Date: 2025-03-29T05:58:32+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)
     88:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_scalapack_C", NULL));
     89: #endif
     90: #if defined(PETSC_HAVE_HYPRE)
     91:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_hypre_C", NULL));
     92:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", NULL));
     93: #endif
     94:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_is_C", NULL));
     95:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_is_mpiaij_C", NULL));
     96:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaij_mpiaij_C", NULL));
     97:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetUseScalableIncreaseOverlap_C", NULL));
     98:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijperm_C", NULL));
     99:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijsell_C", NULL));
    100: #if defined(PETSC_HAVE_MKL_SPARSE)
    101:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijmkl_C", NULL));
    102: #endif
    103:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijcrl_C", NULL));
    104:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_is_C", NULL));
    105:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpisell_C", NULL));
    106:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetPreallocationCOO_C", NULL));
    107:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetValuesCOO_C", NULL));
    108:   PetscFunctionReturn(PETSC_SUCCESS);
    109: }

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

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

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

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

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

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

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

    146:   Developer Note:
    147:   Level: beginner

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

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

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

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

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

    167:   Level: beginner

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

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

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

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

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

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

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

    213:   PetscFunctionBegin;
    214:   *keptrows = NULL;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    573:       for (j = 0; j < n; j++) {
    574:         if (v) value = roworiented ? v[i * n + j] : v[i + j * m];
    575:         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
    576:         if (in[j] >= cstart && in[j] < cend) {
    577:           col   = in[j] - cstart;
    578:           nonew = a->nonew;
    579:           MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
    580:         } else if (in[j] < 0) {
    581:           continue;
    582:         } else {
    583:           PetscCheck(in[j] < mat->cmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
    584:           if (mat->was_assembled) {
    585:             if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    586: #if defined(PETSC_USE_CTABLE)
    587:             PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col)); /* map global col ids to local ones */
    588:             col--;
    589: #else
    590:             col = aij->colmap[in[j]] - 1;
    591: #endif
    592:             if (col < 0 && !((Mat_SeqAIJ *)aij->B->data)->nonew) { /* col < 0 means in[j] is a new col for B */
    593:               PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));  /* Change aij->B from reduced/local format to expanded/global format */
    594:               col = in[j];
    595:               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
    596:               B     = aij->B;
    597:               b     = (Mat_SeqAIJ *)B->data;
    598:               bimax = b->imax;
    599:               bi    = b->i;
    600:               bilen = b->ilen;
    601:               bj    = b->j;
    602:               ba    = b->a;
    603:               rp2   = PetscSafePointerPlusOffset(bj, bi[row]);
    604:               ap2   = PetscSafePointerPlusOffset(ba, bi[row]);
    605:               rmax2 = bimax[row];
    606:               nrow2 = bilen[row];
    607:               low2  = 0;
    608:               high2 = nrow2;
    609:               bm    = aij->B->rmap->n;
    610:               ba    = b->a;
    611:             } else if (col < 0 && !(ignorezeroentries && value == 0.0)) {
    612:               if (1 == ((Mat_SeqAIJ *)aij->B->data)->nonew) {
    613:                 PetscCall(PetscInfo(mat, "Skipping of insertion of new nonzero location in off-diagonal portion of matrix %g(%" PetscInt_FMT ",%" PetscInt_FMT ")\n", (double)PetscRealPart(value), im[i], in[j]));
    614:               } else SETERRQ(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]);
    615:             }
    616:           } else col = in[j];
    617:           nonew = b->nonew;
    618:           MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
    619:         }
    620:       }
    621:     } else {
    622:       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]);
    623:       if (!aij->donotstash) {
    624:         mat->assembled = PETSC_FALSE;
    625:         if (roworiented) {
    626:           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, PetscSafePointerPlusOffset(v, i * n), (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    627:         } else {
    628:           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, PetscSafePointerPlusOffset(v, i), m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    629:         }
    630:       }
    631:     }
    632:   }
    633:   PetscCall(MatSeqAIJRestoreArray(A, &aa)); /* aa, bb might have been free'd due to reallocation above. But we don't access them here */
    634:   PetscCall(MatSeqAIJRestoreArray(B, &ba));
    635:   PetscFunctionReturn(PETSC_SUCCESS);
    636: }

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

    657:   PetscFunctionBegin;
    658:   /* Iterate over all rows of the matrix */
    659:   for (j = 0; j < am; j++) {
    660:     dnz = onz = 0;
    661:     /*  Iterate over all non-zero columns of the current row */
    662:     for (col = mat_i[j]; col < mat_i[j + 1]; col++) {
    663:       /* If column is in the diagonal */
    664:       if (mat_j[col] >= cstart && mat_j[col] < cend) {
    665:         aj[diag_so_far++] = mat_j[col] - cstart;
    666:         dnz++;
    667:       } else { /* off-diagonal entries */
    668:         bj[offd_so_far++] = mat_j[col];
    669:         onz++;
    670:       }
    671:     }
    672:     ailen[j] = dnz;
    673:     bilen[j] = onz;
    674:   }
    675:   PetscFunctionReturn(PETSC_SUCCESS);
    676: }

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

    701:   PetscFunctionBegin;
    702:   /* Iterate over all rows of the matrix */
    703:   for (j = 0; j < am; j++) {
    704:     dnz_row = onz_row = 0;
    705:     rowstart_offd     = full_offd_i[j];
    706:     rowstart_diag     = full_diag_i[j];
    707:     /*  Iterate over all non-zero columns of the current row */
    708:     for (col = mat_i[j]; col < mat_i[j + 1]; col++) {
    709:       /* If column is in the diagonal */
    710:       if (mat_j[col] >= cstart && mat_j[col] < cend) {
    711:         aj[rowstart_diag + dnz_row] = mat_j[col] - cstart;
    712:         aa[rowstart_diag + dnz_row] = mat_a[col];
    713:         dnz_row++;
    714:       } else { /* off-diagonal entries */
    715:         bj[rowstart_offd + onz_row] = mat_j[col];
    716:         ba[rowstart_offd + onz_row] = mat_a[col];
    717:         onz_row++;
    718:       }
    719:     }
    720:     ailen[j] = dnz_row;
    721:     bilen[j] = onz_row;
    722:   }
    723:   PetscFunctionReturn(PETSC_SUCCESS);
    724: }

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

    732:   PetscFunctionBegin;
    733:   for (i = 0; i < m; i++) {
    734:     if (idxm[i] < 0) continue; /* negative row */
    735:     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);
    736:     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);
    737:     row = idxm[i] - rstart;
    738:     for (j = 0; j < n; j++) {
    739:       if (idxn[j] < 0) continue; /* negative column */
    740:       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);
    741:       if (idxn[j] >= cstart && idxn[j] < cend) {
    742:         col = idxn[j] - cstart;
    743:         PetscCall(MatGetValues(aij->A, 1, &row, 1, &col, v + i * n + j));
    744:       } else {
    745:         if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    746: #if defined(PETSC_USE_CTABLE)
    747:         PetscCall(PetscHMapIGetWithDefault(aij->colmap, idxn[j] + 1, 0, &col));
    748:         col--;
    749: #else
    750:         col = aij->colmap[idxn[j]] - 1;
    751: #endif
    752:         if ((col < 0) || (aij->garray[col] != idxn[j])) *(v + i * n + j) = 0.0;
    753:         else PetscCall(MatGetValues(aij->B, 1, &row, 1, &col, v + i * n + j));
    754:       }
    755:     }
    756:   }
    757:   PetscFunctionReturn(PETSC_SUCCESS);
    758: }

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

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

    768:   PetscCall(MatStashScatterBegin_Private(mat, &mat->stash, mat->rmap->range));
    769:   PetscCall(MatStashGetInfo_Private(&mat->stash, &nstash, &reallocs));
    770:   PetscCall(PetscInfo(aij->A, "Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
    771:   PetscFunctionReturn(PETSC_SUCCESS);
    772: }

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

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

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

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

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

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

    838:   aij->rowvalues = NULL;

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

    842:   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
    843:   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ *)aij->A->data)->nonew) {
    844:     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
    845:     PetscCallMPI(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));
    846:   }
    847: #if defined(PETSC_HAVE_DEVICE)
    848:   mat->offloadmask = PETSC_OFFLOAD_BOTH;
    849: #endif
    850:   PetscFunctionReturn(PETSC_SUCCESS);
    851: }

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

    857:   PetscFunctionBegin;
    858:   PetscCall(MatZeroEntries(l->A));
    859:   PetscCall(MatZeroEntries(l->B));
    860:   PetscFunctionReturn(PETSC_SUCCESS);
    861: }

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

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

    879:     PetscCheck(cong, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Need matching row/col layout");
    880:     PetscCall(VecGetArrayRead(x, &xx));
    881:     PetscCall(VecGetArray(b, &bb));
    882:     for (r = 0; r < len; ++r) bb[lrows[r]] = diag * xx[lrows[r]];
    883:     PetscCall(VecRestoreArrayRead(x, &xx));
    884:     PetscCall(VecRestoreArray(b, &bb));
    885:   }

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

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

    926:   /* only change matrix nonzero state if pattern was allowed to be changed */
    927:   if (!((Mat_SeqAIJ *)mat->A->data)->keepnonzeropattern || !((Mat_SeqAIJ *)mat->A->data)->nonew) {
    928:     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
    929:     PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
    930:   }
    931:   PetscFunctionReturn(PETSC_SUCCESS);
    932: }

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

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

    987:     PetscCall(MatHasCongruentLayouts(A, &cong));
    988:     PetscCheck(cong, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Need matching row/col layout");
    989:     PetscCall(VecScatterBegin(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
    990:     PetscCall(VecScatterEnd(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
    991:     PetscCall(VecGetArrayRead(l->lvec, &xx));
    992:     PetscCall(VecGetArray(b, &bb));
    993:   }
    994:   PetscCall(VecGetArray(lmask, &mask));
    995:   /* remove zeroed rows of off-diagonal matrix */
    996:   PetscCall(MatSeqAIJGetArray(l->B, &aij_a));
    997:   ii = aij->i;
    998:   for (i = 0; i < len; i++) PetscCall(PetscArrayzero(PetscSafePointerPlusOffset(aij_a, ii[lrows[i]]), ii[lrows[i] + 1] - ii[lrows[i]]));
    999:   /* loop over all elements of off process part of matrix zeroing removed columns*/
    1000:   if (aij->compressedrow.use) {
    1001:     m    = aij->compressedrow.nrows;
    1002:     ii   = aij->compressedrow.i;
    1003:     ridx = aij->compressedrow.rindex;
    1004:     for (i = 0; i < m; i++) {
    1005:       n  = ii[i + 1] - ii[i];
    1006:       aj = aij->j + ii[i];
    1007:       aa = aij_a + ii[i];

    1009:       for (j = 0; j < n; j++) {
    1010:         if (PetscAbsScalar(mask[*aj])) {
    1011:           if (b) bb[*ridx] -= *aa * xx[*aj];
    1012:           *aa = 0.0;
    1013:         }
    1014:         aa++;
    1015:         aj++;
    1016:       }
    1017:       ridx++;
    1018:     }
    1019:   } else { /* do not use compressed row format */
    1020:     m = l->B->rmap->n;
    1021:     for (i = 0; i < m; i++) {
    1022:       n  = ii[i + 1] - ii[i];
    1023:       aj = aij->j + ii[i];
    1024:       aa = aij_a + ii[i];
    1025:       for (j = 0; j < n; j++) {
    1026:         if (PetscAbsScalar(mask[*aj])) {
    1027:           if (b) bb[i] -= *aa * xx[*aj];
    1028:           *aa = 0.0;
    1029:         }
    1030:         aa++;
    1031:         aj++;
    1032:       }
    1033:     }
    1034:   }
    1035:   if (x && b) {
    1036:     PetscCall(VecRestoreArray(b, &bb));
    1037:     PetscCall(VecRestoreArrayRead(l->lvec, &xx));
    1038:   }
    1039:   PetscCall(MatSeqAIJRestoreArray(l->B, &aij_a));
    1040:   PetscCall(VecRestoreArray(lmask, &mask));
    1041:   PetscCall(VecDestroy(&lmask));
    1042:   PetscCall(PetscFree(lrows));

    1044:   /* only change matrix nonzero state if pattern was allowed to be changed */
    1045:   if (!((Mat_SeqAIJ *)l->A->data)->nonew) {
    1046:     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
    1047:     PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
    1048:   }
    1049:   PetscFunctionReturn(PETSC_SUCCESS);
    1050: }

    1052: static PetscErrorCode MatMult_MPIAIJ(Mat A, Vec xx, Vec yy)
    1053: {
    1054:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    1055:   PetscInt    nt;
    1056:   VecScatter  Mvctx = a->Mvctx;

    1058:   PetscFunctionBegin;
    1059:   PetscCall(VecGetLocalSize(xx, &nt));
    1060:   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);
    1061:   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1062:   PetscUseTypeMethod(a->A, mult, xx, yy);
    1063:   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1064:   PetscUseTypeMethod(a->B, multadd, a->lvec, yy, yy);
    1065:   PetscFunctionReturn(PETSC_SUCCESS);
    1066: }

    1068: static PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A, Vec bb, Vec xx)
    1069: {
    1070:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1072:   PetscFunctionBegin;
    1073:   PetscCall(MatMultDiagonalBlock(a->A, bb, xx));
    1074:   PetscFunctionReturn(PETSC_SUCCESS);
    1075: }

    1077: static PetscErrorCode MatMultAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
    1078: {
    1079:   Mat_MPIAIJ *a     = (Mat_MPIAIJ *)A->data;
    1080:   VecScatter  Mvctx = a->Mvctx;

    1082:   PetscFunctionBegin;
    1083:   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1084:   PetscCall((*a->A->ops->multadd)(a->A, xx, yy, zz));
    1085:   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1086:   PetscCall((*a->B->ops->multadd)(a->B, a->lvec, zz, zz));
    1087:   PetscFunctionReturn(PETSC_SUCCESS);
    1088: }

    1090: static PetscErrorCode MatMultTranspose_MPIAIJ(Mat A, Vec xx, Vec yy)
    1091: {
    1092:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1094:   PetscFunctionBegin;
    1095:   /* do nondiagonal part */
    1096:   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
    1097:   /* do local part */
    1098:   PetscCall((*a->A->ops->multtranspose)(a->A, xx, yy));
    1099:   /* add partial results together */
    1100:   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
    1101:   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
    1102:   PetscFunctionReturn(PETSC_SUCCESS);
    1103: }

    1105: static PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat, Mat Bmat, PetscReal tol, PetscBool *f)
    1106: {
    1107:   MPI_Comm    comm;
    1108:   Mat_MPIAIJ *Aij = (Mat_MPIAIJ *)Amat->data, *Bij = (Mat_MPIAIJ *)Bmat->data;
    1109:   Mat         Adia = Aij->A, Bdia = Bij->A, Aoff, Boff, *Aoffs, *Boffs;
    1110:   IS          Me, Notme;
    1111:   PetscInt    M, N, first, last, *notme, i;
    1112:   PetscBool   lf;
    1113:   PetscMPIInt size;

    1115:   PetscFunctionBegin;
    1116:   /* Easy test: symmetric diagonal block */
    1117:   PetscCall(MatIsTranspose(Adia, Bdia, tol, &lf));
    1118:   PetscCallMPI(MPIU_Allreduce(&lf, f, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)Amat)));
    1119:   if (!*f) PetscFunctionReturn(PETSC_SUCCESS);
    1120:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
    1121:   PetscCallMPI(MPI_Comm_size(comm, &size));
    1122:   if (size == 1) PetscFunctionReturn(PETSC_SUCCESS);

    1124:   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
    1125:   PetscCall(MatGetSize(Amat, &M, &N));
    1126:   PetscCall(MatGetOwnershipRange(Amat, &first, &last));
    1127:   PetscCall(PetscMalloc1(N - last + first, &notme));
    1128:   for (i = 0; i < first; i++) notme[i] = i;
    1129:   for (i = last; i < M; i++) notme[i - last + first] = i;
    1130:   PetscCall(ISCreateGeneral(MPI_COMM_SELF, N - last + first, notme, PETSC_COPY_VALUES, &Notme));
    1131:   PetscCall(ISCreateStride(MPI_COMM_SELF, last - first, first, 1, &Me));
    1132:   PetscCall(MatCreateSubMatrices(Amat, 1, &Me, &Notme, MAT_INITIAL_MATRIX, &Aoffs));
    1133:   Aoff = Aoffs[0];
    1134:   PetscCall(MatCreateSubMatrices(Bmat, 1, &Notme, &Me, MAT_INITIAL_MATRIX, &Boffs));
    1135:   Boff = Boffs[0];
    1136:   PetscCall(MatIsTranspose(Aoff, Boff, tol, f));
    1137:   PetscCall(MatDestroyMatrices(1, &Aoffs));
    1138:   PetscCall(MatDestroyMatrices(1, &Boffs));
    1139:   PetscCall(ISDestroy(&Me));
    1140:   PetscCall(ISDestroy(&Notme));
    1141:   PetscCall(PetscFree(notme));
    1142:   PetscFunctionReturn(PETSC_SUCCESS);
    1143: }

    1145: static PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
    1146: {
    1147:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1149:   PetscFunctionBegin;
    1150:   /* do nondiagonal part */
    1151:   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
    1152:   /* do local part */
    1153:   PetscCall((*a->A->ops->multtransposeadd)(a->A, xx, yy, zz));
    1154:   /* add partial results together */
    1155:   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
    1156:   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
    1157:   PetscFunctionReturn(PETSC_SUCCESS);
    1158: }

    1160: /*
    1161:   This only works correctly for square matrices where the subblock A->A is the
    1162:    diagonal block
    1163: */
    1164: static PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A, Vec v)
    1165: {
    1166:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1168:   PetscFunctionBegin;
    1169:   PetscCheck(A->rmap->N == A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Supports only square matrix where A->A is diag block");
    1170:   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");
    1171:   PetscCall(MatGetDiagonal(a->A, v));
    1172:   PetscFunctionReturn(PETSC_SUCCESS);
    1173: }

    1175: static PetscErrorCode MatScale_MPIAIJ(Mat A, PetscScalar aa)
    1176: {
    1177:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1179:   PetscFunctionBegin;
    1180:   PetscCall(MatScale(a->A, aa));
    1181:   PetscCall(MatScale(a->B, aa));
    1182:   PetscFunctionReturn(PETSC_SUCCESS);
    1183: }

    1185: static PetscErrorCode MatView_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
    1186: {
    1187:   Mat_MPIAIJ        *aij    = (Mat_MPIAIJ *)mat->data;
    1188:   Mat_SeqAIJ        *A      = (Mat_SeqAIJ *)aij->A->data;
    1189:   Mat_SeqAIJ        *B      = (Mat_SeqAIJ *)aij->B->data;
    1190:   const PetscInt    *garray = aij->garray;
    1191:   const PetscScalar *aa, *ba;
    1192:   PetscInt           header[4], M, N, m, rs, cs, cnt, i, ja, jb;
    1193:   PetscInt64         nz, hnz;
    1194:   PetscInt          *rowlens;
    1195:   PetscInt          *colidxs;
    1196:   PetscScalar       *matvals;
    1197:   PetscMPIInt        rank;

    1199:   PetscFunctionBegin;
    1200:   PetscCall(PetscViewerSetUp(viewer));

    1202:   M  = mat->rmap->N;
    1203:   N  = mat->cmap->N;
    1204:   m  = mat->rmap->n;
    1205:   rs = mat->rmap->rstart;
    1206:   cs = mat->cmap->rstart;
    1207:   nz = A->nz + B->nz;

    1209:   /* write matrix header */
    1210:   header[0] = MAT_FILE_CLASSID;
    1211:   header[1] = M;
    1212:   header[2] = N;
    1213:   PetscCallMPI(MPI_Reduce(&nz, &hnz, 1, MPIU_INT64, MPI_SUM, 0, PetscObjectComm((PetscObject)mat)));
    1214:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
    1215:   if (rank == 0) PetscCall(PetscIntCast(hnz, &header[3]));
    1216:   PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));

    1218:   /* fill in and store row lengths  */
    1219:   PetscCall(PetscMalloc1(m, &rowlens));
    1220:   for (i = 0; i < m; i++) rowlens[i] = A->i[i + 1] - A->i[i] + B->i[i + 1] - B->i[i];
    1221:   PetscCall(PetscViewerBinaryWriteAll(viewer, rowlens, m, rs, M, PETSC_INT));
    1222:   PetscCall(PetscFree(rowlens));

    1224:   /* fill in and store column indices */
    1225:   PetscCall(PetscMalloc1(nz, &colidxs));
    1226:   for (cnt = 0, i = 0; i < m; i++) {
    1227:     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
    1228:       if (garray[B->j[jb]] > cs) break;
    1229:       colidxs[cnt++] = garray[B->j[jb]];
    1230:     }
    1231:     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) colidxs[cnt++] = A->j[ja] + cs;
    1232:     for (; jb < B->i[i + 1]; jb++) colidxs[cnt++] = garray[B->j[jb]];
    1233:   }
    1234:   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
    1235:   PetscCall(PetscViewerBinaryWriteAll(viewer, colidxs, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
    1236:   PetscCall(PetscFree(colidxs));

    1238:   /* fill in and store nonzero values */
    1239:   PetscCall(MatSeqAIJGetArrayRead(aij->A, &aa));
    1240:   PetscCall(MatSeqAIJGetArrayRead(aij->B, &ba));
    1241:   PetscCall(PetscMalloc1(nz, &matvals));
    1242:   for (cnt = 0, i = 0; i < m; i++) {
    1243:     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
    1244:       if (garray[B->j[jb]] > cs) break;
    1245:       matvals[cnt++] = ba[jb];
    1246:     }
    1247:     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) matvals[cnt++] = aa[ja];
    1248:     for (; jb < B->i[i + 1]; jb++) matvals[cnt++] = ba[jb];
    1249:   }
    1250:   PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &aa));
    1251:   PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &ba));
    1252:   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_LIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
    1253:   PetscCall(PetscViewerBinaryWriteAll(viewer, matvals, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
    1254:   PetscCall(PetscFree(matvals));

    1256:   /* write block size option to the viewer's .info file */
    1257:   PetscCall(MatView_Binary_BlockSizes(mat, viewer));
    1258:   PetscFunctionReturn(PETSC_SUCCESS);
    1259: }

    1261: #include <petscdraw.h>
    1262: static PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat, PetscViewer viewer)
    1263: {
    1264:   Mat_MPIAIJ       *aij  = (Mat_MPIAIJ *)mat->data;
    1265:   PetscMPIInt       rank = aij->rank, size = aij->size;
    1266:   PetscBool         isdraw, iascii, isbinary;
    1267:   PetscViewer       sviewer;
    1268:   PetscViewerFormat format;

    1270:   PetscFunctionBegin;
    1271:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
    1272:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    1273:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    1274:   if (iascii) {
    1275:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1276:     if (format == PETSC_VIEWER_LOAD_BALANCE) {
    1277:       PetscInt i, nmax = 0, nmin = PETSC_INT_MAX, navg = 0, *nz, nzlocal = ((Mat_SeqAIJ *)aij->A->data)->nz + ((Mat_SeqAIJ *)aij->B->data)->nz;
    1278:       PetscCall(PetscMalloc1(size, &nz));
    1279:       PetscCallMPI(MPI_Allgather(&nzlocal, 1, MPIU_INT, nz, 1, MPIU_INT, PetscObjectComm((PetscObject)mat)));
    1280:       for (i = 0; i < size; i++) {
    1281:         nmax = PetscMax(nmax, nz[i]);
    1282:         nmin = PetscMin(nmin, nz[i]);
    1283:         navg += nz[i];
    1284:       }
    1285:       PetscCall(PetscFree(nz));
    1286:       navg = navg / size;
    1287:       PetscCall(PetscViewerASCIIPrintf(viewer, "Load Balance - Nonzeros: Min %" PetscInt_FMT "  avg %" PetscInt_FMT "  max %" PetscInt_FMT "\n", nmin, navg, nmax));
    1288:       PetscFunctionReturn(PETSC_SUCCESS);
    1289:     }
    1290:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1291:     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1292:       MatInfo   info;
    1293:       PetscInt *inodes = NULL;

    1295:       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
    1296:       PetscCall(MatGetInfo(mat, MAT_LOCAL, &info));
    1297:       PetscCall(MatInodeGetInodeSizes(aij->A, NULL, &inodes, NULL));
    1298:       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    1299:       if (!inodes) {
    1300:         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,
    1301:                                                      info.memory));
    1302:       } else {
    1303:         PetscCall(
    1304:           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));
    1305:       }
    1306:       PetscCall(MatGetInfo(aij->A, MAT_LOCAL, &info));
    1307:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] on-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
    1308:       PetscCall(MatGetInfo(aij->B, MAT_LOCAL, &info));
    1309:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] off-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
    1310:       PetscCall(PetscViewerFlush(viewer));
    1311:       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    1312:       PetscCall(PetscViewerASCIIPrintf(viewer, "Information on VecScatter used in matrix-vector product: \n"));
    1313:       PetscCall(VecScatterView(aij->Mvctx, viewer));
    1314:       PetscFunctionReturn(PETSC_SUCCESS);
    1315:     } else if (format == PETSC_VIEWER_ASCII_INFO) {
    1316:       PetscInt inodecount, inodelimit, *inodes;
    1317:       PetscCall(MatInodeGetInodeSizes(aij->A, &inodecount, &inodes, &inodelimit));
    1318:       if (inodes) {
    1319:         PetscCall(PetscViewerASCIIPrintf(viewer, "using I-node (on process 0) routines: found %" PetscInt_FMT " nodes, limit used is %" PetscInt_FMT "\n", inodecount, inodelimit));
    1320:       } else {
    1321:         PetscCall(PetscViewerASCIIPrintf(viewer, "not using I-node (on process 0) routines\n"));
    1322:       }
    1323:       PetscFunctionReturn(PETSC_SUCCESS);
    1324:     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
    1325:       PetscFunctionReturn(PETSC_SUCCESS);
    1326:     }
    1327:   } else if (isbinary) {
    1328:     if (size == 1) {
    1329:       PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
    1330:       PetscCall(MatView(aij->A, viewer));
    1331:     } else {
    1332:       PetscCall(MatView_MPIAIJ_Binary(mat, viewer));
    1333:     }
    1334:     PetscFunctionReturn(PETSC_SUCCESS);
    1335:   } else if (iascii && size == 1) {
    1336:     PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
    1337:     PetscCall(MatView(aij->A, viewer));
    1338:     PetscFunctionReturn(PETSC_SUCCESS);
    1339:   } else if (isdraw) {
    1340:     PetscDraw draw;
    1341:     PetscBool isnull;
    1342:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
    1343:     PetscCall(PetscDrawIsNull(draw, &isnull));
    1344:     if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
    1345:   }

    1347:   { /* assemble the entire matrix onto first processor */
    1348:     Mat A = NULL, Av;
    1349:     IS  isrow, iscol;

    1351:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->rmap->N : 0, 0, 1, &isrow));
    1352:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->cmap->N : 0, 0, 1, &iscol));
    1353:     PetscCall(MatCreateSubMatrix(mat, isrow, iscol, MAT_INITIAL_MATRIX, &A));
    1354:     PetscCall(MatMPIAIJGetSeqAIJ(A, &Av, NULL, NULL));
    1355:     /*  The commented code uses MatCreateSubMatrices instead */
    1356:     /*
    1357:     Mat *AA, A = NULL, Av;
    1358:     IS  isrow,iscol;

    1360:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->rmap->N : 0,0,1,&isrow));
    1361:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->cmap->N : 0,0,1,&iscol));
    1362:     PetscCall(MatCreateSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&AA));
    1363:     if (rank == 0) {
    1364:        PetscCall(PetscObjectReference((PetscObject)AA[0]));
    1365:        A    = AA[0];
    1366:        Av   = AA[0];
    1367:     }
    1368:     PetscCall(MatDestroySubMatrices(1,&AA));
    1369: */
    1370:     PetscCall(ISDestroy(&iscol));
    1371:     PetscCall(ISDestroy(&isrow));
    1372:     /*
    1373:        Everyone has to call to draw the matrix since the graphics waits are
    1374:        synchronized across all processors that share the PetscDraw object
    1375:     */
    1376:     PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    1377:     if (rank == 0) {
    1378:       if (((PetscObject)mat)->name) PetscCall(PetscObjectSetName((PetscObject)Av, ((PetscObject)mat)->name));
    1379:       PetscCall(MatView_SeqAIJ(Av, sviewer));
    1380:     }
    1381:     PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    1382:     PetscCall(MatDestroy(&A));
    1383:   }
    1384:   PetscFunctionReturn(PETSC_SUCCESS);
    1385: }

    1387: PetscErrorCode MatView_MPIAIJ(Mat mat, PetscViewer viewer)
    1388: {
    1389:   PetscBool iascii, isdraw, issocket, isbinary;

    1391:   PetscFunctionBegin;
    1392:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    1393:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
    1394:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    1395:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSOCKET, &issocket));
    1396:   if (iascii || isdraw || isbinary || issocket) PetscCall(MatView_MPIAIJ_ASCIIorDraworSocket(mat, viewer));
    1397:   PetscFunctionReturn(PETSC_SUCCESS);
    1398: }

    1400: static PetscErrorCode MatSOR_MPIAIJ(Mat matin, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
    1401: {
    1402:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)matin->data;
    1403:   Vec         bb1 = NULL;
    1404:   PetscBool   hasop;

    1406:   PetscFunctionBegin;
    1407:   if (flag == SOR_APPLY_UPPER) {
    1408:     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1409:     PetscFunctionReturn(PETSC_SUCCESS);
    1410:   }

    1412:   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) PetscCall(VecDuplicate(bb, &bb1));

    1414:   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
    1415:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1416:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1417:       its--;
    1418:     }

    1420:     while (its--) {
    1421:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1422:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1424:       /* update rhs: bb1 = bb - B*x */
    1425:       PetscCall(VecScale(mat->lvec, -1.0));
    1426:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1428:       /* local sweep */
    1429:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_SYMMETRIC_SWEEP, fshift, lits, 1, xx));
    1430:     }
    1431:   } else if (flag & SOR_LOCAL_FORWARD_SWEEP) {
    1432:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1433:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1434:       its--;
    1435:     }
    1436:     while (its--) {
    1437:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1438:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1440:       /* update rhs: bb1 = bb - B*x */
    1441:       PetscCall(VecScale(mat->lvec, -1.0));
    1442:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1444:       /* local sweep */
    1445:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_FORWARD_SWEEP, fshift, lits, 1, xx));
    1446:     }
    1447:   } else if (flag & SOR_LOCAL_BACKWARD_SWEEP) {
    1448:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1449:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1450:       its--;
    1451:     }
    1452:     while (its--) {
    1453:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1454:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1456:       /* update rhs: bb1 = bb - B*x */
    1457:       PetscCall(VecScale(mat->lvec, -1.0));
    1458:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1460:       /* local sweep */
    1461:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_BACKWARD_SWEEP, fshift, lits, 1, xx));
    1462:     }
    1463:   } else if (flag & SOR_EISENSTAT) {
    1464:     Vec xx1;

    1466:     PetscCall(VecDuplicate(bb, &xx1));
    1467:     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP), fshift, lits, 1, xx));

    1469:     PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1470:     PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1471:     if (!mat->diag) {
    1472:       PetscCall(MatCreateVecs(matin, &mat->diag, NULL));
    1473:       PetscCall(MatGetDiagonal(matin, mat->diag));
    1474:     }
    1475:     PetscCall(MatHasOperation(matin, MATOP_MULT_DIAGONAL_BLOCK, &hasop));
    1476:     if (hasop) {
    1477:       PetscCall(MatMultDiagonalBlock(matin, xx, bb1));
    1478:     } else {
    1479:       PetscCall(VecPointwiseMult(bb1, mat->diag, xx));
    1480:     }
    1481:     PetscCall(VecAYPX(bb1, (omega - 2.0) / omega, bb));

    1483:     PetscCall(MatMultAdd(mat->B, mat->lvec, bb1, bb1));

    1485:     /* local sweep */
    1486:     PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP), fshift, lits, 1, xx1));
    1487:     PetscCall(VecAXPY(xx, 1.0, xx1));
    1488:     PetscCall(VecDestroy(&xx1));
    1489:   } else SETERRQ(PetscObjectComm((PetscObject)matin), PETSC_ERR_SUP, "Parallel SOR not supported");

    1491:   PetscCall(VecDestroy(&bb1));

    1493:   matin->factorerrortype = mat->A->factorerrortype;
    1494:   PetscFunctionReturn(PETSC_SUCCESS);
    1495: }

    1497: static PetscErrorCode MatPermute_MPIAIJ(Mat A, IS rowp, IS colp, Mat *B)
    1498: {
    1499:   Mat             aA, aB, Aperm;
    1500:   const PetscInt *rwant, *cwant, *gcols, *ai, *bi, *aj, *bj;
    1501:   PetscScalar    *aa, *ba;
    1502:   PetscInt        i, j, m, n, ng, anz, bnz, *dnnz, *onnz, *tdnnz, *tonnz, *rdest, *cdest, *work, *gcdest;
    1503:   PetscSF         rowsf, sf;
    1504:   IS              parcolp = NULL;
    1505:   PetscBool       done;

    1507:   PetscFunctionBegin;
    1508:   PetscCall(MatGetLocalSize(A, &m, &n));
    1509:   PetscCall(ISGetIndices(rowp, &rwant));
    1510:   PetscCall(ISGetIndices(colp, &cwant));
    1511:   PetscCall(PetscMalloc3(PetscMax(m, n), &work, m, &rdest, n, &cdest));

    1513:   /* Invert row permutation to find out where my rows should go */
    1514:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &rowsf));
    1515:   PetscCall(PetscSFSetGraphLayout(rowsf, A->rmap, A->rmap->n, NULL, PETSC_OWN_POINTER, rwant));
    1516:   PetscCall(PetscSFSetFromOptions(rowsf));
    1517:   for (i = 0; i < m; i++) work[i] = A->rmap->rstart + i;
    1518:   PetscCall(PetscSFReduceBegin(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));
    1519:   PetscCall(PetscSFReduceEnd(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));

    1521:   /* Invert column permutation to find out where my columns should go */
    1522:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1523:   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, A->cmap->n, NULL, PETSC_OWN_POINTER, cwant));
    1524:   PetscCall(PetscSFSetFromOptions(sf));
    1525:   for (i = 0; i < n; i++) work[i] = A->cmap->rstart + i;
    1526:   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, work, cdest, MPI_REPLACE));
    1527:   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, work, cdest, MPI_REPLACE));
    1528:   PetscCall(PetscSFDestroy(&sf));

    1530:   PetscCall(ISRestoreIndices(rowp, &rwant));
    1531:   PetscCall(ISRestoreIndices(colp, &cwant));
    1532:   PetscCall(MatMPIAIJGetSeqAIJ(A, &aA, &aB, &gcols));

    1534:   /* Find out where my gcols should go */
    1535:   PetscCall(MatGetSize(aB, NULL, &ng));
    1536:   PetscCall(PetscMalloc1(ng, &gcdest));
    1537:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1538:   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, ng, NULL, PETSC_OWN_POINTER, gcols));
    1539:   PetscCall(PetscSFSetFromOptions(sf));
    1540:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
    1541:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
    1542:   PetscCall(PetscSFDestroy(&sf));

    1544:   PetscCall(PetscCalloc4(m, &dnnz, m, &onnz, m, &tdnnz, m, &tonnz));
    1545:   PetscCall(MatGetRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
    1546:   PetscCall(MatGetRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
    1547:   for (i = 0; i < m; i++) {
    1548:     PetscInt    row = rdest[i];
    1549:     PetscMPIInt rowner;
    1550:     PetscCall(PetscLayoutFindOwner(A->rmap, row, &rowner));
    1551:     for (j = ai[i]; j < ai[i + 1]; j++) {
    1552:       PetscInt    col = cdest[aj[j]];
    1553:       PetscMPIInt cowner;
    1554:       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner)); /* Could build an index for the columns to eliminate this search */
    1555:       if (rowner == cowner) dnnz[i]++;
    1556:       else onnz[i]++;
    1557:     }
    1558:     for (j = bi[i]; j < bi[i + 1]; j++) {
    1559:       PetscInt    col = gcdest[bj[j]];
    1560:       PetscMPIInt cowner;
    1561:       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner));
    1562:       if (rowner == cowner) dnnz[i]++;
    1563:       else onnz[i]++;
    1564:     }
    1565:   }
    1566:   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
    1567:   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
    1568:   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
    1569:   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
    1570:   PetscCall(PetscSFDestroy(&rowsf));

    1572:   PetscCall(MatCreateAIJ(PetscObjectComm((PetscObject)A), A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N, 0, tdnnz, 0, tonnz, &Aperm));
    1573:   PetscCall(MatSeqAIJGetArray(aA, &aa));
    1574:   PetscCall(MatSeqAIJGetArray(aB, &ba));
    1575:   for (i = 0; i < m; i++) {
    1576:     PetscInt *acols = dnnz, *bcols = onnz; /* Repurpose now-unneeded arrays */
    1577:     PetscInt  j0, rowlen;
    1578:     rowlen = ai[i + 1] - ai[i];
    1579:     for (j0 = j = 0; j < rowlen; j0 = j) { /* rowlen could be larger than number of rows m, so sum in batches */
    1580:       for (; j < PetscMin(rowlen, j0 + m); j++) acols[j - j0] = cdest[aj[ai[i] + j]];
    1581:       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, acols, aa + ai[i] + j0, INSERT_VALUES));
    1582:     }
    1583:     rowlen = bi[i + 1] - bi[i];
    1584:     for (j0 = j = 0; j < rowlen; j0 = j) {
    1585:       for (; j < PetscMin(rowlen, j0 + m); j++) bcols[j - j0] = gcdest[bj[bi[i] + j]];
    1586:       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, bcols, ba + bi[i] + j0, INSERT_VALUES));
    1587:     }
    1588:   }
    1589:   PetscCall(MatAssemblyBegin(Aperm, MAT_FINAL_ASSEMBLY));
    1590:   PetscCall(MatAssemblyEnd(Aperm, MAT_FINAL_ASSEMBLY));
    1591:   PetscCall(MatRestoreRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
    1592:   PetscCall(MatRestoreRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
    1593:   PetscCall(MatSeqAIJRestoreArray(aA, &aa));
    1594:   PetscCall(MatSeqAIJRestoreArray(aB, &ba));
    1595:   PetscCall(PetscFree4(dnnz, onnz, tdnnz, tonnz));
    1596:   PetscCall(PetscFree3(work, rdest, cdest));
    1597:   PetscCall(PetscFree(gcdest));
    1598:   if (parcolp) PetscCall(ISDestroy(&colp));
    1599:   *B = Aperm;
    1600:   PetscFunctionReturn(PETSC_SUCCESS);
    1601: }

    1603: static PetscErrorCode MatGetGhosts_MPIAIJ(Mat mat, PetscInt *nghosts, const PetscInt *ghosts[])
    1604: {
    1605:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    1607:   PetscFunctionBegin;
    1608:   PetscCall(MatGetSize(aij->B, NULL, nghosts));
    1609:   if (ghosts) *ghosts = aij->garray;
    1610:   PetscFunctionReturn(PETSC_SUCCESS);
    1611: }

    1613: static PetscErrorCode MatGetInfo_MPIAIJ(Mat matin, MatInfoType flag, MatInfo *info)
    1614: {
    1615:   Mat_MPIAIJ    *mat = (Mat_MPIAIJ *)matin->data;
    1616:   Mat            A = mat->A, B = mat->B;
    1617:   PetscLogDouble isend[5], irecv[5];

    1619:   PetscFunctionBegin;
    1620:   info->block_size = 1.0;
    1621:   PetscCall(MatGetInfo(A, MAT_LOCAL, info));

    1623:   isend[0] = info->nz_used;
    1624:   isend[1] = info->nz_allocated;
    1625:   isend[2] = info->nz_unneeded;
    1626:   isend[3] = info->memory;
    1627:   isend[4] = info->mallocs;

    1629:   PetscCall(MatGetInfo(B, MAT_LOCAL, info));

    1631:   isend[0] += info->nz_used;
    1632:   isend[1] += info->nz_allocated;
    1633:   isend[2] += info->nz_unneeded;
    1634:   isend[3] += info->memory;
    1635:   isend[4] += info->mallocs;
    1636:   if (flag == MAT_LOCAL) {
    1637:     info->nz_used      = isend[0];
    1638:     info->nz_allocated = isend[1];
    1639:     info->nz_unneeded  = isend[2];
    1640:     info->memory       = isend[3];
    1641:     info->mallocs      = isend[4];
    1642:   } else if (flag == MAT_GLOBAL_MAX) {
    1643:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)matin)));

    1645:     info->nz_used      = irecv[0];
    1646:     info->nz_allocated = irecv[1];
    1647:     info->nz_unneeded  = irecv[2];
    1648:     info->memory       = irecv[3];
    1649:     info->mallocs      = irecv[4];
    1650:   } else if (flag == MAT_GLOBAL_SUM) {
    1651:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)matin)));

    1653:     info->nz_used      = irecv[0];
    1654:     info->nz_allocated = irecv[1];
    1655:     info->nz_unneeded  = irecv[2];
    1656:     info->memory       = irecv[3];
    1657:     info->mallocs      = irecv[4];
    1658:   }
    1659:   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
    1660:   info->fill_ratio_needed = 0;
    1661:   info->factor_mallocs    = 0;
    1662:   PetscFunctionReturn(PETSC_SUCCESS);
    1663: }

    1665: PetscErrorCode MatSetOption_MPIAIJ(Mat A, MatOption op, PetscBool flg)
    1666: {
    1667:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1669:   PetscFunctionBegin;
    1670:   switch (op) {
    1671:   case MAT_NEW_NONZERO_LOCATIONS:
    1672:   case MAT_NEW_NONZERO_ALLOCATION_ERR:
    1673:   case MAT_UNUSED_NONZERO_LOCATION_ERR:
    1674:   case MAT_KEEP_NONZERO_PATTERN:
    1675:   case MAT_NEW_NONZERO_LOCATION_ERR:
    1676:   case MAT_USE_INODES:
    1677:   case MAT_IGNORE_ZERO_ENTRIES:
    1678:   case MAT_FORM_EXPLICIT_TRANSPOSE:
    1679:     MatCheckPreallocated(A, 1);
    1680:     PetscCall(MatSetOption(a->A, op, flg));
    1681:     PetscCall(MatSetOption(a->B, op, flg));
    1682:     break;
    1683:   case MAT_ROW_ORIENTED:
    1684:     MatCheckPreallocated(A, 1);
    1685:     a->roworiented = flg;

    1687:     PetscCall(MatSetOption(a->A, op, flg));
    1688:     PetscCall(MatSetOption(a->B, op, flg));
    1689:     break;
    1690:   case MAT_IGNORE_OFF_PROC_ENTRIES:
    1691:     a->donotstash = flg;
    1692:     break;
    1693:   /* Symmetry flags are handled directly by MatSetOption() and they don't affect preallocation */
    1694:   case MAT_SPD:
    1695:   case MAT_SYMMETRIC:
    1696:   case MAT_STRUCTURALLY_SYMMETRIC:
    1697:   case MAT_HERMITIAN:
    1698:   case MAT_SYMMETRY_ETERNAL:
    1699:   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
    1700:   case MAT_SPD_ETERNAL:
    1701:     /* if the diagonal matrix is square it inherits some of the properties above */
    1702:     if (a->A && A->rmap->n == A->cmap->n) PetscCall(MatSetOption(a->A, op, flg));
    1703:     break;
    1704:   case MAT_SUBMAT_SINGLEIS:
    1705:     A->submat_singleis = flg;
    1706:     break;
    1707:   default:
    1708:     break;
    1709:   }
    1710:   PetscFunctionReturn(PETSC_SUCCESS);
    1711: }

