    2429:       a[r] = offdiagA[r];
    2430:       if (idx) idx[r] = offdiagIdx[r];
    2431:     }
    2432:   }
    2433:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2434:   PetscCall(VecRestoreArrayWrite(v, &a));
    2435:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2436:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2437:   PetscCall(VecDestroy(&diagV));
    2438:   PetscCall(VecDestroy(&offdiagV));
    2439:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2440:   PetscFunctionReturn(PETSC_SUCCESS);
    2441: }

    2443: static PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2444: {
    2445:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2446:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2447:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2448:   PetscInt          *cmap = mat->garray;
    2449:   PetscInt          *diagIdx, *offdiagIdx;
    2450:   Vec                diagV, offdiagV;
    2451:   PetscScalar       *a, *diagA, *offdiagA;
    2452:   const PetscScalar *ba, *bav;
    2453:   PetscInt           r, j, col, ncols, *bi, *bj;
    2454:   Mat                B = mat->B;
    2455:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2457:   PetscFunctionBegin;
    2458:   /* When a process holds entire A and other processes have no entry */
    2459:   if (A->cmap->N == n) {
    2460:     PetscCall(VecGetArrayWrite(v, &diagA));
    2461:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2462:     PetscCall(MatGetRowMax(mat->A, diagV, idx));
    2463:     PetscCall(VecDestroy(&diagV));
    2464:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2465:     PetscFunctionReturn(PETSC_SUCCESS);
    2466:   } else if (n == 0) {
    2467:     if (m) {
    2468:       PetscCall(VecGetArrayWrite(v, &a));
    2469:       for (r = 0; r < m; r++) {
    2470:         a[r] = PETSC_MIN_REAL;
    2471:         if (idx) idx[r] = -1;
    2472:       }
    2473:       PetscCall(VecRestoreArrayWrite(v, &a));
    2474:     }
    2475:     PetscFunctionReturn(PETSC_SUCCESS);
    2476:   }

    2478:   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
    2479:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2480:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2481:   PetscCall(MatGetRowMax(mat->A, diagV, diagIdx));

    2483:   /* Get offdiagIdx[] for implicit 0.0 */
    2484:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2485:   ba = bav;
    2486:   bi = b->i;
    2487:   bj = b->j;
    2488:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2489:   for (r = 0; r < m; r++) {
    2490:     ncols = bi[r + 1] - bi[r];
    2491:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2492:       offdiagA[r]   = *ba;
    2493:       offdiagIdx[r] = cmap[0];
    2494:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2495:       offdiagA[r] = 0.0;

    2497:       /* Find first hole in the cmap */
    2498:       for (j = 0; j < ncols; j++) {
    2499:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2500:         if (col > j && j < cstart) {
    2501:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2502:           break;
    2503:         } else if (col > j + n && j >= cstart) {
    2504:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2505:           break;
    2506:         }
    2507:       }
    2508:       if (j == ncols && ncols < A->cmap->N - n) {
    2509:         /* a hole is outside compressed Bcols */
    2510:         if (ncols == 0) {
    2511:           if (cstart) {
    2512:             offdiagIdx[r] = 0;
    2513:           } else offdiagIdx[r] = cend;
    2514:         } else { /* ncols > 0 */
    2515:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2516:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2517:         }
    2518:       }
    2519:     }

    2521:     for (j = 0; j < ncols; j++) {
    2522:       if (PetscRealPart(offdiagA[r]) < PetscRealPart(*ba)) {
    2523:         offdiagA[r]   = *ba;
    2524:         offdiagIdx[r] = cmap[*bj];
    2525:       }
    2526:       ba++;
    2527:       bj++;
    2528:     }
    2529:   }

    2531:   PetscCall(VecGetArrayWrite(v, &a));
    2532:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2533:   for (r = 0; r < m; ++r) {
    2534:     if (PetscRealPart(diagA[r]) > PetscRealPart(offdiagA[r])) {
    2535:       a[r] = diagA[r];
    2536:       if (idx) idx[r] = cstart + diagIdx[r];
    2537:     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
    2538:       a[r] = diagA[r];
    2539:       if (idx) {
    2540:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2541:           idx[r] = cstart + diagIdx[r];
    2542:         } else idx[r] = offdiagIdx[r];
    2543:       }
    2544:     } else {
    2545:       a[r] = offdiagA[r];
    2546:       if (idx) idx[r] = offdiagIdx[r];
    2547:     }
    2548:   }
    2549:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2550:   PetscCall(VecRestoreArrayWrite(v, &a));
    2551:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2552:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2553:   PetscCall(VecDestroy(&diagV));
    2554:   PetscCall(VecDestroy(&offdiagV));
    2555:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2556:   PetscFunctionReturn(PETSC_SUCCESS);
    2557: }

    2559: PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat, Mat *newmat)
    2560: {
    2561:   Mat *dummy;

    2563:   PetscFunctionBegin;
    2564:   PetscCall(MatCreateSubMatrix_MPIAIJ_All(mat, MAT_DO_NOT_GET_VALUES, MAT_INITIAL_MATRIX, &dummy));
    2565:   *newmat = *dummy;
    2566:   PetscCall(PetscFree(dummy));
    2567:   PetscFunctionReturn(PETSC_SUCCESS);
    2568: }

    2570: static PetscErrorCode MatInvertBlockDiagonal_MPIAIJ(Mat A, const PetscScalar **values)
    2571: {
    2572:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2574:   PetscFunctionBegin;
    2575:   PetscCall(MatInvertBlockDiagonal(a->A, values));
    2576:   A->factorerrortype = a->A->factorerrortype;
    2577:   PetscFunctionReturn(PETSC_SUCCESS);
    2578: }

    2580: static PetscErrorCode MatSetRandom_MPIAIJ(Mat x, PetscRandom rctx)
    2581: {
    2582:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)x->data;

    2584:   PetscFunctionBegin;
    2585:   PetscCheck(x->assembled || x->preallocated, PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_WRONGSTATE, "MatSetRandom on an unassembled and unpreallocated MATMPIAIJ is not allowed");
    2586:   PetscCall(MatSetRandom(aij->A, rctx));
    2587:   if (x->assembled) {
    2588:     PetscCall(MatSetRandom(aij->B, rctx));
    2589:   } else {
    2590:     PetscCall(MatSetRandomSkipColumnRange_SeqAIJ_Private(aij->B, x->cmap->rstart, x->cmap->rend, rctx));
    2591:   }
    2592:   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
    2593:   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
    2594:   PetscFunctionReturn(PETSC_SUCCESS);
    2595: }

    2597: static PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A, PetscBool sc)
    2598: {
    2599:   PetscFunctionBegin;
    2600:   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
    2601:   else A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ;
    2602:   PetscFunctionReturn(PETSC_SUCCESS);
    2603: }

    2605: /*@
    2606:   MatMPIAIJGetNumberNonzeros - gets the number of nonzeros in the matrix on this MPI rank

    2608:   Not Collective

    2610:   Input Parameter:
    2611: . A - the matrix

    2613:   Output Parameter:
    2614: . nz - the number of nonzeros

    2616:   Level: advanced

    2618: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
    2619: @*/
    2620: PetscErrorCode MatMPIAIJGetNumberNonzeros(Mat A, PetscCount *nz)
    2621: {
    2622:   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)A->data;
    2623:   Mat_SeqAIJ *aaij = (Mat_SeqAIJ *)maij->A->data, *baij = (Mat_SeqAIJ *)maij->B->data;
    2624:   PetscBool   isaij;

    2626:   PetscFunctionBegin;
    2627:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIAIJ, &isaij));
    2628:   PetscCheck(isaij, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for type %s", ((PetscObject)A)->type_name);
    2629:   *nz = aaij->i[A->rmap->n] + baij->i[A->rmap->n];
    2630:   PetscFunctionReturn(PETSC_SUCCESS);
    2631: }

    2633: /*@
    2634:   MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap

    2636:   Collective

    2638:   Input Parameters:
    2639: + A  - the matrix
    2640: - sc - `PETSC_TRUE` indicates use the scalable algorithm (default is not to use the scalable algorithm)

    2642:   Level: advanced

    2644: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
    2645: @*/
    2646: PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A, PetscBool sc)
    2647: {
    2648:   PetscFunctionBegin;
    2649:   PetscTryMethod(A, "MatMPIAIJSetUseScalableIncreaseOverlap_C", (Mat, PetscBool), (A, sc));
    2650:   PetscFunctionReturn(PETSC_SUCCESS);
    2651: }

    2653: PetscErrorCode MatSetFromOptions_MPIAIJ(Mat A, PetscOptionItems PetscOptionsObject)
    2654: {
    2655:   PetscBool sc = PETSC_FALSE, flg;

    2657:   PetscFunctionBegin;
    2658:   PetscOptionsHeadBegin(PetscOptionsObject, "MPIAIJ options");
    2659:   if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
    2660:   PetscCall(PetscOptionsBool("-mat_increase_overlap_scalable", "Use a scalable algorithm to compute the overlap", "MatIncreaseOverlap", sc, &sc, &flg));
    2661:   if (flg) PetscCall(MatMPIAIJSetUseScalableIncreaseOverlap(A, sc));
    2662:   PetscOptionsHeadEnd();
    2663:   PetscFunctionReturn(PETSC_SUCCESS);
    2664: }

    2666: static PetscErrorCode MatShift_MPIAIJ(Mat Y, PetscScalar a)
    2667: {
    2668:   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)Y->data;
    2669:   Mat_SeqAIJ *aij  = (Mat_SeqAIJ *)maij->A->data;

    2671:   PetscFunctionBegin;
    2672:   if (!Y->preallocated) {
    2673:     PetscCall(MatMPIAIJSetPreallocation(Y, 1, NULL, 0, NULL));
    2674:   } else if (!aij->nz) { /* It does not matter if diagonals of Y only partially lie in maij->A. We just need an estimated preallocation. */
    2675:     PetscInt nonew = aij->nonew;
    2676:     PetscCall(MatSeqAIJSetPreallocation(maij->A, 1, NULL));
    2677:     aij->nonew = nonew;
    2678:   }
    2679:   PetscCall(MatShift_Basic(Y, a));
    2680:   PetscFunctionReturn(PETSC_SUCCESS);
    2681: }

    2683: static PetscErrorCode MatInvertVariableBlockDiagonal_MPIAIJ(Mat A, PetscInt nblocks, const PetscInt *bsizes, PetscScalar *diag)
    2684: {
    2685:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2687:   PetscFunctionBegin;
    2688:   PetscCall(MatInvertVariableBlockDiagonal(a->A, nblocks, bsizes, diag));
    2689:   PetscFunctionReturn(PETSC_SUCCESS);
    2690: }

    2692: static PetscErrorCode MatEliminateZeros_MPIAIJ(Mat A, PetscBool keep)
    2693: {
    2694:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2696:   PetscFunctionBegin;
    2697:   PetscCall(MatEliminateZeros_SeqAIJ(a->A, keep));        // possibly keep zero diagonal coefficients
    2698:   PetscCall(MatEliminateZeros_SeqAIJ(a->B, PETSC_FALSE)); // never keep zero diagonal coefficients
    2699:   PetscFunctionReturn(PETSC_SUCCESS);
    2700: }

    2702: static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
    2703:                                        MatGetRow_MPIAIJ,
    2704:                                        MatRestoreRow_MPIAIJ,
    2705:                                        MatMult_MPIAIJ,
    2706:                                        /* 4*/ MatMultAdd_MPIAIJ,
    2707:                                        MatMultTranspose_MPIAIJ,
    2708:                                        MatMultTransposeAdd_MPIAIJ,
    2709:                                        NULL,
    2710:                                        NULL,
    2711:                                        NULL,
    2712:                                        /*10*/ NULL,
    2713:                                        NULL,
    2714:                                        NULL,
    2715:                                        MatSOR_MPIAIJ,
    2716:                                        MatTranspose_MPIAIJ,
    2717:                                        /*15*/ MatGetInfo_MPIAIJ,
    2718:                                        MatEqual_MPIAIJ,
    2719:                                        MatGetDiagonal_MPIAIJ,
    2720:                                        MatDiagonalScale_MPIAIJ,
    2721:                                        MatNorm_MPIAIJ,
    2722:                                        /*20*/ MatAssemblyBegin_MPIAIJ,
    2723:                                        MatAssemblyEnd_MPIAIJ,
    2724:                                        MatSetOption_MPIAIJ,
    2725:                                        MatZeroEntries_MPIAIJ,
    2726:                                        /*24*/ MatZeroRows_MPIAIJ,
    2727:                                        NULL,
    2728:                                        NULL,
    2729:                                        NULL,
    2730:                                        NULL,
    2731:                                        /*29*/ MatSetUp_MPI_Hash,
    2732:                                        NULL,
    2733:                                        NULL,
    2734:                                        MatGetDiagonalBlock_MPIAIJ,
    2735:                                        NULL,
    2736:                                        /*34*/ MatDuplicate_MPIAIJ,
    2737:                                        NULL,
    2738:                                        NULL,
    2739:                                        NULL,
    2740:                                        NULL,
    2741:                                        /*39*/ MatAXPY_MPIAIJ,
    2742:                                        MatCreateSubMatrices_MPIAIJ,
    2743:                                        MatIncreaseOverlap_MPIAIJ,
    2744:                                        MatGetValues_MPIAIJ,
    2745:                                        MatCopy_MPIAIJ,
    2746:                                        /*44*/ MatGetRowMax_MPIAIJ,
    2747:                                        MatScale_MPIAIJ,
    2748:                                        MatShift_MPIAIJ,
    2749:                                        MatDiagonalSet_MPIAIJ,
    2750:                                        MatZeroRowsColumns_MPIAIJ,
    2751:                                        /*49*/ MatSetRandom_MPIAIJ,
    2752:                                        MatGetRowIJ_MPIAIJ,
    2753:                                        MatRestoreRowIJ_MPIAIJ,
    2754:                                        NULL,
    2755:                                        NULL,
    2756:                                        /*54*/ MatFDColoringCreate_MPIXAIJ,
    2757:                                        NULL,
    2758:                                        MatSetUnfactored_MPIAIJ,
    2759:                                        MatPermute_MPIAIJ,
    2760:                                        NULL,
    2761:                                        /*59*/ MatCreateSubMatrix_MPIAIJ,
    2762:                                        MatDestroy_MPIAIJ,
    2763:                                        MatView_MPIAIJ,
    2764:                                        NULL,
    2765:                                        NULL,
    2766:                                        /*64*/ MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
    2767:                                        NULL,
    2768:                                        NULL,
    2769:                                        NULL,
    2770:                                        MatGetRowMaxAbs_MPIAIJ,
    2771:                                        /*69*/ MatGetRowMinAbs_MPIAIJ,
    2772:                                        NULL,
    2773:                                        NULL,
    2774:                                        MatFDColoringApply_AIJ,
    2775:                                        MatSetFromOptions_MPIAIJ,
    2776:                                        MatFindZeroDiagonals_MPIAIJ,
    2777:                                        /*75*/ NULL,
    2778:                                        NULL,
    2779:                                        NULL,
    2780:                                        MatLoad_MPIAIJ,
    2781:                                        NULL,
    2782:                                        /*80*/ NULL,
    2783:                                        NULL,
    2784:                                        NULL,
    2785:                                        /*83*/ NULL,
    2786:                                        NULL,
    2787:                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
    2788:                                        MatPtAPNumeric_MPIAIJ_MPIAIJ,
    2789:                                        NULL,
    2790:                                        NULL,
    2791:                                        /*89*/ MatBindToCPU_MPIAIJ,
    2792:                                        MatProductSetFromOptions_MPIAIJ,
    2793:                                        NULL,
    2794:                                        NULL,
    2795:                                        MatConjugate_MPIAIJ,
    2796:                                        /*94*/ NULL,
    2797:                                        MatSetValuesRow_MPIAIJ,
    2798:                                        MatRealPart_MPIAIJ,
    2799:                                        MatImaginaryPart_MPIAIJ,
    2800:                                        NULL,
    2801:                                        /*99*/ NULL,
    2802:                                        NULL,
    2803:                                        NULL,
    2804:                                        MatGetRowMin_MPIAIJ,
    2805:                                        NULL,
    2806:                                        /*104*/ MatGetSeqNonzeroStructure_MPIAIJ,
    2807:                                        NULL,
    2808:                                        MatGetGhosts_MPIAIJ,
    2809:                                        NULL,
    2810:                                        NULL,
    2811:                                        /*109*/ MatMultDiagonalBlock_MPIAIJ,
    2812:                                        NULL,
    2813:                                        NULL,
    2814:                                        NULL,
    2815:                                        MatGetMultiProcBlock_MPIAIJ,
    2816:                                        /*114*/ MatFindNonzeroRows_MPIAIJ,
    2817:                                        MatGetColumnReductions_MPIAIJ,
    2818:                                        MatInvertBlockDiagonal_MPIAIJ,
    2819:                                        MatInvertVariableBlockDiagonal_MPIAIJ,
    2820:                                        MatCreateSubMatricesMPI_MPIAIJ,
    2821:                                        /*119*/ NULL,
    2822:                                        NULL,
    2823:                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
    2824:                                        NULL,
    2825:                                        NULL,
    2826:                                        /*124*/ NULL,
    2827:                                        NULL,
    2828:                                        MatSetBlockSizes_MPIAIJ,
    2829:                                        NULL,
    2830:                                        MatFDColoringSetUp_MPIXAIJ,
    2831:                                        /*129*/ MatFindOffBlockDiagonalEntries_MPIAIJ,
    2832:                                        MatCreateMPIMatConcatenateSeqMat_MPIAIJ,
    2833:                                        NULL,
    2834:                                        NULL,
    2835:                                        NULL,
    2836:                                        /*134*/ MatCreateGraph_Simple_AIJ,
    2837:                                        NULL,
    2838:                                        MatEliminateZeros_MPIAIJ,
    2839:                                        MatGetRowSumAbs_MPIAIJ,
    2840:                                        NULL,
    2841:                                        /*139*/ NULL,
    2842:                                        NULL,
    2843:                                        MatCopyHashToXAIJ_MPI_Hash,
    2844:                                        MatGetCurrentMemType_MPIAIJ,
    2845:                                        NULL,
    2846:                                        /*144*/ MatADot_Default,
    2847:                                        MatANorm_Default,
    2848:                                        NULL,
    2849:                                        NULL};

    2851: static PetscErrorCode MatStoreValues_MPIAIJ(Mat mat)
    2852: {
    2853:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2855:   PetscFunctionBegin;
    2856:   PetscCall(MatStoreValues(aij->A));
    2857:   PetscCall(MatStoreValues(aij->B));
    2858:   PetscFunctionReturn(PETSC_SUCCESS);
    2859: }

    2861: static PetscErrorCode MatRetrieveValues_MPIAIJ(Mat mat)
    2862: {
    2863:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2865:   PetscFunctionBegin;
    2866:   PetscCall(MatRetrieveValues(aij->A));
    2867:   PetscCall(MatRetrieveValues(aij->B));
    2868:   PetscFunctionReturn(PETSC_SUCCESS);
    2869: }

    2871: PetscErrorCode MatMPIAIJSetPreallocation_MPIAIJ(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
    2872: {
    2873:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
    2874:   PetscMPIInt size;

    2876:   PetscFunctionBegin;
    2877:   if (B->hash_active) {
    2878:     B->ops[0]      = b->cops;
    2879:     B->hash_active = PETSC_FALSE;
    2880:   }
    2881:   PetscCall(PetscLayoutSetUp(B->rmap));
    2882:   PetscCall(PetscLayoutSetUp(B->cmap));

    2884: #if defined(PETSC_USE_CTABLE)
    2885:   PetscCall(PetscHMapIDestroy(&b->colmap));
    2886: #else
    2887:   PetscCall(PetscFree(b->colmap));
    2888: #endif
    2889:   PetscCall(PetscFree(b->garray));
    2890:   PetscCall(VecDestroy(&b->lvec));
    2891:   PetscCall(VecScatterDestroy(&b->Mvctx));

    2893:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

    2895:   MatSeqXAIJGetOptions_Private(b->B);
    2896:   PetscCall(MatDestroy(&b->B));
    2897:   PetscCall(MatCreate(PETSC_COMM_SELF, &b->B));
    2898:   PetscCall(MatSetSizes(b->B, B->rmap->n, size > 1 ? B->cmap->N : 0, B->rmap->n, size > 1 ? B->cmap->N : 0));
    2899:   PetscCall(MatSetBlockSizesFromMats(b->B, B, B));
    2900:   PetscCall(MatSetType(b->B, MATSEQAIJ));
    2901:   MatSeqXAIJRestoreOptions_Private(b->B);

    2903:   MatSeqXAIJGetOptions_Private(b->A);
    2904:   PetscCall(MatDestroy(&b->A));
    2905:   PetscCall(MatCreate(PETSC_COMM_SELF, &b->A));
    2906:   PetscCall(MatSetSizes(b->A, B->rmap->n, B->cmap->n, B->rmap->n, B->cmap->n));
    2907:   PetscCall(MatSetBlockSizesFromMats(b->A, B, B));
    2908:   PetscCall(MatSetType(b->A, MATSEQAIJ));
    2909:   MatSeqXAIJRestoreOptions_Private(b->A);

    2911:   PetscCall(MatSeqAIJSetPreallocation(b->A, d_nz, d_nnz));
    2912:   PetscCall(MatSeqAIJSetPreallocation(b->B, o_nz, o_nnz));
    2913:   B->preallocated  = PETSC_TRUE;
    2914:   B->was_assembled = PETSC_FALSE;
    2915:   B->assembled     = PETSC_FALSE;
    2916:   PetscFunctionReturn(PETSC_SUCCESS);
    2917: }

    2919: static PetscErrorCode MatResetPreallocation_MPIAIJ(Mat B)
    2920: {
    2921:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
    2922:   PetscBool   ondiagreset, offdiagreset, memoryreset;

    2924:   PetscFunctionBegin;
    2926:   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()");
    2927:   if (B->num_ass == 0) PetscFunctionReturn(PETSC_SUCCESS);

    2929:   PetscCall(MatResetPreallocation_SeqAIJ_Private(b->A, &ondiagreset));
    2930:   PetscCall(MatResetPreallocation_SeqAIJ_Private(b->B, &offdiagreset));
    2931:   memoryreset = (PetscBool)(ondiagreset || offdiagreset);
    2932:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &memoryreset, 1, MPI_C_BOOL, MPI_LOR, PetscObjectComm((PetscObject)B)));
    2933:   if (!memoryreset) PetscFunctionReturn(PETSC_SUCCESS);

    2935:   PetscCall(PetscLayoutSetUp(B->rmap));
    2936:   PetscCall(PetscLayoutSetUp(B->cmap));
    2937:   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");
    2938:   PetscCall(MatDisAssemble_MPIAIJ(B, PETSC_TRUE));
    2939:   PetscCall(VecScatterDestroy(&b->Mvctx));

    2941:   B->preallocated  = PETSC_TRUE;
    2942:   B->was_assembled = PETSC_FALSE;
    2943:   B->assembled     = PETSC_FALSE;
    2944:   /* Log that the state of this object has changed; this will help guarantee that preconditioners get re-setup */
    2945:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    2946:   PetscFunctionReturn(PETSC_SUCCESS);
    2947: }

    2949: PetscErrorCode MatDuplicate_MPIAIJ(Mat matin, MatDuplicateOption cpvalues, Mat *newmat)
    2950: {
    2951:   Mat         mat;
    2952:   Mat_MPIAIJ *a, *oldmat = (Mat_MPIAIJ *)matin->data;

    2954:   PetscFunctionBegin;
    2955:   *newmat = NULL;
    2956:   PetscCall(MatCreate(PetscObjectComm((PetscObject)matin), &mat));
    2957:   PetscCall(MatSetSizes(mat, matin->rmap->n, matin->cmap->n, matin->rmap->N, matin->cmap->N));
    2958:   PetscCall(MatSetBlockSizesFromMats(mat, matin, matin));
    2959:   PetscCall(MatSetType(mat, ((PetscObject)matin)->type_name));
    2960:   a = (Mat_MPIAIJ *)mat->data;

    2962:   mat->factortype = matin->factortype;
    2963:   mat->assembled  = matin->assembled;
    2964:   mat->insertmode = NOT_SET_VALUES;

    2966:   a->size         = oldmat->size;
    2967:   a->rank         = oldmat->rank;
    2968:   a->donotstash   = oldmat->donotstash;
    2969:   a->roworiented  = oldmat->roworiented;
    2970:   a->rowindices   = NULL;
    2971:   a->rowvalues    = NULL;
    2972:   a->getrowactive = PETSC_FALSE;

    2974:   PetscCall(PetscLayoutReference(matin->rmap, &mat->rmap));
    2975:   PetscCall(PetscLayoutReference(matin->cmap, &mat->cmap));
    2976:   if (matin->hash_active) PetscCall(MatSetUp(mat));
    2977:   else {
    2978:     mat->preallocated = matin->preallocated;
    2979:     if (oldmat->colmap) {
    2980: #if defined(PETSC_USE_CTABLE)
    2981:       PetscCall(PetscHMapIDuplicate(oldmat->colmap, &a->colmap));
    2982: #else
    2983:       PetscCall(PetscMalloc1(mat->cmap->N, &a->colmap));
    2984:       PetscCall(PetscArraycpy(a->colmap, oldmat->colmap, mat->cmap->N));
    2985: #endif
    2986:     } else a->colmap = NULL;
    2987:     if (oldmat->garray) {
    2988:       PetscInt len;
    2989:       len = oldmat->B->cmap->n;
    2990:       PetscCall(PetscMalloc1(len, &a->garray));
    2991:       if (len) PetscCall(PetscArraycpy(a->garray, oldmat->garray, len));
    2992:     } else a->garray = NULL;

    2994:     /* It may happen MatDuplicate is called with a non-assembled matrix
    2995:       In fact, MatDuplicate only requires the matrix to be preallocated
    2996:       This may happen inside a DMCreateMatrix_Shell */
    2997:     if (oldmat->lvec) PetscCall(VecDuplicate(oldmat->lvec, &a->lvec));
    2998:     if (oldmat->Mvctx) {
    2999:       a->Mvctx = oldmat->Mvctx;
    3000:       PetscCall(PetscObjectReference((PetscObject)oldmat->Mvctx));
    3001:     }
    3002:     PetscCall(MatDuplicate(oldmat->A, cpvalues, &a->A));
    3003:     PetscCall(MatDuplicate(oldmat->B, cpvalues, &a->B));
    3004:   }
    3005:   PetscCall(PetscFunctionListDuplicate(((PetscObject)matin)->qlist, &((PetscObject)mat)->qlist));
    3006:   *newmat = mat;
    3007:   PetscFunctionReturn(PETSC_SUCCESS);
    3008: }

    3010: PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
    3011: {
    3012:   PetscBool isbinary, ishdf5;

    3014:   PetscFunctionBegin;
    3017:   /* force binary viewer to load .info file if it has not yet done so */
    3018:   PetscCall(PetscViewerSetUp(viewer));
    3019:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    3020:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
    3021:   if (isbinary) {
    3022:     PetscCall(MatLoad_MPIAIJ_Binary(newMat, viewer));
    3023:   } else if (ishdf5) {
    3024: #if defined(PETSC_HAVE_HDF5)
    3025:     PetscCall(MatLoad_AIJ_HDF5(newMat, viewer));
    3026: #else
    3027:     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
    3028: #endif
    3029:   } else {
    3030:     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);
    3031:   }
    3032:   PetscFunctionReturn(PETSC_SUCCESS);
    3033: }

    3035: PetscErrorCode MatLoad_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
    3036: {
    3037:   PetscInt     header[4], M, N, m, nz, rows, cols, sum, i;
    3038:   PetscInt    *rowidxs, *colidxs;
    3039:   PetscScalar *matvals;

    3041:   PetscFunctionBegin;
    3042:   PetscCall(PetscViewerSetUp(viewer));

    3044:   /* read in matrix header */
    3045:   PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
    3046:   PetscCheck(header[0] == MAT_FILE_CLASSID, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Not a matrix object in file");
    3047:   M  = header[1];
    3048:   N  = header[2];
    3049:   nz = header[3];
    3050:   PetscCheck(M >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix row size (%" PetscInt_FMT ") in file is negative", M);
    3051:   PetscCheck(N >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix column size (%" PetscInt_FMT ") in file is negative", N);
    3052:   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix stored in special format on disk, cannot load as MPIAIJ");

    3054:   /* set block sizes from the viewer's .info file */
    3055:   PetscCall(MatLoad_Binary_BlockSizes(mat, viewer));
    3056:   /* set global sizes if not set already */
    3057:   if (mat->rmap->N < 0) mat->rmap->N = M;
    3058:   if (mat->cmap->N < 0) mat->cmap->N = N;
    3059:   PetscCall(PetscLayoutSetUp(mat->rmap));
    3060:   PetscCall(PetscLayoutSetUp(mat->cmap));

    3062:   /* check if the matrix sizes are correct */
    3063:   PetscCall(MatGetSize(mat, &rows, &cols));
    3064:   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);

    3066:   /* read in row lengths and build row indices */
    3067:   PetscCall(MatGetLocalSize(mat, &m, NULL));
    3068:   PetscCall(PetscMalloc1(m + 1, &rowidxs));
    3069:   PetscCall(PetscViewerBinaryReadAll(viewer, rowidxs + 1, m, PETSC_DECIDE, M, PETSC_INT));
    3070:   rowidxs[0] = 0;
    3071:   for (i = 0; i < m; i++) rowidxs[i + 1] += rowidxs[i];
    3072:   if (nz != PETSC_INT_MAX) {
    3073:     PetscCallMPI(MPIU_Allreduce(&rowidxs[m], &sum, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)viewer)));
    3074:     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);
    3075:   }

    3077:   /* read in column indices and matrix values */
    3078:   PetscCall(PetscMalloc2(rowidxs[m], &colidxs, rowidxs[m], &matvals));
    3079:   PetscCall(PetscViewerBinaryReadAll(viewer, colidxs, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
    3080:   PetscCall(PetscViewerBinaryReadAll(viewer, matvals, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
    3081:   /* store matrix indices and values */
    3082:   PetscCall(MatMPIAIJSetPreallocationCSR(mat, rowidxs, colidxs, matvals));
    3083:   PetscCall(PetscFree(rowidxs));
    3084:   PetscCall(PetscFree2(colidxs, matvals));
    3085:   PetscFunctionReturn(PETSC_SUCCESS);
    3086: }

    3088: /* Not scalable because of ISAllGather() unless getting all columns. */
    3089: static PetscErrorCode ISGetSeqIS_Private(Mat mat, IS iscol, IS *isseq)
    3090: {
    3091:   IS          iscol_local;
    3092:   PetscBool   isstride;
    3093:   PetscMPIInt gisstride = 0;

    3095:   PetscFunctionBegin;
    3096:   /* check if we are grabbing all columns*/
    3097:   PetscCall(PetscObjectTypeCompare((PetscObject)iscol, ISSTRIDE, &isstride));

    3099:   if (isstride) {
    3100:     PetscInt start, len, mstart, mlen;
    3101:     PetscCall(ISStrideGetInfo(iscol, &start, NULL));
    3102:     PetscCall(ISGetLocalSize(iscol, &len));
    3103:     PetscCall(MatGetOwnershipRangeColumn(mat, &mstart, &mlen));
    3104:     if (mstart == start && mlen - mstart == len) gisstride = 1;
    3105:   }

    3107:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &gisstride, 1, MPI_INT, MPI_MIN, PetscObjectComm((PetscObject)mat)));
    3108:   if (gisstride) {
    3109:     PetscInt N;
    3110:     PetscCall(MatGetSize(mat, NULL, &N));
    3111:     PetscCall(ISCreateStride(PETSC_COMM_SELF, N, 0, 1, &iscol_local));
    3112:     PetscCall(ISSetIdentity(iscol_local));
    3113:     PetscCall(PetscInfo(mat, "Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n"));
    3114:   } else {
    3115:     PetscInt cbs;
    3116:     PetscCall(ISGetBlockSize(iscol, &cbs));
    3117:     PetscCall(ISAllGather(iscol, &iscol_local));
    3118:     PetscCall(ISSetBlockSize(iscol_local, cbs));
    3119:   }

    3121:   *isseq = iscol_local;
    3122:   PetscFunctionReturn(PETSC_SUCCESS);
    3123: }

    3125: /*
    3126:  Used by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
    3127:  (see MatCreateSubMatrix_MPIAIJ_nonscalable)

    3129:  Input Parameters:
    3130: +   mat - matrix
    3131: .   isrow - parallel row index set; its local indices are a subset of local columns of `mat`,
    3132:            i.e., mat->rstart <= isrow[i] < mat->rend
    3133: -   iscol - parallel column index set; its local indices are a subset of local columns of `mat`,
    3134:            i.e., mat->cstart <= iscol[i] < mat->cend

    3136:  Output Parameters:
    3137: +   isrow_d - sequential row index set for retrieving mat->A
    3138: .   iscol_d - sequential  column index set for retrieving mat->A
    3139: .   iscol_o - sequential column index set for retrieving mat->B
    3140: -   garray - column map; garray[i] indicates global location of iscol_o[i] in `iscol`
    3141:  */
    3142: static PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat, IS isrow, IS iscol, IS *isrow_d, IS *iscol_d, IS *iscol_o, PetscInt *garray[])
    3143: {
    3144:   Vec             x, cmap;
    3145:   const PetscInt *is_idx;
    3146:   PetscScalar    *xarray, *cmaparray;
    3147:   PetscInt        ncols, isstart, *idx, m, rstart, *cmap1, count;
    3148:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ *)mat->data;
    3149:   Mat             B    = a->B;
    3150:   Vec             lvec = a->lvec, lcmap;
    3151:   PetscInt        i, cstart, cend, Bn = B->cmap->N;
    3152:   MPI_Comm        comm;
    3153:   VecScatter      Mvctx = a->Mvctx;

    3155:   PetscFunctionBegin;
    3156:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3157:   PetscCall(ISGetLocalSize(iscol, &ncols));

    3159:   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
    3160:   PetscCall(MatCreateVecs(mat, &x, NULL));
    3161:   PetscCall(VecSet(x, -1.0));
    3162:   PetscCall(VecDuplicate(x, &cmap));
    3163:   PetscCall(VecSet(cmap, -1.0));

