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: PetscErrorCode MatDestroy_MPIAIJ(Mat mat)
     10: {
     11:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

     13:   PetscFunctionBegin;
     14:   PetscCall(PetscLogObjectState((PetscObject)mat, "Rows=%" PetscInt_FMT ", Cols=%" PetscInt_FMT, mat->rmap->N, mat->cmap->N));
     15:   PetscCall(MatStashDestroy_Private(&mat->stash));
     16:   PetscCall(VecDestroy(&aij->diag));
     17:   PetscCall(MatDestroy(&aij->A));
     18:   PetscCall(MatDestroy(&aij->B));
     19: #if defined(PETSC_USE_CTABLE)
     20:   PetscCall(PetscHMapIDestroy(&aij->colmap));
     21: #else
     22:   PetscCall(PetscFree(aij->colmap));
     23: #endif
     24:   PetscCall(PetscFree(aij->garray));
     25:   PetscCall(VecDestroy(&aij->lvec));
     26:   PetscCall(VecScatterDestroy(&aij->Mvctx));
     27:   PetscCall(PetscFree2(aij->rowvalues, aij->rowindices));
     28:   PetscCall(PetscFree(aij->ld));

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

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

     35:   PetscCall(PetscObjectChangeTypeName((PetscObject)mat, NULL));
     36:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatStoreValues_C", NULL));
     37:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatRetrieveValues_C", NULL));
     38:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatIsTranspose_C", NULL));
     39:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetPreallocation_C", NULL));
     40:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatResetPreallocation_C", NULL));
     41:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetPreallocationCSR_C", NULL));
     42:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatDiagonalScaleLocal_C", NULL));
     43:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpibaij_C", NULL));
     44:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpisbaij_C", NULL));
     45: #if defined(PETSC_HAVE_CUDA)
     46:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijcusparse_C", NULL));
     47: #endif
     48: #if defined(PETSC_HAVE_HIP)
     49:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijhipsparse_C", NULL));
     50: #endif
     51: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
     52:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijkokkos_C", NULL));
     53: #endif
     54:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpidense_C", NULL));
     55: #if defined(PETSC_HAVE_ELEMENTAL)
     56:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_elemental_C", NULL));
     57: #endif
     58: #if defined(PETSC_HAVE_SCALAPACK)
     59:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_scalapack_C", NULL));
     60: #endif
     61: #if defined(PETSC_HAVE_HYPRE)
     62:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_hypre_C", NULL));
     63:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", NULL));
     64: #endif
     65:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_is_C", NULL));
     66:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_is_mpiaij_C", NULL));
     67:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatProductSetFromOptions_mpiaij_mpiaij_C", NULL));
     68:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatMPIAIJSetUseScalableIncreaseOverlap_C", NULL));
     69:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijperm_C", NULL));
     70:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijsell_C", NULL));
     71: #if defined(PETSC_HAVE_MKL_SPARSE)
     72:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijmkl_C", NULL));
     73: #endif
     74:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpiaijcrl_C", NULL));
     75:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_is_C", NULL));
     76:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatConvert_mpiaij_mpisell_C", NULL));
     77:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetPreallocationCOO_C", NULL));
     78:   PetscCall(PetscObjectComposeFunction((PetscObject)mat, "MatSetValuesCOO_C", NULL));
     79:   PetscFunctionReturn(PETSC_SUCCESS);
     80: }

     82: /* defines MatSetValues_MPI_Hash(), MatAssemblyBegin_MPI_Hash(), and  MatAssemblyEnd_MPI_Hash() */
     83: #define TYPE AIJ
     84: #define TYPE_AIJ
     85: #include "../src/mat/impls/aij/mpi/mpihashmat.h"
     86: #undef TYPE
     87: #undef TYPE_AIJ

     89: static PetscErrorCode MatGetRowIJ_MPIAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *m, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
     90: {
     91:   Mat B;

     93:   PetscFunctionBegin;
     94:   PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, &B));
     95:   PetscCall(PetscObjectCompose((PetscObject)A, "MatGetRowIJ_MPIAIJ", (PetscObject)B));
     96:   PetscCall(MatGetRowIJ(B, oshift, symmetric, inodecompressed, m, ia, ja, done));
     97:   PetscCall(MatDestroy(&B));
     98:   PetscFunctionReturn(PETSC_SUCCESS);
     99: }

    101: static PetscErrorCode MatRestoreRowIJ_MPIAIJ(Mat A, PetscInt oshift, PetscBool symmetric, PetscBool inodecompressed, PetscInt *m, const PetscInt *ia[], const PetscInt *ja[], PetscBool *done)
    102: {
    103:   Mat B;

    105:   PetscFunctionBegin;
    106:   PetscCall(PetscObjectQuery((PetscObject)A, "MatGetRowIJ_MPIAIJ", (PetscObject *)&B));
    107:   PetscCall(MatRestoreRowIJ(B, oshift, symmetric, inodecompressed, m, ia, ja, done));
    108:   PetscCall(PetscObjectCompose((PetscObject)A, "MatGetRowIJ_MPIAIJ", NULL));
    109:   PetscFunctionReturn(PETSC_SUCCESS);
    110: }

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

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

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

    124:   Developer Note:
    125:   Level: beginner

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

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

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

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

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

    145:   Level: beginner

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

    150: static PetscErrorCode MatBindToCPU_MPIAIJ(Mat A, PetscBool flg)
    151: {
    152:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    154:   PetscFunctionBegin;
    155: #if defined(PETSC_HAVE_CUDA) || defined(PETSC_HAVE_HIP) || defined(PETSC_HAVE_VIENNACL)
    156:   A->boundtocpu = flg;
    157: #endif
    158:   if (a->A) PetscCall(MatBindToCPU(a->A, flg));
    159:   if (a->B) PetscCall(MatBindToCPU(a->B, flg));

    161:   /* In addition to binding the diagonal and off-diagonal matrices, bind the local vectors used for matrix-vector products.
    162:    * This maybe seems a little odd for a MatBindToCPU() call to do, but it makes no sense for the binding of these vectors
    163:    * to differ from the parent matrix. */
    164:   if (a->lvec) PetscCall(VecBindToCPU(a->lvec, flg));
    165:   if (a->diag) PetscCall(VecBindToCPU(a->diag, flg));
    166:   PetscFunctionReturn(PETSC_SUCCESS);
    167: }

    169: static PetscErrorCode MatSetBlockSizes_MPIAIJ(Mat M, PetscInt rbs, PetscInt cbs)
    170: {
    171:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)M->data;

    173:   PetscFunctionBegin;
    174:   if (mat->A) {
    175:     PetscCall(MatSetBlockSizes(mat->A, rbs, cbs));
    176:     PetscCall(MatSetBlockSizes(mat->B, rbs, 1));
    177:   }
    178:   PetscFunctionReturn(PETSC_SUCCESS);
    179: }

    181: static PetscErrorCode MatFindNonzeroRows_MPIAIJ(Mat M, IS *keptrows)
    182: {
    183:   Mat_MPIAIJ      *mat = (Mat_MPIAIJ *)M->data;
    184:   Mat_SeqAIJ      *a   = (Mat_SeqAIJ *)mat->A->data;
    185:   Mat_SeqAIJ      *b   = (Mat_SeqAIJ *)mat->B->data;
    186:   const PetscInt  *ia, *ib;
    187:   const MatScalar *aa, *bb, *aav, *bav;
    188:   PetscInt         na, nb, i, j, *rows, cnt = 0, n0rows;
    189:   PetscInt         m = M->rmap->n, rstart = M->rmap->rstart;

    191:   PetscFunctionBegin;
    192:   *keptrows = NULL;

    194:   ia = a->i;
    195:   ib = b->i;
    196:   PetscCall(MatSeqAIJGetArrayRead(mat->A, &aav));
    197:   PetscCall(MatSeqAIJGetArrayRead(mat->B, &bav));
    198:   for (i = 0; i < m; i++) {
    199:     na = ia[i + 1] - ia[i];
    200:     nb = ib[i + 1] - ib[i];
    201:     if (!na && !nb) {
    202:       cnt++;
    203:       goto ok1;
    204:     }
    205:     aa = aav + ia[i];
    206:     for (j = 0; j < na; j++) {
    207:       if (aa[j] != 0.0) goto ok1;
    208:     }
    209:     bb = PetscSafePointerPlusOffset(bav, ib[i]);
    210:     for (j = 0; j < nb; j++) {
    211:       if (bb[j] != 0.0) goto ok1;
    212:     }
    213:     cnt++;
    214:   ok1:;
    215:   }
    216:   PetscCallMPI(MPIU_Allreduce(&cnt, &n0rows, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)M)));
    217:   if (!n0rows) {
    218:     PetscCall(MatSeqAIJRestoreArrayRead(mat->A, &aav));
    219:     PetscCall(MatSeqAIJRestoreArrayRead(mat->B, &bav));
    220:     PetscFunctionReturn(PETSC_SUCCESS);
    221:   }
    222:   PetscCall(PetscMalloc1(M->rmap->n - cnt, &rows));
    223:   cnt = 0;
    224:   for (i = 0; i < m; i++) {
    225:     na = ia[i + 1] - ia[i];
    226:     nb = ib[i + 1] - ib[i];
    227:     if (!na && !nb) continue;
    228:     aa = aav + ia[i];
    229:     for (j = 0; j < na; j++) {
    230:       if (aa[j] != 0.0) {
    231:         rows[cnt++] = rstart + i;
    232:         goto ok2;
    233:       }
    234:     }
    235:     bb = PetscSafePointerPlusOffset(bav, ib[i]);
    236:     for (j = 0; j < nb; j++) {
    237:       if (bb[j] != 0.0) {
    238:         rows[cnt++] = rstart + i;
    239:         goto ok2;
    240:       }
    241:     }
    242:   ok2:;
    243:   }
    244:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)M), cnt, rows, PETSC_OWN_POINTER, keptrows));
    245:   PetscCall(MatSeqAIJRestoreArrayRead(mat->A, &aav));
    246:   PetscCall(MatSeqAIJRestoreArrayRead(mat->B, &bav));
    247:   PetscFunctionReturn(PETSC_SUCCESS);
    248: }

    250: static PetscErrorCode MatDiagonalSet_MPIAIJ(Mat Y, Vec D, InsertMode is)
    251: {
    252:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)Y->data;
    253:   PetscBool   cong;

    255:   PetscFunctionBegin;
    256:   PetscCall(MatHasCongruentLayouts(Y, &cong));
    257:   if (Y->assembled && cong) {
    258:     PetscCall(MatDiagonalSet(aij->A, D, is));
    259:   } else {
    260:     PetscCall(MatDiagonalSet_Default(Y, D, is));
    261:   }
    262:   PetscFunctionReturn(PETSC_SUCCESS);
    263: }

    265: static PetscErrorCode MatFindZeroDiagonals_MPIAIJ(Mat M, IS *zrows)
    266: {
    267:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)M->data;
    268:   PetscInt    i, rstart, nrows, *rows;

    270:   PetscFunctionBegin;
    271:   *zrows = NULL;
    272:   PetscCall(MatFindZeroDiagonals_SeqAIJ_Private(aij->A, &nrows, &rows));
    273:   PetscCall(MatGetOwnershipRange(M, &rstart, NULL));
    274:   for (i = 0; i < nrows; i++) rows[i] += rstart;
    275:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)M), nrows, rows, PETSC_OWN_POINTER, zrows));
    276:   PetscFunctionReturn(PETSC_SUCCESS);
    277: }

    279: static PetscErrorCode MatGetColumnReductions_MPIAIJ(Mat A, PetscInt type, PetscReal *reductions)
    280: {
    281:   Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)A->data;
    282:   PetscInt           i, m, n, *garray = aij->garray;
    283:   Mat_SeqAIJ        *a_aij = (Mat_SeqAIJ *)aij->A->data;
    284:   Mat_SeqAIJ        *b_aij = (Mat_SeqAIJ *)aij->B->data;
    285:   PetscReal         *work;
    286:   const PetscScalar *dummy;
    287:   PetscMPIInt        in;

    289:   PetscFunctionBegin;
    290:   PetscCall(MatGetSize(A, &m, &n));
    291:   PetscCall(PetscCalloc1(n, &work));
    292:   PetscCall(MatSeqAIJGetArrayRead(aij->A, &dummy));
    293:   PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &dummy));
    294:   PetscCall(MatSeqAIJGetArrayRead(aij->B, &dummy));
    295:   PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &dummy));
    296:   if (type == NORM_2) {
    297:     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]);
    298:     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]);
    299:   } else if (type == NORM_1) {
    300:     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]);
    301:     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscAbsScalar(b_aij->a[i]);
    302:   } else if (type == NORM_INFINITY) {
    303:     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]]);
    304:     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]]]);
    305:   } else if (type == REDUCTION_SUM_REALPART || type == REDUCTION_MEAN_REALPART) {
    306:     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]);
    307:     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscRealPart(b_aij->a[i]);
    308:   } else if (type == REDUCTION_SUM_IMAGINARYPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    309:     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]);
    310:     for (i = 0; i < b_aij->i[aij->B->rmap->n]; i++) work[garray[b_aij->j[i]]] += PetscImaginaryPart(b_aij->a[i]);
    311:   } else SETERRQ(PetscObjectComm((PetscObject)A), PETSC_ERR_ARG_WRONG, "Unknown reduction type");
    312:   PetscCall(PetscMPIIntCast(n, &in));
    313:   if (type == NORM_INFINITY) {
    314:     PetscCallMPI(MPIU_Allreduce(work, reductions, in, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)A)));
    315:   } else {
    316:     PetscCallMPI(MPIU_Allreduce(work, reductions, in, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)A)));
    317:   }
    318:   PetscCall(PetscFree(work));
    319:   if (type == NORM_2) {
    320:     for (i = 0; i < n; i++) reductions[i] = PetscSqrtReal(reductions[i]);
    321:   } else if (type == REDUCTION_MEAN_REALPART || type == REDUCTION_MEAN_IMAGINARYPART) {
    322:     for (i = 0; i < n; i++) reductions[i] /= m;
    323:   }
    324:   PetscFunctionReturn(PETSC_SUCCESS);
    325: }