    1713: PetscErrorCode MatGetRow_MPIAIJ(Mat matin, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    1714: {
    1715:   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)matin->data;
    1716:   PetscScalar *vworkA, *vworkB, **pvA, **pvB, *v_p;
    1717:   PetscInt     i, *cworkA, *cworkB, **pcA, **pcB, cstart = matin->cmap->rstart;
    1718:   PetscInt     nztot, nzA, nzB, lrow, rstart = matin->rmap->rstart, rend = matin->rmap->rend;
    1719:   PetscInt    *cmap, *idx_p;

    1721:   PetscFunctionBegin;
    1722:   PetscCheck(!mat->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Already active");
    1723:   mat->getrowactive = PETSC_TRUE;

    1725:   if (!mat->rowvalues && (idx || v)) {
    1726:     /*
    1727:         allocate enough space to hold information from the longest row.
    1728:     */
    1729:     Mat_SeqAIJ *Aa = (Mat_SeqAIJ *)mat->A->data, *Ba = (Mat_SeqAIJ *)mat->B->data;
    1730:     PetscInt    max = 1, tmp;
    1731:     for (i = 0; i < matin->rmap->n; i++) {
    1732:       tmp = Aa->i[i + 1] - Aa->i[i] + Ba->i[i + 1] - Ba->i[i];
    1733:       if (max < tmp) max = tmp;
    1734:     }
    1735:     PetscCall(PetscMalloc2(max, &mat->rowvalues, max, &mat->rowindices));
    1736:   }

    1738:   PetscCheck(row >= rstart && row < rend, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Only local rows");
    1739:   lrow = row - rstart;

    1741:   pvA = &vworkA;
    1742:   pcA = &cworkA;
    1743:   pvB = &vworkB;
    1744:   pcB = &cworkB;
    1745:   if (!v) {
    1746:     pvA = NULL;
    1747:     pvB = NULL;
    1748:   }
    1749:   if (!idx) {
    1750:     pcA = NULL;
    1751:     if (!v) pcB = NULL;
    1752:   }
    1753:   PetscCall((*mat->A->ops->getrow)(mat->A, lrow, &nzA, pcA, pvA));
    1754:   PetscCall((*mat->B->ops->getrow)(mat->B, lrow, &nzB, pcB, pvB));
    1755:   nztot = nzA + nzB;

    1757:   cmap = mat->garray;
    1758:   if (v || idx) {
    1759:     if (nztot) {
    1760:       /* Sort by increasing column numbers, assuming A and B already sorted */
    1761:       PetscInt imark = -1;
    1762:       if (v) {
    1763:         *v = v_p = mat->rowvalues;
    1764:         for (i = 0; i < nzB; i++) {
    1765:           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
    1766:           else break;
    1767:         }
    1768:         imark = i;
    1769:         for (i = 0; i < nzA; i++) v_p[imark + i] = vworkA[i];
    1770:         for (i = imark; i < nzB; i++) v_p[nzA + i] = vworkB[i];
    1771:       }
    1772:       if (idx) {
    1773:         *idx = idx_p = mat->rowindices;
    1774:         if (imark > -1) {
    1775:           for (i = 0; i < imark; i++) idx_p[i] = cmap[cworkB[i]];
    1776:         } else {
    1777:           for (i = 0; i < nzB; i++) {
    1778:             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
    1779:             else break;
    1780:           }
    1781:           imark = i;
    1782:         }
    1783:         for (i = 0; i < nzA; i++) idx_p[imark + i] = cstart + cworkA[i];
    1784:         for (i = imark; i < nzB; i++) idx_p[nzA + i] = cmap[cworkB[i]];
    1785:       }
    1786:     } else {
    1787:       if (idx) *idx = NULL;
    1788:       if (v) *v = NULL;
    1789:     }
    1790:   }
    1791:   *nz = nztot;
    1792:   PetscCall((*mat->A->ops->restorerow)(mat->A, lrow, &nzA, pcA, pvA));
    1793:   PetscCall((*mat->B->ops->restorerow)(mat->B, lrow, &nzB, pcB, pvB));
    1794:   PetscFunctionReturn(PETSC_SUCCESS);
    1795: }

    1797: PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    1798: {
    1799:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    1801:   PetscFunctionBegin;
    1802:   PetscCheck(aij->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "MatGetRow() must be called first");
    1803:   aij->getrowactive = PETSC_FALSE;
    1804:   PetscFunctionReturn(PETSC_SUCCESS);
    1805: }

    1807: static PetscErrorCode MatNorm_MPIAIJ(Mat mat, NormType type, PetscReal *norm)
    1808: {
    1809:   Mat_MPIAIJ      *aij  = (Mat_MPIAIJ *)mat->data;
    1810:   Mat_SeqAIJ      *amat = (Mat_SeqAIJ *)aij->A->data, *bmat = (Mat_SeqAIJ *)aij->B->data;
    1811:   PetscInt         i, j, cstart = mat->cmap->rstart;
    1812:   PetscReal        sum = 0.0;
    1813:   const MatScalar *v, *amata, *bmata;

    1815:   PetscFunctionBegin;
    1816:   if (aij->size == 1) {
    1817:     PetscCall(MatNorm(aij->A, type, norm));
    1818:   } else {
    1819:     PetscCall(MatSeqAIJGetArrayRead(aij->A, &amata));
    1820:     PetscCall(MatSeqAIJGetArrayRead(aij->B, &bmata));
    1821:     if (type == NORM_FROBENIUS) {
    1822:       v = amata;
    1823:       for (i = 0; i < amat->nz; i++) {
    1824:         sum += PetscRealPart(PetscConj(*v) * (*v));
    1825:         v++;
    1826:       }
    1827:       v = bmata;
    1828:       for (i = 0; i < bmat->nz; i++) {
    1829:         sum += PetscRealPart(PetscConj(*v) * (*v));
    1830:         v++;
    1831:       }
    1832:       PetscCallMPI(MPIU_Allreduce(&sum, norm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
    1833:       *norm = PetscSqrtReal(*norm);
    1834:       PetscCall(PetscLogFlops(2.0 * amat->nz + 2.0 * bmat->nz));
    1835:     } else if (type == NORM_1) { /* max column norm */
    1836:       PetscReal *tmp;
    1837:       PetscInt  *jj, *garray = aij->garray;
    1838:       PetscCall(PetscCalloc1(mat->cmap->N + 1, &tmp));
    1839:       *norm = 0.0;
    1840:       v     = amata;
    1841:       jj    = amat->j;
    1842:       for (j = 0; j < amat->nz; j++) {
    1843:         tmp[cstart + *jj++] += PetscAbsScalar(*v);
    1844:         v++;
    1845:       }
    1846:       v  = bmata;
    1847:       jj = bmat->j;
    1848:       for (j = 0; j < bmat->nz; j++) {
    1849:         tmp[garray[*jj++]] += PetscAbsScalar(*v);
    1850:         v++;
    1851:       }
    1852:       PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, tmp, mat->cmap->N, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
    1853:       for (j = 0; j < mat->cmap->N; j++) {
    1854:         if (tmp[j] > *norm) *norm = tmp[j];
    1855:       }
    1856:       PetscCall(PetscFree(tmp));
    1857:       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
    1858:     } else if (type == NORM_INFINITY) { /* max row norm */
    1859:       PetscReal ntemp = 0.0;
    1860:       for (j = 0; j < aij->A->rmap->n; j++) {
    1861:         v   = PetscSafePointerPlusOffset(amata, amat->i[j]);
    1862:         sum = 0.0;
    1863:         for (i = 0; i < amat->i[j + 1] - amat->i[j]; i++) {
    1864:           sum += PetscAbsScalar(*v);
    1865:           v++;
    1866:         }
    1867:         v = PetscSafePointerPlusOffset(bmata, bmat->i[j]);
    1868:         for (i = 0; i < bmat->i[j + 1] - bmat->i[j]; i++) {
    1869:           sum += PetscAbsScalar(*v);
    1870:           v++;
    1871:         }
    1872:         if (sum > ntemp) ntemp = sum;
    1873:       }
    1874:       PetscCallMPI(MPIU_Allreduce(&ntemp, norm, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)mat)));
    1875:       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
    1876:     } else SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "No support for two norm");
    1877:     PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &amata));
    1878:     PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &bmata));
    1879:   }
    1880:   PetscFunctionReturn(PETSC_SUCCESS);
    1881: }

    1883: static PetscErrorCode MatTranspose_MPIAIJ(Mat A, MatReuse reuse, Mat *matout)
    1884: {
    1885:   Mat_MPIAIJ      *a    = (Mat_MPIAIJ *)A->data, *b;
    1886:   Mat_SeqAIJ      *Aloc = (Mat_SeqAIJ *)a->A->data, *Bloc = (Mat_SeqAIJ *)a->B->data, *sub_B_diag;
    1887:   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;
    1888:   const PetscInt  *ai, *aj, *bi, *bj, *B_diag_i;
    1889:   Mat              B, A_diag, *B_diag;
    1890:   const MatScalar *pbv, *bv;

    1892:   PetscFunctionBegin;
    1893:   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *matout));
    1894:   ma = A->rmap->n;
    1895:   na = A->cmap->n;
    1896:   mb = a->B->rmap->n;
    1897:   nb = a->B->cmap->n;
    1898:   ai = Aloc->i;
    1899:   aj = Aloc->j;
    1900:   bi = Bloc->i;
    1901:   bj = Bloc->j;
    1902:   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
    1903:     PetscInt            *d_nnz, *g_nnz, *o_nnz;
    1904:     PetscSFNode         *oloc;
    1905:     PETSC_UNUSED PetscSF sf;

    1907:     PetscCall(PetscMalloc4(na, &d_nnz, na, &o_nnz, nb, &g_nnz, nb, &oloc));
    1908:     /* compute d_nnz for preallocation */
    1909:     PetscCall(PetscArrayzero(d_nnz, na));
    1910:     for (i = 0; i < ai[ma]; i++) d_nnz[aj[i]]++;
    1911:     /* compute local off-diagonal contributions */
    1912:     PetscCall(PetscArrayzero(g_nnz, nb));
    1913:     for (i = 0; i < bi[ma]; i++) g_nnz[bj[i]]++;
    1914:     /* map those to global */
    1915:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1916:     PetscCall(PetscSFSetGraphLayout(sf, A->cmap, nb, NULL, PETSC_USE_POINTER, a->garray));
    1917:     PetscCall(PetscSFSetFromOptions(sf));
    1918:     PetscCall(PetscArrayzero(o_nnz, na));
    1919:     PetscCall(PetscSFReduceBegin(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
    1920:     PetscCall(PetscSFReduceEnd(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
    1921:     PetscCall(PetscSFDestroy(&sf));

    1923:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    1924:     PetscCall(MatSetSizes(B, A->cmap->n, A->rmap->n, N, M));
    1925:     PetscCall(MatSetBlockSizes(B, A->cmap->bs, A->rmap->bs));
    1926:     PetscCall(MatSetType(B, ((PetscObject)A)->type_name));
    1927:     PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
    1928:     PetscCall(PetscFree4(d_nnz, o_nnz, g_nnz, oloc));
    1929:   } else {
    1930:     B = *matout;
    1931:     PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
    1932:   }

    1934:   b           = (Mat_MPIAIJ *)B->data;
    1935:   A_diag      = a->A;
    1936:   B_diag      = &b->A;
    1937:   sub_B_diag  = (Mat_SeqAIJ *)(*B_diag)->data;
    1938:   A_diag_ncol = A_diag->cmap->N;
    1939:   B_diag_ilen = sub_B_diag->ilen;
    1940:   B_diag_i    = sub_B_diag->i;

    1942:   /* Set ilen for diagonal of B */
    1943:   for (i = 0; i < A_diag_ncol; i++) B_diag_ilen[i] = B_diag_i[i + 1] - B_diag_i[i];

    1945:   /* Transpose the diagonal part of the matrix. In contrast to the off-diagonal part, this can be done
    1946:   very quickly (=without using MatSetValues), because all writes are local. */
    1947:   PetscCall(MatTransposeSetPrecursor(A_diag, *B_diag));
    1948:   PetscCall(MatTranspose(A_diag, MAT_REUSE_MATRIX, B_diag));

    1950:   /* copy over the B part */
    1951:   PetscCall(PetscMalloc1(bi[mb], &cols));
    1952:   PetscCall(MatSeqAIJGetArrayRead(a->B, &bv));
    1953:   pbv = bv;
    1954:   row = A->rmap->rstart;
    1955:   for (i = 0; i < bi[mb]; i++) cols[i] = a->garray[bj[i]];
    1956:   cols_tmp = cols;
    1957:   for (i = 0; i < mb; i++) {
    1958:     ncol = bi[i + 1] - bi[i];
    1959:     PetscCall(MatSetValues(B, ncol, cols_tmp, 1, &row, pbv, INSERT_VALUES));
    1960:     row++;
    1961:     if (pbv) pbv += ncol;
    1962:     if (cols_tmp) cols_tmp += ncol;
    1963:   }
    1964:   PetscCall(PetscFree(cols));
    1965:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &bv));

    1967:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    1968:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    1969:   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
    1970:     *matout = B;
    1971:   } else {
    1972:     PetscCall(MatHeaderMerge(A, &B));
    1973:   }
    1974:   PetscFunctionReturn(PETSC_SUCCESS);
    1975: }

    1977: static PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat, Vec ll, Vec rr)
    1978: {
    1979:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    1980:   Mat         a = aij->A, b = aij->B;
    1981:   PetscInt    s1, s2, s3;

    1983:   PetscFunctionBegin;
    1984:   PetscCall(MatGetLocalSize(mat, &s2, &s3));
    1985:   if (rr) {
    1986:     PetscCall(VecGetLocalSize(rr, &s1));
    1987:     PetscCheck(s1 == s3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "right vector non-conforming local size");
    1988:     /* Overlap communication with computation. */
    1989:     PetscCall(VecScatterBegin(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1990:   }
    1991:   if (ll) {
    1992:     PetscCall(VecGetLocalSize(ll, &s1));
    1993:     PetscCheck(s1 == s2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "left vector non-conforming local size");
    1994:     PetscUseTypeMethod(b, diagonalscale, ll, NULL);
    1995:   }
    1996:   /* scale  the diagonal block */
    1997:   PetscUseTypeMethod(a, diagonalscale, ll, rr);

    1999:   if (rr) {
    2000:     /* Do a scatter end and then right scale the off-diagonal block */
    2001:     PetscCall(VecScatterEnd(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    2002:     PetscUseTypeMethod(b, diagonalscale, NULL, aij->lvec);
    2003:   }
    2004:   PetscFunctionReturn(PETSC_SUCCESS);
    2005: }

    2007: static PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
    2008: {
    2009:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2011:   PetscFunctionBegin;
    2012:   PetscCall(MatSetUnfactored(a->A));
    2013:   PetscFunctionReturn(PETSC_SUCCESS);
    2014: }

    2016: static PetscErrorCode MatEqual_MPIAIJ(Mat A, Mat B, PetscBool *flag)
    2017: {
    2018:   Mat_MPIAIJ *matB = (Mat_MPIAIJ *)B->data, *matA = (Mat_MPIAIJ *)A->data;
    2019:   Mat         a, b, c, d;
    2020:   PetscBool   flg;

    2022:   PetscFunctionBegin;
    2023:   a = matA->A;
    2024:   b = matA->B;
    2025:   c = matB->A;
    2026:   d = matB->B;

    2028:   PetscCall(MatEqual(a, c, &flg));
    2029:   if (flg) PetscCall(MatEqual(b, d, &flg));
    2030:   PetscCallMPI(MPIU_Allreduce(&flg, flag, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
    2031:   PetscFunctionReturn(PETSC_SUCCESS);
    2032: }

    2034: static PetscErrorCode MatCopy_MPIAIJ(Mat A, Mat B, MatStructure str)
    2035: {
    2036:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    2037:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;

    2039:   PetscFunctionBegin;
    2040:   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
    2041:   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
    2042:     /* because of the column compression in the off-processor part of the matrix a->B,
    2043:        the number of columns in a->B and b->B may be different, hence we cannot call
    2044:        the MatCopy() directly on the two parts. If need be, we can provide a more
    2045:        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
    2046:        then copying the submatrices */
    2047:     PetscCall(MatCopy_Basic(A, B, str));
    2048:   } else {
    2049:     PetscCall(MatCopy(a->A, b->A, str));
    2050:     PetscCall(MatCopy(a->B, b->B, str));
    2051:   }
    2052:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    2053:   PetscFunctionReturn(PETSC_SUCCESS);
    2054: }

    2056: /*
    2057:    Computes the number of nonzeros per row needed for preallocation when X and Y
    2058:    have different nonzero structure.
    2059: */
    2060: 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)
    2061: {
    2062:   PetscInt i, j, k, nzx, nzy;

    2064:   PetscFunctionBegin;
    2065:   /* Set the number of nonzeros in the new matrix */
    2066:   for (i = 0; i < m; i++) {
    2067:     const PetscInt *xjj = PetscSafePointerPlusOffset(xj, xi[i]), *yjj = PetscSafePointerPlusOffset(yj, yi[i]);
    2068:     nzx    = xi[i + 1] - xi[i];
    2069:     nzy    = yi[i + 1] - yi[i];
    2070:     nnz[i] = 0;
    2071:     for (j = 0, k = 0; j < nzx; j++) {                                /* Point in X */
    2072:       for (; k < nzy && yltog[yjj[k]] < xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
    2073:       if (k < nzy && yltog[yjj[k]] == xltog[xjj[j]]) k++;             /* Skip duplicate */
    2074:       nnz[i]++;
    2075:     }
    2076:     for (; k < nzy; k++) nnz[i]++;
    2077:   }
    2078:   PetscFunctionReturn(PETSC_SUCCESS);
    2079: }

    2081: /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
    2082: static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y, const PetscInt *yltog, Mat X, const PetscInt *xltog, PetscInt *nnz)
    2083: {
    2084:   PetscInt    m = Y->rmap->N;
    2085:   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data;
    2086:   Mat_SeqAIJ *y = (Mat_SeqAIJ *)Y->data;

    2088:   PetscFunctionBegin;
    2089:   PetscCall(MatAXPYGetPreallocation_MPIX_private(m, x->i, x->j, xltog, y->i, y->j, yltog, nnz));
    2090:   PetscFunctionReturn(PETSC_SUCCESS);
    2091: }

    2093: static PetscErrorCode MatAXPY_MPIAIJ(Mat Y, PetscScalar a, Mat X, MatStructure str)
    2094: {
    2095:   Mat_MPIAIJ *xx = (Mat_MPIAIJ *)X->data, *yy = (Mat_MPIAIJ *)Y->data;

    2097:   PetscFunctionBegin;
    2098:   if (str == SAME_NONZERO_PATTERN) {
    2099:     PetscCall(MatAXPY(yy->A, a, xx->A, str));
    2100:     PetscCall(MatAXPY(yy->B, a, xx->B, str));
    2101:   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
    2102:     PetscCall(MatAXPY_Basic(Y, a, X, str));
    2103:   } else {
    2104:     Mat       B;
    2105:     PetscInt *nnz_d, *nnz_o;

    2107:     PetscCall(PetscMalloc1(yy->A->rmap->N, &nnz_d));
    2108:     PetscCall(PetscMalloc1(yy->B->rmap->N, &nnz_o));
    2109:     PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
    2110:     PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
    2111:     PetscCall(MatSetLayouts(B, Y->rmap, Y->cmap));
    2112:     PetscCall(MatSetType(B, ((PetscObject)Y)->type_name));
    2113:     PetscCall(MatAXPYGetPreallocation_SeqAIJ(yy->A, xx->A, nnz_d));
    2114:     PetscCall(MatAXPYGetPreallocation_MPIAIJ(yy->B, yy->garray, xx->B, xx->garray, nnz_o));
    2115:     PetscCall(MatMPIAIJSetPreallocation(B, 0, nnz_d, 0, nnz_o));
    2116:     PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
    2117:     PetscCall(MatHeaderMerge(Y, &B));
    2118:     PetscCall(PetscFree(nnz_d));
    2119:     PetscCall(PetscFree(nnz_o));
    2120:   }
    2121:   PetscFunctionReturn(PETSC_SUCCESS);
    2122: }

    2124: PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat);

    2126: static PetscErrorCode MatConjugate_MPIAIJ(Mat mat)
    2127: {
    2128:   PetscFunctionBegin;
    2129:   if (PetscDefined(USE_COMPLEX)) {
    2130:     Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2132:     PetscCall(MatConjugate_SeqAIJ(aij->A));
    2133:     PetscCall(MatConjugate_SeqAIJ(aij->B));
    2134:   }
    2135:   PetscFunctionReturn(PETSC_SUCCESS);
    2136: }

    2138: static PetscErrorCode MatRealPart_MPIAIJ(Mat A)
    2139: {
    2140:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2142:   PetscFunctionBegin;
    2143:   PetscCall(MatRealPart(a->A));
    2144:   PetscCall(MatRealPart(a->B));
    2145:   PetscFunctionReturn(PETSC_SUCCESS);
    2146: }

    2148: static PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
    2149: {
    2150:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2152:   PetscFunctionBegin;
    2153:   PetscCall(MatImaginaryPart(a->A));
    2154:   PetscCall(MatImaginaryPart(a->B));
    2155:   PetscFunctionReturn(PETSC_SUCCESS);
    2156: }

    2158: static PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2159: {
    2160:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
    2161:   PetscInt           i, *idxb = NULL, m = A->rmap->n;
    2162:   PetscScalar       *vv;
    2163:   Vec                vB, vA;
    2164:   const PetscScalar *va, *vb;

    2166:   PetscFunctionBegin;
    2167:   PetscCall(MatCreateVecs(a->A, NULL, &vA));
    2168:   PetscCall(MatGetRowMaxAbs(a->A, vA, idx));

    2170:   PetscCall(VecGetArrayRead(vA, &va));
    2171:   if (idx) {
    2172:     for (i = 0; i < m; i++) {
    2173:       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
    2174:     }
    2175:   }

    2177:   PetscCall(MatCreateVecs(a->B, NULL, &vB));
    2178:   PetscCall(PetscMalloc1(m, &idxb));
    2179:   PetscCall(MatGetRowMaxAbs(a->B, vB, idxb));

    2181:   PetscCall(VecGetArrayWrite(v, &vv));
    2182:   PetscCall(VecGetArrayRead(vB, &vb));
    2183:   for (i = 0; i < m; i++) {
    2184:     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
    2185:       vv[i] = vb[i];
    2186:       if (idx) idx[i] = a->garray[idxb[i]];
    2187:     } else {
    2188:       vv[i] = va[i];
    2189:       if (idx && PetscAbsScalar(va[i]) == PetscAbsScalar(vb[i]) && idxb[i] != -1 && idx[i] > a->garray[idxb[i]]) idx[i] = a->garray[idxb[i]];
    2190:     }
    2191:   }
    2192:   PetscCall(VecRestoreArrayWrite(v, &vv));
    2193:   PetscCall(VecRestoreArrayRead(vA, &va));
    2194:   PetscCall(VecRestoreArrayRead(vB, &vb));
    2195:   PetscCall(PetscFree(idxb));
    2196:   PetscCall(VecDestroy(&vA));
    2197:   PetscCall(VecDestroy(&vB));
    2198:   PetscFunctionReturn(PETSC_SUCCESS);
    2199: }

    2201: static PetscErrorCode MatGetRowSumAbs_MPIAIJ(Mat A, Vec v)
    2202: {
    2203:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    2204:   Vec         vB, vA;

    2206:   PetscFunctionBegin;
    2207:   PetscCall(MatCreateVecs(a->A, NULL, &vA));
    2208:   PetscCall(MatGetRowSumAbs(a->A, vA));
    2209:   PetscCall(MatCreateVecs(a->B, NULL, &vB));
    2210:   PetscCall(MatGetRowSumAbs(a->B, vB));
    2211:   PetscCall(VecAXPY(vA, 1.0, vB));
    2212:   PetscCall(VecDestroy(&vB));
    2213:   PetscCall(VecCopy(vA, v));
    2214:   PetscCall(VecDestroy(&vA));
    2215:   PetscFunctionReturn(PETSC_SUCCESS);
    2216: }

    2218: static PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2219: {
    2220:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2221:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2222:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2223:   PetscInt          *cmap = mat->garray;
    2224:   PetscInt          *diagIdx, *offdiagIdx;
    2225:   Vec                diagV, offdiagV;
    2226:   PetscScalar       *a, *diagA, *offdiagA;
    2227:   const PetscScalar *ba, *bav;
    2228:   PetscInt           r, j, col, ncols, *bi, *bj;
    2229:   Mat                B = mat->B;
    2230:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2232:   PetscFunctionBegin;
    2233:   /* When a process holds entire A and other processes have no entry */
    2234:   if (A->cmap->N == n) {
    2235:     PetscCall(VecGetArrayWrite(v, &diagA));
    2236:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2237:     PetscCall(MatGetRowMinAbs(mat->A, diagV, idx));
    2238:     PetscCall(VecDestroy(&diagV));
    2239:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2240:     PetscFunctionReturn(PETSC_SUCCESS);
    2241:   } else if (n == 0) {
    2242:     if (m) {
    2243:       PetscCall(VecGetArrayWrite(v, &a));
    2244:       for (r = 0; r < m; r++) {
    2245:         a[r] = 0.0;
    2246:         if (idx) idx[r] = -1;
    2247:       }
    2248:       PetscCall(VecRestoreArrayWrite(v, &a));
    2249:     }
    2250:     PetscFunctionReturn(PETSC_SUCCESS);
    2251:   }

    2253:   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
    2254:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2255:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2256:   PetscCall(MatGetRowMinAbs(mat->A, diagV, diagIdx));

    2258:   /* Get offdiagIdx[] for implicit 0.0 */
    2259:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2260:   ba = bav;
    2261:   bi = b->i;
    2262:   bj = b->j;
    2263:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2264:   for (r = 0; r < m; r++) {
    2265:     ncols = bi[r + 1] - bi[r];
    2266:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2267:       offdiagA[r]   = *ba;
    2268:       offdiagIdx[r] = cmap[0];
    2269:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2270:       offdiagA[r] = 0.0;

    2272:       /* Find first hole in the cmap */
    2273:       for (j = 0; j < ncols; j++) {
    2274:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2275:         if (col > j && j < cstart) {
    2276:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2277:           break;
    2278:         } else if (col > j + n && j >= cstart) {
    2279:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2280:           break;
    2281:         }
    2282:       }
    2283:       if (j == ncols && ncols < A->cmap->N - n) {
    2284:         /* a hole is outside compressed Bcols */
    2285:         if (ncols == 0) {
    2286:           if (cstart) {
    2287:             offdiagIdx[r] = 0;
    2288:           } else offdiagIdx[r] = cend;
    2289:         } else { /* ncols > 0 */
    2290:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2291:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2292:         }
    2293:       }
    2294:     }

    2296:     for (j = 0; j < ncols; j++) {
    2297:       if (PetscAbsScalar(offdiagA[r]) > PetscAbsScalar(*ba)) {
    2298:         offdiagA[r]   = *ba;
    2299:         offdiagIdx[r] = cmap[*bj];
    2300:       }
    2301:       ba++;
    2302:       bj++;
    2303:     }
    2304:   }

    2306:   PetscCall(VecGetArrayWrite(v, &a));
    2307:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2308:   for (r = 0; r < m; ++r) {
    2309:     if (PetscAbsScalar(diagA[r]) < PetscAbsScalar(offdiagA[r])) {
    2310:       a[r] = diagA[r];
    2311:       if (idx) idx[r] = cstart + diagIdx[r];
    2312:     } else if (PetscAbsScalar(diagA[r]) == PetscAbsScalar(offdiagA[r])) {
    2313:       a[r] = diagA[r];
    2314:       if (idx) {
    2315:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2316:           idx[r] = cstart + diagIdx[r];
    2317:         } else idx[r] = offdiagIdx[r];
    2318:       }
    2319:     } else {
    2320:       a[r] = offdiagA[r];
    2321:       if (idx) idx[r] = offdiagIdx[r];
    2322:     }
    2323:   }
    2324:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2325:   PetscCall(VecRestoreArrayWrite(v, &a));
    2326:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2327:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2328:   PetscCall(VecDestroy(&diagV));
    2329:   PetscCall(VecDestroy(&offdiagV));
    2330:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2331:   PetscFunctionReturn(PETSC_SUCCESS);
    2332: }

    2334: static PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2335: {
    2336:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2337:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2338:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2339:   PetscInt          *cmap = mat->garray;
    2340:   PetscInt          *diagIdx, *offdiagIdx;
    2341:   Vec                diagV, offdiagV;
    2342:   PetscScalar       *a, *diagA, *offdiagA;
    2343:   const PetscScalar *ba, *bav;
    2344:   PetscInt           r, j, col, ncols, *bi, *bj;
    2345:   Mat                B = mat->B;
    2346:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2348:   PetscFunctionBegin;
    2349:   /* When a process holds entire A and other processes have no entry */
    2350:   if (A->cmap->N == n) {
    2351:     PetscCall(VecGetArrayWrite(v, &diagA));
    2352:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2353:     PetscCall(MatGetRowMin(mat->A, diagV, idx));
    2354:     PetscCall(VecDestroy(&diagV));
    2355:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2356:     PetscFunctionReturn(PETSC_SUCCESS);
    2357:   } else if (n == 0) {
    2358:     if (m) {
    2359:       PetscCall(VecGetArrayWrite(v, &a));
    2360:       for (r = 0; r < m; r++) {
    2361:         a[r] = PETSC_MAX_REAL;
    2362:         if (idx) idx[r] = -1;
    2363:       }
    2364:       PetscCall(VecRestoreArrayWrite(v, &a));
    2365:     }
    2366:     PetscFunctionReturn(PETSC_SUCCESS);
    2367:   }

    2369:   PetscCall(PetscCalloc2(m, &diagIdx, m, &offdiagIdx));
    2370:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2371:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2372:   PetscCall(MatGetRowMin(mat->A, diagV, diagIdx));

    2374:   /* Get offdiagIdx[] for implicit 0.0 */
    2375:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2376:   ba = bav;
    2377:   bi = b->i;
    2378:   bj = b->j;
    2379:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2380:   for (r = 0; r < m; r++) {
    2381:     ncols = bi[r + 1] - bi[r];
    2382:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2383:       offdiagA[r]   = *ba;
    2384:       offdiagIdx[r] = cmap[0];
    2385:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2386:       offdiagA[r] = 0.0;

    2388:       /* Find first hole in the cmap */
    2389:       for (j = 0; j < ncols; j++) {
    2390:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2391:         if (col > j && j < cstart) {
    2392:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2393:           break;
    2394:         } else if (col > j + n && j >= cstart) {
    2395:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2396:           break;
    2397:         }
    2398:       }
    2399:       if (j == ncols && ncols < A->cmap->N - n) {
    2400:         /* a hole is outside compressed Bcols */
    2401:         if (ncols == 0) {
    2402:           if (cstart) {
    2403:             offdiagIdx[r] = 0;
    2404:           } else offdiagIdx[r] = cend;
    2405:         } else { /* ncols > 0 */
    2406:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2407:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2408:         }
    2409:       }
    2410:     }

    2412:     for (j = 0; j < ncols; j++) {
    2413:       if (PetscRealPart(offdiagA[r]) > PetscRealPart(*ba)) {
    2414:         offdiagA[r]   = *ba;
    2415:         offdiagIdx[r] = cmap[*bj];
    2416:       }
    2417:       ba++;
    2418:       bj++;
    2419:     }
    2420:   }

    2422:   PetscCall(VecGetArrayWrite(v, &a));
    2423:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2424:   for (r = 0; r < m; ++r) {
    2425:     if (PetscRealPart(diagA[r]) < PetscRealPart(offdiagA[r])) {
    2426:       a[r] = diagA[r];
    2427:       if (idx) idx[r] = cstart + diagIdx[r];
    2428:     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
    2429:       a[r] = diagA[r];
    2430:       if (idx) {
    2431:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2432:           idx[r] = cstart + diagIdx[r];
    2433:         } else idx[r] = offdiagIdx[r];
    2434:       }
    2435:     } else {
    2436:       a[r] = offdiagA[r];
    2437:       if (idx) idx[r] = offdiagIdx[r];
    2438:     }
    2439:   }
    2440:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2441:   PetscCall(VecRestoreArrayWrite(v, &a));
    2442:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2443:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2444:   PetscCall(VecDestroy(&diagV));
    2445:   PetscCall(VecDestroy(&offdiagV));
    2446:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2447:   PetscFunctionReturn(PETSC_SUCCESS);
    2448: }

    2450: static PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2451: {
    2452:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2453:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2454:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2455:   PetscInt          *cmap = mat->garray;
    2456:   PetscInt          *diagIdx, *offdiagIdx;
    2457:   Vec                diagV, offdiagV;
    2458:   PetscScalar       *a, *diagA, *offdiagA;
    2459:   const PetscScalar *ba, *bav;
    2460:   PetscInt           r, j, col, ncols, *bi, *bj;
    2461:   Mat                B = mat->B;
    2462:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2464:   PetscFunctionBegin;
    2465:   /* When a process holds entire A and other processes have no entry */
    2466:   if (A->cmap->N == n) {
    2467:     PetscCall(VecGetArrayWrite(v, &diagA));
    2468:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2469:     PetscCall(MatGetRowMax(mat->A, diagV, idx));
    2470:     PetscCall(VecDestroy(&diagV));
    2471:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2472:     PetscFunctionReturn(PETSC_SUCCESS);
    2473:   } else if (n == 0) {
    2474:     if (m) {
    2475:       PetscCall(VecGetArrayWrite(v, &a));
    2476:       for (r = 0; r < m; r++) {
    2477:         a[r] = PETSC_MIN_REAL;
    2478:         if (idx) idx[r] = -1;
    2479:       }
    2480:       PetscCall(VecRestoreArrayWrite(v, &a));
    2481:     }
    2482:     PetscFunctionReturn(PETSC_SUCCESS);
    2483:   }

    2485:   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
    2486:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2487:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2488:   PetscCall(MatGetRowMax(mat->A, diagV, diagIdx));

    2490:   /* Get offdiagIdx[] for implicit 0.0 */
    2491:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2492:   ba = bav;
    2493:   bi = b->i;
    2494:   bj = b->j;
    2495:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2496:   for (r = 0; r < m; r++) {
    2497:     ncols = bi[r + 1] - bi[r];
    2498:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2499:       offdiagA[r]   = *ba;
    2500:       offdiagIdx[r] = cmap[0];
    2501:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2502:       offdiagA[r] = 0.0;

    2504:       /* Find first hole in the cmap */
    2505:       for (j = 0; j < ncols; j++) {
    2506:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2507:         if (col > j && j < cstart) {
    2508:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2509:           break;
    2510:         } else if (col > j + n && j >= cstart) {
    2511:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2512:           break;
    2513:         }
    2514:       }
    2515:       if (j == ncols && ncols < A->cmap->N - n) {
    2516:         /* a hole is outside compressed Bcols */
    2517:         if (ncols == 0) {
    2518:           if (cstart) {
    2519:             offdiagIdx[r] = 0;
    2520:           } else offdiagIdx[r] = cend;
    2521:         } else { /* ncols > 0 */
    2522:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2523:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2524:         }
    2525:       }
    2526:     }

    2528:     for (j = 0; j < ncols; j++) {
    2529:       if (PetscRealPart(offdiagA[r]) < PetscRealPart(*ba)) {
    2530:         offdiagA[r]   = *ba;
    2531:         offdiagIdx[r] = cmap[*bj];
    2532:       }
    2533:       ba++;
    2534:       bj++;
    2535:     }
    2536:   }

    2538:   PetscCall(VecGetArrayWrite(v, &a));
    2539:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2540:   for (r = 0; r < m; ++r) {
    2541:     if (PetscRealPart(diagA[r]) > PetscRealPart(offdiagA[r])) {
    2542:       a[r] = diagA[r];
    2543:       if (idx) idx[r] = cstart + diagIdx[r];
    2544:     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
    2545:       a[r] = diagA[r];
    2546:       if (idx) {
    2547:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2548:           idx[r] = cstart + diagIdx[r];
    2549:         } else idx[r] = offdiagIdx[r];
    2550:       }
    2551:     } else {
    2552:       a[r] = offdiagA[r];
    2553:       if (idx) idx[r] = offdiagIdx[r];
    2554:     }
    2555:   }
    2556:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2557:   PetscCall(VecRestoreArrayWrite(v, &a));
    2558:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2559:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2560:   PetscCall(VecDestroy(&diagV));
    2561:   PetscCall(VecDestroy(&offdiagV));
    2562:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2563:   PetscFunctionReturn(PETSC_SUCCESS);
    2564: }

    2566: PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat, Mat *newmat)
    2567: {
    2568:   Mat *dummy;

    2570:   PetscFunctionBegin;
    2571:   PetscCall(MatCreateSubMatrix_MPIAIJ_All(mat, MAT_DO_NOT_GET_VALUES, MAT_INITIAL_MATRIX, &dummy));
    2572:   *newmat = *dummy;
    2573:   PetscCall(PetscFree(dummy));
    2574:   PetscFunctionReturn(PETSC_SUCCESS);
    2575: }

    2577: static PetscErrorCode MatInvertBlockDiagonal_MPIAIJ(Mat A, const PetscScalar **values)
    2578: {
    2579:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2581:   PetscFunctionBegin;
    2582:   PetscCall(MatInvertBlockDiagonal(a->A, values));
    2583:   A->factorerrortype = a->A->factorerrortype;
    2584:   PetscFunctionReturn(PETSC_SUCCESS);
    2585: }

    2587: static PetscErrorCode MatSetRandom_MPIAIJ(Mat x, PetscRandom rctx)
    2588: {
    2589:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)x->data;

    2591:   PetscFunctionBegin;
    2592:   PetscCheck(x->assembled || x->preallocated, PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_WRONGSTATE, "MatSetRandom on an unassembled and unpreallocated MATMPIAIJ is not allowed");
    2593:   PetscCall(MatSetRandom(aij->A, rctx));
    2594:   if (x->assembled) {
    2595:     PetscCall(MatSetRandom(aij->B, rctx));
    2596:   } else {
    2597:     PetscCall(MatSetRandomSkipColumnRange_SeqAIJ_Private(aij->B, x->cmap->rstart, x->cmap->rend, rctx));
    2598:   }
    2599:   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
    2600:   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
    2601:   PetscFunctionReturn(PETSC_SUCCESS);
    2602: }

    2604: static PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A, PetscBool sc)
    2605: {
    2606:   PetscFunctionBegin;
    2607:   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
    2608:   else A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ;
    2609:   PetscFunctionReturn(PETSC_SUCCESS);
    2610: }

    2612: /*@
    2613:   MatMPIAIJGetNumberNonzeros - gets the number of nonzeros in the matrix on this MPI rank

    2615:   Not Collective

    2617:   Input Parameter:
    2618: . A - the matrix

    2620:   Output Parameter:
    2621: . nz - the number of nonzeros

    2623:   Level: advanced

    2625: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
    2626: @*/
    2627: PetscErrorCode MatMPIAIJGetNumberNonzeros(Mat A, PetscCount *nz)
    2628: {
    2629:   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)A->data;
    2630:   Mat_SeqAIJ *aaij = (Mat_SeqAIJ *)maij->A->data, *baij = (Mat_SeqAIJ *)maij->B->data;
    2631:   PetscBool   isaij;

    2633:   PetscFunctionBegin;
    2634:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIAIJ, &isaij));
    2635:   PetscCheck(isaij, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for type %s", ((PetscObject)A)->type_name);
    2636:   *nz = aaij->i[A->rmap->n] + baij->i[A->rmap->n];
    2637:   PetscFunctionReturn(PETSC_SUCCESS);
    2638: }

    2640: /*@
    2641:   MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap

    2643:   Collective

    2645:   Input Parameters:
    2646: + A  - the matrix
    2647: - sc - `PETSC_TRUE` indicates use the scalable algorithm (default is not to use the scalable algorithm)

    2649:   Level: advanced

    2651: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
    2652: @*/
    2653: PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A, PetscBool sc)
    2654: {
    2655:   PetscFunctionBegin;
    2656:   PetscTryMethod(A, "MatMPIAIJSetUseScalableIncreaseOverlap_C", (Mat, PetscBool), (A, sc));
    2657:   PetscFunctionReturn(PETSC_SUCCESS);
    2658: }

    2660: PetscErrorCode MatSetFromOptions_MPIAIJ(Mat A, PetscOptionItems PetscOptionsObject)
    2661: {
    2662:   PetscBool sc = PETSC_FALSE, flg;

    2664:   PetscFunctionBegin;
    2665:   PetscOptionsHeadBegin(PetscOptionsObject, "MPIAIJ options");
    2666:   if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
    2667:   PetscCall(PetscOptionsBool("-mat_increase_overlap_scalable", "Use a scalable algorithm to compute the overlap", "MatIncreaseOverlap", sc, &sc, &flg));
    2668:   if (flg) PetscCall(MatMPIAIJSetUseScalableIncreaseOverlap(A, sc));
    2669:   PetscOptionsHeadEnd();
    2670:   PetscFunctionReturn(PETSC_SUCCESS);
    2671: }

    2673: static PetscErrorCode MatShift_MPIAIJ(Mat Y, PetscScalar a)
    2674: {
    2675:   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)Y->data;
    2676:   Mat_SeqAIJ *aij  = (Mat_SeqAIJ *)maij->A->data;

    2678:   PetscFunctionBegin;
    2679:   if (!Y->preallocated) {
    2680:     PetscCall(MatMPIAIJSetPreallocation(Y, 1, NULL, 0, NULL));
    2681:   } else if (!aij->nz) { /* It does not matter if diagonals of Y only partially lie in maij->A. We just need an estimated preallocation. */
    2682:     PetscInt nonew = aij->nonew;
    2683:     PetscCall(MatSeqAIJSetPreallocation(maij->A, 1, NULL));
    2684:     aij->nonew = nonew;
    2685:   }
    2686:   PetscCall(MatShift_Basic(Y, a));
    2687:   PetscFunctionReturn(PETSC_SUCCESS);
    2688: }

    2690: static PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A, PetscBool *missing, PetscInt *d)
    2691: {
    2692:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2694:   PetscFunctionBegin;
    2695:   PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only works for square matrices");
    2696:   PetscCall(MatMissingDiagonal(a->A, missing, d));
    2697:   if (d) {
    2698:     PetscInt rstart;
    2699:     PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
    2700:     *d += rstart;
    2701:   }
    2702:   PetscFunctionReturn(PETSC_SUCCESS);
    2703: }

    2705: static PetscErrorCode MatInvertVariableBlockDiagonal_MPIAIJ(Mat A, PetscInt nblocks, const PetscInt *bsizes, PetscScalar *diag)
    2706: {
    2707:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2709:   PetscFunctionBegin;
    2710:   PetscCall(MatInvertVariableBlockDiagonal(a->A, nblocks, bsizes, diag));
    2711:   PetscFunctionReturn(PETSC_SUCCESS);
    2712: }

    2714: static PetscErrorCode MatEliminateZeros_MPIAIJ(Mat A, PetscBool keep)
    2715: {
    2716:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2718:   PetscFunctionBegin;
    2719:   PetscCall(MatEliminateZeros_SeqAIJ(a->A, keep));        // possibly keep zero diagonal coefficients
    2720:   PetscCall(MatEliminateZeros_SeqAIJ(a->B, PETSC_FALSE)); // never keep zero diagonal coefficients
    2721:   PetscFunctionReturn(PETSC_SUCCESS);
    2722: }