    3165:   /* Get start indices */
    3166:   PetscCallMPI(MPI_Scan(&ncols, &isstart, 1, MPIU_INT, MPI_SUM, comm));
    3167:   isstart -= ncols;
    3168:   PetscCall(MatGetOwnershipRangeColumn(mat, &cstart, &cend));

    3170:   PetscCall(ISGetIndices(iscol, &is_idx));
    3171:   PetscCall(VecGetArray(x, &xarray));
    3172:   PetscCall(VecGetArray(cmap, &cmaparray));
    3173:   PetscCall(PetscMalloc1(ncols, &idx));
    3174:   for (i = 0; i < ncols; i++) {
    3175:     xarray[is_idx[i] - cstart]    = (PetscScalar)is_idx[i];
    3176:     cmaparray[is_idx[i] - cstart] = i + isstart;        /* global index of iscol[i] */
    3177:     idx[i]                        = is_idx[i] - cstart; /* local index of iscol[i]  */
    3178:   }
    3179:   PetscCall(VecRestoreArray(x, &xarray));
    3180:   PetscCall(VecRestoreArray(cmap, &cmaparray));
    3181:   PetscCall(ISRestoreIndices(iscol, &is_idx));

    3183:   /* Get iscol_d */
    3184:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, iscol_d));
    3185:   PetscCall(ISGetBlockSize(iscol, &i));
    3186:   PetscCall(ISSetBlockSize(*iscol_d, i));

    3188:   /* Get isrow_d */
    3189:   PetscCall(ISGetLocalSize(isrow, &m));
    3190:   rstart = mat->rmap->rstart;
    3191:   PetscCall(PetscMalloc1(m, &idx));
    3192:   PetscCall(ISGetIndices(isrow, &is_idx));
    3193:   for (i = 0; i < m; i++) idx[i] = is_idx[i] - rstart;
    3194:   PetscCall(ISRestoreIndices(isrow, &is_idx));

    3196:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, idx, PETSC_OWN_POINTER, isrow_d));
    3197:   PetscCall(ISGetBlockSize(isrow, &i));
    3198:   PetscCall(ISSetBlockSize(*isrow_d, i));

    3200:   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
    3201:   PetscCall(VecScatterBegin(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));
    3202:   PetscCall(VecScatterEnd(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));

    3204:   PetscCall(VecDuplicate(lvec, &lcmap));

    3206:   PetscCall(VecScatterBegin(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));
    3207:   PetscCall(VecScatterEnd(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));

    3209:   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
    3210:   /* off-process column indices */
    3211:   count = 0;
    3212:   PetscCall(PetscMalloc1(Bn, &idx));
    3213:   PetscCall(PetscMalloc1(Bn, &cmap1));

    3215:   PetscCall(VecGetArray(lvec, &xarray));
    3216:   PetscCall(VecGetArray(lcmap, &cmaparray));
    3217:   for (i = 0; i < Bn; i++) {
    3218:     if (PetscRealPart(xarray[i]) > -1.0) {
    3219:       idx[count]   = i;                                     /* local column index in off-diagonal part B */
    3220:       cmap1[count] = (PetscInt)PetscRealPart(cmaparray[i]); /* column index in submat */
    3221:       count++;
    3222:     }
    3223:   }
    3224:   PetscCall(VecRestoreArray(lvec, &xarray));
    3225:   PetscCall(VecRestoreArray(lcmap, &cmaparray));

    3227:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_COPY_VALUES, iscol_o));
    3228:   /* cannot ensure iscol_o has same blocksize as iscol! */

    3230:   PetscCall(PetscFree(idx));
    3231:   *garray = cmap1;

    3233:   PetscCall(VecDestroy(&x));
    3234:   PetscCall(VecDestroy(&cmap));
    3235:   PetscCall(VecDestroy(&lcmap));
    3236:   PetscFunctionReturn(PETSC_SUCCESS);
    3237: }

    3239: /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
    3240: PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *submat)
    3241: {
    3242:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)mat->data, *asub;
    3243:   Mat         M = NULL;
    3244:   MPI_Comm    comm;
    3245:   IS          iscol_d, isrow_d, iscol_o;
    3246:   Mat         Asub = NULL, Bsub = NULL;
    3247:   PetscInt    n, count, M_size, N_size;

    3249:   PetscFunctionBegin;
    3250:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));

    3252:   if (call == MAT_REUSE_MATRIX) {
    3253:     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
    3254:     PetscCall(PetscObjectQuery((PetscObject)*submat, "isrow_d", (PetscObject *)&isrow_d));
    3255:     PetscCheck(isrow_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "isrow_d passed in was not used before, cannot reuse");

    3257:     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_d", (PetscObject *)&iscol_d));
    3258:     PetscCheck(iscol_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_d passed in was not used before, cannot reuse");

    3260:     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_o", (PetscObject *)&iscol_o));
    3261:     PetscCheck(iscol_o, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_o passed in was not used before, cannot reuse");

    3263:     /* Update diagonal and off-diagonal portions of submat */
    3264:     asub = (Mat_MPIAIJ *)(*submat)->data;
    3265:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->A));
    3266:     PetscCall(ISGetLocalSize(iscol_o, &n));
    3267:     if (n) PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->B));
    3268:     PetscCall(MatAssemblyBegin(*submat, MAT_FINAL_ASSEMBLY));
    3269:     PetscCall(MatAssemblyEnd(*submat, MAT_FINAL_ASSEMBLY));

    3271:   } else { /* call == MAT_INITIAL_MATRIX) */
    3272:     PetscInt *garray, *garray_compact;
    3273:     PetscInt  BsubN;

    3275:     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
    3276:     PetscCall(ISGetSeqIS_SameColDist_Private(mat, isrow, iscol, &isrow_d, &iscol_d, &iscol_o, &garray));

    3278:     /* Create local submatrices Asub and Bsub */
    3279:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Asub));
    3280:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Bsub));

    3282:     // Compact garray so its not of size Bn
    3283:     PetscCall(ISGetSize(iscol_o, &count));
    3284:     PetscCall(PetscMalloc1(count, &garray_compact));
    3285:     PetscCall(PetscArraycpy(garray_compact, garray, count));

    3287:     /* Create submatrix M */
    3288:     PetscCall(ISGetSize(isrow, &M_size));
    3289:     PetscCall(ISGetSize(iscol, &N_size));
    3290:     PetscCall(MatCreateMPIAIJWithSeqAIJ(comm, M_size, N_size, Asub, Bsub, garray_compact, &M));

    3292:     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
    3293:     asub = (Mat_MPIAIJ *)M->data;

    3295:     PetscCall(ISGetLocalSize(iscol_o, &BsubN));
    3296:     n = asub->B->cmap->N;
    3297:     if (BsubN > n) {
    3298:       /* This case can be tested using ~petsc/src/tao/bound/tutorials/runplate2_3 */
    3299:       const PetscInt *idx;
    3300:       PetscInt        i, j, *idx_new, *subgarray = asub->garray;
    3301:       PetscCall(PetscInfo(M, "submatrix Bn %" PetscInt_FMT " != BsubN %" PetscInt_FMT ", update iscol_o\n", n, BsubN));

    3303:       PetscCall(PetscMalloc1(n, &idx_new));
    3304:       j = 0;
    3305:       PetscCall(ISGetIndices(iscol_o, &idx));
    3306:       for (i = 0; i < n; i++) {
    3307:         if (j >= BsubN) break;
    3308:         while (subgarray[i] > garray[j]) j++;

    3310:         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]);
    3311:         idx_new[i] = idx[j++];
    3312:       }
    3313:       PetscCall(ISRestoreIndices(iscol_o, &idx));

    3315:       PetscCall(ISDestroy(&iscol_o));
    3316:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, idx_new, PETSC_OWN_POINTER, &iscol_o));

    3318:     } 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);

    3320:     PetscCall(PetscFree(garray));
    3321:     *submat = M;

    3323:     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
    3324:     PetscCall(PetscObjectCompose((PetscObject)M, "isrow_d", (PetscObject)isrow_d));
    3325:     PetscCall(ISDestroy(&isrow_d));

    3327:     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_d", (PetscObject)iscol_d));
    3328:     PetscCall(ISDestroy(&iscol_d));

    3330:     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_o", (PetscObject)iscol_o));
    3331:     PetscCall(ISDestroy(&iscol_o));
    3332:   }
    3333:   PetscFunctionReturn(PETSC_SUCCESS);
    3334: }

    3336: PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *newmat)
    3337: {
    3338:   IS        iscol_local = NULL, isrow_d;
    3339:   PetscInt  csize;
    3340:   PetscInt  n, i, j, start, end;
    3341:   PetscBool sameRowDist = PETSC_FALSE, sameDist[2], tsameDist[2];
    3342:   MPI_Comm  comm;

    3344:   PetscFunctionBegin;
    3345:   /* If isrow has same processor distribution as mat,
    3346:      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
    3347:   if (call == MAT_REUSE_MATRIX) {
    3348:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "isrow_d", (PetscObject *)&isrow_d));
    3349:     if (isrow_d) {
    3350:       sameRowDist  = PETSC_TRUE;
    3351:       tsameDist[1] = PETSC_TRUE; /* sameColDist */
    3352:     } else {
    3353:       PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_local));
    3354:       if (iscol_local) {
    3355:         sameRowDist  = PETSC_TRUE;
    3356:         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
    3357:       }
    3358:     }
    3359:   } else {
    3360:     /* Check if isrow has same processor distribution as mat */
    3361:     sameDist[0] = PETSC_FALSE;
    3362:     PetscCall(ISGetLocalSize(isrow, &n));
    3363:     if (!n) {
    3364:       sameDist[0] = PETSC_TRUE;
    3365:     } else {
    3366:       PetscCall(ISGetMinMax(isrow, &i, &j));
    3367:       PetscCall(MatGetOwnershipRange(mat, &start, &end));
    3368:       if (i >= start && j < end) sameDist[0] = PETSC_TRUE;
    3369:     }

    3371:     /* Check if iscol has same processor distribution as mat */
    3372:     sameDist[1] = PETSC_FALSE;
    3373:     PetscCall(ISGetLocalSize(iscol, &n));
    3374:     if (!n) {
    3375:       sameDist[1] = PETSC_TRUE;
    3376:     } else {
    3377:       PetscCall(ISGetMinMax(iscol, &i, &j));
    3378:       PetscCall(MatGetOwnershipRangeColumn(mat, &start, &end));
    3379:       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
    3380:     }

    3382:     PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3383:     PetscCallMPI(MPIU_Allreduce(&sameDist, &tsameDist, 2, MPI_C_BOOL, MPI_LAND, comm));
    3384:     sameRowDist = tsameDist[0];
    3385:   }

    3387:   if (sameRowDist) {
    3388:     if (tsameDist[1]) { /* sameRowDist & sameColDist */
    3389:       /* isrow and iscol have same processor distribution as mat */
    3390:       PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat, isrow, iscol, call, newmat));
    3391:       PetscFunctionReturn(PETSC_SUCCESS);
    3392:     } else { /* sameRowDist */
    3393:       /* isrow has same processor distribution as mat */
    3394:       if (call == MAT_INITIAL_MATRIX) {
    3395:         PetscBool sorted;
    3396:         PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
    3397:         PetscCall(ISGetLocalSize(iscol_local, &n)); /* local size of iscol_local = global columns of newmat */
    3398:         PetscCall(ISGetSize(iscol, &i));
    3399:         PetscCheck(n == i, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "n %" PetscInt_FMT " != size of iscol %" PetscInt_FMT, n, i);

    3401:         PetscCall(ISSorted(iscol_local, &sorted));
    3402:         if (sorted) {
    3403:           /* MatCreateSubMatrix_MPIAIJ_SameRowDist() requires iscol_local be sorted; it can have duplicate indices */
    3404:           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, iscol_local, MAT_INITIAL_MATRIX, newmat));
    3405:           PetscFunctionReturn(PETSC_SUCCESS);
    3406:         }
    3407:       } else { /* call == MAT_REUSE_MATRIX */
    3408:         IS iscol_sub;
    3409:         PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
    3410:         if (iscol_sub) {
    3411:           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, NULL, call, newmat));
    3412:           PetscFunctionReturn(PETSC_SUCCESS);
    3413:         }
    3414:       }
    3415:     }
    3416:   }

    3418:   /* General case: iscol -> iscol_local which has global size of iscol */
    3419:   if (call == MAT_REUSE_MATRIX) {
    3420:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "ISAllGather", (PetscObject *)&iscol_local));
    3421:     PetscCheck(iscol_local, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    3422:   } else {
    3423:     if (!iscol_local) PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
    3424:   }

    3426:   PetscCall(ISGetLocalSize(iscol, &csize));
    3427:   PetscCall(MatCreateSubMatrix_MPIAIJ_nonscalable(mat, isrow, iscol_local, csize, call, newmat));

    3429:   if (call == MAT_INITIAL_MATRIX) {
    3430:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    3431:     PetscCall(ISDestroy(&iscol_local));
    3432:   }
    3433:   PetscFunctionReturn(PETSC_SUCCESS);
    3434: }

    3436: /*@C
    3437:   MatCreateMPIAIJWithSeqAIJ - creates a `MATMPIAIJ` matrix using `MATSEQAIJ` matrices that contain the "diagonal"
    3438:   and "off-diagonal" part of the matrix in CSR format.

    3440:   Collective

    3442:   Input Parameters:
    3443: + comm   - MPI communicator
    3444: . M      - the global row size
    3445: . N      - the global column size
    3446: . A      - "diagonal" portion of matrix
    3447: . 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
    3448: - 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.

    3450:   Output Parameter:
    3451: . mat - the matrix, with input `A` as its local diagonal matrix

    3453:   Level: advanced

    3455:   Notes:
    3456:   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix.

    3458:   `A` and `B` becomes part of output mat. The user cannot use `A` and `B` anymore.

    3460:   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
    3461:   `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
    3462:   `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`
    3463:   yourself, see algorithms in the private function `MatSetUpMultiply_MPIAIJ()`.

    3465:   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.

    3467: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MATSEQAIJ`, `MatCreateMPIAIJWithSplitArrays()`
    3468: @*/
    3469: PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm, PetscInt M, PetscInt N, Mat A, Mat B, PetscInt *garray, Mat *mat)
    3470: {
    3471:   PetscInt    m, n;
    3472:   MatType     mpi_mat_type;
    3473:   Mat_MPIAIJ *mpiaij;
    3474:   Mat         C;

    3476:   PetscFunctionBegin;
    3477:   PetscCall(MatCreate(comm, &C));
    3478:   PetscCall(MatGetSize(A, &m, &n));
    3479:   PetscCheck(m == B->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Am %" PetscInt_FMT " != Bm %" PetscInt_FMT, m, B->rmap->N);
    3480:   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);

    3482:   PetscCall(MatSetSizes(C, m, n, M, N));
    3483:   /* Determine the type of MPI matrix that should be created from the type of matrix A, which holds the "diagonal" portion. */
    3484:   PetscCall(MatGetMPIMatType_Private(A, &mpi_mat_type));
    3485:   PetscCall(MatSetType(C, mpi_mat_type));
    3486:   if (!garray) {
    3487:     const PetscScalar *ba;

    3489:     B->nonzerostate++;
    3490:     PetscCall(MatSeqAIJGetArrayRead(B, &ba)); /* Since we will destroy B's device copy, we need to make sure the host copy is up to date */
    3491:     PetscCall(MatSeqAIJRestoreArrayRead(B, &ba));
    3492:   }

    3494:   PetscCall(MatSetBlockSizes(C, A->rmap->bs, A->cmap->bs));
    3495:   PetscCall(PetscLayoutSetUp(C->rmap));
    3496:   PetscCall(PetscLayoutSetUp(C->cmap));

    3498:   mpiaij              = (Mat_MPIAIJ *)C->data;
    3499:   mpiaij->A           = A;
    3500:   mpiaij->B           = B;
    3501:   mpiaij->garray      = garray;
    3502:   C->preallocated     = PETSC_TRUE;
    3503:   C->nooffprocentries = PETSC_TRUE; /* See MatAssemblyBegin_MPIAIJ. In effect, making MatAssemblyBegin a nop */

    3505:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    3506:   PetscCall(MatAssemblyBegin(C, MAT_FINAL_ASSEMBLY));
    3507:   /* MatAssemblyEnd is critical here. It sets mat->offloadmask according to A and B's, and
    3508:    also gets mpiaij->B compacted (if garray is NULL), with its col ids and size reduced
    3509:    */
    3510:   PetscCall(MatAssemblyEnd(C, MAT_FINAL_ASSEMBLY));
    3511:   PetscCall(MatSetOption(C, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    3512:   PetscCall(MatSetOption(C, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    3513:   *mat = C;
    3514:   PetscFunctionReturn(PETSC_SUCCESS);
    3515: }

    3517: extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat, PetscInt, const IS[], const IS[], MatReuse, PetscBool, Mat *);

    3519: PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat, IS isrow, IS iscol, IS iscol_local, MatReuse call, Mat *newmat)
    3520: {
    3521:   PetscInt        i, m, n, rstart, row, rend, nz, j, bs, cbs;
    3522:   PetscInt       *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
    3523:   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)mat->data;
    3524:   Mat             M, Msub, B = a->B;
    3525:   MatScalar      *aa;
    3526:   Mat_SeqAIJ     *aij;
    3527:   PetscInt       *garray = a->garray, *colsub, Ncols;
    3528:   PetscInt        count, Bn = B->cmap->N, cstart = mat->cmap->rstart, cend = mat->cmap->rend;
    3529:   IS              iscol_sub, iscmap;
    3530:   const PetscInt *is_idx, *cmap;
    3531:   PetscBool       allcolumns = PETSC_FALSE;
    3532:   MPI_Comm        comm;

    3534:   PetscFunctionBegin;
    3535:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3536:   if (call == MAT_REUSE_MATRIX) {
    3537:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
    3538:     PetscCheck(iscol_sub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "SubIScol passed in was not used before, cannot reuse");
    3539:     PetscCall(ISGetLocalSize(iscol_sub, &count));

    3541:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "Subcmap", (PetscObject *)&iscmap));
    3542:     PetscCheck(iscmap, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Subcmap passed in was not used before, cannot reuse");

    3544:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Msub));
    3545:     PetscCheck(Msub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");

    3547:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_REUSE_MATRIX, PETSC_FALSE, &Msub));

    3549:   } else { /* call == MAT_INITIAL_MATRIX) */
    3550:     PetscBool flg;

    3552:     PetscCall(ISGetLocalSize(iscol, &n));
    3553:     PetscCall(ISGetSize(iscol, &Ncols));

    3555:     /* (1) iscol -> nonscalable iscol_local */
    3556:     /* Check for special case: each processor gets entire matrix columns */
    3557:     PetscCall(ISIdentity(iscol_local, &flg));
    3558:     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
    3559:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    3560:     if (allcolumns) {
    3561:       iscol_sub = iscol_local;
    3562:       PetscCall(PetscObjectReference((PetscObject)iscol_local));
    3563:       PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &iscmap));

    3565:     } else {
    3566:       /* (2) iscol_local -> iscol_sub and iscmap. Implementation below requires iscol_local be sorted, it can have duplicate indices */
    3567:       PetscInt *idx, *cmap1, k;
    3568:       PetscCall(PetscMalloc1(Ncols, &idx));
    3569:       PetscCall(PetscMalloc1(Ncols, &cmap1));
    3570:       PetscCall(ISGetIndices(iscol_local, &is_idx));
    3571:       count = 0;
    3572:       k     = 0;
    3573:       for (i = 0; i < Ncols; i++) {
    3574:         j = is_idx[i];
    3575:         if (j >= cstart && j < cend) {
    3576:           /* diagonal part of mat */
    3577:           idx[count]     = j;
    3578:           cmap1[count++] = i; /* column index in submat */
    3579:         } else if (Bn) {
    3580:           /* off-diagonal part of mat */
    3581:           if (j == garray[k]) {
    3582:             idx[count]     = j;
    3583:             cmap1[count++] = i; /* column index in submat */
    3584:           } else if (j > garray[k]) {
    3585:             while (j > garray[k] && k < Bn - 1) k++;
    3586:             if (j == garray[k]) {
    3587:               idx[count]     = j;
    3588:               cmap1[count++] = i; /* column index in submat */
    3589:             }
    3590:           }
    3591:         }
    3592:       }
    3593:       PetscCall(ISRestoreIndices(iscol_local, &is_idx));

    3595:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_OWN_POINTER, &iscol_sub));
    3596:       PetscCall(ISGetBlockSize(iscol, &cbs));
    3597:       PetscCall(ISSetBlockSize(iscol_sub, cbs));

    3599:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local), count, cmap1, PETSC_OWN_POINTER, &iscmap));
    3600:     }

    3602:     /* (3) Create sequential Msub */
    3603:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_INITIAL_MATRIX, allcolumns, &Msub));
    3604:   }

    3606:   PetscCall(ISGetLocalSize(iscol_sub, &count));
    3607:   aij = (Mat_SeqAIJ *)Msub->data;
    3608:   ii  = aij->i;
    3609:   PetscCall(ISGetIndices(iscmap, &cmap));

    3611:   /*
    3612:       m - number of local rows
    3613:       Ncols - number of columns (same on all processors)
    3614:       rstart - first row in new global matrix generated
    3615:   */
    3616:   PetscCall(MatGetSize(Msub, &m, NULL));

    3618:   if (call == MAT_INITIAL_MATRIX) {
    3619:     /* (4) Create parallel newmat */
    3620:     PetscMPIInt rank, size;
    3621:     PetscInt    csize;

    3623:     PetscCallMPI(MPI_Comm_size(comm, &size));
    3624:     PetscCallMPI(MPI_Comm_rank(comm, &rank));

    3626:     /*
    3627:         Determine the number of non-zeros in the diagonal and off-diagonal
    3628:         portions of the matrix in order to do correct preallocation
    3629:     */

    3631:     /* first get start and end of "diagonal" columns */
    3632:     PetscCall(ISGetLocalSize(iscol, &csize));
    3633:     if (csize == PETSC_DECIDE) {
    3634:       PetscCall(ISGetSize(isrow, &mglobal));
    3635:       if (mglobal == Ncols) { /* square matrix */
    3636:         nlocal = m;
    3637:       } else {
    3638:         nlocal = Ncols / size + ((Ncols % size) > rank);
    3639:       }
    3640:     } else {
    3641:       nlocal = csize;
    3642:     }
    3643:     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    3644:     rstart = rend - nlocal;
    3645:     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);

    3647:     /* next, compute all the lengths */
    3648:     jj = aij->j;
    3649:     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
    3650:     olens = dlens + m;
    3651:     for (i = 0; i < m; i++) {
    3652:       jend = ii[i + 1] - ii[i];
    3653:       olen = 0;
    3654:       dlen = 0;
    3655:       for (j = 0; j < jend; j++) {
    3656:         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
    3657:         else dlen++;
    3658:         jj++;
    3659:       }
    3660:       olens[i] = olen;
    3661:       dlens[i] = dlen;
    3662:     }

    3664:     PetscCall(ISGetBlockSize(isrow, &bs));
    3665:     PetscCall(ISGetBlockSize(iscol, &cbs));

    3667:     PetscCall(MatCreate(comm, &M));
    3668:     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, Ncols));
    3669:     PetscCall(MatSetBlockSizes(M, bs, cbs));
    3670:     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
    3671:     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
    3672:     PetscCall(PetscFree(dlens));

    3674:   } else { /* call == MAT_REUSE_MATRIX */
    3675:     M = *newmat;
    3676:     PetscCall(MatGetLocalSize(M, &i, NULL));
    3677:     PetscCheck(i == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    3678:     PetscCall(MatZeroEntries(M));
    3679:     /*
    3680:          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
    3681:        rather than the slower MatSetValues().
    3682:     */
    3683:     M->was_assembled = PETSC_TRUE;
    3684:     M->assembled     = PETSC_FALSE;
    3685:   }

    3687:   /* (5) Set values of Msub to *newmat */
    3688:   PetscCall(PetscMalloc1(count, &colsub));
    3689:   PetscCall(MatGetOwnershipRange(M, &rstart, NULL));

    3691:   jj = aij->j;
    3692:   PetscCall(MatSeqAIJGetArrayRead(Msub, (const PetscScalar **)&aa));
    3693:   for (i = 0; i < m; i++) {
    3694:     row = rstart + i;
    3695:     nz  = ii[i + 1] - ii[i];
    3696:     for (j = 0; j < nz; j++) colsub[j] = cmap[jj[j]];
    3697:     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, colsub, aa, INSERT_VALUES));
    3698:     jj += nz;
    3699:     aa += nz;
    3700:   }
    3701:   PetscCall(MatSeqAIJRestoreArrayRead(Msub, (const PetscScalar **)&aa));
    3702:   PetscCall(ISRestoreIndices(iscmap, &cmap));

    3704:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
    3705:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));

    3707:   PetscCall(PetscFree(colsub));

    3709:   /* save Msub, iscol_sub and iscmap used in processor for next request */
    3710:   if (call == MAT_INITIAL_MATRIX) {
    3711:     *newmat = M;
    3712:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "SubMatrix", (PetscObject)Msub));
    3713:     PetscCall(MatDestroy(&Msub));

    3715:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "SubIScol", (PetscObject)iscol_sub));
    3716:     PetscCall(ISDestroy(&iscol_sub));

    3718:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "Subcmap", (PetscObject)iscmap));
    3719:     PetscCall(ISDestroy(&iscmap));

    3721:     if (iscol_local) {
    3722:       PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    3723:       PetscCall(ISDestroy(&iscol_local));
    3724:     }
    3725:   }
    3726:   PetscFunctionReturn(PETSC_SUCCESS);
    3727: }

    3729: /*
    3730:     Not great since it makes two copies of the submatrix, first an SeqAIJ
    3731:   in local and then by concatenating the local matrices the end result.
    3732:   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()

    3734:   This requires a sequential iscol with all indices.
    3735: */
    3736: PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat, IS isrow, IS iscol, PetscInt csize, MatReuse call, Mat *newmat)
    3737: {
    3738:   PetscMPIInt rank, size;
    3739:   PetscInt    i, m, n, rstart, row, rend, nz, *cwork, j, bs, cbs;
    3740:   PetscInt   *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
    3741:   Mat         M, Mreuse;
    3742:   MatScalar  *aa, *vwork;
    3743:   MPI_Comm    comm;
    3744:   Mat_SeqAIJ *aij;
    3745:   PetscBool   colflag, allcolumns = PETSC_FALSE;

    3747:   PetscFunctionBegin;
    3748:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3749:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    3750:   PetscCallMPI(MPI_Comm_size(comm, &size));

    3752:   /* Check for special case: each processor gets entire matrix columns */
    3753:   PetscCall(ISIdentity(iscol, &colflag));
    3754:   PetscCall(ISGetLocalSize(iscol, &n));
    3755:   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
    3756:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPI_C_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));

    3758:   if (call == MAT_REUSE_MATRIX) {
    3759:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Mreuse));
    3760:     PetscCheck(Mreuse, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    3761:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_REUSE_MATRIX, allcolumns, &Mreuse));
    3762:   } else {
    3763:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_INITIAL_MATRIX, allcolumns, &Mreuse));
    3764:   }

    3766:   /*
    3767:       m - number of local rows
    3768:       n - number of columns (same on all processors)
    3769:       rstart - first row in new global matrix generated
    3770:   */
    3771:   PetscCall(MatGetSize(Mreuse, &m, &n));
    3772:   PetscCall(MatGetBlockSizes(Mreuse, &bs, &cbs));
    3773:   if (call == MAT_INITIAL_MATRIX) {
    3774:     aij = (Mat_SeqAIJ *)Mreuse->data;
    3775:     ii  = aij->i;
    3776:     jj  = aij->j;

    3778:     /*
    3779:         Determine the number of non-zeros in the diagonal and off-diagonal
    3780:         portions of the matrix in order to do correct preallocation
    3781:     */

    3783:     /* first get start and end of "diagonal" columns */
    3784:     if (csize == PETSC_DECIDE) {
    3785:       PetscCall(ISGetSize(isrow, &mglobal));
    3786:       if (mglobal == n) { /* square matrix */
    3787:         nlocal = m;
    3788:       } else {
    3789:         nlocal = n / size + ((n % size) > rank);
    3790:       }
    3791:     } else {
    3792:       nlocal = csize;
    3793:     }
    3794:     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    3795:     rstart = rend - nlocal;
    3796:     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);

    3798:     /* next, compute all the lengths */
    3799:     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
    3800:     olens = dlens + m;
    3801:     for (i = 0; i < m; i++) {
    3802:       jend = ii[i + 1] - ii[i];
    3803:       olen = 0;
    3804:       dlen = 0;
    3805:       for (j = 0; j < jend; j++) {
    3806:         if (*jj < rstart || *jj >= rend) olen++;
    3807:         else dlen++;
    3808:         jj++;
    3809:       }
    3810:       olens[i] = olen;
    3811:       dlens[i] = dlen;
    3812:     }
    3813:     PetscCall(MatCreate(comm, &M));
    3814:     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, n));
    3815:     PetscCall(MatSetBlockSizes(M, bs, cbs));
    3816:     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
    3817:     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
    3818:     PetscCall(PetscFree(dlens));
    3819:   } else {
    3820:     PetscInt ml, nl;

    3822:     M = *newmat;
    3823:     PetscCall(MatGetLocalSize(M, &ml, &nl));
    3824:     PetscCheck(ml == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    3825:     PetscCall(MatZeroEntries(M));
    3826:     /*
    3827:          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
    3828:        rather than the slower MatSetValues().
    3829:     */
    3830:     M->was_assembled = PETSC_TRUE;
    3831:     M->assembled     = PETSC_FALSE;
    3832:   }
    3833:   PetscCall(MatGetOwnershipRange(M, &rstart, &rend));
    3834:   aij = (Mat_SeqAIJ *)Mreuse->data;
    3835:   ii  = aij->i;
    3836:   jj  = aij->j;

    3838:   /* trigger copy to CPU if needed */
    3839:   PetscCall(MatSeqAIJGetArrayRead(Mreuse, (const PetscScalar **)&aa));
    3840:   for (i = 0; i < m; i++) {
    3841:     row   = rstart + i;
    3842:     nz    = ii[i + 1] - ii[i];
    3843:     cwork = jj;
    3844:     jj    = PetscSafePointerPlusOffset(jj, nz);
    3845:     vwork = aa;
    3846:     aa    = PetscSafePointerPlusOffset(aa, nz);
    3847:     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, cwork, vwork, INSERT_VALUES));
    3848:   }
    3849:   PetscCall(MatSeqAIJRestoreArrayRead(Mreuse, (const PetscScalar **)&aa));

    3851:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
    3852:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
    3853:   *newmat = M;

    3855:   /* save submatrix used in processor for next request */
    3856:   if (call == MAT_INITIAL_MATRIX) {
    3857:     PetscCall(PetscObjectCompose((PetscObject)M, "SubMatrix", (PetscObject)Mreuse));
    3858:     PetscCall(MatDestroy(&Mreuse));
    3859:   }
    3860:   PetscFunctionReturn(PETSC_SUCCESS);
    3861: }

    3863: static PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
    3864: {
    3865:   PetscInt        m, cstart, cend, j, nnz, i, d, *ld;
    3866:   PetscInt       *d_nnz, *o_nnz, nnz_max = 0, rstart, ii, irstart;
    3867:   const PetscInt *JJ;
    3868:   PetscBool       nooffprocentries;
    3869:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)B->data;

    3871:   PetscFunctionBegin;
    3872:   PetscCall(PetscLayoutSetUp(B->rmap));
    3873:   PetscCall(PetscLayoutSetUp(B->cmap));
    3874:   m       = B->rmap->n;
    3875:   cstart  = B->cmap->rstart;
    3876:   cend    = B->cmap->rend;
    3877:   rstart  = B->rmap->rstart;
    3878:   irstart = Ii[0];

    3880:   PetscCall(PetscCalloc2(m, &d_nnz, m, &o_nnz));

    3882:   if (PetscDefined(USE_DEBUG)) {
    3883:     for (i = 0; i < m; i++) {
    3884:       nnz = Ii[i + 1] - Ii[i];
    3885:       JJ  = PetscSafePointerPlusOffset(J, Ii[i] - irstart);
    3886:       PetscCheck(nnz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative %" PetscInt_FMT " number of columns", i, nnz);
    3887:       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]);
    3888:       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);
    3889:     }
    3890:   }

    3892:   for (i = 0; i < m; i++) {
    3893:     nnz     = Ii[i + 1] - Ii[i];
    3894:     JJ      = PetscSafePointerPlusOffset(J, Ii[i] - irstart);
    3895:     nnz_max = PetscMax(nnz_max, nnz);
    3896:     d       = 0;
    3897:     for (j = 0; j < nnz; j++) {
    3898:       if (cstart <= JJ[j] && JJ[j] < cend) d++;
    3899:     }
    3900:     d_nnz[i] = d;
    3901:     o_nnz[i] = nnz - d;
    3902:   }
    3903:   PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
    3904:   PetscCall(PetscFree2(d_nnz, o_nnz));

    3906:   for (i = 0; i < m; i++) {
    3907:     ii = i + rstart;
    3908:     PetscCall(MatSetValues_MPIAIJ(B, 1, &ii, Ii[i + 1] - Ii[i], PetscSafePointerPlusOffset(J, Ii[i] - irstart), PetscSafePointerPlusOffset(v, Ii[i] - irstart), INSERT_VALUES));
    3909:   }
    3910:   nooffprocentries    = B->nooffprocentries;
    3911:   B->nooffprocentries = PETSC_TRUE;
    3912:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    3913:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    3914:   B->nooffprocentries = nooffprocentries;

    3916:   /* count number of entries below block diagonal */
    3917:   PetscCall(PetscFree(Aij->ld));
    3918:   PetscCall(PetscCalloc1(m, &ld));
    3919:   Aij->ld = ld;
    3920:   for (i = 0; i < m; i++) {
    3921:     nnz = Ii[i + 1] - Ii[i];
    3922:     j   = 0;
    3923:     while (j < nnz && J[j] < cstart) j++;
    3924:     ld[i] = j;
    3925:     if (J) J += nnz;
    3926:   }

    3928:   PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    3929:   PetscFunctionReturn(PETSC_SUCCESS);
    3930: }

    3932: /*@
    3933:   MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in `MATAIJ` format
    3934:   (the default parallel PETSc format).