    327: static PetscErrorCode MatFindOffBlockDiagonalEntries_MPIAIJ(Mat A, IS *is)
    328: {
    329:   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)A->data;
    330:   IS              sis, gis;
    331:   const PetscInt *isis, *igis;
    332:   PetscInt        n, *iis, nsis, ngis, rstart, i;

    334:   PetscFunctionBegin;
    335:   PetscCall(MatFindOffBlockDiagonalEntries(a->A, &sis));
    336:   PetscCall(MatFindNonzeroRows(a->B, &gis));
    337:   PetscCall(ISGetSize(gis, &ngis));
    338:   PetscCall(ISGetSize(sis, &nsis));
    339:   PetscCall(ISGetIndices(sis, &isis));
    340:   PetscCall(ISGetIndices(gis, &igis));

    342:   PetscCall(PetscMalloc1(ngis + nsis, &iis));
    343:   PetscCall(PetscArraycpy(iis, igis, ngis));
    344:   PetscCall(PetscArraycpy(iis + ngis, isis, nsis));
    345:   n = ngis + nsis;
    346:   PetscCall(PetscSortRemoveDupsInt(&n, iis));
    347:   PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
    348:   for (i = 0; i < n; i++) iis[i] += rstart;
    349:   PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)A), n, iis, PETSC_OWN_POINTER, is));

    351:   PetscCall(ISRestoreIndices(sis, &isis));
    352:   PetscCall(ISRestoreIndices(gis, &igis));
    353:   PetscCall(ISDestroy(&sis));
    354:   PetscCall(ISDestroy(&gis));
    355:   PetscFunctionReturn(PETSC_SUCCESS);
    356: }

    358: /*
    359:   Local utility routine that creates a mapping from the global column
    360: number to the local number in the off-diagonal part of the local
    361: storage of the matrix.  When PETSC_USE_CTABLE is used this is scalable at
    362: a slightly higher hash table cost; without it it is not scalable (each processor
    363: has an order N integer array but is fast to access.
    364: */
    365: PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat mat)
    366: {
    367:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    368:   PetscInt    n   = aij->B->cmap->n, i;

    370:   PetscFunctionBegin;
    371:   PetscCheck(!n || aij->garray, PETSC_COMM_SELF, PETSC_ERR_PLIB, "MPIAIJ Matrix was assembled but is missing garray");
    372: #if defined(PETSC_USE_CTABLE)
    373:   PetscCall(PetscHMapICreateWithSize(n, &aij->colmap));
    374:   for (i = 0; i < n; i++) PetscCall(PetscHMapISet(aij->colmap, aij->garray[i] + 1, i + 1));
    375: #else
    376:   PetscCall(PetscCalloc1(mat->cmap->N + 1, &aij->colmap));
    377:   for (i = 0; i < n; i++) aij->colmap[aij->garray[i]] = i + 1;
    378: #endif
    379:   PetscFunctionReturn(PETSC_SUCCESS);
    380: }

    382: #define MatSetValues_SeqAIJ_A_Private(row, col, value, addv, orow, ocol) \
    383:   do { \
    384:     if (col <= lastcol1) low1 = 0; \
    385:     else high1 = nrow1; \
    386:     lastcol1 = col; \
    387:     while (high1 - low1 > 5) { \
    388:       t = (low1 + high1) / 2; \
    389:       if (rp1[t] > col) high1 = t; \
    390:       else low1 = t; \
    391:     } \
    392:     for (_i = low1; _i < high1; _i++) { \
    393:       if (rp1[_i] > col) break; \
    394:       if (rp1[_i] == col) { \
    395:         if (addv == ADD_VALUES) { \
    396:           ap1[_i] += value; \
    397:           /* Not sure LogFlops will slow dow the code or not */ \
    398:           (void)PetscLogFlops(1.0); \
    399:         } else ap1[_i] = value; \
    400:         goto a_noinsert; \
    401:       } \
    402:     } \
    403:     if (value == 0.0 && ignorezeroentries && row != col) { \
    404:       low1  = 0; \
    405:       high1 = nrow1; \
    406:       goto a_noinsert; \
    407:     } \
    408:     if (nonew == 1) { \
    409:       low1  = 0; \
    410:       high1 = nrow1; \
    411:       goto a_noinsert; \
    412:     } \
    413:     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); \
    414:     MatSeqXAIJReallocateAIJ(A, am, 1, nrow1, row, col, rmax1, aa, ai, aj, rp1, ap1, aimax, nonew, MatScalar); \
    415:     N = nrow1++ - 1; \
    416:     a->nz++; \
    417:     high1++; \
    418:     /* shift up all the later entries in this row */ \
    419:     PetscCall(PetscArraymove(rp1 + _i + 1, rp1 + _i, N - _i + 1)); \
    420:     PetscCall(PetscArraymove(ap1 + _i + 1, ap1 + _i, N - _i + 1)); \
    421:     rp1[_i] = col; \
    422:     ap1[_i] = value; \
    423:   a_noinsert:; \
    424:     ailen[row] = nrow1; \
    425:   } while (0)

    427: #define MatSetValues_SeqAIJ_B_Private(row, col, value, addv, orow, ocol) \
    428:   do { \
    429:     if (col <= lastcol2) low2 = 0; \
    430:     else high2 = nrow2; \
    431:     lastcol2 = col; \
    432:     while (high2 - low2 > 5) { \
    433:       t = (low2 + high2) / 2; \
    434:       if (rp2[t] > col) high2 = t; \
    435:       else low2 = t; \
    436:     } \
    437:     for (_i = low2; _i < high2; _i++) { \
    438:       if (rp2[_i] > col) break; \
    439:       if (rp2[_i] == col) { \
    440:         if (addv == ADD_VALUES) { \
    441:           ap2[_i] += value; \
    442:           (void)PetscLogFlops(1.0); \
    443:         } else ap2[_i] = value; \
    444:         goto b_noinsert; \
    445:       } \
    446:     } \
    447:     if (value == 0.0 && ignorezeroentries) { \
    448:       low2  = 0; \
    449:       high2 = nrow2; \
    450:       goto b_noinsert; \
    451:     } \
    452:     if (nonew == 1) { \
    453:       low2  = 0; \
    454:       high2 = nrow2; \
    455:       goto b_noinsert; \
    456:     } \
    457:     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); \
    458:     MatSeqXAIJReallocateAIJ(B, bm, 1, nrow2, row, col, rmax2, ba, bi, bj, rp2, ap2, bimax, nonew, MatScalar); \
    459:     N = nrow2++ - 1; \
    460:     b->nz++; \
    461:     high2++; \
    462:     /* shift up all the later entries in this row */ \
    463:     PetscCall(PetscArraymove(rp2 + _i + 1, rp2 + _i, N - _i + 1)); \
    464:     PetscCall(PetscArraymove(ap2 + _i + 1, ap2 + _i, N - _i + 1)); \
    465:     rp2[_i] = col; \
    466:     ap2[_i] = value; \
    467:   b_noinsert:; \
    468:     bilen[row] = nrow2; \
    469:   } while (0)

    471: static PetscErrorCode MatSetValuesRow_MPIAIJ(Mat A, PetscInt row, const PetscScalar v[])
    472: {
    473:   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)A->data;
    474:   Mat_SeqAIJ  *a = (Mat_SeqAIJ *)mat->A->data, *b = (Mat_SeqAIJ *)mat->B->data;
    475:   PetscInt     l, *garray                         = mat->garray, diag;
    476:   PetscScalar *aa, *ba;

    478:   PetscFunctionBegin;
    479:   /* code only works for square matrices A */

    481:   /* find size of row to the left of the diagonal part */
    482:   PetscCall(MatGetOwnershipRange(A, &diag, NULL));
    483:   row = row - diag;
    484:   for (l = 0; l < b->i[row + 1] - b->i[row]; l++) {
    485:     if (garray[b->j[b->i[row] + l]] > diag) break;
    486:   }
    487:   if (l) {
    488:     PetscCall(MatSeqAIJGetArray(mat->B, &ba));
    489:     PetscCall(PetscArraycpy(ba + b->i[row], v, l));
    490:     PetscCall(MatSeqAIJRestoreArray(mat->B, &ba));
    491:   }

    493:   /* diagonal part */
    494:   if (a->i[row + 1] - a->i[row]) {
    495:     PetscCall(MatSeqAIJGetArray(mat->A, &aa));
    496:     PetscCall(PetscArraycpy(aa + a->i[row], v + l, a->i[row + 1] - a->i[row]));
    497:     PetscCall(MatSeqAIJRestoreArray(mat->A, &aa));
    498:   }

    500:   /* right of diagonal part */
    501:   if (b->i[row + 1] - b->i[row] - l) {
    502:     PetscCall(MatSeqAIJGetArray(mat->B, &ba));
    503:     PetscCall(PetscArraycpy(ba + b->i[row] + l, v + l + a->i[row + 1] - a->i[row], b->i[row + 1] - b->i[row] - l));
    504:     PetscCall(MatSeqAIJRestoreArray(mat->B, &ba));
    505:   }
    506:   PetscFunctionReturn(PETSC_SUCCESS);
    507: }

    509: PetscErrorCode MatSetValues_MPIAIJ(Mat mat, PetscInt m, const PetscInt im[], PetscInt n, const PetscInt in[], const PetscScalar v[], InsertMode addv)
    510: {
    511:   Mat_MPIAIJ *aij   = (Mat_MPIAIJ *)mat->data;
    512:   PetscScalar value = 0.0;
    513:   PetscInt    i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    514:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
    515:   PetscBool   roworiented = aij->roworiented;

    517:   /* Some Variables required in the macro */
    518:   Mat         A     = aij->A;
    519:   Mat_SeqAIJ *a     = (Mat_SeqAIJ *)A->data;
    520:   PetscInt   *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
    521:   PetscBool   ignorezeroentries = a->ignorezeroentries;
    522:   Mat         B                 = aij->B;
    523:   Mat_SeqAIJ *b                 = (Mat_SeqAIJ *)B->data;
    524:   PetscInt   *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j, bm = aij->B->rmap->n, am = aij->A->rmap->n;
    525:   MatScalar  *aa, *ba;
    526:   PetscInt   *rp1, *rp2, ii, nrow1, nrow2, _i, rmax1, rmax2, N, low1, high1, low2, high2, t, lastcol1, lastcol2;
    527:   PetscInt    nonew;
    528:   MatScalar  *ap1, *ap2;

    530:   PetscFunctionBegin;
    531:   PetscCall(MatSeqAIJGetArray(A, &aa));
    532:   PetscCall(MatSeqAIJGetArray(B, &ba));
    533:   for (i = 0; i < m; i++) {
    534:     if (im[i] < 0) continue;
    535:     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);
    536:     if (im[i] >= rstart && im[i] < rend) {
    537:       row      = im[i] - rstart;
    538:       lastcol1 = -1;
    539:       rp1      = PetscSafePointerPlusOffset(aj, ai[row]);
    540:       ap1      = PetscSafePointerPlusOffset(aa, ai[row]);
    541:       rmax1    = aimax[row];
    542:       nrow1    = ailen[row];
    543:       low1     = 0;
    544:       high1    = nrow1;
    545:       lastcol2 = -1;
    546:       rp2      = PetscSafePointerPlusOffset(bj, bi[row]);
    547:       ap2      = PetscSafePointerPlusOffset(ba, bi[row]);
    548:       rmax2    = bimax[row];
    549:       nrow2    = bilen[row];
    550:       low2     = 0;
    551:       high2    = nrow2;

    553:       for (j = 0; j < n; j++) {
    554:         if (v) value = roworiented ? v[i * n + j] : v[i + j * m];
    555:         if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
    556:         if (in[j] >= cstart && in[j] < cend) {
    557:           col   = in[j] - cstart;
    558:           nonew = a->nonew;
    559:           MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
    560:         } else if (in[j] < 0) {
    561:           continue;
    562:         } else {
    563:           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);
    564:           if (mat->was_assembled) {
    565:             if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    566: #if defined(PETSC_USE_CTABLE)
    567:             PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col)); /* map global col ids to local ones */
    568:             col--;
    569: #else
    570:             col = aij->colmap[in[j]] - 1;
    571: #endif
    572:             if (col < 0 && !((Mat_SeqAIJ *)aij->B->data)->nonew) { /* col < 0 means in[j] is a new col for B */
    573:               PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));  /* Change aij->B from reduced/local format to expanded/global format */
    574:               col = in[j];
    575:               /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
    576:               B     = aij->B;
    577:               b     = (Mat_SeqAIJ *)B->data;
    578:               bimax = b->imax;
    579:               bi    = b->i;
    580:               bilen = b->ilen;
    581:               bj    = b->j;
    582:               ba    = b->a;
    583:               rp2   = PetscSafePointerPlusOffset(bj, bi[row]);
    584:               ap2   = PetscSafePointerPlusOffset(ba, bi[row]);
    585:               rmax2 = bimax[row];
    586:               nrow2 = bilen[row];
    587:               low2  = 0;
    588:               high2 = nrow2;
    589:               bm    = aij->B->rmap->n;
    590:               ba    = b->a;
    591:             } else if (col < 0 && !(ignorezeroentries && value == 0.0)) {
    592:               if (1 == ((Mat_SeqAIJ *)aij->B->data)->nonew) {
    593:                 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]));
    594:               } 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]);
    595:             }
    596:           } else col = in[j];
    597:           nonew = b->nonew;
    598:           MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
    599:         }
    600:       }
    601:     } else {
    602:       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]);
    603:       if (!aij->donotstash) {
    604:         mat->assembled = PETSC_FALSE;
    605:         if (roworiented) {
    606:           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, PetscSafePointerPlusOffset(v, i * n), (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    607:         } else {
    608:           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, PetscSafePointerPlusOffset(v, i), m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    609:         }
    610:       }
    611:     }
    612:   }
    613:   PetscCall(MatSeqAIJRestoreArray(A, &aa)); /* aa, bb might have been free'd due to reallocation above. But we don't access them here */
    614:   PetscCall(MatSeqAIJRestoreArray(B, &ba));
    615:   PetscFunctionReturn(PETSC_SUCCESS);
    616: }