    2724: static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
    2725:                                        MatGetRow_MPIAIJ,
    2726:                                        MatRestoreRow_MPIAIJ,
    2727:                                        MatMult_MPIAIJ,
    2728:                                        /* 4*/ MatMultAdd_MPIAIJ,
    2729:                                        MatMultTranspose_MPIAIJ,
    2730:                                        MatMultTransposeAdd_MPIAIJ,
    2731:                                        NULL,
    2732:                                        NULL,
    2733:                                        NULL,
    2734:                                        /*10*/ NULL,
    2735:                                        NULL,
    2736:                                        NULL,
    2737:                                        MatSOR_MPIAIJ,
    2738:                                        MatTranspose_MPIAIJ,
    2739:                                        /*15*/ MatGetInfo_MPIAIJ,
    2740:                                        MatEqual_MPIAIJ,
    2741:                                        MatGetDiagonal_MPIAIJ,
    2742:                                        MatDiagonalScale_MPIAIJ,
    2743:                                        MatNorm_MPIAIJ,
    2744:                                        /*20*/ MatAssemblyBegin_MPIAIJ,
    2745:                                        MatAssemblyEnd_MPIAIJ,
    2746:                                        MatSetOption_MPIAIJ,
    2747:                                        MatZeroEntries_MPIAIJ,
    2748:                                        /*24*/ MatZeroRows_MPIAIJ,
    2749:                                        NULL,
    2750:                                        NULL,
    2751:                                        NULL,
    2752:                                        NULL,
    2753:                                        /*29*/ MatSetUp_MPI_Hash,
    2754:                                        NULL,
    2755:                                        NULL,
    2756:                                        MatGetDiagonalBlock_MPIAIJ,
    2757:                                        NULL,
    2758:                                        /*34*/ MatDuplicate_MPIAIJ,
    2759:                                        NULL,
    2760:                                        NULL,
    2761:                                        NULL,
    2762:                                        NULL,
    2763:                                        /*39*/ MatAXPY_MPIAIJ,
    2764:                                        MatCreateSubMatrices_MPIAIJ,
    2765:                                        MatIncreaseOverlap_MPIAIJ,
    2766:                                        MatGetValues_MPIAIJ,
    2767:                                        MatCopy_MPIAIJ,
    2768:                                        /*44*/ MatGetRowMax_MPIAIJ,
    2769:                                        MatScale_MPIAIJ,
    2770:                                        MatShift_MPIAIJ,
    2771:                                        MatDiagonalSet_MPIAIJ,
    2772:                                        MatZeroRowsColumns_MPIAIJ,
    2773:                                        /*49*/ MatSetRandom_MPIAIJ,
    2774:                                        MatGetRowIJ_MPIAIJ,
    2775:                                        MatRestoreRowIJ_MPIAIJ,
    2776:                                        NULL,
    2777:                                        NULL,
    2778:                                        /*54*/ MatFDColoringCreate_MPIXAIJ,
    2779:                                        NULL,
    2780:                                        MatSetUnfactored_MPIAIJ,
    2781:                                        MatPermute_MPIAIJ,
    2782:                                        NULL,
    2783:                                        /*59*/ MatCreateSubMatrix_MPIAIJ,
    2784:                                        MatDestroy_MPIAIJ,
    2785:                                        MatView_MPIAIJ,
    2786:                                        NULL,
    2787:                                        NULL,
    2788:                                        /*64*/ NULL,
    2789:                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
    2790:                                        NULL,
    2791:                                        NULL,
    2792:                                        NULL,
    2793:                                        /*69*/ MatGetRowMaxAbs_MPIAIJ,
    2794:                                        MatGetRowMinAbs_MPIAIJ,
    2795:                                        NULL,
    2796:                                        NULL,
    2797:                                        NULL,
    2798:                                        NULL,
    2799:                                        /*75*/ MatFDColoringApply_AIJ,
    2800:                                        MatSetFromOptions_MPIAIJ,
    2801:                                        NULL,
    2802:                                        NULL,
    2803:                                        MatFindZeroDiagonals_MPIAIJ,
    2804:                                        /*80*/ NULL,
    2805:                                        NULL,
    2806:                                        NULL,
    2807:                                        /*83*/ MatLoad_MPIAIJ,
    2808:                                        NULL,
    2809:                                        NULL,
    2810:                                        NULL,
    2811:                                        NULL,
    2812:                                        NULL,
    2813:                                        /*89*/ NULL,
    2814:                                        NULL,
    2815:                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
    2816:                                        NULL,
    2817:                                        NULL,
    2818:                                        /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
    2819:                                        NULL,
    2820:                                        NULL,
    2821:                                        NULL,
    2822:                                        MatBindToCPU_MPIAIJ,
    2823:                                        /*99*/ MatProductSetFromOptions_MPIAIJ,
    2824:                                        NULL,
    2825:                                        NULL,
    2826:                                        MatConjugate_MPIAIJ,
    2827:                                        NULL,
    2828:                                        /*104*/ MatSetValuesRow_MPIAIJ,
    2829:                                        MatRealPart_MPIAIJ,
    2830:                                        MatImaginaryPart_MPIAIJ,
    2831:                                        NULL,
    2832:                                        NULL,
    2833:                                        /*109*/ NULL,
    2834:                                        NULL,
    2835:                                        MatGetRowMin_MPIAIJ,
    2836:                                        NULL,
    2837:                                        MatMissingDiagonal_MPIAIJ,
    2838:                                        /*114*/ MatGetSeqNonzeroStructure_MPIAIJ,
    2839:                                        NULL,
    2840:                                        MatGetGhosts_MPIAIJ,
    2841:                                        NULL,
    2842:                                        NULL,
    2843:                                        /*119*/ MatMultDiagonalBlock_MPIAIJ,
    2844:                                        NULL,
    2845:                                        NULL,
    2846:                                        NULL,
    2847:                                        MatGetMultiProcBlock_MPIAIJ,
    2848:                                        /*124*/ MatFindNonzeroRows_MPIAIJ,
    2849:                                        MatGetColumnReductions_MPIAIJ,
    2850:                                        MatInvertBlockDiagonal_MPIAIJ,
    2851:                                        MatInvertVariableBlockDiagonal_MPIAIJ,
    2852:                                        MatCreateSubMatricesMPI_MPIAIJ,
    2853:                                        /*129*/ NULL,
    2854:                                        NULL,
    2855:                                        NULL,
    2856:                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
    2857:                                        NULL,
    2858:                                        /*134*/ NULL,
    2859:                                        NULL,
    2860:                                        NULL,
    2861:                                        NULL,
    2862:                                        NULL,
    2863:                                        /*139*/ MatSetBlockSizes_MPIAIJ,
    2864:                                        NULL,
    2865:                                        NULL,
    2866:                                        MatFDColoringSetUp_MPIXAIJ,
    2867:                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
    2868:                                        MatCreateMPIMatConcatenateSeqMat_MPIAIJ,
    2869:                                        /*145*/ NULL,
    2870:                                        NULL,
    2871:                                        NULL,
    2872:                                        MatCreateGraph_Simple_AIJ,
    2873:                                        NULL,
    2874:                                        /*150*/ NULL,
    2875:                                        MatEliminateZeros_MPIAIJ,
    2876:                                        MatGetRowSumAbs_MPIAIJ,
    2877:                                        NULL,
    2878:                                        NULL,
    2879:                                        /*155*/ NULL,
    2880:                                        MatCopyHashToXAIJ_MPI_Hash};

    2882: static PetscErrorCode MatStoreValues_MPIAIJ(Mat mat)
    2883: {
    2884:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2886:   PetscFunctionBegin;
    2887:   PetscCall(MatStoreValues(aij->A));
    2888:   PetscCall(MatStoreValues(aij->B));
    2889:   PetscFunctionReturn(PETSC_SUCCESS);
    2890: }

    2892: static PetscErrorCode MatRetrieveValues_MPIAIJ(Mat mat)
    2893: {
    2894:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2896:   PetscFunctionBegin;
    2897:   PetscCall(MatRetrieveValues(aij->A));
    2898:   PetscCall(MatRetrieveValues(aij->B));
    2899:   PetscFunctionReturn(PETSC_SUCCESS);
    2900: }

    2902: PetscErrorCode MatMPIAIJSetPreallocation_MPIAIJ(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
    2903: {
    2904:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
    2905:   PetscMPIInt size;

    2907:   PetscFunctionBegin;
    2908:   if (B->hash_active) {
    2909:     B->ops[0]      = b->cops;
    2910:     B->hash_active = PETSC_FALSE;
    2911:   }
    2912:   PetscCall(PetscLayoutSetUp(B->rmap));
    2913:   PetscCall(PetscLayoutSetUp(B->cmap));

    2915: #if defined(PETSC_USE_CTABLE)
    2916:   PetscCall(PetscHMapIDestroy(&b->colmap));
    2917: #else
    2918:   PetscCall(PetscFree(b->colmap));
    2919: #endif
    2920:   PetscCall(PetscFree(b->garray));
    2921:   PetscCall(VecDestroy(&b->lvec));
    2922:   PetscCall(VecScatterDestroy(&b->Mvctx));

    2924:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

    2926:   MatSeqXAIJGetOptions_Private(b->B);
    2927:   PetscCall(MatDestroy(&b->B));
    2928:   PetscCall(MatCreate(PETSC_COMM_SELF, &b->B));
    2929:   PetscCall(MatSetSizes(b->B, B->rmap->n, size > 1 ? B->cmap->N : 0, B->rmap->n, size > 1 ? B->cmap->N : 0));
    2930:   PetscCall(MatSetBlockSizesFromMats(b->B, B, B));
    2931:   PetscCall(MatSetType(b->B, MATSEQAIJ));
    2932:   MatSeqXAIJRestoreOptions_Private(b->B);

    2934:   MatSeqXAIJGetOptions_Private(b->A);
    2935:   PetscCall(MatDestroy(&b->A));
    2936:   PetscCall(MatCreate(PETSC_COMM_SELF, &b->A));
    2937:   PetscCall(MatSetSizes(b->A, B->rmap->n, B->cmap->n, B->rmap->n, B->cmap->n));
    2938:   PetscCall(MatSetBlockSizesFromMats(b->A, B, B));
    2939:   PetscCall(MatSetType(b->A, MATSEQAIJ));
    2940:   MatSeqXAIJRestoreOptions_Private(b->A);

    2942:   PetscCall(MatSeqAIJSetPreallocation(b->A, d_nz, d_nnz));
    2943:   PetscCall(MatSeqAIJSetPreallocation(b->B, o_nz, o_nnz));
    2944:   B->preallocated  = PETSC_TRUE;
    2945:   B->was_assembled = PETSC_FALSE;
    2946:   B->assembled     = PETSC_FALSE;
    2947:   PetscFunctionReturn(PETSC_SUCCESS);
    2948: }

    2950: static PetscErrorCode MatResetPreallocation_MPIAIJ(Mat B)
    2951: {
    2952:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
    2953:   PetscBool   ondiagreset, offdiagreset, memoryreset;

    2955:   PetscFunctionBegin;
    2957:   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()");
    2958:   if (B->num_ass == 0) PetscFunctionReturn(PETSC_SUCCESS);

    2960:   PetscCall(MatResetPreallocation_SeqAIJ_Private(b->A, &ondiagreset));
    2961:   PetscCall(MatResetPreallocation_SeqAIJ_Private(b->B, &offdiagreset));
    2962:   memoryreset = (PetscBool)(ondiagreset || offdiagreset);
    2963:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &memoryreset, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)B)));
    2964:   if (!memoryreset) PetscFunctionReturn(PETSC_SUCCESS);

    2966:   PetscCall(PetscLayoutSetUp(B->rmap));
    2967:   PetscCall(PetscLayoutSetUp(B->cmap));
    2968:   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");
    2969:   PetscCall(MatDisAssemble_MPIAIJ(B, PETSC_TRUE));
    2970:   PetscCall(VecScatterDestroy(&b->Mvctx));

    2972:   B->preallocated  = PETSC_TRUE;
    2973:   B->was_assembled = PETSC_FALSE;
    2974:   B->assembled     = PETSC_FALSE;
    2975:   /* Log that the state of this object has changed; this will help guarantee that preconditioners get re-setup */
    2976:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    2977:   PetscFunctionReturn(PETSC_SUCCESS);
    2978: }

    2980: PetscErrorCode MatDuplicate_MPIAIJ(Mat matin, MatDuplicateOption cpvalues, Mat *newmat)
    2981: {
    2982:   Mat         mat;
    2983:   Mat_MPIAIJ *a, *oldmat = (Mat_MPIAIJ *)matin->data;

    2985:   PetscFunctionBegin;
    2986:   *newmat = NULL;
    2987:   PetscCall(MatCreate(PetscObjectComm((PetscObject)matin), &mat));
    2988:   PetscCall(MatSetSizes(mat, matin->rmap->n, matin->cmap->n, matin->rmap->N, matin->cmap->N));
    2989:   PetscCall(MatSetBlockSizesFromMats(mat, matin, matin));
    2990:   PetscCall(MatSetType(mat, ((PetscObject)matin)->type_name));
    2991:   a = (Mat_MPIAIJ *)mat->data;

    2993:   mat->factortype = matin->factortype;
    2994:   mat->assembled  = matin->assembled;
    2995:   mat->insertmode = NOT_SET_VALUES;

    2997:   a->size         = oldmat->size;
    2998:   a->rank         = oldmat->rank;
    2999:   a->donotstash   = oldmat->donotstash;
    3000:   a->roworiented  = oldmat->roworiented;
    3001:   a->rowindices   = NULL;
    3002:   a->rowvalues    = NULL;
    3003:   a->getrowactive = PETSC_FALSE;

    3005:   PetscCall(PetscLayoutReference(matin->rmap, &mat->rmap));
    3006:   PetscCall(PetscLayoutReference(matin->cmap, &mat->cmap));
    3007:   if (matin->hash_active) {
    3008:     PetscCall(MatSetUp(mat));
    3009:   } else {
    3010:     mat->preallocated = matin->preallocated;
    3011:     if (oldmat->colmap) {
    3012: #if defined(PETSC_USE_CTABLE)
    3013:       PetscCall(PetscHMapIDuplicate(oldmat->colmap, &a->colmap));
    3014: #else
    3015:       PetscCall(PetscMalloc1(mat->cmap->N, &a->colmap));
    3016:       PetscCall(PetscArraycpy(a->colmap, oldmat->colmap, mat->cmap->N));
    3017: #endif
    3018:     } else a->colmap = NULL;
    3019:     if (oldmat->garray) {
    3020:       PetscInt len;
    3021:       len = oldmat->B->cmap->n;
    3022:       PetscCall(PetscMalloc1(len + 1, &a->garray));
    3023:       if (len) PetscCall(PetscArraycpy(a->garray, oldmat->garray, len));
    3024:     } else a->garray = NULL;

    3026:     /* It may happen MatDuplicate is called with a non-assembled matrix
    3027:       In fact, MatDuplicate only requires the matrix to be preallocated
    3028:       This may happen inside a DMCreateMatrix_Shell */
    3029:     if (oldmat->lvec) PetscCall(VecDuplicate(oldmat->lvec, &a->lvec));
    3030:     if (oldmat->Mvctx) {
    3031:       a->Mvctx = oldmat->Mvctx;
    3032:       PetscCall(PetscObjectReference((PetscObject)oldmat->Mvctx));
    3033:     }
    3034:     PetscCall(MatDuplicate(oldmat->A, cpvalues, &a->A));
    3035:     PetscCall(MatDuplicate(oldmat->B, cpvalues, &a->B));
    3036:   }
    3037:   PetscCall(PetscFunctionListDuplicate(((PetscObject)matin)->qlist, &((PetscObject)mat)->qlist));
    3038:   *newmat = mat;
    3039:   PetscFunctionReturn(PETSC_SUCCESS);
    3040: }

    3042: PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
    3043: {
    3044:   PetscBool isbinary, ishdf5;

    3046:   PetscFunctionBegin;
    3049:   /* force binary viewer to load .info file if it has not yet done so */
    3050:   PetscCall(PetscViewerSetUp(viewer));
    3051:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    3052:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
    3053:   if (isbinary) {
    3054:     PetscCall(MatLoad_MPIAIJ_Binary(newMat, viewer));
    3055:   } else if (ishdf5) {
    3056: #if defined(PETSC_HAVE_HDF5)
    3057:     PetscCall(MatLoad_AIJ_HDF5(newMat, viewer));
    3058: #else
    3059:     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
    3060: #endif
    3061:   } else {
    3062:     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);
    3063:   }
    3064:   PetscFunctionReturn(PETSC_SUCCESS);
    3065: }

    3067: PetscErrorCode MatLoad_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
    3068: {
    3069:   PetscInt     header[4], M, N, m, nz, rows, cols, sum, i;
    3070:   PetscInt    *rowidxs, *colidxs;
    3071:   PetscScalar *matvals;

    3073:   PetscFunctionBegin;
    3074:   PetscCall(PetscViewerSetUp(viewer));

    3076:   /* read in matrix header */
    3077:   PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
    3078:   PetscCheck(header[0] == MAT_FILE_CLASSID, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Not a matrix object in file");
    3079:   M  = header[1];
    3080:   N  = header[2];
    3081:   nz = header[3];
    3082:   PetscCheck(M >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix row size (%" PetscInt_FMT ") in file is negative", M);
    3083:   PetscCheck(N >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix column size (%" PetscInt_FMT ") in file is negative", N);
    3084:   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix stored in special format on disk, cannot load as MPIAIJ");

    3086:   /* set block sizes from the viewer's .info file */
    3087:   PetscCall(MatLoad_Binary_BlockSizes(mat, viewer));
    3088:   /* set global sizes if not set already */
    3089:   if (mat->rmap->N < 0) mat->rmap->N = M;
    3090:   if (mat->cmap->N < 0) mat->cmap->N = N;
    3091:   PetscCall(PetscLayoutSetUp(mat->rmap));
    3092:   PetscCall(PetscLayoutSetUp(mat->cmap));

    3094:   /* check if the matrix sizes are correct */
    3095:   PetscCall(MatGetSize(mat, &rows, &cols));
    3096:   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);

    3098:   /* read in row lengths and build row indices */
    3099:   PetscCall(MatGetLocalSize(mat, &m, NULL));
    3100:   PetscCall(PetscMalloc1(m + 1, &rowidxs));
    3101:   PetscCall(PetscViewerBinaryReadAll(viewer, rowidxs + 1, m, PETSC_DECIDE, M, PETSC_INT));
    3102:   rowidxs[0] = 0;
    3103:   for (i = 0; i < m; i++) rowidxs[i + 1] += rowidxs[i];
    3104:   if (nz != PETSC_INT_MAX) {
    3105:     PetscCallMPI(MPIU_Allreduce(&rowidxs[m], &sum, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)viewer)));
    3106:     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);
    3107:   }

    3109:   /* read in column indices and matrix values */
    3110:   PetscCall(PetscMalloc2(rowidxs[m], &colidxs, rowidxs[m], &matvals));
    3111:   PetscCall(PetscViewerBinaryReadAll(viewer, colidxs, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
    3112:   PetscCall(PetscViewerBinaryReadAll(viewer, matvals, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
    3113:   /* store matrix indices and values */
    3114:   PetscCall(MatMPIAIJSetPreallocationCSR(mat, rowidxs, colidxs, matvals));
    3115:   PetscCall(PetscFree(rowidxs));
    3116:   PetscCall(PetscFree2(colidxs, matvals));
    3117:   PetscFunctionReturn(PETSC_SUCCESS);
    3118: }

    3120: /* Not scalable because of ISAllGather() unless getting all columns. */
    3121: static PetscErrorCode ISGetSeqIS_Private(Mat mat, IS iscol, IS *isseq)
    3122: {
    3123:   IS          iscol_local;
    3124:   PetscBool   isstride;
    3125:   PetscMPIInt gisstride = 0;

    3127:   PetscFunctionBegin;
    3128:   /* check if we are grabbing all columns*/
    3129:   PetscCall(PetscObjectTypeCompare((PetscObject)iscol, ISSTRIDE, &isstride));

    3131:   if (isstride) {
    3132:     PetscInt start, len, mstart, mlen;
    3133:     PetscCall(ISStrideGetInfo(iscol, &start, NULL));
    3134:     PetscCall(ISGetLocalSize(iscol, &len));
    3135:     PetscCall(MatGetOwnershipRangeColumn(mat, &mstart, &mlen));
    3136:     if (mstart == start && mlen - mstart == len) gisstride = 1;
    3137:   }

    3139:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &gisstride, 1, MPI_INT, MPI_MIN, PetscObjectComm((PetscObject)mat)));
    3140:   if (gisstride) {
    3141:     PetscInt N;
    3142:     PetscCall(MatGetSize(mat, NULL, &N));
    3143:     PetscCall(ISCreateStride(PETSC_COMM_SELF, N, 0, 1, &iscol_local));
    3144:     PetscCall(ISSetIdentity(iscol_local));
    3145:     PetscCall(PetscInfo(mat, "Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n"));
    3146:   } else {
    3147:     PetscInt cbs;
    3148:     PetscCall(ISGetBlockSize(iscol, &cbs));
    3149:     PetscCall(ISAllGather(iscol, &iscol_local));
    3150:     PetscCall(ISSetBlockSize(iscol_local, cbs));
    3151:   }

    3153:   *isseq = iscol_local;
    3154:   PetscFunctionReturn(PETSC_SUCCESS);
    3155: }

    3157: /*
    3158:  Used by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
    3159:  (see MatCreateSubMatrix_MPIAIJ_nonscalable)

    3161:  Input Parameters:
    3162: +   mat - matrix
    3163: .   isrow - parallel row index set; its local indices are a subset of local columns of `mat`,
    3164:            i.e., mat->rstart <= isrow[i] < mat->rend
    3165: -   iscol - parallel column index set; its local indices are a subset of local columns of `mat`,
    3166:            i.e., mat->cstart <= iscol[i] < mat->cend

    3168:  Output Parameters:
    3169: +   isrow_d - sequential row index set for retrieving mat->A
    3170: .   iscol_d - sequential  column index set for retrieving mat->A
    3171: .   iscol_o - sequential column index set for retrieving mat->B
    3172: -   garray - column map; garray[i] indicates global location of iscol_o[i] in `iscol`
    3173:  */
    3174: static PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat, IS isrow, IS iscol, IS *isrow_d, IS *iscol_d, IS *iscol_o, PetscInt *garray[])
    3175: {
    3176:   Vec             x, cmap;
    3177:   const PetscInt *is_idx;
    3178:   PetscScalar    *xarray, *cmaparray;
    3179:   PetscInt        ncols, isstart, *idx, m, rstart, *cmap1, count;
    3180:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ *)mat->data;
    3181:   Mat             B    = a->B;
    3182:   Vec             lvec = a->lvec, lcmap;
    3183:   PetscInt        i, cstart, cend, Bn = B->cmap->N;
    3184:   MPI_Comm        comm;
    3185:   VecScatter      Mvctx = a->Mvctx;

    3187:   PetscFunctionBegin;
    3188:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3189:   PetscCall(ISGetLocalSize(iscol, &ncols));

    3191:   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
    3192:   PetscCall(MatCreateVecs(mat, &x, NULL));
    3193:   PetscCall(VecSet(x, -1.0));
    3194:   PetscCall(VecDuplicate(x, &cmap));
    3195:   PetscCall(VecSet(cmap, -1.0));

    3197:   /* Get start indices */
    3198:   PetscCallMPI(MPI_Scan(&ncols, &isstart, 1, MPIU_INT, MPI_SUM, comm));
    3199:   isstart -= ncols;
    3200:   PetscCall(MatGetOwnershipRangeColumn(mat, &cstart, &cend));

    3202:   PetscCall(ISGetIndices(iscol, &is_idx));
    3203:   PetscCall(VecGetArray(x, &xarray));
    3204:   PetscCall(VecGetArray(cmap, &cmaparray));
    3205:   PetscCall(PetscMalloc1(ncols, &idx));
    3206:   for (i = 0; i < ncols; i++) {
    3207:     xarray[is_idx[i] - cstart]    = (PetscScalar)is_idx[i];
    3208:     cmaparray[is_idx[i] - cstart] = i + isstart;        /* global index of iscol[i] */
    3209:     idx[i]                        = is_idx[i] - cstart; /* local index of iscol[i]  */
    3210:   }
    3211:   PetscCall(VecRestoreArray(x, &xarray));
    3212:   PetscCall(VecRestoreArray(cmap, &cmaparray));
    3213:   PetscCall(ISRestoreIndices(iscol, &is_idx));

    3215:   /* Get iscol_d */
    3216:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, iscol_d));
    3217:   PetscCall(ISGetBlockSize(iscol, &i));
    3218:   PetscCall(ISSetBlockSize(*iscol_d, i));

    3220:   /* Get isrow_d */
    3221:   PetscCall(ISGetLocalSize(isrow, &m));
    3222:   rstart = mat->rmap->rstart;
    3223:   PetscCall(PetscMalloc1(m, &idx));
    3224:   PetscCall(ISGetIndices(isrow, &is_idx));
    3225:   for (i = 0; i < m; i++) idx[i] = is_idx[i] - rstart;
    3226:   PetscCall(ISRestoreIndices(isrow, &is_idx));

    3228:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, idx, PETSC_OWN_POINTER, isrow_d));
    3229:   PetscCall(ISGetBlockSize(isrow, &i));
    3230:   PetscCall(ISSetBlockSize(*isrow_d, i));

    3232:   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
    3233:   PetscCall(VecScatterBegin(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));
    3234:   PetscCall(VecScatterEnd(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));

    3236:   PetscCall(VecDuplicate(lvec, &lcmap));

    3238:   PetscCall(VecScatterBegin(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));
    3239:   PetscCall(VecScatterEnd(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));

    3241:   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
    3242:   /* off-process column indices */
    3243:   count = 0;
    3244:   PetscCall(PetscMalloc1(Bn, &idx));
    3245:   PetscCall(PetscMalloc1(Bn, &cmap1));

    3247:   PetscCall(VecGetArray(lvec, &xarray));
    3248:   PetscCall(VecGetArray(lcmap, &cmaparray));
    3249:   for (i = 0; i < Bn; i++) {
    3250:     if (PetscRealPart(xarray[i]) > -1.0) {
    3251:       idx[count]   = i;                                     /* local column index in off-diagonal part B */
    3252:       cmap1[count] = (PetscInt)PetscRealPart(cmaparray[i]); /* column index in submat */
    3253:       count++;
    3254:     }
    3255:   }
    3256:   PetscCall(VecRestoreArray(lvec, &xarray));
    3257:   PetscCall(VecRestoreArray(lcmap, &cmaparray));

    3259:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_COPY_VALUES, iscol_o));
    3260:   /* cannot ensure iscol_o has same blocksize as iscol! */

    3262:   PetscCall(PetscFree(idx));
    3263:   *garray = cmap1;

    3265:   PetscCall(VecDestroy(&x));
    3266:   PetscCall(VecDestroy(&cmap));
    3267:   PetscCall(VecDestroy(&lcmap));
    3268:   PetscFunctionReturn(PETSC_SUCCESS);
    3269: }

    3271: /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
    3272: PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *submat)
    3273: {
    3274:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)mat->data, *asub;
    3275:   Mat         M = NULL;
    3276:   MPI_Comm    comm;
    3277:   IS          iscol_d, isrow_d, iscol_o;
    3278:   Mat         Asub = NULL, Bsub = NULL;
    3279:   PetscInt    n, count, M_size, N_size;

    3281:   PetscFunctionBegin;
    3282:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));

    3284:   if (call == MAT_REUSE_MATRIX) {
    3285:     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
    3286:     PetscCall(PetscObjectQuery((PetscObject)*submat, "isrow_d", (PetscObject *)&isrow_d));
    3287:     PetscCheck(isrow_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "isrow_d passed in was not used before, cannot reuse");

    3289:     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_d", (PetscObject *)&iscol_d));
    3290:     PetscCheck(iscol_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_d passed in was not used before, cannot reuse");

    3292:     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_o", (PetscObject *)&iscol_o));
    3293:     PetscCheck(iscol_o, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_o passed in was not used before, cannot reuse");

    3295:     /* Update diagonal and off-diagonal portions of submat */
    3296:     asub = (Mat_MPIAIJ *)(*submat)->data;
    3297:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->A));
    3298:     PetscCall(ISGetLocalSize(iscol_o, &n));
    3299:     if (n) PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->B));
    3300:     PetscCall(MatAssemblyBegin(*submat, MAT_FINAL_ASSEMBLY));
    3301:     PetscCall(MatAssemblyEnd(*submat, MAT_FINAL_ASSEMBLY));

    3303:   } else { /* call == MAT_INITIAL_MATRIX) */
    3304:     PetscInt *garray, *garray_compact;
    3305:     PetscInt  BsubN;

    3307:     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
    3308:     PetscCall(ISGetSeqIS_SameColDist_Private(mat, isrow, iscol, &isrow_d, &iscol_d, &iscol_o, &garray));

    3310:     /* Create local submatrices Asub and Bsub */
    3311:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Asub));
    3312:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Bsub));

    3314:     // Compact garray so its not of size Bn
    3315:     PetscCall(ISGetSize(iscol_o, &count));
    3316:     PetscCall(PetscMalloc1(count, &garray_compact));
    3317:     PetscCall(PetscArraycpy(garray_compact, garray, count));

    3319:     /* Create submatrix M */
    3320:     PetscCall(ISGetSize(isrow, &M_size));
    3321:     PetscCall(ISGetSize(iscol, &N_size));
    3322:     PetscCall(MatCreateMPIAIJWithSeqAIJ(comm, M_size, N_size, Asub, Bsub, garray_compact, &M));

    3324:     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
    3325:     asub = (Mat_MPIAIJ *)M->data;

    3327:     PetscCall(ISGetLocalSize(iscol_o, &BsubN));
    3328:     n = asub->B->cmap->N;
    3329:     if (BsubN > n) {
    3330:       /* This case can be tested using ~petsc/src/tao/bound/tutorials/runplate2_3 */
    3331:       const PetscInt *idx;
    3332:       PetscInt        i, j, *idx_new, *subgarray = asub->garray;
    3333:       PetscCall(PetscInfo(M, "submatrix Bn %" PetscInt_FMT " != BsubN %" PetscInt_FMT ", update iscol_o\n", n, BsubN));

    3335:       PetscCall(PetscMalloc1(n, &idx_new));
    3336:       j = 0;
    3337:       PetscCall(ISGetIndices(iscol_o, &idx));
    3338:       for (i = 0; i < n; i++) {
    3339:         if (j >= BsubN) break;
    3340:         while (subgarray[i] > garray[j]) j++;

    3342:         if (subgarray[i] == garray[j]) {
    3343:           idx_new[i] = idx[j++];
    3344:         } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "subgarray[%" PetscInt_FMT "]=%" PetscInt_FMT " cannot < garray[%" PetscInt_FMT "]=%" PetscInt_FMT, i, subgarray[i], j, garray[j]);
    3345:       }
    3346:       PetscCall(ISRestoreIndices(iscol_o, &idx));

    3348:       PetscCall(ISDestroy(&iscol_o));
    3349:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, n, idx_new, PETSC_OWN_POINTER, &iscol_o));

    3351:     } else if (BsubN < n) {
    3352:       SETERRQ(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);
    3353:     }

    3355:     PetscCall(PetscFree(garray));
    3356:     *submat = M;

    3358:     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
    3359:     PetscCall(PetscObjectCompose((PetscObject)M, "isrow_d", (PetscObject)isrow_d));
    3360:     PetscCall(ISDestroy(&isrow_d));

    3362:     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_d", (PetscObject)iscol_d));
    3363:     PetscCall(ISDestroy(&iscol_d));

    3365:     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_o", (PetscObject)iscol_o));
    3366:     PetscCall(ISDestroy(&iscol_o));
    3367:   }
    3368:   PetscFunctionReturn(PETSC_SUCCESS);
    3369: }

    3371: PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *newmat)
    3372: {
    3373:   IS        iscol_local = NULL, isrow_d;
    3374:   PetscInt  csize;
    3375:   PetscInt  n, i, j, start, end;
    3376:   PetscBool sameRowDist = PETSC_FALSE, sameDist[2], tsameDist[2];
    3377:   MPI_Comm  comm;

    3379:   PetscFunctionBegin;
    3380:   /* If isrow has same processor distribution as mat,
    3381:      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
    3382:   if (call == MAT_REUSE_MATRIX) {
    3383:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "isrow_d", (PetscObject *)&isrow_d));
    3384:     if (isrow_d) {
    3385:       sameRowDist  = PETSC_TRUE;
    3386:       tsameDist[1] = PETSC_TRUE; /* sameColDist */
    3387:     } else {
    3388:       PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_local));
    3389:       if (iscol_local) {
    3390:         sameRowDist  = PETSC_TRUE;
    3391:         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
    3392:       }
    3393:     }
    3394:   } else {
    3395:     /* Check if isrow has same processor distribution as mat */
    3396:     sameDist[0] = PETSC_FALSE;
    3397:     PetscCall(ISGetLocalSize(isrow, &n));
    3398:     if (!n) {
    3399:       sameDist[0] = PETSC_TRUE;
    3400:     } else {
    3401:       PetscCall(ISGetMinMax(isrow, &i, &j));
    3402:       PetscCall(MatGetOwnershipRange(mat, &start, &end));
    3403:       if (i >= start && j < end) sameDist[0] = PETSC_TRUE;
    3404:     }

    3406:     /* Check if iscol has same processor distribution as mat */
    3407:     sameDist[1] = PETSC_FALSE;
    3408:     PetscCall(ISGetLocalSize(iscol, &n));
    3409:     if (!n) {
    3410:       sameDist[1] = PETSC_TRUE;
    3411:     } else {
    3412:       PetscCall(ISGetMinMax(iscol, &i, &j));
    3413:       PetscCall(MatGetOwnershipRangeColumn(mat, &start, &end));
    3414:       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
    3415:     }

    3417:     PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3418:     PetscCallMPI(MPIU_Allreduce(&sameDist, &tsameDist, 2, MPIU_BOOL, MPI_LAND, comm));
    3419:     sameRowDist = tsameDist[0];
    3420:   }

    3422:   if (sameRowDist) {
    3423:     if (tsameDist[1]) { /* sameRowDist & sameColDist */
    3424:       /* isrow and iscol have same processor distribution as mat */
    3425:       PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat, isrow, iscol, call, newmat));
    3426:       PetscFunctionReturn(PETSC_SUCCESS);
    3427:     } else { /* sameRowDist */
    3428:       /* isrow has same processor distribution as mat */
    3429:       if (call == MAT_INITIAL_MATRIX) {
    3430:         PetscBool sorted;
    3431:         PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
    3432:         PetscCall(ISGetLocalSize(iscol_local, &n)); /* local size of iscol_local = global columns of newmat */
    3433:         PetscCall(ISGetSize(iscol, &i));
    3434:         PetscCheck(n == i, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "n %" PetscInt_FMT " != size of iscol %" PetscInt_FMT, n, i);

    3436:         PetscCall(ISSorted(iscol_local, &sorted));
    3437:         if (sorted) {
    3438:           /* MatCreateSubMatrix_MPIAIJ_SameRowDist() requires iscol_local be sorted; it can have duplicate indices */
    3439:           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, iscol_local, MAT_INITIAL_MATRIX, newmat));
    3440:           PetscFunctionReturn(PETSC_SUCCESS);
    3441:         }
    3442:       } else { /* call == MAT_REUSE_MATRIX */
    3443:         IS iscol_sub;
    3444:         PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
    3445:         if (iscol_sub) {
    3446:           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, NULL, call, newmat));
    3447:           PetscFunctionReturn(PETSC_SUCCESS);
    3448:         }
    3449:       }
    3450:     }
    3451:   }

    3453:   /* General case: iscol -> iscol_local which has global size of iscol */
    3454:   if (call == MAT_REUSE_MATRIX) {
    3455:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "ISAllGather", (PetscObject *)&iscol_local));
    3456:     PetscCheck(iscol_local, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    3457:   } else {
    3458:     if (!iscol_local) PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
    3459:   }

    3461:   PetscCall(ISGetLocalSize(iscol, &csize));
    3462:   PetscCall(MatCreateSubMatrix_MPIAIJ_nonscalable(mat, isrow, iscol_local, csize, call, newmat));

    3464:   if (call == MAT_INITIAL_MATRIX) {
    3465:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    3466:     PetscCall(ISDestroy(&iscol_local));
    3467:   }
    3468:   PetscFunctionReturn(PETSC_SUCCESS);
    3469: }

    3471: /*@C
    3472:   MatCreateMPIAIJWithSeqAIJ - creates a `MATMPIAIJ` matrix using `MATSEQAIJ` matrices that contain the "diagonal"
    3473:   and "off-diagonal" part of the matrix in CSR format.

    3475:   Collective

    3477:   Input Parameters:
    3478: + comm   - MPI communicator
    3479: . M      - the global row size
    3480: . N      - the global column size
    3481: . A      - "diagonal" portion of matrix
    3482: . 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
    3483: - garray - either `NULL` or the global index of `B` columns

    3485:   Output Parameter:
    3486: . mat - the matrix, with input `A` as its local diagonal matrix

    3488:   Level: advanced

    3490:   Notes:
    3491:   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix.

    3493:   `A` and `B` becomes part of output mat. The user cannot use `A` and `B` anymore.

    3495: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MATSEQAIJ`, `MatCreateMPIAIJWithSplitArrays()`
    3496: @*/
    3497: PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm, PetscInt M, PetscInt N, Mat A, Mat B, PetscInt *garray, Mat *mat)
    3498: {
    3499:   PetscInt m, n;
    3500:   MatType  mpi_mat_type;

    3502:   PetscFunctionBegin;
    3503:   PetscCall(MatCreate(comm, mat));
    3504:   PetscCall(MatGetSize(A, &m, &n));
    3505:   PetscCheck(m == B->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Am %" PetscInt_FMT " != Bm %" PetscInt_FMT, m, B->rmap->N);
    3506:   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);

    3508:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    3509:   /* Determine the type of MPI matrix that should be created from the type of matrix A, which holds the "diagonal" portion. */
    3510:   PetscCall(MatGetMPIMatType_Private(A, &mpi_mat_type));
    3511:   PetscCall(MatSetType(*mat, mpi_mat_type));

    3513:   PetscCall(MatSetBlockSizes(*mat, A->rmap->bs, A->cmap->bs));

    3515:   PetscCall(PetscLayoutSetUp((*mat)->rmap));
    3516:   PetscCall(PetscLayoutSetUp((*mat)->cmap));
    3517:   PetscCall(MatSetMPIAIJWithSplitSeqAIJ(*mat, A, B, garray));
    3518:   PetscFunctionReturn(PETSC_SUCCESS);
    3519: }

    3521: /*
    3522:   MatSetMPIAIJWithSplitSeqAIJ - Set the diag and offdiag matrices of a `MATMPIAIJ` matrix.
    3523:    It is similar to `MatCreateMPIAIJWithSplitArrays()`. This routine allows passing in
    3524:    B with local indices and the correct size, along with the accompanying
    3525:    garray, hence skipping compactification

    3527:   Collective

    3529:   Input Parameters:
    3530: +  mat    - the MATMPIAIJ matrix, which should have its type and layout set, but should not have its diag, offdiag matrices set
    3531: .  A      - the diag matrix using local col ids
    3532: .  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
    3533: -  garray - either `NULL` or the global index of `B` columns

    3535:   Output Parameter:
    3536: .  mat   - the updated `MATMPIAIJ` matrix

    3538:   Level: advanced

    3540:   Notes:
    3541:   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix.

    3543:   `A` and `B` become part of output mat. The user cannot use `A` and `B` anymore.