    3936:   Collective

    3938:   Input Parameters:
    3939: + B - the matrix
    3940: . i - the indices into `j` for the start of each local row (indices start with zero)
    3941: . j - the column indices for each local row (indices start with zero)
    3942: - v - optional values in the matrix

    3944:   Level: developer

    3946:   Notes:
    3947:   The `i`, `j`, and `v` arrays ARE copied by this routine into the internal format used by PETSc;
    3948:   thus you CANNOT change the matrix entries by changing the values of `v` after you have
    3949:   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

    3951:   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

    3953:   A convenience routine for this functionality is `MatCreateMPIAIJWithArrays()`.

    3955:   You can update the matrix with new numerical values using `MatUpdateMPIAIJWithArrays()` after this call if the column indices in `j` are sorted.

    3957:   If you do **not** use `MatUpdateMPIAIJWithArrays()`, the column indices in `j` do not need to be sorted. If you will use
    3958:   `MatUpdateMPIAIJWithArrays()`, the column indices **must** be sorted.

    3960:   The format which is used for the sparse matrix input, is equivalent to a
    3961:   row-major ordering.. i.e for the following matrix, the input data expected is
    3962:   as shown
    3963: .vb
    3964:         1 0 0
    3965:         2 0 3     P0
    3966:        -------
    3967:         4 5 6     P1

    3969:      Process0 [P0] rows_owned=[0,1]
    3970:         i =  {0,1,3}  [size = nrow+1  = 2+1]
    3971:         j =  {0,0,2}  [size = 3]
    3972:         v =  {1,2,3}  [size = 3]

    3974:      Process1 [P1] rows_owned=[2]
    3975:         i =  {0,3}    [size = nrow+1  = 1+1]
    3976:         j =  {0,1,2}  [size = 3]
    3977:         v =  {4,5,6}  [size = 3]
    3978: .ve

    3980: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatCreateAIJ()`,
    3981:           `MatCreateSeqAIJWithArrays()`, `MatCreateMPIAIJWithSplitArrays()`, `MatCreateMPIAIJWithArrays()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    3982: @*/
    3983: PetscErrorCode MatMPIAIJSetPreallocationCSR(Mat B, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
    3984: {
    3985:   PetscFunctionBegin;
    3986:   PetscTryMethod(B, "MatMPIAIJSetPreallocationCSR_C", (Mat, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, i, j, v));
    3987:   PetscFunctionReturn(PETSC_SUCCESS);
    3988: }

    3990: /*@
    3991:   MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in `MATMPIAIJ` format
    3992:   (the default parallel PETSc format).  For good matrix assembly performance
    3993:   the user should preallocate the matrix storage by setting the parameters
    3994:   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).

    3996:   Collective

    3998:   Input Parameters:
    3999: + B     - the matrix
    4000: . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
    4001:            (same value is used for all local rows)
    4002: . d_nnz - array containing the number of nonzeros in the various rows of the
    4003:            DIAGONAL portion of the local submatrix (possibly different for each row)
    4004:            or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `d_nz` is used to specify the nonzero structure.
    4005:            The size of this array is equal to the number of local rows, i.e 'm'.
    4006:            For matrices that will be factored, you must leave room for (and set)
    4007:            the diagonal entry even if it is zero.
    4008: . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
    4009:            submatrix (same value is used for all local rows).
    4010: - o_nnz - array containing the number of nonzeros in the various rows of the
    4011:            OFF-DIAGONAL portion of the local submatrix (possibly different for
    4012:            each row) or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `o_nz` is used to specify the nonzero
    4013:            structure. The size of this array is equal to the number
    4014:            of local rows, i.e 'm'.

    4016:   Example Usage:
    4017:   Consider the following 8x8 matrix with 34 non-zero values, that is
    4018:   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
    4019:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    4020:   as follows

    4022: .vb
    4023:             1  2  0  |  0  3  0  |  0  4
    4024:     Proc0   0  5  6  |  7  0  0  |  8  0
    4025:             9  0 10  | 11  0  0  | 12  0
    4026:     -------------------------------------
    4027:            13  0 14  | 15 16 17  |  0  0
    4028:     Proc1   0 18  0  | 19 20 21  |  0  0
    4029:             0  0  0  | 22 23  0  | 24  0
    4030:     -------------------------------------
    4031:     Proc2  25 26 27  |  0  0 28  | 29  0
    4032:            30  0  0  | 31 32 33  |  0 34
    4033: .ve

    4035:   This can be represented as a collection of submatrices as
    4036: .vb
    4037:       A B C
    4038:       D E F
    4039:       G H I
    4040: .ve

    4042:   Where the submatrices A,B,C are owned by proc0, D,E,F are
    4043:   owned by proc1, G,H,I are owned by proc2.

    4045:   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4046:   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4047:   The 'M','N' parameters are 8,8, and have the same values on all procs.

    4049:   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
    4050:   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
    4051:   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
    4052:   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
    4053:   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
    4054:   matrix, and [DF] as another `MATSEQAIJ` matrix.

    4056:   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
    4057:   allocated for every row of the local DIAGONAL submatrix, and `o_nz`
    4058:   storage locations are allocated for every row of the OFF-DIAGONAL submatrix.
    4059:   One way to choose `d_nz` and `o_nz` is to use the maximum number of nonzeros over
    4060:   the local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
    4061:   In this case, the values of `d_nz`, `o_nz` are
    4062: .vb
    4063:      proc0  dnz = 2, o_nz = 2
    4064:      proc1  dnz = 3, o_nz = 2
    4065:      proc2  dnz = 1, o_nz = 4
    4066: .ve
    4067:   We are allocating `m`*(`d_nz`+`o_nz`) storage locations for every proc. This
    4068:   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
    4069:   for proc3. i.e we are using 12+15+10=37 storage locations to store
    4070:   34 values.

    4072:   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
    4073:   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
    4074:   In the above case the values for `d_nnz`, `o_nnz` are
    4075: .vb
    4076:      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
    4077:      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
    4078:      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
    4079: .ve
    4080:   Here the space allocated is sum of all the above values i.e 34, and
    4081:   hence pre-allocation is perfect.

    4083:   Level: intermediate

    4085:   Notes:
    4086:   If the *_nnz parameter is given then the *_nz parameter is ignored

    4088:   The `MATAIJ` format, also called compressed row storage (CSR), is compatible with standard Fortran
    4089:   storage.  The stored row and column indices begin with zero.
    4090:   See [Sparse Matrices](sec_matsparse) for details.

    4092:   The parallel matrix is partitioned such that the first m0 rows belong to
    4093:   process 0, the next m1 rows belong to process 1, the next m2 rows belong
    4094:   to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.

    4096:   The DIAGONAL portion of the local submatrix of a processor can be defined
    4097:   as the submatrix which is obtained by extraction the part corresponding to
    4098:   the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
    4099:   first row that belongs to the processor, r2 is the last row belonging to
    4100:   the this processor, and c1-c2 is range of indices of the local part of a
    4101:   vector suitable for applying the matrix to.  This is an mxn matrix.  In the
    4102:   common case of a square matrix, the row and column ranges are the same and
    4103:   the DIAGONAL part is also square. The remaining portion of the local
    4104:   submatrix (mxN) constitute the OFF-DIAGONAL portion.

    4106:   If `o_nnz` and `d_nnz` are specified, then `o_nz` and `d_nz` are ignored.

    4108:   You can call `MatGetInfo()` to get information on how effective the preallocation was;
    4109:   for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
    4110:   You can also run with the option `-info` and look for messages with the string
    4111:   malloc in them to see if additional memory allocation was needed.

    4113: .seealso: [](ch_matrices), `Mat`, [Sparse Matrices](sec_matsparse), `MATMPIAIJ`, `MATAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatCreateAIJ()`, `MatMPIAIJSetPreallocationCSR()`,
    4114:           `MatGetInfo()`, `PetscSplitOwnership()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4115: @*/
    4116: PetscErrorCode MatMPIAIJSetPreallocation(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
    4117: {
    4118:   PetscFunctionBegin;
    4121:   PetscTryMethod(B, "MatMPIAIJSetPreallocation_C", (Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]), (B, d_nz, d_nnz, o_nz, o_nnz));
    4122:   PetscFunctionReturn(PETSC_SUCCESS);
    4123: }

    4125: /*@
    4126:   MatCreateMPIAIJWithArrays - creates a `MATMPIAIJ` matrix using arrays that contain in standard
    4127:   CSR format for the local rows.

    4129:   Collective

    4131:   Input Parameters:
    4132: + comm - MPI communicator
    4133: . m    - number of local rows (Cannot be `PETSC_DECIDE`)
    4134: . n    - This value should be the same as the local size used in creating the
    4135:          x vector for the matrix-vector product $ y = Ax$. (or `PETSC_DECIDE` to have
    4136:          calculated if `N` is given) For square matrices n is almost always `m`.
    4137: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    4138: . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    4139: . 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
    4140: . j    - global column indices
    4141: - a    - optional matrix values

    4143:   Output Parameter:
    4144: . mat - the matrix

    4146:   Level: intermediate

    4148:   Notes:
    4149:   The `i`, `j`, and `a` arrays ARE copied by this routine into the internal format used by PETSc;
    4150:   thus you CANNOT change the matrix entries by changing the values of `a[]` after you have
    4151:   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

    4153:   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

    4155:   Once you have created the matrix you can update it with new numerical values using `MatUpdateMPIAIJWithArray()`

    4157:   If you do **not** use `MatUpdateMPIAIJWithArray()`, the column indices in `j` do not need to be sorted. If you will use
    4158:   `MatUpdateMPIAIJWithArrays()`, the column indices **must** be sorted.

    4160:   The format which is used for the sparse matrix input, is equivalent to a
    4161:   row-major ordering, i.e., for the following matrix, the input data expected is
    4162:   as shown
    4163: .vb
    4164:         1 0 0
    4165:         2 0 3     P0
    4166:        -------
    4167:         4 5 6     P1

    4169:      Process0 [P0] rows_owned=[0,1]
    4170:         i =  {0,1,3}  [size = nrow+1  = 2+1]
    4171:         j =  {0,0,2}  [size = 3]
    4172:         v =  {1,2,3}  [size = 3]

    4174:      Process1 [P1] rows_owned=[2]
    4175:         i =  {0,3}    [size = nrow+1  = 1+1]
    4176:         j =  {0,1,2}  [size = 3]
    4177:         v =  {4,5,6}  [size = 3]
    4178: .ve

    4180: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4181:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4182: @*/
    4183: PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt i[], const PetscInt j[], const PetscScalar a[], Mat *mat)
    4184: {
    4185:   PetscFunctionBegin;
    4186:   PetscCheck(!i || !i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    4187:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    4188:   PetscCall(MatCreate(comm, mat));
    4189:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    4190:   /* PetscCall(MatSetBlockSizes(M,bs,cbs)); */
    4191:   PetscCall(MatSetType(*mat, MATMPIAIJ));
    4192:   PetscCall(MatMPIAIJSetPreallocationCSR(*mat, i, j, a));
    4193:   PetscFunctionReturn(PETSC_SUCCESS);
    4194: }

    4196: /*@
    4197:   MatUpdateMPIAIJWithArrays - updates a `MATMPIAIJ` matrix using arrays that contain in standard
    4198:   CSR format for the local rows. Only the numerical values are updated the other arrays must be identical to what was passed
    4199:   from `MatCreateMPIAIJWithArrays()`

    4201:   Deprecated: Use `MatUpdateMPIAIJWithArray()`

    4203:   Collective

    4205:   Input Parameters:
    4206: + mat - the matrix
    4207: . m   - number of local rows (Cannot be `PETSC_DECIDE`)
    4208: . n   - This value should be the same as the local size used in creating the
    4209:        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
    4210:        calculated if N is given) For square matrices n is almost always m.
    4211: . M   - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
    4212: . N   - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
    4213: . Ii  - row indices; that is Ii[0] = 0, Ii[row] = Ii[row-1] + number of elements in that row of the matrix
    4214: . J   - column indices
    4215: - v   - matrix values

    4217:   Level: deprecated

    4219: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4220:           `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4221: @*/
    4222: PetscErrorCode MatUpdateMPIAIJWithArrays(Mat mat, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
    4223: {
    4224:   PetscInt        nnz, i;
    4225:   PetscBool       nooffprocentries;
    4226:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
    4227:   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
    4228:   PetscScalar    *ad, *ao;
    4229:   PetscInt        ldi, Iii, md;
    4230:   const PetscInt *Adi = Ad->i;
    4231:   PetscInt       *ld  = Aij->ld;

    4233:   PetscFunctionBegin;
    4234:   PetscCheck(Ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    4235:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    4236:   PetscCheck(m == mat->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of rows cannot change from call to MatUpdateMPIAIJWithArrays()");
    4237:   PetscCheck(n == mat->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of columns cannot change from call to MatUpdateMPIAIJWithArrays()");

    4239:   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
    4240:   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));

    4242:   for (i = 0; i < m; i++) {
    4243:     if (PetscDefined(USE_DEBUG)) {
    4244:       for (PetscInt j = Ii[i] + 1; j < Ii[i + 1]; ++j) {
    4245:         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);
    4246:         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);
    4247:       }
    4248:     }
    4249:     nnz = Ii[i + 1] - Ii[i];
    4250:     Iii = Ii[i];
    4251:     ldi = ld[i];
    4252:     md  = Adi[i + 1] - Adi[i];
    4253:     PetscCall(PetscArraycpy(ao, v + Iii, ldi));
    4254:     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
    4255:     PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
    4256:     ad += md;
    4257:     ao += nnz - md;
    4258:   }
    4259:   nooffprocentries      = mat->nooffprocentries;
    4260:   mat->nooffprocentries = PETSC_TRUE;
    4261:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
    4262:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
    4263:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
    4264:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
    4265:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    4266:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    4267:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    4268:   mat->nooffprocentries = nooffprocentries;
    4269:   PetscFunctionReturn(PETSC_SUCCESS);
    4270: }

    4272: /*@
    4273:   MatUpdateMPIAIJWithArray - updates an `MATMPIAIJ` matrix using an array that contains the nonzero values

    4275:   Collective

    4277:   Input Parameters:
    4278: + mat - the matrix
    4279: - v   - matrix values, stored by row

    4281:   Level: intermediate

    4283:   Notes:
    4284:   The matrix must have been obtained with `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()`

    4286:   The column indices in the call to `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()` must have been sorted for this call to work correctly

    4288: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4289:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArrays()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4290: @*/
    4291: PetscErrorCode MatUpdateMPIAIJWithArray(Mat mat, const PetscScalar v[])
    4292: {
    4293:   PetscInt        nnz, i, m;
    4294:   PetscBool       nooffprocentries;
    4295:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
    4296:   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
    4297:   Mat_SeqAIJ     *Ao  = (Mat_SeqAIJ *)Aij->B->data;
    4298:   PetscScalar    *ad, *ao;
    4299:   const PetscInt *Adi = Ad->i, *Adj = Ao->i;
    4300:   PetscInt        ldi, Iii, md;
    4301:   PetscInt       *ld = Aij->ld;

    4303:   PetscFunctionBegin;
    4304:   m = mat->rmap->n;

    4306:   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
    4307:   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));
    4308:   Iii = 0;
    4309:   for (i = 0; i < m; i++) {
    4310:     nnz = Adi[i + 1] - Adi[i] + Adj[i + 1] - Adj[i];
    4311:     ldi = ld[i];
    4312:     md  = Adi[i + 1] - Adi[i];
    4313:     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
    4314:     ad += md;
    4315:     if (ao) {
    4316:       PetscCall(PetscArraycpy(ao, v + Iii, ldi));
    4317:       PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
    4318:       ao += nnz - md;
    4319:     }
    4320:     Iii += nnz;
    4321:   }
    4322:   nooffprocentries      = mat->nooffprocentries;
    4323:   mat->nooffprocentries = PETSC_TRUE;
    4324:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
    4325:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
    4326:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
    4327:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
    4328:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    4329:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    4330:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    4331:   mat->nooffprocentries = nooffprocentries;
    4332:   PetscFunctionReturn(PETSC_SUCCESS);
    4333: }

    4335: /*@
    4336:   MatCreateAIJ - Creates a sparse parallel matrix in `MATAIJ` format
    4337:   (the default parallel PETSc format).  For good matrix assembly performance
    4338:   the user should preallocate the matrix storage by setting the parameters
    4339:   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).

    4341:   Collective

    4343:   Input Parameters:
    4344: + comm  - MPI communicator
    4345: . m     - number of local rows (or `PETSC_DECIDE` to have calculated if M is given)
    4346:           This value should be the same as the local size used in creating the
    4347:           y vector for the matrix-vector product y = Ax.
    4348: . n     - This value should be the same as the local size used in creating the
    4349:           x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
    4350:           calculated if N is given) For square matrices n is almost always m.
    4351: . M     - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
    4352: . N     - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
    4353: . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
    4354:           (same value is used for all local rows)
    4355: . d_nnz - array containing the number of nonzeros in the various rows of the
    4356:           DIAGONAL portion of the local submatrix (possibly different for each row)
    4357:           or `NULL`, if `d_nz` is used to specify the nonzero structure.
    4358:           The size of this array is equal to the number of local rows, i.e 'm'.
    4359: . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
    4360:           submatrix (same value is used for all local rows).
    4361: - o_nnz - array containing the number of nonzeros in the various rows of the
    4362:           OFF-DIAGONAL portion of the local submatrix (possibly different for
    4363:           each row) or `NULL`, if `o_nz` is used to specify the nonzero
    4364:           structure. The size of this array is equal to the number
    4365:           of local rows, i.e 'm'.

    4367:   Output Parameter:
    4368: . A - the matrix

    4370:   Options Database Keys:
    4371: + -mat_no_inode                   - Do not use inodes
    4372: . -mat_inode_limit limit          - Sets inode limit (max limit=5)
    4373: - -matmult_vecscatter_view viewer - View the vecscatter (i.e., communication pattern) used in `MatMult()` of sparse parallel matrices.
    4374:                                     See viewer types in manual of `MatView()`. Of them, ascii_matlab, draw or binary cause the `VecScatter`
    4375:                                     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.

    4377:   Level: intermediate

    4379:   Notes:
    4380:   It is recommended that one use `MatCreateFromOptions()` or the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
    4381:   MatXXXXSetPreallocation() paradigm instead of this routine directly.
    4382:   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]

    4384:   If the *_nnz parameter is given then the *_nz parameter is ignored

    4386:   The `m`,`n`,`M`,`N` parameters specify the size of the matrix, and its partitioning across
    4387:   processors, while `d_nz`,`d_nnz`,`o_nz`,`o_nnz` parameters specify the approximate
    4388:   storage requirements for this matrix.

    4390:   If `PETSC_DECIDE` or  `PETSC_DETERMINE` is used for a particular argument on one
    4391:   processor than it must be used on all processors that share the object for
    4392:   that argument.

    4394:   If `m` and `n` are not `PETSC_DECIDE`, then the values determine the `PetscLayout` of the matrix and the ranges returned by
    4395:   `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`, and `MatGetOwnershipRangesColumn()`.

    4397:   The user MUST specify either the local or global matrix dimensions
    4398:   (possibly both).

    4400:   The parallel matrix is partitioned across processors such that the
    4401:   first `m0` rows belong to process 0, the next `m1` rows belong to
    4402:   process 1, the next `m2` rows belong to process 2, etc., where
    4403:   `m0`, `m1`, `m2`... are the input parameter `m` on each MPI process. I.e., each MPI process stores
    4404:   values corresponding to [m x N] submatrix.

    4406:   The columns are logically partitioned with the n0 columns belonging
    4407:   to 0th partition, the next n1 columns belonging to the next
    4408:   partition etc.. where n0,n1,n2... are the input parameter 'n'.

    4410:   The DIAGONAL portion of the local submatrix on any given processor
    4411:   is the submatrix corresponding to the rows and columns m,n
    4412:   corresponding to the given processor. i.e diagonal matrix on
    4413:   process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
    4414:   etc. The remaining portion of the local submatrix [m x (N-n)]
    4415:   constitute the OFF-DIAGONAL portion. The example below better
    4416:   illustrates this concept. The two matrices, the DIAGONAL portion and
    4417:   the OFF-DIAGONAL portion are each stored as `MATSEQAIJ` matrices.

    4419:   For a square global matrix we define each processor's diagonal portion
    4420:   to be its local rows and the corresponding columns (a square submatrix);
    4421:   each processor's off-diagonal portion encompasses the remainder of the
    4422:   local matrix (a rectangular submatrix).

    4424:   If `o_nnz`, `d_nnz` are specified, then `o_nz`, and `d_nz` are ignored.

    4426:   When calling this routine with a single process communicator, a matrix of
    4427:   type `MATSEQAIJ` is returned.  If a matrix of type `MATMPIAIJ` is desired for this
    4428:   type of communicator, use the construction mechanism
    4429: .vb
    4430:   MatCreate(..., &A);
    4431:   MatSetType(A, MATMPIAIJ);
    4432:   MatSetSizes(A, m, n, M, N);
    4433:   MatMPIAIJSetPreallocation(A, ...);
    4434: .ve

    4436:   By default, this format uses inodes (identical nodes) when possible.
    4437:   We search for consecutive rows with the same nonzero structure, thereby
    4438:   reusing matrix information to achieve increased efficiency.

    4440:   Example Usage:
    4441:   Consider the following 8x8 matrix with 34 non-zero values, that is
    4442:   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
    4443:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    4444:   as follows

    4446: .vb
    4447:             1  2  0  |  0  3  0  |  0  4
    4448:     Proc0   0  5  6  |  7  0  0  |  8  0
    4449:             9  0 10  | 11  0  0  | 12  0
    4450:     -------------------------------------
    4451:            13  0 14  | 15 16 17  |  0  0
    4452:     Proc1   0 18  0  | 19 20 21  |  0  0
    4453:             0  0  0  | 22 23  0  | 24  0
    4454:     -------------------------------------
    4455:     Proc2  25 26 27  |  0  0 28  | 29  0
    4456:            30  0  0  | 31 32 33  |  0 34
    4457: .ve

    4459:   This can be represented as a collection of submatrices as

    4461: .vb
    4462:       A B C
    4463:       D E F
    4464:       G H I
    4465: .ve

    4467:   Where the submatrices A,B,C are owned by proc0, D,E,F are
    4468:   owned by proc1, G,H,I are owned by proc2.

    4470:   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4471:   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4472:   The 'M','N' parameters are 8,8, and have the same values on all procs.

    4474:   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
    4475:   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
    4476:   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
    4477:   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
    4478:   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
    4479:   matrix, and [DF] as another SeqAIJ matrix.

    4481:   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
    4482:   allocated for every row of the local DIAGONAL submatrix, and `o_nz`
    4483:   storage locations are allocated for every row of the OFF-DIAGONAL submatrix.
    4484:   One way to choose `d_nz` and `o_nz` is to use the maximum number of nonzeros over
    4485:   the local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
    4486:   In this case, the values of `d_nz`,`o_nz` are
    4487: .vb
    4488:      proc0  dnz = 2, o_nz = 2
    4489:      proc1  dnz = 3, o_nz = 2
    4490:      proc2  dnz = 1, o_nz = 4
    4491: .ve
    4492:   We are allocating m*(`d_nz`+`o_nz`) storage locations for every proc. This
    4493:   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
    4494:   for proc3. i.e we are using 12+15+10=37 storage locations to store
    4495:   34 values.

    4497:   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
    4498:   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
    4499:   In the above case the values for d_nnz,o_nnz are
    4500: .vb
    4501:      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
    4502:      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
    4503:      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
    4504: .ve
    4505:   Here the space allocated is sum of all the above values i.e 34, and
    4506:   hence pre-allocation is perfect.

    4508: .seealso: [](ch_matrices), `Mat`, [Sparse Matrix Creation](sec_matsparse), `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4509:           `MATMPIAIJ`, `MatCreateMPIAIJWithArrays()`, `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`,
    4510:           `MatGetOwnershipRangesColumn()`, `PetscLayout`
    4511: @*/
    4512: 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)
    4513: {
    4514:   PetscMPIInt size;

    4516:   PetscFunctionBegin;
    4517:   PetscCall(MatCreate(comm, A));
    4518:   PetscCall(MatSetSizes(*A, m, n, M, N));
    4519:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4520:   if (size > 1) {
    4521:     PetscCall(MatSetType(*A, MATMPIAIJ));
    4522:     PetscCall(MatMPIAIJSetPreallocation(*A, d_nz, d_nnz, o_nz, o_nnz));
    4523:   } else {
    4524:     PetscCall(MatSetType(*A, MATSEQAIJ));
    4525:     PetscCall(MatSeqAIJSetPreallocation(*A, d_nz, d_nnz));
    4526:   }
    4527:   PetscFunctionReturn(PETSC_SUCCESS);
    4528: }

    4530: /*@C
    4531:   MatMPIAIJGetSeqAIJ - Returns the local pieces of this distributed matrix

    4533:   Not Collective

    4535:   Input Parameter:
    4536: . A - The `MATMPIAIJ` matrix

    4538:   Output Parameters:
    4539: + Ad     - The local diagonal block as a `MATSEQAIJ` matrix
    4540: . Ao     - The local off-diagonal block as a `MATSEQAIJ` matrix
    4541: - colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix

    4543:   Level: intermediate

    4545:   Note:
    4546:   The rows in `Ad` and `Ao` are in [0, Nr), where Nr is the number of local rows on this process. The columns
    4547:   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
    4548:   the number of nonzero columns in the local off-diagonal piece of the matrix `A`. The array colmap maps these
    4549:   local column numbers to global column numbers in the original matrix.

    4551: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`, `MatCreateAIJ()`, `MATSEQAIJ`
    4552: @*/
    4553: PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A, Mat *Ad, Mat *Ao, const PetscInt *colmap[])
    4554: {
    4555:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    4556:   PetscBool   flg;

    4558:   PetscFunctionBegin;
    4559:   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &flg));
    4560:   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "This function requires a MATMPIAIJ matrix as input");
    4561:   if (Ad) *Ad = a->A;
    4562:   if (Ao) *Ao = a->B;
    4563:   if (colmap) *colmap = a->garray;
    4564:   PetscFunctionReturn(PETSC_SUCCESS);
    4565: }

    4567: PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
    4568: {
    4569:   PetscInt     m, N, i, rstart, nnz, Ii;
    4570:   PetscInt    *indx;
    4571:   PetscScalar *values;
    4572:   MatType      rootType;

    4574:   PetscFunctionBegin;
    4575:   PetscCall(MatGetSize(inmat, &m, &N));
    4576:   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
    4577:     PetscInt *dnz, *onz, sum, bs, cbs;

    4579:     if (n == PETSC_DECIDE) PetscCall(PetscSplitOwnership(comm, &n, &N));
    4580:     /* Check sum(n) = N */
    4581:     PetscCallMPI(MPIU_Allreduce(&n, &sum, 1, MPIU_INT, MPI_SUM, comm));
    4582:     PetscCheck(sum == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Sum of local columns %" PetscInt_FMT " != global columns %" PetscInt_FMT, sum, N);

    4584:     PetscCallMPI(MPI_Scan(&m, &rstart, 1, MPIU_INT, MPI_SUM, comm));
    4585:     rstart -= m;

    4587:     MatPreallocateBegin(comm, m, n, dnz, onz);
    4588:     for (i = 0; i < m; i++) {
    4589:       PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
    4590:       PetscCall(MatPreallocateSet(i + rstart, nnz, indx, dnz, onz));
    4591:       PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
    4592:     }

    4594:     PetscCall(MatCreate(comm, outmat));
    4595:     PetscCall(MatSetSizes(*outmat, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    4596:     PetscCall(MatGetBlockSizes(inmat, &bs, &cbs));
    4597:     PetscCall(MatSetBlockSizes(*outmat, bs, cbs));
    4598:     PetscCall(MatGetRootType_Private(inmat, &rootType));
    4599:     PetscCall(MatSetType(*outmat, rootType));
    4600:     PetscCall(MatSeqAIJSetPreallocation(*outmat, 0, dnz));
    4601:     PetscCall(MatMPIAIJSetPreallocation(*outmat, 0, dnz, 0, onz));
    4602:     MatPreallocateEnd(dnz, onz);
    4603:     PetscCall(MatSetOption(*outmat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    4604:   }

    4606:   /* numeric phase */
    4607:   PetscCall(MatGetOwnershipRange(*outmat, &rstart, NULL));
    4608:   for (i = 0; i < m; i++) {
    4609:     PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
    4610:     Ii = i + rstart;
    4611:     PetscCall(MatSetValues(*outmat, 1, &Ii, nnz, indx, values, INSERT_VALUES));
    4612:     PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
    4613:   }
    4614:   PetscCall(MatAssemblyBegin(*outmat, MAT_FINAL_ASSEMBLY));
    4615:   PetscCall(MatAssemblyEnd(*outmat, MAT_FINAL_ASSEMBLY));
    4616:   PetscFunctionReturn(PETSC_SUCCESS);
    4617: }

    4619: static PetscErrorCode MatMergeSeqsToMPIDestroy(PetscCtxRt data)
    4620: {
    4621:   MatMergeSeqsToMPI *merge = *(MatMergeSeqsToMPI **)data;

    4623:   PetscFunctionBegin;
    4624:   if (!merge) PetscFunctionReturn(PETSC_SUCCESS);
    4625:   PetscCall(PetscFree(merge->id_r));
    4626:   PetscCall(PetscFree(merge->len_s));
    4627:   PetscCall(PetscFree(merge->len_r));
    4628:   PetscCall(PetscFree(merge->bi));
    4629:   PetscCall(PetscFree(merge->bj));
    4630:   PetscCall(PetscFree(merge->buf_ri[0]));
    4631:   PetscCall(PetscFree(merge->buf_ri));
    4632:   PetscCall(PetscFree(merge->buf_rj[0]));
    4633:   PetscCall(PetscFree(merge->buf_rj));
    4634:   PetscCall(PetscFree(merge->coi));
    4635:   PetscCall(PetscFree(merge->coj));
    4636:   PetscCall(PetscFree(merge->owners_co));
    4637:   PetscCall(PetscLayoutDestroy(&merge->rowmap));
    4638:   PetscCall(PetscFree(merge));
    4639:   PetscFunctionReturn(PETSC_SUCCESS);
    4640: }

    4642: #include <../src/mat/utils/freespace.h>
    4643: #include <petscbt.h>

    4645: PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat, Mat mpimat)
    4646: {
    4647:   MPI_Comm           comm;
    4648:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)seqmat->data;
    4649:   PetscMPIInt        size, rank, taga, *len_s;
    4650:   PetscInt           N = mpimat->cmap->N, i, j, *owners, *ai = a->i, *aj, m;
    4651:   PetscMPIInt        proc, k;
    4652:   PetscInt         **buf_ri, **buf_rj;
    4653:   PetscInt           anzi, *bj_i, *bi, *bj, arow, bnzi, nextaj;
    4654:   PetscInt           nrows, **buf_ri_k, **nextrow, **nextai;
    4655:   MPI_Request       *s_waits, *r_waits;
    4656:   MPI_Status        *status;
    4657:   const MatScalar   *aa, *a_a;
    4658:   MatScalar        **abuf_r, *ba_i;
    4659:   MatMergeSeqsToMPI *merge;
    4660:   PetscContainer     container;

    4662:   PetscFunctionBegin;
    4663:   PetscCall(PetscObjectGetComm((PetscObject)mpimat, &comm));
    4664:   PetscCall(PetscLogEventBegin(MAT_Seqstompinum, seqmat, 0, 0, 0));

    4666:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4667:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    4669:   PetscCall(PetscObjectQuery((PetscObject)mpimat, "MatMergeSeqsToMPI", (PetscObject *)&container));
    4670:   PetscCheck(container, PetscObjectComm((PetscObject)mpimat), PETSC_ERR_PLIB, "Mat not created from MatCreateMPIAIJSumSeqAIJSymbolic");
    4671:   PetscCall(PetscContainerGetPointer(container, &merge));
    4672:   PetscCall(MatSeqAIJGetArrayRead(seqmat, &a_a));
    4673:   aa = a_a;

    4675:   bi     = merge->bi;
    4676:   bj     = merge->bj;
    4677:   buf_ri = merge->buf_ri;
    4678:   buf_rj = merge->buf_rj;

    4680:   PetscCall(PetscMalloc1(size, &status));
    4681:   owners = merge->rowmap->range;
    4682:   len_s  = merge->len_s;

    4684:   /* send and recv matrix values */
    4685:   PetscCall(PetscObjectGetNewTag((PetscObject)mpimat, &taga));
    4686:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

    4688:   PetscCall(PetscMalloc1(merge->nsend + 1, &s_waits));
    4689:   for (proc = 0, k = 0; proc < size; proc++) {
    4690:     if (!len_s[proc]) continue;
    4691:     i = owners[proc];
    4692:     PetscCallMPI(MPIU_Isend(aa + ai[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
    4693:     k++;
    4694:   }

    4696:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
    4697:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));
    4698:   PetscCall(PetscFree(status));

    4700:   PetscCall(PetscFree(s_waits));
    4701:   PetscCall(PetscFree(r_waits));

    4703:   /* insert mat values of mpimat */
    4704:   PetscCall(PetscMalloc1(N, &ba_i));
    4705:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));

    4707:   for (k = 0; k < merge->nrecv; k++) {
    4708:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    4709:     nrows       = *buf_ri_k[k];
    4710:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    4711:     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    4712:   }

    4714:   /* set values of ba */
    4715:   m = merge->rowmap->n;
    4716:   for (i = 0; i < m; i++) {
    4717:     arow = owners[rank] + i;
    4718:     bj_i = bj + bi[i]; /* col indices of the i-th row of mpimat */
    4719:     bnzi = bi[i + 1] - bi[i];
    4720:     PetscCall(PetscArrayzero(ba_i, bnzi));