    618: /*
    619:     This function sets the j and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
    620:     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
    621:     No off-processor parts off the matrix are allowed here and mat->was_assembled has to be PETSC_FALSE.
    622: */
    623: PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat_Symbolic(Mat mat, const PetscInt mat_j[], const PetscInt mat_i[])
    624: {
    625:   Mat_MPIAIJ *aij    = (Mat_MPIAIJ *)mat->data;
    626:   Mat         A      = aij->A; /* diagonal part of the matrix */
    627:   Mat         B      = aij->B; /* off-diagonal part of the matrix */
    628:   Mat_SeqAIJ *a      = (Mat_SeqAIJ *)A->data;
    629:   Mat_SeqAIJ *b      = (Mat_SeqAIJ *)B->data;
    630:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, col;
    631:   PetscInt   *ailen = a->ilen, *aj = a->j;
    632:   PetscInt   *bilen = b->ilen, *bj = b->j;
    633:   PetscInt    am          = aij->A->rmap->n, j;
    634:   PetscInt    diag_so_far = 0, dnz;
    635:   PetscInt    offd_so_far = 0, onz;

    637:   PetscFunctionBegin;
    638:   /* Iterate over all rows of the matrix */
    639:   for (j = 0; j < am; j++) {
    640:     dnz = onz = 0;
    641:     /*  Iterate over all non-zero columns of the current row */
    642:     for (col = mat_i[j]; col < mat_i[j + 1]; col++) {
    643:       /* If column is in the diagonal */
    644:       if (mat_j[col] >= cstart && mat_j[col] < cend) {
    645:         aj[diag_so_far++] = mat_j[col] - cstart;
    646:         dnz++;
    647:       } else { /* off-diagonal entries */
    648:         bj[offd_so_far++] = mat_j[col];
    649:         onz++;
    650:       }
    651:     }
    652:     ailen[j] = dnz;
    653:     bilen[j] = onz;
    654:   }
    655:   PetscFunctionReturn(PETSC_SUCCESS);
    656: }

    658: /*
    659:     This function sets the local j, a and ilen arrays (of the diagonal and off-diagonal part) of an MPIAIJ-matrix.
    660:     The values in mat_i have to be sorted and the values in mat_j have to be sorted for each row (CSR-like).
    661:     No off-processor parts off the matrix are allowed here, they are set at a later point by MatSetValues_MPIAIJ.
    662:     Also, mat->was_assembled has to be false, otherwise the statement aj[rowstart_diag+dnz_row] = mat_j[col] - cstart;
    663:     would not be true and the more complex MatSetValues_MPIAIJ has to be used.
    664: */
    665: PetscErrorCode MatSetValues_MPIAIJ_CopyFromCSRFormat(Mat mat, const PetscInt mat_j[], const PetscInt mat_i[], const PetscScalar mat_a[])
    666: {
    667:   Mat_MPIAIJ  *aij  = (Mat_MPIAIJ *)mat->data;
    668:   Mat          A    = aij->A; /* diagonal part of the matrix */
    669:   Mat          B    = aij->B; /* off-diagonal part of the matrix */
    670:   Mat_SeqAIJ  *aijd = (Mat_SeqAIJ *)aij->A->data, *aijo = (Mat_SeqAIJ *)aij->B->data;
    671:   Mat_SeqAIJ  *a      = (Mat_SeqAIJ *)A->data;
    672:   Mat_SeqAIJ  *b      = (Mat_SeqAIJ *)B->data;
    673:   PetscInt     cstart = mat->cmap->rstart, cend = mat->cmap->rend;
    674:   PetscInt    *ailen = a->ilen, *aj = a->j;
    675:   PetscInt    *bilen = b->ilen, *bj = b->j;
    676:   PetscInt     am          = aij->A->rmap->n, j;
    677:   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. */
    678:   PetscInt     col, dnz_row, onz_row, rowstart_diag, rowstart_offd;
    679:   PetscScalar *aa = a->a, *ba = b->a;

    681:   PetscFunctionBegin;
    682:   /* Iterate over all rows of the matrix */
    683:   for (j = 0; j < am; j++) {
    684:     dnz_row = onz_row = 0;
    685:     rowstart_offd     = full_offd_i[j];
    686:     rowstart_diag     = full_diag_i[j];
    687:     /*  Iterate over all non-zero columns of the current row */
    688:     for (col = mat_i[j]; col < mat_i[j + 1]; col++) {
    689:       /* If column is in the diagonal */
    690:       if (mat_j[col] >= cstart && mat_j[col] < cend) {
    691:         aj[rowstart_diag + dnz_row] = mat_j[col] - cstart;
    692:         aa[rowstart_diag + dnz_row] = mat_a[col];
    693:         dnz_row++;
    694:       } else { /* off-diagonal entries */
    695:         bj[rowstart_offd + onz_row] = mat_j[col];
    696:         ba[rowstart_offd + onz_row] = mat_a[col];
    697:         onz_row++;
    698:       }
    699:     }
    700:     ailen[j] = dnz_row;
    701:     bilen[j] = onz_row;
    702:   }
    703:   PetscFunctionReturn(PETSC_SUCCESS);
    704: }

    706: static PetscErrorCode MatGetValues_MPIAIJ(Mat mat, PetscInt m, const PetscInt idxm[], PetscInt n, const PetscInt idxn[], PetscScalar v[])
    707: {
    708:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    709:   PetscInt    i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    710:   PetscInt    cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;

    712:   PetscFunctionBegin;
    713:   for (i = 0; i < m; i++) {
    714:     if (idxm[i] < 0) continue; /* negative row */
    715:     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);
    716:     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);
    717:     row = idxm[i] - rstart;
    718:     for (j = 0; j < n; j++) {
    719:       if (idxn[j] < 0) continue; /* negative column */
    720:       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);
    721:       if (idxn[j] >= cstart && idxn[j] < cend) {
    722:         col = idxn[j] - cstart;
    723:         PetscCall(MatGetValues(aij->A, 1, &row, 1, &col, v + i * n + j));
    724:       } else {
    725:         if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    726: #if defined(PETSC_USE_CTABLE)
    727:         PetscCall(PetscHMapIGetWithDefault(aij->colmap, idxn[j] + 1, 0, &col));
    728:         col--;
    729: #else
    730:         col = aij->colmap[idxn[j]] - 1;
    731: #endif
    732:         if ((col < 0) || (aij->garray[col] != idxn[j])) *(v + i * n + j) = 0.0;
    733:         else PetscCall(MatGetValues(aij->B, 1, &row, 1, &col, v + i * n + j));
    734:       }
    735:     }
    736:   }
    737:   PetscFunctionReturn(PETSC_SUCCESS);
    738: }

    740: static PetscErrorCode MatAssemblyBegin_MPIAIJ(Mat mat, MatAssemblyType mode)
    741: {
    742:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    743:   PetscInt    nstash, reallocs;

    745:   PetscFunctionBegin;
    746:   if (aij->donotstash || mat->nooffprocentries) PetscFunctionReturn(PETSC_SUCCESS);

    748:   PetscCall(MatStashScatterBegin_Private(mat, &mat->stash, mat->rmap->range));
    749:   PetscCall(MatStashGetInfo_Private(&mat->stash, &nstash, &reallocs));
    750:   PetscCall(PetscInfo(aij->A, "Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
    751:   PetscFunctionReturn(PETSC_SUCCESS);
    752: }

    754: PetscErrorCode MatAssemblyEnd_MPIAIJ(Mat mat, MatAssemblyType mode)
    755: {
    756:   Mat_MPIAIJ  *aij = (Mat_MPIAIJ *)mat->data;
    757:   PetscMPIInt  n;
    758:   PetscInt     i, j, rstart, ncols, flg;
    759:   PetscInt    *row, *col;
    760:   PetscBool    other_disassembled;
    761:   PetscScalar *val;

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

    765:   PetscFunctionBegin;
    766:   if (!aij->donotstash && !mat->nooffprocentries) {
    767:     while (1) {
    768:       PetscCall(MatStashScatterGetMesg_Private(&mat->stash, &n, &row, &col, &val, &flg));
    769:       if (!flg) break;

    771:       for (i = 0; i < n;) {
    772:         /* Now identify the consecutive vals belonging to the same row */
    773:         for (j = i, rstart = row[j]; j < n; j++) {
    774:           if (row[j] != rstart) break;
    775:         }
    776:         if (j < n) ncols = j - i;
    777:         else ncols = n - i;
    778:         /* Now assemble all these values with a single function call */
    779:         PetscCall(MatSetValues_MPIAIJ(mat, 1, row + i, ncols, col + i, val + i, mat->insertmode));
    780:         i = j;
    781:       }
    782:     }
    783:     PetscCall(MatStashScatterEnd_Private(&mat->stash));
    784:   }
    785: #if defined(PETSC_HAVE_DEVICE)
    786:   if (mat->offloadmask == PETSC_OFFLOAD_CPU) aij->A->offloadmask = PETSC_OFFLOAD_CPU;
    787:   /* We call MatBindToCPU() on aij->A and aij->B here, because if MatBindToCPU_MPIAIJ() is called before assembly, it cannot bind these. */
    788:   if (mat->boundtocpu) {
    789:     PetscCall(MatBindToCPU(aij->A, PETSC_TRUE));
    790:     PetscCall(MatBindToCPU(aij->B, PETSC_TRUE));
    791:   }
    792: #endif
    793:   PetscCall(MatAssemblyBegin(aij->A, mode));
    794:   PetscCall(MatAssemblyEnd(aij->A, mode));

    796:   /* determine if any processor has disassembled, if so we must
    797:      also disassemble ourself, in order that we may reassemble. */
    798:   /*
    799:      if nonzero structure of submatrix B cannot change then we know that
    800:      no processor disassembled thus we can skip this stuff
    801:   */
    802:   if (!((Mat_SeqAIJ *)aij->B->data)->nonew) {
    803:     PetscCallMPI(MPIU_Allreduce(&mat->was_assembled, &other_disassembled, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    804:     if (mat->was_assembled && !other_disassembled) { /* mat on this rank has reduced off-diag B with local col ids, but globally it does not */
    805:       PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));
    806:     }
    807:   }
    808:   if (!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) PetscCall(MatSetUpMultiply_MPIAIJ(mat));
    809:   PetscCall(MatSetOption(aij->B, MAT_USE_INODES, PETSC_FALSE));
    810: #if defined(PETSC_HAVE_DEVICE)
    811:   if (mat->offloadmask == PETSC_OFFLOAD_CPU && aij->B->offloadmask != PETSC_OFFLOAD_UNALLOCATED) aij->B->offloadmask = PETSC_OFFLOAD_CPU;
    812: #endif
    813:   PetscCall(MatAssemblyBegin(aij->B, mode));
    814:   PetscCall(MatAssemblyEnd(aij->B, mode));

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

    818:   aij->rowvalues = NULL;

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

    822:   /* if no new nonzero locations are allowed in matrix then only set the matrix state the first time through */
    823:   if ((!mat->was_assembled && mode == MAT_FINAL_ASSEMBLY) || !((Mat_SeqAIJ *)aij->A->data)->nonew) {
    824:     PetscObjectState state = aij->A->nonzerostate + aij->B->nonzerostate;
    825:     PetscCallMPI(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));
    826:   }
    827: #if defined(PETSC_HAVE_DEVICE)
    828:   mat->offloadmask = PETSC_OFFLOAD_BOTH;
    829: #endif
    830:   PetscFunctionReturn(PETSC_SUCCESS);
    831: }

    833: static PetscErrorCode MatZeroEntries_MPIAIJ(Mat A)
    834: {
    835:   Mat_MPIAIJ *l = (Mat_MPIAIJ *)A->data;

    837:   PetscFunctionBegin;
    838:   PetscCall(MatZeroEntries(l->A));
    839:   PetscCall(MatZeroEntries(l->B));
    840:   PetscFunctionReturn(PETSC_SUCCESS);
    841: }

    843: static PetscErrorCode MatZeroRows_MPIAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    844: {
    845:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)A->data;
    846:   PetscInt   *lrows;
    847:   PetscInt    r, len;
    848:   PetscBool   cong;

    850:   PetscFunctionBegin;
    851:   /* get locally owned rows */
    852:   PetscCall(MatZeroRowsMapLocal_Private(A, N, rows, &len, &lrows));
    853:   PetscCall(MatHasCongruentLayouts(A, &cong));
    854:   /* fix right-hand side if needed */
    855:   if (x && b) {
    856:     const PetscScalar *xx;
    857:     PetscScalar       *bb;

    859:     PetscCheck(cong, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Need matching row/col layout");
    860:     PetscCall(VecGetArrayRead(x, &xx));
    861:     PetscCall(VecGetArray(b, &bb));
    862:     for (r = 0; r < len; ++r) bb[lrows[r]] = diag * xx[lrows[r]];
    863:     PetscCall(VecRestoreArrayRead(x, &xx));
    864:     PetscCall(VecRestoreArray(b, &bb));
    865:   }

    867:   if (diag != 0.0 && cong) {
    868:     PetscCall(MatZeroRows(mat->A, len, lrows, diag, NULL, NULL));
    869:     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
    870:   } else if (diag != 0.0) { /* non-square or non congruent layouts -> if keepnonzeropattern is false, we allow for new insertion */
    871:     Mat_SeqAIJ *aijA = (Mat_SeqAIJ *)mat->A->data;
    872:     Mat_SeqAIJ *aijB = (Mat_SeqAIJ *)mat->B->data;
    873:     PetscInt    nnwA, nnwB;
    874:     PetscBool   nnzA, nnzB;