    3545: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MATSEQAIJ`, `MatCreateMPIAIJWithSplitArrays()`
    3546: */
    3547: PETSC_INTERN PetscErrorCode MatSetMPIAIJWithSplitSeqAIJ(Mat mat, Mat A, Mat B, PetscInt *garray)
    3548: {
    3549:   PetscFunctionBegin;
    3550:   Mat_MPIAIJ *mpiaij = (Mat_MPIAIJ *)mat->data;
    3551:   PetscInt    m, n, M, N, Am, An, Bm, Bn;

    3553:   PetscCall(MatGetSize(mat, &M, &N));
    3554:   PetscCall(MatGetLocalSize(mat, &m, &n));
    3555:   PetscCall(MatGetLocalSize(A, &Am, &An));
    3556:   PetscCall(MatGetLocalSize(B, &Bm, &Bn));

    3558:   PetscCheck(m == Am && m == Bm, PETSC_COMM_SELF, PETSC_ERR_PLIB, "local number of rows do not match");
    3559:   PetscCheck(n == An, PETSC_COMM_SELF, PETSC_ERR_PLIB, "local number of columns do not match");
    3560:   PetscCheck(!mpiaij->A && !mpiaij->B, PETSC_COMM_SELF, PETSC_ERR_PLIB, "A, B of the MPIAIJ matrix are not empty");
    3561:   mpiaij->A      = A;
    3562:   mpiaij->B      = B;
    3563:   mpiaij->garray = garray;

    3565:   mat->preallocated     = PETSC_TRUE;
    3566:   mat->nooffprocentries = PETSC_TRUE; /* See MatAssemblyBegin_MPIAIJ. In effect, making MatAssemblyBegin a nop */

    3568:   PetscCall(MatSetOption(mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    3569:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    3570:   /* MatAssemblyEnd is critical here. It sets mat->offloadmask according to A and B's, and
    3571:    also gets mpiaij->B compacted (if garray is NULL), with its col ids and size reduced
    3572:    */
    3573:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    3574:   PetscCall(MatSetOption(mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    3575:   PetscCall(MatSetOption(mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    3576:   PetscFunctionReturn(PETSC_SUCCESS);
    3577: }

    3579: extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat, PetscInt, const IS[], const IS[], MatReuse, PetscBool, Mat *);

    3581: PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat, IS isrow, IS iscol, IS iscol_local, MatReuse call, Mat *newmat)
    3582: {
    3583:   PetscInt        i, m, n, rstart, row, rend, nz, j, bs, cbs;
    3584:   PetscInt       *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
    3585:   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)mat->data;
    3586:   Mat             M, Msub, B = a->B;
    3587:   MatScalar      *aa;
    3588:   Mat_SeqAIJ     *aij;
    3589:   PetscInt       *garray = a->garray, *colsub, Ncols;
    3590:   PetscInt        count, Bn = B->cmap->N, cstart = mat->cmap->rstart, cend = mat->cmap->rend;
    3591:   IS              iscol_sub, iscmap;
    3592:   const PetscInt *is_idx, *cmap;
    3593:   PetscBool       allcolumns = PETSC_FALSE;
    3594:   MPI_Comm        comm;

    3596:   PetscFunctionBegin;
    3597:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3598:   if (call == MAT_REUSE_MATRIX) {
    3599:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
    3600:     PetscCheck(iscol_sub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "SubIScol passed in was not used before, cannot reuse");
    3601:     PetscCall(ISGetLocalSize(iscol_sub, &count));

    3603:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "Subcmap", (PetscObject *)&iscmap));
    3604:     PetscCheck(iscmap, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Subcmap passed in was not used before, cannot reuse");

    3606:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Msub));
    3607:     PetscCheck(Msub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");

    3609:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_REUSE_MATRIX, PETSC_FALSE, &Msub));

    3611:   } else { /* call == MAT_INITIAL_MATRIX) */
    3612:     PetscBool flg;

    3614:     PetscCall(ISGetLocalSize(iscol, &n));
    3615:     PetscCall(ISGetSize(iscol, &Ncols));

    3617:     /* (1) iscol -> nonscalable iscol_local */
    3618:     /* Check for special case: each processor gets entire matrix columns */
    3619:     PetscCall(ISIdentity(iscol_local, &flg));
    3620:     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
    3621:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    3622:     if (allcolumns) {
    3623:       iscol_sub = iscol_local;
    3624:       PetscCall(PetscObjectReference((PetscObject)iscol_local));
    3625:       PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &iscmap));

    3627:     } else {
    3628:       /* (2) iscol_local -> iscol_sub and iscmap. Implementation below requires iscol_local be sorted, it can have duplicate indices */
    3629:       PetscInt *idx, *cmap1, k;
    3630:       PetscCall(PetscMalloc1(Ncols, &idx));
    3631:       PetscCall(PetscMalloc1(Ncols, &cmap1));
    3632:       PetscCall(ISGetIndices(iscol_local, &is_idx));
    3633:       count = 0;
    3634:       k     = 0;
    3635:       for (i = 0; i < Ncols; i++) {
    3636:         j = is_idx[i];
    3637:         if (j >= cstart && j < cend) {
    3638:           /* diagonal part of mat */
    3639:           idx[count]     = j;
    3640:           cmap1[count++] = i; /* column index in submat */
    3641:         } else if (Bn) {
    3642:           /* off-diagonal part of mat */
    3643:           if (j == garray[k]) {
    3644:             idx[count]     = j;
    3645:             cmap1[count++] = i; /* column index in submat */
    3646:           } else if (j > garray[k]) {
    3647:             while (j > garray[k] && k < Bn - 1) k++;
    3648:             if (j == garray[k]) {
    3649:               idx[count]     = j;
    3650:               cmap1[count++] = i; /* column index in submat */
    3651:             }
    3652:           }
    3653:         }
    3654:       }
    3655:       PetscCall(ISRestoreIndices(iscol_local, &is_idx));

    3657:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_OWN_POINTER, &iscol_sub));
    3658:       PetscCall(ISGetBlockSize(iscol, &cbs));
    3659:       PetscCall(ISSetBlockSize(iscol_sub, cbs));

    3661:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local), count, cmap1, PETSC_OWN_POINTER, &iscmap));
    3662:     }

    3664:     /* (3) Create sequential Msub */
    3665:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_INITIAL_MATRIX, allcolumns, &Msub));
    3666:   }

    3668:   PetscCall(ISGetLocalSize(iscol_sub, &count));
    3669:   aij = (Mat_SeqAIJ *)Msub->data;
    3670:   ii  = aij->i;
    3671:   PetscCall(ISGetIndices(iscmap, &cmap));

    3673:   /*
    3674:       m - number of local rows
    3675:       Ncols - number of columns (same on all processors)
    3676:       rstart - first row in new global matrix generated
    3677:   */
    3678:   PetscCall(MatGetSize(Msub, &m, NULL));

    3680:   if (call == MAT_INITIAL_MATRIX) {
    3681:     /* (4) Create parallel newmat */
    3682:     PetscMPIInt rank, size;
    3683:     PetscInt    csize;

    3685:     PetscCallMPI(MPI_Comm_size(comm, &size));
    3686:     PetscCallMPI(MPI_Comm_rank(comm, &rank));

    3688:     /*
    3689:         Determine the number of non-zeros in the diagonal and off-diagonal
    3690:         portions of the matrix in order to do correct preallocation
    3691:     */

    3693:     /* first get start and end of "diagonal" columns */
    3694:     PetscCall(ISGetLocalSize(iscol, &csize));
    3695:     if (csize == PETSC_DECIDE) {
    3696:       PetscCall(ISGetSize(isrow, &mglobal));
    3697:       if (mglobal == Ncols) { /* square matrix */
    3698:         nlocal = m;
    3699:       } else {
    3700:         nlocal = Ncols / size + ((Ncols % size) > rank);
    3701:       }
    3702:     } else {
    3703:       nlocal = csize;
    3704:     }
    3705:     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    3706:     rstart = rend - nlocal;
    3707:     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);

    3709:     /* next, compute all the lengths */
    3710:     jj = aij->j;
    3711:     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
    3712:     olens = dlens + m;
    3713:     for (i = 0; i < m; i++) {
    3714:       jend = ii[i + 1] - ii[i];
    3715:       olen = 0;
    3716:       dlen = 0;
    3717:       for (j = 0; j < jend; j++) {
    3718:         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
    3719:         else dlen++;
    3720:         jj++;
    3721:       }
    3722:       olens[i] = olen;
    3723:       dlens[i] = dlen;
    3724:     }

    3726:     PetscCall(ISGetBlockSize(isrow, &bs));
    3727:     PetscCall(ISGetBlockSize(iscol, &cbs));

    3729:     PetscCall(MatCreate(comm, &M));
    3730:     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, Ncols));
    3731:     PetscCall(MatSetBlockSizes(M, bs, cbs));
    3732:     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
    3733:     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
    3734:     PetscCall(PetscFree(dlens));

    3736:   } else { /* call == MAT_REUSE_MATRIX */
    3737:     M = *newmat;
    3738:     PetscCall(MatGetLocalSize(M, &i, NULL));
    3739:     PetscCheck(i == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    3740:     PetscCall(MatZeroEntries(M));
    3741:     /*
    3742:          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
    3743:        rather than the slower MatSetValues().
    3744:     */
    3745:     M->was_assembled = PETSC_TRUE;
    3746:     M->assembled     = PETSC_FALSE;
    3747:   }

    3749:   /* (5) Set values of Msub to *newmat */
    3750:   PetscCall(PetscMalloc1(count, &colsub));
    3751:   PetscCall(MatGetOwnershipRange(M, &rstart, NULL));

    3753:   jj = aij->j;
    3754:   PetscCall(MatSeqAIJGetArrayRead(Msub, (const PetscScalar **)&aa));
    3755:   for (i = 0; i < m; i++) {
    3756:     row = rstart + i;
    3757:     nz  = ii[i + 1] - ii[i];
    3758:     for (j = 0; j < nz; j++) colsub[j] = cmap[jj[j]];
    3759:     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, colsub, aa, INSERT_VALUES));
    3760:     jj += nz;
    3761:     aa += nz;
    3762:   }
    3763:   PetscCall(MatSeqAIJRestoreArrayRead(Msub, (const PetscScalar **)&aa));
    3764:   PetscCall(ISRestoreIndices(iscmap, &cmap));

    3766:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
    3767:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));

    3769:   PetscCall(PetscFree(colsub));

    3771:   /* save Msub, iscol_sub and iscmap used in processor for next request */
    3772:   if (call == MAT_INITIAL_MATRIX) {
    3773:     *newmat = M;
    3774:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "SubMatrix", (PetscObject)Msub));
    3775:     PetscCall(MatDestroy(&Msub));

    3777:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "SubIScol", (PetscObject)iscol_sub));
    3778:     PetscCall(ISDestroy(&iscol_sub));

    3780:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "Subcmap", (PetscObject)iscmap));
    3781:     PetscCall(ISDestroy(&iscmap));

    3783:     if (iscol_local) {
    3784:       PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    3785:       PetscCall(ISDestroy(&iscol_local));
    3786:     }
    3787:   }
    3788:   PetscFunctionReturn(PETSC_SUCCESS);
    3789: }

    3791: /*
    3792:     Not great since it makes two copies of the submatrix, first an SeqAIJ
    3793:   in local and then by concatenating the local matrices the end result.
    3794:   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()

    3796:   This requires a sequential iscol with all indices.
    3797: */
    3798: PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat, IS isrow, IS iscol, PetscInt csize, MatReuse call, Mat *newmat)
    3799: {
    3800:   PetscMPIInt rank, size;
    3801:   PetscInt    i, m, n, rstart, row, rend, nz, *cwork, j, bs, cbs;
    3802:   PetscInt   *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
    3803:   Mat         M, Mreuse;
    3804:   MatScalar  *aa, *vwork;
    3805:   MPI_Comm    comm;
    3806:   Mat_SeqAIJ *aij;
    3807:   PetscBool   colflag, allcolumns = PETSC_FALSE;

    3809:   PetscFunctionBegin;
    3810:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3811:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    3812:   PetscCallMPI(MPI_Comm_size(comm, &size));

    3814:   /* Check for special case: each processor gets entire matrix columns */
    3815:   PetscCall(ISIdentity(iscol, &colflag));
    3816:   PetscCall(ISGetLocalSize(iscol, &n));
    3817:   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
    3818:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));

    3820:   if (call == MAT_REUSE_MATRIX) {
    3821:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Mreuse));
    3822:     PetscCheck(Mreuse, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    3823:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_REUSE_MATRIX, allcolumns, &Mreuse));
    3824:   } else {
    3825:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_INITIAL_MATRIX, allcolumns, &Mreuse));
    3826:   }

    3828:   /*
    3829:       m - number of local rows
    3830:       n - number of columns (same on all processors)
    3831:       rstart - first row in new global matrix generated
    3832:   */
    3833:   PetscCall(MatGetSize(Mreuse, &m, &n));
    3834:   PetscCall(MatGetBlockSizes(Mreuse, &bs, &cbs));
    3835:   if (call == MAT_INITIAL_MATRIX) {
    3836:     aij = (Mat_SeqAIJ *)Mreuse->data;
    3837:     ii  = aij->i;
    3838:     jj  = aij->j;

    3840:     /*
    3841:         Determine the number of non-zeros in the diagonal and off-diagonal
    3842:         portions of the matrix in order to do correct preallocation
    3843:     */

    3845:     /* first get start and end of "diagonal" columns */
    3846:     if (csize == PETSC_DECIDE) {
    3847:       PetscCall(ISGetSize(isrow, &mglobal));
    3848:       if (mglobal == n) { /* square matrix */
    3849:         nlocal = m;
    3850:       } else {
    3851:         nlocal = n / size + ((n % size) > rank);
    3852:       }
    3853:     } else {
    3854:       nlocal = csize;
    3855:     }
    3856:     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    3857:     rstart = rend - nlocal;
    3858:     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);

    3860:     /* next, compute all the lengths */
    3861:     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
    3862:     olens = dlens + m;
    3863:     for (i = 0; i < m; i++) {
    3864:       jend = ii[i + 1] - ii[i];
    3865:       olen = 0;
    3866:       dlen = 0;
    3867:       for (j = 0; j < jend; j++) {
    3868:         if (*jj < rstart || *jj >= rend) olen++;
    3869:         else dlen++;
    3870:         jj++;
    3871:       }
    3872:       olens[i] = olen;
    3873:       dlens[i] = dlen;
    3874:     }
    3875:     PetscCall(MatCreate(comm, &M));
    3876:     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, n));
    3877:     PetscCall(MatSetBlockSizes(M, bs, cbs));
    3878:     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
    3879:     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
    3880:     PetscCall(PetscFree(dlens));
    3881:   } else {
    3882:     PetscInt ml, nl;

    3884:     M = *newmat;
    3885:     PetscCall(MatGetLocalSize(M, &ml, &nl));
    3886:     PetscCheck(ml == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    3887:     PetscCall(MatZeroEntries(M));
    3888:     /*
    3889:          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
    3890:        rather than the slower MatSetValues().
    3891:     */
    3892:     M->was_assembled = PETSC_TRUE;
    3893:     M->assembled     = PETSC_FALSE;
    3894:   }
    3895:   PetscCall(MatGetOwnershipRange(M, &rstart, &rend));
    3896:   aij = (Mat_SeqAIJ *)Mreuse->data;
    3897:   ii  = aij->i;
    3898:   jj  = aij->j;

    3900:   /* trigger copy to CPU if needed */
    3901:   PetscCall(MatSeqAIJGetArrayRead(Mreuse, (const PetscScalar **)&aa));
    3902:   for (i = 0; i < m; i++) {
    3903:     row   = rstart + i;
    3904:     nz    = ii[i + 1] - ii[i];
    3905:     cwork = jj;
    3906:     jj    = PetscSafePointerPlusOffset(jj, nz);
    3907:     vwork = aa;
    3908:     aa    = PetscSafePointerPlusOffset(aa, nz);
    3909:     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, cwork, vwork, INSERT_VALUES));
    3910:   }
    3911:   PetscCall(MatSeqAIJRestoreArrayRead(Mreuse, (const PetscScalar **)&aa));

    3913:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
    3914:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
    3915:   *newmat = M;

    3917:   /* save submatrix used in processor for next request */
    3918:   if (call == MAT_INITIAL_MATRIX) {
    3919:     PetscCall(PetscObjectCompose((PetscObject)M, "SubMatrix", (PetscObject)Mreuse));
    3920:     PetscCall(MatDestroy(&Mreuse));
    3921:   }
    3922:   PetscFunctionReturn(PETSC_SUCCESS);
    3923: }

    3925: static PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
    3926: {
    3927:   PetscInt        m, cstart, cend, j, nnz, i, d, *ld;
    3928:   PetscInt       *d_nnz, *o_nnz, nnz_max = 0, rstart, ii, irstart;
    3929:   const PetscInt *JJ;
    3930:   PetscBool       nooffprocentries;
    3931:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)B->data;

    3933:   PetscFunctionBegin;
    3934:   PetscCall(PetscLayoutSetUp(B->rmap));
    3935:   PetscCall(PetscLayoutSetUp(B->cmap));
    3936:   m       = B->rmap->n;
    3937:   cstart  = B->cmap->rstart;
    3938:   cend    = B->cmap->rend;
    3939:   rstart  = B->rmap->rstart;
    3940:   irstart = Ii[0];

    3942:   PetscCall(PetscCalloc2(m, &d_nnz, m, &o_nnz));

    3944:   if (PetscDefined(USE_DEBUG)) {
    3945:     for (i = 0; i < m; i++) {
    3946:       nnz = Ii[i + 1] - Ii[i];
    3947:       JJ  = PetscSafePointerPlusOffset(J, Ii[i] - irstart);
    3948:       PetscCheck(nnz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative %" PetscInt_FMT " number of columns", i, nnz);
    3949:       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]);
    3950:       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);
    3951:     }
    3952:   }

    3954:   for (i = 0; i < m; i++) {
    3955:     nnz     = Ii[i + 1] - Ii[i];
    3956:     JJ      = PetscSafePointerPlusOffset(J, Ii[i] - irstart);
    3957:     nnz_max = PetscMax(nnz_max, nnz);
    3958:     d       = 0;
    3959:     for (j = 0; j < nnz; j++) {
    3960:       if (cstart <= JJ[j] && JJ[j] < cend) d++;
    3961:     }
    3962:     d_nnz[i] = d;
    3963:     o_nnz[i] = nnz - d;
    3964:   }
    3965:   PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
    3966:   PetscCall(PetscFree2(d_nnz, o_nnz));

    3968:   for (i = 0; i < m; i++) {
    3969:     ii = i + rstart;
    3970:     PetscCall(MatSetValues_MPIAIJ(B, 1, &ii, Ii[i + 1] - Ii[i], PetscSafePointerPlusOffset(J, Ii[i] - irstart), PetscSafePointerPlusOffset(v, Ii[i] - irstart), INSERT_VALUES));
    3971:   }
    3972:   nooffprocentries    = B->nooffprocentries;
    3973:   B->nooffprocentries = PETSC_TRUE;
    3974:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    3975:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    3976:   B->nooffprocentries = nooffprocentries;

    3978:   /* count number of entries below block diagonal */
    3979:   PetscCall(PetscFree(Aij->ld));
    3980:   PetscCall(PetscCalloc1(m, &ld));
    3981:   Aij->ld = ld;
    3982:   for (i = 0; i < m; i++) {
    3983:     nnz = Ii[i + 1] - Ii[i];
    3984:     j   = 0;
    3985:     while (j < nnz && J[j] < cstart) j++;
    3986:     ld[i] = j;
    3987:     if (J) J += nnz;
    3988:   }

    3990:   PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    3991:   PetscFunctionReturn(PETSC_SUCCESS);
    3992: }

    3994: /*@
    3995:   MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in `MATAIJ` format
    3996:   (the default parallel PETSc format).

    3998:   Collective

    4000:   Input Parameters:
    4001: + B - the matrix
    4002: . i - the indices into `j` for the start of each local row (indices start with zero)
    4003: . j - the column indices for each local row (indices start with zero)
    4004: - v - optional values in the matrix

    4006:   Level: developer

    4008:   Notes:
    4009:   The `i`, `j`, and `v` arrays ARE copied by this routine into the internal format used by PETSc;
    4010:   thus you CANNOT change the matrix entries by changing the values of `v` after you have
    4011:   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

    4013:   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

    4015:   A convenience routine for this functionality is `MatCreateMPIAIJWithArrays()`.

    4017:   You can update the matrix with new numerical values using `MatUpdateMPIAIJWithArrays()` after this call if the column indices in `j` are sorted.

    4019:   If you do **not** use `MatUpdateMPIAIJWithArrays()`, the column indices in `j` do not need to be sorted. If you will use
    4020:   `MatUpdateMPIAIJWithArrays()`, the column indices **must** be sorted.

    4022:   The format which is used for the sparse matrix input, is equivalent to a
    4023:   row-major ordering.. i.e for the following matrix, the input data expected is
    4024:   as shown
    4025: .vb
    4026:         1 0 0
    4027:         2 0 3     P0
    4028:        -------
    4029:         4 5 6     P1

    4031:      Process0 [P0] rows_owned=[0,1]
    4032:         i =  {0,1,3}  [size = nrow+1  = 2+1]
    4033:         j =  {0,0,2}  [size = 3]
    4034:         v =  {1,2,3}  [size = 3]

    4036:      Process1 [P1] rows_owned=[2]
    4037:         i =  {0,3}    [size = nrow+1  = 1+1]
    4038:         j =  {0,1,2}  [size = 3]
    4039:         v =  {4,5,6}  [size = 3]
    4040: .ve

    4042: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatCreateAIJ()`,
    4043:           `MatCreateSeqAIJWithArrays()`, `MatCreateMPIAIJWithSplitArrays()`, `MatCreateMPIAIJWithArrays()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4044: @*/
    4045: PetscErrorCode MatMPIAIJSetPreallocationCSR(Mat B, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
    4046: {
    4047:   PetscFunctionBegin;
    4048:   PetscTryMethod(B, "MatMPIAIJSetPreallocationCSR_C", (Mat, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, i, j, v));
    4049:   PetscFunctionReturn(PETSC_SUCCESS);
    4050: }

    4052: /*@
    4053:   MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in `MATMPIAIJ` format
    4054:   (the default parallel PETSc format).  For good matrix assembly performance
    4055:   the user should preallocate the matrix storage by setting the parameters
    4056:   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).

    4058:   Collective

    4060:   Input Parameters:
    4061: + B     - the matrix
    4062: . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
    4063:            (same value is used for all local rows)
    4064: . d_nnz - array containing the number of nonzeros in the various rows of the
    4065:            DIAGONAL portion of the local submatrix (possibly different for each row)
    4066:            or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `d_nz` is used to specify the nonzero structure.
    4067:            The size of this array is equal to the number of local rows, i.e 'm'.
    4068:            For matrices that will be factored, you must leave room for (and set)
    4069:            the diagonal entry even if it is zero.
    4070: . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
    4071:            submatrix (same value is used for all local rows).
    4072: - o_nnz - array containing the number of nonzeros in the various rows of the
    4073:            OFF-DIAGONAL portion of the local submatrix (possibly different for
    4074:            each row) or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `o_nz` is used to specify the nonzero
    4075:            structure. The size of this array is equal to the number
    4076:            of local rows, i.e 'm'.

    4078:   Example Usage:
    4079:   Consider the following 8x8 matrix with 34 non-zero values, that is
    4080:   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
    4081:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    4082:   as follows

    4084: .vb
    4085:             1  2  0  |  0  3  0  |  0  4
    4086:     Proc0   0  5  6  |  7  0  0  |  8  0
    4087:             9  0 10  | 11  0  0  | 12  0
    4088:     -------------------------------------
    4089:            13  0 14  | 15 16 17  |  0  0
    4090:     Proc1   0 18  0  | 19 20 21  |  0  0
    4091:             0  0  0  | 22 23  0  | 24  0
    4092:     -------------------------------------
    4093:     Proc2  25 26 27  |  0  0 28  | 29  0
    4094:            30  0  0  | 31 32 33  |  0 34
    4095: .ve

    4097:   This can be represented as a collection of submatrices as
    4098: .vb
    4099:       A B C
    4100:       D E F
    4101:       G H I
    4102: .ve

    4104:   Where the submatrices A,B,C are owned by proc0, D,E,F are
    4105:   owned by proc1, G,H,I are owned by proc2.

    4107:   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4108:   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4109:   The 'M','N' parameters are 8,8, and have the same values on all procs.

    4111:   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
    4112:   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
    4113:   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
    4114:   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
    4115:   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
    4116:   matrix, and [DF] as another `MATSEQAIJ` matrix.

    4118:   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
    4119:   allocated for every row of the local DIAGONAL submatrix, and `o_nz`
    4120:   storage locations are allocated for every row of the OFF-DIAGONAL submatrix.
    4121:   One way to choose `d_nz` and `o_nz` is to use the maximum number of nonzeros over
    4122:   the local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
    4123:   In this case, the values of `d_nz`, `o_nz` are
    4124: .vb
    4125:      proc0  dnz = 2, o_nz = 2
    4126:      proc1  dnz = 3, o_nz = 2
    4127:      proc2  dnz = 1, o_nz = 4
    4128: .ve
    4129:   We are allocating `m`*(`d_nz`+`o_nz`) storage locations for every proc. This
    4130:   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
    4131:   for proc3. i.e we are using 12+15+10=37 storage locations to store
    4132:   34 values.

    4134:   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
    4135:   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
    4136:   In the above case the values for `d_nnz`, `o_nnz` are
    4137: .vb
    4138:      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
    4139:      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
    4140:      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
    4141: .ve
    4142:   Here the space allocated is sum of all the above values i.e 34, and
    4143:   hence pre-allocation is perfect.

    4145:   Level: intermediate

    4147:   Notes:
    4148:   If the *_nnz parameter is given then the *_nz parameter is ignored

    4150:   The `MATAIJ` format, also called compressed row storage (CSR), is compatible with standard Fortran
    4151:   storage.  The stored row and column indices begin with zero.
    4152:   See [Sparse Matrices](sec_matsparse) for details.

    4154:   The parallel matrix is partitioned such that the first m0 rows belong to
    4155:   process 0, the next m1 rows belong to process 1, the next m2 rows belong
    4156:   to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.

    4158:   The DIAGONAL portion of the local submatrix of a processor can be defined
    4159:   as the submatrix which is obtained by extraction the part corresponding to
    4160:   the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
    4161:   first row that belongs to the processor, r2 is the last row belonging to
    4162:   the this processor, and c1-c2 is range of indices of the local part of a
    4163:   vector suitable for applying the matrix to.  This is an mxn matrix.  In the
    4164:   common case of a square matrix, the row and column ranges are the same and
    4165:   the DIAGONAL part is also square. The remaining portion of the local
    4166:   submatrix (mxN) constitute the OFF-DIAGONAL portion.

    4168:   If `o_nnz` and `d_nnz` are specified, then `o_nz` and `d_nz` are ignored.

    4170:   You can call `MatGetInfo()` to get information on how effective the preallocation was;
    4171:   for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
    4172:   You can also run with the option `-info` and look for messages with the string
    4173:   malloc in them to see if additional memory allocation was needed.

    4175: .seealso: [](ch_matrices), `Mat`, [Sparse Matrices](sec_matsparse), `MATMPIAIJ`, `MATAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatCreateAIJ()`, `MatMPIAIJSetPreallocationCSR()`,
    4176:           `MatGetInfo()`, `PetscSplitOwnership()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4177: @*/
    4178: PetscErrorCode MatMPIAIJSetPreallocation(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
    4179: {
    4180:   PetscFunctionBegin;
    4183:   PetscTryMethod(B, "MatMPIAIJSetPreallocation_C", (Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]), (B, d_nz, d_nnz, o_nz, o_nnz));
    4184:   PetscFunctionReturn(PETSC_SUCCESS);
    4185: }

    4187: /*@
    4188:   MatCreateMPIAIJWithArrays - creates a `MATMPIAIJ` matrix using arrays that contain in standard
    4189:   CSR format for the local rows.

    4191:   Collective

    4193:   Input Parameters:
    4194: + comm - MPI communicator
    4195: . m    - number of local rows (Cannot be `PETSC_DECIDE`)
    4196: . n    - This value should be the same as the local size used in creating the
    4197:          x vector for the matrix-vector product $ y = Ax$. (or `PETSC_DECIDE` to have
    4198:          calculated if `N` is given) For square matrices n is almost always `m`.
    4199: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    4200: . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    4201: . 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
    4202: . j    - global column indices
    4203: - a    - optional matrix values

    4205:   Output Parameter:
    4206: . mat - the matrix

    4208:   Level: intermediate

    4210:   Notes:
    4211:   The `i`, `j`, and `a` arrays ARE copied by this routine into the internal format used by PETSc;
    4212:   thus you CANNOT change the matrix entries by changing the values of `a[]` after you have
    4213:   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

    4215:   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

    4217:   Once you have created the matrix you can update it with new numerical values using `MatUpdateMPIAIJWithArray()`

    4219:   If you do **not** use `MatUpdateMPIAIJWithArray()`, the column indices in `j` do not need to be sorted. If you will use
    4220:   `MatUpdateMPIAIJWithArrays()`, the column indices **must** be sorted.

    4222:   The format which is used for the sparse matrix input, is equivalent to a
    4223:   row-major ordering, i.e., for the following matrix, the input data expected is
    4224:   as shown
    4225: .vb
    4226:         1 0 0
    4227:         2 0 3     P0
    4228:        -------
    4229:         4 5 6     P1

    4231:      Process0 [P0] rows_owned=[0,1]
    4232:         i =  {0,1,3}  [size = nrow+1  = 2+1]
    4233:         j =  {0,0,2}  [size = 3]
    4234:         v =  {1,2,3}  [size = 3]

    4236:      Process1 [P1] rows_owned=[2]
    4237:         i =  {0,3}    [size = nrow+1  = 1+1]
    4238:         j =  {0,1,2}  [size = 3]
    4239:         v =  {4,5,6}  [size = 3]
    4240: .ve

    4242: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4243:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4244: @*/
    4245: PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt i[], const PetscInt j[], const PetscScalar a[], Mat *mat)
    4246: {
    4247:   PetscFunctionBegin;
    4248:   PetscCheck(!i || !i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    4249:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    4250:   PetscCall(MatCreate(comm, mat));
    4251:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    4252:   /* PetscCall(MatSetBlockSizes(M,bs,cbs)); */
    4253:   PetscCall(MatSetType(*mat, MATMPIAIJ));
    4254:   PetscCall(MatMPIAIJSetPreallocationCSR(*mat, i, j, a));
    4255:   PetscFunctionReturn(PETSC_SUCCESS);
    4256: }

    4258: /*@
    4259:   MatUpdateMPIAIJWithArrays - updates a `MATMPIAIJ` matrix using arrays that contain in standard
    4260:   CSR format for the local rows. Only the numerical values are updated the other arrays must be identical to what was passed
    4261:   from `MatCreateMPIAIJWithArrays()`

    4263:   Deprecated: Use `MatUpdateMPIAIJWithArray()`

    4265:   Collective

    4267:   Input Parameters:
    4268: + mat - the matrix
    4269: . m   - number of local rows (Cannot be `PETSC_DECIDE`)
    4270: . n   - This value should be the same as the local size used in creating the
    4271:        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
    4272:        calculated if N is given) For square matrices n is almost always m.
    4273: . M   - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
    4274: . N   - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
    4275: . Ii  - row indices; that is Ii[0] = 0, Ii[row] = Ii[row-1] + number of elements in that row of the matrix
    4276: . J   - column indices
    4277: - v   - matrix values

    4279:   Level: deprecated

    4281: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4282:           `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4283: @*/
    4284: PetscErrorCode MatUpdateMPIAIJWithArrays(Mat mat, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
    4285: {
    4286:   PetscInt        nnz, i;
    4287:   PetscBool       nooffprocentries;
    4288:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
    4289:   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
    4290:   PetscScalar    *ad, *ao;
    4291:   PetscInt        ldi, Iii, md;
    4292:   const PetscInt *Adi = Ad->i;
    4293:   PetscInt       *ld  = Aij->ld;

    4295:   PetscFunctionBegin;
    4296:   PetscCheck(Ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    4297:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    4298:   PetscCheck(m == mat->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of rows cannot change from call to MatUpdateMPIAIJWithArrays()");
    4299:   PetscCheck(n == mat->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of columns cannot change from call to MatUpdateMPIAIJWithArrays()");

    4301:   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
    4302:   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));

    4304:   for (i = 0; i < m; i++) {
    4305:     if (PetscDefined(USE_DEBUG)) {
    4306:       for (PetscInt j = Ii[i] + 1; j < Ii[i + 1]; ++j) {
    4307:         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);
    4308:         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);
    4309:       }
    4310:     }
    4311:     nnz = Ii[i + 1] - Ii[i];
    4312:     Iii = Ii[i];
    4313:     ldi = ld[i];
    4314:     md  = Adi[i + 1] - Adi[i];
    4315:     PetscCall(PetscArraycpy(ao, v + Iii, ldi));
    4316:     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
    4317:     PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
    4318:     ad += md;
    4319:     ao += nnz - md;
    4320:   }
    4321:   nooffprocentries      = mat->nooffprocentries;
    4322:   mat->nooffprocentries = PETSC_TRUE;
    4323:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
    4324:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
    4325:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
    4326:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
    4327:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    4328:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    4329:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    4330:   mat->nooffprocentries = nooffprocentries;
    4331:   PetscFunctionReturn(PETSC_SUCCESS);
    4332: }

    4334: /*@
    4335:   MatUpdateMPIAIJWithArray - updates an `MATMPIAIJ` matrix using an array that contains the nonzero values

    4337:   Collective

    4339:   Input Parameters:
    4340: + mat - the matrix
    4341: - v   - matrix values, stored by row

    4343:   Level: intermediate

    4345:   Notes:
    4346:   The matrix must have been obtained with `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()`

    4348:   The column indices in the call to `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()` must have been sorted for this call to work correctly

    4350: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4351:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArrays()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4352: @*/
    4353: PetscErrorCode MatUpdateMPIAIJWithArray(Mat mat, const PetscScalar v[])
    4354: {
    4355:   PetscInt        nnz, i, m;
    4356:   PetscBool       nooffprocentries;
    4357:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
    4358:   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
    4359:   Mat_SeqAIJ     *Ao  = (Mat_SeqAIJ *)Aij->B->data;
    4360:   PetscScalar    *ad, *ao;
    4361:   const PetscInt *Adi = Ad->i, *Adj = Ao->i;
    4362:   PetscInt        ldi, Iii, md;
    4363:   PetscInt       *ld = Aij->ld;

    4365:   PetscFunctionBegin;
    4366:   m = mat->rmap->n;

    4368:   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
    4369:   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));
    4370:   Iii = 0;
    4371:   for (i = 0; i < m; i++) {
    4372:     nnz = Adi[i + 1] - Adi[i] + Adj[i + 1] - Adj[i];
    4373:     ldi = ld[i];
    4374:     md  = Adi[i + 1] - Adi[i];
    4375:     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
    4376:     ad += md;
    4377:     if (ao) {
    4378:       PetscCall(PetscArraycpy(ao, v + Iii, ldi));
    4379:       PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
    4380:       ao += nnz - md;
    4381:     }
    4382:     Iii += nnz;
    4383:   }
    4384:   nooffprocentries      = mat->nooffprocentries;
    4385:   mat->nooffprocentries = PETSC_TRUE;
    4386:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
    4387:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
    4388:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
    4389:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
    4390:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    4391:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    4392:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    4393:   mat->nooffprocentries = nooffprocentries;
    4394:   PetscFunctionReturn(PETSC_SUCCESS);
    4395: }

    4397: /*@
    4398:   MatCreateAIJ - Creates a sparse parallel matrix in `MATAIJ` format
    4399:   (the default parallel PETSc format).  For good matrix assembly performance
    4400:   the user should preallocate the matrix storage by setting the parameters
    4401:   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).

    4403:   Collective

    4405:   Input Parameters:
    4406: + comm  - MPI communicator
    4407: . m     - number of local rows (or `PETSC_DECIDE` to have calculated if M is given)
    4408:           This value should be the same as the local size used in creating the
    4409:           y vector for the matrix-vector product y = Ax.
    4410: . n     - This value should be the same as the local size used in creating the
    4411:           x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
    4412:           calculated if N is given) For square matrices n is almost always m.
    4413: . M     - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
    4414: . N     - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
    4415: . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
    4416:           (same value is used for all local rows)
    4417: . d_nnz - array containing the number of nonzeros in the various rows of the
    4418:           DIAGONAL portion of the local submatrix (possibly different for each row)
    4419:           or `NULL`, if `d_nz` is used to specify the nonzero structure.
    4420:           The size of this array is equal to the number of local rows, i.e 'm'.
    4421: . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
    4422:           submatrix (same value is used for all local rows).
    4423: - o_nnz - array containing the number of nonzeros in the various rows of the
    4424:           OFF-DIAGONAL portion of the local submatrix (possibly different for
    4425:           each row) or `NULL`, if `o_nz` is used to specify the nonzero
    4426:           structure. The size of this array is equal to the number
    4427:           of local rows, i.e 'm'.

    4429:   Output Parameter:
    4430: . A - the matrix

    4432:   Options Database Keys:
    4433: + -mat_no_inode                     - Do not use inodes
    4434: . -mat_inode_limit <limit>          - Sets inode limit (max limit=5)
    4435: - -matmult_vecscatter_view <viewer> - View the vecscatter (i.e., communication pattern) used in `MatMult()` of sparse parallel matrices.
    4436:                                       See viewer types in manual of `MatView()`. Of them, ascii_matlab, draw or binary cause the `VecScatter`
    4437:                                       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.

    4439:   Level: intermediate

    4441:   Notes:
    4442:   It is recommended that one use `MatCreateFromOptions()` or the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
    4443:   MatXXXXSetPreallocation() paradigm instead of this routine directly.
    4444:   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]

    4446:   If the *_nnz parameter is given then the *_nz parameter is ignored

    4448:   The `m`,`n`,`M`,`N` parameters specify the size of the matrix, and its partitioning across
    4449:   processors, while `d_nz`,`d_nnz`,`o_nz`,`o_nnz` parameters specify the approximate
    4450:   storage requirements for this matrix.

    4452:   If `PETSC_DECIDE` or  `PETSC_DETERMINE` is used for a particular argument on one
    4453:   processor than it must be used on all processors that share the object for
    4454:   that argument.

    4456:   If `m` and `n` are not `PETSC_DECIDE`, then the values determine the `PetscLayout` of the matrix and the ranges returned by
    4457:   `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`, and `MatGetOwnershipRangesColumn()`.

    4459:   The user MUST specify either the local or global matrix dimensions
    4460:   (possibly both).

    4462:   The parallel matrix is partitioned across processors such that the
    4463:   first `m0` rows belong to process 0, the next `m1` rows belong to
    4464:   process 1, the next `m2` rows belong to process 2, etc., where
    4465:   `m0`, `m1`, `m2`... are the input parameter `m` on each MPI process. I.e., each MPI process stores
    4466:   values corresponding to [m x N] submatrix.

    4468:   The columns are logically partitioned with the n0 columns belonging
    4469:   to 0th partition, the next n1 columns belonging to the next
    4470:   partition etc.. where n0,n1,n2... are the input parameter 'n'.

    4472:   The DIAGONAL portion of the local submatrix on any given processor
    4473:   is the submatrix corresponding to the rows and columns m,n
    4474:   corresponding to the given processor. i.e diagonal matrix on
    4475:   process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
    4476:   etc. The remaining portion of the local submatrix [m x (N-n)]
    4477:   constitute the OFF-DIAGONAL portion. The example below better
    4478:   illustrates this concept. The two matrices, the DIAGONAL portion and
    4479:   the OFF-DIAGONAL portion are each stored as `MATSEQAIJ` matrices.

    4481:   For a square global matrix we define each processor's diagonal portion
    4482:   to be its local rows and the corresponding columns (a square submatrix);
    4483:   each processor's off-diagonal portion encompasses the remainder of the
    4484:   local matrix (a rectangular submatrix).

    4486:   If `o_nnz`, `d_nnz` are specified, then `o_nz`, and `d_nz` are ignored.

    4488:   When calling this routine with a single process communicator, a matrix of
    4489:   type `MATSEQAIJ` is returned.  If a matrix of type `MATMPIAIJ` is desired for this
    4490:   type of communicator, use the construction mechanism
    4491: .vb
    4492:   MatCreate(..., &A);
    4493:   MatSetType(A, MATMPIAIJ);
    4494:   MatSetSizes(A, m, n, M, N);
    4495:   MatMPIAIJSetPreallocation(A, ...);
    4496: .ve

    4498:   By default, this format uses inodes (identical nodes) when possible.
    4499:   We search for consecutive rows with the same nonzero structure, thereby
    4500:   reusing matrix information to achieve increased efficiency.

    4502:   Example Usage:
    4503:   Consider the following 8x8 matrix with 34 non-zero values, that is
    4504:   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
    4505:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    4506:   as follows

    4508: .vb
    4509:             1  2  0  |  0  3  0  |  0  4
    4510:     Proc0   0  5  6  |  7  0  0  |  8  0
    4511:             9  0 10  | 11  0  0  | 12  0
    4512:     -------------------------------------
    4513:            13  0 14  | 15 16 17  |  0  0
    4514:     Proc1   0 18  0  | 19 20 21  |  0  0
    4515:             0  0  0  | 22 23  0  | 24  0
    4516:     -------------------------------------
    4517:     Proc2  25 26 27  |  0  0 28  | 29  0
    4518:            30  0  0  | 31 32 33  |  0 34
    4519: .ve

    4521:   This can be represented as a collection of submatrices as

    4523: .vb
    4524:       A B C
    4525:       D E F
    4526:       G H I
    4527: .ve

    4529:   Where the submatrices A,B,C are owned by proc0, D,E,F are
    4530:   owned by proc1, G,H,I are owned by proc2.

    4532:   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4533:   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4534:   The 'M','N' parameters are 8,8, and have the same values on all procs.

    4536:   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
    4537:   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
    4538:   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
    4539:   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
    4540:   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
    4541:   matrix, and [DF] as another SeqAIJ matrix.

    4543:   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
    4544:   allocated for every row of the local DIAGONAL submatrix, and `o_nz`
    4545:   storage locations are allocated for every row of the OFF-DIAGONAL submatrix.
    4546:   One way to choose `d_nz` and `o_nz` is to use the maximum number of nonzeros over
    4547:   the local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
    4548:   In this case, the values of `d_nz`,`o_nz` are
    4549: .vb
    4550:      proc0  dnz = 2, o_nz = 2
    4551:      proc1  dnz = 3, o_nz = 2
    4552:      proc2  dnz = 1, o_nz = 4
    4553: .ve
    4554:   We are allocating m*(`d_nz`+`o_nz`) storage locations for every proc. This
    4555:   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
    4556:   for proc3. i.e we are using 12+15+10=37 storage locations to store
    4557:   34 values.

    4559:   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
    4560:   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
    4561:   In the above case the values for d_nnz,o_nnz are
    4562: .vb
    4563:      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
    4564:      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
    4565:      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
    4566: .ve
    4567:   Here the space allocated is sum of all the above values i.e 34, and
    4568:   hence pre-allocation is perfect.

    4570: .seealso: [](ch_matrices), `Mat`, [Sparse Matrix Creation](sec_matsparse), `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4571:           `MATMPIAIJ`, `MatCreateMPIAIJWithArrays()`, `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`,
    4572:           `MatGetOwnershipRangesColumn()`, `PetscLayout`
    4573: @*/
    4574: 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)
    4575: {
    4576:   PetscMPIInt size;

    4578:   PetscFunctionBegin;
    4579:   PetscCall(MatCreate(comm, A));
    4580:   PetscCall(MatSetSizes(*A, m, n, M, N));
    4581:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4582:   if (size > 1) {
    4583:     PetscCall(MatSetType(*A, MATMPIAIJ));
    4584:     PetscCall(MatMPIAIJSetPreallocation(*A, d_nz, d_nnz, o_nz, o_nnz));
    4585:   } else {
    4586:     PetscCall(MatSetType(*A, MATSEQAIJ));
    4587:     PetscCall(MatSeqAIJSetPreallocation(*A, d_nz, d_nnz));
    4588:   }
    4589:   PetscFunctionReturn(PETSC_SUCCESS);
    4590: }

    4592: /*@C
    4593:   MatMPIAIJGetSeqAIJ - Returns the local pieces of this distributed matrix

    4595:   Not Collective

    4597:   Input Parameter:
    4598: . A - The `MATMPIAIJ` matrix

    4600:   Output Parameters:
    4601: + Ad     - The local diagonal block as a `MATSEQAIJ` matrix
    4602: . Ao     - The local off-diagonal block as a `MATSEQAIJ` matrix
    4603: - colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix

    4605:   Level: intermediate

    4607:   Note:
    4608:   The rows in `Ad` and `Ao` are in [0, Nr), where Nr is the number of local rows on this process. The columns
    4609:   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
    4610:   the number of nonzero columns in the local off-diagonal piece of the matrix `A`. The array colmap maps these
    4611:   local column numbers to global column numbers in the original matrix.