    4722:     /* add local non-zero vals of this proc's seqmat into ba */
    4723:     anzi   = ai[arow + 1] - ai[arow];
    4724:     aj     = a->j + ai[arow];
    4725:     aa     = a_a + ai[arow];
    4726:     nextaj = 0;
    4727:     for (j = 0; nextaj < anzi; j++) {
    4728:       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
    4729:         ba_i[j] += aa[nextaj++];
    4730:       }
    4731:     }

    4733:     /* add received vals into ba */
    4734:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    4735:       /* i-th row */
    4736:       if (i == *nextrow[k]) {
    4737:         anzi   = *(nextai[k] + 1) - *nextai[k];
    4738:         aj     = buf_rj[k] + *nextai[k];
    4739:         aa     = abuf_r[k] + *nextai[k];
    4740:         nextaj = 0;
    4741:         for (j = 0; nextaj < anzi; j++) {
    4742:           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
    4743:             ba_i[j] += aa[nextaj++];
    4744:           }
    4745:         }
    4746:         nextrow[k]++;
    4747:         nextai[k]++;
    4748:       }
    4749:     }
    4750:     PetscCall(MatSetValues(mpimat, 1, &arow, bnzi, bj_i, ba_i, INSERT_VALUES));
    4751:   }
    4752:   PetscCall(MatSeqAIJRestoreArrayRead(seqmat, &a_a));
    4753:   PetscCall(MatAssemblyBegin(mpimat, MAT_FINAL_ASSEMBLY));
    4754:   PetscCall(MatAssemblyEnd(mpimat, MAT_FINAL_ASSEMBLY));

    4756:   PetscCall(PetscFree(abuf_r[0]));
    4757:   PetscCall(PetscFree(abuf_r));
    4758:   PetscCall(PetscFree(ba_i));
    4759:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));
    4760:   PetscCall(PetscLogEventEnd(MAT_Seqstompinum, seqmat, 0, 0, 0));
    4761:   PetscFunctionReturn(PETSC_SUCCESS);
    4762: }

    4764: PetscErrorCode MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, Mat *mpimat)
    4765: {
    4766:   Mat                B_mpi;
    4767:   Mat_SeqAIJ        *a = (Mat_SeqAIJ *)seqmat->data;
    4768:   PetscMPIInt        size, rank, tagi, tagj, *len_s, *len_si, *len_ri;
    4769:   PetscInt         **buf_rj, **buf_ri, **buf_ri_k;
    4770:   PetscInt           M = seqmat->rmap->n, N = seqmat->cmap->n, i, *owners, *ai = a->i, *aj = a->j;
    4771:   PetscInt           len, *dnz, *onz, bs, cbs;
    4772:   PetscInt           k, anzi, *bi, *bj, *lnk, nlnk, arow, bnzi;
    4773:   PetscInt           nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextai;
    4774:   MPI_Request       *si_waits, *sj_waits, *ri_waits, *rj_waits;
    4775:   MPI_Status        *status;
    4776:   PetscFreeSpaceList free_space = NULL, current_space = NULL;
    4777:   PetscBT            lnkbt;
    4778:   MatMergeSeqsToMPI *merge;
    4779:   PetscContainer     container;

    4781:   PetscFunctionBegin;
    4782:   PetscCall(PetscLogEventBegin(MAT_Seqstompisym, seqmat, 0, 0, 0));

    4784:   /* make sure it is a PETSc comm */
    4785:   PetscCall(PetscCommDuplicate(comm, &comm, NULL));
    4786:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4787:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    4789:   PetscCall(PetscNew(&merge));
    4790:   PetscCall(PetscMalloc1(size, &status));

    4792:   /* determine row ownership */
    4793:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));
    4794:   PetscCall(PetscLayoutSetLocalSize(merge->rowmap, m));
    4795:   PetscCall(PetscLayoutSetSize(merge->rowmap, M));
    4796:   PetscCall(PetscLayoutSetBlockSize(merge->rowmap, 1));
    4797:   PetscCall(PetscLayoutSetUp(merge->rowmap));
    4798:   PetscCall(PetscMalloc1(size, &len_si));
    4799:   PetscCall(PetscMalloc1(size, &merge->len_s));

    4801:   m      = merge->rowmap->n;
    4802:   owners = merge->rowmap->range;

    4804:   /* determine the number of messages to send, their lengths */
    4805:   len_s = merge->len_s;

    4807:   len          = 0; /* length of buf_si[] */
    4808:   merge->nsend = 0;
    4809:   for (PetscMPIInt proc = 0; proc < size; proc++) {
    4810:     len_si[proc] = 0;
    4811:     if (proc == rank) {
    4812:       len_s[proc] = 0;
    4813:     } else {
    4814:       PetscCall(PetscMPIIntCast(owners[proc + 1] - owners[proc] + 1, &len_si[proc]));
    4815:       PetscCall(PetscMPIIntCast(ai[owners[proc + 1]] - ai[owners[proc]], &len_s[proc])); /* num of rows to be sent to [proc] */
    4816:     }
    4817:     if (len_s[proc]) {
    4818:       merge->nsend++;
    4819:       nrows = 0;
    4820:       for (i = owners[proc]; i < owners[proc + 1]; i++) {
    4821:         if (ai[i + 1] > ai[i]) nrows++;
    4822:       }
    4823:       PetscCall(PetscMPIIntCast(2 * (nrows + 1), &len_si[proc]));
    4824:       len += len_si[proc];
    4825:     }
    4826:   }

    4828:   /* determine the number and length of messages to receive for ij-structure */
    4829:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
    4830:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

    4832:   /* post the Irecv of j-structure */
    4833:   PetscCall(PetscCommGetNewTag(comm, &tagj));
    4834:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rj_waits));

    4836:   /* post the Isend of j-structure */
    4837:   PetscCall(PetscMalloc2(merge->nsend, &si_waits, merge->nsend, &sj_waits));

    4839:   for (PetscMPIInt proc = 0, k = 0; proc < size; proc++) {
    4840:     if (!len_s[proc]) continue;
    4841:     i = owners[proc];
    4842:     PetscCallMPI(MPIU_Isend(aj + ai[i], len_s[proc], MPIU_INT, proc, tagj, comm, sj_waits + k));
    4843:     k++;
    4844:   }

    4846:   /* receives and sends of j-structure are complete */
    4847:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, rj_waits, status));
    4848:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, sj_waits, status));

    4850:   /* send and recv i-structure */
    4851:   PetscCall(PetscCommGetNewTag(comm, &tagi));
    4852:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &ri_waits));

    4854:   PetscCall(PetscMalloc1(len + 1, &buf_s));
    4855:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
    4856:   for (PetscMPIInt proc = 0, k = 0; proc < size; proc++) {
    4857:     if (!len_s[proc]) continue;
    4858:     /* form outgoing message for i-structure:
    4859:          buf_si[0]:                 nrows to be sent
    4860:                [1:nrows]:           row index (global)
    4861:                [nrows+1:2*nrows+1]: i-structure index
    4862:     */
    4863:     nrows       = len_si[proc] / 2 - 1;
    4864:     buf_si_i    = buf_si + nrows + 1;
    4865:     buf_si[0]   = nrows;
    4866:     buf_si_i[0] = 0;
    4867:     nrows       = 0;
    4868:     for (i = owners[proc]; i < owners[proc + 1]; i++) {
    4869:       anzi = ai[i + 1] - ai[i];
    4870:       if (anzi) {
    4871:         buf_si_i[nrows + 1] = buf_si_i[nrows] + anzi; /* i-structure */
    4872:         buf_si[nrows + 1]   = i - owners[proc];       /* local row index */
    4873:         nrows++;
    4874:       }
    4875:     }
    4876:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, si_waits + k));
    4877:     k++;
    4878:     buf_si += len_si[proc];
    4879:   }

    4881:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, ri_waits, status));
    4882:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, si_waits, status));

    4884:   PetscCall(PetscInfo(seqmat, "nsend: %d, nrecv: %d\n", merge->nsend, merge->nrecv));
    4885:   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]));

    4887:   PetscCall(PetscFree(len_si));
    4888:   PetscCall(PetscFree(len_ri));
    4889:   PetscCall(PetscFree(rj_waits));
    4890:   PetscCall(PetscFree2(si_waits, sj_waits));
    4891:   PetscCall(PetscFree(ri_waits));
    4892:   PetscCall(PetscFree(buf_s));
    4893:   PetscCall(PetscFree(status));

    4895:   /* compute a local seq matrix in each processor */
    4896:   /* allocate bi array and free space for accumulating nonzero column info */
    4897:   PetscCall(PetscMalloc1(m + 1, &bi));
    4898:   bi[0] = 0;

    4900:   /* create and initialize a linked list */
    4901:   nlnk = N + 1;
    4902:   PetscCall(PetscLLCreate(N, N, nlnk, lnk, lnkbt));

    4904:   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
    4905:   len = ai[owners[rank + 1]] - ai[owners[rank]];
    4906:   PetscCall(PetscFreeSpaceGet(PetscIntMultTruncate(2, len) + 1, &free_space));

    4908:   current_space = free_space;

    4910:   /* determine symbolic info for each local row */
    4911:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));

    4913:   for (k = 0; k < merge->nrecv; k++) {
    4914:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    4915:     nrows       = *buf_ri_k[k];
    4916:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    4917:     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    4918:   }

    4920:   MatPreallocateBegin(comm, m, n, dnz, onz);
    4921:   len = 0;
    4922:   for (i = 0; i < m; i++) {
    4923:     bnzi = 0;
    4924:     /* add local non-zero cols of this proc's seqmat into lnk */
    4925:     arow = owners[rank] + i;
    4926:     anzi = ai[arow + 1] - ai[arow];
    4927:     aj   = a->j + ai[arow];
    4928:     PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
    4929:     bnzi += nlnk;
    4930:     /* add received col data into lnk */
    4931:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    4932:       if (i == *nextrow[k]) {            /* i-th row */
    4933:         anzi = *(nextai[k] + 1) - *nextai[k];
    4934:         aj   = buf_rj[k] + *nextai[k];
    4935:         PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
    4936:         bnzi += nlnk;
    4937:         nextrow[k]++;
    4938:         nextai[k]++;
    4939:       }
    4940:     }
    4941:     if (len < bnzi) len = bnzi; /* =max(bnzi) */

    4943:     /* if free space is not available, make more free space */
    4944:     if (current_space->local_remaining < bnzi) PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(bnzi, current_space->total_array_size), &current_space));
    4945:     /* copy data into free space, then initialize lnk */
    4946:     PetscCall(PetscLLClean(N, N, bnzi, lnk, current_space->array, lnkbt));
    4947:     PetscCall(MatPreallocateSet(i + owners[rank], bnzi, current_space->array, dnz, onz));

    4949:     current_space->array += bnzi;
    4950:     current_space->local_used += bnzi;
    4951:     current_space->local_remaining -= bnzi;

    4953:     bi[i + 1] = bi[i] + bnzi;
    4954:   }

    4956:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));

    4958:   PetscCall(PetscMalloc1(bi[m], &bj));
    4959:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
    4960:   PetscCall(PetscLLDestroy(lnk, lnkbt));

    4962:   /* create symbolic parallel matrix B_mpi */
    4963:   PetscCall(MatGetBlockSizes(seqmat, &bs, &cbs));
    4964:   PetscCall(MatCreate(comm, &B_mpi));
    4965:   if (n == PETSC_DECIDE) PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, N));
    4966:   else PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    4967:   PetscCall(MatSetBlockSizes(B_mpi, bs, cbs));
    4968:   PetscCall(MatSetType(B_mpi, MATMPIAIJ));
    4969:   PetscCall(MatMPIAIJSetPreallocation(B_mpi, 0, dnz, 0, onz));
    4970:   MatPreallocateEnd(dnz, onz);
    4971:   PetscCall(MatSetOption(B_mpi, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));

    4973:   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
    4974:   B_mpi->assembled = PETSC_FALSE;
    4975:   merge->bi        = bi;
    4976:   merge->bj        = bj;
    4977:   merge->buf_ri    = buf_ri;
    4978:   merge->buf_rj    = buf_rj;
    4979:   merge->coi       = NULL;
    4980:   merge->coj       = NULL;
    4981:   merge->owners_co = NULL;

    4983:   PetscCall(PetscCommDestroy(&comm));

    4985:   /* attach the supporting struct to B_mpi for reuse */
    4986:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    4987:   PetscCall(PetscContainerSetPointer(container, merge));
    4988:   PetscCall(PetscContainerSetCtxDestroy(container, MatMergeSeqsToMPIDestroy));
    4989:   PetscCall(PetscObjectCompose((PetscObject)B_mpi, "MatMergeSeqsToMPI", (PetscObject)container));
    4990:   PetscCall(PetscContainerDestroy(&container));
    4991:   *mpimat = B_mpi;

    4993:   PetscCall(PetscLogEventEnd(MAT_Seqstompisym, seqmat, 0, 0, 0));
    4994:   PetscFunctionReturn(PETSC_SUCCESS);
    4995: }

    4997: /*@
    4998:   MatCreateMPIAIJSumSeqAIJ - Creates a `MATMPIAIJ` matrix by adding sequential
    4999:   matrices from each processor

    5001:   Collective

    5003:   Input Parameters:
    5004: + comm   - the communicators the parallel matrix will live on
    5005: . seqmat - the input sequential matrices
    5006: . m      - number of local rows (or `PETSC_DECIDE`)
    5007: . n      - number of local columns (or `PETSC_DECIDE`)
    5008: - scall  - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5010:   Output Parameter:
    5011: . mpimat - the parallel matrix generated

    5013:   Level: advanced

    5015:   Note:
    5016:   The dimensions of the sequential matrix in each processor MUST be the same.
    5017:   The input seqmat is included into the container `MatMergeSeqsToMPIDestroy`, and will be
    5018:   destroyed when `mpimat` is destroyed. Call `PetscObjectQuery()` to access `seqmat`.

    5020: .seealso: [](ch_matrices), `Mat`, `MatCreateAIJ()`
    5021: @*/
    5022: PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, MatReuse scall, Mat *mpimat)
    5023: {
    5024:   PetscMPIInt size;

    5026:   PetscFunctionBegin;
    5027:   PetscCallMPI(MPI_Comm_size(comm, &size));
    5028:   if (size == 1) {
    5029:     PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
    5030:     if (scall == MAT_INITIAL_MATRIX) PetscCall(MatDuplicate(seqmat, MAT_COPY_VALUES, mpimat));
    5031:     else PetscCall(MatCopy(seqmat, *mpimat, SAME_NONZERO_PATTERN));
    5032:     PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
    5033:     PetscFunctionReturn(PETSC_SUCCESS);
    5034:   }
    5035:   PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
    5036:   if (scall == MAT_INITIAL_MATRIX) PetscCall(MatCreateMPIAIJSumSeqAIJSymbolic(comm, seqmat, m, n, mpimat));
    5037:   PetscCall(MatCreateMPIAIJSumSeqAIJNumeric(seqmat, *mpimat));
    5038:   PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
    5039:   PetscFunctionReturn(PETSC_SUCCESS);
    5040: }

    5042: /*@
    5043:   MatAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATAIJ` matrix.

    5045:   Not Collective

    5047:   Input Parameter:
    5048: . A - the matrix

    5050:   Output Parameter:
    5051: . A_loc - the local sequential matrix generated

    5053:   Level: developer

    5055:   Notes:
    5056:   The matrix is created by taking `A`'s local rows and putting them into a sequential matrix
    5057:   with `mlocal` rows and `n` columns. Where `mlocal` is obtained with `MatGetLocalSize()` and
    5058:   `n` is the global column count obtained with `MatGetSize()`

    5060:   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.

    5062:   For parallel matrices this creates an entirely new matrix. If the matrix is sequential it merely increases the reference count.

    5064:   Destroy the matrix with `MatDestroy()`

    5066: .seealso: [](ch_matrices), `Mat`, `MatMPIAIJGetLocalMat()`
    5067: @*/
    5068: PetscErrorCode MatAIJGetLocalMat(Mat A, Mat *A_loc)
    5069: {
    5070:   PetscBool mpi;

    5072:   PetscFunctionBegin;
    5073:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &mpi));
    5074:   if (mpi) PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, A_loc));
    5075:   else {
    5076:     *A_loc = A;
    5077:     PetscCall(PetscObjectReference((PetscObject)*A_loc));
    5078:   }
    5079:   PetscFunctionReturn(PETSC_SUCCESS);
    5080: }

    5082: /*@
    5083:   MatMPIAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix.

    5085:   Not Collective

    5087:   Input Parameters:
    5088: + A     - the matrix
    5089: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5091:   Output Parameter:
    5092: . A_loc - the local sequential matrix generated

    5094:   Level: developer

    5096:   Notes:
    5097:   The matrix is created by taking all `A`'s local rows and putting them into a sequential
    5098:   matrix with `mlocal` rows and `n` columns.`mlocal` is the row count obtained with
    5099:   `MatGetLocalSize()` and `n` is the global column count obtained with `MatGetSize()`.

    5101:   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.

    5103:   When `A` is sequential and `MAT_INITIAL_MATRIX` is requested, the matrix returned is the diagonal part of `A` (which contains the entire matrix),
    5104:   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
    5105:   then `MatCopy`(Adiag,*`A_loc`,`SAME_NONZERO_PATTERN`) is called to fill `A_loc`. Thus one can preallocate the appropriate sequential matrix `A_loc`
    5106:   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.

    5108: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMatCondensed()`, `MatMPIAIJGetLocalMatMerge()`
    5109: @*/
    5110: PetscErrorCode MatMPIAIJGetLocalMat(Mat A, MatReuse scall, Mat *A_loc)
    5111: {
    5112:   Mat_MPIAIJ        *mpimat = (Mat_MPIAIJ *)A->data;
    5113:   Mat_SeqAIJ        *mat, *a, *b;
    5114:   PetscInt          *ai, *aj, *bi, *bj, *cmap = mpimat->garray;
    5115:   const PetscScalar *aa, *ba, *aav, *bav;
    5116:   PetscScalar       *ca, *cam;
    5117:   PetscMPIInt        size;
    5118:   PetscInt           am = A->rmap->n, i, j, k, cstart = A->cmap->rstart;
    5119:   PetscInt          *ci, *cj, col, ncols_d, ncols_o, jo;
    5120:   PetscBool          match;

    5122:   PetscFunctionBegin;
    5123:   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &match));
    5124:   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
    5125:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    5126:   if (size == 1) {
    5127:     if (scall == MAT_INITIAL_MATRIX) {
    5128:       PetscCall(PetscObjectReference((PetscObject)mpimat->A));
    5129:       *A_loc = mpimat->A;
    5130:     } else if (scall == MAT_REUSE_MATRIX) {
    5131:       PetscCall(MatCopy(mpimat->A, *A_loc, SAME_NONZERO_PATTERN));
    5132:     }
    5133:     PetscFunctionReturn(PETSC_SUCCESS);
    5134:   }

    5136:   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
    5137:   a  = (Mat_SeqAIJ *)mpimat->A->data;
    5138:   b  = (Mat_SeqAIJ *)mpimat->B->data;
    5139:   ai = a->i;
    5140:   aj = a->j;
    5141:   bi = b->i;
    5142:   bj = b->j;
    5143:   PetscCall(MatSeqAIJGetArrayRead(mpimat->A, &aav));
    5144:   PetscCall(MatSeqAIJGetArrayRead(mpimat->B, &bav));
    5145:   aa = aav;
    5146:   ba = bav;
    5147:   if (scall == MAT_INITIAL_MATRIX) {
    5148:     PetscCall(PetscMalloc1(1 + am, &ci));
    5149:     ci[0] = 0;
    5150:     for (i = 0; i < am; i++) ci[i + 1] = ci[i] + (ai[i + 1] - ai[i]) + (bi[i + 1] - bi[i]);
    5151:     PetscCall(PetscMalloc1(1 + ci[am], &cj));
    5152:     PetscCall(PetscMalloc1(1 + ci[am], &ca));
    5153:     k = 0;
    5154:     for (i = 0; i < am; i++) {
    5155:       ncols_o = bi[i + 1] - bi[i];
    5156:       ncols_d = ai[i + 1] - ai[i];
    5157:       /* off-diagonal portion of A */
    5158:       for (jo = 0; jo < ncols_o; jo++) {
    5159:         col = cmap[*bj];
    5160:         if (col >= cstart) break;
    5161:         cj[k] = col;
    5162:         bj++;
    5163:         ca[k++] = *ba++;
    5164:       }
    5165:       /* diagonal portion of A */
    5166:       for (j = 0; j < ncols_d; j++) {
    5167:         cj[k]   = cstart + *aj++;
    5168:         ca[k++] = *aa++;
    5169:       }
    5170:       /* off-diagonal portion of A */
    5171:       for (j = jo; j < ncols_o; j++) {
    5172:         cj[k]   = cmap[*bj++];
    5173:         ca[k++] = *ba++;
    5174:       }
    5175:     }
    5176:     /* put together the new matrix */
    5177:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, A->cmap->N, ci, cj, ca, A_loc));
    5178:     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5179:     /* Since these are PETSc arrays, change flags to free them as necessary. */
    5180:     mat          = (Mat_SeqAIJ *)(*A_loc)->data;
    5181:     mat->free_a  = PETSC_TRUE;
    5182:     mat->free_ij = PETSC_TRUE;
    5183:     mat->nonew   = 0;
    5184:   } else if (scall == MAT_REUSE_MATRIX) {
    5185:     mat = (Mat_SeqAIJ *)(*A_loc)->data;
    5186:     ci  = mat->i;
    5187:     cj  = mat->j;
    5188:     PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &cam));
    5189:     for (i = 0; i < am; i++) {
    5190:       /* off-diagonal portion of A */
    5191:       ncols_o = bi[i + 1] - bi[i];
    5192:       for (jo = 0; jo < ncols_o; jo++) {
    5193:         col = cmap[*bj];
    5194:         if (col >= cstart) break;
    5195:         *cam++ = *ba++;
    5196:         bj++;
    5197:       }
    5198:       /* diagonal portion of A */
    5199:       ncols_d = ai[i + 1] - ai[i];
    5200:       for (j = 0; j < ncols_d; j++) *cam++ = *aa++;
    5201:       /* off-diagonal portion of A */
    5202:       for (j = jo; j < ncols_o; j++) {
    5203:         *cam++ = *ba++;
    5204:         bj++;
    5205:       }
    5206:     }
    5207:     PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &cam));
    5208:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
    5209:   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->A, &aav));
    5210:   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->B, &bav));
    5211:   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
    5212:   PetscFunctionReturn(PETSC_SUCCESS);
    5213: }

    5215: /*@
    5216:   MatMPIAIJGetLocalMatMerge - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix by taking all its local rows and putting them into a sequential matrix with
    5217:   mlocal rows and n columns. Where n is the sum of the number of columns of the diagonal and off-diagonal part

    5219:   Not Collective

    5221:   Input Parameters:
    5222: + A     - the matrix
    5223: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5225:   Output Parameters:
    5226: + glob  - sequential `IS` with global indices associated with the columns of the local sequential matrix generated (can be `NULL`)
    5227: - A_loc - the local sequential matrix generated

    5229:   Level: developer

    5231:   Note:
    5232:   This is different from `MatMPIAIJGetLocalMat()` since the first columns in the returning matrix are those associated with the diagonal
    5233:   part, then those associated with the off-diagonal part (in its local ordering)

    5235: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`
    5236: @*/
    5237: PetscErrorCode MatMPIAIJGetLocalMatMerge(Mat A, MatReuse scall, IS *glob, Mat *A_loc)
    5238: {
    5239:   Mat             Ao, Ad;
    5240:   const PetscInt *cmap;
    5241:   PetscMPIInt     size;
    5242:   PetscErrorCode (*f)(Mat, MatReuse, IS *, Mat *);

    5244:   PetscFunctionBegin;
    5245:   PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &cmap));
    5246:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    5247:   if (size == 1) {
    5248:     if (scall == MAT_INITIAL_MATRIX) {
    5249:       PetscCall(PetscObjectReference((PetscObject)Ad));
    5250:       *A_loc = Ad;
    5251:     } else if (scall == MAT_REUSE_MATRIX) {
    5252:       PetscCall(MatCopy(Ad, *A_loc, SAME_NONZERO_PATTERN));
    5253:     }
    5254:     if (glob) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)Ad), Ad->cmap->n, Ad->cmap->rstart, 1, glob));
    5255:     PetscFunctionReturn(PETSC_SUCCESS);
    5256:   }
    5257:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatMPIAIJGetLocalMatMerge_C", &f));
    5258:   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
    5259:   if (f) PetscCall((*f)(A, scall, glob, A_loc));
    5260:   else {
    5261:     Mat_SeqAIJ        *a = (Mat_SeqAIJ *)Ad->data;
    5262:     Mat_SeqAIJ        *b = (Mat_SeqAIJ *)Ao->data;
    5263:     Mat_SeqAIJ        *c;
    5264:     PetscInt          *ai = a->i, *aj = a->j;
    5265:     PetscInt          *bi = b->i, *bj = b->j;
    5266:     PetscInt          *ci, *cj;
    5267:     const PetscScalar *aa, *ba;
    5268:     PetscScalar       *ca;
    5269:     PetscInt           i, j, am, dn, on;

    5271:     PetscCall(MatGetLocalSize(Ad, &am, &dn));
    5272:     PetscCall(MatGetLocalSize(Ao, NULL, &on));
    5273:     PetscCall(MatSeqAIJGetArrayRead(Ad, &aa));
    5274:     PetscCall(MatSeqAIJGetArrayRead(Ao, &ba));
    5275:     if (scall == MAT_INITIAL_MATRIX) {
    5276:       PetscInt k;
    5277:       PetscCall(PetscMalloc1(1 + am, &ci));
    5278:       PetscCall(PetscMalloc1(ai[am] + bi[am], &cj));
    5279:       PetscCall(PetscMalloc1(ai[am] + bi[am], &ca));
    5280:       ci[0] = 0;
    5281:       for (i = 0, k = 0; i < am; i++) {
    5282:         const PetscInt ncols_o = bi[i + 1] - bi[i];
    5283:         const PetscInt ncols_d = ai[i + 1] - ai[i];
    5284:         ci[i + 1]              = ci[i] + ncols_o + ncols_d;
    5285:         /* diagonal portion of A */
    5286:         for (j = 0; j < ncols_d; j++, k++) {
    5287:           cj[k] = *aj++;
    5288:           ca[k] = *aa++;
    5289:         }
    5290:         /* off-diagonal portion of A */
    5291:         for (j = 0; j < ncols_o; j++, k++) {
    5292:           cj[k] = dn + *bj++;
    5293:           ca[k] = *ba++;
    5294:         }
    5295:       }
    5296:       /* put together the new matrix */
    5297:       PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, dn + on, ci, cj, ca, A_loc));
    5298:       /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5299:       /* Since these are PETSc arrays, change flags to free them as necessary. */
    5300:       c          = (Mat_SeqAIJ *)(*A_loc)->data;
    5301:       c->free_a  = PETSC_TRUE;
    5302:       c->free_ij = PETSC_TRUE;
    5303:       c->nonew   = 0;
    5304:       PetscCall(MatSetType(*A_loc, ((PetscObject)Ad)->type_name));
    5305:     } else if (scall == MAT_REUSE_MATRIX) {
    5306:       PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &ca));
    5307:       for (i = 0; i < am; i++) {
    5308:         const PetscInt ncols_d = ai[i + 1] - ai[i];
    5309:         const PetscInt ncols_o = bi[i + 1] - bi[i];
    5310:         /* diagonal portion of A */
    5311:         for (j = 0; j < ncols_d; j++) *ca++ = *aa++;
    5312:         /* off-diagonal portion of A */
    5313:         for (j = 0; j < ncols_o; j++) *ca++ = *ba++;
    5314:       }
    5315:       PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &ca));
    5316:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
    5317:     PetscCall(MatSeqAIJRestoreArrayRead(Ad, &aa));
    5318:     PetscCall(MatSeqAIJRestoreArrayRead(Ao, &aa));
    5319:     if (glob) {
    5320:       PetscInt cst, *gidx;

    5322:       PetscCall(MatGetOwnershipRangeColumn(A, &cst, NULL));
    5323:       PetscCall(PetscMalloc1(dn + on, &gidx));
    5324:       for (i = 0; i < dn; i++) gidx[i] = cst + i;
    5325:       for (i = 0; i < on; i++) gidx[i + dn] = cmap[i];
    5326:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)Ad), dn + on, gidx, PETSC_OWN_POINTER, glob));
    5327:     }
    5328:   }
    5329:   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
    5330:   PetscFunctionReturn(PETSC_SUCCESS);
    5331: }

    5333: /*@C
    5334:   MatMPIAIJGetLocalMatCondensed - Creates a `MATSEQAIJ` matrix from an `MATMPIAIJ` matrix by taking all its local rows and NON-ZERO columns

    5336:   Not Collective

    5338:   Input Parameters:
    5339: + A     - the matrix
    5340: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    5341: . row   - index set of rows to extract (or `NULL`)
    5342: - col   - index set of columns to extract (or `NULL`)

    5344:   Output Parameter:
    5345: . A_loc - the local sequential matrix generated

    5347:   Level: developer

    5349: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`
    5350: @*/
    5351: PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A, MatReuse scall, IS *row, IS *col, Mat *A_loc)
    5352: {
    5353:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    5354:   PetscInt    i, start, end, ncols, nzA, nzB, *cmap, imark, *idx;
    5355:   IS          isrowa, iscola;
    5356:   Mat        *aloc;
    5357:   PetscBool   match;

    5359:   PetscFunctionBegin;
    5360:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &match));
    5361:   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
    5362:   PetscCall(PetscLogEventBegin(MAT_Getlocalmatcondensed, A, 0, 0, 0));
    5363:   if (!row) {
    5364:     start = A->rmap->rstart;
    5365:     end   = A->rmap->rend;
    5366:     PetscCall(ISCreateStride(PETSC_COMM_SELF, end - start, start, 1, &isrowa));
    5367:   } else {
    5368:     isrowa = *row;
    5369:   }
    5370:   if (!col) {
    5371:     start = A->cmap->rstart;
    5372:     cmap  = a->garray;
    5373:     nzA   = a->A->cmap->n;
    5374:     nzB   = a->B->cmap->n;
    5375:     PetscCall(PetscMalloc1(nzA + nzB, &idx));
    5376:     ncols = 0;
    5377:     for (i = 0; i < nzB; i++) {
    5378:       if (cmap[i] < start) idx[ncols++] = cmap[i];
    5379:       else break;
    5380:     }
    5381:     imark = i;
    5382:     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;
    5383:     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i];
    5384:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &iscola));
    5385:   } else {
    5386:     iscola = *col;
    5387:   }
    5388:   if (scall != MAT_INITIAL_MATRIX) {
    5389:     PetscCall(PetscMalloc1(1, &aloc));
    5390:     aloc[0] = *A_loc;
    5391:   }
    5392:   PetscCall(MatCreateSubMatrices(A, 1, &isrowa, &iscola, scall, &aloc));
    5393:   if (!col) { /* attach global id of condensed columns */
    5394:     PetscCall(PetscObjectCompose((PetscObject)aloc[0], "_petsc_GetLocalMatCondensed_iscol", (PetscObject)iscola));
    5395:   }
    5396:   *A_loc = aloc[0];
    5397:   PetscCall(PetscFree(aloc));
    5398:   if (!row) PetscCall(ISDestroy(&isrowa));
    5399:   if (!col) PetscCall(ISDestroy(&iscola));
    5400:   PetscCall(PetscLogEventEnd(MAT_Getlocalmatcondensed, A, 0, 0, 0));
    5401:   PetscFunctionReturn(PETSC_SUCCESS);
    5402: }

    5404: /*
    5405:  * Create a sequential AIJ matrix based on row indices. a whole column is extracted once a row is matched.
    5406:  * Row could be local or remote.The routine is designed to be scalable in memory so that nothing is based
    5407:  * on a global size.
    5408:  * */
    5409: static PetscErrorCode MatCreateSeqSubMatrixWithRows_Private(Mat P, IS rows, Mat *P_oth)
    5410: {
    5411:   Mat_MPIAIJ            *p  = (Mat_MPIAIJ *)P->data;
    5412:   Mat_SeqAIJ            *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data, *p_oth;
    5413:   PetscInt               plocalsize, nrows, *ilocal, *oilocal, i, lidx, *nrcols, *nlcols, ncol;
    5414:   PetscMPIInt            owner;
    5415:   PetscSFNode           *iremote, *oiremote;
    5416:   const PetscInt        *lrowindices;
    5417:   PetscSF                sf, osf;
    5418:   PetscInt               pcstart, *roffsets, *loffsets, *pnnz, j;
    5419:   PetscInt               ontotalcols, dntotalcols, ntotalcols, nout;
    5420:   MPI_Comm               comm;
    5421:   ISLocalToGlobalMapping mapping;
    5422:   const PetscScalar     *pd_a, *po_a;

    5424:   PetscFunctionBegin;
    5425:   PetscCall(PetscObjectGetComm((PetscObject)P, &comm));
    5426:   /* plocalsize is the number of roots
    5427:    * nrows is the number of leaves
    5428:    * */
    5429:   PetscCall(MatGetLocalSize(P, &plocalsize, NULL));
    5430:   PetscCall(ISGetLocalSize(rows, &nrows));
    5431:   PetscCall(PetscCalloc1(nrows, &iremote));
    5432:   PetscCall(ISGetIndices(rows, &lrowindices));
    5433:   for (i = 0; i < nrows; i++) {
    5434:     /* Find a remote index and an owner for a row
    5435:      * The row could be local or remote
    5436:      * */
    5437:     owner = 0;
    5438:     lidx  = 0;
    5439:     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, &lidx));
    5440:     iremote[i].index = lidx;
    5441:     iremote[i].rank  = owner;
    5442:   }
    5443:   /* Create SF to communicate how many nonzero columns for each row */
    5444:   PetscCall(PetscSFCreate(comm, &sf));
    5445:   /* SF will figure out the number of nonzero columns for each row, and their
    5446:    * offsets
    5447:    * */
    5448:   PetscCall(PetscSFSetGraph(sf, plocalsize, nrows, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    5449:   PetscCall(PetscSFSetFromOptions(sf));
    5450:   PetscCall(PetscSFSetUp(sf));