    876:     nnwA = aijA->nonew;
    877:     nnwB = aijB->nonew;
    878:     nnzA = aijA->keepnonzeropattern;
    879:     nnzB = aijB->keepnonzeropattern;
    880:     if (!nnzA) {
    881:       PetscCall(PetscInfo(mat->A, "Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on diagonal block.\n"));
    882:       aijA->nonew = 0;
    883:     }
    884:     if (!nnzB) {
    885:       PetscCall(PetscInfo(mat->B, "Requested to not keep the pattern and add a nonzero diagonal; may encounter reallocations on off-diagonal block.\n"));
    886:       aijB->nonew = 0;
    887:     }
    888:     /* Must zero here before the next loop */
    889:     PetscCall(MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL));
    890:     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
    891:     for (r = 0; r < len; ++r) {
    892:       const PetscInt row = lrows[r] + A->rmap->rstart;
    893:       if (row >= A->cmap->N) continue;
    894:       PetscCall(MatSetValues(A, 1, &row, 1, &row, &diag, INSERT_VALUES));
    895:     }
    896:     aijA->nonew = nnwA;
    897:     aijB->nonew = nnwB;
    898:   } else {
    899:     PetscCall(MatZeroRows(mat->A, len, lrows, 0.0, NULL, NULL));
    900:     PetscCall(MatZeroRows(mat->B, len, lrows, 0.0, NULL, NULL));
    901:   }
    902:   PetscCall(PetscFree(lrows));
    903:   PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
    904:   PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));

    906:   /* only change matrix nonzero state if pattern was allowed to be changed */
    907:   if (!((Mat_SeqAIJ *)mat->A->data)->keepnonzeropattern || !((Mat_SeqAIJ *)mat->A->data)->nonew) {
    908:     PetscObjectState state = mat->A->nonzerostate + mat->B->nonzerostate;
    909:     PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
    910:   }
    911:   PetscFunctionReturn(PETSC_SUCCESS);
    912: }

    914: static PetscErrorCode MatZeroRowsColumns_MPIAIJ(Mat A, PetscInt N, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
    915: {
    916:   Mat_MPIAIJ        *l = (Mat_MPIAIJ *)A->data;
    917:   PetscInt           n = A->rmap->n;
    918:   PetscInt           i, j, r, m, len = 0;
    919:   PetscInt          *lrows, *owners = A->rmap->range;
    920:   PetscMPIInt        p = 0;
    921:   PetscSFNode       *rrows;
    922:   PetscSF            sf;
    923:   const PetscScalar *xx;
    924:   PetscScalar       *bb, *mask, *aij_a;
    925:   Vec                xmask, lmask;
    926:   Mat_SeqAIJ        *aij = (Mat_SeqAIJ *)l->B->data;
    927:   const PetscInt    *aj, *ii, *ridx;
    928:   PetscScalar       *aa;

    930:   PetscFunctionBegin;
    931:   /* Create SF where leaves are input rows and roots are owned rows */
    932:   PetscCall(PetscMalloc1(n, &lrows));
    933:   for (r = 0; r < n; ++r) lrows[r] = -1;
    934:   PetscCall(PetscMalloc1(N, &rrows));
    935:   for (r = 0; r < N; ++r) {
    936:     const PetscInt idx = rows[r];
    937:     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);
    938:     if (idx < owners[p] || owners[p + 1] <= idx) { /* short-circuit the search if the last p owns this row too */
    939:       PetscCall(PetscLayoutFindOwner(A->rmap, idx, &p));
    940:     }
    941:     rrows[r].rank  = p;
    942:     rrows[r].index = rows[r] - owners[p];
    943:   }
    944:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    945:   PetscCall(PetscSFSetGraph(sf, n, N, NULL, PETSC_OWN_POINTER, rrows, PETSC_OWN_POINTER));
    946:   /* Collect flags for rows to be zeroed */
    947:   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, (PetscInt *)rows, lrows, MPI_LOR));
    948:   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, (PetscInt *)rows, lrows, MPI_LOR));
    949:   PetscCall(PetscSFDestroy(&sf));
    950:   /* Compress and put in row numbers */
    951:   for (r = 0; r < n; ++r)
    952:     if (lrows[r] >= 0) lrows[len++] = r;
    953:   /* zero diagonal part of matrix */
    954:   PetscCall(MatZeroRowsColumns(l->A, len, lrows, diag, x, b));
    955:   /* handle off-diagonal part of matrix */
    956:   PetscCall(MatCreateVecs(A, &xmask, NULL));
    957:   PetscCall(VecDuplicate(l->lvec, &lmask));
    958:   PetscCall(VecGetArray(xmask, &bb));
    959:   for (i = 0; i < len; i++) bb[lrows[i]] = 1;
    960:   PetscCall(VecRestoreArray(xmask, &bb));
    961:   PetscCall(VecScatterBegin(l->Mvctx, xmask, lmask, ADD_VALUES, SCATTER_FORWARD));
    962:   PetscCall(VecScatterEnd(l->Mvctx, xmask, lmask, ADD_VALUES, SCATTER_FORWARD));
    963:   PetscCall(VecDestroy(&xmask));
    964:   if (x && b) { /* this code is buggy when the row and column layout don't match */
    965:     PetscBool cong;

    967:     PetscCall(MatHasCongruentLayouts(A, &cong));
    968:     PetscCheck(cong, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Need matching row/col layout");
    969:     PetscCall(VecScatterBegin(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
    970:     PetscCall(VecScatterEnd(l->Mvctx, x, l->lvec, INSERT_VALUES, SCATTER_FORWARD));
    971:     PetscCall(VecGetArrayRead(l->lvec, &xx));
    972:     PetscCall(VecGetArray(b, &bb));
    973:   }
    974:   PetscCall(VecGetArray(lmask, &mask));
    975:   /* remove zeroed rows of off-diagonal matrix */
    976:   PetscCall(MatSeqAIJGetArray(l->B, &aij_a));
    977:   ii = aij->i;
    978:   for (i = 0; i < len; i++) PetscCall(PetscArrayzero(PetscSafePointerPlusOffset(aij_a, ii[lrows[i]]), ii[lrows[i] + 1] - ii[lrows[i]]));
    979:   /* loop over all elements of off process part of matrix zeroing removed columns*/
    980:   if (aij->compressedrow.use) {
    981:     m    = aij->compressedrow.nrows;
    982:     ii   = aij->compressedrow.i;
    983:     ridx = aij->compressedrow.rindex;
    984:     for (i = 0; i < m; i++) {
    985:       n  = ii[i + 1] - ii[i];
    986:       aj = aij->j + ii[i];
    987:       aa = aij_a + ii[i];

    989:       for (j = 0; j < n; j++) {
    990:         if (PetscAbsScalar(mask[*aj])) {
    991:           if (b) bb[*ridx] -= *aa * xx[*aj];
    992:           *aa = 0.0;
    993:         }
    994:         aa++;
    995:         aj++;
    996:       }
    997:       ridx++;
    998:     }
    999:   } else { /* do not use compressed row format */
    1000:     m = l->B->rmap->n;
    1001:     for (i = 0; i < m; i++) {
    1002:       n  = ii[i + 1] - ii[i];
    1003:       aj = aij->j + ii[i];
    1004:       aa = aij_a + ii[i];
    1005:       for (j = 0; j < n; j++) {
    1006:         if (PetscAbsScalar(mask[*aj])) {
    1007:           if (b) bb[i] -= *aa * xx[*aj];
    1008:           *aa = 0.0;
    1009:         }
    1010:         aa++;
    1011:         aj++;
    1012:       }
    1013:     }
    1014:   }
    1015:   if (x && b) {
    1016:     PetscCall(VecRestoreArray(b, &bb));
    1017:     PetscCall(VecRestoreArrayRead(l->lvec, &xx));
    1018:   }
    1019:   PetscCall(MatSeqAIJRestoreArray(l->B, &aij_a));
    1020:   PetscCall(VecRestoreArray(lmask, &mask));
    1021:   PetscCall(VecDestroy(&lmask));
    1022:   PetscCall(PetscFree(lrows));

    1024:   /* only change matrix nonzero state if pattern was allowed to be changed */
    1025:   if (!((Mat_SeqAIJ *)l->A->data)->nonew) {
    1026:     PetscObjectState state = l->A->nonzerostate + l->B->nonzerostate;
    1027:     PetscCallMPI(MPIU_Allreduce(&state, &A->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)A)));
    1028:   }
    1029:   PetscFunctionReturn(PETSC_SUCCESS);
    1030: }

    1032: static PetscErrorCode MatMult_MPIAIJ(Mat A, Vec xx, Vec yy)
    1033: {
    1034:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    1035:   PetscInt    nt;
    1036:   VecScatter  Mvctx = a->Mvctx;

    1038:   PetscFunctionBegin;
    1039:   PetscCall(VecGetLocalSize(xx, &nt));
    1040:   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);
    1041:   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1042:   PetscUseTypeMethod(a->A, mult, xx, yy);
    1043:   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1044:   PetscUseTypeMethod(a->B, multadd, a->lvec, yy, yy);
    1045:   PetscFunctionReturn(PETSC_SUCCESS);
    1046: }

    1048: static PetscErrorCode MatMultDiagonalBlock_MPIAIJ(Mat A, Vec bb, Vec xx)
    1049: {
    1050:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1052:   PetscFunctionBegin;
    1053:   PetscCall(MatMultDiagonalBlock(a->A, bb, xx));
    1054:   PetscFunctionReturn(PETSC_SUCCESS);
    1055: }

    1057: static PetscErrorCode MatMultAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
    1058: {
    1059:   Mat_MPIAIJ *a     = (Mat_MPIAIJ *)A->data;
    1060:   VecScatter  Mvctx = a->Mvctx;

    1062:   PetscFunctionBegin;
    1063:   PetscCall(VecScatterBegin(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1064:   PetscCall((*a->A->ops->multadd)(a->A, xx, yy, zz));
    1065:   PetscCall(VecScatterEnd(Mvctx, xx, a->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1066:   PetscCall((*a->B->ops->multadd)(a->B, a->lvec, zz, zz));
    1067:   PetscFunctionReturn(PETSC_SUCCESS);
    1068: }

    1070: static PetscErrorCode MatMultTranspose_MPIAIJ(Mat A, Vec xx, Vec yy)
    1071: {
    1072:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1074:   PetscFunctionBegin;
    1075:   /* do nondiagonal part */
    1076:   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
    1077:   /* do local part */
    1078:   PetscCall((*a->A->ops->multtranspose)(a->A, xx, yy));
    1079:   /* add partial results together */
    1080:   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
    1081:   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, yy, ADD_VALUES, SCATTER_REVERSE));
    1082:   PetscFunctionReturn(PETSC_SUCCESS);
    1083: }

    1085: static PetscErrorCode MatIsTranspose_MPIAIJ(Mat Amat, Mat Bmat, PetscReal tol, PetscBool *f)
    1086: {
    1087:   MPI_Comm    comm;
    1088:   Mat_MPIAIJ *Aij = (Mat_MPIAIJ *)Amat->data, *Bij = (Mat_MPIAIJ *)Bmat->data;
    1089:   Mat         Adia = Aij->A, Bdia = Bij->A, Aoff, Boff, *Aoffs, *Boffs;
    1090:   IS          Me, Notme;
    1091:   PetscInt    M, N, first, last, *notme, i;
    1092:   PetscBool   lf;
    1093:   PetscMPIInt size;

    1095:   PetscFunctionBegin;
    1096:   /* Easy test: symmetric diagonal block */
    1097:   PetscCall(MatIsTranspose(Adia, Bdia, tol, &lf));
    1098:   PetscCallMPI(MPIU_Allreduce(&lf, f, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)Amat)));
    1099:   if (!*f) PetscFunctionReturn(PETSC_SUCCESS);
    1100:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
    1101:   PetscCallMPI(MPI_Comm_size(comm, &size));
    1102:   if (size == 1) PetscFunctionReturn(PETSC_SUCCESS);

    1104:   /* Hard test: off-diagonal block. This takes a MatCreateSubMatrix. */
    1105:   PetscCall(MatGetSize(Amat, &M, &N));
    1106:   PetscCall(MatGetOwnershipRange(Amat, &first, &last));
    1107:   PetscCall(PetscMalloc1(N - last + first, &notme));
    1108:   for (i = 0; i < first; i++) notme[i] = i;
    1109:   for (i = last; i < M; i++) notme[i - last + first] = i;
    1110:   PetscCall(ISCreateGeneral(MPI_COMM_SELF, N - last + first, notme, PETSC_COPY_VALUES, &Notme));
    1111:   PetscCall(ISCreateStride(MPI_COMM_SELF, last - first, first, 1, &Me));
    1112:   PetscCall(MatCreateSubMatrices(Amat, 1, &Me, &Notme, MAT_INITIAL_MATRIX, &Aoffs));
    1113:   Aoff = Aoffs[0];
    1114:   PetscCall(MatCreateSubMatrices(Bmat, 1, &Notme, &Me, MAT_INITIAL_MATRIX, &Boffs));
    1115:   Boff = Boffs[0];
    1116:   PetscCall(MatIsTranspose(Aoff, Boff, tol, f));
    1117:   PetscCall(MatDestroyMatrices(1, &Aoffs));
    1118:   PetscCall(MatDestroyMatrices(1, &Boffs));
    1119:   PetscCall(ISDestroy(&Me));
    1120:   PetscCall(ISDestroy(&Notme));
    1121:   PetscCall(PetscFree(notme));
    1122:   PetscFunctionReturn(PETSC_SUCCESS);
    1123: }

    1125: static PetscErrorCode MatMultTransposeAdd_MPIAIJ(Mat A, Vec xx, Vec yy, Vec zz)
    1126: {
    1127:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1129:   PetscFunctionBegin;
    1130:   /* do nondiagonal part */
    1131:   PetscCall((*a->B->ops->multtranspose)(a->B, xx, a->lvec));
    1132:   /* do local part */
    1133:   PetscCall((*a->A->ops->multtransposeadd)(a->A, xx, yy, zz));
    1134:   /* add partial results together */
    1135:   PetscCall(VecScatterBegin(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
    1136:   PetscCall(VecScatterEnd(a->Mvctx, a->lvec, zz, ADD_VALUES, SCATTER_REVERSE));
    1137:   PetscFunctionReturn(PETSC_SUCCESS);
    1138: }

    1140: /*
    1141:   This only works correctly for square matrices where the subblock A->A is the
    1142:    diagonal block
    1143: */
    1144: static PetscErrorCode MatGetDiagonal_MPIAIJ(Mat A, Vec v)
    1145: {
    1146:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1148:   PetscFunctionBegin;
    1149:   PetscCheck(A->rmap->N == A->cmap->N, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Supports only square matrix where A->A is diag block");
    1150:   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");
    1151:   PetscCall(MatGetDiagonal(a->A, v));
    1152:   PetscFunctionReturn(PETSC_SUCCESS);
    1153: }