    4613: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`, `MatCreateAIJ()`, `MATSEQAIJ`
    4614: @*/
    4615: PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A, Mat *Ad, Mat *Ao, const PetscInt *colmap[])
    4616: {
    4617:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    4618:   PetscBool   flg;

    4620:   PetscFunctionBegin;
    4621:   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &flg));
    4622:   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "This function requires a MATMPIAIJ matrix as input");
    4623:   if (Ad) *Ad = a->A;
    4624:   if (Ao) *Ao = a->B;
    4625:   if (colmap) *colmap = a->garray;
    4626:   PetscFunctionReturn(PETSC_SUCCESS);
    4627: }

    4629: PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
    4630: {
    4631:   PetscInt     m, N, i, rstart, nnz, Ii;
    4632:   PetscInt    *indx;
    4633:   PetscScalar *values;
    4634:   MatType      rootType;

    4636:   PetscFunctionBegin;
    4637:   PetscCall(MatGetSize(inmat, &m, &N));
    4638:   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
    4639:     PetscInt *dnz, *onz, sum, bs, cbs;

    4641:     if (n == PETSC_DECIDE) PetscCall(PetscSplitOwnership(comm, &n, &N));
    4642:     /* Check sum(n) = N */
    4643:     PetscCallMPI(MPIU_Allreduce(&n, &sum, 1, MPIU_INT, MPI_SUM, comm));
    4644:     PetscCheck(sum == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Sum of local columns %" PetscInt_FMT " != global columns %" PetscInt_FMT, sum, N);

    4646:     PetscCallMPI(MPI_Scan(&m, &rstart, 1, MPIU_INT, MPI_SUM, comm));
    4647:     rstart -= m;

    4649:     MatPreallocateBegin(comm, m, n, dnz, onz);
    4650:     for (i = 0; i < m; i++) {
    4651:       PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
    4652:       PetscCall(MatPreallocateSet(i + rstart, nnz, indx, dnz, onz));
    4653:       PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
    4654:     }

    4656:     PetscCall(MatCreate(comm, outmat));
    4657:     PetscCall(MatSetSizes(*outmat, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    4658:     PetscCall(MatGetBlockSizes(inmat, &bs, &cbs));
    4659:     PetscCall(MatSetBlockSizes(*outmat, bs, cbs));
    4660:     PetscCall(MatGetRootType_Private(inmat, &rootType));
    4661:     PetscCall(MatSetType(*outmat, rootType));
    4662:     PetscCall(MatSeqAIJSetPreallocation(*outmat, 0, dnz));
    4663:     PetscCall(MatMPIAIJSetPreallocation(*outmat, 0, dnz, 0, onz));
    4664:     MatPreallocateEnd(dnz, onz);
    4665:     PetscCall(MatSetOption(*outmat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    4666:   }

    4668:   /* numeric phase */
    4669:   PetscCall(MatGetOwnershipRange(*outmat, &rstart, NULL));
    4670:   for (i = 0; i < m; i++) {
    4671:     PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
    4672:     Ii = i + rstart;
    4673:     PetscCall(MatSetValues(*outmat, 1, &Ii, nnz, indx, values, INSERT_VALUES));
    4674:     PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
    4675:   }
    4676:   PetscCall(MatAssemblyBegin(*outmat, MAT_FINAL_ASSEMBLY));
    4677:   PetscCall(MatAssemblyEnd(*outmat, MAT_FINAL_ASSEMBLY));
    4678:   PetscFunctionReturn(PETSC_SUCCESS);
    4679: }

    4681: static PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(void **data)
    4682: {
    4683:   Mat_Merge_SeqsToMPI *merge = (Mat_Merge_SeqsToMPI *)*data;

    4685:   PetscFunctionBegin;
    4686:   if (!merge) PetscFunctionReturn(PETSC_SUCCESS);
    4687:   PetscCall(PetscFree(merge->id_r));
    4688:   PetscCall(PetscFree(merge->len_s));
    4689:   PetscCall(PetscFree(merge->len_r));
    4690:   PetscCall(PetscFree(merge->bi));
    4691:   PetscCall(PetscFree(merge->bj));
    4692:   PetscCall(PetscFree(merge->buf_ri[0]));
    4693:   PetscCall(PetscFree(merge->buf_ri));
    4694:   PetscCall(PetscFree(merge->buf_rj[0]));
    4695:   PetscCall(PetscFree(merge->buf_rj));
    4696:   PetscCall(PetscFree(merge->coi));
    4697:   PetscCall(PetscFree(merge->coj));
    4698:   PetscCall(PetscFree(merge->owners_co));
    4699:   PetscCall(PetscLayoutDestroy(&merge->rowmap));
    4700:   PetscCall(PetscFree(merge));
    4701:   PetscFunctionReturn(PETSC_SUCCESS);
    4702: }

    4704: #include <../src/mat/utils/freespace.h>
    4705: #include <petscbt.h>

    4707: PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat, Mat mpimat)
    4708: {
    4709:   MPI_Comm             comm;
    4710:   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)seqmat->data;
    4711:   PetscMPIInt          size, rank, taga, *len_s;
    4712:   PetscInt             N = mpimat->cmap->N, i, j, *owners, *ai = a->i, *aj, m;
    4713:   PetscMPIInt          proc, k;
    4714:   PetscInt           **buf_ri, **buf_rj;
    4715:   PetscInt             anzi, *bj_i, *bi, *bj, arow, bnzi, nextaj;
    4716:   PetscInt             nrows, **buf_ri_k, **nextrow, **nextai;
    4717:   MPI_Request         *s_waits, *r_waits;
    4718:   MPI_Status          *status;
    4719:   const MatScalar     *aa, *a_a;
    4720:   MatScalar          **abuf_r, *ba_i;
    4721:   Mat_Merge_SeqsToMPI *merge;
    4722:   PetscContainer       container;

    4724:   PetscFunctionBegin;
    4725:   PetscCall(PetscObjectGetComm((PetscObject)mpimat, &comm));
    4726:   PetscCall(PetscLogEventBegin(MAT_Seqstompinum, seqmat, 0, 0, 0));

    4728:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4729:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    4731:   PetscCall(PetscObjectQuery((PetscObject)mpimat, "MatMergeSeqsToMPI", (PetscObject *)&container));
    4732:   PetscCheck(container, PetscObjectComm((PetscObject)mpimat), PETSC_ERR_PLIB, "Mat not created from MatCreateMPIAIJSumSeqAIJSymbolic");
    4733:   PetscCall(PetscContainerGetPointer(container, (void **)&merge));
    4734:   PetscCall(MatSeqAIJGetArrayRead(seqmat, &a_a));
    4735:   aa = a_a;

    4737:   bi     = merge->bi;
    4738:   bj     = merge->bj;
    4739:   buf_ri = merge->buf_ri;
    4740:   buf_rj = merge->buf_rj;

    4742:   PetscCall(PetscMalloc1(size, &status));
    4743:   owners = merge->rowmap->range;
    4744:   len_s  = merge->len_s;

    4746:   /* send and recv matrix values */
    4747:   PetscCall(PetscObjectGetNewTag((PetscObject)mpimat, &taga));
    4748:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

    4750:   PetscCall(PetscMalloc1(merge->nsend + 1, &s_waits));
    4751:   for (proc = 0, k = 0; proc < size; proc++) {
    4752:     if (!len_s[proc]) continue;
    4753:     i = owners[proc];
    4754:     PetscCallMPI(MPIU_Isend(aa + ai[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
    4755:     k++;
    4756:   }

    4758:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
    4759:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));
    4760:   PetscCall(PetscFree(status));

    4762:   PetscCall(PetscFree(s_waits));
    4763:   PetscCall(PetscFree(r_waits));

    4765:   /* insert mat values of mpimat */
    4766:   PetscCall(PetscMalloc1(N, &ba_i));
    4767:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));

    4769:   for (k = 0; k < merge->nrecv; k++) {
    4770:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    4771:     nrows       = *buf_ri_k[k];
    4772:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    4773:     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    4774:   }

    4776:   /* set values of ba */
    4777:   m = merge->rowmap->n;
    4778:   for (i = 0; i < m; i++) {
    4779:     arow = owners[rank] + i;
    4780:     bj_i = bj + bi[i]; /* col indices of the i-th row of mpimat */
    4781:     bnzi = bi[i + 1] - bi[i];
    4782:     PetscCall(PetscArrayzero(ba_i, bnzi));

    4784:     /* add local non-zero vals of this proc's seqmat into ba */
    4785:     anzi   = ai[arow + 1] - ai[arow];
    4786:     aj     = a->j + ai[arow];
    4787:     aa     = a_a + ai[arow];
    4788:     nextaj = 0;
    4789:     for (j = 0; nextaj < anzi; j++) {
    4790:       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
    4791:         ba_i[j] += aa[nextaj++];
    4792:       }
    4793:     }

    4795:     /* add received vals into ba */
    4796:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    4797:       /* i-th row */
    4798:       if (i == *nextrow[k]) {
    4799:         anzi   = *(nextai[k] + 1) - *nextai[k];
    4800:         aj     = buf_rj[k] + *nextai[k];
    4801:         aa     = abuf_r[k] + *nextai[k];
    4802:         nextaj = 0;
    4803:         for (j = 0; nextaj < anzi; j++) {
    4804:           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
    4805:             ba_i[j] += aa[nextaj++];
    4806:           }
    4807:         }
    4808:         nextrow[k]++;
    4809:         nextai[k]++;
    4810:       }
    4811:     }
    4812:     PetscCall(MatSetValues(mpimat, 1, &arow, bnzi, bj_i, ba_i, INSERT_VALUES));
    4813:   }
    4814:   PetscCall(MatSeqAIJRestoreArrayRead(seqmat, &a_a));
    4815:   PetscCall(MatAssemblyBegin(mpimat, MAT_FINAL_ASSEMBLY));
    4816:   PetscCall(MatAssemblyEnd(mpimat, MAT_FINAL_ASSEMBLY));

    4818:   PetscCall(PetscFree(abuf_r[0]));
    4819:   PetscCall(PetscFree(abuf_r));
    4820:   PetscCall(PetscFree(ba_i));
    4821:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));
    4822:   PetscCall(PetscLogEventEnd(MAT_Seqstompinum, seqmat, 0, 0, 0));
    4823:   PetscFunctionReturn(PETSC_SUCCESS);
    4824: }

    4826: PetscErrorCode MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, Mat *mpimat)
    4827: {
    4828:   Mat                  B_mpi;
    4829:   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)seqmat->data;
    4830:   PetscMPIInt          size, rank, tagi, tagj, *len_s, *len_si, *len_ri;
    4831:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
    4832:   PetscInt             M = seqmat->rmap->n, N = seqmat->cmap->n, i, *owners, *ai = a->i, *aj = a->j;
    4833:   PetscInt             len, *dnz, *onz, bs, cbs;
    4834:   PetscInt             k, anzi, *bi, *bj, *lnk, nlnk, arow, bnzi;
    4835:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextai;
    4836:   MPI_Request         *si_waits, *sj_waits, *ri_waits, *rj_waits;
    4837:   MPI_Status          *status;
    4838:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
    4839:   PetscBT              lnkbt;
    4840:   Mat_Merge_SeqsToMPI *merge;
    4841:   PetscContainer       container;

    4843:   PetscFunctionBegin;
    4844:   PetscCall(PetscLogEventBegin(MAT_Seqstompisym, seqmat, 0, 0, 0));

    4846:   /* make sure it is a PETSc comm */
    4847:   PetscCall(PetscCommDuplicate(comm, &comm, NULL));
    4848:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4849:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    4851:   PetscCall(PetscNew(&merge));
    4852:   PetscCall(PetscMalloc1(size, &status));

    4854:   /* determine row ownership */
    4855:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));
    4856:   PetscCall(PetscLayoutSetLocalSize(merge->rowmap, m));
    4857:   PetscCall(PetscLayoutSetSize(merge->rowmap, M));
    4858:   PetscCall(PetscLayoutSetBlockSize(merge->rowmap, 1));
    4859:   PetscCall(PetscLayoutSetUp(merge->rowmap));
    4860:   PetscCall(PetscMalloc1(size, &len_si));
    4861:   PetscCall(PetscMalloc1(size, &merge->len_s));

    4863:   m      = merge->rowmap->n;
    4864:   owners = merge->rowmap->range;

    4866:   /* determine the number of messages to send, their lengths */
    4867:   len_s = merge->len_s;

    4869:   len          = 0; /* length of buf_si[] */
    4870:   merge->nsend = 0;
    4871:   for (PetscMPIInt proc = 0; proc < size; proc++) {
    4872:     len_si[proc] = 0;
    4873:     if (proc == rank) {
    4874:       len_s[proc] = 0;
    4875:     } else {
    4876:       PetscCall(PetscMPIIntCast(owners[proc + 1] - owners[proc] + 1, &len_si[proc]));
    4877:       PetscCall(PetscMPIIntCast(ai[owners[proc + 1]] - ai[owners[proc]], &len_s[proc])); /* num of rows to be sent to [proc] */
    4878:     }
    4879:     if (len_s[proc]) {
    4880:       merge->nsend++;
    4881:       nrows = 0;
    4882:       for (i = owners[proc]; i < owners[proc + 1]; i++) {
    4883:         if (ai[i + 1] > ai[i]) nrows++;
    4884:       }
    4885:       PetscCall(PetscMPIIntCast(2 * (nrows + 1), &len_si[proc]));
    4886:       len += len_si[proc];
    4887:     }
    4888:   }

    4890:   /* determine the number and length of messages to receive for ij-structure */
    4891:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
    4892:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

    4894:   /* post the Irecv of j-structure */
    4895:   PetscCall(PetscCommGetNewTag(comm, &tagj));
    4896:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rj_waits));

    4898:   /* post the Isend of j-structure */
    4899:   PetscCall(PetscMalloc2(merge->nsend, &si_waits, merge->nsend, &sj_waits));

    4901:   for (PetscMPIInt proc = 0, k = 0; proc < size; proc++) {
    4902:     if (!len_s[proc]) continue;
    4903:     i = owners[proc];
    4904:     PetscCallMPI(MPIU_Isend(aj + ai[i], len_s[proc], MPIU_INT, proc, tagj, comm, sj_waits + k));
    4905:     k++;
    4906:   }

    4908:   /* receives and sends of j-structure are complete */
    4909:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, rj_waits, status));
    4910:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, sj_waits, status));

    4912:   /* send and recv i-structure */
    4913:   PetscCall(PetscCommGetNewTag(comm, &tagi));
    4914:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &ri_waits));

    4916:   PetscCall(PetscMalloc1(len + 1, &buf_s));
    4917:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
    4918:   for (PetscMPIInt proc = 0, k = 0; proc < size; proc++) {
    4919:     if (!len_s[proc]) continue;
    4920:     /* form outgoing message for i-structure:
    4921:          buf_si[0]:                 nrows to be sent
    4922:                [1:nrows]:           row index (global)
    4923:                [nrows+1:2*nrows+1]: i-structure index
    4924:     */
    4925:     nrows       = len_si[proc] / 2 - 1;
    4926:     buf_si_i    = buf_si + nrows + 1;
    4927:     buf_si[0]   = nrows;
    4928:     buf_si_i[0] = 0;
    4929:     nrows       = 0;
    4930:     for (i = owners[proc]; i < owners[proc + 1]; i++) {
    4931:       anzi = ai[i + 1] - ai[i];
    4932:       if (anzi) {
    4933:         buf_si_i[nrows + 1] = buf_si_i[nrows] + anzi; /* i-structure */
    4934:         buf_si[nrows + 1]   = i - owners[proc];       /* local row index */
    4935:         nrows++;
    4936:       }
    4937:     }
    4938:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, si_waits + k));
    4939:     k++;
    4940:     buf_si += len_si[proc];
    4941:   }

    4943:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, ri_waits, status));
    4944:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, si_waits, status));

    4946:   PetscCall(PetscInfo(seqmat, "nsend: %d, nrecv: %d\n", merge->nsend, merge->nrecv));
    4947:   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]));

    4949:   PetscCall(PetscFree(len_si));
    4950:   PetscCall(PetscFree(len_ri));
    4951:   PetscCall(PetscFree(rj_waits));
    4952:   PetscCall(PetscFree2(si_waits, sj_waits));
    4953:   PetscCall(PetscFree(ri_waits));
    4954:   PetscCall(PetscFree(buf_s));
    4955:   PetscCall(PetscFree(status));

    4957:   /* compute a local seq matrix in each processor */
    4958:   /* allocate bi array and free space for accumulating nonzero column info */
    4959:   PetscCall(PetscMalloc1(m + 1, &bi));
    4960:   bi[0] = 0;

    4962:   /* create and initialize a linked list */
    4963:   nlnk = N + 1;
    4964:   PetscCall(PetscLLCreate(N, N, nlnk, lnk, lnkbt));

    4966:   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
    4967:   len = ai[owners[rank + 1]] - ai[owners[rank]];
    4968:   PetscCall(PetscFreeSpaceGet(PetscIntMultTruncate(2, len) + 1, &free_space));

    4970:   current_space = free_space;

    4972:   /* determine symbolic info for each local row */
    4973:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));

    4975:   for (k = 0; k < merge->nrecv; k++) {
    4976:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    4977:     nrows       = *buf_ri_k[k];
    4978:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    4979:     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    4980:   }

    4982:   MatPreallocateBegin(comm, m, n, dnz, onz);
    4983:   len = 0;
    4984:   for (i = 0; i < m; i++) {
    4985:     bnzi = 0;
    4986:     /* add local non-zero cols of this proc's seqmat into lnk */
    4987:     arow = owners[rank] + i;
    4988:     anzi = ai[arow + 1] - ai[arow];
    4989:     aj   = a->j + ai[arow];
    4990:     PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
    4991:     bnzi += nlnk;
    4992:     /* add received col data into lnk */
    4993:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    4994:       if (i == *nextrow[k]) {            /* i-th row */
    4995:         anzi = *(nextai[k] + 1) - *nextai[k];
    4996:         aj   = buf_rj[k] + *nextai[k];
    4997:         PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
    4998:         bnzi += nlnk;
    4999:         nextrow[k]++;
    5000:         nextai[k]++;
    5001:       }
    5002:     }
    5003:     if (len < bnzi) len = bnzi; /* =max(bnzi) */

    5005:     /* if free space is not available, make more free space */
    5006:     if (current_space->local_remaining < bnzi) PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(bnzi, current_space->total_array_size), &current_space));
    5007:     /* copy data into free space, then initialize lnk */
    5008:     PetscCall(PetscLLClean(N, N, bnzi, lnk, current_space->array, lnkbt));
    5009:     PetscCall(MatPreallocateSet(i + owners[rank], bnzi, current_space->array, dnz, onz));

    5011:     current_space->array += bnzi;
    5012:     current_space->local_used += bnzi;
    5013:     current_space->local_remaining -= bnzi;

    5015:     bi[i + 1] = bi[i] + bnzi;
    5016:   }

    5018:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));

    5020:   PetscCall(PetscMalloc1(bi[m] + 1, &bj));
    5021:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
    5022:   PetscCall(PetscLLDestroy(lnk, lnkbt));

    5024:   /* create symbolic parallel matrix B_mpi */
    5025:   PetscCall(MatGetBlockSizes(seqmat, &bs, &cbs));
    5026:   PetscCall(MatCreate(comm, &B_mpi));
    5027:   if (n == PETSC_DECIDE) {
    5028:     PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, N));
    5029:   } else {
    5030:     PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    5031:   }
    5032:   PetscCall(MatSetBlockSizes(B_mpi, bs, cbs));
    5033:   PetscCall(MatSetType(B_mpi, MATMPIAIJ));
    5034:   PetscCall(MatMPIAIJSetPreallocation(B_mpi, 0, dnz, 0, onz));
    5035:   MatPreallocateEnd(dnz, onz);
    5036:   PetscCall(MatSetOption(B_mpi, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));

    5038:   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
    5039:   B_mpi->assembled = PETSC_FALSE;
    5040:   merge->bi        = bi;
    5041:   merge->bj        = bj;
    5042:   merge->buf_ri    = buf_ri;
    5043:   merge->buf_rj    = buf_rj;
    5044:   merge->coi       = NULL;
    5045:   merge->coj       = NULL;
    5046:   merge->owners_co = NULL;

    5048:   PetscCall(PetscCommDestroy(&comm));

    5050:   /* attach the supporting struct to B_mpi for reuse */
    5051:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    5052:   PetscCall(PetscContainerSetPointer(container, merge));
    5053:   PetscCall(PetscContainerSetCtxDestroy(container, MatDestroy_MPIAIJ_SeqsToMPI));
    5054:   PetscCall(PetscObjectCompose((PetscObject)B_mpi, "MatMergeSeqsToMPI", (PetscObject)container));
    5055:   PetscCall(PetscContainerDestroy(&container));
    5056:   *mpimat = B_mpi;

    5058:   PetscCall(PetscLogEventEnd(MAT_Seqstompisym, seqmat, 0, 0, 0));
    5059:   PetscFunctionReturn(PETSC_SUCCESS);
    5060: }

    5062: /*@
    5063:   MatCreateMPIAIJSumSeqAIJ - Creates a `MATMPIAIJ` matrix by adding sequential
    5064:   matrices from each processor

    5066:   Collective

    5068:   Input Parameters:
    5069: + comm   - the communicators the parallel matrix will live on
    5070: . seqmat - the input sequential matrices
    5071: . m      - number of local rows (or `PETSC_DECIDE`)
    5072: . n      - number of local columns (or `PETSC_DECIDE`)
    5073: - scall  - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5075:   Output Parameter:
    5076: . mpimat - the parallel matrix generated

    5078:   Level: advanced

    5080:   Note:
    5081:   The dimensions of the sequential matrix in each processor MUST be the same.
    5082:   The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
    5083:   destroyed when `mpimat` is destroyed. Call `PetscObjectQuery()` to access `seqmat`.

    5085: .seealso: [](ch_matrices), `Mat`, `MatCreateAIJ()`
    5086: @*/
    5087: PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, MatReuse scall, Mat *mpimat)
    5088: {
    5089:   PetscMPIInt size;

    5091:   PetscFunctionBegin;
    5092:   PetscCallMPI(MPI_Comm_size(comm, &size));
    5093:   if (size == 1) {
    5094:     PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
    5095:     if (scall == MAT_INITIAL_MATRIX) {
    5096:       PetscCall(MatDuplicate(seqmat, MAT_COPY_VALUES, mpimat));
    5097:     } else {
    5098:       PetscCall(MatCopy(seqmat, *mpimat, SAME_NONZERO_PATTERN));
    5099:     }
    5100:     PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
    5101:     PetscFunctionReturn(PETSC_SUCCESS);
    5102:   }
    5103:   PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
    5104:   if (scall == MAT_INITIAL_MATRIX) PetscCall(MatCreateMPIAIJSumSeqAIJSymbolic(comm, seqmat, m, n, mpimat));
    5105:   PetscCall(MatCreateMPIAIJSumSeqAIJNumeric(seqmat, *mpimat));
    5106:   PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
    5107:   PetscFunctionReturn(PETSC_SUCCESS);
    5108: }

    5110: /*@
    5111:   MatAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATAIJ` matrix.

    5113:   Not Collective

    5115:   Input Parameter:
    5116: . A - the matrix

    5118:   Output Parameter:
    5119: . A_loc - the local sequential matrix generated

    5121:   Level: developer

    5123:   Notes:
    5124:   The matrix is created by taking `A`'s local rows and putting them into a sequential matrix
    5125:   with `mlocal` rows and `n` columns. Where `mlocal` is obtained with `MatGetLocalSize()` and
    5126:   `n` is the global column count obtained with `MatGetSize()`

    5128:   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.

    5130:   For parallel matrices this creates an entirely new matrix. If the matrix is sequential it merely increases the reference count.

    5132:   Destroy the matrix with `MatDestroy()`

    5134: .seealso: [](ch_matrices), `Mat`, `MatMPIAIJGetLocalMat()`
    5135: @*/
    5136: PetscErrorCode MatAIJGetLocalMat(Mat A, Mat *A_loc)
    5137: {
    5138:   PetscBool mpi;

    5140:   PetscFunctionBegin;
    5141:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &mpi));
    5142:   if (mpi) {
    5143:     PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, A_loc));
    5144:   } else {
    5145:     *A_loc = A;
    5146:     PetscCall(PetscObjectReference((PetscObject)*A_loc));
    5147:   }
    5148:   PetscFunctionReturn(PETSC_SUCCESS);
    5149: }

    5151: /*@
    5152:   MatMPIAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix.

    5154:   Not Collective

    5156:   Input Parameters:
    5157: + A     - the matrix
    5158: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5160:   Output Parameter:
    5161: . A_loc - the local sequential matrix generated

    5163:   Level: developer

    5165:   Notes:
    5166:   The matrix is created by taking all `A`'s local rows and putting them into a sequential
    5167:   matrix with `mlocal` rows and `n` columns.`mlocal` is the row count obtained with
    5168:   `MatGetLocalSize()` and `n` is the global column count obtained with `MatGetSize()`.

    5170:   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.

    5172:   When `A` is sequential and `MAT_INITIAL_MATRIX` is requested, the matrix returned is the diagonal part of `A` (which contains the entire matrix),
    5173:   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
    5174:   then `MatCopy`(Adiag,*`A_loc`,`SAME_NONZERO_PATTERN`) is called to fill `A_loc`. Thus one can preallocate the appropriate sequential matrix `A_loc`
    5175:   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.

    5177: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMatCondensed()`, `MatMPIAIJGetLocalMatMerge()`
    5178: @*/
    5179: PetscErrorCode MatMPIAIJGetLocalMat(Mat A, MatReuse scall, Mat *A_loc)
    5180: {
    5181:   Mat_MPIAIJ        *mpimat = (Mat_MPIAIJ *)A->data;
    5182:   Mat_SeqAIJ        *mat, *a, *b;
    5183:   PetscInt          *ai, *aj, *bi, *bj, *cmap = mpimat->garray;
    5184:   const PetscScalar *aa, *ba, *aav, *bav;
    5185:   PetscScalar       *ca, *cam;
    5186:   PetscMPIInt        size;
    5187:   PetscInt           am = A->rmap->n, i, j, k, cstart = A->cmap->rstart;
    5188:   PetscInt          *ci, *cj, col, ncols_d, ncols_o, jo;
    5189:   PetscBool          match;

    5191:   PetscFunctionBegin;
    5192:   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &match));
    5193:   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
    5194:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    5195:   if (size == 1) {
    5196:     if (scall == MAT_INITIAL_MATRIX) {
    5197:       PetscCall(PetscObjectReference((PetscObject)mpimat->A));
    5198:       *A_loc = mpimat->A;
    5199:     } else if (scall == MAT_REUSE_MATRIX) {
    5200:       PetscCall(MatCopy(mpimat->A, *A_loc, SAME_NONZERO_PATTERN));
    5201:     }
    5202:     PetscFunctionReturn(PETSC_SUCCESS);
    5203:   }

    5205:   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
    5206:   a  = (Mat_SeqAIJ *)mpimat->A->data;
    5207:   b  = (Mat_SeqAIJ *)mpimat->B->data;
    5208:   ai = a->i;
    5209:   aj = a->j;
    5210:   bi = b->i;
    5211:   bj = b->j;
    5212:   PetscCall(MatSeqAIJGetArrayRead(mpimat->A, &aav));
    5213:   PetscCall(MatSeqAIJGetArrayRead(mpimat->B, &bav));
    5214:   aa = aav;
    5215:   ba = bav;
    5216:   if (scall == MAT_INITIAL_MATRIX) {
    5217:     PetscCall(PetscMalloc1(1 + am, &ci));
    5218:     ci[0] = 0;
    5219:     for (i = 0; i < am; i++) ci[i + 1] = ci[i] + (ai[i + 1] - ai[i]) + (bi[i + 1] - bi[i]);
    5220:     PetscCall(PetscMalloc1(1 + ci[am], &cj));
    5221:     PetscCall(PetscMalloc1(1 + ci[am], &ca));
    5222:     k = 0;
    5223:     for (i = 0; i < am; i++) {
    5224:       ncols_o = bi[i + 1] - bi[i];
    5225:       ncols_d = ai[i + 1] - ai[i];
    5226:       /* off-diagonal portion of A */
    5227:       for (jo = 0; jo < ncols_o; jo++) {
    5228:         col = cmap[*bj];
    5229:         if (col >= cstart) break;
    5230:         cj[k] = col;
    5231:         bj++;
    5232:         ca[k++] = *ba++;
    5233:       }
    5234:       /* diagonal portion of A */
    5235:       for (j = 0; j < ncols_d; j++) {
    5236:         cj[k]   = cstart + *aj++;
    5237:         ca[k++] = *aa++;
    5238:       }
    5239:       /* off-diagonal portion of A */
    5240:       for (j = jo; j < ncols_o; j++) {
    5241:         cj[k]   = cmap[*bj++];
    5242:         ca[k++] = *ba++;
    5243:       }
    5244:     }
    5245:     /* put together the new matrix */
    5246:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, A->cmap->N, ci, cj, ca, A_loc));
    5247:     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5248:     /* Since these are PETSc arrays, change flags to free them as necessary. */
    5249:     mat          = (Mat_SeqAIJ *)(*A_loc)->data;
    5250:     mat->free_a  = PETSC_TRUE;
    5251:     mat->free_ij = PETSC_TRUE;
    5252:     mat->nonew   = 0;
    5253:   } else if (scall == MAT_REUSE_MATRIX) {
    5254:     mat = (Mat_SeqAIJ *)(*A_loc)->data;
    5255:     ci  = mat->i;
    5256:     cj  = mat->j;
    5257:     PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &cam));
    5258:     for (i = 0; i < am; i++) {
    5259:       /* off-diagonal portion of A */
    5260:       ncols_o = bi[i + 1] - bi[i];
    5261:       for (jo = 0; jo < ncols_o; jo++) {
    5262:         col = cmap[*bj];
    5263:         if (col >= cstart) break;
    5264:         *cam++ = *ba++;
    5265:         bj++;
    5266:       }
    5267:       /* diagonal portion of A */
    5268:       ncols_d = ai[i + 1] - ai[i];
    5269:       for (j = 0; j < ncols_d; j++) *cam++ = *aa++;
    5270:       /* off-diagonal portion of A */
    5271:       for (j = jo; j < ncols_o; j++) {
    5272:         *cam++ = *ba++;
    5273:         bj++;
    5274:       }
    5275:     }
    5276:     PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &cam));
    5277:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
    5278:   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->A, &aav));
    5279:   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->B, &bav));
    5280:   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
    5281:   PetscFunctionReturn(PETSC_SUCCESS);
    5282: }

    5284: /*@
    5285:   MatMPIAIJGetLocalMatMerge - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix by taking all its local rows and putting them into a sequential matrix with
    5286:   mlocal rows and n columns. Where n is the sum of the number of columns of the diagonal and off-diagonal part

    5288:   Not Collective

    5290:   Input Parameters:
    5291: + A     - the matrix
    5292: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5294:   Output Parameters:
    5295: + glob  - sequential `IS` with global indices associated with the columns of the local sequential matrix generated (can be `NULL`)
    5296: - A_loc - the local sequential matrix generated

    5298:   Level: developer

    5300:   Note:
    5301:   This is different from `MatMPIAIJGetLocalMat()` since the first columns in the returning matrix are those associated with the diagonal
    5302:   part, then those associated with the off-diagonal part (in its local ordering)

    5304: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`
    5305: @*/
    5306: PetscErrorCode MatMPIAIJGetLocalMatMerge(Mat A, MatReuse scall, IS *glob, Mat *A_loc)
    5307: {
    5308:   Mat             Ao, Ad;
    5309:   const PetscInt *cmap;
    5310:   PetscMPIInt     size;
    5311:   PetscErrorCode (*f)(Mat, MatReuse, IS *, Mat *);

    5313:   PetscFunctionBegin;
    5314:   PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &cmap));
    5315:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    5316:   if (size == 1) {
    5317:     if (scall == MAT_INITIAL_MATRIX) {
    5318:       PetscCall(PetscObjectReference((PetscObject)Ad));
    5319:       *A_loc = Ad;
    5320:     } else if (scall == MAT_REUSE_MATRIX) {
    5321:       PetscCall(MatCopy(Ad, *A_loc, SAME_NONZERO_PATTERN));
    5322:     }
    5323:     if (glob) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)Ad), Ad->cmap->n, Ad->cmap->rstart, 1, glob));
    5324:     PetscFunctionReturn(PETSC_SUCCESS);
    5325:   }
    5326:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatMPIAIJGetLocalMatMerge_C", &f));
    5327:   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
    5328:   if (f) {
    5329:     PetscCall((*f)(A, scall, glob, A_loc));
    5330:   } else {
    5331:     Mat_SeqAIJ        *a = (Mat_SeqAIJ *)Ad->data;
    5332:     Mat_SeqAIJ        *b = (Mat_SeqAIJ *)Ao->data;
    5333:     Mat_SeqAIJ        *c;
    5334:     PetscInt          *ai = a->i, *aj = a->j;
    5335:     PetscInt          *bi = b->i, *bj = b->j;
    5336:     PetscInt          *ci, *cj;
    5337:     const PetscScalar *aa, *ba;
    5338:     PetscScalar       *ca;
    5339:     PetscInt           i, j, am, dn, on;

    5341:     PetscCall(MatGetLocalSize(Ad, &am, &dn));
    5342:     PetscCall(MatGetLocalSize(Ao, NULL, &on));
    5343:     PetscCall(MatSeqAIJGetArrayRead(Ad, &aa));
    5344:     PetscCall(MatSeqAIJGetArrayRead(Ao, &ba));
    5345:     if (scall == MAT_INITIAL_MATRIX) {
    5346:       PetscInt k;
    5347:       PetscCall(PetscMalloc1(1 + am, &ci));
    5348:       PetscCall(PetscMalloc1(ai[am] + bi[am], &cj));
    5349:       PetscCall(PetscMalloc1(ai[am] + bi[am], &ca));
    5350:       ci[0] = 0;
    5351:       for (i = 0, k = 0; i < am; i++) {
    5352:         const PetscInt ncols_o = bi[i + 1] - bi[i];
    5353:         const PetscInt ncols_d = ai[i + 1] - ai[i];
    5354:         ci[i + 1]              = ci[i] + ncols_o + ncols_d;
    5355:         /* diagonal portion of A */
    5356:         for (j = 0; j < ncols_d; j++, k++) {
    5357:           cj[k] = *aj++;
    5358:           ca[k] = *aa++;
    5359:         }
    5360:         /* off-diagonal portion of A */
    5361:         for (j = 0; j < ncols_o; j++, k++) {
    5362:           cj[k] = dn + *bj++;
    5363:           ca[k] = *ba++;
    5364:         }
    5365:       }
    5366:       /* put together the new matrix */
    5367:       PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, dn + on, ci, cj, ca, A_loc));
    5368:       /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5369:       /* Since these are PETSc arrays, change flags to free them as necessary. */
    5370:       c          = (Mat_SeqAIJ *)(*A_loc)->data;
    5371:       c->free_a  = PETSC_TRUE;
    5372:       c->free_ij = PETSC_TRUE;
    5373:       c->nonew   = 0;
    5374:       PetscCall(MatSetType(*A_loc, ((PetscObject)Ad)->type_name));
    5375:     } else if (scall == MAT_REUSE_MATRIX) {
    5376:       PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &ca));
    5377:       for (i = 0; i < am; i++) {
    5378:         const PetscInt ncols_d = ai[i + 1] - ai[i];
    5379:         const PetscInt ncols_o = bi[i + 1] - bi[i];
    5380:         /* diagonal portion of A */
    5381:         for (j = 0; j < ncols_d; j++) *ca++ = *aa++;
    5382:         /* off-diagonal portion of A */
    5383:         for (j = 0; j < ncols_o; j++) *ca++ = *ba++;
    5384:       }
    5385:       PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &ca));
    5386:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
    5387:     PetscCall(MatSeqAIJRestoreArrayRead(Ad, &aa));
    5388:     PetscCall(MatSeqAIJRestoreArrayRead(Ao, &aa));
    5389:     if (glob) {
    5390:       PetscInt cst, *gidx;

    5392:       PetscCall(MatGetOwnershipRangeColumn(A, &cst, NULL));
    5393:       PetscCall(PetscMalloc1(dn + on, &gidx));
    5394:       for (i = 0; i < dn; i++) gidx[i] = cst + i;
    5395:       for (i = 0; i < on; i++) gidx[i + dn] = cmap[i];
    5396:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)Ad), dn + on, gidx, PETSC_OWN_POINTER, glob));
    5397:     }
    5398:   }
    5399:   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
    5400:   PetscFunctionReturn(PETSC_SUCCESS);
    5401: }

    5403: /*@C
    5404:   MatMPIAIJGetLocalMatCondensed - Creates a `MATSEQAIJ` matrix from an `MATMPIAIJ` matrix by taking all its local rows and NON-ZERO columns

    5406:   Not Collective

    5408:   Input Parameters:
    5409: + A     - the matrix
    5410: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    5411: . row   - index set of rows to extract (or `NULL`)
    5412: - col   - index set of columns to extract (or `NULL`)

    5414:   Output Parameter:
    5415: . A_loc - the local sequential matrix generated

    5417:   Level: developer

    5419: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`
    5420: @*/
    5421: PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A, MatReuse scall, IS *row, IS *col, Mat *A_loc)
    5422: {
    5423:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    5424:   PetscInt    i, start, end, ncols, nzA, nzB, *cmap, imark, *idx;
    5425:   IS          isrowa, iscola;
    5426:   Mat        *aloc;
    5427:   PetscBool   match;

    5429:   PetscFunctionBegin;
    5430:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &match));
    5431:   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
    5432:   PetscCall(PetscLogEventBegin(MAT_Getlocalmatcondensed, A, 0, 0, 0));
    5433:   if (!row) {
    5434:     start = A->rmap->rstart;
    5435:     end   = A->rmap->rend;
    5436:     PetscCall(ISCreateStride(PETSC_COMM_SELF, end - start, start, 1, &isrowa));
    5437:   } else {
    5438:     isrowa = *row;
    5439:   }
    5440:   if (!col) {
    5441:     start = A->cmap->rstart;
    5442:     cmap  = a->garray;
    5443:     nzA   = a->A->cmap->n;
    5444:     nzB   = a->B->cmap->n;
    5445:     PetscCall(PetscMalloc1(nzA + nzB, &idx));
    5446:     ncols = 0;
    5447:     for (i = 0; i < nzB; i++) {
    5448:       if (cmap[i] < start) idx[ncols++] = cmap[i];
    5449:       else break;
    5450:     }
    5451:     imark = i;
    5452:     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;
    5453:     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i];
    5454:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &iscola));
    5455:   } else {
    5456:     iscola = *col;
    5457:   }
    5458:   if (scall != MAT_INITIAL_MATRIX) {
    5459:     PetscCall(PetscMalloc1(1, &aloc));
    5460:     aloc[0] = *A_loc;
    5461:   }
    5462:   PetscCall(MatCreateSubMatrices(A, 1, &isrowa, &iscola, scall, &aloc));
    5463:   if (!col) { /* attach global id of condensed columns */
    5464:     PetscCall(PetscObjectCompose((PetscObject)aloc[0], "_petsc_GetLocalMatCondensed_iscol", (PetscObject)iscola));
    5465:   }
    5466:   *A_loc = aloc[0];
    5467:   PetscCall(PetscFree(aloc));
    5468:   if (!row) PetscCall(ISDestroy(&isrowa));
    5469:   if (!col) PetscCall(ISDestroy(&iscola));
    5470:   PetscCall(PetscLogEventEnd(MAT_Getlocalmatcondensed, A, 0, 0, 0));
    5471:   PetscFunctionReturn(PETSC_SUCCESS);
    5472: }

    5474: /*
    5475:  * Create a sequential AIJ matrix based on row indices. a whole column is extracted once a row is matched.
    5476:  * Row could be local or remote.The routine is designed to be scalable in memory so that nothing is based
    5477:  * on a global size.
    5478:  * */
    5479: static PetscErrorCode MatCreateSeqSubMatrixWithRows_Private(Mat P, IS rows, Mat *P_oth)
    5480: {
    5481:   Mat_MPIAIJ            *p  = (Mat_MPIAIJ *)P->data;
    5482:   Mat_SeqAIJ            *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data, *p_oth;
    5483:   PetscInt               plocalsize, nrows, *ilocal, *oilocal, i, lidx, *nrcols, *nlcols, ncol;
    5484:   PetscMPIInt            owner;
    5485:   PetscSFNode           *iremote, *oiremote;
    5486:   const PetscInt        *lrowindices;
    5487:   PetscSF                sf, osf;
    5488:   PetscInt               pcstart, *roffsets, *loffsets, *pnnz, j;
    5489:   PetscInt               ontotalcols, dntotalcols, ntotalcols, nout;
    5490:   MPI_Comm               comm;
    5491:   ISLocalToGlobalMapping mapping;
    5492:   const PetscScalar     *pd_a, *po_a;

    5494:   PetscFunctionBegin;
    5495:   PetscCall(PetscObjectGetComm((PetscObject)P, &comm));
    5496:   /* plocalsize is the number of roots
    5497:    * nrows is the number of leaves
    5498:    * */
    5499:   PetscCall(MatGetLocalSize(P, &plocalsize, NULL));
    5500:   PetscCall(ISGetLocalSize(rows, &nrows));
    5501:   PetscCall(PetscCalloc1(nrows, &iremote));
    5502:   PetscCall(ISGetIndices(rows, &lrowindices));
    5503:   for (i = 0; i < nrows; i++) {
    5504:     /* Find a remote index and an owner for a row
    5505:      * The row could be local or remote
    5506:      * */
    5507:     owner = 0;
    5508:     lidx  = 0;
    5509:     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, &lidx));
    5510:     iremote[i].index = lidx;
    5511:     iremote[i].rank  = owner;
    5512:   }
    5513:   /* Create SF to communicate how many nonzero columns for each row */
    5514:   PetscCall(PetscSFCreate(comm, &sf));
    5515:   /* SF will figure out the number of nonzero columns for each row, and their
    5516:    * offsets
    5517:    * */
    5518:   PetscCall(PetscSFSetGraph(sf, plocalsize, nrows, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    5519:   PetscCall(PetscSFSetFromOptions(sf));
    5520:   PetscCall(PetscSFSetUp(sf));

    5522:   PetscCall(PetscCalloc1(2 * (plocalsize + 1), &roffsets));
    5523:   PetscCall(PetscCalloc1(2 * plocalsize, &nrcols));
    5524:   PetscCall(PetscCalloc1(nrows, &pnnz));
    5525:   roffsets[0] = 0;
    5526:   roffsets[1] = 0;
    5527:   for (i = 0; i < plocalsize; i++) {
    5528:     /* diagonal */
    5529:     nrcols[i * 2 + 0] = pd->i[i + 1] - pd->i[i];
    5530:     /* off-diagonal */
    5531:     nrcols[i * 2 + 1] = po->i[i + 1] - po->i[i];
    5532:     /* compute offsets so that we relative location for each row */
    5533:     roffsets[(i + 1) * 2 + 0] = roffsets[i * 2 + 0] + nrcols[i * 2 + 0];
    5534:     roffsets[(i + 1) * 2 + 1] = roffsets[i * 2 + 1] + nrcols[i * 2 + 1];
    5535:   }
    5536:   PetscCall(PetscCalloc1(2 * nrows, &nlcols));
    5537:   PetscCall(PetscCalloc1(2 * nrows, &loffsets));
    5538:   /* 'r' means root, and 'l' means leaf */
    5539:   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
    5540:   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
    5541:   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
    5542:   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
    5543:   PetscCall(PetscSFDestroy(&sf));
    5544:   PetscCall(PetscFree(roffsets));
    5545:   PetscCall(PetscFree(nrcols));
    5546:   dntotalcols = 0;
    5547:   ontotalcols = 0;
    5548:   ncol        = 0;
    5549:   for (i = 0; i < nrows; i++) {
    5550:     pnnz[i] = nlcols[i * 2 + 0] + nlcols[i * 2 + 1];
    5551:     ncol    = PetscMax(pnnz[i], ncol);
    5552:     /* diagonal */
    5553:     dntotalcols += nlcols[i * 2 + 0];
    5554:     /* off-diagonal */
    5555:     ontotalcols += nlcols[i * 2 + 1];
    5556:   }
    5557:   /* We do not need to figure the right number of columns
    5558:    * since all the calculations will be done by going through the raw data
    5559:    * */
    5560:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nrows, ncol, 0, pnnz, P_oth));
    5561:   PetscCall(MatSetUp(*P_oth));
    5562:   PetscCall(PetscFree(pnnz));
    5563:   p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
    5564:   /* diagonal */
    5565:   PetscCall(PetscCalloc1(dntotalcols, &iremote));
    5566:   /* off-diagonal */
    5567:   PetscCall(PetscCalloc1(ontotalcols, &oiremote));
    5568:   /* diagonal */
    5569:   PetscCall(PetscCalloc1(dntotalcols, &ilocal));
    5570:   /* off-diagonal */
    5571:   PetscCall(PetscCalloc1(ontotalcols, &oilocal));
    5572:   dntotalcols = 0;
    5573:   ontotalcols = 0;
    5574:   ntotalcols  = 0;
    5575:   for (i = 0; i < nrows; i++) {
    5576:     owner = 0;
    5577:     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, NULL));
    5578:     /* Set iremote for diag matrix */
    5579:     for (j = 0; j < nlcols[i * 2 + 0]; j++) {
    5580:       iremote[dntotalcols].index = loffsets[i * 2 + 0] + j;
    5581:       iremote[dntotalcols].rank  = owner;
    5582:       /* P_oth is seqAIJ so that ilocal need to point to the first part of memory */
    5583:       ilocal[dntotalcols++] = ntotalcols++;
    5584:     }
    5585:     /* off-diagonal */
    5586:     for (j = 0; j < nlcols[i * 2 + 1]; j++) {
    5587:       oiremote[ontotalcols].index = loffsets[i * 2 + 1] + j;
    5588:       oiremote[ontotalcols].rank  = owner;
    5589:       oilocal[ontotalcols++]      = ntotalcols++;
    5590:     }
    5591:   }
    5592:   PetscCall(ISRestoreIndices(rows, &lrowindices));
    5593:   PetscCall(PetscFree(loffsets));
    5594:   PetscCall(PetscFree(nlcols));
    5595:   PetscCall(PetscSFCreate(comm, &sf));
    5596:   /* P serves as roots and P_oth is leaves
    5597:    * Diag matrix
    5598:    * */
    5599:   PetscCall(PetscSFSetGraph(sf, pd->i[plocalsize], dntotalcols, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    5600:   PetscCall(PetscSFSetFromOptions(sf));
    5601:   PetscCall(PetscSFSetUp(sf));