    5452:   PetscCall(PetscCalloc1(2 * (plocalsize + 1), &roffsets));
    5453:   PetscCall(PetscCalloc1(2 * plocalsize, &nrcols));
    5454:   PetscCall(PetscCalloc1(nrows, &pnnz));
    5455:   roffsets[0] = 0;
    5456:   roffsets[1] = 0;
    5457:   for (i = 0; i < plocalsize; i++) {
    5458:     /* diagonal */
    5459:     nrcols[i * 2 + 0] = pd->i[i + 1] - pd->i[i];
    5460:     /* off-diagonal */
    5461:     nrcols[i * 2 + 1] = po->i[i + 1] - po->i[i];
    5462:     /* compute offsets so that we relative location for each row */
    5463:     roffsets[(i + 1) * 2 + 0] = roffsets[i * 2 + 0] + nrcols[i * 2 + 0];
    5464:     roffsets[(i + 1) * 2 + 1] = roffsets[i * 2 + 1] + nrcols[i * 2 + 1];
    5465:   }
    5466:   PetscCall(PetscCalloc1(2 * nrows, &nlcols));
    5467:   PetscCall(PetscCalloc1(2 * nrows, &loffsets));
    5468:   /* 'r' means root, and 'l' means leaf */
    5469:   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
    5470:   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
    5471:   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
    5472:   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
    5473:   PetscCall(PetscSFDestroy(&sf));
    5474:   PetscCall(PetscFree(roffsets));
    5475:   PetscCall(PetscFree(nrcols));
    5476:   dntotalcols = 0;
    5477:   ontotalcols = 0;
    5478:   ncol        = 0;
    5479:   for (i = 0; i < nrows; i++) {
    5480:     pnnz[i] = nlcols[i * 2 + 0] + nlcols[i * 2 + 1];
    5481:     ncol    = PetscMax(pnnz[i], ncol);
    5482:     /* diagonal */
    5483:     dntotalcols += nlcols[i * 2 + 0];
    5484:     /* off-diagonal */
    5485:     ontotalcols += nlcols[i * 2 + 1];
    5486:   }
    5487:   /* We do not need to figure the right number of columns
    5488:    * since all the calculations will be done by going through the raw data
    5489:    * */
    5490:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nrows, ncol, 0, pnnz, P_oth));
    5491:   PetscCall(MatSetUp(*P_oth));
    5492:   PetscCall(PetscFree(pnnz));
    5493:   p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
    5494:   /* diagonal */
    5495:   PetscCall(PetscCalloc1(dntotalcols, &iremote));
    5496:   /* off-diagonal */
    5497:   PetscCall(PetscCalloc1(ontotalcols, &oiremote));
    5498:   /* diagonal */
    5499:   PetscCall(PetscCalloc1(dntotalcols, &ilocal));
    5500:   /* off-diagonal */
    5501:   PetscCall(PetscCalloc1(ontotalcols, &oilocal));
    5502:   dntotalcols = 0;
    5503:   ontotalcols = 0;
    5504:   ntotalcols  = 0;
    5505:   for (i = 0; i < nrows; i++) {
    5506:     owner = 0;
    5507:     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, NULL));
    5508:     /* Set iremote for diag matrix */
    5509:     for (j = 0; j < nlcols[i * 2 + 0]; j++) {
    5510:       iremote[dntotalcols].index = loffsets[i * 2 + 0] + j;
    5511:       iremote[dntotalcols].rank  = owner;
    5512:       /* P_oth is seqAIJ so that ilocal need to point to the first part of memory */
    5513:       ilocal[dntotalcols++] = ntotalcols++;
    5514:     }
    5515:     /* off-diagonal */
    5516:     for (j = 0; j < nlcols[i * 2 + 1]; j++) {
    5517:       oiremote[ontotalcols].index = loffsets[i * 2 + 1] + j;
    5518:       oiremote[ontotalcols].rank  = owner;
    5519:       oilocal[ontotalcols++]      = ntotalcols++;
    5520:     }
    5521:   }
    5522:   PetscCall(ISRestoreIndices(rows, &lrowindices));
    5523:   PetscCall(PetscFree(loffsets));
    5524:   PetscCall(PetscFree(nlcols));
    5525:   PetscCall(PetscSFCreate(comm, &sf));
    5526:   /* P serves as roots and P_oth is leaves
    5527:    * Diag matrix
    5528:    * */
    5529:   PetscCall(PetscSFSetGraph(sf, pd->i[plocalsize], dntotalcols, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    5530:   PetscCall(PetscSFSetFromOptions(sf));
    5531:   PetscCall(PetscSFSetUp(sf));

    5533:   PetscCall(PetscSFCreate(comm, &osf));
    5534:   /* off-diagonal */
    5535:   PetscCall(PetscSFSetGraph(osf, po->i[plocalsize], ontotalcols, oilocal, PETSC_OWN_POINTER, oiremote, PETSC_OWN_POINTER));
    5536:   PetscCall(PetscSFSetFromOptions(osf));
    5537:   PetscCall(PetscSFSetUp(osf));
    5538:   PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
    5539:   PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
    5540:   /* operate on the matrix internal data to save memory */
    5541:   PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5542:   PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5543:   PetscCall(MatGetOwnershipRangeColumn(P, &pcstart, NULL));
    5544:   /* Convert to global indices for diag matrix */
    5545:   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] += pcstart;
    5546:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
    5547:   /* We want P_oth store global indices */
    5548:   PetscCall(ISLocalToGlobalMappingCreate(comm, 1, p->B->cmap->n, p->garray, PETSC_COPY_VALUES, &mapping));
    5549:   /* Use memory scalable approach */
    5550:   PetscCall(ISLocalToGlobalMappingSetType(mapping, ISLOCALTOGLOBALMAPPINGHASH));
    5551:   PetscCall(ISLocalToGlobalMappingApply(mapping, po->i[plocalsize], po->j, po->j));
    5552:   PetscCall(PetscSFBcastBegin(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
    5553:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
    5554:   /* Convert back to local indices */
    5555:   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] -= pcstart;
    5556:   PetscCall(PetscSFBcastEnd(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
    5557:   nout = 0;
    5558:   PetscCall(ISGlobalToLocalMappingApply(mapping, IS_GTOLM_DROP, po->i[plocalsize], po->j, &nout, po->j));
    5559:   PetscCheck(nout == po->i[plocalsize], comm, PETSC_ERR_ARG_INCOMP, "n %" PetscInt_FMT " does not equal to nout %" PetscInt_FMT " ", po->i[plocalsize], nout);
    5560:   PetscCall(ISLocalToGlobalMappingDestroy(&mapping));
    5561:   /* Exchange values */
    5562:   PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5563:   PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5564:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
    5565:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
    5566:   /* Stop PETSc from shrinking memory */
    5567:   for (i = 0; i < nrows; i++) p_oth->ilen[i] = p_oth->imax[i];
    5568:   PetscCall(MatAssemblyBegin(*P_oth, MAT_FINAL_ASSEMBLY));
    5569:   PetscCall(MatAssemblyEnd(*P_oth, MAT_FINAL_ASSEMBLY));
    5570:   /* Attach PetscSF objects to P_oth so that we can reuse it later */
    5571:   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "diagsf", (PetscObject)sf));
    5572:   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "offdiagsf", (PetscObject)osf));
    5573:   PetscCall(PetscSFDestroy(&sf));
    5574:   PetscCall(PetscSFDestroy(&osf));
    5575:   PetscFunctionReturn(PETSC_SUCCESS);
    5576: }

    5578: /*
    5579:  * Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
    5580:  * This supports MPIAIJ and MAIJ
    5581:  * */
    5582: PetscErrorCode MatGetBrowsOfAcols_MPIXAIJ(Mat A, Mat P, PetscInt dof, MatReuse reuse, Mat *P_oth)
    5583: {
    5584:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data, *p = (Mat_MPIAIJ *)P->data;
    5585:   Mat_SeqAIJ *p_oth;
    5586:   IS          rows, map;
    5587:   PetscHMapI  hamp;
    5588:   PetscInt    i, htsize, *rowindices, off, *mapping, key, count;
    5589:   MPI_Comm    comm;
    5590:   PetscSF     sf, osf;
    5591:   PetscBool   has;

    5593:   PetscFunctionBegin;
    5594:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    5595:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, P, 0, 0));
    5596:   /* If it is the first time, create an index set of off-diag nonzero columns of A,
    5597:    *  and then create a submatrix (that often is an overlapping matrix)
    5598:    * */
    5599:   if (reuse == MAT_INITIAL_MATRIX) {
    5600:     /* Use a hash table to figure out unique keys */
    5601:     PetscCall(PetscHMapICreateWithSize(a->B->cmap->n, &hamp));
    5602:     PetscCall(PetscCalloc1(a->B->cmap->n, &mapping));
    5603:     count = 0;
    5604:     /* Assume that  a->g is sorted, otherwise the following does not make sense */
    5605:     for (i = 0; i < a->B->cmap->n; i++) {
    5606:       key = a->garray[i] / dof;
    5607:       PetscCall(PetscHMapIHas(hamp, key, &has));
    5608:       if (!has) {
    5609:         mapping[i] = count;
    5610:         PetscCall(PetscHMapISet(hamp, key, count++));
    5611:       } else {
    5612:         /* Current 'i' has the same value the previous step */
    5613:         mapping[i] = count - 1;
    5614:       }
    5615:     }
    5616:     PetscCall(ISCreateGeneral(comm, a->B->cmap->n, mapping, PETSC_OWN_POINTER, &map));
    5617:     PetscCall(PetscHMapIGetSize(hamp, &htsize));
    5618:     PetscCheck(htsize == count, comm, PETSC_ERR_ARG_INCOMP, " Size of hash map %" PetscInt_FMT " is inconsistent with count %" PetscInt_FMT, htsize, count);
    5619:     PetscCall(PetscCalloc1(htsize, &rowindices));
    5620:     off = 0;
    5621:     PetscCall(PetscHMapIGetKeys(hamp, &off, rowindices));
    5622:     PetscCall(PetscHMapIDestroy(&hamp));
    5623:     PetscCall(PetscSortInt(htsize, rowindices));
    5624:     PetscCall(ISCreateGeneral(comm, htsize, rowindices, PETSC_OWN_POINTER, &rows));
    5625:     /* In case, the matrix was already created but users want to recreate the matrix */
    5626:     PetscCall(MatDestroy(P_oth));
    5627:     PetscCall(MatCreateSeqSubMatrixWithRows_Private(P, rows, P_oth));
    5628:     PetscCall(PetscObjectCompose((PetscObject)*P_oth, "aoffdiagtopothmapping", (PetscObject)map));
    5629:     PetscCall(ISDestroy(&map));
    5630:     PetscCall(ISDestroy(&rows));
    5631:   } else if (reuse == MAT_REUSE_MATRIX) {
    5632:     /* If matrix was already created, we simply update values using SF objects
    5633:      * that as attached to the matrix earlier.
    5634:      */
    5635:     const PetscScalar *pd_a, *po_a;

    5637:     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "diagsf", (PetscObject *)&sf));
    5638:     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "offdiagsf", (PetscObject *)&osf));
    5639:     PetscCheck(sf && osf, comm, PETSC_ERR_ARG_NULL, "Matrix is not initialized yet");
    5640:     p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
    5641:     /* Update values in place */
    5642:     PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
    5643:     PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
    5644:     PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5645:     PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5646:     PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5647:     PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5648:     PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
    5649:     PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
    5650:   } else SETERRQ(comm, PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown reuse type");
    5651:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, P, 0, 0));
    5652:   PetscFunctionReturn(PETSC_SUCCESS);
    5653: }

    5655: /*@C
    5656:   MatGetBrowsOfAcols - Returns `IS` that contain rows of `B` that equal to nonzero columns of local `A`

    5658:   Collective

    5660:   Input Parameters:
    5661: + A     - the first matrix in `MATMPIAIJ` format
    5662: . B     - the second matrix in `MATMPIAIJ` format
    5663: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5665:   Output Parameters:
    5666: + rowb  - On input index sets of rows of B to extract (or `NULL`), modified on output
    5667: . colb  - On input index sets of columns of B to extract (or `NULL`), modified on output
    5668: - B_seq - the sequential matrix generated

    5670:   Level: developer

    5672: .seealso: `Mat`, `MATMPIAIJ`, `IS`, `MatReuse`
    5673: @*/
    5674: PetscErrorCode MatGetBrowsOfAcols(Mat A, Mat B, MatReuse scall, IS *rowb, IS *colb, Mat *B_seq)
    5675: {
    5676:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    5677:   PetscInt   *idx, i, start, ncols, nzA, nzB, *cmap, imark;
    5678:   IS          isrowb, iscolb;
    5679:   Mat        *bseq = NULL;

    5681:   PetscFunctionBegin;
    5682:   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 ")",
    5683:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    5684:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAcols, A, B, 0, 0));

    5686:   if (scall == MAT_INITIAL_MATRIX) {
    5687:     start = A->cmap->rstart;
    5688:     cmap  = a->garray;
    5689:     nzA   = a->A->cmap->n;
    5690:     nzB   = a->B->cmap->n;
    5691:     PetscCall(PetscMalloc1(nzA + nzB, &idx));
    5692:     ncols = 0;
    5693:     for (i = 0; i < nzB; i++) { /* row < local row index */
    5694:       if (cmap[i] < start) idx[ncols++] = cmap[i];
    5695:       else break;
    5696:     }
    5697:     imark = i;
    5698:     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;   /* local rows */
    5699:     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
    5700:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &isrowb));
    5701:     PetscCall(ISCreateStride(PETSC_COMM_SELF, B->cmap->N, 0, 1, &iscolb));
    5702:   } else {
    5703:     PetscCheck(rowb && colb, PETSC_COMM_SELF, PETSC_ERR_SUP, "IS rowb and colb must be provided for MAT_REUSE_MATRIX");
    5704:     isrowb = *rowb;
    5705:     iscolb = *colb;
    5706:     PetscCall(PetscMalloc1(1, &bseq));
    5707:     bseq[0] = *B_seq;
    5708:   }
    5709:   PetscCall(MatCreateSubMatrices(B, 1, &isrowb, &iscolb, scall, &bseq));
    5710:   *B_seq = bseq[0];
    5711:   PetscCall(PetscFree(bseq));
    5712:   if (!rowb) {
    5713:     PetscCall(ISDestroy(&isrowb));
    5714:   } else {
    5715:     *rowb = isrowb;
    5716:   }
    5717:   if (!colb) {
    5718:     PetscCall(ISDestroy(&iscolb));
    5719:   } else {
    5720:     *colb = iscolb;
    5721:   }
    5722:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAcols, A, B, 0, 0));
    5723:   PetscFunctionReturn(PETSC_SUCCESS);
    5724: }

    5726: /*
    5727:     MatGetBrowsOfAoCols_MPIAIJ - Creates a `MATSEQAIJ` matrix by taking rows of B that equal to nonzero columns
    5728:     of the OFF-DIAGONAL portion of local A

    5730:     Collective

    5732:    Input Parameters:
    5733: +    A,B - the matrices in `MATMPIAIJ` format
    5734: -    scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5736:    Output Parameter:
    5737: +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
    5738: .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
    5739: .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
    5740: -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N

    5742:     Developer Note:
    5743:     This directly accesses information inside the VecScatter associated with the matrix-vector product
    5744:      for this matrix. This is not desirable..

    5746:     Level: developer

    5748: */

    5750: PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A, Mat B, MatReuse scall, PetscInt **startsj_s, PetscInt **startsj_r, MatScalar **bufa_ptr, Mat *B_oth)
    5751: {
    5752:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
    5753:   VecScatter         ctx;
    5754:   MPI_Comm           comm;
    5755:   const PetscMPIInt *rprocs, *sprocs;
    5756:   PetscMPIInt        nrecvs, nsends;
    5757:   const PetscInt    *srow, *rstarts, *sstarts;
    5758:   PetscInt          *rowlen, *bufj, *bufJ, ncols = 0, aBn = a->B->cmap->n, row, *b_othi, *b_othj, *rvalues = NULL, *svalues = NULL, *cols, sbs, rbs;
    5759:   PetscInt           i, j, k = 0, l, ll, nrows, *rstartsj = NULL, *sstartsj, len;
    5760:   PetscScalar       *b_otha, *bufa, *bufA, *vals = NULL;
    5761:   MPI_Request       *reqs = NULL, *rwaits = NULL, *swaits = NULL;
    5762:   PetscMPIInt        size, tag, rank, nreqs;

    5764:   PetscFunctionBegin;
    5765:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    5766:   PetscCallMPI(MPI_Comm_size(comm, &size));

    5768:   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 ")",
    5769:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    5770:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, B, 0, 0));
    5771:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    5773:   if (size == 1) {
    5774:     startsj_s = NULL;
    5775:     bufa_ptr  = NULL;
    5776:     *B_oth    = NULL;
    5777:     PetscFunctionReturn(PETSC_SUCCESS);
    5778:   }

    5780:   ctx = a->Mvctx;
    5781:   tag = ((PetscObject)ctx)->tag;

    5783:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &srow, &sprocs, &sbs));
    5784:   /* rprocs[] must be ordered so that indices received from them are ordered in rvalues[], which is key to algorithms used in this subroutine */
    5785:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL /*indices not needed*/, &rprocs, &rbs));
    5786:   PetscCall(PetscMPIIntCast(nsends + nrecvs, &nreqs));
    5787:   PetscCall(PetscMalloc1(nreqs, &reqs));
    5788:   rwaits = reqs;
    5789:   swaits = PetscSafePointerPlusOffset(reqs, nrecvs);

    5791:   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
    5792:   if (scall == MAT_INITIAL_MATRIX) {
    5793:     /* i-array */
    5794:     /*  post receives */
    5795:     if (nrecvs) PetscCall(PetscMalloc1(rbs * (rstarts[nrecvs] - rstarts[0]), &rvalues)); /* rstarts can be NULL when nrecvs=0 */
    5796:     for (i = 0; i < nrecvs; i++) {
    5797:       rowlen = rvalues + rstarts[i] * rbs;
    5798:       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of indices to be received */
    5799:       PetscCallMPI(MPIU_Irecv(rowlen, nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
    5800:     }

    5802:     /* pack the outgoing message */
    5803:     PetscCall(PetscMalloc2(nsends + 1, &sstartsj, nrecvs + 1, &rstartsj));

    5805:     sstartsj[0] = 0;
    5806:     rstartsj[0] = 0;
    5807:     len         = 0; /* total length of j or a array to be sent */
    5808:     if (nsends) {
    5809:       k = sstarts[0]; /* ATTENTION: sstarts[0] and rstarts[0] are not necessarily zero */
    5810:       PetscCall(PetscMalloc1(sbs * (sstarts[nsends] - sstarts[0]), &svalues));
    5811:     }
    5812:     for (i = 0; i < nsends; i++) {
    5813:       rowlen = svalues + (sstarts[i] - sstarts[0]) * sbs;
    5814:       nrows  = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5815:       for (j = 0; j < nrows; j++) {
    5816:         row = srow[k] + B->rmap->range[rank]; /* global row idx */
    5817:         for (l = 0; l < sbs; l++) {
    5818:           PetscCall(MatGetRow_MPIAIJ(B, row + l, &ncols, NULL, NULL)); /* rowlength */

    5820:           rowlen[j * sbs + l] = ncols;

    5822:           len += ncols;
    5823:           PetscCall(MatRestoreRow_MPIAIJ(B, row + l, &ncols, NULL, NULL));
    5824:         }
    5825:         k++;
    5826:       }
    5827:       PetscCallMPI(MPIU_Isend(rowlen, nrows * sbs, MPIU_INT, sprocs[i], tag, comm, swaits + i));

    5829:       sstartsj[i + 1] = len; /* starting point of (i+1)-th outgoing msg in bufj and bufa */
    5830:     }
    5831:     /* recvs and sends of i-array are completed */
    5832:     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5833:     PetscCall(PetscFree(svalues));

    5835:     /* allocate buffers for sending j and a arrays */
    5836:     PetscCall(PetscMalloc1(len, &bufj));
    5837:     PetscCall(PetscMalloc1(len, &bufa));

    5839:     /* create i-array of B_oth */
    5840:     PetscCall(PetscMalloc1(aBn + 1, &b_othi));

    5842:     b_othi[0] = 0;
    5843:     len       = 0; /* total length of j or a array to be received */
    5844:     k         = 0;
    5845:     for (i = 0; i < nrecvs; i++) {
    5846:       rowlen = rvalues + (rstarts[i] - rstarts[0]) * rbs;
    5847:       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of rows to be received */
    5848:       for (j = 0; j < nrows; j++) {
    5849:         b_othi[k + 1] = b_othi[k] + rowlen[j];
    5850:         PetscCall(PetscIntSumError(rowlen[j], len, &len));
    5851:         k++;
    5852:       }
    5853:       rstartsj[i + 1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
    5854:     }
    5855:     PetscCall(PetscFree(rvalues));

    5857:     /* allocate space for j and a arrays of B_oth */
    5858:     PetscCall(PetscMalloc1(b_othi[aBn], &b_othj));
    5859:     PetscCall(PetscMalloc1(b_othi[aBn], &b_otha));

    5861:     /* j-array */
    5862:     /*  post receives of j-array */
    5863:     for (i = 0; i < nrecvs; i++) {
    5864:       nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
    5865:       PetscCallMPI(MPIU_Irecv(PetscSafePointerPlusOffset(b_othj, rstartsj[i]), nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
    5866:     }

    5868:     /* pack the outgoing message j-array */
    5869:     if (nsends) k = sstarts[0];
    5870:     for (i = 0; i < nsends; i++) {
    5871:       nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5872:       bufJ  = PetscSafePointerPlusOffset(bufj, sstartsj[i]);
    5873:       for (j = 0; j < nrows; j++) {
    5874:         row = srow[k++] + B->rmap->range[rank]; /* global row idx */
    5875:         for (ll = 0; ll < sbs; ll++) {
    5876:           PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
    5877:           for (l = 0; l < ncols; l++) *bufJ++ = cols[l];
    5878:           PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
    5879:         }
    5880:       }
    5881:       PetscCallMPI(MPIU_Isend(PetscSafePointerPlusOffset(bufj, sstartsj[i]), sstartsj[i + 1] - sstartsj[i], MPIU_INT, sprocs[i], tag, comm, swaits + i));
    5882:     }

    5884:     /* recvs and sends of j-array are completed */
    5885:     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5886:   } else if (scall == MAT_REUSE_MATRIX) {
    5887:     sstartsj = *startsj_s;
    5888:     rstartsj = *startsj_r;
    5889:     bufa     = *bufa_ptr;
    5890:     PetscCall(MatSeqAIJGetArrayWrite(*B_oth, &b_otha));
    5891:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not possess an object container");

    5893:   /* a-array */
    5894:   /*  post receives of a-array */
    5895:   for (i = 0; i < nrecvs; i++) {
    5896:     nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
    5897:     PetscCallMPI(MPIU_Irecv(PetscSafePointerPlusOffset(b_otha, rstartsj[i]), nrows, MPIU_SCALAR, rprocs[i], tag, comm, rwaits + i));
    5898:   }

    5900:   /* pack the outgoing message a-array */
    5901:   if (nsends) k = sstarts[0];
    5902:   for (i = 0; i < nsends; i++) {
    5903:     nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5904:     bufA  = PetscSafePointerPlusOffset(bufa, sstartsj[i]);
    5905:     for (j = 0; j < nrows; j++) {
    5906:       row = srow[k++] + B->rmap->range[rank]; /* global row idx */
    5907:       for (ll = 0; ll < sbs; ll++) {
    5908:         PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
    5909:         for (l = 0; l < ncols; l++) *bufA++ = vals[l];
    5910:         PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
    5911:       }
    5912:     }
    5913:     PetscCallMPI(MPIU_Isend(PetscSafePointerPlusOffset(bufa, sstartsj[i]), sstartsj[i + 1] - sstartsj[i], MPIU_SCALAR, sprocs[i], tag, comm, swaits + i));
    5914:   }
    5915:   /* recvs and sends of a-array are completed */
    5916:   if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5917:   PetscCall(PetscFree(reqs));

    5919:   if (scall == MAT_INITIAL_MATRIX) {
    5920:     Mat_SeqAIJ *b_oth;

    5922:     /* put together the new matrix */
    5923:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, aBn, B->cmap->N, b_othi, b_othj, b_otha, B_oth));

    5925:     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5926:     /* Since these are PETSc arrays, change flags to free them as necessary. */
    5927:     b_oth          = (Mat_SeqAIJ *)(*B_oth)->data;
    5928:     b_oth->free_a  = PETSC_TRUE;
    5929:     b_oth->free_ij = PETSC_TRUE;
    5930:     b_oth->nonew   = 0;

    5932:     PetscCall(PetscFree(bufj));
    5933:     if (!startsj_s || !bufa_ptr) {
    5934:       PetscCall(PetscFree2(sstartsj, rstartsj));
    5935:       PetscCall(PetscFree(bufa_ptr));
    5936:     } else {
    5937:       *startsj_s = sstartsj;
    5938:       *startsj_r = rstartsj;
    5939:       *bufa_ptr  = bufa;
    5940:     }
    5941:   } else if (scall == MAT_REUSE_MATRIX) {
    5942:     PetscCall(MatSeqAIJRestoreArrayWrite(*B_oth, &b_otha));
    5943:   }

    5945:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE, &nsends, &sstarts, &srow, &sprocs, &sbs));
    5946:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE, &nrecvs, &rstarts, NULL, &rprocs, &rbs));
    5947:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, B, 0, 0));
    5948:   PetscFunctionReturn(PETSC_SUCCESS);
    5949: }

    5951: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat, MatType, MatReuse, Mat *);
    5952: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat, MatType, MatReuse, Mat *);
    5953: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJSELL(Mat, MatType, MatReuse, Mat *);
    5954: #if defined(PETSC_HAVE_MKL_SPARSE)
    5955: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJMKL(Mat, MatType, MatReuse, Mat *);
    5956: #endif
    5957: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIBAIJ(Mat, MatType, MatReuse, Mat *);
    5958: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat, MatType, MatReuse, Mat *);
    5959: #if defined(PETSC_HAVE_ELEMENTAL)
    5960: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
    5961: #endif
    5962: #if defined(PETSC_HAVE_SCALAPACK) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
    5963: PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
    5964: #endif
    5965: #if defined(PETSC_HAVE_HYPRE)
    5966: PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat, MatType, MatReuse, Mat *);
    5967: #endif
    5968: #if defined(PETSC_HAVE_CUDA)
    5969: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
    5970: #endif
    5971: #if defined(PETSC_HAVE_HIP)
    5972: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJHIPSPARSE(Mat, MatType, MatReuse, Mat *);
    5973: #endif
    5974: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    5975: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJKokkos(Mat, MatType, MatReuse, Mat *);
    5976: #endif
    5977: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISELL(Mat, MatType, MatReuse, Mat *);
    5978: PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);
    5979: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);

    5981: /*
    5982:     Computes (B'*A')' since computing B*A directly is untenable

    5984:                n                       p                          p
    5985:         [             ]       [             ]         [                 ]
    5986:       m [      A      ]  *  n [       B     ]   =   m [         C       ]
    5987:         [             ]       [             ]         [                 ]

    5989: */
    5990: static PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A, Mat B, Mat C)
    5991: {
    5992:   Mat At, Bt, Ct;

    5994:   PetscFunctionBegin;
    5995:   PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
    5996:   PetscCall(MatTranspose(B, MAT_INITIAL_MATRIX, &Bt));
    5997:   PetscCall(MatMatMult(Bt, At, MAT_INITIAL_MATRIX, PETSC_CURRENT, &Ct));
    5998:   PetscCall(MatDestroy(&At));
    5999:   PetscCall(MatDestroy(&Bt));
    6000:   PetscCall(MatTransposeSetPrecursor(Ct, C));
    6001:   PetscCall(MatTranspose(Ct, MAT_REUSE_MATRIX, &C));
    6002:   PetscCall(MatDestroy(&Ct));
    6003:   PetscFunctionReturn(PETSC_SUCCESS);
    6004: }

    6006: static PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A, Mat B, PetscReal fill, Mat C)
    6007: {
    6008:   PetscBool cisdense;

    6010:   PetscFunctionBegin;
    6011:   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);
    6012:   PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
    6013:   PetscCall(MatSetBlockSizesFromMats(C, A, B));
    6014:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATMPIDENSE, MATMPIDENSECUDA, MATMPIDENSEHIP, ""));
    6015:   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    6016:   PetscCall(MatSetUp(C));

    6018:   C->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
    6019:   PetscFunctionReturn(PETSC_SUCCESS);
    6020: }

    6022: static PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ_AB(Mat C)
    6023: {
    6024:   Mat_Product *product = C->product;
    6025:   Mat          A = product->A, B = product->B;

    6027:   PetscFunctionBegin;
    6028:   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 ")",
    6029:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    6030:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIDense_MPIAIJ;
    6031:   C->ops->productsymbolic = MatProductSymbolic_AB;
    6032:   PetscFunctionReturn(PETSC_SUCCESS);
    6033: }

    6035: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ(Mat C)
    6036: {
    6037:   Mat_Product *product = C->product;

    6039:   PetscFunctionBegin;
    6040:   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_MPIDense_MPIAIJ_AB(C));
    6041:   PetscFunctionReturn(PETSC_SUCCESS);
    6042: }

    6044: /*
    6045:    Merge two sets of sorted nonzeros and return a CSR for the merged (sequential) matrix

    6047:   Input Parameters:

    6049:     j1,rowBegin1,rowEnd1,jmap1: describe the first set of nonzeros (Set1)
    6050:     j2,rowBegin2,rowEnd2,jmap2: describe the second set of nonzeros (Set2)

    6052:     mat: both sets' nonzeros are on m rows, where m is the number of local rows of the matrix mat

    6054:     For Set1, j1[] contains column indices of the nonzeros.
    6055:     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
    6056:     respectively (note rowEnd1[k] is not necessarily equal to rwoBegin1[k+1]). Indices in this range of j1[] are sorted,
    6057:     but might have repeats. jmap1[t+1] - jmap1[t] is the number of repeats for the t-th unique nonzero in Set1.

    6059:     Similar for Set2.

    6061:     This routine merges the two sets of nonzeros row by row and removes repeats.

    6063:   Output Parameters: (memory is allocated by the caller)

    6065:     i[],j[]: the CSR of the merged matrix, which has m rows.
    6066:     imap1[]: the k-th unique nonzero in Set1 (k=0,1,...) corresponds to imap1[k]-th unique nonzero in the merged matrix.
    6067:     imap2[]: similar to imap1[], but for Set2.
    6068:     Note we order nonzeros row-by-row and from left to right.
    6069: */
    6070: 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[])
    6071: {
    6072:   PetscInt   r, m; /* Row index of mat */
    6073:   PetscCount t, t1, t2, b1, e1, b2, e2;

    6075:   PetscFunctionBegin;
    6076:   PetscCall(MatGetLocalSize(mat, &m, NULL));
    6077:   t1 = t2 = t = 0; /* Count unique nonzeros of in Set1, Set1 and the merged respectively */
    6078:   i[0]        = 0;
    6079:   for (r = 0; r < m; r++) { /* Do row by row merging */
    6080:     b1 = rowBegin1[r];
    6081:     e1 = rowEnd1[r];
    6082:     b2 = rowBegin2[r];
    6083:     e2 = rowEnd2[r];
    6084:     while (b1 < e1 && b2 < e2) {
    6085:       if (j1[b1] == j2[b2]) { /* Same column index and hence same nonzero */
    6086:         j[t]      = j1[b1];
    6087:         imap1[t1] = t;
    6088:         imap2[t2] = t;
    6089:         b1 += jmap1[t1 + 1] - jmap1[t1]; /* Jump to next unique local nonzero */
    6090:         b2 += jmap2[t2 + 1] - jmap2[t2]; /* Jump to next unique remote nonzero */
    6091:         t1++;
    6092:         t2++;
    6093:         t++;
    6094:       } else if (j1[b1] < j2[b2]) {
    6095:         j[t]      = j1[b1];
    6096:         imap1[t1] = t;
    6097:         b1 += jmap1[t1 + 1] - jmap1[t1];
    6098:         t1++;
    6099:         t++;
    6100:       } else {
    6101:         j[t]      = j2[b2];
    6102:         imap2[t2] = t;
    6103:         b2 += jmap2[t2 + 1] - jmap2[t2];
    6104:         t2++;
    6105:         t++;
    6106:       }
    6107:     }
    6108:     /* Merge the remaining in either j1[] or j2[] */
    6109:     while (b1 < e1) {
    6110:       j[t]      = j1[b1];
    6111:       imap1[t1] = t;
    6112:       b1 += jmap1[t1 + 1] - jmap1[t1];
    6113:       t1++;
    6114:       t++;
    6115:     }
    6116:     while (b2 < e2) {
    6117:       j[t]      = j2[b2];
    6118:       imap2[t2] = t;
    6119:       b2 += jmap2[t2 + 1] - jmap2[t2];
    6120:       t2++;
    6121:       t++;
    6122:     }
    6123:     PetscCall(PetscIntCast(t, i + r + 1));
    6124:   }
    6125:   PetscFunctionReturn(PETSC_SUCCESS);
    6126: }

    6128: /*
    6129:   Split nonzeros in a block of local rows into two subsets: those in the diagonal block and those in the off-diagonal block

    6131:   Input Parameters:
    6132:     mat: an MPI matrix that provides row and column layout information for splitting. Let's say its number of local rows is m.
    6133:     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[]
    6134:       respectively, along with a permutation array perm[]. Length of the i[],j[],perm[] arrays is n.

    6136:       i[] is already sorted, but within a row, j[] is not sorted and might have repeats.
    6137:       i[] might contain negative indices at the beginning, which means the corresponding entries should be ignored in the splitting.

    6139:   Output Parameters:
    6140:     j[],perm[]: the routine needs to sort j[] within each row along with perm[].
    6141:     rowBegin[],rowMid[],rowEnd[]: of length m, and the memory is preallocated and zeroed by the caller.
    6142:       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,
    6143:       and [rowMid[r],rowEnd[r]) point to begin/end entries of row r of the off-diagonal block.