    1155: static PetscErrorCode MatScale_MPIAIJ(Mat A, PetscScalar aa)
    1156: {
    1157:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1159:   PetscFunctionBegin;
    1160:   PetscCall(MatScale(a->A, aa));
    1161:   PetscCall(MatScale(a->B, aa));
    1162:   PetscFunctionReturn(PETSC_SUCCESS);
    1163: }

    1165: static PetscErrorCode MatView_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
    1166: {
    1167:   Mat_MPIAIJ        *aij    = (Mat_MPIAIJ *)mat->data;
    1168:   Mat_SeqAIJ        *A      = (Mat_SeqAIJ *)aij->A->data;
    1169:   Mat_SeqAIJ        *B      = (Mat_SeqAIJ *)aij->B->data;
    1170:   const PetscInt    *garray = aij->garray;
    1171:   const PetscScalar *aa, *ba;
    1172:   PetscInt           header[4], M, N, m, rs, cs, cnt, i, ja, jb;
    1173:   PetscInt64         nz, hnz;
    1174:   PetscInt          *rowlens;
    1175:   PetscInt          *colidxs;
    1176:   PetscScalar       *matvals;
    1177:   PetscMPIInt        rank;

    1179:   PetscFunctionBegin;
    1180:   PetscCall(PetscViewerSetUp(viewer));

    1182:   M  = mat->rmap->N;
    1183:   N  = mat->cmap->N;
    1184:   m  = mat->rmap->n;
    1185:   rs = mat->rmap->rstart;
    1186:   cs = mat->cmap->rstart;
    1187:   nz = A->nz + B->nz;

    1189:   /* write matrix header */
    1190:   header[0] = MAT_FILE_CLASSID;
    1191:   header[1] = M;
    1192:   header[2] = N;
    1193:   PetscCallMPI(MPI_Reduce(&nz, &hnz, 1, MPIU_INT64, MPI_SUM, 0, PetscObjectComm((PetscObject)mat)));
    1194:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
    1195:   if (rank == 0) {
    1196:     if (hnz > PETSC_INT_MAX) header[3] = PETSC_INT_MAX;
    1197:     else header[3] = (PetscInt)hnz;
    1198:   }
    1199:   PetscCall(PetscViewerBinaryWrite(viewer, header, 4, PETSC_INT));

    1201:   /* fill in and store row lengths  */
    1202:   PetscCall(PetscMalloc1(m, &rowlens));
    1203:   for (i = 0; i < m; i++) rowlens[i] = A->i[i + 1] - A->i[i] + B->i[i + 1] - B->i[i];
    1204:   PetscCall(PetscViewerBinaryWriteAll(viewer, rowlens, m, rs, M, PETSC_INT));
    1205:   PetscCall(PetscFree(rowlens));

    1207:   /* fill in and store column indices */
    1208:   PetscCall(PetscMalloc1(nz, &colidxs));
    1209:   for (cnt = 0, i = 0; i < m; i++) {
    1210:     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
    1211:       if (garray[B->j[jb]] > cs) break;
    1212:       colidxs[cnt++] = garray[B->j[jb]];
    1213:     }
    1214:     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) colidxs[cnt++] = A->j[ja] + cs;
    1215:     for (; jb < B->i[i + 1]; jb++) colidxs[cnt++] = garray[B->j[jb]];
    1216:   }
    1217:   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
    1218:   PetscCall(PetscViewerBinaryWriteAll(viewer, colidxs, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
    1219:   PetscCall(PetscFree(colidxs));

    1221:   /* fill in and store nonzero values */
    1222:   PetscCall(MatSeqAIJGetArrayRead(aij->A, &aa));
    1223:   PetscCall(MatSeqAIJGetArrayRead(aij->B, &ba));
    1224:   PetscCall(PetscMalloc1(nz, &matvals));
    1225:   for (cnt = 0, i = 0; i < m; i++) {
    1226:     for (jb = B->i[i]; jb < B->i[i + 1]; jb++) {
    1227:       if (garray[B->j[jb]] > cs) break;
    1228:       matvals[cnt++] = ba[jb];
    1229:     }
    1230:     for (ja = A->i[i]; ja < A->i[i + 1]; ja++) matvals[cnt++] = aa[ja];
    1231:     for (; jb < B->i[i + 1]; jb++) matvals[cnt++] = ba[jb];
    1232:   }
    1233:   PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &aa));
    1234:   PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &ba));
    1235:   PetscCheck(cnt == nz, PETSC_COMM_SELF, PETSC_ERR_LIB, "Internal PETSc error: cnt = %" PetscInt_FMT " nz = %" PetscInt64_FMT, cnt, nz);
    1236:   PetscCall(PetscViewerBinaryWriteAll(viewer, matvals, nz, PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
    1237:   PetscCall(PetscFree(matvals));

    1239:   /* write block size option to the viewer's .info file */
    1240:   PetscCall(MatView_Binary_BlockSizes(mat, viewer));
    1241:   PetscFunctionReturn(PETSC_SUCCESS);
    1242: }

    1244: #include <petscdraw.h>
    1245: static PetscErrorCode MatView_MPIAIJ_ASCIIorDraworSocket(Mat mat, PetscViewer viewer)
    1246: {
    1247:   Mat_MPIAIJ       *aij  = (Mat_MPIAIJ *)mat->data;
    1248:   PetscMPIInt       rank = aij->rank, size = aij->size;
    1249:   PetscBool         isdraw, iascii, isbinary;
    1250:   PetscViewer       sviewer;
    1251:   PetscViewerFormat format;

    1253:   PetscFunctionBegin;
    1254:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
    1255:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    1256:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    1257:   if (iascii) {
    1258:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1259:     if (format == PETSC_VIEWER_LOAD_BALANCE) {
    1260:       PetscInt i, nmax = 0, nmin = PETSC_INT_MAX, navg = 0, *nz, nzlocal = ((Mat_SeqAIJ *)aij->A->data)->nz + ((Mat_SeqAIJ *)aij->B->data)->nz;
    1261:       PetscCall(PetscMalloc1(size, &nz));
    1262:       PetscCallMPI(MPI_Allgather(&nzlocal, 1, MPIU_INT, nz, 1, MPIU_INT, PetscObjectComm((PetscObject)mat)));
    1263:       for (i = 0; i < (PetscInt)size; i++) {
    1264:         nmax = PetscMax(nmax, nz[i]);
    1265:         nmin = PetscMin(nmin, nz[i]);
    1266:         navg += nz[i];
    1267:       }
    1268:       PetscCall(PetscFree(nz));
    1269:       navg = navg / size;
    1270:       PetscCall(PetscViewerASCIIPrintf(viewer, "Load Balance - Nonzeros: Min %" PetscInt_FMT "  avg %" PetscInt_FMT "  max %" PetscInt_FMT "\n", nmin, navg, nmax));
    1271:       PetscFunctionReturn(PETSC_SUCCESS);
    1272:     }
    1273:     PetscCall(PetscViewerGetFormat(viewer, &format));
    1274:     if (format == PETSC_VIEWER_ASCII_INFO_DETAIL) {
    1275:       MatInfo   info;
    1276:       PetscInt *inodes = NULL;

    1278:       PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)mat), &rank));
    1279:       PetscCall(MatGetInfo(mat, MAT_LOCAL, &info));
    1280:       PetscCall(MatInodeGetInodeSizes(aij->A, NULL, &inodes, NULL));
    1281:       PetscCall(PetscViewerASCIIPushSynchronized(viewer));
    1282:       if (!inodes) {
    1283:         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,
    1284:                                                      (double)info.memory));
    1285:       } else {
    1286:         PetscCall(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,
    1287:                                                      (double)info.memory));
    1288:       }
    1289:       PetscCall(MatGetInfo(aij->A, MAT_LOCAL, &info));
    1290:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] on-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
    1291:       PetscCall(MatGetInfo(aij->B, MAT_LOCAL, &info));
    1292:       PetscCall(PetscViewerASCIISynchronizedPrintf(viewer, "[%d] off-diagonal part: nz %" PetscInt_FMT " \n", rank, (PetscInt)info.nz_used));
    1293:       PetscCall(PetscViewerFlush(viewer));
    1294:       PetscCall(PetscViewerASCIIPopSynchronized(viewer));
    1295:       PetscCall(PetscViewerASCIIPrintf(viewer, "Information on VecScatter used in matrix-vector product: \n"));
    1296:       PetscCall(VecScatterView(aij->Mvctx, viewer));
    1297:       PetscFunctionReturn(PETSC_SUCCESS);
    1298:     } else if (format == PETSC_VIEWER_ASCII_INFO) {
    1299:       PetscInt inodecount, inodelimit, *inodes;
    1300:       PetscCall(MatInodeGetInodeSizes(aij->A, &inodecount, &inodes, &inodelimit));
    1301:       if (inodes) {
    1302:         PetscCall(PetscViewerASCIIPrintf(viewer, "using I-node (on process 0) routines: found %" PetscInt_FMT " nodes, limit used is %" PetscInt_FMT "\n", inodecount, inodelimit));
    1303:       } else {
    1304:         PetscCall(PetscViewerASCIIPrintf(viewer, "not using I-node (on process 0) routines\n"));
    1305:       }
    1306:       PetscFunctionReturn(PETSC_SUCCESS);
    1307:     } else if (format == PETSC_VIEWER_ASCII_FACTOR_INFO) {
    1308:       PetscFunctionReturn(PETSC_SUCCESS);
    1309:     }
    1310:   } else if (isbinary) {
    1311:     if (size == 1) {
    1312:       PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
    1313:       PetscCall(MatView(aij->A, viewer));
    1314:     } else {
    1315:       PetscCall(MatView_MPIAIJ_Binary(mat, viewer));
    1316:     }
    1317:     PetscFunctionReturn(PETSC_SUCCESS);
    1318:   } else if (iascii && size == 1) {
    1319:     PetscCall(PetscObjectSetName((PetscObject)aij->A, ((PetscObject)mat)->name));
    1320:     PetscCall(MatView(aij->A, viewer));
    1321:     PetscFunctionReturn(PETSC_SUCCESS);
    1322:   } else if (isdraw) {
    1323:     PetscDraw draw;
    1324:     PetscBool isnull;
    1325:     PetscCall(PetscViewerDrawGetDraw(viewer, 0, &draw));
    1326:     PetscCall(PetscDrawIsNull(draw, &isnull));
    1327:     if (isnull) PetscFunctionReturn(PETSC_SUCCESS);
    1328:   }

    1330:   { /* assemble the entire matrix onto first processor */
    1331:     Mat A = NULL, Av;
    1332:     IS  isrow, iscol;

    1334:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->rmap->N : 0, 0, 1, &isrow));
    1335:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat), rank == 0 ? mat->cmap->N : 0, 0, 1, &iscol));
    1336:     PetscCall(MatCreateSubMatrix(mat, isrow, iscol, MAT_INITIAL_MATRIX, &A));
    1337:     PetscCall(MatMPIAIJGetSeqAIJ(A, &Av, NULL, NULL));
    1338:     /*  The commented code uses MatCreateSubMatrices instead */
    1339:     /*
    1340:     Mat *AA, A = NULL, Av;
    1341:     IS  isrow,iscol;

    1343:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->rmap->N : 0,0,1,&isrow));
    1344:     PetscCall(ISCreateStride(PetscObjectComm((PetscObject)mat),rank == 0 ? mat->cmap->N : 0,0,1,&iscol));
    1345:     PetscCall(MatCreateSubMatrices(mat,1,&isrow,&iscol,MAT_INITIAL_MATRIX,&AA));
    1346:     if (rank == 0) {
    1347:        PetscCall(PetscObjectReference((PetscObject)AA[0]));
    1348:        A    = AA[0];
    1349:        Av   = AA[0];
    1350:     }
    1351:     PetscCall(MatDestroySubMatrices(1,&AA));
    1352: */
    1353:     PetscCall(ISDestroy(&iscol));
    1354:     PetscCall(ISDestroy(&isrow));
    1355:     /*
    1356:        Everyone has to call to draw the matrix since the graphics waits are
    1357:        synchronized across all processors that share the PetscDraw object
    1358:     */
    1359:     PetscCall(PetscViewerGetSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    1360:     if (rank == 0) {
    1361:       if (((PetscObject)mat)->name) PetscCall(PetscObjectSetName((PetscObject)Av, ((PetscObject)mat)->name));
    1362:       PetscCall(MatView_SeqAIJ(Av, sviewer));
    1363:     }
    1364:     PetscCall(PetscViewerRestoreSubViewer(viewer, PETSC_COMM_SELF, &sviewer));
    1365:     PetscCall(MatDestroy(&A));
    1366:   }
    1367:   PetscFunctionReturn(PETSC_SUCCESS);
    1368: }

    1370: PetscErrorCode MatView_MPIAIJ(Mat mat, PetscViewer viewer)
    1371: {
    1372:   PetscBool iascii, isdraw, issocket, isbinary;

    1374:   PetscFunctionBegin;
    1375:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
    1376:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERDRAW, &isdraw));
    1377:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    1378:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERSOCKET, &issocket));
    1379:   if (iascii || isdraw || isbinary || issocket) PetscCall(MatView_MPIAIJ_ASCIIorDraworSocket(mat, viewer));
    1380:   PetscFunctionReturn(PETSC_SUCCESS);
    1381: }

    1383: static PetscErrorCode MatSOR_MPIAIJ(Mat matin, Vec bb, PetscReal omega, MatSORType flag, PetscReal fshift, PetscInt its, PetscInt lits, Vec xx)
    1384: {
    1385:   Mat_MPIAIJ *mat = (Mat_MPIAIJ *)matin->data;
    1386:   Vec         bb1 = NULL;
    1387:   PetscBool   hasop;

    1389:   PetscFunctionBegin;
    1390:   if (flag == SOR_APPLY_UPPER) {
    1391:     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1392:     PetscFunctionReturn(PETSC_SUCCESS);
    1393:   }