    5603:   PetscCall(PetscSFCreate(comm, &osf));
    5604:   /* off-diagonal */
    5605:   PetscCall(PetscSFSetGraph(osf, po->i[plocalsize], ontotalcols, oilocal, PETSC_OWN_POINTER, oiremote, PETSC_OWN_POINTER));
    5606:   PetscCall(PetscSFSetFromOptions(osf));
    5607:   PetscCall(PetscSFSetUp(osf));
    5608:   PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
    5609:   PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
    5610:   /* operate on the matrix internal data to save memory */
    5611:   PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5612:   PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5613:   PetscCall(MatGetOwnershipRangeColumn(P, &pcstart, NULL));
    5614:   /* Convert to global indices for diag matrix */
    5615:   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] += pcstart;
    5616:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
    5617:   /* We want P_oth store global indices */
    5618:   PetscCall(ISLocalToGlobalMappingCreate(comm, 1, p->B->cmap->n, p->garray, PETSC_COPY_VALUES, &mapping));
    5619:   /* Use memory scalable approach */
    5620:   PetscCall(ISLocalToGlobalMappingSetType(mapping, ISLOCALTOGLOBALMAPPINGHASH));
    5621:   PetscCall(ISLocalToGlobalMappingApply(mapping, po->i[plocalsize], po->j, po->j));
    5622:   PetscCall(PetscSFBcastBegin(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
    5623:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
    5624:   /* Convert back to local indices */
    5625:   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] -= pcstart;
    5626:   PetscCall(PetscSFBcastEnd(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
    5627:   nout = 0;
    5628:   PetscCall(ISGlobalToLocalMappingApply(mapping, IS_GTOLM_DROP, po->i[plocalsize], po->j, &nout, po->j));
    5629:   PetscCheck(nout == po->i[plocalsize], comm, PETSC_ERR_ARG_INCOMP, "n %" PetscInt_FMT " does not equal to nout %" PetscInt_FMT " ", po->i[plocalsize], nout);
    5630:   PetscCall(ISLocalToGlobalMappingDestroy(&mapping));
    5631:   /* Exchange values */
    5632:   PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5633:   PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5634:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
    5635:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
    5636:   /* Stop PETSc from shrinking memory */
    5637:   for (i = 0; i < nrows; i++) p_oth->ilen[i] = p_oth->imax[i];
    5638:   PetscCall(MatAssemblyBegin(*P_oth, MAT_FINAL_ASSEMBLY));
    5639:   PetscCall(MatAssemblyEnd(*P_oth, MAT_FINAL_ASSEMBLY));
    5640:   /* Attach PetscSF objects to P_oth so that we can reuse it later */
    5641:   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "diagsf", (PetscObject)sf));
    5642:   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "offdiagsf", (PetscObject)osf));
    5643:   PetscCall(PetscSFDestroy(&sf));
    5644:   PetscCall(PetscSFDestroy(&osf));
    5645:   PetscFunctionReturn(PETSC_SUCCESS);
    5646: }

    5648: /*
    5649:  * Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
    5650:  * This supports MPIAIJ and MAIJ
    5651:  * */
    5652: PetscErrorCode MatGetBrowsOfAcols_MPIXAIJ(Mat A, Mat P, PetscInt dof, MatReuse reuse, Mat *P_oth)
    5653: {
    5654:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data, *p = (Mat_MPIAIJ *)P->data;
    5655:   Mat_SeqAIJ *p_oth;
    5656:   IS          rows, map;
    5657:   PetscHMapI  hamp;
    5658:   PetscInt    i, htsize, *rowindices, off, *mapping, key, count;
    5659:   MPI_Comm    comm;
    5660:   PetscSF     sf, osf;
    5661:   PetscBool   has;

    5663:   PetscFunctionBegin;
    5664:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    5665:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, P, 0, 0));
    5666:   /* If it is the first time, create an index set of off-diag nonzero columns of A,
    5667:    *  and then create a submatrix (that often is an overlapping matrix)
    5668:    * */
    5669:   if (reuse == MAT_INITIAL_MATRIX) {
    5670:     /* Use a hash table to figure out unique keys */
    5671:     PetscCall(PetscHMapICreateWithSize(a->B->cmap->n, &hamp));
    5672:     PetscCall(PetscCalloc1(a->B->cmap->n, &mapping));
    5673:     count = 0;
    5674:     /* Assume that  a->g is sorted, otherwise the following does not make sense */
    5675:     for (i = 0; i < a->B->cmap->n; i++) {
    5676:       key = a->garray[i] / dof;
    5677:       PetscCall(PetscHMapIHas(hamp, key, &has));
    5678:       if (!has) {
    5679:         mapping[i] = count;
    5680:         PetscCall(PetscHMapISet(hamp, key, count++));
    5681:       } else {
    5682:         /* Current 'i' has the same value the previous step */
    5683:         mapping[i] = count - 1;
    5684:       }
    5685:     }
    5686:     PetscCall(ISCreateGeneral(comm, a->B->cmap->n, mapping, PETSC_OWN_POINTER, &map));
    5687:     PetscCall(PetscHMapIGetSize(hamp, &htsize));
    5688:     PetscCheck(htsize == count, comm, PETSC_ERR_ARG_INCOMP, " Size of hash map %" PetscInt_FMT " is inconsistent with count %" PetscInt_FMT, htsize, count);
    5689:     PetscCall(PetscCalloc1(htsize, &rowindices));
    5690:     off = 0;
    5691:     PetscCall(PetscHMapIGetKeys(hamp, &off, rowindices));
    5692:     PetscCall(PetscHMapIDestroy(&hamp));
    5693:     PetscCall(PetscSortInt(htsize, rowindices));
    5694:     PetscCall(ISCreateGeneral(comm, htsize, rowindices, PETSC_OWN_POINTER, &rows));
    5695:     /* In case, the matrix was already created but users want to recreate the matrix */
    5696:     PetscCall(MatDestroy(P_oth));
    5697:     PetscCall(MatCreateSeqSubMatrixWithRows_Private(P, rows, P_oth));
    5698:     PetscCall(PetscObjectCompose((PetscObject)*P_oth, "aoffdiagtopothmapping", (PetscObject)map));
    5699:     PetscCall(ISDestroy(&map));
    5700:     PetscCall(ISDestroy(&rows));
    5701:   } else if (reuse == MAT_REUSE_MATRIX) {
    5702:     /* If matrix was already created, we simply update values using SF objects
    5703:      * that as attached to the matrix earlier.
    5704:      */
    5705:     const PetscScalar *pd_a, *po_a;

    5707:     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "diagsf", (PetscObject *)&sf));
    5708:     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "offdiagsf", (PetscObject *)&osf));
    5709:     PetscCheck(sf && osf, comm, PETSC_ERR_ARG_NULL, "Matrix is not initialized yet");
    5710:     p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
    5711:     /* Update values in place */
    5712:     PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
    5713:     PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
    5714:     PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5715:     PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5716:     PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5717:     PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5718:     PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
    5719:     PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
    5720:   } else SETERRQ(comm, PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown reuse type");
    5721:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, P, 0, 0));
    5722:   PetscFunctionReturn(PETSC_SUCCESS);
    5723: }

    5725: /*@C
    5726:   MatGetBrowsOfAcols - Returns `IS` that contain rows of `B` that equal to nonzero columns of local `A`

    5728:   Collective

    5730:   Input Parameters:
    5731: + A     - the first matrix in `MATMPIAIJ` format
    5732: . B     - the second matrix in `MATMPIAIJ` format
    5733: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5735:   Output Parameters:
    5736: + rowb  - On input index sets of rows of B to extract (or `NULL`), modified on output
    5737: . colb  - On input index sets of columns of B to extract (or `NULL`), modified on output
    5738: - B_seq - the sequential matrix generated

    5740:   Level: developer

    5742: .seealso: `Mat`, `MATMPIAIJ`, `IS`, `MatReuse`
    5743: @*/
    5744: PetscErrorCode MatGetBrowsOfAcols(Mat A, Mat B, MatReuse scall, IS *rowb, IS *colb, Mat *B_seq)
    5745: {
    5746:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    5747:   PetscInt   *idx, i, start, ncols, nzA, nzB, *cmap, imark;
    5748:   IS          isrowb, iscolb;
    5749:   Mat        *bseq = NULL;

    5751:   PetscFunctionBegin;
    5752:   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 ")",
    5753:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    5754:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAcols, A, B, 0, 0));

    5756:   if (scall == MAT_INITIAL_MATRIX) {
    5757:     start = A->cmap->rstart;
    5758:     cmap  = a->garray;
    5759:     nzA   = a->A->cmap->n;
    5760:     nzB   = a->B->cmap->n;
    5761:     PetscCall(PetscMalloc1(nzA + nzB, &idx));
    5762:     ncols = 0;
    5763:     for (i = 0; i < nzB; i++) { /* row < local row index */
    5764:       if (cmap[i] < start) idx[ncols++] = cmap[i];
    5765:       else break;
    5766:     }
    5767:     imark = i;
    5768:     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;   /* local rows */
    5769:     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
    5770:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &isrowb));
    5771:     PetscCall(ISCreateStride(PETSC_COMM_SELF, B->cmap->N, 0, 1, &iscolb));
    5772:   } else {
    5773:     PetscCheck(rowb && colb, PETSC_COMM_SELF, PETSC_ERR_SUP, "IS rowb and colb must be provided for MAT_REUSE_MATRIX");
    5774:     isrowb = *rowb;
    5775:     iscolb = *colb;
    5776:     PetscCall(PetscMalloc1(1, &bseq));
    5777:     bseq[0] = *B_seq;
    5778:   }
    5779:   PetscCall(MatCreateSubMatrices(B, 1, &isrowb, &iscolb, scall, &bseq));
    5780:   *B_seq = bseq[0];
    5781:   PetscCall(PetscFree(bseq));
    5782:   if (!rowb) {
    5783:     PetscCall(ISDestroy(&isrowb));
    5784:   } else {
    5785:     *rowb = isrowb;
    5786:   }
    5787:   if (!colb) {
    5788:     PetscCall(ISDestroy(&iscolb));
    5789:   } else {
    5790:     *colb = iscolb;
    5791:   }
    5792:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAcols, A, B, 0, 0));
    5793:   PetscFunctionReturn(PETSC_SUCCESS);
    5794: }

    5796: /*
    5797:     MatGetBrowsOfAoCols_MPIAIJ - Creates a `MATSEQAIJ` matrix by taking rows of B that equal to nonzero columns
    5798:     of the OFF-DIAGONAL portion of local A

    5800:     Collective

    5802:    Input Parameters:
    5803: +    A,B - the matrices in `MATMPIAIJ` format
    5804: -    scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5806:    Output Parameter:
    5807: +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
    5808: .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
    5809: .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
    5810: -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N

    5812:     Developer Note:
    5813:     This directly accesses information inside the VecScatter associated with the matrix-vector product
    5814:      for this matrix. This is not desirable..

    5816:     Level: developer

    5818: */

    5820: PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A, Mat B, MatReuse scall, PetscInt **startsj_s, PetscInt **startsj_r, MatScalar **bufa_ptr, Mat *B_oth)
    5821: {
    5822:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
    5823:   VecScatter         ctx;
    5824:   MPI_Comm           comm;
    5825:   const PetscMPIInt *rprocs, *sprocs;
    5826:   PetscMPIInt        nrecvs, nsends;
    5827:   const PetscInt    *srow, *rstarts, *sstarts;
    5828:   PetscInt          *rowlen, *bufj, *bufJ, ncols = 0, aBn = a->B->cmap->n, row, *b_othi, *b_othj, *rvalues = NULL, *svalues = NULL, *cols, sbs, rbs;
    5829:   PetscInt           i, j, k = 0, l, ll, nrows, *rstartsj = NULL, *sstartsj, len;
    5830:   PetscScalar       *b_otha, *bufa, *bufA, *vals = NULL;
    5831:   MPI_Request       *reqs = NULL, *rwaits = NULL, *swaits = NULL;
    5832:   PetscMPIInt        size, tag, rank, nreqs;

    5834:   PetscFunctionBegin;
    5835:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    5836:   PetscCallMPI(MPI_Comm_size(comm, &size));

    5838:   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 ")",
    5839:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    5840:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, B, 0, 0));
    5841:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    5843:   if (size == 1) {
    5844:     startsj_s = NULL;
    5845:     bufa_ptr  = NULL;
    5846:     *B_oth    = NULL;
    5847:     PetscFunctionReturn(PETSC_SUCCESS);
    5848:   }

    5850:   ctx = a->Mvctx;
    5851:   tag = ((PetscObject)ctx)->tag;

    5853:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &srow, &sprocs, &sbs));
    5854:   /* rprocs[] must be ordered so that indices received from them are ordered in rvalues[], which is key to algorithms used in this subroutine */
    5855:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL /*indices not needed*/, &rprocs, &rbs));
    5856:   PetscCall(PetscMPIIntCast(nsends + nrecvs, &nreqs));
    5857:   PetscCall(PetscMalloc1(nreqs, &reqs));
    5858:   rwaits = reqs;
    5859:   swaits = PetscSafePointerPlusOffset(reqs, nrecvs);

    5861:   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
    5862:   if (scall == MAT_INITIAL_MATRIX) {
    5863:     /* i-array */
    5864:     /*  post receives */
    5865:     if (nrecvs) PetscCall(PetscMalloc1(rbs * (rstarts[nrecvs] - rstarts[0]), &rvalues)); /* rstarts can be NULL when nrecvs=0 */
    5866:     for (i = 0; i < nrecvs; i++) {
    5867:       rowlen = rvalues + rstarts[i] * rbs;
    5868:       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of indices to be received */
    5869:       PetscCallMPI(MPIU_Irecv(rowlen, nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
    5870:     }

    5872:     /* pack the outgoing message */
    5873:     PetscCall(PetscMalloc2(nsends + 1, &sstartsj, nrecvs + 1, &rstartsj));

    5875:     sstartsj[0] = 0;
    5876:     rstartsj[0] = 0;
    5877:     len         = 0; /* total length of j or a array to be sent */
    5878:     if (nsends) {
    5879:       k = sstarts[0]; /* ATTENTION: sstarts[0] and rstarts[0] are not necessarily zero */
    5880:       PetscCall(PetscMalloc1(sbs * (sstarts[nsends] - sstarts[0]), &svalues));
    5881:     }
    5882:     for (i = 0; i < nsends; i++) {
    5883:       rowlen = svalues + (sstarts[i] - sstarts[0]) * sbs;
    5884:       nrows  = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5885:       for (j = 0; j < nrows; j++) {
    5886:         row = srow[k] + B->rmap->range[rank]; /* global row idx */
    5887:         for (l = 0; l < sbs; l++) {
    5888:           PetscCall(MatGetRow_MPIAIJ(B, row + l, &ncols, NULL, NULL)); /* rowlength */

    5890:           rowlen[j * sbs + l] = ncols;

    5892:           len += ncols;
    5893:           PetscCall(MatRestoreRow_MPIAIJ(B, row + l, &ncols, NULL, NULL));
    5894:         }
    5895:         k++;
    5896:       }
    5897:       PetscCallMPI(MPIU_Isend(rowlen, nrows * sbs, MPIU_INT, sprocs[i], tag, comm, swaits + i));

    5899:       sstartsj[i + 1] = len; /* starting point of (i+1)-th outgoing msg in bufj and bufa */
    5900:     }
    5901:     /* recvs and sends of i-array are completed */
    5902:     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5903:     PetscCall(PetscFree(svalues));

    5905:     /* allocate buffers for sending j and a arrays */
    5906:     PetscCall(PetscMalloc1(len + 1, &bufj));
    5907:     PetscCall(PetscMalloc1(len + 1, &bufa));

    5909:     /* create i-array of B_oth */
    5910:     PetscCall(PetscMalloc1(aBn + 2, &b_othi));

    5912:     b_othi[0] = 0;
    5913:     len       = 0; /* total length of j or a array to be received */
    5914:     k         = 0;
    5915:     for (i = 0; i < nrecvs; i++) {
    5916:       rowlen = rvalues + (rstarts[i] - rstarts[0]) * rbs;
    5917:       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of rows to be received */
    5918:       for (j = 0; j < nrows; j++) {
    5919:         b_othi[k + 1] = b_othi[k] + rowlen[j];
    5920:         PetscCall(PetscIntSumError(rowlen[j], len, &len));
    5921:         k++;
    5922:       }
    5923:       rstartsj[i + 1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
    5924:     }
    5925:     PetscCall(PetscFree(rvalues));

    5927:     /* allocate space for j and a arrays of B_oth */
    5928:     PetscCall(PetscMalloc1(b_othi[aBn] + 1, &b_othj));
    5929:     PetscCall(PetscMalloc1(b_othi[aBn] + 1, &b_otha));

    5931:     /* j-array */
    5932:     /*  post receives of j-array */
    5933:     for (i = 0; i < nrecvs; i++) {
    5934:       nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
    5935:       PetscCallMPI(MPIU_Irecv(b_othj + rstartsj[i], nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
    5936:     }

    5938:     /* pack the outgoing message j-array */
    5939:     if (nsends) k = sstarts[0];
    5940:     for (i = 0; i < nsends; i++) {
    5941:       nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5942:       bufJ  = bufj + sstartsj[i];
    5943:       for (j = 0; j < nrows; j++) {
    5944:         row = srow[k++] + B->rmap->range[rank]; /* global row idx */
    5945:         for (ll = 0; ll < sbs; ll++) {
    5946:           PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
    5947:           for (l = 0; l < ncols; l++) *bufJ++ = cols[l];
    5948:           PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
    5949:         }
    5950:       }
    5951:       PetscCallMPI(MPIU_Isend(bufj + sstartsj[i], sstartsj[i + 1] - sstartsj[i], MPIU_INT, sprocs[i], tag, comm, swaits + i));
    5952:     }

    5954:     /* recvs and sends of j-array are completed */
    5955:     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5956:   } else if (scall == MAT_REUSE_MATRIX) {
    5957:     sstartsj = *startsj_s;
    5958:     rstartsj = *startsj_r;
    5959:     bufa     = *bufa_ptr;
    5960:     PetscCall(MatSeqAIJGetArrayWrite(*B_oth, &b_otha));
    5961:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not possess an object container");

    5963:   /* a-array */
    5964:   /*  post receives of a-array */
    5965:   for (i = 0; i < nrecvs; i++) {
    5966:     nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
    5967:     PetscCallMPI(MPIU_Irecv(b_otha + rstartsj[i], nrows, MPIU_SCALAR, rprocs[i], tag, comm, rwaits + i));
    5968:   }

    5970:   /* pack the outgoing message a-array */
    5971:   if (nsends) k = sstarts[0];
    5972:   for (i = 0; i < nsends; i++) {
    5973:     nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5974:     bufA  = bufa + sstartsj[i];
    5975:     for (j = 0; j < nrows; j++) {
    5976:       row = srow[k++] + B->rmap->range[rank]; /* global row idx */
    5977:       for (ll = 0; ll < sbs; ll++) {
    5978:         PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
    5979:         for (l = 0; l < ncols; l++) *bufA++ = vals[l];
    5980:         PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
    5981:       }
    5982:     }
    5983:     PetscCallMPI(MPIU_Isend(bufa + sstartsj[i], sstartsj[i + 1] - sstartsj[i], MPIU_SCALAR, sprocs[i], tag, comm, swaits + i));
    5984:   }
    5985:   /* recvs and sends of a-array are completed */
    5986:   if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5987:   PetscCall(PetscFree(reqs));

    5989:   if (scall == MAT_INITIAL_MATRIX) {
    5990:     Mat_SeqAIJ *b_oth;

    5992:     /* put together the new matrix */
    5993:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, aBn, B->cmap->N, b_othi, b_othj, b_otha, B_oth));

    5995:     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5996:     /* Since these are PETSc arrays, change flags to free them as necessary. */
    5997:     b_oth          = (Mat_SeqAIJ *)(*B_oth)->data;
    5998:     b_oth->free_a  = PETSC_TRUE;
    5999:     b_oth->free_ij = PETSC_TRUE;
    6000:     b_oth->nonew   = 0;

    6002:     PetscCall(PetscFree(bufj));
    6003:     if (!startsj_s || !bufa_ptr) {
    6004:       PetscCall(PetscFree2(sstartsj, rstartsj));
    6005:       PetscCall(PetscFree(bufa_ptr));
    6006:     } else {
    6007:       *startsj_s = sstartsj;
    6008:       *startsj_r = rstartsj;
    6009:       *bufa_ptr  = bufa;
    6010:     }
    6011:   } else if (scall == MAT_REUSE_MATRIX) {
    6012:     PetscCall(MatSeqAIJRestoreArrayWrite(*B_oth, &b_otha));
    6013:   }

    6015:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE, &nsends, &sstarts, &srow, &sprocs, &sbs));
    6016:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE, &nrecvs, &rstarts, NULL, &rprocs, &rbs));
    6017:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, B, 0, 0));
    6018:   PetscFunctionReturn(PETSC_SUCCESS);
    6019: }

    6021: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat, MatType, MatReuse, Mat *);
    6022: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat, MatType, MatReuse, Mat *);
    6023: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJSELL(Mat, MatType, MatReuse, Mat *);
    6024: #if defined(PETSC_HAVE_MKL_SPARSE)
    6025: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJMKL(Mat, MatType, MatReuse, Mat *);
    6026: #endif
    6027: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIBAIJ(Mat, MatType, MatReuse, Mat *);
    6028: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat, MatType, MatReuse, Mat *);
    6029: #if defined(PETSC_HAVE_ELEMENTAL)
    6030: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
    6031: #endif
    6032: #if defined(PETSC_HAVE_SCALAPACK)
    6033: PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
    6034: #endif
    6035: #if defined(PETSC_HAVE_HYPRE)
    6036: PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat, MatType, MatReuse, Mat *);
    6037: #endif
    6038: #if defined(PETSC_HAVE_CUDA)
    6039: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
    6040: #endif
    6041: #if defined(PETSC_HAVE_HIP)
    6042: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJHIPSPARSE(Mat, MatType, MatReuse, Mat *);
    6043: #endif
    6044: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    6045: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJKokkos(Mat, MatType, MatReuse, Mat *);
    6046: #endif
    6047: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISELL(Mat, MatType, MatReuse, Mat *);
    6048: PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);
    6049: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);

    6051: /*
    6052:     Computes (B'*A')' since computing B*A directly is untenable

    6054:                n                       p                          p
    6055:         [             ]       [             ]         [                 ]
    6056:       m [      A      ]  *  n [       B     ]   =   m [         C       ]
    6057:         [             ]       [             ]         [                 ]

    6059: */
    6060: static PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A, Mat B, Mat C)
    6061: {
    6062:   Mat At, Bt, Ct;

    6064:   PetscFunctionBegin;
    6065:   PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
    6066:   PetscCall(MatTranspose(B, MAT_INITIAL_MATRIX, &Bt));
    6067:   PetscCall(MatMatMult(Bt, At, MAT_INITIAL_MATRIX, PETSC_CURRENT, &Ct));
    6068:   PetscCall(MatDestroy(&At));
    6069:   PetscCall(MatDestroy(&Bt));
    6070:   PetscCall(MatTransposeSetPrecursor(Ct, C));
    6071:   PetscCall(MatTranspose(Ct, MAT_REUSE_MATRIX, &C));
    6072:   PetscCall(MatDestroy(&Ct));
    6073:   PetscFunctionReturn(PETSC_SUCCESS);
    6074: }

    6076: static PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A, Mat B, PetscReal fill, Mat C)
    6077: {
    6078:   PetscBool cisdense;

    6080:   PetscFunctionBegin;
    6081:   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);
    6082:   PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
    6083:   PetscCall(MatSetBlockSizesFromMats(C, A, B));
    6084:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATMPIDENSE, MATMPIDENSECUDA, MATMPIDENSEHIP, ""));
    6085:   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    6086:   PetscCall(MatSetUp(C));

    6088:   C->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
    6089:   PetscFunctionReturn(PETSC_SUCCESS);
    6090: }

    6092: static PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ_AB(Mat C)
    6093: {
    6094:   Mat_Product *product = C->product;
    6095:   Mat          A = product->A, B = product->B;

    6097:   PetscFunctionBegin;
    6098:   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 ")",
    6099:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    6100:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIDense_MPIAIJ;
    6101:   C->ops->productsymbolic = MatProductSymbolic_AB;
    6102:   PetscFunctionReturn(PETSC_SUCCESS);
    6103: }

    6105: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ(Mat C)
    6106: {
    6107:   Mat_Product *product = C->product;

    6109:   PetscFunctionBegin;
    6110:   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_MPIDense_MPIAIJ_AB(C));
    6111:   PetscFunctionReturn(PETSC_SUCCESS);
    6112: }

    6114: /*
    6115:    Merge two sets of sorted nonzeros and return a CSR for the merged (sequential) matrix

    6117:   Input Parameters:

    6119:     j1,rowBegin1,rowEnd1,jmap1: describe the first set of nonzeros (Set1)
    6120:     j2,rowBegin2,rowEnd2,jmap2: describe the second set of nonzeros (Set2)

    6122:     mat: both sets' nonzeros are on m rows, where m is the number of local rows of the matrix mat

    6124:     For Set1, j1[] contains column indices of the nonzeros.
    6125:     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
    6126:     respectively (note rowEnd1[k] is not necessarily equal to rwoBegin1[k+1]). Indices in this range of j1[] are sorted,
    6127:     but might have repeats. jmap1[t+1] - jmap1[t] is the number of repeats for the t-th unique nonzero in Set1.

    6129:     Similar for Set2.

    6131:     This routine merges the two sets of nonzeros row by row and removes repeats.

    6133:   Output Parameters: (memory is allocated by the caller)

    6135:     i[],j[]: the CSR of the merged matrix, which has m rows.
    6136:     imap1[]: the k-th unique nonzero in Set1 (k=0,1,...) corresponds to imap1[k]-th unique nonzero in the merged matrix.
    6137:     imap2[]: similar to imap1[], but for Set2.
    6138:     Note we order nonzeros row-by-row and from left to right.
    6139: */
    6140: 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[])
    6141: {
    6142:   PetscInt   r, m; /* Row index of mat */
    6143:   PetscCount t, t1, t2, b1, e1, b2, e2;

    6145:   PetscFunctionBegin;
    6146:   PetscCall(MatGetLocalSize(mat, &m, NULL));
    6147:   t1 = t2 = t = 0; /* Count unique nonzeros of in Set1, Set1 and the merged respectively */
    6148:   i[0]        = 0;
    6149:   for (r = 0; r < m; r++) { /* Do row by row merging */
    6150:     b1 = rowBegin1[r];
    6151:     e1 = rowEnd1[r];
    6152:     b2 = rowBegin2[r];
    6153:     e2 = rowEnd2[r];
    6154:     while (b1 < e1 && b2 < e2) {
    6155:       if (j1[b1] == j2[b2]) { /* Same column index and hence same nonzero */
    6156:         j[t]      = j1[b1];
    6157:         imap1[t1] = t;
    6158:         imap2[t2] = t;
    6159:         b1 += jmap1[t1 + 1] - jmap1[t1]; /* Jump to next unique local nonzero */
    6160:         b2 += jmap2[t2 + 1] - jmap2[t2]; /* Jump to next unique remote nonzero */
    6161:         t1++;
    6162:         t2++;
    6163:         t++;
    6164:       } else if (j1[b1] < j2[b2]) {
    6165:         j[t]      = j1[b1];
    6166:         imap1[t1] = t;
    6167:         b1 += jmap1[t1 + 1] - jmap1[t1];
    6168:         t1++;
    6169:         t++;
    6170:       } else {
    6171:         j[t]      = j2[b2];
    6172:         imap2[t2] = t;
    6173:         b2 += jmap2[t2 + 1] - jmap2[t2];
    6174:         t2++;
    6175:         t++;
    6176:       }
    6177:     }
    6178:     /* Merge the remaining in either j1[] or j2[] */
    6179:     while (b1 < e1) {
    6180:       j[t]      = j1[b1];
    6181:       imap1[t1] = t;
    6182:       b1 += jmap1[t1 + 1] - jmap1[t1];
    6183:       t1++;
    6184:       t++;
    6185:     }
    6186:     while (b2 < e2) {
    6187:       j[t]      = j2[b2];
    6188:       imap2[t2] = t;
    6189:       b2 += jmap2[t2 + 1] - jmap2[t2];
    6190:       t2++;
    6191:       t++;
    6192:     }
    6193:     PetscCall(PetscIntCast(t, i + r + 1));
    6194:   }
    6195:   PetscFunctionReturn(PETSC_SUCCESS);
    6196: }

    6198: /*
    6199:   Split nonzeros in a block of local rows into two subsets: those in the diagonal block and those in the off-diagonal block

    6201:   Input Parameters:
    6202:     mat: an MPI matrix that provides row and column layout information for splitting. Let's say its number of local rows is m.
    6203:     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[]
    6204:       respectively, along with a permutation array perm[]. Length of the i[],j[],perm[] arrays is n.

    6206:       i[] is already sorted, but within a row, j[] is not sorted and might have repeats.
    6207:       i[] might contain negative indices at the beginning, which means the corresponding entries should be ignored in the splitting.

    6209:   Output Parameters:
    6210:     j[],perm[]: the routine needs to sort j[] within each row along with perm[].
    6211:     rowBegin[],rowMid[],rowEnd[]: of length m, and the memory is preallocated and zeroed by the caller.
    6212:       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,
    6213:       and [rowMid[r],rowEnd[r]) point to begin/end entries of row r of the off-diagonal block.

    6215:     Aperm[],Ajmap[],Atot,Annz: Arrays are allocated by this routine.
    6216:       Atot: number of entries belonging to the diagonal block.
    6217:       Annz: number of unique nonzeros belonging to the diagonal block.
    6218:       Aperm[Atot] stores values from perm[] for entries belonging to the diagonal block. Length of Aperm[] is Atot, though it may also count
    6219:         repeats (i.e., same 'i,j' pair).
    6220:       Ajmap[Annz+1] stores the number of repeats of each unique entry belonging to the diagonal block. More precisely, Ajmap[t+1] - Ajmap[t]
    6221:         is the number of repeats for the t-th unique entry in the diagonal block. Ajmap[0] is always 0.

    6223:       Atot: number of entries belonging to the diagonal block
    6224:       Annz: number of unique nonzeros belonging to the diagonal block.

    6226:     Bperm[], Bjmap[], Btot, Bnnz are similar but for the off-diagonal block.

    6228:     Aperm[],Bperm[],Ajmap[] and Bjmap[] are allocated separately by this routine with PetscMalloc1().
    6229: */
    6230: 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_)
    6231: {
    6232:   PetscInt    cstart, cend, rstart, rend, row, col;
    6233:   PetscCount  Atot = 0, Btot = 0; /* Total number of nonzeros in the diagonal and off-diagonal blocks */
    6234:   PetscCount  Annz = 0, Bnnz = 0; /* Number of unique nonzeros in the diagonal and off-diagonal blocks */
    6235:   PetscCount  k, m, p, q, r, s, mid;
    6236:   PetscCount *Aperm, *Bperm, *Ajmap, *Bjmap;

    6238:   PetscFunctionBegin;
    6239:   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
    6240:   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
    6241:   m = rend - rstart;

    6243:   /* Skip negative rows */
    6244:   for (k = 0; k < n; k++)
    6245:     if (i[k] >= 0) break;

    6247:   /* Process [k,n): sort and partition each local row into diag and offdiag portions,
    6248:      fill rowBegin[], rowMid[], rowEnd[], and count Atot, Btot, Annz, Bnnz.
    6249:   */
    6250:   while (k < n) {
    6251:     row = i[k];
    6252:     /* Entries in [k,s) are in one row. Shift diagonal block col indices so that diag is ahead of offdiag after sorting the row */
    6253:     for (s = k; s < n; s++)
    6254:       if (i[s] != row) break;

    6256:     /* Shift diag columns to range of [-PETSC_INT_MAX, -1] */
    6257:     for (p = k; p < s; p++) {
    6258:       if (j[p] >= cstart && j[p] < cend) j[p] -= PETSC_INT_MAX;
    6259:       else PetscAssert((j[p] >= 0) && (j[p] <= mat->cmap->N), PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column index %" PetscInt_FMT " is out of range", j[p]);
    6260:     }
    6261:     PetscCall(PetscSortIntWithCountArray(s - k, j + k, perm + k));
    6262:     PetscCall(PetscSortedIntUpperBound(j, k, s, -1, &mid)); /* Separate [k,s) into [k,mid) for diag and [mid,s) for offdiag */
    6263:     rowBegin[row - rstart] = k;
    6264:     rowMid[row - rstart]   = mid;
    6265:     rowEnd[row - rstart]   = s;

    6267:     /* Count nonzeros of this diag/offdiag row, which might have repeats */
    6268:     Atot += mid - k;
    6269:     Btot += s - mid;

    6271:     /* Count unique nonzeros of this diag row */
    6272:     for (p = k; p < mid;) {
    6273:       col = j[p];
    6274:       do {
    6275:         j[p] += PETSC_INT_MAX; /* Revert the modified diagonal indices */
    6276:         p++;
    6277:       } while (p < mid && j[p] == col);
    6278:       Annz++;
    6279:     }

    6281:     /* Count unique nonzeros of this offdiag row */
    6282:     for (p = mid; p < s;) {
    6283:       col = j[p];
    6284:       do {
    6285:         p++;
    6286:       } while (p < s && j[p] == col);
    6287:       Bnnz++;
    6288:     }
    6289:     k = s;
    6290:   }

    6292:   /* Allocation according to Atot, Btot, Annz, Bnnz */
    6293:   PetscCall(PetscMalloc1(Atot, &Aperm));
    6294:   PetscCall(PetscMalloc1(Btot, &Bperm));
    6295:   PetscCall(PetscMalloc1(Annz + 1, &Ajmap));
    6296:   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap));

    6298:   /* Re-scan indices and copy diag/offdiag permutation indices to Aperm, Bperm and also fill Ajmap and Bjmap */
    6299:   Ajmap[0] = Bjmap[0] = Atot = Btot = Annz = Bnnz = 0;
    6300:   for (r = 0; r < m; r++) {
    6301:     k   = rowBegin[r];
    6302:     mid = rowMid[r];
    6303:     s   = rowEnd[r];
    6304:     PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(Aperm, Atot), PetscSafePointerPlusOffset(perm, k), mid - k));
    6305:     PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(Bperm, Btot), PetscSafePointerPlusOffset(perm, mid), s - mid));
    6306:     Atot += mid - k;
    6307:     Btot += s - mid;

    6309:     /* Scan column indices in this row and find out how many repeats each unique nonzero has */
    6310:     for (p = k; p < mid;) {
    6311:       col = j[p];
    6312:       q   = p;
    6313:       do {
    6314:         p++;
    6315:       } while (p < mid && j[p] == col);
    6316:       Ajmap[Annz + 1] = Ajmap[Annz] + (p - q);
    6317:       Annz++;
    6318:     }

    6320:     for (p = mid; p < s;) {
    6321:       col = j[p];
    6322:       q   = p;
    6323:       do {
    6324:         p++;
    6325:       } while (p < s && j[p] == col);
    6326:       Bjmap[Bnnz + 1] = Bjmap[Bnnz] + (p - q);
    6327:       Bnnz++;
    6328:     }
    6329:   }
    6330:   /* Output */
    6331:   *Aperm_ = Aperm;
    6332:   *Annz_  = Annz;
    6333:   *Atot_  = Atot;
    6334:   *Ajmap_ = Ajmap;
    6335:   *Bperm_ = Bperm;
    6336:   *Bnnz_  = Bnnz;
    6337:   *Btot_  = Btot;
    6338:   *Bjmap_ = Bjmap;
    6339:   PetscFunctionReturn(PETSC_SUCCESS);
    6340: }

    6342: /*
    6343:   Expand the jmap[] array to make a new one in view of nonzeros in the merged matrix

    6345:   Input Parameters:
    6346:     nnz1: number of unique nonzeros in a set that was used to produce imap[], jmap[]
    6347:     nnz:  number of unique nonzeros in the merged matrix
    6348:     imap[nnz1]: i-th nonzero in the set is the imap[i]-th nonzero in the merged matrix
    6349:     jmap[nnz1+1]: i-th nonzero in the set has jmap[i+1] - jmap[i] repeats in the set

    6351:   Output Parameter: (memory is allocated by the caller)
    6352:     jmap_new[nnz+1]: i-th nonzero in the merged matrix has jmap_new[i+1] - jmap_new[i] repeats in the set

    6354:   Example:
    6355:     nnz1 = 4
    6356:     nnz  = 6
    6357:     imap = [1,3,4,5]
    6358:     jmap = [0,3,5,6,7]
    6359:    then,
    6360:     jmap_new = [0,0,3,3,5,6,7]
    6361: */
    6362: static PetscErrorCode ExpandJmap_Internal(PetscCount nnz1, PetscCount nnz, const PetscCount imap[], const PetscCount jmap[], PetscCount jmap_new[])
    6363: {
    6364:   PetscCount k, p;

    6366:   PetscFunctionBegin;
    6367:   jmap_new[0] = 0;
    6368:   p           = nnz;                /* p loops over jmap_new[] backwards */
    6369:   for (k = nnz1 - 1; k >= 0; k--) { /* k loops over imap[] */
    6370:     for (; p > imap[k]; p--) jmap_new[p] = jmap[k + 1];
    6371:   }
    6372:   for (; p >= 0; p--) jmap_new[p] = jmap[0];
    6373:   PetscFunctionReturn(PETSC_SUCCESS);
    6374: }

    6376: static PetscErrorCode MatCOOStructDestroy_MPIAIJ(void **data)
    6377: {
    6378:   MatCOOStruct_MPIAIJ *coo = (MatCOOStruct_MPIAIJ *)*data;

    6380:   PetscFunctionBegin;
    6381:   PetscCall(PetscSFDestroy(&coo->sf));
    6382:   PetscCall(PetscFree(coo->Aperm1));
    6383:   PetscCall(PetscFree(coo->Bperm1));
    6384:   PetscCall(PetscFree(coo->Ajmap1));
    6385:   PetscCall(PetscFree(coo->Bjmap1));
    6386:   PetscCall(PetscFree(coo->Aimap2));
    6387:   PetscCall(PetscFree(coo->Bimap2));
    6388:   PetscCall(PetscFree(coo->Aperm2));
    6389:   PetscCall(PetscFree(coo->Bperm2));
    6390:   PetscCall(PetscFree(coo->Ajmap2));
    6391:   PetscCall(PetscFree(coo->Bjmap2));
    6392:   PetscCall(PetscFree(coo->Cperm1));
    6393:   PetscCall(PetscFree2(coo->sendbuf, coo->recvbuf));
    6394:   PetscCall(PetscFree(coo));
    6395:   PetscFunctionReturn(PETSC_SUCCESS);
    6396: }

    6398: PetscErrorCode MatSetPreallocationCOO_MPIAIJ(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
    6399: {
    6400:   MPI_Comm             comm;
    6401:   PetscMPIInt          rank, size;
    6402:   PetscInt             m, n, M, N, rstart, rend, cstart, cend; /* Sizes, indices of row/col, therefore with type PetscInt */
    6403:   PetscCount           k, p, q, rem;                           /* Loop variables over coo arrays */
    6404:   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
    6405:   PetscContainer       container;
    6406:   MatCOOStruct_MPIAIJ *coo;

    6408:   PetscFunctionBegin;
    6409:   PetscCall(PetscFree(mpiaij->garray));
    6410:   PetscCall(VecDestroy(&mpiaij->lvec));
    6411: #if defined(PETSC_USE_CTABLE)
    6412:   PetscCall(PetscHMapIDestroy(&mpiaij->colmap));
    6413: #else
    6414:   PetscCall(PetscFree(mpiaij->colmap));
    6415: #endif
    6416:   PetscCall(VecScatterDestroy(&mpiaij->Mvctx));
    6417:   mat->assembled     = PETSC_FALSE;
    6418:   mat->was_assembled = PETSC_FALSE;

    6420:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    6421:   PetscCallMPI(MPI_Comm_size(comm, &size));
    6422:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    6423:   PetscCall(PetscLayoutSetUp(mat->rmap));
    6424:   PetscCall(PetscLayoutSetUp(mat->cmap));
    6425:   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
    6426:   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
    6427:   PetscCall(MatGetLocalSize(mat, &m, &n));
    6428:   PetscCall(MatGetSize(mat, &M, &N));

    6430:   /* Sort (i,j) by row along with a permutation array, so that the to-be-ignored */
    6431:   /* entries come first, then local rows, then remote rows.                     */
    6432:   PetscCount n1 = coo_n, *perm1;
    6433:   PetscInt  *i1 = coo_i, *j1 = coo_j;

    6435:   PetscCall(PetscMalloc1(n1, &perm1));
    6436:   for (k = 0; k < n1; k++) perm1[k] = k;

    6438:   /* Manipulate indices so that entries with negative row or col indices will have smallest
    6439:      row indices, local entries will have greater but negative row indices, and remote entries
    6440:      will have positive row indices.
    6441:   */
    6442:   for (k = 0; k < n1; k++) {
    6443:     if (i1[k] < 0 || j1[k] < 0) i1[k] = PETSC_INT_MIN;                /* e.g., -2^31, minimal to move them ahead */
    6444:     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] */
    6445:     else {
    6446:       PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "MAT_NO_OFF_PROC_ENTRIES is set but insert to remote rows");
    6447:       if (mpiaij->donotstash) i1[k] = PETSC_INT_MIN; /* Ignore offproc entries as if they had negative indices */
    6448:     }
    6449:   }

    6451:   /* Sort by row; after that, [0,k) have ignored entries, [k,rem) have local rows and [rem,n1) have remote rows */
    6452:   PetscCall(PetscSortIntWithIntCountArrayPair(n1, i1, j1, perm1));

    6454:   /* Advance k to the first entry we need to take care of */
    6455:   for (k = 0; k < n1; k++)
    6456:     if (i1[k] > PETSC_INT_MIN) break;
    6457:   PetscCount i1start = k;

    6459:   PetscCall(PetscSortedIntUpperBound(i1, k, n1, rend - 1 - PETSC_INT_MAX, &rem)); /* rem is upper bound of the last local row */
    6460:   for (; k < rem; k++) i1[k] += PETSC_INT_MAX;                                    /* Revert row indices of local rows*/

    6462:   /*           Send remote rows to their owner                                  */
    6463:   /* Find which rows should be sent to which remote ranks*/
    6464:   PetscInt        nsend = 0; /* Number of MPI ranks to send data to */
    6465:   PetscMPIInt    *sendto;    /* [nsend], storing remote ranks */
    6466:   PetscInt       *nentries;  /* [nsend], storing number of entries sent to remote ranks; Assume PetscInt is big enough for this count, and error if not */
    6467:   const PetscInt *ranges;
    6468:   PetscInt        maxNsend = size >= 128 ? 128 : size; /* Assume max 128 neighbors; realloc when needed */

    6470:   PetscCall(PetscLayoutGetRanges(mat->rmap, &ranges));
    6471:   PetscCall(PetscMalloc2(maxNsend, &sendto, maxNsend, &nentries));
    6472:   for (k = rem; k < n1;) {
    6473:     PetscMPIInt owner;
    6474:     PetscInt    firstRow, lastRow;

    6476:     /* Locate a row range */
    6477:     firstRow = i1[k]; /* first row of this owner */
    6478:     PetscCall(PetscLayoutFindOwner(mat->rmap, firstRow, &owner));
    6479:     lastRow = ranges[owner + 1] - 1; /* last row of this owner */