    6145:     Aperm[],Ajmap[],Atot,Annz: Arrays are allocated by this routine.
    6146:       Atot: number of entries belonging to the diagonal block.
    6147:       Annz: number of unique nonzeros belonging to the diagonal block.
    6148:       Aperm[Atot] stores values from perm[] for entries belonging to the diagonal block. Length of Aperm[] is Atot, though it may also count
    6149:         repeats (i.e., same 'i,j' pair).
    6150:       Ajmap[Annz+1] stores the number of repeats of each unique entry belonging to the diagonal block. More precisely, Ajmap[t+1] - Ajmap[t]
    6151:         is the number of repeats for the t-th unique entry in the diagonal block. Ajmap[0] is always 0.

    6153:       Atot: number of entries belonging to the diagonal block
    6154:       Annz: number of unique nonzeros belonging to the diagonal block.

    6156:     Bperm[], Bjmap[], Btot, Bnnz are similar but for the off-diagonal block.

    6158:     Aperm[],Bperm[],Ajmap[] and Bjmap[] are allocated separately by this routine with PetscMalloc1().
    6159: */
    6160: 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_)
    6161: {
    6162:   PetscInt    cstart, cend, rstart, rend, row, col;
    6163:   PetscCount  Atot = 0, Btot = 0; /* Total number of nonzeros in the diagonal and off-diagonal blocks */
    6164:   PetscCount  Annz = 0, Bnnz = 0; /* Number of unique nonzeros in the diagonal and off-diagonal blocks */
    6165:   PetscCount  k, m, p, q, r, s, mid;
    6166:   PetscCount *Aperm, *Bperm, *Ajmap, *Bjmap;

    6168:   PetscFunctionBegin;
    6169:   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
    6170:   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
    6171:   m = rend - rstart;

    6173:   /* Skip negative rows */
    6174:   for (k = 0; k < n; k++)
    6175:     if (i[k] >= 0) break;

    6177:   /* Process [k,n): sort and partition each local row into diag and offdiag portions,
    6178:      fill rowBegin[], rowMid[], rowEnd[], and count Atot, Btot, Annz, Bnnz.
    6179:   */
    6180:   while (k < n) {
    6181:     row = i[k];
    6182:     /* Entries in [k,s) are in one row. Shift diagonal block col indices so that diag is ahead of offdiag after sorting the row */
    6183:     for (s = k; s < n; s++)
    6184:       if (i[s] != row) break;

    6186:     /* Shift diag columns to range of [-PETSC_INT_MAX, -1] */
    6187:     for (p = k; p < s; p++) {
    6188:       if (j[p] >= cstart && j[p] < cend) j[p] -= PETSC_INT_MAX;
    6189:     }
    6190:     PetscCall(PetscSortIntWithCountArray(s - k, j + k, perm + k));
    6191:     PetscCall(PetscSortedIntUpperBound(j, k, s, -1, &mid)); /* Separate [k,s) into [k,mid) for diag and [mid,s) for offdiag */
    6192:     rowBegin[row - rstart] = k;
    6193:     rowMid[row - rstart]   = mid;
    6194:     rowEnd[row - rstart]   = s;
    6195:     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);

    6197:     /* Count nonzeros of this diag/offdiag row, which might have repeats */
    6198:     Atot += mid - k;
    6199:     Btot += s - mid;

    6201:     /* Count unique nonzeros of this diag row */
    6202:     for (p = k; p < mid;) {
    6203:       col = j[p];
    6204:       do {
    6205:         j[p] += PETSC_INT_MAX; /* Revert the modified diagonal indices */
    6206:         p++;
    6207:       } while (p < mid && j[p] == col);
    6208:       Annz++;
    6209:     }

    6211:     /* Count unique nonzeros of this offdiag row */
    6212:     for (p = mid; p < s;) {
    6213:       col = j[p];
    6214:       do {
    6215:         p++;
    6216:       } while (p < s && j[p] == col);
    6217:       Bnnz++;
    6218:     }
    6219:     k = s;
    6220:   }

    6222:   /* Allocation according to Atot, Btot, Annz, Bnnz */
    6223:   PetscCall(PetscMalloc1(Atot, &Aperm));
    6224:   PetscCall(PetscMalloc1(Btot, &Bperm));
    6225:   PetscCall(PetscMalloc1(Annz + 1, &Ajmap));
    6226:   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap));

    6228:   /* Re-scan indices and copy diag/offdiag permutation indices to Aperm, Bperm and also fill Ajmap and Bjmap */
    6229:   Ajmap[0] = Bjmap[0] = Atot = Btot = Annz = Bnnz = 0;
    6230:   for (r = 0; r < m; r++) {
    6231:     k   = rowBegin[r];
    6232:     mid = rowMid[r];
    6233:     s   = rowEnd[r];
    6234:     PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(Aperm, Atot), PetscSafePointerPlusOffset(perm, k), mid - k));
    6235:     PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(Bperm, Btot), PetscSafePointerPlusOffset(perm, mid), s - mid));
    6236:     Atot += mid - k;
    6237:     Btot += s - mid;

    6239:     /* Scan column indices in this row and find out how many repeats each unique nonzero has */
    6240:     for (p = k; p < mid;) {
    6241:       col = j[p];
    6242:       q   = p;
    6243:       do {
    6244:         p++;
    6245:       } while (p < mid && j[p] == col);
    6246:       Ajmap[Annz + 1] = Ajmap[Annz] + (p - q);
    6247:       Annz++;
    6248:     }

    6250:     for (p = mid; p < s;) {
    6251:       col = j[p];
    6252:       q   = p;
    6253:       do {
    6254:         p++;
    6255:       } while (p < s && j[p] == col);
    6256:       Bjmap[Bnnz + 1] = Bjmap[Bnnz] + (p - q);
    6257:       Bnnz++;
    6258:     }
    6259:   }
    6260:   /* Output */
    6261:   *Aperm_ = Aperm;
    6262:   *Annz_  = Annz;
    6263:   *Atot_  = Atot;
    6264:   *Ajmap_ = Ajmap;
    6265:   *Bperm_ = Bperm;
    6266:   *Bnnz_  = Bnnz;
    6267:   *Btot_  = Btot;
    6268:   *Bjmap_ = Bjmap;
    6269:   PetscFunctionReturn(PETSC_SUCCESS);
    6270: }

    6272: /*
    6273:   Expand the jmap[] array to make a new one in view of nonzeros in the merged matrix

    6275:   Input Parameters:
    6276:     nnz1: number of unique nonzeros in a set that was used to produce imap[], jmap[]
    6277:     nnz:  number of unique nonzeros in the merged matrix
    6278:     imap[nnz1]: i-th nonzero in the set is the imap[i]-th nonzero in the merged matrix
    6279:     jmap[nnz1+1]: i-th nonzero in the set has jmap[i+1] - jmap[i] repeats in the set

    6281:   Output Parameter: (memory is allocated by the caller)
    6282:     jmap_new[nnz+1]: i-th nonzero in the merged matrix has jmap_new[i+1] - jmap_new[i] repeats in the set

    6284:   Example:
    6285:     nnz1 = 4
    6286:     nnz  = 6
    6287:     imap = [1,3,4,5]
    6288:     jmap = [0,3,5,6,7]
    6289:    then,
    6290:     jmap_new = [0,0,3,3,5,6,7]
    6291: */
    6292: static PetscErrorCode ExpandJmap_Internal(PetscCount nnz1, PetscCount nnz, const PetscCount imap[], const PetscCount jmap[], PetscCount jmap_new[])
    6293: {
    6294:   PetscCount k, p;

    6296:   PetscFunctionBegin;
    6297:   jmap_new[0] = 0;
    6298:   p           = nnz;                /* p loops over jmap_new[] backwards */
    6299:   for (k = nnz1 - 1; k >= 0; k--) { /* k loops over imap[] */
    6300:     for (; p > imap[k]; p--) jmap_new[p] = jmap[k + 1];
    6301:   }
    6302:   for (; p >= 0; p--) jmap_new[p] = jmap[0];
    6303:   PetscFunctionReturn(PETSC_SUCCESS);
    6304: }

    6306: static PetscErrorCode MatCOOStructDestroy_MPIAIJ(PetscCtxRt data)
    6307: {
    6308:   MatCOOStruct_MPIAIJ *coo = *(MatCOOStruct_MPIAIJ **)data;

    6310:   PetscFunctionBegin;
    6311:   PetscCall(PetscSFDestroy(&coo->sf));
    6312:   PetscCall(PetscFree(coo->Aperm1));
    6313:   PetscCall(PetscFree(coo->Bperm1));
    6314:   PetscCall(PetscFree(coo->Ajmap1));
    6315:   PetscCall(PetscFree(coo->Bjmap1));
    6316:   PetscCall(PetscFree(coo->Aimap2));
    6317:   PetscCall(PetscFree(coo->Bimap2));
    6318:   PetscCall(PetscFree(coo->Aperm2));
    6319:   PetscCall(PetscFree(coo->Bperm2));
    6320:   PetscCall(PetscFree(coo->Ajmap2));
    6321:   PetscCall(PetscFree(coo->Bjmap2));
    6322:   PetscCall(PetscFree(coo->Cperm1));
    6323:   PetscCall(PetscFree2(coo->sendbuf, coo->recvbuf));
    6324:   PetscCall(PetscFree(coo));
    6325:   PetscFunctionReturn(PETSC_SUCCESS);
    6326: }

    6328: PetscErrorCode MatSetPreallocationCOO_MPIAIJ(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
    6329: {
    6330:   MPI_Comm             comm;
    6331:   PetscMPIInt          rank, size;
    6332:   PetscInt             m, n, M, N, rstart, rend, cstart, cend; /* Sizes, indices of row/col, therefore with type PetscInt */
    6333:   PetscCount           k, p, q, rem;                           /* Loop variables over coo arrays */
    6334:   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
    6335:   PetscContainer       container;
    6336:   MatCOOStruct_MPIAIJ *coo;

    6338:   PetscFunctionBegin;
    6339:   PetscCall(PetscFree(mpiaij->garray));
    6340:   PetscCall(VecDestroy(&mpiaij->lvec));
    6341: #if defined(PETSC_USE_CTABLE)
    6342:   PetscCall(PetscHMapIDestroy(&mpiaij->colmap));
    6343: #else
    6344:   PetscCall(PetscFree(mpiaij->colmap));
    6345: #endif
    6346:   PetscCall(VecScatterDestroy(&mpiaij->Mvctx));
    6347:   mat->assembled     = PETSC_FALSE;
    6348:   mat->was_assembled = PETSC_FALSE;

    6350:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    6351:   PetscCallMPI(MPI_Comm_size(comm, &size));
    6352:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    6353:   PetscCall(PetscLayoutSetUp(mat->rmap));
    6354:   PetscCall(PetscLayoutSetUp(mat->cmap));
    6355:   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
    6356:   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
    6357:   PetscCall(MatGetLocalSize(mat, &m, &n));
    6358:   PetscCall(MatGetSize(mat, &M, &N));

    6360:   /* Sort (i,j) by row along with a permutation array, so that the to-be-ignored */
    6361:   /* entries come first, then local rows, then remote rows.                     */
    6362:   PetscCount n1 = coo_n, *perm1;
    6363:   PetscInt  *i1 = coo_i, *j1 = coo_j;

    6365:   PetscCall(PetscMalloc1(n1, &perm1));
    6366:   for (k = 0; k < n1; k++) perm1[k] = k;

    6368:   /* Manipulate indices so that entries with negative row or col indices will have smallest
    6369:      row indices, local entries will have greater but negative row indices, and remote entries
    6370:      will have positive row indices.
    6371:   */
    6372:   for (k = 0; k < n1; k++) {
    6373:     if (i1[k] < 0 || j1[k] < 0) i1[k] = PETSC_INT_MIN;                /* e.g., -2^31, minimal to move them ahead */
    6374:     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] */
    6375:     else {
    6376:       PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "MAT_NO_OFF_PROC_ENTRIES is set but insert to remote rows");
    6377:       if (mpiaij->donotstash) i1[k] = PETSC_INT_MIN; /* Ignore offproc entries as if they had negative indices */
    6378:     }
    6379:   }

    6381:   /* Sort by row; after that, [0,k) have ignored entries, [k,rem) have local rows and [rem,n1) have remote rows */
    6382:   PetscCall(PetscSortIntWithIntCountArrayPair(n1, i1, j1, perm1));

    6384:   /* Advance k to the first entry we need to take care of */
    6385:   for (k = 0; k < n1; k++)
    6386:     if (i1[k] > PETSC_INT_MIN) break;
    6387:   PetscCount i1start = k;

    6389:   PetscCall(PetscSortedIntUpperBound(i1, k, n1, rend - 1 - PETSC_INT_MAX, &rem)); /* rem is upper bound of the last local row */
    6390:   for (; k < rem; k++) i1[k] += PETSC_INT_MAX;                                    /* Revert row indices of local rows*/

    6392:   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);

    6394:   /*           Send remote rows to their owner                                  */
    6395:   /* Find which rows should be sent to which remote ranks*/
    6396:   PetscInt        nsend = 0; /* Number of MPI ranks to send data to */
    6397:   PetscMPIInt    *sendto;    /* [nsend], storing remote ranks */
    6398:   PetscInt       *nentries;  /* [nsend], storing number of entries sent to remote ranks; Assume PetscInt is big enough for this count, and error if not */
    6399:   const PetscInt *ranges;
    6400:   PetscInt        maxNsend = size >= 128 ? 128 : size; /* Assume max 128 neighbors; realloc when needed */

    6402:   PetscCall(PetscLayoutGetRanges(mat->rmap, &ranges));
    6403:   PetscCall(PetscMalloc2(maxNsend, &sendto, maxNsend, &nentries));
    6404:   for (k = rem; k < n1;) {
    6405:     PetscMPIInt owner;
    6406:     PetscInt    firstRow, lastRow;

    6408:     /* Locate a row range */
    6409:     firstRow = i1[k]; /* first row of this owner */
    6410:     PetscCall(PetscLayoutFindOwner(mat->rmap, firstRow, &owner));
    6411:     lastRow = ranges[owner + 1] - 1; /* last row of this owner */

    6413:     /* Find the first index 'p' in [k,n) with i1[p] belonging to next owner */
    6414:     PetscCall(PetscSortedIntUpperBound(i1, k, n1, lastRow, &p));

    6416:     /* All entries in [k,p) belong to this remote owner */
    6417:     if (nsend >= maxNsend) { /* Double the remote ranks arrays if not long enough */
    6418:       PetscMPIInt *sendto2;
    6419:       PetscInt    *nentries2;
    6420:       PetscInt     maxNsend2 = (maxNsend <= size / 2) ? maxNsend * 2 : size;

    6422:       PetscCall(PetscMalloc2(maxNsend2, &sendto2, maxNsend2, &nentries2));
    6423:       PetscCall(PetscArraycpy(sendto2, sendto, maxNsend));
    6424:       PetscCall(PetscArraycpy(nentries2, nentries, maxNsend));
    6425:       PetscCall(PetscFree2(sendto, nentries));
    6426:       sendto   = sendto2;
    6427:       nentries = nentries2;
    6428:       maxNsend = maxNsend2;
    6429:     }
    6430:     sendto[nsend] = owner;
    6431:     PetscCall(PetscIntCast(p - k, &nentries[nsend]));
    6432:     nsend++;
    6433:     k = p;
    6434:   }

    6436:   /* Build 1st SF to know offsets on remote to send data */
    6437:   PetscSF      sf1;
    6438:   PetscInt     nroots = 1, nroots2 = 0;
    6439:   PetscInt     nleaves = nsend, nleaves2 = 0;
    6440:   PetscInt    *offsets;
    6441:   PetscSFNode *iremote;

    6443:   PetscCall(PetscSFCreate(comm, &sf1));
    6444:   PetscCall(PetscMalloc1(nsend, &iremote));
    6445:   PetscCall(PetscMalloc1(nsend, &offsets));
    6446:   for (k = 0; k < nsend; k++) {
    6447:     iremote[k].rank  = sendto[k];
    6448:     iremote[k].index = 0;
    6449:     nleaves2 += nentries[k];
    6450:     PetscCheck(nleaves2 >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF leaves is too large for PetscInt");
    6451:   }
    6452:   PetscCall(PetscSFSetGraph(sf1, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    6453:   PetscCall(PetscSFFetchAndOpWithMemTypeBegin(sf1, MPIU_INT, PETSC_MEMTYPE_HOST, &nroots2 /*rootdata*/, PETSC_MEMTYPE_HOST, nentries /*leafdata*/, PETSC_MEMTYPE_HOST, offsets /*leafupdate*/, MPI_SUM));
    6454:   PetscCall(PetscSFFetchAndOpEnd(sf1, MPIU_INT, &nroots2, nentries, offsets, MPI_SUM)); /* Would nroots2 overflow, we check offsets[] below */
    6455:   PetscCall(PetscSFDestroy(&sf1));
    6456:   PetscAssert(nleaves2 == n1 - rem, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nleaves2 %" PetscInt_FMT " != number of remote entries %" PetscCount_FMT, nleaves2, n1 - rem);

    6458:   /* Build 2nd SF to send remote COOs to their owner */
    6459:   PetscSF sf2;
    6460:   nroots  = nroots2;
    6461:   nleaves = nleaves2;
    6462:   PetscCall(PetscSFCreate(comm, &sf2));
    6463:   PetscCall(PetscSFSetFromOptions(sf2));
    6464:   PetscCall(PetscMalloc1(nleaves, &iremote));
    6465:   p = 0;
    6466:   for (k = 0; k < nsend; k++) {
    6467:     PetscCheck(offsets[k] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF roots is too large for PetscInt");
    6468:     for (q = 0; q < nentries[k]; q++, p++) {
    6469:       iremote[p].rank = sendto[k];
    6470:       PetscCall(PetscIntCast(offsets[k] + q, &iremote[p].index));
    6471:     }
    6472:   }
    6473:   PetscCall(PetscSFSetGraph(sf2, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));

    6475:   /* Send the remote COOs to their owner */
    6476:   PetscInt    n2 = nroots, *i2, *j2; /* Buffers for received COOs from other ranks, along with a permutation array */
    6477:   PetscCount *perm2;                 /* Though PetscInt is enough for remote entries, we use PetscCount here as we want to reuse MatSplitEntries_Internal() */
    6478:   PetscCall(PetscMalloc3(n2, &i2, n2, &j2, n2, &perm2));
    6479:   PetscAssert(rem == 0 || i1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6480:   PetscAssert(rem == 0 || j1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6481:   PetscInt *i1prem = PetscSafePointerPlusOffset(i1, rem);
    6482:   PetscInt *j1prem = PetscSafePointerPlusOffset(j1, rem);
    6483:   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, i1prem, PETSC_MEMTYPE_HOST, i2, MPI_REPLACE));
    6484:   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, i1prem, i2, MPI_REPLACE));
    6485:   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, j1prem, PETSC_MEMTYPE_HOST, j2, MPI_REPLACE));
    6486:   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, j1prem, j2, MPI_REPLACE));

    6488:   PetscCall(PetscFree(offsets));
    6489:   PetscCall(PetscFree2(sendto, nentries));

    6491:   /* Sort received COOs by row along with the permutation array     */
    6492:   for (k = 0; k < n2; k++) perm2[k] = k;
    6493:   PetscCall(PetscSortIntWithIntCountArrayPair(n2, i2, j2, perm2));

    6495:   /* sf2 only sends contiguous leafdata to contiguous rootdata. We record the permutation which will be used to fill leafdata */
    6496:   PetscCount *Cperm1;
    6497:   PetscAssert(rem == 0 || perm1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6498:   PetscCount *perm1prem = PetscSafePointerPlusOffset(perm1, rem);
    6499:   PetscCall(PetscMalloc1(nleaves, &Cperm1));
    6500:   PetscCall(PetscArraycpy(Cperm1, perm1prem, nleaves));

    6502:   /* Support for HYPRE matrices, kind of a hack.
    6503:      Swap min column with diagonal so that diagonal values will go first */
    6504:   PetscBool hypre;
    6505:   PetscCall(PetscStrcmp("_internal_COO_mat_for_hypre", ((PetscObject)mat)->name, &hypre));
    6506:   if (hypre) {
    6507:     PetscInt *minj;
    6508:     PetscBT   hasdiag;

    6510:     PetscCall(PetscBTCreate(m, &hasdiag));
    6511:     PetscCall(PetscMalloc1(m, &minj));
    6512:     for (k = 0; k < m; k++) minj[k] = PETSC_INT_MAX;
    6513:     for (k = i1start; k < rem; k++) {
    6514:       if (j1[k] < cstart || j1[k] >= cend) continue;
    6515:       const PetscInt rindex = i1[k] - rstart;
    6516:       if ((j1[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
    6517:       minj[rindex] = PetscMin(minj[rindex], j1[k]);
    6518:     }
    6519:     for (k = 0; k < n2; k++) {
    6520:       if (j2[k] < cstart || j2[k] >= cend) continue;
    6521:       const PetscInt rindex = i2[k] - rstart;
    6522:       if ((j2[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
    6523:       minj[rindex] = PetscMin(minj[rindex], j2[k]);
    6524:     }
    6525:     for (k = i1start; k < rem; k++) {
    6526:       const PetscInt rindex = i1[k] - rstart;
    6527:       if (j1[k] < cstart || j1[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
    6528:       if (j1[k] == minj[rindex]) j1[k] = i1[k] + (cstart - rstart);
    6529:       else if ((j1[k] - cstart) == rindex) j1[k] = minj[rindex];
    6530:     }
    6531:     for (k = 0; k < n2; k++) {
    6532:       const PetscInt rindex = i2[k] - rstart;
    6533:       if (j2[k] < cstart || j2[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
    6534:       if (j2[k] == minj[rindex]) j2[k] = i2[k] + (cstart - rstart);
    6535:       else if ((j2[k] - cstart) == rindex) j2[k] = minj[rindex];
    6536:     }
    6537:     PetscCall(PetscBTDestroy(&hasdiag));
    6538:     PetscCall(PetscFree(minj));
    6539:   }

    6541:   /* Split local COOs and received COOs into diag/offdiag portions */
    6542:   PetscCount *rowBegin1, *rowMid1, *rowEnd1;
    6543:   PetscCount *Ajmap1, *Aperm1, *Bjmap1, *Bperm1;
    6544:   PetscCount  Annz1, Bnnz1, Atot1, Btot1;
    6545:   PetscCount *rowBegin2, *rowMid2, *rowEnd2;
    6546:   PetscCount *Ajmap2, *Aperm2, *Bjmap2, *Bperm2;
    6547:   PetscCount  Annz2, Bnnz2, Atot2, Btot2;

    6549:   PetscCall(PetscCalloc3(m, &rowBegin1, m, &rowMid1, m, &rowEnd1));
    6550:   PetscCall(PetscCalloc3(m, &rowBegin2, m, &rowMid2, m, &rowEnd2));
    6551:   PetscCall(MatSplitEntries_Internal(mat, rem, i1, j1, perm1, rowBegin1, rowMid1, rowEnd1, &Atot1, &Aperm1, &Annz1, &Ajmap1, &Btot1, &Bperm1, &Bnnz1, &Bjmap1));
    6552:   PetscCall(MatSplitEntries_Internal(mat, n2, i2, j2, perm2, rowBegin2, rowMid2, rowEnd2, &Atot2, &Aperm2, &Annz2, &Ajmap2, &Btot2, &Bperm2, &Bnnz2, &Bjmap2));

    6554:   /* Merge local COOs with received COOs: diag with diag, offdiag with offdiag */
    6555:   PetscInt *Ai, *Bi;
    6556:   PetscInt *Aj, *Bj;

    6558:   PetscCall(PetscMalloc1(m + 1, &Ai));
    6559:   PetscCall(PetscMalloc1(m + 1, &Bi));
    6560:   PetscCall(PetscMalloc1(Annz1 + Annz2, &Aj)); /* Since local and remote entries might have dups, we might allocate excess memory */
    6561:   PetscCall(PetscMalloc1(Bnnz1 + Bnnz2, &Bj));

    6563:   PetscCount *Aimap1, *Bimap1, *Aimap2, *Bimap2;
    6564:   PetscCall(PetscMalloc1(Annz1, &Aimap1));
    6565:   PetscCall(PetscMalloc1(Bnnz1, &Bimap1));
    6566:   PetscCall(PetscMalloc1(Annz2, &Aimap2));
    6567:   PetscCall(PetscMalloc1(Bnnz2, &Bimap2));

    6569:   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowBegin1, rowMid1, rowBegin2, rowMid2, Ajmap1, Ajmap2, Aimap1, Aimap2, Ai, Aj));
    6570:   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowMid1, rowEnd1, rowMid2, rowEnd2, Bjmap1, Bjmap2, Bimap1, Bimap2, Bi, Bj));

    6572:   /* Expand Ajmap1/Bjmap1 to make them based off nonzeros in A/B, since we     */
    6573:   /* expect nonzeros in A/B most likely have local contributing entries        */
    6574:   PetscInt    Annz = Ai[m];
    6575:   PetscInt    Bnnz = Bi[m];
    6576:   PetscCount *Ajmap1_new, *Bjmap1_new;

    6578:   PetscCall(PetscMalloc1(Annz + 1, &Ajmap1_new));
    6579:   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap1_new));

    6581:   PetscCall(ExpandJmap_Internal(Annz1, Annz, Aimap1, Ajmap1, Ajmap1_new));
    6582:   PetscCall(ExpandJmap_Internal(Bnnz1, Bnnz, Bimap1, Bjmap1, Bjmap1_new));

    6584:   PetscCall(PetscFree(Aimap1));
    6585:   PetscCall(PetscFree(Ajmap1));
    6586:   PetscCall(PetscFree(Bimap1));
    6587:   PetscCall(PetscFree(Bjmap1));
    6588:   PetscCall(PetscFree3(rowBegin1, rowMid1, rowEnd1));
    6589:   PetscCall(PetscFree3(rowBegin2, rowMid2, rowEnd2));
    6590:   PetscCall(PetscFree(perm1));
    6591:   PetscCall(PetscFree3(i2, j2, perm2));

    6593:   Ajmap1 = Ajmap1_new;
    6594:   Bjmap1 = Bjmap1_new;

    6596:   /* Reallocate Aj, Bj once we know actual numbers of unique nonzeros in A and B */
    6597:   if (Annz < Annz1 + Annz2) {
    6598:     PetscInt *Aj_new;
    6599:     PetscCall(PetscMalloc1(Annz, &Aj_new));
    6600:     PetscCall(PetscArraycpy(Aj_new, Aj, Annz));
    6601:     PetscCall(PetscFree(Aj));
    6602:     Aj = Aj_new;
    6603:   }

    6605:   if (Bnnz < Bnnz1 + Bnnz2) {
    6606:     PetscInt *Bj_new;
    6607:     PetscCall(PetscMalloc1(Bnnz, &Bj_new));
    6608:     PetscCall(PetscArraycpy(Bj_new, Bj, Bnnz));
    6609:     PetscCall(PetscFree(Bj));
    6610:     Bj = Bj_new;
    6611:   }

    6613:   /* Create new submatrices for on-process and off-process coupling                  */
    6614:   PetscScalar     *Aa, *Ba;
    6615:   MatType          rtype;
    6616:   Mat_SeqAIJ      *a, *b;
    6617:   PetscObjectState state;
    6618:   PetscCall(PetscCalloc1(Annz, &Aa)); /* Zero matrix on device */
    6619:   PetscCall(PetscCalloc1(Bnnz, &Ba));
    6620:   /* make Aj[] local, i.e, based off the start column of the diagonal portion */
    6621:   if (cstart) {
    6622:     for (k = 0; k < Annz; k++) Aj[k] -= cstart;
    6623:   }

    6625:   PetscCall(MatGetRootType_Private(mat, &rtype));

    6627:   MatSeqXAIJGetOptions_Private(mpiaij->A);
    6628:   PetscCall(MatDestroy(&mpiaij->A));
    6629:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, Ai, Aj, Aa, &mpiaij->A));
    6630:   PetscCall(MatSetBlockSizesFromMats(mpiaij->A, mat, mat));
    6631:   MatSeqXAIJRestoreOptions_Private(mpiaij->A);

    6633:   MatSeqXAIJGetOptions_Private(mpiaij->B);
    6634:   PetscCall(MatDestroy(&mpiaij->B));
    6635:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, mat->cmap->N, Bi, Bj, Ba, &mpiaij->B));
    6636:   PetscCall(MatSetBlockSizesFromMats(mpiaij->B, mat, mat));
    6637:   MatSeqXAIJRestoreOptions_Private(mpiaij->B);

    6639:   PetscCall(MatSetUpMultiply_MPIAIJ(mat));
    6640:   mat->was_assembled = PETSC_TRUE; // was_assembled in effect means the Mvctx is built; doing so avoids redundant MatSetUpMultiply_MPIAIJ
    6641:   state              = mpiaij->A->nonzerostate + mpiaij->B->nonzerostate;
    6642:   PetscCallMPI(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));

    6644:   a          = (Mat_SeqAIJ *)mpiaij->A->data;
    6645:   b          = (Mat_SeqAIJ *)mpiaij->B->data;
    6646:   a->free_a  = PETSC_TRUE;
    6647:   a->free_ij = PETSC_TRUE;
    6648:   b->free_a  = PETSC_TRUE;
    6649:   b->free_ij = PETSC_TRUE;
    6650:   a->maxnz   = a->nz;
    6651:   b->maxnz   = b->nz;

    6653:   /* conversion must happen AFTER multiply setup */
    6654:   PetscCall(MatConvert(mpiaij->A, rtype, MAT_INPLACE_MATRIX, &mpiaij->A));
    6655:   PetscCall(MatConvert(mpiaij->B, rtype, MAT_INPLACE_MATRIX, &mpiaij->B));
    6656:   PetscCall(VecDestroy(&mpiaij->lvec));
    6657:   PetscCall(MatCreateVecs(mpiaij->B, &mpiaij->lvec, NULL));

    6659:   // Put the COO struct in a container and then attach that to the matrix
    6660:   PetscCall(PetscMalloc1(1, &coo));
    6661:   coo->n       = coo_n;
    6662:   coo->sf      = sf2;
    6663:   coo->sendlen = nleaves;
    6664:   coo->recvlen = nroots;
    6665:   coo->Annz    = Annz;
    6666:   coo->Bnnz    = Bnnz;
    6667:   coo->Annz2   = Annz2;
    6668:   coo->Bnnz2   = Bnnz2;
    6669:   coo->Atot1   = Atot1;
    6670:   coo->Atot2   = Atot2;
    6671:   coo->Btot1   = Btot1;
    6672:   coo->Btot2   = Btot2;
    6673:   coo->Ajmap1  = Ajmap1;
    6674:   coo->Aperm1  = Aperm1;
    6675:   coo->Bjmap1  = Bjmap1;
    6676:   coo->Bperm1  = Bperm1;
    6677:   coo->Aimap2  = Aimap2;
    6678:   coo->Ajmap2  = Ajmap2;
    6679:   coo->Aperm2  = Aperm2;
    6680:   coo->Bimap2  = Bimap2;
    6681:   coo->Bjmap2  = Bjmap2;
    6682:   coo->Bperm2  = Bperm2;
    6683:   coo->Cperm1  = Cperm1;
    6684:   // Allocate in preallocation. If not used, it has zero cost on host
    6685:   PetscCall(PetscMalloc2(coo->sendlen, &coo->sendbuf, coo->recvlen, &coo->recvbuf));
    6686:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    6687:   PetscCall(PetscContainerSetPointer(container, coo));
    6688:   PetscCall(PetscContainerSetCtxDestroy(container, MatCOOStructDestroy_MPIAIJ));
    6689:   PetscCall(PetscObjectCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject)container));
    6690:   PetscCall(PetscContainerDestroy(&container));
    6691:   PetscFunctionReturn(PETSC_SUCCESS);
    6692: }

    6694: static PetscErrorCode MatSetValuesCOO_MPIAIJ(Mat mat, const PetscScalar v[], InsertMode imode)
    6695: {
    6696:   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
    6697:   Mat                  A = mpiaij->A, B = mpiaij->B;
    6698:   PetscScalar         *Aa, *Ba;
    6699:   PetscScalar         *sendbuf, *recvbuf;
    6700:   const PetscCount    *Ajmap1, *Ajmap2, *Aimap2;
    6701:   const PetscCount    *Bjmap1, *Bjmap2, *Bimap2;
    6702:   const PetscCount    *Aperm1, *Aperm2, *Bperm1, *Bperm2;
    6703:   const PetscCount    *Cperm1;
    6704:   PetscContainer       container;
    6705:   MatCOOStruct_MPIAIJ *coo;

    6707:   PetscFunctionBegin;
    6708:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container));
    6709:   PetscCheck(container, PetscObjectComm((PetscObject)mat), PETSC_ERR_PLIB, "Not found MatCOOStruct on this matrix");
    6710:   PetscCall(PetscContainerGetPointer(container, &coo));
    6711:   sendbuf = coo->sendbuf;
    6712:   recvbuf = coo->recvbuf;
    6713:   Ajmap1  = coo->Ajmap1;
    6714:   Ajmap2  = coo->Ajmap2;
    6715:   Aimap2  = coo->Aimap2;
    6716:   Bjmap1  = coo->Bjmap1;
    6717:   Bjmap2  = coo->Bjmap2;
    6718:   Bimap2  = coo->Bimap2;
    6719:   Aperm1  = coo->Aperm1;
    6720:   Aperm2  = coo->Aperm2;
    6721:   Bperm1  = coo->Bperm1;
    6722:   Bperm2  = coo->Bperm2;
    6723:   Cperm1  = coo->Cperm1;

    6725:   PetscCall(MatSeqAIJGetArray(A, &Aa)); /* Might read and write matrix values */
    6726:   PetscCall(MatSeqAIJGetArray(B, &Ba));

    6728:   /* Pack entries to be sent to remote */
    6729:   for (PetscCount i = 0; i < coo->sendlen; i++) sendbuf[i] = v[Cperm1[i]];

    6731:   /* Send remote entries to their owner and overlap the communication with local computation */
    6732:   PetscCall(PetscSFReduceWithMemTypeBegin(coo->sf, MPIU_SCALAR, PETSC_MEMTYPE_HOST, sendbuf, PETSC_MEMTYPE_HOST, recvbuf, MPI_REPLACE));
    6733:   /* Add local entries to A and B */
    6734:   for (PetscCount i = 0; i < coo->Annz; i++) { /* All nonzeros in A are either zero'ed or added with a value (i.e., initialized) */
    6735:     PetscScalar sum = 0.0;                     /* Do partial summation first to improve numerical stability */
    6736:     for (PetscCount k = Ajmap1[i]; k < Ajmap1[i + 1]; k++) sum += v[Aperm1[k]];
    6737:     Aa[i] = (imode == INSERT_VALUES ? 0.0 : Aa[i]) + sum;
    6738:   }
    6739:   for (PetscCount i = 0; i < coo->Bnnz; i++) {
    6740:     PetscScalar sum = 0.0;
    6741:     for (PetscCount k = Bjmap1[i]; k < Bjmap1[i + 1]; k++) sum += v[Bperm1[k]];
    6742:     Ba[i] = (imode == INSERT_VALUES ? 0.0 : Ba[i]) + sum;
    6743:   }
    6744:   PetscCall(PetscSFReduceEnd(coo->sf, MPIU_SCALAR, sendbuf, recvbuf, MPI_REPLACE));

    6746:   /* Add received remote entries to A and B */
    6747:   for (PetscCount i = 0; i < coo->Annz2; i++) {
    6748:     for (PetscCount k = Ajmap2[i]; k < Ajmap2[i + 1]; k++) Aa[Aimap2[i]] += recvbuf[Aperm2[k]];
    6749:   }
    6750:   for (PetscCount i = 0; i < coo->Bnnz2; i++) {
    6751:     for (PetscCount k = Bjmap2[i]; k < Bjmap2[i + 1]; k++) Ba[Bimap2[i]] += recvbuf[Bperm2[k]];
    6752:   }
    6753:   PetscCall(MatSeqAIJRestoreArray(A, &Aa));
    6754:   PetscCall(MatSeqAIJRestoreArray(B, &Ba));
    6755:   PetscFunctionReturn(PETSC_SUCCESS);
    6756: }

    6758: /*MC
    6759:    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.