    1395:   if (its > 1 || ~flag & SOR_ZERO_INITIAL_GUESS || flag & SOR_EISENSTAT) PetscCall(VecDuplicate(bb, &bb1));

    1397:   if ((flag & SOR_LOCAL_SYMMETRIC_SWEEP) == SOR_LOCAL_SYMMETRIC_SWEEP) {
    1398:     if (flag & SOR_ZERO_INITIAL_GUESS) {
    1399:       PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, flag, fshift, lits, 1, xx));
    1400:       its--;
    1401:     }

    1403:     while (its--) {
    1404:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1405:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

    1407:       /* update rhs: bb1 = bb - B*x */
    1408:       PetscCall(VecScale(mat->lvec, -1.0));
    1409:       PetscCall((*mat->B->ops->multadd)(mat->B, mat->lvec, bb, bb1));

    1411:       /* local sweep */
    1412:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_SYMMETRIC_SWEEP, fshift, lits, 1, xx));
    1413:     }
    1414:   } else if (flag & SOR_LOCAL_FORWARD_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:     }
    1419:     while (its--) {
    1420:       PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1421:       PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));

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

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

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

    1443:       /* local sweep */
    1444:       PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, SOR_BACKWARD_SWEEP, fshift, lits, 1, xx));
    1445:     }
    1446:   } else if (flag & SOR_EISENSTAT) {
    1447:     Vec xx1;

    1449:     PetscCall(VecDuplicate(bb, &xx1));
    1450:     PetscCall((*mat->A->ops->sor)(mat->A, bb, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_BACKWARD_SWEEP), fshift, lits, 1, xx));

    1452:     PetscCall(VecScatterBegin(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1453:     PetscCall(VecScatterEnd(mat->Mvctx, xx, mat->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1454:     if (!mat->diag) {
    1455:       PetscCall(MatCreateVecs(matin, &mat->diag, NULL));
    1456:       PetscCall(MatGetDiagonal(matin, mat->diag));
    1457:     }
    1458:     PetscCall(MatHasOperation(matin, MATOP_MULT_DIAGONAL_BLOCK, &hasop));
    1459:     if (hasop) {
    1460:       PetscCall(MatMultDiagonalBlock(matin, xx, bb1));
    1461:     } else {
    1462:       PetscCall(VecPointwiseMult(bb1, mat->diag, xx));
    1463:     }
    1464:     PetscCall(VecAYPX(bb1, (omega - 2.0) / omega, bb));

    1466:     PetscCall(MatMultAdd(mat->B, mat->lvec, bb1, bb1));

    1468:     /* local sweep */
    1469:     PetscCall((*mat->A->ops->sor)(mat->A, bb1, omega, (MatSORType)(SOR_ZERO_INITIAL_GUESS | SOR_LOCAL_FORWARD_SWEEP), fshift, lits, 1, xx1));
    1470:     PetscCall(VecAXPY(xx, 1.0, xx1));
    1471:     PetscCall(VecDestroy(&xx1));
    1472:   } else SETERRQ(PetscObjectComm((PetscObject)matin), PETSC_ERR_SUP, "Parallel SOR not supported");

    1474:   PetscCall(VecDestroy(&bb1));

    1476:   matin->factorerrortype = mat->A->factorerrortype;
    1477:   PetscFunctionReturn(PETSC_SUCCESS);
    1478: }

    1480: static PetscErrorCode MatPermute_MPIAIJ(Mat A, IS rowp, IS colp, Mat *B)
    1481: {
    1482:   Mat             aA, aB, Aperm;
    1483:   const PetscInt *rwant, *cwant, *gcols, *ai, *bi, *aj, *bj;
    1484:   PetscScalar    *aa, *ba;
    1485:   PetscInt        i, j, m, n, ng, anz, bnz, *dnnz, *onnz, *tdnnz, *tonnz, *rdest, *cdest, *work, *gcdest;
    1486:   PetscSF         rowsf, sf;
    1487:   IS              parcolp = NULL;
    1488:   PetscBool       done;

    1490:   PetscFunctionBegin;
    1491:   PetscCall(MatGetLocalSize(A, &m, &n));
    1492:   PetscCall(ISGetIndices(rowp, &rwant));
    1493:   PetscCall(ISGetIndices(colp, &cwant));
    1494:   PetscCall(PetscMalloc3(PetscMax(m, n), &work, m, &rdest, n, &cdest));

    1496:   /* Invert row permutation to find out where my rows should go */
    1497:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &rowsf));
    1498:   PetscCall(PetscSFSetGraphLayout(rowsf, A->rmap, A->rmap->n, NULL, PETSC_OWN_POINTER, rwant));
    1499:   PetscCall(PetscSFSetFromOptions(rowsf));
    1500:   for (i = 0; i < m; i++) work[i] = A->rmap->rstart + i;
    1501:   PetscCall(PetscSFReduceBegin(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));
    1502:   PetscCall(PetscSFReduceEnd(rowsf, MPIU_INT, work, rdest, MPI_REPLACE));

    1504:   /* Invert column permutation to find out where my columns should go */
    1505:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1506:   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, A->cmap->n, NULL, PETSC_OWN_POINTER, cwant));
    1507:   PetscCall(PetscSFSetFromOptions(sf));
    1508:   for (i = 0; i < n; i++) work[i] = A->cmap->rstart + i;
    1509:   PetscCall(PetscSFReduceBegin(sf, MPIU_INT, work, cdest, MPI_REPLACE));
    1510:   PetscCall(PetscSFReduceEnd(sf, MPIU_INT, work, cdest, MPI_REPLACE));
    1511:   PetscCall(PetscSFDestroy(&sf));

    1513:   PetscCall(ISRestoreIndices(rowp, &rwant));
    1514:   PetscCall(ISRestoreIndices(colp, &cwant));
    1515:   PetscCall(MatMPIAIJGetSeqAIJ(A, &aA, &aB, &gcols));

    1517:   /* Find out where my gcols should go */
    1518:   PetscCall(MatGetSize(aB, NULL, &ng));
    1519:   PetscCall(PetscMalloc1(ng, &gcdest));
    1520:   PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1521:   PetscCall(PetscSFSetGraphLayout(sf, A->cmap, ng, NULL, PETSC_OWN_POINTER, gcols));
    1522:   PetscCall(PetscSFSetFromOptions(sf));
    1523:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
    1524:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, cdest, gcdest, MPI_REPLACE));
    1525:   PetscCall(PetscSFDestroy(&sf));

    1527:   PetscCall(PetscCalloc4(m, &dnnz, m, &onnz, m, &tdnnz, m, &tonnz));
    1528:   PetscCall(MatGetRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
    1529:   PetscCall(MatGetRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
    1530:   for (i = 0; i < m; i++) {
    1531:     PetscInt    row = rdest[i];
    1532:     PetscMPIInt rowner;
    1533:     PetscCall(PetscLayoutFindOwner(A->rmap, row, &rowner));
    1534:     for (j = ai[i]; j < ai[i + 1]; j++) {
    1535:       PetscInt    col = cdest[aj[j]];
    1536:       PetscMPIInt cowner;
    1537:       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner)); /* Could build an index for the columns to eliminate this search */
    1538:       if (rowner == cowner) dnnz[i]++;
    1539:       else onnz[i]++;
    1540:     }
    1541:     for (j = bi[i]; j < bi[i + 1]; j++) {
    1542:       PetscInt    col = gcdest[bj[j]];
    1543:       PetscMPIInt cowner;
    1544:       PetscCall(PetscLayoutFindOwner(A->cmap, col, &cowner));
    1545:       if (rowner == cowner) dnnz[i]++;
    1546:       else onnz[i]++;
    1547:     }
    1548:   }
    1549:   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
    1550:   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, dnnz, tdnnz, MPI_REPLACE));
    1551:   PetscCall(PetscSFBcastBegin(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
    1552:   PetscCall(PetscSFBcastEnd(rowsf, MPIU_INT, onnz, tonnz, MPI_REPLACE));
    1553:   PetscCall(PetscSFDestroy(&rowsf));

    1555:   PetscCall(MatCreateAIJ(PetscObjectComm((PetscObject)A), A->rmap->n, A->cmap->n, A->rmap->N, A->cmap->N, 0, tdnnz, 0, tonnz, &Aperm));
    1556:   PetscCall(MatSeqAIJGetArray(aA, &aa));
    1557:   PetscCall(MatSeqAIJGetArray(aB, &ba));
    1558:   for (i = 0; i < m; i++) {
    1559:     PetscInt *acols = dnnz, *bcols = onnz; /* Repurpose now-unneeded arrays */
    1560:     PetscInt  j0, rowlen;
    1561:     rowlen = ai[i + 1] - ai[i];
    1562:     for (j0 = j = 0; j < rowlen; j0 = j) { /* rowlen could be larger than number of rows m, so sum in batches */
    1563:       for (; j < PetscMin(rowlen, j0 + m); j++) acols[j - j0] = cdest[aj[ai[i] + j]];
    1564:       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, acols, aa + ai[i] + j0, INSERT_VALUES));
    1565:     }
    1566:     rowlen = bi[i + 1] - bi[i];
    1567:     for (j0 = j = 0; j < rowlen; j0 = j) {
    1568:       for (; j < PetscMin(rowlen, j0 + m); j++) bcols[j - j0] = gcdest[bj[bi[i] + j]];
    1569:       PetscCall(MatSetValues(Aperm, 1, &rdest[i], j - j0, bcols, ba + bi[i] + j0, INSERT_VALUES));
    1570:     }
    1571:   }
    1572:   PetscCall(MatAssemblyBegin(Aperm, MAT_FINAL_ASSEMBLY));
    1573:   PetscCall(MatAssemblyEnd(Aperm, MAT_FINAL_ASSEMBLY));
    1574:   PetscCall(MatRestoreRowIJ(aA, 0, PETSC_FALSE, PETSC_FALSE, &anz, &ai, &aj, &done));
    1575:   PetscCall(MatRestoreRowIJ(aB, 0, PETSC_FALSE, PETSC_FALSE, &bnz, &bi, &bj, &done));
    1576:   PetscCall(MatSeqAIJRestoreArray(aA, &aa));
    1577:   PetscCall(MatSeqAIJRestoreArray(aB, &ba));
    1578:   PetscCall(PetscFree4(dnnz, onnz, tdnnz, tonnz));
    1579:   PetscCall(PetscFree3(work, rdest, cdest));
    1580:   PetscCall(PetscFree(gcdest));
    1581:   if (parcolp) PetscCall(ISDestroy(&colp));
    1582:   *B = Aperm;
    1583:   PetscFunctionReturn(PETSC_SUCCESS);
    1584: }

    1586: static PetscErrorCode MatGetGhosts_MPIAIJ(Mat mat, PetscInt *nghosts, const PetscInt *ghosts[])
    1587: {
    1588:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    1590:   PetscFunctionBegin;
    1591:   PetscCall(MatGetSize(aij->B, NULL, nghosts));
    1592:   if (ghosts) *ghosts = aij->garray;
    1593:   PetscFunctionReturn(PETSC_SUCCESS);
    1594: }

    1596: static PetscErrorCode MatGetInfo_MPIAIJ(Mat matin, MatInfoType flag, MatInfo *info)
    1597: {
    1598:   Mat_MPIAIJ    *mat = (Mat_MPIAIJ *)matin->data;
    1599:   Mat            A = mat->A, B = mat->B;
    1600:   PetscLogDouble isend[5], irecv[5];

    1602:   PetscFunctionBegin;
    1603:   info->block_size = 1.0;
    1604:   PetscCall(MatGetInfo(A, MAT_LOCAL, info));

    1606:   isend[0] = info->nz_used;
    1607:   isend[1] = info->nz_allocated;
    1608:   isend[2] = info->nz_unneeded;
    1609:   isend[3] = info->memory;
    1610:   isend[4] = info->mallocs;

    1612:   PetscCall(MatGetInfo(B, MAT_LOCAL, info));

    1614:   isend[0] += info->nz_used;
    1615:   isend[1] += info->nz_allocated;
    1616:   isend[2] += info->nz_unneeded;
    1617:   isend[3] += info->memory;
    1618:   isend[4] += info->mallocs;
    1619:   if (flag == MAT_LOCAL) {
    1620:     info->nz_used      = isend[0];
    1621:     info->nz_allocated = isend[1];
    1622:     info->nz_unneeded  = isend[2];
    1623:     info->memory       = isend[3];
    1624:     info->mallocs      = isend[4];
    1625:   } else if (flag == MAT_GLOBAL_MAX) {
    1626:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_MAX, PetscObjectComm((PetscObject)matin)));

    1628:     info->nz_used      = irecv[0];
    1629:     info->nz_allocated = irecv[1];
    1630:     info->nz_unneeded  = irecv[2];
    1631:     info->memory       = irecv[3];
    1632:     info->mallocs      = irecv[4];
    1633:   } else if (flag == MAT_GLOBAL_SUM) {
    1634:     PetscCallMPI(MPIU_Allreduce(isend, irecv, 5, MPIU_PETSCLOGDOUBLE, MPI_SUM, PetscObjectComm((PetscObject)matin)));

    1636:     info->nz_used      = irecv[0];
    1637:     info->nz_allocated = irecv[1];
    1638:     info->nz_unneeded  = irecv[2];
    1639:     info->memory       = irecv[3];
    1640:     info->mallocs      = irecv[4];
    1641:   }
    1642:   info->fill_ratio_given  = 0; /* no parallel LU/ILU/Cholesky */
    1643:   info->fill_ratio_needed = 0;
    1644:   info->factor_mallocs    = 0;
    1645:   PetscFunctionReturn(PETSC_SUCCESS);
    1646: }