    6481:     /* Find the first index 'p' in [k,n) with i[p] belonging to next owner */
    6482:     PetscCall(PetscSortedIntUpperBound(i1, k, n1, lastRow, &p));

    6484:     /* All entries in [k,p) belong to this remote owner */
    6485:     if (nsend >= maxNsend) { /* Double the remote ranks arrays if not long enough */
    6486:       PetscMPIInt *sendto2;
    6487:       PetscInt    *nentries2;
    6488:       PetscInt     maxNsend2 = (maxNsend <= size / 2) ? maxNsend * 2 : size;

    6490:       PetscCall(PetscMalloc2(maxNsend2, &sendto2, maxNsend2, &nentries2));
    6491:       PetscCall(PetscArraycpy(sendto2, sendto, maxNsend));
    6492:       PetscCall(PetscArraycpy(nentries2, nentries2, maxNsend + 1));
    6493:       PetscCall(PetscFree2(sendto, nentries2));
    6494:       sendto   = sendto2;
    6495:       nentries = nentries2;
    6496:       maxNsend = maxNsend2;
    6497:     }
    6498:     sendto[nsend] = owner;
    6499:     PetscCall(PetscIntCast(p - k, &nentries[nsend]));
    6500:     nsend++;
    6501:     k = p;
    6502:   }

    6504:   /* Build 1st SF to know offsets on remote to send data */
    6505:   PetscSF      sf1;
    6506:   PetscInt     nroots = 1, nroots2 = 0;
    6507:   PetscInt     nleaves = nsend, nleaves2 = 0;
    6508:   PetscInt    *offsets;
    6509:   PetscSFNode *iremote;

    6511:   PetscCall(PetscSFCreate(comm, &sf1));
    6512:   PetscCall(PetscMalloc1(nsend, &iremote));
    6513:   PetscCall(PetscMalloc1(nsend, &offsets));
    6514:   for (k = 0; k < nsend; k++) {
    6515:     iremote[k].rank  = sendto[k];
    6516:     iremote[k].index = 0;
    6517:     nleaves2 += nentries[k];
    6518:     PetscCheck(nleaves2 >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF leaves is too large for PetscInt");
    6519:   }
    6520:   PetscCall(PetscSFSetGraph(sf1, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    6521:   PetscCall(PetscSFFetchAndOpWithMemTypeBegin(sf1, MPIU_INT, PETSC_MEMTYPE_HOST, &nroots2 /*rootdata*/, PETSC_MEMTYPE_HOST, nentries /*leafdata*/, PETSC_MEMTYPE_HOST, offsets /*leafupdate*/, MPI_SUM));
    6522:   PetscCall(PetscSFFetchAndOpEnd(sf1, MPIU_INT, &nroots2, nentries, offsets, MPI_SUM)); /* Would nroots2 overflow, we check offsets[] below */
    6523:   PetscCall(PetscSFDestroy(&sf1));
    6524:   PetscAssert(nleaves2 == n1 - rem, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nleaves2 %" PetscInt_FMT " != number of remote entries %" PetscCount_FMT, nleaves2, n1 - rem);

    6526:   /* Build 2nd SF to send remote COOs to their owner */
    6527:   PetscSF sf2;
    6528:   nroots  = nroots2;
    6529:   nleaves = nleaves2;
    6530:   PetscCall(PetscSFCreate(comm, &sf2));
    6531:   PetscCall(PetscSFSetFromOptions(sf2));
    6532:   PetscCall(PetscMalloc1(nleaves, &iremote));
    6533:   p = 0;
    6534:   for (k = 0; k < nsend; k++) {
    6535:     PetscCheck(offsets[k] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF roots is too large for PetscInt");
    6536:     for (q = 0; q < nentries[k]; q++, p++) {
    6537:       iremote[p].rank = sendto[k];
    6538:       PetscCall(PetscIntCast(offsets[k] + q, &iremote[p].index));
    6539:     }
    6540:   }
    6541:   PetscCall(PetscSFSetGraph(sf2, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));

    6543:   /* Send the remote COOs to their owner */
    6544:   PetscInt    n2 = nroots, *i2, *j2; /* Buffers for received COOs from other ranks, along with a permutation array */
    6545:   PetscCount *perm2;                 /* Though PetscInt is enough for remote entries, we use PetscCount here as we want to reuse MatSplitEntries_Internal() */
    6546:   PetscCall(PetscMalloc3(n2, &i2, n2, &j2, n2, &perm2));
    6547:   PetscAssert(rem == 0 || i1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6548:   PetscAssert(rem == 0 || j1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6549:   PetscInt *i1prem = PetscSafePointerPlusOffset(i1, rem);
    6550:   PetscInt *j1prem = PetscSafePointerPlusOffset(j1, rem);
    6551:   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, i1prem, PETSC_MEMTYPE_HOST, i2, MPI_REPLACE));
    6552:   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, i1prem, i2, MPI_REPLACE));
    6553:   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, j1prem, PETSC_MEMTYPE_HOST, j2, MPI_REPLACE));
    6554:   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, j1prem, j2, MPI_REPLACE));

    6556:   PetscCall(PetscFree(offsets));
    6557:   PetscCall(PetscFree2(sendto, nentries));

    6559:   /* Sort received COOs by row along with the permutation array     */
    6560:   for (k = 0; k < n2; k++) perm2[k] = k;
    6561:   PetscCall(PetscSortIntWithIntCountArrayPair(n2, i2, j2, perm2));

    6563:   /* sf2 only sends contiguous leafdata to contiguous rootdata. We record the permutation which will be used to fill leafdata */
    6564:   PetscCount *Cperm1;
    6565:   PetscAssert(rem == 0 || perm1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6566:   PetscCount *perm1prem = PetscSafePointerPlusOffset(perm1, rem);
    6567:   PetscCall(PetscMalloc1(nleaves, &Cperm1));
    6568:   PetscCall(PetscArraycpy(Cperm1, perm1prem, nleaves));

    6570:   /* Support for HYPRE matrices, kind of a hack.
    6571:      Swap min column with diagonal so that diagonal values will go first */
    6572:   PetscBool hypre;
    6573:   PetscCall(PetscStrcmp("_internal_COO_mat_for_hypre", ((PetscObject)mat)->name, &hypre));
    6574:   if (hypre) {
    6575:     PetscInt *minj;
    6576:     PetscBT   hasdiag;

    6578:     PetscCall(PetscBTCreate(m, &hasdiag));
    6579:     PetscCall(PetscMalloc1(m, &minj));
    6580:     for (k = 0; k < m; k++) minj[k] = PETSC_INT_MAX;
    6581:     for (k = i1start; k < rem; k++) {
    6582:       if (j1[k] < cstart || j1[k] >= cend) continue;
    6583:       const PetscInt rindex = i1[k] - rstart;
    6584:       if ((j1[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
    6585:       minj[rindex] = PetscMin(minj[rindex], j1[k]);
    6586:     }
    6587:     for (k = 0; k < n2; k++) {
    6588:       if (j2[k] < cstart || j2[k] >= cend) continue;
    6589:       const PetscInt rindex = i2[k] - rstart;
    6590:       if ((j2[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
    6591:       minj[rindex] = PetscMin(minj[rindex], j2[k]);
    6592:     }
    6593:     for (k = i1start; k < rem; k++) {
    6594:       const PetscInt rindex = i1[k] - rstart;
    6595:       if (j1[k] < cstart || j1[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
    6596:       if (j1[k] == minj[rindex]) j1[k] = i1[k] + (cstart - rstart);
    6597:       else if ((j1[k] - cstart) == rindex) j1[k] = minj[rindex];
    6598:     }
    6599:     for (k = 0; k < n2; k++) {
    6600:       const PetscInt rindex = i2[k] - rstart;
    6601:       if (j2[k] < cstart || j2[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
    6602:       if (j2[k] == minj[rindex]) j2[k] = i2[k] + (cstart - rstart);
    6603:       else if ((j2[k] - cstart) == rindex) j2[k] = minj[rindex];
    6604:     }
    6605:     PetscCall(PetscBTDestroy(&hasdiag));
    6606:     PetscCall(PetscFree(minj));
    6607:   }

    6609:   /* Split local COOs and received COOs into diag/offdiag portions */
    6610:   PetscCount *rowBegin1, *rowMid1, *rowEnd1;
    6611:   PetscCount *Ajmap1, *Aperm1, *Bjmap1, *Bperm1;
    6612:   PetscCount  Annz1, Bnnz1, Atot1, Btot1;
    6613:   PetscCount *rowBegin2, *rowMid2, *rowEnd2;
    6614:   PetscCount *Ajmap2, *Aperm2, *Bjmap2, *Bperm2;
    6615:   PetscCount  Annz2, Bnnz2, Atot2, Btot2;

    6617:   PetscCall(PetscCalloc3(m, &rowBegin1, m, &rowMid1, m, &rowEnd1));
    6618:   PetscCall(PetscCalloc3(m, &rowBegin2, m, &rowMid2, m, &rowEnd2));
    6619:   PetscCall(MatSplitEntries_Internal(mat, rem, i1, j1, perm1, rowBegin1, rowMid1, rowEnd1, &Atot1, &Aperm1, &Annz1, &Ajmap1, &Btot1, &Bperm1, &Bnnz1, &Bjmap1));
    6620:   PetscCall(MatSplitEntries_Internal(mat, n2, i2, j2, perm2, rowBegin2, rowMid2, rowEnd2, &Atot2, &Aperm2, &Annz2, &Ajmap2, &Btot2, &Bperm2, &Bnnz2, &Bjmap2));

    6622:   /* Merge local COOs with received COOs: diag with diag, offdiag with offdiag */
    6623:   PetscInt *Ai, *Bi;
    6624:   PetscInt *Aj, *Bj;

    6626:   PetscCall(PetscMalloc1(m + 1, &Ai));
    6627:   PetscCall(PetscMalloc1(m + 1, &Bi));
    6628:   PetscCall(PetscMalloc1(Annz1 + Annz2, &Aj)); /* Since local and remote entries might have dups, we might allocate excess memory */
    6629:   PetscCall(PetscMalloc1(Bnnz1 + Bnnz2, &Bj));

    6631:   PetscCount *Aimap1, *Bimap1, *Aimap2, *Bimap2;
    6632:   PetscCall(PetscMalloc1(Annz1, &Aimap1));
    6633:   PetscCall(PetscMalloc1(Bnnz1, &Bimap1));
    6634:   PetscCall(PetscMalloc1(Annz2, &Aimap2));
    6635:   PetscCall(PetscMalloc1(Bnnz2, &Bimap2));

    6637:   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowBegin1, rowMid1, rowBegin2, rowMid2, Ajmap1, Ajmap2, Aimap1, Aimap2, Ai, Aj));
    6638:   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowMid1, rowEnd1, rowMid2, rowEnd2, Bjmap1, Bjmap2, Bimap1, Bimap2, Bi, Bj));

    6640:   /* Expand Ajmap1/Bjmap1 to make them based off nonzeros in A/B, since we     */
    6641:   /* expect nonzeros in A/B most likely have local contributing entries        */
    6642:   PetscInt    Annz = Ai[m];
    6643:   PetscInt    Bnnz = Bi[m];
    6644:   PetscCount *Ajmap1_new, *Bjmap1_new;

    6646:   PetscCall(PetscMalloc1(Annz + 1, &Ajmap1_new));
    6647:   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap1_new));

    6649:   PetscCall(ExpandJmap_Internal(Annz1, Annz, Aimap1, Ajmap1, Ajmap1_new));
    6650:   PetscCall(ExpandJmap_Internal(Bnnz1, Bnnz, Bimap1, Bjmap1, Bjmap1_new));

    6652:   PetscCall(PetscFree(Aimap1));
    6653:   PetscCall(PetscFree(Ajmap1));
    6654:   PetscCall(PetscFree(Bimap1));
    6655:   PetscCall(PetscFree(Bjmap1));
    6656:   PetscCall(PetscFree3(rowBegin1, rowMid1, rowEnd1));
    6657:   PetscCall(PetscFree3(rowBegin2, rowMid2, rowEnd2));
    6658:   PetscCall(PetscFree(perm1));
    6659:   PetscCall(PetscFree3(i2, j2, perm2));

    6661:   Ajmap1 = Ajmap1_new;
    6662:   Bjmap1 = Bjmap1_new;

    6664:   /* Reallocate Aj, Bj once we know actual numbers of unique nonzeros in A and B */
    6665:   if (Annz < Annz1 + Annz2) {
    6666:     PetscInt *Aj_new;
    6667:     PetscCall(PetscMalloc1(Annz, &Aj_new));
    6668:     PetscCall(PetscArraycpy(Aj_new, Aj, Annz));
    6669:     PetscCall(PetscFree(Aj));
    6670:     Aj = Aj_new;
    6671:   }

    6673:   if (Bnnz < Bnnz1 + Bnnz2) {
    6674:     PetscInt *Bj_new;
    6675:     PetscCall(PetscMalloc1(Bnnz, &Bj_new));
    6676:     PetscCall(PetscArraycpy(Bj_new, Bj, Bnnz));
    6677:     PetscCall(PetscFree(Bj));
    6678:     Bj = Bj_new;
    6679:   }

    6681:   /* Create new submatrices for on-process and off-process coupling                  */
    6682:   PetscScalar     *Aa, *Ba;
    6683:   MatType          rtype;
    6684:   Mat_SeqAIJ      *a, *b;
    6685:   PetscObjectState state;
    6686:   PetscCall(PetscCalloc1(Annz, &Aa)); /* Zero matrix on device */
    6687:   PetscCall(PetscCalloc1(Bnnz, &Ba));
    6688:   /* make Aj[] local, i.e, based off the start column of the diagonal portion */
    6689:   if (cstart) {
    6690:     for (k = 0; k < Annz; k++) Aj[k] -= cstart;
    6691:   }

    6693:   PetscCall(MatGetRootType_Private(mat, &rtype));

    6695:   MatSeqXAIJGetOptions_Private(mpiaij->A);
    6696:   PetscCall(MatDestroy(&mpiaij->A));
    6697:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, Ai, Aj, Aa, &mpiaij->A));
    6698:   PetscCall(MatSetBlockSizesFromMats(mpiaij->A, mat, mat));
    6699:   MatSeqXAIJRestoreOptions_Private(mpiaij->A);

    6701:   MatSeqXAIJGetOptions_Private(mpiaij->B);
    6702:   PetscCall(MatDestroy(&mpiaij->B));
    6703:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, mat->cmap->N, Bi, Bj, Ba, &mpiaij->B));
    6704:   PetscCall(MatSetBlockSizesFromMats(mpiaij->B, mat, mat));
    6705:   MatSeqXAIJRestoreOptions_Private(mpiaij->B);

    6707:   PetscCall(MatSetUpMultiply_MPIAIJ(mat));
    6708:   mat->was_assembled = PETSC_TRUE; // was_assembled in effect means the Mvctx is built; doing so avoids redundant MatSetUpMultiply_MPIAIJ
    6709:   state              = mpiaij->A->nonzerostate + mpiaij->B->nonzerostate;
    6710:   PetscCallMPI(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));

    6712:   a          = (Mat_SeqAIJ *)mpiaij->A->data;
    6713:   b          = (Mat_SeqAIJ *)mpiaij->B->data;
    6714:   a->free_a  = PETSC_TRUE;
    6715:   a->free_ij = PETSC_TRUE;
    6716:   b->free_a  = PETSC_TRUE;
    6717:   b->free_ij = PETSC_TRUE;
    6718:   a->maxnz   = a->nz;
    6719:   b->maxnz   = b->nz;

    6721:   /* conversion must happen AFTER multiply setup */
    6722:   PetscCall(MatConvert(mpiaij->A, rtype, MAT_INPLACE_MATRIX, &mpiaij->A));
    6723:   PetscCall(MatConvert(mpiaij->B, rtype, MAT_INPLACE_MATRIX, &mpiaij->B));
    6724:   PetscCall(VecDestroy(&mpiaij->lvec));
    6725:   PetscCall(MatCreateVecs(mpiaij->B, &mpiaij->lvec, NULL));

    6727:   // Put the COO struct in a container and then attach that to the matrix
    6728:   PetscCall(PetscMalloc1(1, &coo));
    6729:   coo->n       = coo_n;
    6730:   coo->sf      = sf2;
    6731:   coo->sendlen = nleaves;
    6732:   coo->recvlen = nroots;
    6733:   coo->Annz    = Annz;
    6734:   coo->Bnnz    = Bnnz;
    6735:   coo->Annz2   = Annz2;
    6736:   coo->Bnnz2   = Bnnz2;
    6737:   coo->Atot1   = Atot1;
    6738:   coo->Atot2   = Atot2;
    6739:   coo->Btot1   = Btot1;
    6740:   coo->Btot2   = Btot2;
    6741:   coo->Ajmap1  = Ajmap1;
    6742:   coo->Aperm1  = Aperm1;
    6743:   coo->Bjmap1  = Bjmap1;
    6744:   coo->Bperm1  = Bperm1;
    6745:   coo->Aimap2  = Aimap2;
    6746:   coo->Ajmap2  = Ajmap2;
    6747:   coo->Aperm2  = Aperm2;
    6748:   coo->Bimap2  = Bimap2;
    6749:   coo->Bjmap2  = Bjmap2;
    6750:   coo->Bperm2  = Bperm2;
    6751:   coo->Cperm1  = Cperm1;
    6752:   // Allocate in preallocation. If not used, it has zero cost on host
    6753:   PetscCall(PetscMalloc2(coo->sendlen, &coo->sendbuf, coo->recvlen, &coo->recvbuf));
    6754:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    6755:   PetscCall(PetscContainerSetPointer(container, coo));
    6756:   PetscCall(PetscContainerSetCtxDestroy(container, MatCOOStructDestroy_MPIAIJ));
    6757:   PetscCall(PetscObjectCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject)container));
    6758:   PetscCall(PetscContainerDestroy(&container));
    6759:   PetscFunctionReturn(PETSC_SUCCESS);
    6760: }

    6762: static PetscErrorCode MatSetValuesCOO_MPIAIJ(Mat mat, const PetscScalar v[], InsertMode imode)
    6763: {
    6764:   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
    6765:   Mat                  A = mpiaij->A, B = mpiaij->B;
    6766:   PetscScalar         *Aa, *Ba;
    6767:   PetscScalar         *sendbuf, *recvbuf;
    6768:   const PetscCount    *Ajmap1, *Ajmap2, *Aimap2;
    6769:   const PetscCount    *Bjmap1, *Bjmap2, *Bimap2;
    6770:   const PetscCount    *Aperm1, *Aperm2, *Bperm1, *Bperm2;
    6771:   const PetscCount    *Cperm1;
    6772:   PetscContainer       container;
    6773:   MatCOOStruct_MPIAIJ *coo;

    6775:   PetscFunctionBegin;
    6776:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container));
    6777:   PetscCheck(container, PetscObjectComm((PetscObject)mat), PETSC_ERR_PLIB, "Not found MatCOOStruct on this matrix");
    6778:   PetscCall(PetscContainerGetPointer(container, (void **)&coo));
    6779:   sendbuf = coo->sendbuf;
    6780:   recvbuf = coo->recvbuf;
    6781:   Ajmap1  = coo->Ajmap1;
    6782:   Ajmap2  = coo->Ajmap2;
    6783:   Aimap2  = coo->Aimap2;
    6784:   Bjmap1  = coo->Bjmap1;
    6785:   Bjmap2  = coo->Bjmap2;
    6786:   Bimap2  = coo->Bimap2;
    6787:   Aperm1  = coo->Aperm1;
    6788:   Aperm2  = coo->Aperm2;
    6789:   Bperm1  = coo->Bperm1;
    6790:   Bperm2  = coo->Bperm2;
    6791:   Cperm1  = coo->Cperm1;

    6793:   PetscCall(MatSeqAIJGetArray(A, &Aa)); /* Might read and write matrix values */
    6794:   PetscCall(MatSeqAIJGetArray(B, &Ba));

    6796:   /* Pack entries to be sent to remote */
    6797:   for (PetscCount i = 0; i < coo->sendlen; i++) sendbuf[i] = v[Cperm1[i]];

    6799:   /* Send remote entries to their owner and overlap the communication with local computation */
    6800:   PetscCall(PetscSFReduceWithMemTypeBegin(coo->sf, MPIU_SCALAR, PETSC_MEMTYPE_HOST, sendbuf, PETSC_MEMTYPE_HOST, recvbuf, MPI_REPLACE));
    6801:   /* Add local entries to A and B */
    6802:   for (PetscCount i = 0; i < coo->Annz; i++) { /* All nonzeros in A are either zero'ed or added with a value (i.e., initialized) */
    6803:     PetscScalar sum = 0.0;                     /* Do partial summation first to improve numerical stability */
    6804:     for (PetscCount k = Ajmap1[i]; k < Ajmap1[i + 1]; k++) sum += v[Aperm1[k]];
    6805:     Aa[i] = (imode == INSERT_VALUES ? 0.0 : Aa[i]) + sum;
    6806:   }
    6807:   for (PetscCount i = 0; i < coo->Bnnz; i++) {
    6808:     PetscScalar sum = 0.0;
    6809:     for (PetscCount k = Bjmap1[i]; k < Bjmap1[i + 1]; k++) sum += v[Bperm1[k]];
    6810:     Ba[i] = (imode == INSERT_VALUES ? 0.0 : Ba[i]) + sum;
    6811:   }
    6812:   PetscCall(PetscSFReduceEnd(coo->sf, MPIU_SCALAR, sendbuf, recvbuf, MPI_REPLACE));

    6814:   /* Add received remote entries to A and B */
    6815:   for (PetscCount i = 0; i < coo->Annz2; i++) {
    6816:     for (PetscCount k = Ajmap2[i]; k < Ajmap2[i + 1]; k++) Aa[Aimap2[i]] += recvbuf[Aperm2[k]];
    6817:   }
    6818:   for (PetscCount i = 0; i < coo->Bnnz2; i++) {
    6819:     for (PetscCount k = Bjmap2[i]; k < Bjmap2[i + 1]; k++) Ba[Bimap2[i]] += recvbuf[Bperm2[k]];
    6820:   }
    6821:   PetscCall(MatSeqAIJRestoreArray(A, &Aa));
    6822:   PetscCall(MatSeqAIJRestoreArray(B, &Ba));
    6823:   PetscFunctionReturn(PETSC_SUCCESS);
    6824: }

    6826: /*MC
    6827:    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.

    6829:    Options Database Keys:
    6830: . -mat_type mpiaij - sets the matrix type to `MATMPIAIJ` during a call to `MatSetFromOptions()`

    6832:    Level: beginner

    6834:    Notes:
    6835:    `MatSetValues()` may be called for this matrix type with a `NULL` argument for the numerical values,
    6836:     in this case the values associated with the rows and columns one passes in are set to zero
    6837:     in the matrix

    6839:     `MatSetOptions`(,`MAT_STRUCTURE_ONLY`,`PETSC_TRUE`) may be called for this matrix type. In this no
    6840:     space is allocated for the nonzero entries and any entries passed with `MatSetValues()` are ignored

    6842: .seealso: [](ch_matrices), `Mat`, `MATSEQAIJ`, `MATAIJ`, `MatCreateAIJ()`
    6843: M*/
    6844: PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
    6845: {
    6846:   Mat_MPIAIJ *b;
    6847:   PetscMPIInt size;

    6849:   PetscFunctionBegin;
    6850:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

    6852:   PetscCall(PetscNew(&b));
    6853:   B->data       = (void *)b;
    6854:   B->ops[0]     = MatOps_Values;
    6855:   B->assembled  = PETSC_FALSE;
    6856:   B->insertmode = NOT_SET_VALUES;
    6857:   b->size       = size;

    6859:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)B), &b->rank));

    6861:   /* build cache for off array entries formed */
    6862:   PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)B), 1, &B->stash));

    6864:   b->donotstash  = PETSC_FALSE;
    6865:   b->colmap      = NULL;
    6866:   b->garray      = NULL;
    6867:   b->roworiented = PETSC_TRUE;

    6869:   /* stuff used for matrix vector multiply */
    6870:   b->lvec  = NULL;
    6871:   b->Mvctx = NULL;

    6873:   /* stuff for MatGetRow() */
    6874:   b->rowindices   = NULL;
    6875:   b->rowvalues    = NULL;
    6876:   b->getrowactive = PETSC_FALSE;

    6878:   /* flexible pointer used in CUSPARSE classes */
    6879:   b->spptr = NULL;

    6881:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetUseScalableIncreaseOverlap_C", MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ));
    6882:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_MPIAIJ));
    6883:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_MPIAIJ));
    6884:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsTranspose_C", MatIsTranspose_MPIAIJ));
    6885:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocation_C", MatMPIAIJSetPreallocation_MPIAIJ));
    6886:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetPreallocation_C", MatResetPreallocation_MPIAIJ));
    6887:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetHash_C", MatResetHash_MPIAIJ));
    6888:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocationCSR_C", MatMPIAIJSetPreallocationCSR_MPIAIJ));
    6889:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDiagonalScaleLocal_C", MatDiagonalScaleLocal_MPIAIJ));
    6890:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijperm_C", MatConvert_MPIAIJ_MPIAIJPERM));
    6891:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijsell_C", MatConvert_MPIAIJ_MPIAIJSELL));
    6892: #if defined(PETSC_HAVE_CUDA)
    6893:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcusparse_C", MatConvert_MPIAIJ_MPIAIJCUSPARSE));
    6894: #endif
    6895: #if defined(PETSC_HAVE_HIP)
    6896:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijhipsparse_C", MatConvert_MPIAIJ_MPIAIJHIPSPARSE));
    6897: #endif
    6898: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    6899:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijkokkos_C", MatConvert_MPIAIJ_MPIAIJKokkos));
    6900: #endif
    6901: #if defined(PETSC_HAVE_MKL_SPARSE)
    6902:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijmkl_C", MatConvert_MPIAIJ_MPIAIJMKL));
    6903: #endif
    6904:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcrl_C", MatConvert_MPIAIJ_MPIAIJCRL));
    6905:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpibaij_C", MatConvert_MPIAIJ_MPIBAIJ));
    6906:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisbaij_C", MatConvert_MPIAIJ_MPISBAIJ));
    6907:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpidense_C", MatConvert_MPIAIJ_MPIDense));
    6908: #if defined(PETSC_HAVE_ELEMENTAL)
    6909:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_elemental_C", MatConvert_MPIAIJ_Elemental));
    6910: #endif
    6911: #if defined(PETSC_HAVE_SCALAPACK)
    6912:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_scalapack_C", MatConvert_AIJ_ScaLAPACK));
    6913: #endif
    6914:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_is_C", MatConvert_XAIJ_IS));
    6915:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisell_C", MatConvert_MPIAIJ_MPISELL));
    6916: #if defined(PETSC_HAVE_HYPRE)
    6917:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_hypre_C", MatConvert_AIJ_HYPRE));
    6918:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", MatProductSetFromOptions_Transpose_AIJ_AIJ));
    6919: #endif
    6920:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_is_mpiaij_C", MatProductSetFromOptions_IS_XAIJ));
    6921:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_mpiaij_mpiaij_C", MatProductSetFromOptions_MPIAIJ));
    6922:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_MPIAIJ));
    6923:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetValuesCOO_C", MatSetValuesCOO_MPIAIJ));
    6924:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATMPIAIJ));
    6925:   PetscFunctionReturn(PETSC_SUCCESS);
    6926: }

    6928: /*@
    6929:   MatCreateMPIAIJWithSplitArrays - creates a `MATMPIAIJ` matrix using arrays that contain the "diagonal"
    6930:   and "off-diagonal" part of the matrix in CSR format.

    6932:   Collective

    6934:   Input Parameters:
    6935: + comm - MPI communicator
    6936: . m    - number of local rows (Cannot be `PETSC_DECIDE`)
    6937: . n    - This value should be the same as the local size used in creating the
    6938:          x vector for the matrix-vector product $y = Ax$. (or `PETSC_DECIDE` to have
    6939:          calculated if `N` is given) For square matrices `n` is almost always `m`.
    6940: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    6941: . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    6942: . 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
    6943: . j    - column indices, which must be local, i.e., based off the start column of the diagonal portion
    6944: . a    - matrix values
    6945: . 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
    6946: . oj   - column indices, which must be global, representing global columns in the `MATMPIAIJ` matrix
    6947: - oa   - matrix values

    6949:   Output Parameter:
    6950: . mat - the matrix

    6952:   Level: advanced

    6954:   Notes:
    6955:   The `i`, `j`, and `a` arrays ARE NOT copied by this routine into the internal format used by PETSc (even in Fortran). The user
    6956:   must free the arrays once the matrix has been destroyed and not before.

    6958:   The `i` and `j` indices are 0 based

    6960:   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix

    6962:   This sets local rows and cannot be used to set off-processor values.

    6964:   Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
    6965:   legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
    6966:   not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
    6967:   the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
    6968:   keep track of the underlying array. Use `MatSetOption`(A,`MAT_NO_OFF_PROC_ENTRIES`,`PETSC_TRUE`) to disable all
    6969:   communication if it is known that only local entries will be set.

    6971: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    6972:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithArrays()`
    6973: @*/
    6974: 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)
    6975: {
    6976:   Mat_MPIAIJ *maij;

    6978:   PetscFunctionBegin;
    6979:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    6980:   PetscCheck(i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    6981:   PetscCheck(oi[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "oi (row indices) must start with 0");
    6982:   PetscCall(MatCreate(comm, mat));
    6983:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    6984:   PetscCall(MatSetType(*mat, MATMPIAIJ));
    6985:   maij = (Mat_MPIAIJ *)(*mat)->data;

    6987:   (*mat)->preallocated = PETSC_TRUE;

    6989:   PetscCall(PetscLayoutSetUp((*mat)->rmap));
    6990:   PetscCall(PetscLayoutSetUp((*mat)->cmap));

    6992:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, i, j, a, &maij->A));
    6993:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, (*mat)->cmap->N, oi, oj, oa, &maij->B));

    6995:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    6996:   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
    6997:   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
    6998:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    6999:   PetscCall(MatSetOption(*mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    7000:   PetscFunctionReturn(PETSC_SUCCESS);
    7001: }

    7003: typedef struct {
    7004:   Mat       *mp;    /* intermediate products */
    7005:   PetscBool *mptmp; /* is the intermediate product temporary ? */
    7006:   PetscInt   cp;    /* number of intermediate products */

    7008:   /* support for MatGetBrowsOfAoCols_MPIAIJ for P_oth */
    7009:   PetscInt    *startsj_s, *startsj_r;
    7010:   PetscScalar *bufa;
    7011:   Mat          P_oth;

    7013:   /* may take advantage of merging product->B */
    7014:   Mat Bloc; /* B-local by merging diag and off-diag */

    7016:   /* cusparse does not have support to split between symbolic and numeric phases.
    7017:      When api_user is true, we don't need to update the numerical values
    7018:      of the temporary storage */
    7019:   PetscBool reusesym;

    7021:   /* support for COO values insertion */
    7022:   PetscScalar *coo_v, *coo_w; /* store on-process and off-process COO scalars, and used as MPI recv/send buffers respectively */
    7023:   PetscInt   **own;           /* own[i] points to address of on-process COO indices for Mat mp[i] */
    7024:   PetscInt   **off;           /* off[i] points to address of off-process COO indices for Mat mp[i] */
    7025:   PetscBool    hasoffproc;    /* if true, have off-process values insertion (i.e. AtB or PtAP) */
    7026:   PetscSF      sf;            /* used for non-local values insertion and memory malloc */
    7027:   PetscMemType mtype;

    7029:   /* customization */
    7030:   PetscBool abmerge;
    7031:   PetscBool P_oth_bind;
    7032: } MatMatMPIAIJBACKEND;

    7034: static PetscErrorCode MatDestroy_MatMatMPIAIJBACKEND(void *data)
    7035: {
    7036:   MatMatMPIAIJBACKEND *mmdata = (MatMatMPIAIJBACKEND *)data;
    7037:   PetscInt             i;

    7039:   PetscFunctionBegin;
    7040:   PetscCall(PetscFree2(mmdata->startsj_s, mmdata->startsj_r));
    7041:   PetscCall(PetscFree(mmdata->bufa));
    7042:   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_v));
    7043:   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_w));
    7044:   PetscCall(MatDestroy(&mmdata->P_oth));
    7045:   PetscCall(MatDestroy(&mmdata->Bloc));
    7046:   PetscCall(PetscSFDestroy(&mmdata->sf));
    7047:   for (i = 0; i < mmdata->cp; i++) PetscCall(MatDestroy(&mmdata->mp[i]));
    7048:   PetscCall(PetscFree2(mmdata->mp, mmdata->mptmp));
    7049:   PetscCall(PetscFree(mmdata->own[0]));
    7050:   PetscCall(PetscFree(mmdata->own));
    7051:   PetscCall(PetscFree(mmdata->off[0]));
    7052:   PetscCall(PetscFree(mmdata->off));
    7053:   PetscCall(PetscFree(mmdata));
    7054:   PetscFunctionReturn(PETSC_SUCCESS);
    7055: }

    7057: /* Copy selected n entries with indices in idx[] of A to v[].
    7058:    If idx is NULL, copy the whole data array of A to v[]
    7059:  */
    7060: static PetscErrorCode MatSeqAIJCopySubArray(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
    7061: {
    7062:   PetscErrorCode (*f)(Mat, PetscInt, const PetscInt[], PetscScalar[]);

    7064:   PetscFunctionBegin;
    7065:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", &f));
    7066:   if (f) {
    7067:     PetscCall((*f)(A, n, idx, v));
    7068:   } else {
    7069:     const PetscScalar *vv;

    7071:     PetscCall(MatSeqAIJGetArrayRead(A, &vv));
    7072:     if (n && idx) {
    7073:       PetscScalar    *w  = v;
    7074:       const PetscInt *oi = idx;
    7075:       PetscInt        j;

    7077:       for (j = 0; j < n; j++) *w++ = vv[*oi++];
    7078:     } else {
    7079:       PetscCall(PetscArraycpy(v, vv, n));
    7080:     }
    7081:     PetscCall(MatSeqAIJRestoreArrayRead(A, &vv));
    7082:   }
    7083:   PetscFunctionReturn(PETSC_SUCCESS);
    7084: }

    7086: static PetscErrorCode MatProductNumeric_MPIAIJBACKEND(Mat C)
    7087: {
    7088:   MatMatMPIAIJBACKEND *mmdata;
    7089:   PetscInt             i, n_d, n_o;

    7091:   PetscFunctionBegin;
    7092:   MatCheckProduct(C, 1);
    7093:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
    7094:   mmdata = (MatMatMPIAIJBACKEND *)C->product->data;
    7095:   if (!mmdata->reusesym) { /* update temporary matrices */
    7096:     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));
    7097:     if (mmdata->Bloc) PetscCall(MatMPIAIJGetLocalMatMerge(C->product->B, MAT_REUSE_MATRIX, NULL, &mmdata->Bloc));
    7098:   }
    7099:   mmdata->reusesym = PETSC_FALSE;

    7101:   for (i = 0; i < mmdata->cp; i++) {
    7102:     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]);
    7103:     PetscCall((*mmdata->mp[i]->ops->productnumeric)(mmdata->mp[i]));
    7104:   }
    7105:   for (i = 0, n_d = 0, n_o = 0; i < mmdata->cp; i++) {
    7106:     PetscInt noff;

    7108:     PetscCall(PetscIntCast(mmdata->off[i + 1] - mmdata->off[i], &noff));
    7109:     if (mmdata->mptmp[i]) continue;
    7110:     if (noff) {
    7111:       PetscInt nown;

    7113:       PetscCall(PetscIntCast(mmdata->own[i + 1] - mmdata->own[i], &nown));
    7114:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], noff, mmdata->off[i], mmdata->coo_w + n_o));
    7115:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], nown, mmdata->own[i], mmdata->coo_v + n_d));
    7116:       n_o += noff;
    7117:       n_d += nown;
    7118:     } else {
    7119:       Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mmdata->mp[i]->data;

    7121:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], mm->nz, NULL, mmdata->coo_v + n_d));
    7122:       n_d += mm->nz;
    7123:     }
    7124:   }
    7125:   if (mmdata->hasoffproc) { /* offprocess insertion */
    7126:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
    7127:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
    7128:   }
    7129:   PetscCall(MatSetValuesCOO(C, mmdata->coo_v, INSERT_VALUES));
    7130:   PetscFunctionReturn(PETSC_SUCCESS);
    7131: }

    7133: /* Support for Pt * A, A * P, or Pt * A * P */
    7134: #define MAX_NUMBER_INTERMEDIATE 4
    7135: PetscErrorCode MatProductSymbolic_MPIAIJBACKEND(Mat C)
    7136: {
    7137:   Mat_Product           *product = C->product;
    7138:   Mat                    A, P, mp[MAX_NUMBER_INTERMEDIATE]; /* A, P and a series of intermediate matrices */
    7139:   Mat_MPIAIJ            *a, *p;
    7140:   MatMatMPIAIJBACKEND   *mmdata;
    7141:   ISLocalToGlobalMapping P_oth_l2g = NULL;
    7142:   IS                     glob      = NULL;
    7143:   const char            *prefix;
    7144:   char                   pprefix[256];
    7145:   const PetscInt        *globidx, *P_oth_idx;
    7146:   PetscInt               i, j, cp, m, n, M, N, *coo_i, *coo_j;
    7147:   PetscCount             ncoo, ncoo_d, ncoo_o, ncoo_oown;
    7148:   PetscInt               cmapt[MAX_NUMBER_INTERMEDIATE], rmapt[MAX_NUMBER_INTERMEDIATE]; /* col/row map type for each Mat in mp[]. */
    7149:                                                                                          /* type-0: consecutive, start from 0; type-1: consecutive with */
    7150:                                                                                          /* a base offset; type-2: sparse with a local to global map table */
    7151:   const PetscInt *cmapa[MAX_NUMBER_INTERMEDIATE], *rmapa[MAX_NUMBER_INTERMEDIATE];       /* col/row local to global map array (table) for type-2 map type */

    7153:   MatProductType ptype;
    7154:   PetscBool      mptmp[MAX_NUMBER_INTERMEDIATE], hasoffproc = PETSC_FALSE, iscuda, iship, iskokk;
    7155:   PetscMPIInt    size;

    7157:   PetscFunctionBegin;
    7158:   MatCheckProduct(C, 1);
    7159:   PetscCheck(!product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
    7160:   ptype = product->type;
    7161:   if (product->A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
    7162:     ptype                                          = MATPRODUCT_AB;
    7163:     product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
    7164:   }
    7165:   switch (ptype) {
    7166:   case MATPRODUCT_AB:
    7167:     A          = product->A;
    7168:     P          = product->B;
    7169:     m          = A->rmap->n;
    7170:     n          = P->cmap->n;
    7171:     M          = A->rmap->N;
    7172:     N          = P->cmap->N;
    7173:     hasoffproc = PETSC_FALSE; /* will not scatter mat product values to other processes */
    7174:     break;
    7175:   case MATPRODUCT_AtB:
    7176:     P          = product->A;
    7177:     A          = product->B;
    7178:     m          = P->cmap->n;
    7179:     n          = A->cmap->n;
    7180:     M          = P->cmap->N;
    7181:     N          = A->cmap->N;
    7182:     hasoffproc = PETSC_TRUE;
    7183:     break;
    7184:   case MATPRODUCT_PtAP:
    7185:     A          = product->A;
    7186:     P          = product->B;
    7187:     m          = P->cmap->n;
    7188:     n          = P->cmap->n;
    7189:     M          = P->cmap->N;
    7190:     N          = P->cmap->N;
    7191:     hasoffproc = PETSC_TRUE;
    7192:     break;
    7193:   default:
    7194:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
    7195:   }
    7196:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)C), &size));
    7197:   if (size == 1) hasoffproc = PETSC_FALSE;

    7199:   /* defaults */
    7200:   for (i = 0; i < MAX_NUMBER_INTERMEDIATE; i++) {
    7201:     mp[i]    = NULL;
    7202:     mptmp[i] = PETSC_FALSE;
    7203:     rmapt[i] = -1;
    7204:     cmapt[i] = -1;
    7205:     rmapa[i] = NULL;
    7206:     cmapa[i] = NULL;
    7207:   }

    7209:   /* customization */
    7210:   PetscCall(PetscNew(&mmdata));
    7211:   mmdata->reusesym = product->api_user;
    7212:   if (ptype == MATPRODUCT_AB) {
    7213:     if (product->api_user) {
    7214:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
    7215:       PetscCall(PetscOptionsBool("-matmatmult_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
    7216:       PetscCall(PetscOptionsBool("-matmatmult_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7217:       PetscOptionsEnd();
    7218:     } else {
    7219:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
    7220:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
    7221:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7222:       PetscOptionsEnd();
    7223:     }
    7224:   } else if (ptype == MATPRODUCT_PtAP) {
    7225:     if (product->api_user) {
    7226:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
    7227:       PetscCall(PetscOptionsBool("-matptap_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7228:       PetscOptionsEnd();
    7229:     } else {
    7230:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
    7231:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7232:       PetscOptionsEnd();
    7233:     }
    7234:   }
    7235:   a = (Mat_MPIAIJ *)A->data;
    7236:   p = (Mat_MPIAIJ *)P->data;
    7237:   PetscCall(MatSetSizes(C, m, n, M, N));
    7238:   PetscCall(PetscLayoutSetUp(C->rmap));
    7239:   PetscCall(PetscLayoutSetUp(C->cmap));
    7240:   PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    7241:   PetscCall(MatGetOptionsPrefix(C, &prefix));

    7243:   cp = 0;
    7244:   switch (ptype) {
    7245:   case MATPRODUCT_AB: /* A * P */
    7246:     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));

    7248:     /* A_diag * P_local (merged or not) */
    7249:     if (mmdata->abmerge) { /* P's diagonal and off-diag blocks are merged to one matrix, then multiplied by A_diag */
    7250:       /* P is product->B */
    7251:       PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7252:       PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
    7253:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7254:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7255:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7256:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7257:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7258:       mp[cp]->product->api_user = product->api_user;
    7259:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7260:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7261:       PetscCall(ISGetIndices(glob, &globidx));
    7262:       rmapt[cp] = 1;
    7263:       cmapt[cp] = 2;
    7264:       cmapa[cp] = globidx;
    7265:       mptmp[cp] = PETSC_FALSE;
    7266:       cp++;
    7267:     } else { /* A_diag * P_diag and A_diag * P_off */
    7268:       PetscCall(MatProductCreate(a->A, p->A, NULL, &mp[cp]));
    7269:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7270:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7271:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7272:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7273:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7274:       mp[cp]->product->api_user = product->api_user;
    7275:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7276:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7277:       rmapt[cp] = 1;
    7278:       cmapt[cp] = 1;
    7279:       mptmp[cp] = PETSC_FALSE;
    7280:       cp++;
    7281:       PetscCall(MatProductCreate(a->A, p->B, NULL, &mp[cp]));
    7282:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7283:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7284:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7285:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7286:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7287:       mp[cp]->product->api_user = product->api_user;
    7288:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7289:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7290:       rmapt[cp] = 1;
    7291:       cmapt[cp] = 2;
    7292:       cmapa[cp] = p->garray;
    7293:       mptmp[cp] = PETSC_FALSE;
    7294:       cp++;
    7295:     }

    7297:     /* A_off * P_other */
    7298:     if (mmdata->P_oth) {
    7299:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g)); /* make P_oth use local col ids */
    7300:       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
    7301:       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)a->B)->type_name));
    7302:       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
    7303:       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
    7304:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7305:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7306:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7307:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7308:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7309:       mp[cp]->product->api_user = product->api_user;
    7310:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7311:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7312:       rmapt[cp] = 1;
    7313:       cmapt[cp] = 2;
    7314:       cmapa[cp] = P_oth_idx;
    7315:       mptmp[cp] = PETSC_FALSE;
    7316:       cp++;
    7317:     }
    7318:     break;