    6761:    Options Database Keys:
    6762: . -mat_type mpiaij - sets the matrix type to `MATMPIAIJ` during a call to `MatSetFromOptions()`

    6764:    Level: beginner

    6766:    Notes:
    6767:    `MatSetValues()` may be called for this matrix type with a `NULL` argument for the numerical values,
    6768:     in this case the values associated with the rows and columns one passes in are set to zero
    6769:     in the matrix

    6771:     `MatSetOptions`(,`MAT_STRUCTURE_ONLY`,`PETSC_TRUE`) may be called for this matrix type. In this no
    6772:     space is allocated for the nonzero entries and any entries passed with `MatSetValues()` are ignored

    6774: .seealso: [](ch_matrices), `Mat`, `MATSEQAIJ`, `MATAIJ`, `MatCreateAIJ()`
    6775: M*/
    6776: PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
    6777: {
    6778:   Mat_MPIAIJ *b;
    6779:   PetscMPIInt size;

    6781:   PetscFunctionBegin;
    6782:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

    6784:   PetscCall(PetscNew(&b));
    6785:   B->data       = (void *)b;
    6786:   B->ops[0]     = MatOps_Values;
    6787:   B->assembled  = PETSC_FALSE;
    6788:   B->insertmode = NOT_SET_VALUES;
    6789:   b->size       = size;

    6791:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)B), &b->rank));

    6793:   /* build cache for off array entries formed */
    6794:   PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)B), 1, &B->stash));

    6796:   b->donotstash  = PETSC_FALSE;
    6797:   b->colmap      = NULL;
    6798:   b->garray      = NULL;
    6799:   b->roworiented = PETSC_TRUE;

    6801:   /* stuff used for matrix vector multiply */
    6802:   b->lvec  = NULL;
    6803:   b->Mvctx = NULL;

    6805:   /* stuff for MatGetRow() */
    6806:   b->rowindices   = NULL;
    6807:   b->rowvalues    = NULL;
    6808:   b->getrowactive = PETSC_FALSE;

    6810:   /* flexible pointer used in CUSPARSE classes */
    6811:   b->spptr = NULL;

    6813:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetUseScalableIncreaseOverlap_C", MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ));
    6814:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_MPIAIJ));
    6815:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_MPIAIJ));
    6816:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsTranspose_C", MatIsTranspose_MPIAIJ));
    6817:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocation_C", MatMPIAIJSetPreallocation_MPIAIJ));
    6818:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetPreallocation_C", MatResetPreallocation_MPIAIJ));
    6819:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetHash_C", MatResetHash_MPIAIJ));
    6820:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocationCSR_C", MatMPIAIJSetPreallocationCSR_MPIAIJ));
    6821:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDiagonalScaleLocal_C", MatDiagonalScaleLocal_MPIAIJ));
    6822:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijperm_C", MatConvert_MPIAIJ_MPIAIJPERM));
    6823:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijsell_C", MatConvert_MPIAIJ_MPIAIJSELL));
    6824: #if defined(PETSC_HAVE_CUDA)
    6825:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcusparse_C", MatConvert_MPIAIJ_MPIAIJCUSPARSE));
    6826: #endif
    6827: #if defined(PETSC_HAVE_HIP)
    6828:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijhipsparse_C", MatConvert_MPIAIJ_MPIAIJHIPSPARSE));
    6829: #endif
    6830: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    6831:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijkokkos_C", MatConvert_MPIAIJ_MPIAIJKokkos));
    6832: #endif
    6833: #if defined(PETSC_HAVE_MKL_SPARSE)
    6834:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijmkl_C", MatConvert_MPIAIJ_MPIAIJMKL));
    6835: #endif
    6836:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcrl_C", MatConvert_MPIAIJ_MPIAIJCRL));
    6837:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpibaij_C", MatConvert_MPIAIJ_MPIBAIJ));
    6838:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisbaij_C", MatConvert_MPIAIJ_MPISBAIJ));
    6839:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpidense_C", MatConvert_MPIAIJ_MPIDense));
    6840: #if defined(PETSC_HAVE_ELEMENTAL)
    6841:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_elemental_C", MatConvert_MPIAIJ_Elemental));
    6842: #endif
    6843: #if defined(PETSC_HAVE_SCALAPACK) && (defined(PETSC_USE_REAL_SINGLE) || defined(PETSC_USE_REAL_DOUBLE))
    6844:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_scalapack_C", MatConvert_AIJ_ScaLAPACK));
    6845: #endif
    6846:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_is_C", MatConvert_XAIJ_IS));
    6847:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisell_C", MatConvert_MPIAIJ_MPISELL));
    6848: #if defined(PETSC_HAVE_HYPRE)
    6849:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_hypre_C", MatConvert_AIJ_HYPRE));
    6850:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", MatProductSetFromOptions_Transpose_AIJ_AIJ));
    6851: #endif
    6852:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_is_mpiaij_C", MatProductSetFromOptions_IS_XAIJ));
    6853:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_mpiaij_mpiaij_C", MatProductSetFromOptions_MPIAIJ));
    6854:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_MPIAIJ));
    6855:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetValuesCOO_C", MatSetValuesCOO_MPIAIJ));
    6856:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATMPIAIJ));
    6857:   PetscFunctionReturn(PETSC_SUCCESS);
    6858: }

    6860: /*@
    6861:   MatCreateMPIAIJWithSplitArrays - creates a `MATMPIAIJ` matrix using arrays that contain the "diagonal"
    6862:   and "off-diagonal" part of the matrix in CSR format.

    6864:   Collective

    6866:   Input Parameters:
    6867: + comm - MPI communicator
    6868: . m    - number of local rows (Cannot be `PETSC_DECIDE`)
    6869: . n    - This value should be the same as the local size used in creating the
    6870:          x vector for the matrix-vector product $y = Ax$. (or `PETSC_DECIDE` to have
    6871:          calculated if `N` is given) For square matrices `n` is almost always `m`.
    6872: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    6873: . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    6874: . 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
    6875: . j    - column indices, which must be local, i.e., based off the start column of the diagonal portion
    6876: . a    - matrix values
    6877: . 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
    6878: . oj   - column indices, which must be global, representing global columns in the `MATMPIAIJ` matrix
    6879: - oa   - matrix values

    6881:   Output Parameter:
    6882: . mat - the matrix

    6884:   Level: advanced

    6886:   Notes:
    6887:   The `i`, `j`, and `a` arrays ARE NOT copied by this routine into the internal format used by PETSc (even in Fortran). The user
    6888:   must free the arrays once the matrix has been destroyed and not before.

    6890:   The `i` and `j` indices are 0 based

    6892:   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix

    6894:   This sets local rows and cannot be used to set off-processor values.

    6896:   Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
    6897:   legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
    6898:   not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
    6899:   the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
    6900:   keep track of the underlying array. Use `MatSetOption`(A,`MAT_NO_OFF_PROC_ENTRIES`,`PETSC_TRUE`) to disable all
    6901:   communication if it is known that only local entries will be set.

    6903: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    6904:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithArrays()`
    6905: @*/
    6906: 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)
    6907: {
    6908:   Mat_MPIAIJ *maij;

    6910:   PetscFunctionBegin;
    6911:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    6912:   PetscCheck(i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    6913:   PetscCheck(oi[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "oi (row indices) must start with 0");
    6914:   PetscCall(MatCreate(comm, mat));
    6915:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    6916:   PetscCall(MatSetType(*mat, MATMPIAIJ));
    6917:   maij = (Mat_MPIAIJ *)(*mat)->data;

    6919:   (*mat)->preallocated = PETSC_TRUE;

    6921:   PetscCall(PetscLayoutSetUp((*mat)->rmap));
    6922:   PetscCall(PetscLayoutSetUp((*mat)->cmap));

    6924:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, i, j, a, &maij->A));
    6925:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, (*mat)->cmap->N, oi, oj, oa, &maij->B));

    6927:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    6928:   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
    6929:   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
    6930:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    6931:   PetscCall(MatSetOption(*mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    6932:   PetscFunctionReturn(PETSC_SUCCESS);
    6933: }

    6935: typedef struct {
    6936:   Mat       *mp;    /* intermediate products */
    6937:   PetscBool *mptmp; /* is the intermediate product temporary ? */
    6938:   PetscInt   cp;    /* number of intermediate products */

    6940:   /* support for MatGetBrowsOfAoCols_MPIAIJ for P_oth */
    6941:   PetscInt    *startsj_s, *startsj_r;
    6942:   PetscScalar *bufa;
    6943:   Mat          P_oth;

    6945:   /* may take advantage of merging product->B */
    6946:   Mat Bloc; /* B-local by merging diag and off-diag */

    6948:   /* cusparse does not have support to split between symbolic and numeric phases.
    6949:      When api_user is true, we don't need to update the numerical values
    6950:      of the temporary storage */
    6951:   PetscBool reusesym;

    6953:   /* support for COO values insertion */
    6954:   PetscScalar *coo_v, *coo_w; /* store on-process and off-process COO scalars, and used as MPI recv/send buffers respectively */
    6955:   PetscInt   **own;           /* own[i] points to address of on-process COO indices for Mat mp[i] */
    6956:   PetscInt   **off;           /* off[i] points to address of off-process COO indices for Mat mp[i] */
    6957:   PetscBool    hasoffproc;    /* if true, have off-process values insertion (i.e. AtB or PtAP) */
    6958:   PetscSF      sf;            /* used for non-local values insertion and memory malloc */
    6959:   PetscMemType mtype;

    6961:   /* customization */
    6962:   PetscBool abmerge;
    6963:   PetscBool P_oth_bind;
    6964: } MatMatMPIAIJBACKEND;

    6966: static PetscErrorCode MatProductCtxDestroy_MatMatMPIAIJBACKEND(PetscCtxRt data)
    6967: {
    6968:   MatMatMPIAIJBACKEND *mmdata = *(MatMatMPIAIJBACKEND **)data;
    6969:   PetscInt             i;

    6971:   PetscFunctionBegin;
    6972:   PetscCall(PetscFree2(mmdata->startsj_s, mmdata->startsj_r));
    6973:   PetscCall(PetscFree(mmdata->bufa));
    6974:   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_v));
    6975:   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_w));
    6976:   PetscCall(MatDestroy(&mmdata->P_oth));
    6977:   PetscCall(MatDestroy(&mmdata->Bloc));
    6978:   PetscCall(PetscSFDestroy(&mmdata->sf));
    6979:   for (i = 0; i < mmdata->cp; i++) PetscCall(MatDestroy(&mmdata->mp[i]));
    6980:   PetscCall(PetscFree2(mmdata->mp, mmdata->mptmp));
    6981:   PetscCall(PetscFree(mmdata->own[0]));
    6982:   PetscCall(PetscFree(mmdata->own));
    6983:   PetscCall(PetscFree(mmdata->off[0]));
    6984:   PetscCall(PetscFree(mmdata->off));
    6985:   PetscCall(PetscFree(mmdata));
    6986:   PetscFunctionReturn(PETSC_SUCCESS);
    6987: }

    6989: /* Copy selected n entries with indices in idx[] of A to v[].
    6990:    If idx is NULL, copy the whole data array of A to v[]
    6991:  */
    6992: static PetscErrorCode MatSeqAIJCopySubArray(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
    6993: {
    6994:   PetscErrorCode (*f)(Mat, PetscInt, const PetscInt[], PetscScalar[]);

    6996:   PetscFunctionBegin;
    6997:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", &f));
    6998:   if (f) PetscCall((*f)(A, n, idx, v));
    6999:   else {
    7000:     const PetscScalar *vv;

    7002:     PetscCall(MatSeqAIJGetArrayRead(A, &vv));
    7003:     if (n && idx) {
    7004:       PetscScalar    *w  = v;
    7005:       const PetscInt *oi = idx;
    7006:       PetscInt        j;

    7008:       for (j = 0; j < n; j++) *w++ = vv[*oi++];
    7009:     } else {
    7010:       PetscCall(PetscArraycpy(v, vv, n));
    7011:     }
    7012:     PetscCall(MatSeqAIJRestoreArrayRead(A, &vv));
    7013:   }
    7014:   PetscFunctionReturn(PETSC_SUCCESS);
    7015: }

    7017: static PetscErrorCode MatProductNumeric_MPIAIJBACKEND(Mat C)
    7018: {
    7019:   MatMatMPIAIJBACKEND *mmdata;
    7020:   PetscInt             i, n_d, n_o;

    7022:   PetscFunctionBegin;
    7023:   MatCheckProduct(C, 1);
    7024:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
    7025:   mmdata = (MatMatMPIAIJBACKEND *)C->product->data;
    7026:   if (!mmdata->reusesym) { /* update temporary matrices */
    7027:     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));
    7028:     if (mmdata->Bloc) PetscCall(MatMPIAIJGetLocalMatMerge(C->product->B, MAT_REUSE_MATRIX, NULL, &mmdata->Bloc));
    7029:   }
    7030:   mmdata->reusesym = PETSC_FALSE;

    7032:   for (i = 0; i < mmdata->cp; i++) {
    7033:     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]);
    7034:     PetscCall((*mmdata->mp[i]->ops->productnumeric)(mmdata->mp[i]));
    7035:   }
    7036:   for (i = 0, n_d = 0, n_o = 0; i < mmdata->cp; i++) {
    7037:     PetscInt noff;

    7039:     PetscCall(PetscIntCast(mmdata->off[i + 1] - mmdata->off[i], &noff));
    7040:     if (mmdata->mptmp[i]) continue;
    7041:     if (noff) {
    7042:       PetscInt nown;

    7044:       PetscCall(PetscIntCast(mmdata->own[i + 1] - mmdata->own[i], &nown));
    7045:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], noff, mmdata->off[i], mmdata->coo_w + n_o));
    7046:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], nown, mmdata->own[i], mmdata->coo_v + n_d));
    7047:       n_o += noff;
    7048:       n_d += nown;
    7049:     } else {
    7050:       Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mmdata->mp[i]->data;

    7052:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], mm->nz, NULL, mmdata->coo_v + n_d));
    7053:       n_d += mm->nz;
    7054:     }
    7055:   }
    7056:   if (mmdata->hasoffproc) { /* offprocess insertion */
    7057:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
    7058:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
    7059:   }
    7060:   PetscCall(MatSetValuesCOO(C, mmdata->coo_v, INSERT_VALUES));
    7061:   PetscFunctionReturn(PETSC_SUCCESS);
    7062: }

    7064: /* Support for Pt * A, A * P, or Pt * A * P */
    7065: #define MAX_NUMBER_INTERMEDIATE 4
    7066: PetscErrorCode MatProductSymbolic_MPIAIJBACKEND(Mat C)
    7067: {
    7068:   Mat_Product           *product = C->product;
    7069:   Mat                    A, P, mp[MAX_NUMBER_INTERMEDIATE]; /* A, P and a series of intermediate matrices */
    7070:   Mat_MPIAIJ            *a, *p;
    7071:   MatMatMPIAIJBACKEND   *mmdata;
    7072:   ISLocalToGlobalMapping P_oth_l2g = NULL;
    7073:   IS                     glob      = NULL;
    7074:   const char            *prefix;
    7075:   char                   pprefix[256];
    7076:   const PetscInt        *globidx, *P_oth_idx;
    7077:   PetscInt               i, j, cp, m, n, M, N, *coo_i, *coo_j;
    7078:   PetscCount             ncoo, ncoo_d, ncoo_o, ncoo_oown;
    7079:   PetscInt               cmapt[MAX_NUMBER_INTERMEDIATE], rmapt[MAX_NUMBER_INTERMEDIATE]; /* col/row map type for each Mat in mp[]. */
    7080:                                                                                          /* type-0: consecutive, start from 0; type-1: consecutive with */
    7081:                                                                                          /* a base offset; type-2: sparse with a local to global map table */
    7082:   const PetscInt *cmapa[MAX_NUMBER_INTERMEDIATE], *rmapa[MAX_NUMBER_INTERMEDIATE];       /* col/row local to global map array (table) for type-2 map type */

    7084:   MatProductType ptype;
    7085:   PetscBool      mptmp[MAX_NUMBER_INTERMEDIATE], hasoffproc = PETSC_FALSE, iscuda, iship, iskokk;
    7086:   PetscMPIInt    size;

    7088:   PetscFunctionBegin;
    7089:   MatCheckProduct(C, 1);
    7090:   PetscCheck(!product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
    7091:   ptype = product->type;
    7092:   if (product->A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
    7093:     ptype                                          = MATPRODUCT_AB;
    7094:     product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
    7095:   }
    7096:   switch (ptype) {
    7097:   case MATPRODUCT_AB:
    7098:     A          = product->A;
    7099:     P          = product->B;
    7100:     m          = A->rmap->n;
    7101:     n          = P->cmap->n;
    7102:     M          = A->rmap->N;
    7103:     N          = P->cmap->N;
    7104:     hasoffproc = PETSC_FALSE; /* will not scatter mat product values to other processes */
    7105:     break;
    7106:   case MATPRODUCT_AtB:
    7107:     P          = product->A;
    7108:     A          = product->B;
    7109:     m          = P->cmap->n;
    7110:     n          = A->cmap->n;
    7111:     M          = P->cmap->N;
    7112:     N          = A->cmap->N;
    7113:     hasoffproc = PETSC_TRUE;
    7114:     break;
    7115:   case MATPRODUCT_PtAP:
    7116:     A          = product->A;
    7117:     P          = product->B;
    7118:     m          = P->cmap->n;
    7119:     n          = P->cmap->n;
    7120:     M          = P->cmap->N;
    7121:     N          = P->cmap->N;
    7122:     hasoffproc = PETSC_TRUE;
    7123:     break;
    7124:   default:
    7125:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
    7126:   }
    7127:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)C), &size));
    7128:   if (size == 1) hasoffproc = PETSC_FALSE;

    7130:   /* defaults */
    7131:   for (i = 0; i < MAX_NUMBER_INTERMEDIATE; i++) {
    7132:     mp[i]    = NULL;
    7133:     mptmp[i] = PETSC_FALSE;
    7134:     rmapt[i] = -1;
    7135:     cmapt[i] = -1;
    7136:     rmapa[i] = NULL;
    7137:     cmapa[i] = NULL;
    7138:   }

    7140:   /* customization */
    7141:   PetscCall(PetscNew(&mmdata));
    7142:   mmdata->reusesym = product->api_user;
    7143:   if (ptype == MATPRODUCT_AB) {
    7144:     if (product->api_user) {
    7145:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
    7146:       PetscCall(PetscOptionsBool("-matmatmult_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
    7147:       PetscCall(PetscOptionsBool("-matmatmult_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7148:       PetscOptionsEnd();
    7149:     } else {
    7150:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
    7151:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
    7152:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7153:       PetscOptionsEnd();
    7154:     }
    7155:   } else if (ptype == MATPRODUCT_PtAP) {
    7156:     if (product->api_user) {
    7157:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
    7158:       PetscCall(PetscOptionsBool("-matptap_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7159:       PetscOptionsEnd();
    7160:     } else {
    7161:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
    7162:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7163:       PetscOptionsEnd();
    7164:     }
    7165:   }
    7166:   a = (Mat_MPIAIJ *)A->data;
    7167:   p = (Mat_MPIAIJ *)P->data;
    7168:   PetscCall(MatSetSizes(C, m, n, M, N));
    7169:   PetscCall(PetscLayoutSetUp(C->rmap));
    7170:   PetscCall(PetscLayoutSetUp(C->cmap));
    7171:   PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    7172:   PetscCall(MatGetOptionsPrefix(C, &prefix));

    7174:   cp = 0;
    7175:   switch (ptype) {
    7176:   case MATPRODUCT_AB: /* A * P */
    7177:     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));

    7179:     /* A_diag * P_local (merged or not) */
    7180:     if (mmdata->abmerge) { /* P's diagonal and off-diag blocks are merged to one matrix, then multiplied by A_diag */
    7181:       /* P is product->B */
    7182:       PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7183:       PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
    7184:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7185:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7186:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7187:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7188:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7189:       mp[cp]->product->api_user = product->api_user;
    7190:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7191:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7192:       PetscCall(ISGetIndices(glob, &globidx));
    7193:       rmapt[cp] = 1;
    7194:       cmapt[cp] = 2;
    7195:       cmapa[cp] = globidx;
    7196:       mptmp[cp] = PETSC_FALSE;
    7197:       cp++;
    7198:     } else { /* A_diag * P_diag and A_diag * P_off */
    7199:       PetscCall(MatProductCreate(a->A, p->A, NULL, &mp[cp]));
    7200:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7201:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7202:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7203:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7204:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7205:       mp[cp]->product->api_user = product->api_user;
    7206:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7207:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7208:       rmapt[cp] = 1;
    7209:       cmapt[cp] = 1;
    7210:       mptmp[cp] = PETSC_FALSE;
    7211:       cp++;
    7212:       PetscCall(MatProductCreate(a->A, p->B, NULL, &mp[cp]));
    7213:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7214:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7215:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7216:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7217:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7218:       mp[cp]->product->api_user = product->api_user;
    7219:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7220:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7221:       rmapt[cp] = 1;
    7222:       cmapt[cp] = 2;
    7223:       cmapa[cp] = p->garray;
    7224:       mptmp[cp] = PETSC_FALSE;
    7225:       cp++;
    7226:     }

    7228:     /* A_off * P_other */
    7229:     if (mmdata->P_oth) {
    7230:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g)); /* make P_oth use local col ids */
    7231:       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
    7232:       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)a->B)->type_name));
    7233:       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
    7234:       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
    7235:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7236:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7237:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7238:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7239:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7240:       mp[cp]->product->api_user = product->api_user;
    7241:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7242:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7243:       rmapt[cp] = 1;
    7244:       cmapt[cp] = 2;
    7245:       cmapa[cp] = P_oth_idx;
    7246:       mptmp[cp] = PETSC_FALSE;
    7247:       cp++;
    7248:     }
    7249:     break;

    7251:   case MATPRODUCT_AtB: /* (P^t * A): P_diag * A_loc + P_off * A_loc */
    7252:     /* A is product->B */
    7253:     PetscCall(MatMPIAIJGetLocalMatMerge(A, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7254:     if (A == P) { /* when A==P, we can take advantage of the already merged mmdata->Bloc */
    7255:       PetscCall(MatProductCreate(mmdata->Bloc, mmdata->Bloc, NULL, &mp[cp]));
    7256:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7257:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7258:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7259:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7260:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7261:       mp[cp]->product->api_user = product->api_user;
    7262:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7263:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7264:       PetscCall(ISGetIndices(glob, &globidx));
    7265:       rmapt[cp] = 2;
    7266:       rmapa[cp] = globidx;
    7267:       cmapt[cp] = 2;
    7268:       cmapa[cp] = globidx;
    7269:       mptmp[cp] = PETSC_FALSE;
    7270:       cp++;
    7271:     } else {
    7272:       PetscCall(MatProductCreate(p->A, mmdata->Bloc, NULL, &mp[cp]));
    7273:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7274:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7275:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7276:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7277:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7278:       mp[cp]->product->api_user = product->api_user;
    7279:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7280:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7281:       PetscCall(ISGetIndices(glob, &globidx));
    7282:       rmapt[cp] = 1;
    7283:       cmapt[cp] = 2;
    7284:       cmapa[cp] = globidx;
    7285:       mptmp[cp] = PETSC_FALSE;
    7286:       cp++;
    7287:       PetscCall(MatProductCreate(p->B, mmdata->Bloc, NULL, &mp[cp]));
    7288:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7289:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7290:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7291:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7292:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7293:       mp[cp]->product->api_user = product->api_user;
    7294:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7295:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7296:       rmapt[cp] = 2;
    7297:       rmapa[cp] = p->garray;
    7298:       cmapt[cp] = 2;
    7299:       cmapa[cp] = globidx;
    7300:       mptmp[cp] = PETSC_FALSE;
    7301:       cp++;
    7302:     }
    7303:     break;
    7304:   case MATPRODUCT_PtAP:
    7305:     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));
    7306:     /* P is product->B */
    7307:     PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7308:     PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
    7309:     PetscCall(MatProductSetType(mp[cp], MATPRODUCT_PtAP));
    7310:     PetscCall(MatProductSetFill(mp[cp], product->fill));
    7311:     PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7312:     PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7313:     PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7314:     mp[cp]->product->api_user = product->api_user;
    7315:     PetscCall(MatProductSetFromOptions(mp[cp]));
    7316:     PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7317:     PetscCall(ISGetIndices(glob, &globidx));
    7318:     rmapt[cp] = 2;
    7319:     rmapa[cp] = globidx;
    7320:     cmapt[cp] = 2;
    7321:     cmapa[cp] = globidx;
    7322:     mptmp[cp] = PETSC_FALSE;
    7323:     cp++;
    7324:     if (mmdata->P_oth) {
    7325:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g));
    7326:       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
    7327:       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)a->B)->type_name));
    7328:       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
    7329:       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
    7330:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7331:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7332:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7333:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7334:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7335:       mp[cp]->product->api_user = product->api_user;
    7336:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7337:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7338:       mptmp[cp] = PETSC_TRUE;
    7339:       cp++;
    7340:       PetscCall(MatProductCreate(mmdata->Bloc, mp[1], NULL, &mp[cp]));
    7341:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7342:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7343:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7344:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7345:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7346:       mp[cp]->product->api_user = product->api_user;
    7347:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7348:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7349:       rmapt[cp] = 2;
    7350:       rmapa[cp] = globidx;
    7351:       cmapt[cp] = 2;
    7352:       cmapa[cp] = P_oth_idx;
    7353:       mptmp[cp] = PETSC_FALSE;
    7354:       cp++;
    7355:     }
    7356:     break;
    7357:   default:
    7358:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
    7359:   }
    7360:   /* sanity check */
    7361:   if (size > 1)
    7362:     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);

    7364:   PetscCall(PetscMalloc2(cp, &mmdata->mp, cp, &mmdata->mptmp));
    7365:   for (i = 0; i < cp; i++) {
    7366:     mmdata->mp[i]    = mp[i];
    7367:     mmdata->mptmp[i] = mptmp[i];
    7368:   }
    7369:   mmdata->cp             = cp;
    7370:   C->product->data       = mmdata;
    7371:   C->product->destroy    = MatProductCtxDestroy_MatMatMPIAIJBACKEND;
    7372:   C->ops->productnumeric = MatProductNumeric_MPIAIJBACKEND;

    7374:   /* memory type */
    7375:   mmdata->mtype = PETSC_MEMTYPE_HOST;
    7376:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iscuda, MATSEQAIJCUSPARSE, MATMPIAIJCUSPARSE, ""));
    7377:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iship, MATSEQAIJHIPSPARSE, MATMPIAIJHIPSPARSE, ""));
    7378:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iskokk, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, ""));
    7379:   if (iscuda) mmdata->mtype = PETSC_MEMTYPE_CUDA;
    7380:   else if (iship) mmdata->mtype = PETSC_MEMTYPE_HIP;
    7381:   else if (iskokk) mmdata->mtype = PETSC_MEMTYPE_KOKKOS;

    7383:   /* prepare coo coordinates for values insertion */

    7385:   /* count total nonzeros of those intermediate seqaij Mats
    7386:     ncoo_d:    # of nonzeros of matrices that do not have offproc entries
    7387:     ncoo_o:    # of nonzeros (of matrices that might have offproc entries) that will be inserted to remote procs
    7388:     ncoo_oown: # of nonzeros (of matrices that might have offproc entries) that will be inserted locally
    7389:   */
    7390:   for (cp = 0, ncoo_d = 0, ncoo_o = 0, ncoo_oown = 0; cp < mmdata->cp; cp++) {
    7391:     Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mp[cp]->data;
    7392:     if (mptmp[cp]) continue;
    7393:     if (rmapt[cp] == 2 && hasoffproc) { /* the rows need to be scatter to all processes (might include self) */
    7394:       const PetscInt *rmap = rmapa[cp];
    7395:       const PetscInt  mr   = mp[cp]->rmap->n;
    7396:       const PetscInt  rs   = C->rmap->rstart;
    7397:       const PetscInt  re   = C->rmap->rend;
    7398:       const PetscInt *ii   = mm->i;
    7399:       for (i = 0; i < mr; i++) {
    7400:         const PetscInt gr = rmap[i];
    7401:         const PetscInt nz = ii[i + 1] - ii[i];
    7402:         if (gr < rs || gr >= re) ncoo_o += nz; /* this row is offproc */
    7403:         else ncoo_oown += nz;                  /* this row is local */
    7404:       }
    7405:     } else ncoo_d += mm->nz;
    7406:   }

    7408:   /*
    7409:     ncoo: total number of nonzeros (including those inserted by remote procs) belonging to this proc

    7411:     ncoo = ncoo_d + ncoo_oown + ncoo2, which ncoo2 is number of nonzeros inserted to me by other procs.

    7413:     off[0] points to a big index array, which is shared by off[1,2,...]. Similarly, for own[0].

    7415:     off[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert to others
    7416:     own[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert locally
    7417:     so, off[p+1]-off[p] is the number of nonzeros that mp[p] will send to others.