    1648: PetscErrorCode MatSetOption_MPIAIJ(Mat A, MatOption op, PetscBool flg)
    1649: {
    1650:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    1652:   PetscFunctionBegin;
    1653:   switch (op) {
    1654:   case MAT_NEW_NONZERO_LOCATIONS:
    1655:   case MAT_NEW_NONZERO_ALLOCATION_ERR:
    1656:   case MAT_UNUSED_NONZERO_LOCATION_ERR:
    1657:   case MAT_KEEP_NONZERO_PATTERN:
    1658:   case MAT_NEW_NONZERO_LOCATION_ERR:
    1659:   case MAT_USE_INODES:
    1660:   case MAT_IGNORE_ZERO_ENTRIES:
    1661:   case MAT_FORM_EXPLICIT_TRANSPOSE:
    1662:     MatCheckPreallocated(A, 1);
    1663:     PetscCall(MatSetOption(a->A, op, flg));
    1664:     PetscCall(MatSetOption(a->B, op, flg));
    1665:     break;
    1666:   case MAT_ROW_ORIENTED:
    1667:     MatCheckPreallocated(A, 1);
    1668:     a->roworiented = flg;

    1670:     PetscCall(MatSetOption(a->A, op, flg));
    1671:     PetscCall(MatSetOption(a->B, op, flg));
    1672:     break;
    1673:   case MAT_FORCE_DIAGONAL_ENTRIES:
    1674:   case MAT_SORTED_FULL:
    1675:     PetscCall(PetscInfo(A, "Option %s ignored\n", MatOptions[op]));
    1676:     break;
    1677:   case MAT_IGNORE_OFF_PROC_ENTRIES:
    1678:     a->donotstash = flg;
    1679:     break;
    1680:   /* Symmetry flags are handled directly by MatSetOption() and they don't affect preallocation */
    1681:   case MAT_SPD:
    1682:   case MAT_SYMMETRIC:
    1683:   case MAT_STRUCTURALLY_SYMMETRIC:
    1684:   case MAT_HERMITIAN:
    1685:   case MAT_SYMMETRY_ETERNAL:
    1686:   case MAT_STRUCTURAL_SYMMETRY_ETERNAL:
    1687:   case MAT_SPD_ETERNAL:
    1688:     /* if the diagonal matrix is square it inherits some of the properties above */
    1689:     if (a->A && A->rmap->n == A->cmap->n) PetscCall(MatSetOption(a->A, op, flg));
    1690:     break;
    1691:   case MAT_SUBMAT_SINGLEIS:
    1692:     A->submat_singleis = flg;
    1693:     break;
    1694:   case MAT_STRUCTURE_ONLY:
    1695:     /* The option is handled directly by MatSetOption() */
    1696:     break;
    1697:   default:
    1698:     SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "unknown option %d", op);
    1699:   }
    1700:   PetscFunctionReturn(PETSC_SUCCESS);
    1701: }

    1703: PetscErrorCode MatGetRow_MPIAIJ(Mat matin, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    1704: {
    1705:   Mat_MPIAIJ  *mat = (Mat_MPIAIJ *)matin->data;
    1706:   PetscScalar *vworkA, *vworkB, **pvA, **pvB, *v_p;
    1707:   PetscInt     i, *cworkA, *cworkB, **pcA, **pcB, cstart = matin->cmap->rstart;
    1708:   PetscInt     nztot, nzA, nzB, lrow, rstart = matin->rmap->rstart, rend = matin->rmap->rend;
    1709:   PetscInt    *cmap, *idx_p;

    1711:   PetscFunctionBegin;
    1712:   PetscCheck(!mat->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Already active");
    1713:   mat->getrowactive = PETSC_TRUE;

    1715:   if (!mat->rowvalues && (idx || v)) {
    1716:     /*
    1717:         allocate enough space to hold information from the longest row.
    1718:     */
    1719:     Mat_SeqAIJ *Aa = (Mat_SeqAIJ *)mat->A->data, *Ba = (Mat_SeqAIJ *)mat->B->data;
    1720:     PetscInt    max = 1, tmp;
    1721:     for (i = 0; i < matin->rmap->n; i++) {
    1722:       tmp = Aa->i[i + 1] - Aa->i[i] + Ba->i[i + 1] - Ba->i[i];
    1723:       if (max < tmp) max = tmp;
    1724:     }
    1725:     PetscCall(PetscMalloc2(max, &mat->rowvalues, max, &mat->rowindices));
    1726:   }

    1728:   PetscCheck(row >= rstart && row < rend, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Only local rows");
    1729:   lrow = row - rstart;

    1731:   pvA = &vworkA;
    1732:   pcA = &cworkA;
    1733:   pvB = &vworkB;
    1734:   pcB = &cworkB;
    1735:   if (!v) {
    1736:     pvA = NULL;
    1737:     pvB = NULL;
    1738:   }
    1739:   if (!idx) {
    1740:     pcA = NULL;
    1741:     if (!v) pcB = NULL;
    1742:   }
    1743:   PetscCall((*mat->A->ops->getrow)(mat->A, lrow, &nzA, pcA, pvA));
    1744:   PetscCall((*mat->B->ops->getrow)(mat->B, lrow, &nzB, pcB, pvB));
    1745:   nztot = nzA + nzB;

    1747:   cmap = mat->garray;
    1748:   if (v || idx) {
    1749:     if (nztot) {
    1750:       /* Sort by increasing column numbers, assuming A and B already sorted */
    1751:       PetscInt imark = -1;
    1752:       if (v) {
    1753:         *v = v_p = mat->rowvalues;
    1754:         for (i = 0; i < nzB; i++) {
    1755:           if (cmap[cworkB[i]] < cstart) v_p[i] = vworkB[i];
    1756:           else break;
    1757:         }
    1758:         imark = i;
    1759:         for (i = 0; i < nzA; i++) v_p[imark + i] = vworkA[i];
    1760:         for (i = imark; i < nzB; i++) v_p[nzA + i] = vworkB[i];
    1761:       }
    1762:       if (idx) {
    1763:         *idx = idx_p = mat->rowindices;
    1764:         if (imark > -1) {
    1765:           for (i = 0; i < imark; i++) idx_p[i] = cmap[cworkB[i]];
    1766:         } else {
    1767:           for (i = 0; i < nzB; i++) {
    1768:             if (cmap[cworkB[i]] < cstart) idx_p[i] = cmap[cworkB[i]];
    1769:             else break;
    1770:           }
    1771:           imark = i;
    1772:         }
    1773:         for (i = 0; i < nzA; i++) idx_p[imark + i] = cstart + cworkA[i];
    1774:         for (i = imark; i < nzB; i++) idx_p[nzA + i] = cmap[cworkB[i]];
    1775:       }
    1776:     } else {
    1777:       if (idx) *idx = NULL;
    1778:       if (v) *v = NULL;
    1779:     }
    1780:   }
    1781:   *nz = nztot;
    1782:   PetscCall((*mat->A->ops->restorerow)(mat->A, lrow, &nzA, pcA, pvA));
    1783:   PetscCall((*mat->B->ops->restorerow)(mat->B, lrow, &nzB, pcB, pvB));
    1784:   PetscFunctionReturn(PETSC_SUCCESS);
    1785: }

    1787: PetscErrorCode MatRestoreRow_MPIAIJ(Mat mat, PetscInt row, PetscInt *nz, PetscInt **idx, PetscScalar **v)
    1788: {
    1789:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    1791:   PetscFunctionBegin;
    1792:   PetscCheck(aij->getrowactive, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "MatGetRow() must be called first");
    1793:   aij->getrowactive = PETSC_FALSE;
    1794:   PetscFunctionReturn(PETSC_SUCCESS);
    1795: }

    1797: static PetscErrorCode MatNorm_MPIAIJ(Mat mat, NormType type, PetscReal *norm)
    1798: {
    1799:   Mat_MPIAIJ      *aij  = (Mat_MPIAIJ *)mat->data;
    1800:   Mat_SeqAIJ      *amat = (Mat_SeqAIJ *)aij->A->data, *bmat = (Mat_SeqAIJ *)aij->B->data;
    1801:   PetscInt         i, j, cstart = mat->cmap->rstart;
    1802:   PetscReal        sum = 0.0;
    1803:   const MatScalar *v, *amata, *bmata;
    1804:   PetscMPIInt      iN;

    1806:   PetscFunctionBegin;
    1807:   if (aij->size == 1) {
    1808:     PetscCall(MatNorm(aij->A, type, norm));
    1809:   } else {
    1810:     PetscCall(MatSeqAIJGetArrayRead(aij->A, &amata));
    1811:     PetscCall(MatSeqAIJGetArrayRead(aij->B, &bmata));
    1812:     if (type == NORM_FROBENIUS) {
    1813:       v = amata;
    1814:       for (i = 0; i < amat->nz; i++) {
    1815:         sum += PetscRealPart(PetscConj(*v) * (*v));
    1816:         v++;
    1817:       }
    1818:       v = bmata;
    1819:       for (i = 0; i < bmat->nz; i++) {
    1820:         sum += PetscRealPart(PetscConj(*v) * (*v));
    1821:         v++;
    1822:       }
    1823:       PetscCallMPI(MPIU_Allreduce(&sum, norm, 1, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
    1824:       *norm = PetscSqrtReal(*norm);
    1825:       PetscCall(PetscLogFlops(2.0 * amat->nz + 2.0 * bmat->nz));
    1826:     } else if (type == NORM_1) { /* max column norm */
    1827:       PetscReal *tmp, *tmp2;
    1828:       PetscInt  *jj, *garray = aij->garray;
    1829:       PetscCall(PetscCalloc1(mat->cmap->N + 1, &tmp));
    1830:       PetscCall(PetscMalloc1(mat->cmap->N + 1, &tmp2));
    1831:       *norm = 0.0;
    1832:       v     = amata;
    1833:       jj    = amat->j;
    1834:       for (j = 0; j < amat->nz; j++) {
    1835:         tmp[cstart + *jj++] += PetscAbsScalar(*v);
    1836:         v++;
    1837:       }
    1838:       v  = bmata;
    1839:       jj = bmat->j;
    1840:       for (j = 0; j < bmat->nz; j++) {
    1841:         tmp[garray[*jj++]] += PetscAbsScalar(*v);
    1842:         v++;
    1843:       }
    1844:       PetscCall(PetscMPIIntCast(mat->cmap->N, &iN));
    1845:       PetscCallMPI(MPIU_Allreduce(tmp, tmp2, iN, MPIU_REAL, MPIU_SUM, PetscObjectComm((PetscObject)mat)));
    1846:       for (j = 0; j < mat->cmap->N; j++) {
    1847:         if (tmp2[j] > *norm) *norm = tmp2[j];
    1848:       }
    1849:       PetscCall(PetscFree(tmp));
    1850:       PetscCall(PetscFree(tmp2));
    1851:       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
    1852:     } else if (type == NORM_INFINITY) { /* max row norm */
    1853:       PetscReal ntemp = 0.0;
    1854:       for (j = 0; j < aij->A->rmap->n; j++) {
    1855:         v   = PetscSafePointerPlusOffset(amata, amat->i[j]);
    1856:         sum = 0.0;
    1857:         for (i = 0; i < amat->i[j + 1] - amat->i[j]; i++) {
    1858:           sum += PetscAbsScalar(*v);
    1859:           v++;
    1860:         }
    1861:         v = PetscSafePointerPlusOffset(bmata, bmat->i[j]);
    1862:         for (i = 0; i < bmat->i[j + 1] - bmat->i[j]; i++) {
    1863:           sum += PetscAbsScalar(*v);
    1864:           v++;
    1865:         }
    1866:         if (sum > ntemp) ntemp = sum;
    1867:       }
    1868:       PetscCallMPI(MPIU_Allreduce(&ntemp, norm, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)mat)));
    1869:       PetscCall(PetscLogFlops(PetscMax(amat->nz + bmat->nz - 1, 0)));
    1870:     } else SETERRQ(PetscObjectComm((PetscObject)mat), PETSC_ERR_SUP, "No support for two norm");
    1871:     PetscCall(MatSeqAIJRestoreArrayRead(aij->A, &amata));
    1872:     PetscCall(MatSeqAIJRestoreArrayRead(aij->B, &bmata));
    1873:   }
    1874:   PetscFunctionReturn(PETSC_SUCCESS);
    1875: }

    1877: static PetscErrorCode MatTranspose_MPIAIJ(Mat A, MatReuse reuse, Mat *matout)
    1878: {
    1879:   Mat_MPIAIJ      *a    = (Mat_MPIAIJ *)A->data, *b;
    1880:   Mat_SeqAIJ      *Aloc = (Mat_SeqAIJ *)a->A->data, *Bloc = (Mat_SeqAIJ *)a->B->data, *sub_B_diag;
    1881:   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;
    1882:   const PetscInt  *ai, *aj, *bi, *bj, *B_diag_i;
    1883:   Mat              B, A_diag, *B_diag;
    1884:   const MatScalar *pbv, *bv;

    1886:   PetscFunctionBegin;
    1887:   if (reuse == MAT_REUSE_MATRIX) PetscCall(MatTransposeCheckNonzeroState_Private(A, *matout));
    1888:   ma = A->rmap->n;
    1889:   na = A->cmap->n;
    1890:   mb = a->B->rmap->n;
    1891:   nb = a->B->cmap->n;
    1892:   ai = Aloc->i;
    1893:   aj = Aloc->j;
    1894:   bi = Bloc->i;
    1895:   bj = Bloc->j;
    1896:   if (reuse == MAT_INITIAL_MATRIX || *matout == A) {
    1897:     PetscInt            *d_nnz, *g_nnz, *o_nnz;
    1898:     PetscSFNode         *oloc;
    1899:     PETSC_UNUSED PetscSF sf;

    1901:     PetscCall(PetscMalloc4(na, &d_nnz, na, &o_nnz, nb, &g_nnz, nb, &oloc));
    1902:     /* compute d_nnz for preallocation */
    1903:     PetscCall(PetscArrayzero(d_nnz, na));
    1904:     for (i = 0; i < ai[ma]; i++) d_nnz[aj[i]]++;
    1905:     /* compute local off-diagonal contributions */
    1906:     PetscCall(PetscArrayzero(g_nnz, nb));
    1907:     for (i = 0; i < bi[ma]; i++) g_nnz[bj[i]]++;
    1908:     /* map those to global */
    1909:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)A), &sf));
    1910:     PetscCall(PetscSFSetGraphLayout(sf, A->cmap, nb, NULL, PETSC_USE_POINTER, a->garray));
    1911:     PetscCall(PetscSFSetFromOptions(sf));
    1912:     PetscCall(PetscArrayzero(o_nnz, na));
    1913:     PetscCall(PetscSFReduceBegin(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
    1914:     PetscCall(PetscSFReduceEnd(sf, MPIU_INT, g_nnz, o_nnz, MPI_SUM));
    1915:     PetscCall(PetscSFDestroy(&sf));