    7320:   case MATPRODUCT_AtB: /* (P^t * A): P_diag * A_loc + P_off * A_loc */
    7321:     /* A is product->B */
    7322:     PetscCall(MatMPIAIJGetLocalMatMerge(A, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7323:     if (A == P) { /* when A==P, we can take advantage of the already merged mmdata->Bloc */
    7324:       PetscCall(MatProductCreate(mmdata->Bloc, mmdata->Bloc, NULL, &mp[cp]));
    7325:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7326:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7327:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7328:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7329:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7330:       mp[cp]->product->api_user = product->api_user;
    7331:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7332:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7333:       PetscCall(ISGetIndices(glob, &globidx));
    7334:       rmapt[cp] = 2;
    7335:       rmapa[cp] = globidx;
    7336:       cmapt[cp] = 2;
    7337:       cmapa[cp] = globidx;
    7338:       mptmp[cp] = PETSC_FALSE;
    7339:       cp++;
    7340:     } else {
    7341:       PetscCall(MatProductCreate(p->A, mmdata->Bloc, NULL, &mp[cp]));
    7342:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7343:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7344:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7345:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7346:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7347:       mp[cp]->product->api_user = product->api_user;
    7348:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7349:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7350:       PetscCall(ISGetIndices(glob, &globidx));
    7351:       rmapt[cp] = 1;
    7352:       cmapt[cp] = 2;
    7353:       cmapa[cp] = globidx;
    7354:       mptmp[cp] = PETSC_FALSE;
    7355:       cp++;
    7356:       PetscCall(MatProductCreate(p->B, mmdata->Bloc, NULL, &mp[cp]));
    7357:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7358:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7359:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7360:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7361:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7362:       mp[cp]->product->api_user = product->api_user;
    7363:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7364:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7365:       rmapt[cp] = 2;
    7366:       rmapa[cp] = p->garray;
    7367:       cmapt[cp] = 2;
    7368:       cmapa[cp] = globidx;
    7369:       mptmp[cp] = PETSC_FALSE;
    7370:       cp++;
    7371:     }
    7372:     break;
    7373:   case MATPRODUCT_PtAP:
    7374:     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));
    7375:     /* P is product->B */
    7376:     PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7377:     PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
    7378:     PetscCall(MatProductSetType(mp[cp], MATPRODUCT_PtAP));
    7379:     PetscCall(MatProductSetFill(mp[cp], product->fill));
    7380:     PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7381:     PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7382:     PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7383:     mp[cp]->product->api_user = product->api_user;
    7384:     PetscCall(MatProductSetFromOptions(mp[cp]));
    7385:     PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7386:     PetscCall(ISGetIndices(glob, &globidx));
    7387:     rmapt[cp] = 2;
    7388:     rmapa[cp] = globidx;
    7389:     cmapt[cp] = 2;
    7390:     cmapa[cp] = globidx;
    7391:     mptmp[cp] = PETSC_FALSE;
    7392:     cp++;
    7393:     if (mmdata->P_oth) {
    7394:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g));
    7395:       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
    7396:       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)a->B)->type_name));
    7397:       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
    7398:       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
    7399:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7400:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7401:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7402:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7403:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7404:       mp[cp]->product->api_user = product->api_user;
    7405:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7406:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7407:       mptmp[cp] = PETSC_TRUE;
    7408:       cp++;
    7409:       PetscCall(MatProductCreate(mmdata->Bloc, mp[1], NULL, &mp[cp]));
    7410:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7411:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7412:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7413:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7414:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7415:       mp[cp]->product->api_user = product->api_user;
    7416:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7417:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7418:       rmapt[cp] = 2;
    7419:       rmapa[cp] = globidx;
    7420:       cmapt[cp] = 2;
    7421:       cmapa[cp] = P_oth_idx;
    7422:       mptmp[cp] = PETSC_FALSE;
    7423:       cp++;
    7424:     }
    7425:     break;
    7426:   default:
    7427:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
    7428:   }
    7429:   /* sanity check */
    7430:   if (size > 1)
    7431:     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);

    7433:   PetscCall(PetscMalloc2(cp, &mmdata->mp, cp, &mmdata->mptmp));
    7434:   for (i = 0; i < cp; i++) {
    7435:     mmdata->mp[i]    = mp[i];
    7436:     mmdata->mptmp[i] = mptmp[i];
    7437:   }
    7438:   mmdata->cp             = cp;
    7439:   C->product->data       = mmdata;
    7440:   C->product->destroy    = MatDestroy_MatMatMPIAIJBACKEND;
    7441:   C->ops->productnumeric = MatProductNumeric_MPIAIJBACKEND;

    7443:   /* memory type */
    7444:   mmdata->mtype = PETSC_MEMTYPE_HOST;
    7445:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iscuda, MATSEQAIJCUSPARSE, MATMPIAIJCUSPARSE, ""));
    7446:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iship, MATSEQAIJHIPSPARSE, MATMPIAIJHIPSPARSE, ""));
    7447:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iskokk, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, ""));
    7448:   if (iscuda) mmdata->mtype = PETSC_MEMTYPE_CUDA;
    7449:   else if (iship) mmdata->mtype = PETSC_MEMTYPE_HIP;
    7450:   else if (iskokk) mmdata->mtype = PETSC_MEMTYPE_KOKKOS;

    7452:   /* prepare coo coordinates for values insertion */

    7454:   /* count total nonzeros of those intermediate seqaij Mats
    7455:     ncoo_d:    # of nonzeros of matrices that do not have offproc entries
    7456:     ncoo_o:    # of nonzeros (of matrices that might have offproc entries) that will be inserted to remote procs
    7457:     ncoo_oown: # of nonzeros (of matrices that might have offproc entries) that will be inserted locally
    7458:   */
    7459:   for (cp = 0, ncoo_d = 0, ncoo_o = 0, ncoo_oown = 0; cp < mmdata->cp; cp++) {
    7460:     Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mp[cp]->data;
    7461:     if (mptmp[cp]) continue;
    7462:     if (rmapt[cp] == 2 && hasoffproc) { /* the rows need to be scatter to all processes (might include self) */
    7463:       const PetscInt *rmap = rmapa[cp];
    7464:       const PetscInt  mr   = mp[cp]->rmap->n;
    7465:       const PetscInt  rs   = C->rmap->rstart;
    7466:       const PetscInt  re   = C->rmap->rend;
    7467:       const PetscInt *ii   = mm->i;
    7468:       for (i = 0; i < mr; i++) {
    7469:         const PetscInt gr = rmap[i];
    7470:         const PetscInt nz = ii[i + 1] - ii[i];
    7471:         if (gr < rs || gr >= re) ncoo_o += nz; /* this row is offproc */
    7472:         else ncoo_oown += nz;                  /* this row is local */
    7473:       }
    7474:     } else ncoo_d += mm->nz;
    7475:   }

    7477:   /*
    7478:     ncoo: total number of nonzeros (including those inserted by remote procs) belonging to this proc

    7480:     ncoo = ncoo_d + ncoo_oown + ncoo2, which ncoo2 is number of nonzeros inserted to me by other procs.

    7482:     off[0] points to a big index array, which is shared by off[1,2,...]. Similarly, for own[0].

    7484:     off[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert to others
    7485:     own[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert locally
    7486:     so, off[p+1]-off[p] is the number of nonzeros that mp[p] will send to others.

    7488:     coo_i/j/v[]: [ncoo] row/col/val of nonzeros belonging to this proc.
    7489:     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.
    7490:   */
    7491:   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->off)); /* +1 to make a csr-like data structure */
    7492:   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->own));

    7494:   /* gather (i,j) of nonzeros inserted by remote procs */
    7495:   if (hasoffproc) {
    7496:     PetscSF  msf;
    7497:     PetscInt ncoo2, *coo_i2, *coo_j2;

    7499:     PetscCall(PetscMalloc1(ncoo_o, &mmdata->off[0]));
    7500:     PetscCall(PetscMalloc1(ncoo_oown, &mmdata->own[0]));
    7501:     PetscCall(PetscMalloc2(ncoo_o, &coo_i, ncoo_o, &coo_j)); /* to collect (i,j) of entries to be sent to others */

    7503:     for (cp = 0, ncoo_o = 0; cp < mmdata->cp; cp++) {
    7504:       Mat_SeqAIJ *mm     = (Mat_SeqAIJ *)mp[cp]->data;
    7505:       PetscInt   *idxoff = mmdata->off[cp];
    7506:       PetscInt   *idxown = mmdata->own[cp];
    7507:       if (!mptmp[cp] && rmapt[cp] == 2) { /* row map is sparse */
    7508:         const PetscInt *rmap = rmapa[cp];
    7509:         const PetscInt *cmap = cmapa[cp];
    7510:         const PetscInt *ii   = mm->i;
    7511:         PetscInt       *coi  = coo_i + ncoo_o;
    7512:         PetscInt       *coj  = coo_j + ncoo_o;
    7513:         const PetscInt  mr   = mp[cp]->rmap->n;
    7514:         const PetscInt  rs   = C->rmap->rstart;
    7515:         const PetscInt  re   = C->rmap->rend;
    7516:         const PetscInt  cs   = C->cmap->rstart;
    7517:         for (i = 0; i < mr; i++) {
    7518:           const PetscInt *jj = mm->j + ii[i];
    7519:           const PetscInt  gr = rmap[i];
    7520:           const PetscInt  nz = ii[i + 1] - ii[i];
    7521:           if (gr < rs || gr >= re) { /* this is an offproc row */
    7522:             for (j = ii[i]; j < ii[i + 1]; j++) {
    7523:               *coi++    = gr;
    7524:               *idxoff++ = j;
    7525:             }
    7526:             if (!cmapt[cp]) { /* already global */
    7527:               for (j = 0; j < nz; j++) *coj++ = jj[j];
    7528:             } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
    7529:               for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
    7530:             } else { /* offdiag */
    7531:               for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
    7532:             }
    7533:             ncoo_o += nz;
    7534:           } else { /* this is a local row */
    7535:             for (j = ii[i]; j < ii[i + 1]; j++) *idxown++ = j;
    7536:           }
    7537:         }
    7538:       }
    7539:       mmdata->off[cp + 1] = idxoff;
    7540:       mmdata->own[cp + 1] = idxown;
    7541:     }

    7543:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
    7544:     PetscInt incoo_o;
    7545:     PetscCall(PetscIntCast(ncoo_o, &incoo_o));
    7546:     PetscCall(PetscSFSetGraphLayout(mmdata->sf, C->rmap, incoo_o /*nleaves*/, NULL /*ilocal*/, PETSC_OWN_POINTER, coo_i));
    7547:     PetscCall(PetscSFGetMultiSF(mmdata->sf, &msf));
    7548:     PetscCall(PetscSFGetGraph(msf, &ncoo2 /*nroots*/, NULL, NULL, NULL));
    7549:     ncoo = ncoo_d + ncoo_oown + ncoo2;
    7550:     PetscCall(PetscMalloc2(ncoo, &coo_i2, ncoo, &coo_j2));
    7551:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown)); /* put (i,j) of remote nonzeros at back */
    7552:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown));
    7553:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
    7554:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
    7555:     PetscCall(PetscFree2(coo_i, coo_j));
    7556:     /* allocate MPI send buffer to collect nonzero values to be sent to remote procs */
    7557:     PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo_o * sizeof(PetscScalar), (void **)&mmdata->coo_w));
    7558:     coo_i = coo_i2;
    7559:     coo_j = coo_j2;
    7560:   } else { /* no offproc values insertion */
    7561:     ncoo = ncoo_d;
    7562:     PetscCall(PetscMalloc2(ncoo, &coo_i, ncoo, &coo_j));

    7564:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
    7565:     PetscCall(PetscSFSetGraph(mmdata->sf, 0, 0, NULL, PETSC_OWN_POINTER, NULL, PETSC_OWN_POINTER));
    7566:     PetscCall(PetscSFSetUp(mmdata->sf));
    7567:   }
    7568:   mmdata->hasoffproc = hasoffproc;

    7570:   /* gather (i,j) of nonzeros inserted locally */
    7571:   for (cp = 0, ncoo_d = 0; cp < mmdata->cp; cp++) {
    7572:     Mat_SeqAIJ     *mm   = (Mat_SeqAIJ *)mp[cp]->data;
    7573:     PetscInt       *coi  = coo_i + ncoo_d;
    7574:     PetscInt       *coj  = coo_j + ncoo_d;
    7575:     const PetscInt *jj   = mm->j;
    7576:     const PetscInt *ii   = mm->i;
    7577:     const PetscInt *cmap = cmapa[cp];
    7578:     const PetscInt *rmap = rmapa[cp];
    7579:     const PetscInt  mr   = mp[cp]->rmap->n;
    7580:     const PetscInt  rs   = C->rmap->rstart;
    7581:     const PetscInt  re   = C->rmap->rend;
    7582:     const PetscInt  cs   = C->cmap->rstart;

    7584:     if (mptmp[cp]) continue;
    7585:     if (rmapt[cp] == 1) { /* consecutive rows */
    7586:       /* fill coo_i */
    7587:       for (i = 0; i < mr; i++) {
    7588:         const PetscInt gr = i + rs;
    7589:         for (j = ii[i]; j < ii[i + 1]; j++) coi[j] = gr;
    7590:       }
    7591:       /* fill coo_j */
    7592:       if (!cmapt[cp]) { /* type-0, already global */
    7593:         PetscCall(PetscArraycpy(coj, jj, mm->nz));
    7594:       } else if (cmapt[cp] == 1) {                        /* type-1, local to global for consecutive columns of C */
    7595:         for (j = 0; j < mm->nz; j++) coj[j] = jj[j] + cs; /* lid + col start */
    7596:       } else {                                            /* type-2, local to global for sparse columns */
    7597:         for (j = 0; j < mm->nz; j++) coj[j] = cmap[jj[j]];
    7598:       }
    7599:       ncoo_d += mm->nz;
    7600:     } else if (rmapt[cp] == 2) { /* sparse rows */
    7601:       for (i = 0; i < mr; i++) {
    7602:         const PetscInt *jj = mm->j + ii[i];
    7603:         const PetscInt  gr = rmap[i];
    7604:         const PetscInt  nz = ii[i + 1] - ii[i];
    7605:         if (gr >= rs && gr < re) { /* local rows */
    7606:           for (j = ii[i]; j < ii[i + 1]; j++) *coi++ = gr;
    7607:           if (!cmapt[cp]) { /* type-0, already global */
    7608:             for (j = 0; j < nz; j++) *coj++ = jj[j];
    7609:           } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
    7610:             for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
    7611:           } else { /* type-2, local to global for sparse columns */
    7612:             for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
    7613:           }
    7614:           ncoo_d += nz;
    7615:         }
    7616:       }
    7617:     }
    7618:   }
    7619:   if (glob) PetscCall(ISRestoreIndices(glob, &globidx));
    7620:   PetscCall(ISDestroy(&glob));
    7621:   if (P_oth_l2g) PetscCall(ISLocalToGlobalMappingRestoreIndices(P_oth_l2g, &P_oth_idx));
    7622:   PetscCall(ISLocalToGlobalMappingDestroy(&P_oth_l2g));
    7623:   /* allocate an array to store all nonzeros (inserted locally or remotely) belonging to this proc */
    7624:   PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo * sizeof(PetscScalar), (void **)&mmdata->coo_v));

    7626:   /* set block sizes */
    7627:   A = product->A;
    7628:   P = product->B;
    7629:   switch (ptype) {
    7630:   case MATPRODUCT_PtAP:
    7631:     PetscCall(MatSetBlockSizes(C, P->cmap->bs, P->cmap->bs));
    7632:     break;
    7633:   case MATPRODUCT_RARt:
    7634:     PetscCall(MatSetBlockSizes(C, P->rmap->bs, P->rmap->bs));
    7635:     break;
    7636:   case MATPRODUCT_ABC:
    7637:     PetscCall(MatSetBlockSizesFromMats(C, A, product->C));
    7638:     break;
    7639:   case MATPRODUCT_AB:
    7640:     PetscCall(MatSetBlockSizesFromMats(C, A, P));
    7641:     break;
    7642:   case MATPRODUCT_AtB:
    7643:     PetscCall(MatSetBlockSizes(C, A->cmap->bs, P->cmap->bs));
    7644:     break;
    7645:   case MATPRODUCT_ABt:
    7646:     PetscCall(MatSetBlockSizes(C, A->rmap->bs, P->rmap->bs));
    7647:     break;
    7648:   default:
    7649:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for ProductType %s", MatProductTypes[ptype]);
    7650:   }

    7652:   /* preallocate with COO data */
    7653:   PetscCall(MatSetPreallocationCOO(C, ncoo, coo_i, coo_j));
    7654:   PetscCall(PetscFree2(coo_i, coo_j));
    7655:   PetscFunctionReturn(PETSC_SUCCESS);
    7656: }

    7658: PetscErrorCode MatProductSetFromOptions_MPIAIJBACKEND(Mat mat)
    7659: {
    7660:   Mat_Product *product = mat->product;
    7661: #if defined(PETSC_HAVE_DEVICE)
    7662:   PetscBool match  = PETSC_FALSE;
    7663:   PetscBool usecpu = PETSC_FALSE;
    7664: #else
    7665:   PetscBool match = PETSC_TRUE;
    7666: #endif

    7668:   PetscFunctionBegin;
    7669:   MatCheckProduct(mat, 1);
    7670: #if defined(PETSC_HAVE_DEVICE)
    7671:   if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, ((PetscObject)product->A)->type_name, &match));
    7672:   if (match) { /* we can always fallback to the CPU if requested */
    7673:     switch (product->type) {
    7674:     case MATPRODUCT_AB:
    7675:       if (product->api_user) {
    7676:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
    7677:         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
    7678:         PetscOptionsEnd();
    7679:       } else {
    7680:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
    7681:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
    7682:         PetscOptionsEnd();
    7683:       }
    7684:       break;
    7685:     case MATPRODUCT_AtB:
    7686:       if (product->api_user) {
    7687:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
    7688:         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
    7689:         PetscOptionsEnd();
    7690:       } else {
    7691:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
    7692:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
    7693:         PetscOptionsEnd();
    7694:       }
    7695:       break;
    7696:     case MATPRODUCT_PtAP:
    7697:       if (product->api_user) {
    7698:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
    7699:         PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
    7700:         PetscOptionsEnd();
    7701:       } else {
    7702:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
    7703:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
    7704:         PetscOptionsEnd();
    7705:       }
    7706:       break;
    7707:     default:
    7708:       break;
    7709:     }
    7710:     match = (PetscBool)!usecpu;
    7711:   }
    7712: #endif
    7713:   if (match) {
    7714:     switch (product->type) {
    7715:     case MATPRODUCT_AB:
    7716:     case MATPRODUCT_AtB:
    7717:     case MATPRODUCT_PtAP:
    7718:       mat->ops->productsymbolic = MatProductSymbolic_MPIAIJBACKEND;
    7719:       break;
    7720:     default:
    7721:       break;
    7722:     }
    7723:   }
    7724:   /* fallback to MPIAIJ ops */
    7725:   if (!mat->ops->productsymbolic) PetscCall(MatProductSetFromOptions_MPIAIJ(mat));
    7726:   PetscFunctionReturn(PETSC_SUCCESS);
    7727: }

    7729: /*
    7730:    Produces a set of block column indices of the matrix row, one for each block represented in the original row

    7732:    n - the number of block indices in cc[]
    7733:    cc - the block indices (must be large enough to contain the indices)
    7734: */
    7735: static inline PetscErrorCode MatCollapseRow(Mat Amat, PetscInt row, PetscInt bs, PetscInt *n, PetscInt *cc)
    7736: {
    7737:   PetscInt        cnt = -1, nidx, j;
    7738:   const PetscInt *idx;

    7740:   PetscFunctionBegin;
    7741:   PetscCall(MatGetRow(Amat, row, &nidx, &idx, NULL));
    7742:   if (nidx) {
    7743:     cnt     = 0;
    7744:     cc[cnt] = idx[0] / bs;
    7745:     for (j = 1; j < nidx; j++) {
    7746:       if (cc[cnt] < idx[j] / bs) cc[++cnt] = idx[j] / bs;
    7747:     }
    7748:   }
    7749:   PetscCall(MatRestoreRow(Amat, row, &nidx, &idx, NULL));
    7750:   *n = cnt + 1;
    7751:   PetscFunctionReturn(PETSC_SUCCESS);
    7752: }

    7754: /*
    7755:     Produces a set of block column indices of the matrix block row, one for each block represented in the original set of rows

    7757:     ncollapsed - the number of block indices
    7758:     collapsed - the block indices (must be large enough to contain the indices)
    7759: */
    7760: static inline PetscErrorCode MatCollapseRows(Mat Amat, PetscInt start, PetscInt bs, PetscInt *w0, PetscInt *w1, PetscInt *w2, PetscInt *ncollapsed, PetscInt **collapsed)
    7761: {
    7762:   PetscInt i, nprev, *cprev = w0, ncur = 0, *ccur = w1, *merged = w2, *cprevtmp;

    7764:   PetscFunctionBegin;
    7765:   PetscCall(MatCollapseRow(Amat, start, bs, &nprev, cprev));
    7766:   for (i = start + 1; i < start + bs; i++) {
    7767:     PetscCall(MatCollapseRow(Amat, i, bs, &ncur, ccur));
    7768:     PetscCall(PetscMergeIntArray(nprev, cprev, ncur, ccur, &nprev, &merged));
    7769:     cprevtmp = cprev;
    7770:     cprev    = merged;
    7771:     merged   = cprevtmp;
    7772:   }
    7773:   *ncollapsed = nprev;
    7774:   if (collapsed) *collapsed = cprev;
    7775:   PetscFunctionReturn(PETSC_SUCCESS);
    7776: }

    7778: /*
    7779:  MatCreateGraph_Simple_AIJ - create simple scalar matrix (graph) from potentially blocked matrix

    7781:  Input Parameter:
    7782:  . Amat - matrix
    7783:  - symmetrize - make the result symmetric
    7784:  + scale - scale with diagonal

    7786:  Output Parameter:
    7787:  . a_Gmat - output scalar graph >= 0

    7789: */
    7790: PETSC_INTERN PetscErrorCode MatCreateGraph_Simple_AIJ(Mat Amat, PetscBool symmetrize, PetscBool scale, PetscReal filter, PetscInt index_size, PetscInt index[], Mat *a_Gmat)
    7791: {
    7792:   PetscInt  Istart, Iend, Ii, jj, kk, ncols, nloc, NN, MM, bs;
    7793:   MPI_Comm  comm;
    7794:   Mat       Gmat;
    7795:   PetscBool ismpiaij, isseqaij;
    7796:   Mat       a, b, c;
    7797:   MatType   jtype;

    7799:   PetscFunctionBegin;
    7800:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
    7801:   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
    7802:   PetscCall(MatGetSize(Amat, &MM, &NN));
    7803:   PetscCall(MatGetBlockSize(Amat, &bs));
    7804:   nloc = (Iend - Istart) / bs;

    7806:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATSEQAIJ, &isseqaij));
    7807:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATMPIAIJ, &ismpiaij));
    7808:   PetscCheck(isseqaij || ismpiaij, comm, PETSC_ERR_USER, "Require (MPI)AIJ matrix type");

    7810:   /* TODO GPU: these calls are potentially expensive if matrices are large and we want to use the GPU */
    7811:   /* A solution consists in providing a new API, MatAIJGetCollapsedAIJ, and each class can provide a fast
    7812:      implementation */
    7813:   if (bs > 1) {
    7814:     PetscCall(MatGetType(Amat, &jtype));
    7815:     PetscCall(MatCreate(comm, &Gmat));
    7816:     PetscCall(MatSetType(Gmat, jtype));
    7817:     PetscCall(MatSetSizes(Gmat, nloc, nloc, PETSC_DETERMINE, PETSC_DETERMINE));
    7818:     PetscCall(MatSetBlockSizes(Gmat, 1, 1));
    7819:     if (isseqaij || ((Mat_MPIAIJ *)Amat->data)->garray) {
    7820:       PetscInt  *d_nnz, *o_nnz;
    7821:       MatScalar *aa, val, *AA;
    7822:       PetscInt  *aj, *ai, *AJ, nc, nmax = 0;

    7824:       if (isseqaij) {
    7825:         a = Amat;
    7826:         b = NULL;
    7827:       } else {
    7828:         Mat_MPIAIJ *d = (Mat_MPIAIJ *)Amat->data;
    7829:         a             = d->A;
    7830:         b             = d->B;
    7831:       }
    7832:       PetscCall(PetscInfo(Amat, "New bs>1 Graph. nloc=%" PetscInt_FMT "\n", nloc));
    7833:       PetscCall(PetscMalloc2(nloc, &d_nnz, (isseqaij ? 0 : nloc), &o_nnz));
    7834:       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
    7835:         PetscInt       *nnz = (c == a) ? d_nnz : o_nnz;
    7836:         const PetscInt *cols1, *cols2;

    7838:         for (PetscInt brow = 0, nc1, nc2, ok = 1; brow < nloc * bs; brow += bs) { // block rows
    7839:           PetscCall(MatGetRow(c, brow, &nc2, &cols2, NULL));
    7840:           nnz[brow / bs] = nc2 / bs;
    7841:           if (nc2 % bs) ok = 0;
    7842:           if (nnz[brow / bs] > nmax) nmax = nnz[brow / bs];
    7843:           for (PetscInt ii = 1; ii < bs; ii++) { // check for non-dense blocks
    7844:             PetscCall(MatGetRow(c, brow + ii, &nc1, &cols1, NULL));
    7845:             if (nc1 != nc2) ok = 0;
    7846:             else {
    7847:               for (PetscInt jj = 0; jj < nc1 && ok == 1; jj++) {
    7848:                 if (cols1[jj] != cols2[jj]) ok = 0;
    7849:                 if (cols1[jj] % bs != jj % bs) ok = 0;
    7850:               }
    7851:             }
    7852:             PetscCall(MatRestoreRow(c, brow + ii, &nc1, &cols1, NULL));
    7853:           }
    7854:           PetscCall(MatRestoreRow(c, brow, &nc2, &cols2, NULL));
    7855:           if (!ok) {
    7856:             PetscCall(PetscFree2(d_nnz, o_nnz));
    7857:             PetscCall(PetscInfo(Amat, "Found sparse blocks - revert to slow method\n"));
    7858:             goto old_bs;
    7859:           }
    7860:         }
    7861:       }
    7862:       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
    7863:       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
    7864:       PetscCall(PetscFree2(d_nnz, o_nnz));
    7865:       PetscCall(PetscMalloc2(nmax, &AA, nmax, &AJ));
    7866:       // diag
    7867:       for (PetscInt brow = 0, n, grow; brow < nloc * bs; brow += bs) { // block rows
    7868:         Mat_SeqAIJ *aseq = (Mat_SeqAIJ *)a->data;

    7870:         ai = aseq->i;
    7871:         n  = ai[brow + 1] - ai[brow];
    7872:         aj = aseq->j + ai[brow];
    7873:         for (PetscInt k = 0; k < n; k += bs) {   // block columns
    7874:           AJ[k / bs] = aj[k] / bs + Istart / bs; // diag starts at (Istart,Istart)
    7875:           val        = 0;
    7876:           if (index_size == 0) {
    7877:             for (PetscInt ii = 0; ii < bs; ii++) { // rows in block
    7878:               aa = aseq->a + ai[brow + ii] + k;
    7879:               for (PetscInt jj = 0; jj < bs; jj++) {    // columns in block
    7880:                 val += PetscAbs(PetscRealPart(aa[jj])); // a sort of norm
    7881:               }
    7882:             }
    7883:           } else {                                            // use (index,index) value if provided
    7884:             for (PetscInt iii = 0; iii < index_size; iii++) { // rows in block
    7885:               PetscInt ii = index[iii];
    7886:               aa          = aseq->a + ai[brow + ii] + k;
    7887:               for (PetscInt jjj = 0; jjj < index_size; jjj++) { // columns in block
    7888:                 PetscInt jj = index[jjj];
    7889:                 val += PetscAbs(PetscRealPart(aa[jj]));
    7890:               }
    7891:             }
    7892:           }
    7893:           PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%" PetscInt_FMT ") >= nmax (%" PetscInt_FMT ")", k / bs, nmax);
    7894:           AA[k / bs] = val;
    7895:         }
    7896:         grow = Istart / bs + brow / bs;
    7897:         PetscCall(MatSetValues(Gmat, 1, &grow, n / bs, AJ, AA, ADD_VALUES));
    7898:       }
    7899:       // off-diag
    7900:       if (ismpiaij) {
    7901:         Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)Amat->data;
    7902:         const PetscScalar *vals;
    7903:         const PetscInt    *cols, *garray = aij->garray;

    7905:         PetscCheck(garray, PETSC_COMM_SELF, PETSC_ERR_USER, "No garray ?");
    7906:         for (PetscInt brow = 0, grow; brow < nloc * bs; brow += bs) { // block rows
    7907:           PetscCall(MatGetRow(b, brow, &ncols, &cols, NULL));
    7908:           for (PetscInt k = 0, cidx = 0; k < ncols; k += bs, cidx++) {
    7909:             PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs >= nmax");
    7910:             AA[k / bs] = 0;
    7911:             AJ[cidx]   = garray[cols[k]] / bs;
    7912:           }
    7913:           nc = ncols / bs;
    7914:           PetscCall(MatRestoreRow(b, brow, &ncols, &cols, NULL));
    7915:           if (index_size == 0) {
    7916:             for (PetscInt ii = 0; ii < bs; ii++) { // rows in block
    7917:               PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
    7918:               for (PetscInt k = 0; k < ncols; k += bs) {
    7919:                 for (PetscInt jj = 0; jj < bs; jj++) { // cols in block
    7920:                   PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%" PetscInt_FMT ") >= nmax (%" PetscInt_FMT ")", k / bs, nmax);
    7921:                   AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
    7922:                 }
    7923:               }
    7924:               PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
    7925:             }
    7926:           } else {                                            // use (index,index) value if provided
    7927:             for (PetscInt iii = 0; iii < index_size; iii++) { // rows in block
    7928:               PetscInt ii = index[iii];
    7929:               PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
    7930:               for (PetscInt k = 0; k < ncols; k += bs) {
    7931:                 for (PetscInt jjj = 0; jjj < index_size; jjj++) { // cols in block
    7932:                   PetscInt jj = index[jjj];
    7933:                   AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
    7934:                 }
    7935:               }
    7936:               PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
    7937:             }
    7938:           }
    7939:           grow = Istart / bs + brow / bs;
    7940:           PetscCall(MatSetValues(Gmat, 1, &grow, nc, AJ, AA, ADD_VALUES));
    7941:         }
    7942:       }
    7943:       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
    7944:       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
    7945:       PetscCall(PetscFree2(AA, AJ));
    7946:     } else {
    7947:       const PetscScalar *vals;
    7948:       const PetscInt    *idx;
    7949:       PetscInt          *d_nnz, *o_nnz, *w0, *w1, *w2;
    7950:     old_bs:
    7951:       /*
    7952:        Determine the preallocation needed for the scalar matrix derived from the vector matrix.
    7953:        */
    7954:       PetscCall(PetscInfo(Amat, "OLD bs>1 CreateGraph\n"));
    7955:       PetscCall(PetscMalloc2(nloc, &d_nnz, (isseqaij ? 0 : nloc), &o_nnz));
    7956:       if (isseqaij) {
    7957:         PetscInt max_d_nnz;

    7959:         /*
    7960:          Determine exact preallocation count for (sequential) scalar matrix
    7961:          */
    7962:         PetscCall(MatSeqAIJGetMaxRowNonzeros(Amat, &max_d_nnz));
    7963:         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
    7964:         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
    7965:         for (Ii = 0, jj = 0; Ii < Iend; Ii += bs, jj++) PetscCall(MatCollapseRows(Amat, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
    7966:         PetscCall(PetscFree3(w0, w1, w2));
    7967:       } else if (ismpiaij) {
    7968:         Mat             Daij, Oaij;
    7969:         const PetscInt *garray;
    7970:         PetscInt        max_d_nnz;

    7972:         PetscCall(MatMPIAIJGetSeqAIJ(Amat, &Daij, &Oaij, &garray));
    7973:         /*
    7974:          Determine exact preallocation count for diagonal block portion of scalar matrix
    7975:          */
    7976:         PetscCall(MatSeqAIJGetMaxRowNonzeros(Daij, &max_d_nnz));
    7977:         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
    7978:         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
    7979:         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) PetscCall(MatCollapseRows(Daij, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
    7980:         PetscCall(PetscFree3(w0, w1, w2));
    7981:         /*
    7982:          Over estimate (usually grossly over), preallocation count for off-diagonal portion of scalar matrix
    7983:          */
    7984:         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
    7985:           o_nnz[jj] = 0;
    7986:           for (kk = 0; kk < bs; kk++) { /* rows that get collapsed to a single row */
    7987:             PetscCall(MatGetRow(Oaij, Ii + kk, &ncols, NULL, NULL));
    7988:             o_nnz[jj] += ncols;
    7989:             PetscCall(MatRestoreRow(Oaij, Ii + kk, &ncols, NULL, NULL));
    7990:           }
    7991:           if (o_nnz[jj] > (NN / bs - nloc)) o_nnz[jj] = NN / bs - nloc;
    7992:         }
    7993:       } else SETERRQ(comm, PETSC_ERR_USER, "Require AIJ matrix type");
    7994:       /* get scalar copy (norms) of matrix */
    7995:       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
    7996:       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
    7997:       PetscCall(PetscFree2(d_nnz, o_nnz));
    7998:       for (Ii = Istart; Ii < Iend; Ii++) {
    7999:         PetscInt dest_row = Ii / bs;

    8001:         PetscCall(MatGetRow(Amat, Ii, &ncols, &idx, &vals));
    8002:         for (jj = 0; jj < ncols; jj++) {
    8003:           PetscInt    dest_col = idx[jj] / bs;
    8004:           PetscScalar sv       = PetscAbs(PetscRealPart(vals[jj]));

    8006:           PetscCall(MatSetValues(Gmat, 1, &dest_row, 1, &dest_col, &sv, ADD_VALUES));
    8007:         }
    8008:         PetscCall(MatRestoreRow(Amat, Ii, &ncols, &idx, &vals));
    8009:       }
    8010:       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
    8011:       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
    8012:     }
    8013:   } else {
    8014:     if (symmetrize || filter >= 0 || scale) PetscCall(MatDuplicate(Amat, MAT_COPY_VALUES, &Gmat));
    8015:     else {
    8016:       Gmat = Amat;
    8017:       PetscCall(PetscObjectReference((PetscObject)Gmat));
    8018:     }
    8019:     if (isseqaij) {
    8020:       a = Gmat;
    8021:       b = NULL;
    8022:     } else {
    8023:       Mat_MPIAIJ *d = (Mat_MPIAIJ *)Gmat->data;
    8024:       a             = d->A;
    8025:       b             = d->B;
    8026:     }
    8027:     if (filter >= 0 || scale) {
    8028:       /* take absolute value of each entry */
    8029:       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
    8030:         MatInfo      info;
    8031:         PetscScalar *avals;

    8033:         PetscCall(MatGetInfo(c, MAT_LOCAL, &info));
    8034:         PetscCall(MatSeqAIJGetArray(c, &avals));
    8035:         for (int jj = 0; jj < info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    8036:         PetscCall(MatSeqAIJRestoreArray(c, &avals));
    8037:       }
    8038:     }
    8039:   }
    8040:   if (symmetrize) {
    8041:     PetscBool isset, issym;

    8043:     PetscCall(MatIsSymmetricKnown(Amat, &isset, &issym));
    8044:     if (!isset || !issym) {
    8045:       Mat matTrans;

    8047:       PetscCall(MatTranspose(Gmat, MAT_INITIAL_MATRIX, &matTrans));
    8048:       PetscCall(MatAXPY(Gmat, 1.0, matTrans, Gmat->structurally_symmetric == PETSC_BOOL3_TRUE ? SAME_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN));
    8049:       PetscCall(MatDestroy(&matTrans));
    8050:     }
    8051:     PetscCall(MatSetOption(Gmat, MAT_SYMMETRIC, PETSC_TRUE));
    8052:   } else if (Amat != Gmat) PetscCall(MatPropagateSymmetryOptions(Amat, Gmat));
    8053:   if (scale) {
    8054:     /* scale c for all diagonal values = 1 or -1 */
    8055:     Vec diag;

    8057:     PetscCall(MatCreateVecs(Gmat, &diag, NULL));
    8058:     PetscCall(MatGetDiagonal(Gmat, diag));
    8059:     PetscCall(VecReciprocal(diag));
    8060:     PetscCall(VecSqrtAbs(diag));
    8061:     PetscCall(MatDiagonalScale(Gmat, diag, diag));
    8062:     PetscCall(VecDestroy(&diag));
    8063:   }
    8064:   PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_graph_view"));
    8065:   if (filter >= 0) {
    8066:     PetscCall(MatFilter(Gmat, filter, PETSC_TRUE, PETSC_TRUE));
    8067:     PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_filter_graph_view"));
    8068:   }
    8069:   *a_Gmat = Gmat;
    8070:   PetscFunctionReturn(PETSC_SUCCESS);
    8071: }

    8073: /*
    8074:     Special version for direct calls from Fortran
    8075: */

    8077: /* Change these macros so can be used in void function */
    8078: /* Identical to PetscCallVoid, except it assigns to *_ierr */
    8079: #undef PetscCall
    8080: #define PetscCall(...) \
    8081:   do { \
    8082:     PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__; \
    8083:     if (PetscUnlikely(ierr_msv_mpiaij)) { \
    8084:       *_ierr = PetscError(PETSC_COMM_SELF, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr_msv_mpiaij, PETSC_ERROR_REPEAT, " "); \
    8085:       return; \
    8086:     } \
    8087:   } while (0)

    8089: #undef SETERRQ
    8090: #define SETERRQ(comm, ierr, ...) \
    8091:   do { \
    8092:     *_ierr = PetscError(comm, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr, PETSC_ERROR_INITIAL, __VA_ARGS__); \
    8093:     return; \
    8094:   } while (0)

    8096: #if defined(PETSC_HAVE_FORTRAN_CAPS)
    8097:   #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
    8098: #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
    8099:   #define matsetvaluesmpiaij_ matsetvaluesmpiaij
    8100: #else
    8101: #endif
    8102: PETSC_EXTERN void matsetvaluesmpiaij_(Mat *mmat, PetscInt *mm, const PetscInt im[], PetscInt *mn, const PetscInt in[], const PetscScalar v[], InsertMode *maddv, PetscErrorCode *_ierr)
    8103: {
    8104:   Mat         mat = *mmat;
    8105:   PetscInt    m = *mm, n = *mn;
    8106:   InsertMode  addv = *maddv;
    8107:   Mat_MPIAIJ *aij  = (Mat_MPIAIJ *)mat->data;
    8108:   PetscScalar value;

    8110:   MatCheckPreallocated(mat, 1);
    8111:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    8112:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    8113:   {
    8114:     PetscInt  i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    8115:     PetscInt  cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
    8116:     PetscBool roworiented = aij->roworiented;

    8118:     /* Some Variables required in the macro */
    8119:     Mat         A     = aij->A;
    8120:     Mat_SeqAIJ *a     = (Mat_SeqAIJ *)A->data;
    8121:     PetscInt   *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
    8122:     MatScalar  *aa;
    8123:     PetscBool   ignorezeroentries = ((a->ignorezeroentries && (addv == ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
    8124:     Mat         B                 = aij->B;
    8125:     Mat_SeqAIJ *b                 = (Mat_SeqAIJ *)B->data;
    8126:     PetscInt   *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j, bm = aij->B->rmap->n, am = aij->A->rmap->n;
    8127:     MatScalar  *ba;
    8128:     /* This variable below is only for the PETSC_HAVE_VIENNACL or PETSC_HAVE_CUDA cases, but we define it in all cases because we
    8129:      * cannot use "#if defined" inside a macro. */
    8130:     PETSC_UNUSED PetscBool inserted = PETSC_FALSE;

    8132:     PetscInt  *rp1, *rp2, ii, nrow1, nrow2, _i, rmax1, rmax2, N, low1, high1, low2, high2, t, lastcol1, lastcol2;
    8133:     PetscInt   nonew = a->nonew;
    8134:     MatScalar *ap1, *ap2;

    8136:     PetscFunctionBegin;
    8137:     PetscCall(MatSeqAIJGetArray(A, &aa));
    8138:     PetscCall(MatSeqAIJGetArray(B, &ba));
    8139:     for (i = 0; i < m; i++) {
    8140:       if (im[i] < 0) continue;
    8141:       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);
    8142:       if (im[i] >= rstart && im[i] < rend) {
    8143:         row      = im[i] - rstart;
    8144:         lastcol1 = -1;
    8145:         rp1      = aj + ai[row];
    8146:         ap1      = aa + ai[row];
    8147:         rmax1    = aimax[row];
    8148:         nrow1    = ailen[row];
    8149:         low1     = 0;
    8150:         high1    = nrow1;
    8151:         lastcol2 = -1;
    8152:         rp2      = bj + bi[row];
    8153:         ap2      = ba + bi[row];
    8154:         rmax2    = bimax[row];
    8155:         nrow2    = bilen[row];
    8156:         low2     = 0;
    8157:         high2    = nrow2;

    8159:         for (j = 0; j < n; j++) {
    8160:           if (roworiented) value = v[i * n + j];
    8161:           else value = v[i + j * m];
    8162:           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
    8163:           if (in[j] >= cstart && in[j] < cend) {
    8164:             col = in[j] - cstart;
    8165:             MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
    8166:           } else if (in[j] < 0) continue;
    8167:           else if (PetscUnlikelyDebug(in[j] >= mat->cmap->N)) {
    8168:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
    8169:           } else {
    8170:             if (mat->was_assembled) {
    8171:               if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    8172: #if defined(PETSC_USE_CTABLE)
    8173:               PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col));
    8174:               col--;
    8175: #else
    8176:               col = aij->colmap[in[j]] - 1;
    8177: #endif
    8178:               if (col < 0 && !((Mat_SeqAIJ *)aij->A->data)->nonew) {
    8179:                 PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));
    8180:                 col = in[j];
    8181:                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
    8182:                 B        = aij->B;
    8183:                 b        = (Mat_SeqAIJ *)B->data;
    8184:                 bimax    = b->imax;
    8185:                 bi       = b->i;
    8186:                 bilen    = b->ilen;
    8187:                 bj       = b->j;
    8188:                 rp2      = bj + bi[row];
    8189:                 ap2      = ba + bi[row];
    8190:                 rmax2    = bimax[row];
    8191:                 nrow2    = bilen[row];
    8192:                 low2     = 0;
    8193:                 high2    = nrow2;
    8194:                 bm       = aij->B->rmap->n;
    8195:                 ba       = b->a;
    8196:                 inserted = PETSC_FALSE;
    8197:               }
    8198:             } else col = in[j];
    8199:             MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
    8200:           }
    8201:         }
    8202:       } else if (!aij->donotstash) {
    8203:         if (roworiented) {
    8204:           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, v + i * n, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    8205:         } else {
    8206:           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, v + i, m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    8207:         }
    8208:       }
    8209:     }
    8210:     PetscCall(MatSeqAIJRestoreArray(A, &aa));
    8211:     PetscCall(MatSeqAIJRestoreArray(B, &ba));
    8212:   }
    8213:   PetscFunctionReturnVoid();
    8214: }

    8216: /* Undefining these here since they were redefined from their original definition above! No
    8217:  * other PETSc functions should be defined past this point, as it is impossible to recover the
    8218:  * original definitions */
    8219: #undef PetscCall
    8220: #undef SETERRQ