    7419:     coo_i/j/v[]: [ncoo] row/col/val of nonzeros belonging to this proc.
    7420:     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.
    7421:   */
    7422:   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->off)); /* +1 to make a csr-like data structure */
    7423:   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->own));

    7425:   /* gather (i,j) of nonzeros inserted by remote procs */
    7426:   if (hasoffproc) {
    7427:     PetscSF  msf;
    7428:     PetscInt ncoo2, *coo_i2, *coo_j2;

    7430:     PetscCall(PetscMalloc1(ncoo_o, &mmdata->off[0]));
    7431:     PetscCall(PetscMalloc1(ncoo_oown, &mmdata->own[0]));
    7432:     PetscCall(PetscMalloc2(ncoo_o, &coo_i, ncoo_o, &coo_j)); /* to collect (i,j) of entries to be sent to others */

    7434:     for (cp = 0, ncoo_o = 0; cp < mmdata->cp; cp++) {
    7435:       Mat_SeqAIJ *mm     = (Mat_SeqAIJ *)mp[cp]->data;
    7436:       PetscInt   *idxoff = mmdata->off[cp];
    7437:       PetscInt   *idxown = mmdata->own[cp];
    7438:       if (!mptmp[cp] && rmapt[cp] == 2) { /* row map is sparse */
    7439:         const PetscInt *rmap = rmapa[cp];
    7440:         const PetscInt *cmap = cmapa[cp];
    7441:         const PetscInt *ii   = mm->i;
    7442:         PetscInt       *coi  = coo_i + ncoo_o;
    7443:         PetscInt       *coj  = coo_j + ncoo_o;
    7444:         const PetscInt  mr   = mp[cp]->rmap->n;
    7445:         const PetscInt  rs   = C->rmap->rstart;
    7446:         const PetscInt  re   = C->rmap->rend;
    7447:         const PetscInt  cs   = C->cmap->rstart;
    7448:         for (i = 0; i < mr; i++) {
    7449:           const PetscInt *jj = mm->j + ii[i];
    7450:           const PetscInt  gr = rmap[i];
    7451:           const PetscInt  nz = ii[i + 1] - ii[i];
    7452:           if (gr < rs || gr >= re) { /* this is an offproc row */
    7453:             for (j = ii[i]; j < ii[i + 1]; j++) {
    7454:               *coi++    = gr;
    7455:               *idxoff++ = j;
    7456:             }
    7457:             if (!cmapt[cp]) { /* already global */
    7458:               for (j = 0; j < nz; j++) *coj++ = jj[j];
    7459:             } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
    7460:               for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
    7461:             } else { /* offdiag */
    7462:               for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
    7463:             }
    7464:             ncoo_o += nz;
    7465:           } else { /* this is a local row */
    7466:             for (j = ii[i]; j < ii[i + 1]; j++) *idxown++ = j;
    7467:           }
    7468:         }
    7469:       }
    7470:       mmdata->off[cp + 1] = idxoff;
    7471:       mmdata->own[cp + 1] = idxown;
    7472:     }

    7474:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
    7475:     PetscInt incoo_o;
    7476:     PetscCall(PetscIntCast(ncoo_o, &incoo_o));
    7477:     PetscCall(PetscSFSetGraphLayout(mmdata->sf, C->rmap, incoo_o /*nleaves*/, NULL /*ilocal*/, PETSC_OWN_POINTER, coo_i));
    7478:     PetscCall(PetscSFGetMultiSF(mmdata->sf, &msf));
    7479:     PetscCall(PetscSFGetGraph(msf, &ncoo2 /*nroots*/, NULL, NULL, NULL));
    7480:     ncoo = ncoo_d + ncoo_oown + ncoo2;
    7481:     PetscCall(PetscMalloc2(ncoo, &coo_i2, ncoo, &coo_j2));
    7482:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown)); /* put (i,j) of remote nonzeros at back */
    7483:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown));
    7484:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
    7485:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
    7486:     PetscCall(PetscFree2(coo_i, coo_j));
    7487:     /* allocate MPI send buffer to collect nonzero values to be sent to remote procs */
    7488:     PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo_o * sizeof(PetscScalar), (void **)&mmdata->coo_w));
    7489:     coo_i = coo_i2;
    7490:     coo_j = coo_j2;
    7491:   } else { /* no offproc values insertion */
    7492:     ncoo = ncoo_d;
    7493:     PetscCall(PetscMalloc2(ncoo, &coo_i, ncoo, &coo_j));

    7495:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
    7496:     PetscCall(PetscSFSetGraph(mmdata->sf, 0, 0, NULL, PETSC_OWN_POINTER, NULL, PETSC_OWN_POINTER));
    7497:     PetscCall(PetscSFSetUp(mmdata->sf));
    7498:   }
    7499:   mmdata->hasoffproc = hasoffproc;

    7501:   /* gather (i,j) of nonzeros inserted locally */
    7502:   for (cp = 0, ncoo_d = 0; cp < mmdata->cp; cp++) {
    7503:     Mat_SeqAIJ     *mm   = (Mat_SeqAIJ *)mp[cp]->data;
    7504:     PetscInt       *coi  = coo_i + ncoo_d;
    7505:     PetscInt       *coj  = coo_j + ncoo_d;
    7506:     const PetscInt *jj   = mm->j;
    7507:     const PetscInt *ii   = mm->i;
    7508:     const PetscInt *cmap = cmapa[cp];
    7509:     const PetscInt *rmap = rmapa[cp];
    7510:     const PetscInt  mr   = mp[cp]->rmap->n;
    7511:     const PetscInt  rs   = C->rmap->rstart;
    7512:     const PetscInt  re   = C->rmap->rend;
    7513:     const PetscInt  cs   = C->cmap->rstart;

    7515:     if (mptmp[cp]) continue;
    7516:     if (rmapt[cp] == 1) { /* consecutive rows */
    7517:       /* fill coo_i */
    7518:       for (i = 0; i < mr; i++) {
    7519:         const PetscInt gr = i + rs;
    7520:         for (j = ii[i]; j < ii[i + 1]; j++) coi[j] = gr;
    7521:       }
    7522:       /* fill coo_j */
    7523:       if (!cmapt[cp]) { /* type-0, already global */
    7524:         PetscCall(PetscArraycpy(coj, jj, mm->nz));
    7525:       } else if (cmapt[cp] == 1) {                        /* type-1, local to global for consecutive columns of C */
    7526:         for (j = 0; j < mm->nz; j++) coj[j] = jj[j] + cs; /* lid + col start */
    7527:       } else {                                            /* type-2, local to global for sparse columns */
    7528:         for (j = 0; j < mm->nz; j++) coj[j] = cmap[jj[j]];
    7529:       }
    7530:       ncoo_d += mm->nz;
    7531:     } else if (rmapt[cp] == 2) { /* sparse rows */
    7532:       for (i = 0; i < mr; i++) {
    7533:         const PetscInt *jj = mm->j + ii[i];
    7534:         const PetscInt  gr = rmap[i];
    7535:         const PetscInt  nz = ii[i + 1] - ii[i];
    7536:         if (gr >= rs && gr < re) { /* local rows */
    7537:           for (j = ii[i]; j < ii[i + 1]; j++) *coi++ = gr;
    7538:           if (!cmapt[cp]) { /* type-0, already global */
    7539:             for (j = 0; j < nz; j++) *coj++ = jj[j];
    7540:           } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
    7541:             for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
    7542:           } else { /* type-2, local to global for sparse columns */
    7543:             for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
    7544:           }
    7545:           ncoo_d += nz;
    7546:         }
    7547:       }
    7548:     }
    7549:   }
    7550:   if (glob) PetscCall(ISRestoreIndices(glob, &globidx));
    7551:   PetscCall(ISDestroy(&glob));
    7552:   if (P_oth_l2g) PetscCall(ISLocalToGlobalMappingRestoreIndices(P_oth_l2g, &P_oth_idx));
    7553:   PetscCall(ISLocalToGlobalMappingDestroy(&P_oth_l2g));
    7554:   /* allocate an array to store all nonzeros (inserted locally or remotely) belonging to this proc */
    7555:   PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo * sizeof(PetscScalar), (void **)&mmdata->coo_v));

    7557:   /* set block sizes */
    7558:   A = product->A;
    7559:   P = product->B;
    7560:   switch (ptype) {
    7561:   case MATPRODUCT_PtAP:
    7562:     PetscCall(MatSetBlockSizes(C, P->cmap->bs, P->cmap->bs));
    7563:     break;
    7564:   case MATPRODUCT_RARt:
    7565:     PetscCall(MatSetBlockSizes(C, P->rmap->bs, P->rmap->bs));
    7566:     break;
    7567:   case MATPRODUCT_ABC:
    7568:     PetscCall(MatSetBlockSizesFromMats(C, A, product->C));
    7569:     break;
    7570:   case MATPRODUCT_AB:
    7571:     PetscCall(MatSetBlockSizesFromMats(C, A, P));
    7572:     break;
    7573:   case MATPRODUCT_AtB:
    7574:     PetscCall(MatSetBlockSizes(C, A->cmap->bs, P->cmap->bs));
    7575:     break;
    7576:   case MATPRODUCT_ABt:
    7577:     PetscCall(MatSetBlockSizes(C, A->rmap->bs, P->rmap->bs));
    7578:     break;
    7579:   default:
    7580:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for ProductType %s", MatProductTypes[ptype]);
    7581:   }

    7583:   /* preallocate with COO data */
    7584:   PetscCall(MatSetPreallocationCOO(C, ncoo, coo_i, coo_j));
    7585:   PetscCall(PetscFree2(coo_i, coo_j));
    7586:   PetscFunctionReturn(PETSC_SUCCESS);
    7587: }

    7589: PetscErrorCode MatProductSetFromOptions_MPIAIJBACKEND(Mat mat)
    7590: {
    7591:   Mat_Product *product = mat->product;
    7592: #if defined(PETSC_HAVE_DEVICE)
    7593:   PetscBool match  = PETSC_FALSE;
    7594:   PetscBool usecpu = PETSC_FALSE;
    7595: #else
    7596:   PetscBool match = PETSC_TRUE;
    7597: #endif

    7599:   PetscFunctionBegin;
    7600:   MatCheckProduct(mat, 1);
    7601: #if defined(PETSC_HAVE_DEVICE)
    7602:   if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, ((PetscObject)product->A)->type_name, &match));
    7603:   if (match) { /* we can always fallback to the CPU if requested */
    7604:     switch (product->type) {
    7605:     case MATPRODUCT_AB:
    7606:       if (product->api_user) {
    7607:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
    7608:         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
    7609:         PetscOptionsEnd();
    7610:       } else {
    7611:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
    7612:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
    7613:         PetscOptionsEnd();
    7614:       }
    7615:       break;
    7616:     case MATPRODUCT_AtB:
    7617:       if (product->api_user) {
    7618:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
    7619:         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
    7620:         PetscOptionsEnd();
    7621:       } else {
    7622:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
    7623:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
    7624:         PetscOptionsEnd();
    7625:       }
    7626:       break;
    7627:     case MATPRODUCT_PtAP:
    7628:       if (product->api_user) {
    7629:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
    7630:         PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
    7631:         PetscOptionsEnd();
    7632:       } else {
    7633:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
    7634:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
    7635:         PetscOptionsEnd();
    7636:       }
    7637:       break;
    7638:     default:
    7639:       break;
    7640:     }
    7641:     match = (PetscBool)!usecpu;
    7642:   }
    7643: #endif
    7644:   if (match) {
    7645:     switch (product->type) {
    7646:     case MATPRODUCT_AB:
    7647:     case MATPRODUCT_AtB:
    7648:     case MATPRODUCT_PtAP:
    7649:       mat->ops->productsymbolic = MatProductSymbolic_MPIAIJBACKEND;
    7650:       break;
    7651:     default:
    7652:       break;
    7653:     }
    7654:   }
    7655:   /* fallback to MPIAIJ ops */
    7656:   if (!mat->ops->productsymbolic) PetscCall(MatProductSetFromOptions_MPIAIJ(mat));
    7657:   PetscFunctionReturn(PETSC_SUCCESS);
    7658: }

    7660: /*
    7661:    Produces a set of block column indices of the matrix row, one for each block represented in the original row

    7663:    n - the number of block indices in cc[]
    7664:    cc - the block indices (must be large enough to contain the indices)
    7665: */
    7666: static inline PetscErrorCode MatCollapseRow(Mat Amat, PetscInt row, PetscInt bs, PetscInt *n, PetscInt *cc)
    7667: {
    7668:   PetscInt        cnt = -1, nidx, j;
    7669:   const PetscInt *idx;

    7671:   PetscFunctionBegin;
    7672:   PetscCall(MatGetRow(Amat, row, &nidx, &idx, NULL));
    7673:   if (nidx) {
    7674:     cnt     = 0;
    7675:     cc[cnt] = idx[0] / bs;
    7676:     for (j = 1; j < nidx; j++) {
    7677:       if (cc[cnt] < idx[j] / bs) cc[++cnt] = idx[j] / bs;
    7678:     }
    7679:   }
    7680:   PetscCall(MatRestoreRow(Amat, row, &nidx, &idx, NULL));
    7681:   *n = cnt + 1;
    7682:   PetscFunctionReturn(PETSC_SUCCESS);
    7683: }

    7685: /*
    7686:     Produces a set of block column indices of the matrix block row, one for each block represented in the original set of rows

    7688:     ncollapsed - the number of block indices
    7689:     collapsed - the block indices (must be large enough to contain the indices)
    7690: */
    7691: static inline PetscErrorCode MatCollapseRows(Mat Amat, PetscInt start, PetscInt bs, PetscInt *w0, PetscInt *w1, PetscInt *w2, PetscInt *ncollapsed, PetscInt **collapsed)
    7692: {
    7693:   PetscInt i, nprev, *cprev = w0, ncur = 0, *ccur = w1, *merged = w2, *cprevtmp;

    7695:   PetscFunctionBegin;
    7696:   PetscCall(MatCollapseRow(Amat, start, bs, &nprev, cprev));
    7697:   for (i = start + 1; i < start + bs; i++) {
    7698:     PetscCall(MatCollapseRow(Amat, i, bs, &ncur, ccur));
    7699:     PetscCall(PetscMergeIntArray(nprev, cprev, ncur, ccur, &nprev, &merged));
    7700:     cprevtmp = cprev;
    7701:     cprev    = merged;
    7702:     merged   = cprevtmp;
    7703:   }
    7704:   *ncollapsed = nprev;
    7705:   if (collapsed) *collapsed = cprev;
    7706:   PetscFunctionReturn(PETSC_SUCCESS);
    7707: }

    7709: /*
    7710:  MatCreateGraph_Simple_AIJ - create simple scalar matrix (graph) from potentially blocked matrix

    7712:  Input Parameter:
    7713:  . Amat - matrix
    7714:  - symmetrize - make the result symmetric
    7715:  + scale - scale with diagonal

    7717:  Output Parameter:
    7718:  . a_Gmat - output scalar graph >= 0

    7720: */
    7721: PETSC_INTERN PetscErrorCode MatCreateGraph_Simple_AIJ(Mat Amat, PetscBool symmetrize, PetscBool scale, PetscReal filter, PetscInt index_size, PetscInt index[], Mat *a_Gmat)
    7722: {
    7723:   PetscInt  Istart, Iend, Ii, jj, kk, ncols, nloc, NN, MM, bs;
    7724:   MPI_Comm  comm;
    7725:   Mat       Gmat;
    7726:   PetscBool ismpiaij, isseqaij;
    7727:   Mat       a, b, c;
    7728:   MatType   jtype;

    7730:   PetscFunctionBegin;
    7731:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
    7732:   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
    7733:   PetscCall(MatGetSize(Amat, &MM, &NN));
    7734:   PetscCall(MatGetBlockSize(Amat, &bs));
    7735:   nloc = (Iend - Istart) / bs;

    7737:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATSEQAIJ, &isseqaij));
    7738:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATMPIAIJ, &ismpiaij));
    7739:   PetscCheck(isseqaij || ismpiaij, comm, PETSC_ERR_USER, "Require (MPI)AIJ matrix type");

    7741:   /* TODO GPU: these calls are potentially expensive if matrices are large and we want to use the GPU */
    7742:   /* A solution consists in providing a new API, MatAIJGetCollapsedAIJ, and each class can provide a fast
    7743:      implementation */
    7744:   if (bs > 1) {
    7745:     PetscCall(MatGetType(Amat, &jtype));
    7746:     PetscCall(MatCreate(comm, &Gmat));
    7747:     PetscCall(MatSetType(Gmat, jtype));
    7748:     PetscCall(MatSetSizes(Gmat, nloc, nloc, PETSC_DETERMINE, PETSC_DETERMINE));
    7749:     PetscCall(MatSetBlockSizes(Gmat, 1, 1));
    7750:     if (isseqaij || ((Mat_MPIAIJ *)Amat->data)->garray) {
    7751:       PetscInt  *d_nnz, *o_nnz;
    7752:       MatScalar *aa, val, *AA;
    7753:       PetscInt  *aj, *ai, *AJ, nc, nmax = 0;

    7755:       if (isseqaij) {
    7756:         a = Amat;
    7757:         b = NULL;
    7758:       } else {
    7759:         Mat_MPIAIJ *d = (Mat_MPIAIJ *)Amat->data;
    7760:         a             = d->A;
    7761:         b             = d->B;
    7762:       }
    7763:       PetscCall(PetscInfo(Amat, "New bs>1 Graph. nloc=%" PetscInt_FMT "\n", nloc));
    7764:       PetscCall(PetscMalloc2(nloc, &d_nnz, (isseqaij ? 0 : nloc), &o_nnz));
    7765:       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
    7766:         PetscInt       *nnz = (c == a) ? d_nnz : o_nnz;
    7767:         const PetscInt *cols1, *cols2;

    7769:         for (PetscInt brow = 0, nc1, nc2, ok = 1; brow < nloc * bs; brow += bs) { // block rows
    7770:           PetscCall(MatGetRow(c, brow, &nc2, &cols2, NULL));
    7771:           nnz[brow / bs] = nc2 / bs;
    7772:           if (nc2 % bs) ok = 0;
    7773:           if (nnz[brow / bs] > nmax) nmax = nnz[brow / bs];
    7774:           for (PetscInt ii = 1; ii < bs; ii++) { // check for non-dense blocks
    7775:             PetscCall(MatGetRow(c, brow + ii, &nc1, &cols1, NULL));
    7776:             if (nc1 != nc2) ok = 0;
    7777:             else {
    7778:               for (PetscInt jj = 0; jj < nc1 && ok == 1; jj++) {
    7779:                 if (cols1[jj] != cols2[jj]) ok = 0;
    7780:                 if (cols1[jj] % bs != jj % bs) ok = 0;
    7781:               }
    7782:             }
    7783:             PetscCall(MatRestoreRow(c, brow + ii, &nc1, &cols1, NULL));
    7784:           }
    7785:           PetscCall(MatRestoreRow(c, brow, &nc2, &cols2, NULL));
    7786:           if (!ok) {
    7787:             PetscCall(PetscFree2(d_nnz, o_nnz));
    7788:             PetscCall(PetscInfo(Amat, "Found sparse blocks - revert to slow method\n"));
    7789:             goto old_bs;
    7790:           }
    7791:         }
    7792:       }
    7793:       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
    7794:       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
    7795:       PetscCall(PetscFree2(d_nnz, o_nnz));
    7796:       PetscCall(PetscMalloc2(nmax, &AA, nmax, &AJ));
    7797:       // diag
    7798:       for (PetscInt brow = 0, n, grow; brow < nloc * bs; brow += bs) { // block rows
    7799:         Mat_SeqAIJ *aseq = (Mat_SeqAIJ *)a->data;

    7801:         ai = aseq->i;
    7802:         n  = ai[brow + 1] - ai[brow];
    7803:         aj = aseq->j + ai[brow];
    7804:         for (PetscInt k = 0; k < n; k += bs) {   // block columns
    7805:           AJ[k / bs] = aj[k] / bs + Istart / bs; // diag starts at (Istart,Istart)
    7806:           val        = 0;
    7807:           if (index_size == 0) {
    7808:             for (PetscInt ii = 0; ii < bs; ii++) { // rows in block
    7809:               aa = aseq->a + ai[brow + ii] + k;
    7810:               for (PetscInt jj = 0; jj < bs; jj++) {    // columns in block
    7811:                 val += PetscAbs(PetscRealPart(aa[jj])); // a sort of norm
    7812:               }
    7813:             }
    7814:           } else {                                            // use (index,index) value if provided
    7815:             for (PetscInt iii = 0; iii < index_size; iii++) { // rows in block
    7816:               PetscInt ii = index[iii];
    7817:               aa          = aseq->a + ai[brow + ii] + k;
    7818:               for (PetscInt jjj = 0; jjj < index_size; jjj++) { // columns in block
    7819:                 PetscInt jj = index[jjj];
    7820:                 val += PetscAbs(PetscRealPart(aa[jj]));
    7821:               }
    7822:             }
    7823:           }
    7824:           PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%" PetscInt_FMT ") >= nmax (%" PetscInt_FMT ")", k / bs, nmax);
    7825:           AA[k / bs] = val;
    7826:         }
    7827:         grow = Istart / bs + brow / bs;
    7828:         PetscCall(MatSetValues(Gmat, 1, &grow, n / bs, AJ, AA, ADD_VALUES));
    7829:       }
    7830:       // off-diag
    7831:       if (ismpiaij) {
    7832:         Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)Amat->data;
    7833:         const PetscScalar *vals;
    7834:         const PetscInt    *cols, *garray = aij->garray;

    7836:         PetscCheck(garray, PETSC_COMM_SELF, PETSC_ERR_USER, "No garray ?");
    7837:         for (PetscInt brow = 0, grow; brow < nloc * bs; brow += bs) { // block rows
    7838:           PetscCall(MatGetRow(b, brow, &ncols, &cols, NULL));
    7839:           for (PetscInt k = 0, cidx = 0; k < ncols; k += bs, cidx++) {
    7840:             PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs >= nmax");
    7841:             AA[k / bs] = 0;
    7842:             AJ[cidx]   = garray[cols[k]] / bs;
    7843:           }
    7844:           nc = ncols / bs;
    7845:           PetscCall(MatRestoreRow(b, brow, &ncols, &cols, NULL));
    7846:           if (index_size == 0) {
    7847:             for (PetscInt ii = 0; ii < bs; ii++) { // rows in block
    7848:               PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
    7849:               for (PetscInt k = 0; k < ncols; k += bs) {
    7850:                 for (PetscInt jj = 0; jj < bs; jj++) { // cols in block
    7851:                   PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%" PetscInt_FMT ") >= nmax (%" PetscInt_FMT ")", k / bs, nmax);
    7852:                   AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
    7853:                 }
    7854:               }
    7855:               PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
    7856:             }
    7857:           } else {                                            // use (index,index) value if provided
    7858:             for (PetscInt iii = 0; iii < index_size; iii++) { // rows in block
    7859:               PetscInt ii = index[iii];
    7860:               PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
    7861:               for (PetscInt k = 0; k < ncols; k += bs) {
    7862:                 for (PetscInt jjj = 0; jjj < index_size; jjj++) { // cols in block
    7863:                   PetscInt jj = index[jjj];
    7864:                   AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
    7865:                 }
    7866:               }
    7867:               PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
    7868:             }
    7869:           }
    7870:           grow = Istart / bs + brow / bs;
    7871:           PetscCall(MatSetValues(Gmat, 1, &grow, nc, AJ, AA, ADD_VALUES));
    7872:         }
    7873:       }
    7874:       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
    7875:       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
    7876:       PetscCall(PetscFree2(AA, AJ));
    7877:     } else {
    7878:       const PetscScalar *vals;
    7879:       const PetscInt    *idx;
    7880:       PetscInt          *d_nnz, *o_nnz, *w0, *w1, *w2;
    7881:     old_bs:
    7882:       /*
    7883:        Determine the preallocation needed for the scalar matrix derived from the vector matrix.
    7884:        */
    7885:       PetscCall(PetscInfo(Amat, "OLD bs>1 CreateGraph\n"));
    7886:       PetscCall(PetscMalloc2(nloc, &d_nnz, (isseqaij ? 0 : nloc), &o_nnz));
    7887:       if (isseqaij) {
    7888:         PetscInt max_d_nnz;

    7890:         /*
    7891:          Determine exact preallocation count for (sequential) scalar matrix
    7892:          */
    7893:         PetscCall(MatSeqAIJGetMaxRowNonzeros(Amat, &max_d_nnz));
    7894:         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
    7895:         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
    7896:         for (Ii = 0, jj = 0; Ii < Iend; Ii += bs, jj++) PetscCall(MatCollapseRows(Amat, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
    7897:         PetscCall(PetscFree3(w0, w1, w2));
    7898:       } else if (ismpiaij) {
    7899:         Mat             Daij, Oaij;
    7900:         const PetscInt *garray;
    7901:         PetscInt        max_d_nnz;

    7903:         PetscCall(MatMPIAIJGetSeqAIJ(Amat, &Daij, &Oaij, &garray));
    7904:         /*
    7905:          Determine exact preallocation count for diagonal block portion of scalar matrix
    7906:          */
    7907:         PetscCall(MatSeqAIJGetMaxRowNonzeros(Daij, &max_d_nnz));
    7908:         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
    7909:         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
    7910:         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) PetscCall(MatCollapseRows(Daij, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
    7911:         PetscCall(PetscFree3(w0, w1, w2));
    7912:         /*
    7913:          Over estimate (usually grossly over), preallocation count for off-diagonal portion of scalar matrix
    7914:          */
    7915:         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
    7916:           o_nnz[jj] = 0;
    7917:           for (kk = 0; kk < bs; kk++) { /* rows that get collapsed to a single row */
    7918:             PetscCall(MatGetRow(Oaij, Ii + kk, &ncols, NULL, NULL));
    7919:             o_nnz[jj] += ncols;
    7920:             PetscCall(MatRestoreRow(Oaij, Ii + kk, &ncols, NULL, NULL));
    7921:           }
    7922:           if (o_nnz[jj] > (NN / bs - nloc)) o_nnz[jj] = NN / bs - nloc;
    7923:         }
    7924:       } else SETERRQ(comm, PETSC_ERR_USER, "Require AIJ matrix type");
    7925:       /* get scalar copy (norms) of matrix */
    7926:       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
    7927:       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
    7928:       PetscCall(PetscFree2(d_nnz, o_nnz));
    7929:       for (Ii = Istart; Ii < Iend; Ii++) {
    7930:         PetscInt dest_row = Ii / bs;

    7932:         PetscCall(MatGetRow(Amat, Ii, &ncols, &idx, &vals));
    7933:         for (jj = 0; jj < ncols; jj++) {
    7934:           PetscInt    dest_col = idx[jj] / bs;
    7935:           PetscScalar sv       = PetscAbs(PetscRealPart(vals[jj]));

    7937:           PetscCall(MatSetValues(Gmat, 1, &dest_row, 1, &dest_col, &sv, ADD_VALUES));
    7938:         }
    7939:         PetscCall(MatRestoreRow(Amat, Ii, &ncols, &idx, &vals));
    7940:       }
    7941:       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
    7942:       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
    7943:     }
    7944:   } else {
    7945:     if (symmetrize || filter >= 0 || scale) PetscCall(MatDuplicate(Amat, MAT_COPY_VALUES, &Gmat));
    7946:     else {
    7947:       Gmat = Amat;
    7948:       PetscCall(PetscObjectReference((PetscObject)Gmat));
    7949:     }
    7950:     if (isseqaij) {
    7951:       a = Gmat;
    7952:       b = NULL;
    7953:     } else {
    7954:       Mat_MPIAIJ *d = (Mat_MPIAIJ *)Gmat->data;
    7955:       a             = d->A;
    7956:       b             = d->B;
    7957:     }
    7958:     if (filter >= 0 || scale) {
    7959:       /* take absolute value of each entry */
    7960:       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
    7961:         MatInfo      info;
    7962:         PetscScalar *avals;

    7964:         PetscCall(MatGetInfo(c, MAT_LOCAL, &info));
    7965:         PetscCall(MatSeqAIJGetArray(c, &avals));
    7966:         for (int jj = 0; jj < info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    7967:         PetscCall(MatSeqAIJRestoreArray(c, &avals));
    7968:       }
    7969:     }
    7970:   }
    7971:   if (symmetrize) {
    7972:     PetscBool isset, issym;

    7974:     PetscCall(MatIsSymmetricKnown(Amat, &isset, &issym));
    7975:     if (!isset || !issym) {
    7976:       Mat matTrans;

    7978:       PetscCall(MatTranspose(Gmat, MAT_INITIAL_MATRIX, &matTrans));
    7979:       PetscCall(MatAXPY(Gmat, 1.0, matTrans, Gmat->structurally_symmetric == PETSC_BOOL3_TRUE ? SAME_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN));
    7980:       PetscCall(MatDestroy(&matTrans));
    7981:     }
    7982:     PetscCall(MatSetOption(Gmat, MAT_SYMMETRIC, PETSC_TRUE));
    7983:   } else if (Amat != Gmat) PetscCall(MatPropagateSymmetryOptions(Amat, Gmat));
    7984:   if (scale) {
    7985:     /* scale c for all diagonal values = 1 or -1 */
    7986:     Vec diag;

    7988:     PetscCall(MatCreateVecs(Gmat, &diag, NULL));
    7989:     PetscCall(MatGetDiagonal(Gmat, diag));
    7990:     PetscCall(VecReciprocal(diag));
    7991:     PetscCall(VecSqrtAbs(diag));
    7992:     PetscCall(MatDiagonalScale(Gmat, diag, diag));
    7993:     PetscCall(VecDestroy(&diag));
    7994:   }
    7995:   PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_graph_view"));
    7996:   if (filter >= 0) {
    7997:     PetscCall(MatFilter(Gmat, filter, PETSC_TRUE, PETSC_TRUE));
    7998:     PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_filter_graph_view"));
    7999:   }
    8000:   *a_Gmat = Gmat;
    8001:   PetscFunctionReturn(PETSC_SUCCESS);
    8002: }

    8004: PETSC_INTERN PetscErrorCode MatGetCurrentMemType_MPIAIJ(Mat A, PetscMemType *memtype)
    8005: {
    8006:   Mat_MPIAIJ  *mpiaij = (Mat_MPIAIJ *)A->data;
    8007:   PetscMemType mD = PETSC_MEMTYPE_HOST, mO = PETSC_MEMTYPE_HOST;

    8009:   PetscFunctionBegin;
    8010:   if (mpiaij->A) PetscCall(MatGetCurrentMemType(mpiaij->A, &mD));
    8011:   if (mpiaij->B) PetscCall(MatGetCurrentMemType(mpiaij->B, &mO));
    8012:   *memtype = (mD == mO) ? mD : PETSC_MEMTYPE_HOST;
    8013:   PetscFunctionReturn(PETSC_SUCCESS);
    8014: }

    8016: /*
    8017:     Special version for direct calls from Fortran
    8018: */

    8020: /* Change these macros so can be used in void function */
    8021: /* Identical to PetscCallVoid, except it assigns to *_ierr */
    8022: #undef PetscCall
    8023: #define PetscCall(...) \
    8024:   do { \
    8025:     PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__; \
    8026:     if (PetscUnlikely(ierr_msv_mpiaij)) { \
    8027:       *_ierr = PetscError(PETSC_COMM_SELF, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr_msv_mpiaij, PETSC_ERROR_REPEAT, " "); \
    8028:       return; \
    8029:     } \
    8030:   } while (0)

    8032: #undef SETERRQ
    8033: #define SETERRQ(comm, ierr, ...) \
    8034:   do { \
    8035:     *_ierr = PetscError(comm, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr, PETSC_ERROR_INITIAL, __VA_ARGS__); \
    8036:     return; \
    8037:   } while (0)

    8039: #if defined(PETSC_HAVE_FORTRAN_CAPS)
    8040:   #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
    8041: #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
    8042:   #define matsetvaluesmpiaij_ matsetvaluesmpiaij
    8043: #else
    8044: #endif
    8045: PETSC_EXTERN void matsetvaluesmpiaij_(Mat *mmat, PetscInt *mm, const PetscInt im[], PetscInt *mn, const PetscInt in[], const PetscScalar v[], InsertMode *maddv, PetscErrorCode *_ierr)
    8046: {
    8047:   Mat         mat = *mmat;
    8048:   PetscInt    m = *mm, n = *mn;
    8049:   InsertMode  addv = *maddv;
    8050:   Mat_MPIAIJ *aij  = (Mat_MPIAIJ *)mat->data;
    8051:   PetscScalar value;

    8053:   MatCheckPreallocated(mat, 1);
    8054:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    8055:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    8056:   {
    8057:     PetscInt  i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    8058:     PetscInt  cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
    8059:     PetscBool roworiented = aij->roworiented;

    8061:     /* Some Variables required in the macro */
    8062:     Mat         A     = aij->A;
    8063:     Mat_SeqAIJ *a     = (Mat_SeqAIJ *)A->data;
    8064:     PetscInt   *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
    8065:     MatScalar  *aa;
    8066:     PetscBool   ignorezeroentries = ((a->ignorezeroentries && (addv == ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
    8067:     Mat         B                 = aij->B;
    8068:     Mat_SeqAIJ *b                 = (Mat_SeqAIJ *)B->data;
    8069:     PetscInt   *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j, bm = aij->B->rmap->n, am = aij->A->rmap->n;
    8070:     MatScalar  *ba;
    8071:     /* This variable below is only for the PETSC_HAVE_VIENNACL or PETSC_HAVE_CUDA cases, but we define it in all cases because we
    8072:      * cannot use "#if defined" inside a macro. */
    8073:     PETSC_UNUSED PetscBool inserted = PETSC_FALSE;

    8075:     PetscInt  *rp1, *rp2, ii, nrow1, nrow2, _i, rmax1, rmax2, N, low1, high1, low2, high2, t, lastcol1, lastcol2;
    8076:     PetscInt   nonew = a->nonew;
    8077:     MatScalar *ap1, *ap2;

    8079:     PetscFunctionBegin;
    8080:     PetscCall(MatSeqAIJGetArray(A, &aa));
    8081:     PetscCall(MatSeqAIJGetArray(B, &ba));
    8082:     for (i = 0; i < m; i++) {
    8083:       if (im[i] < 0) continue;
    8084:       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);
    8085:       if (im[i] >= rstart && im[i] < rend) {
    8086:         row      = im[i] - rstart;
    8087:         lastcol1 = -1;
    8088:         rp1      = aj + ai[row];
    8089:         ap1      = aa + ai[row];
    8090:         rmax1    = aimax[row];
    8091:         nrow1    = ailen[row];
    8092:         low1     = 0;
    8093:         high1    = nrow1;
    8094:         lastcol2 = -1;
    8095:         rp2      = bj + bi[row];
    8096:         ap2      = ba + bi[row];
    8097:         rmax2    = bimax[row];
    8098:         nrow2    = bilen[row];
    8099:         low2     = 0;
    8100:         high2    = nrow2;

    8102:         for (j = 0; j < n; j++) {
    8103:           if (roworiented) value = v[i * n + j];
    8104:           else value = v[i + j * m];
    8105:           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
    8106:           if (in[j] >= cstart && in[j] < cend) {
    8107:             col = in[j] - cstart;
    8108:             MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
    8109:           } else if (in[j] < 0) continue;
    8110:           else if (PetscUnlikelyDebug(in[j] >= mat->cmap->N)) {
    8111:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
    8112:           } else {
    8113:             if (mat->was_assembled) {
    8114:               if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    8115: #if defined(PETSC_USE_CTABLE)
    8116:               PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col));
    8117:               col--;
    8118: #else
    8119:               col = aij->colmap[in[j]] - 1;
    8120: #endif
    8121:               if (col < 0 && !((Mat_SeqAIJ *)aij->A->data)->nonew) {
    8122:                 PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));
    8123:                 col = in[j];
    8124:                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
    8125:                 B        = aij->B;
    8126:                 b        = (Mat_SeqAIJ *)B->data;
    8127:                 bimax    = b->imax;
    8128:                 bi       = b->i;
    8129:                 bilen    = b->ilen;
    8130:                 bj       = b->j;
    8131:                 rp2      = bj + bi[row];
    8132:                 ap2      = ba + bi[row];
    8133:                 rmax2    = bimax[row];
    8134:                 nrow2    = bilen[row];
    8135:                 low2     = 0;
    8136:                 high2    = nrow2;
    8137:                 bm       = aij->B->rmap->n;
    8138:                 ba       = b->a;
    8139:                 inserted = PETSC_FALSE;
    8140:               }
    8141:             } else col = in[j];
    8142:             MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
    8143:           }
    8144:         }
    8145:       } else if (!aij->donotstash) {
    8146:         if (roworiented) {
    8147:           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, v + i * n, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    8148:         } else {
    8149:           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, v + i, m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    8150:         }
    8151:       }
    8152:     }
    8153:     PetscCall(MatSeqAIJRestoreArray(A, &aa));
    8154:     PetscCall(MatSeqAIJRestoreArray(B, &ba));
    8155:   }
    8156:   PetscFunctionReturnVoid();
    8157: }

    8159: /* Undefining these here since they were redefined from their original definition above! No
    8160:  * other PETSc functions should be defined past this point, as it is impossible to recover the
    8161:  * original definitions */
    8162: #undef PetscCall
    8163: #undef SETERRQ