    1917:     PetscCall(MatCreate(PetscObjectComm((PetscObject)A), &B));
    1918:     PetscCall(MatSetSizes(B, A->cmap->n, A->rmap->n, N, M));
    1919:     PetscCall(MatSetBlockSizes(B, PetscAbs(A->cmap->bs), PetscAbs(A->rmap->bs)));
    1920:     PetscCall(MatSetType(B, ((PetscObject)A)->type_name));
    1921:     PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
    1922:     PetscCall(PetscFree4(d_nnz, o_nnz, g_nnz, oloc));
    1923:   } else {
    1924:     B = *matout;
    1925:     PetscCall(MatSetOption(B, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_TRUE));
    1926:   }

    1928:   b           = (Mat_MPIAIJ *)B->data;
    1929:   A_diag      = a->A;
    1930:   B_diag      = &b->A;
    1931:   sub_B_diag  = (Mat_SeqAIJ *)(*B_diag)->data;
    1932:   A_diag_ncol = A_diag->cmap->N;
    1933:   B_diag_ilen = sub_B_diag->ilen;
    1934:   B_diag_i    = sub_B_diag->i;

    1936:   /* Set ilen for diagonal of B */
    1937:   for (i = 0; i < A_diag_ncol; i++) B_diag_ilen[i] = B_diag_i[i + 1] - B_diag_i[i];

    1939:   /* Transpose the diagonal part of the matrix. In contrast to the off-diagonal part, this can be done
    1940:   very quickly (=without using MatSetValues), because all writes are local. */
    1941:   PetscCall(MatTransposeSetPrecursor(A_diag, *B_diag));
    1942:   PetscCall(MatTranspose(A_diag, MAT_REUSE_MATRIX, B_diag));

    1944:   /* copy over the B part */
    1945:   PetscCall(PetscMalloc1(bi[mb], &cols));
    1946:   PetscCall(MatSeqAIJGetArrayRead(a->B, &bv));
    1947:   pbv = bv;
    1948:   row = A->rmap->rstart;
    1949:   for (i = 0; i < bi[mb]; i++) cols[i] = a->garray[bj[i]];
    1950:   cols_tmp = cols;
    1951:   for (i = 0; i < mb; i++) {
    1952:     ncol = bi[i + 1] - bi[i];
    1953:     PetscCall(MatSetValues(B, ncol, cols_tmp, 1, &row, pbv, INSERT_VALUES));
    1954:     row++;
    1955:     if (pbv) pbv += ncol;
    1956:     if (cols_tmp) cols_tmp += ncol;
    1957:   }
    1958:   PetscCall(PetscFree(cols));
    1959:   PetscCall(MatSeqAIJRestoreArrayRead(a->B, &bv));

    1961:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    1962:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    1963:   if (reuse == MAT_INITIAL_MATRIX || reuse == MAT_REUSE_MATRIX) {
    1964:     *matout = B;
    1965:   } else {
    1966:     PetscCall(MatHeaderMerge(A, &B));
    1967:   }
    1968:   PetscFunctionReturn(PETSC_SUCCESS);
    1969: }

    1971: static PetscErrorCode MatDiagonalScale_MPIAIJ(Mat mat, Vec ll, Vec rr)
    1972: {
    1973:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;
    1974:   Mat         a = aij->A, b = aij->B;
    1975:   PetscInt    s1, s2, s3;

    1977:   PetscFunctionBegin;
    1978:   PetscCall(MatGetLocalSize(mat, &s2, &s3));
    1979:   if (rr) {
    1980:     PetscCall(VecGetLocalSize(rr, &s1));
    1981:     PetscCheck(s1 == s3, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "right vector non-conforming local size");
    1982:     /* Overlap communication with computation. */
    1983:     PetscCall(VecScatterBegin(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1984:   }
    1985:   if (ll) {
    1986:     PetscCall(VecGetLocalSize(ll, &s1));
    1987:     PetscCheck(s1 == s2, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "left vector non-conforming local size");
    1988:     PetscUseTypeMethod(b, diagonalscale, ll, NULL);
    1989:   }
    1990:   /* scale  the diagonal block */
    1991:   PetscUseTypeMethod(a, diagonalscale, ll, rr);

    1993:   if (rr) {
    1994:     /* Do a scatter end and then right scale the off-diagonal block */
    1995:     PetscCall(VecScatterEnd(aij->Mvctx, rr, aij->lvec, INSERT_VALUES, SCATTER_FORWARD));
    1996:     PetscUseTypeMethod(b, diagonalscale, NULL, aij->lvec);
    1997:   }
    1998:   PetscFunctionReturn(PETSC_SUCCESS);
    1999: }

    2001: static PetscErrorCode MatSetUnfactored_MPIAIJ(Mat A)
    2002: {
    2003:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2005:   PetscFunctionBegin;
    2006:   PetscCall(MatSetUnfactored(a->A));
    2007:   PetscFunctionReturn(PETSC_SUCCESS);
    2008: }

    2010: static PetscErrorCode MatEqual_MPIAIJ(Mat A, Mat B, PetscBool *flag)
    2011: {
    2012:   Mat_MPIAIJ *matB = (Mat_MPIAIJ *)B->data, *matA = (Mat_MPIAIJ *)A->data;
    2013:   Mat         a, b, c, d;
    2014:   PetscBool   flg;

    2016:   PetscFunctionBegin;
    2017:   a = matA->A;
    2018:   b = matA->B;
    2019:   c = matB->A;
    2020:   d = matB->B;

    2022:   PetscCall(MatEqual(a, c, &flg));
    2023:   if (flg) PetscCall(MatEqual(b, d, &flg));
    2024:   PetscCallMPI(MPIU_Allreduce(&flg, flag, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)A)));
    2025:   PetscFunctionReturn(PETSC_SUCCESS);
    2026: }

    2028: static PetscErrorCode MatCopy_MPIAIJ(Mat A, Mat B, MatStructure str)
    2029: {
    2030:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    2031:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;

    2033:   PetscFunctionBegin;
    2034:   /* If the two matrices don't have the same copy implementation, they aren't compatible for fast copy. */
    2035:   if ((str != SAME_NONZERO_PATTERN) || (A->ops->copy != B->ops->copy)) {
    2036:     /* because of the column compression in the off-processor part of the matrix a->B,
    2037:        the number of columns in a->B and b->B may be different, hence we cannot call
    2038:        the MatCopy() directly on the two parts. If need be, we can provide a more
    2039:        efficient copy than the MatCopy_Basic() by first uncompressing the a->B matrices
    2040:        then copying the submatrices */
    2041:     PetscCall(MatCopy_Basic(A, B, str));
    2042:   } else {
    2043:     PetscCall(MatCopy(a->A, b->A, str));
    2044:     PetscCall(MatCopy(a->B, b->B, str));
    2045:   }
    2046:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    2047:   PetscFunctionReturn(PETSC_SUCCESS);
    2048: }

    2050: /*
    2051:    Computes the number of nonzeros per row needed for preallocation when X and Y
    2052:    have different nonzero structure.
    2053: */
    2054: 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)
    2055: {
    2056:   PetscInt i, j, k, nzx, nzy;

    2058:   PetscFunctionBegin;
    2059:   /* Set the number of nonzeros in the new matrix */
    2060:   for (i = 0; i < m; i++) {
    2061:     const PetscInt *xjj = PetscSafePointerPlusOffset(xj, xi[i]), *yjj = PetscSafePointerPlusOffset(yj, yi[i]);
    2062:     nzx    = xi[i + 1] - xi[i];
    2063:     nzy    = yi[i + 1] - yi[i];
    2064:     nnz[i] = 0;
    2065:     for (j = 0, k = 0; j < nzx; j++) {                                /* Point in X */
    2066:       for (; k < nzy && yltog[yjj[k]] < xltog[xjj[j]]; k++) nnz[i]++; /* Catch up to X */
    2067:       if (k < nzy && yltog[yjj[k]] == xltog[xjj[j]]) k++;             /* Skip duplicate */
    2068:       nnz[i]++;
    2069:     }
    2070:     for (; k < nzy; k++) nnz[i]++;
    2071:   }
    2072:   PetscFunctionReturn(PETSC_SUCCESS);
    2073: }

    2075: /* This is the same as MatAXPYGetPreallocation_SeqAIJ, except that the local-to-global map is provided */
    2076: static PetscErrorCode MatAXPYGetPreallocation_MPIAIJ(Mat Y, const PetscInt *yltog, Mat X, const PetscInt *xltog, PetscInt *nnz)
    2077: {
    2078:   PetscInt    m = Y->rmap->N;
    2079:   Mat_SeqAIJ *x = (Mat_SeqAIJ *)X->data;
    2080:   Mat_SeqAIJ *y = (Mat_SeqAIJ *)Y->data;

    2082:   PetscFunctionBegin;
    2083:   PetscCall(MatAXPYGetPreallocation_MPIX_private(m, x->i, x->j, xltog, y->i, y->j, yltog, nnz));
    2084:   PetscFunctionReturn(PETSC_SUCCESS);
    2085: }

    2087: static PetscErrorCode MatAXPY_MPIAIJ(Mat Y, PetscScalar a, Mat X, MatStructure str)
    2088: {
    2089:   Mat_MPIAIJ *xx = (Mat_MPIAIJ *)X->data, *yy = (Mat_MPIAIJ *)Y->data;

    2091:   PetscFunctionBegin;
    2092:   if (str == SAME_NONZERO_PATTERN) {
    2093:     PetscCall(MatAXPY(yy->A, a, xx->A, str));
    2094:     PetscCall(MatAXPY(yy->B, a, xx->B, str));
    2095:   } else if (str == SUBSET_NONZERO_PATTERN) { /* nonzeros of X is a subset of Y's */
    2096:     PetscCall(MatAXPY_Basic(Y, a, X, str));
    2097:   } else {
    2098:     Mat       B;
    2099:     PetscInt *nnz_d, *nnz_o;

    2101:     PetscCall(PetscMalloc1(yy->A->rmap->N, &nnz_d));
    2102:     PetscCall(PetscMalloc1(yy->B->rmap->N, &nnz_o));
    2103:     PetscCall(MatCreate(PetscObjectComm((PetscObject)Y), &B));
    2104:     PetscCall(PetscObjectSetName((PetscObject)B, ((PetscObject)Y)->name));
    2105:     PetscCall(MatSetLayouts(B, Y->rmap, Y->cmap));
    2106:     PetscCall(MatSetType(B, ((PetscObject)Y)->type_name));
    2107:     PetscCall(MatAXPYGetPreallocation_SeqAIJ(yy->A, xx->A, nnz_d));
    2108:     PetscCall(MatAXPYGetPreallocation_MPIAIJ(yy->B, yy->garray, xx->B, xx->garray, nnz_o));
    2109:     PetscCall(MatMPIAIJSetPreallocation(B, 0, nnz_d, 0, nnz_o));
    2110:     PetscCall(MatAXPY_BasicWithPreallocation(B, Y, a, X, str));
    2111:     PetscCall(MatHeaderMerge(Y, &B));
    2112:     PetscCall(PetscFree(nnz_d));
    2113:     PetscCall(PetscFree(nnz_o));
    2114:   }
    2115:   PetscFunctionReturn(PETSC_SUCCESS);
    2116: }

    2118: PETSC_INTERN PetscErrorCode MatConjugate_SeqAIJ(Mat);

    2120: static PetscErrorCode MatConjugate_MPIAIJ(Mat mat)
    2121: {
    2122:   PetscFunctionBegin;
    2123:   if (PetscDefined(USE_COMPLEX)) {
    2124:     Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2126:     PetscCall(MatConjugate_SeqAIJ(aij->A));
    2127:     PetscCall(MatConjugate_SeqAIJ(aij->B));
    2128:   }
    2129:   PetscFunctionReturn(PETSC_SUCCESS);
    2130: }

    2132: static PetscErrorCode MatRealPart_MPIAIJ(Mat A)
    2133: {
    2134:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2136:   PetscFunctionBegin;
    2137:   PetscCall(MatRealPart(a->A));
    2138:   PetscCall(MatRealPart(a->B));
    2139:   PetscFunctionReturn(PETSC_SUCCESS);
    2140: }

    2142: static PetscErrorCode MatImaginaryPart_MPIAIJ(Mat A)
    2143: {
    2144:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2146:   PetscFunctionBegin;
    2147:   PetscCall(MatImaginaryPart(a->A));
    2148:   PetscCall(MatImaginaryPart(a->B));
    2149:   PetscFunctionReturn(PETSC_SUCCESS);
    2150: }

    2152: static PetscErrorCode MatGetRowMaxAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2153: {
    2154:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
    2155:   PetscInt           i, *idxb = NULL, m = A->rmap->n;
    2156:   PetscScalar       *vv;
    2157:   Vec                vB, vA;
    2158:   const PetscScalar *va, *vb;

    2160:   PetscFunctionBegin;
    2161:   PetscCall(MatCreateVecs(a->A, NULL, &vA));
    2162:   PetscCall(MatGetRowMaxAbs(a->A, vA, idx));

    2164:   PetscCall(VecGetArrayRead(vA, &va));
    2165:   if (idx) {
    2166:     for (i = 0; i < m; i++) {
    2167:       if (PetscAbsScalar(va[i])) idx[i] += A->cmap->rstart;
    2168:     }
    2169:   }

    2171:   PetscCall(MatCreateVecs(a->B, NULL, &vB));
    2172:   PetscCall(PetscMalloc1(m, &idxb));
    2173:   PetscCall(MatGetRowMaxAbs(a->B, vB, idxb));

    2175:   PetscCall(VecGetArrayWrite(v, &vv));
    2176:   PetscCall(VecGetArrayRead(vB, &vb));
    2177:   for (i = 0; i < m; i++) {
    2178:     if (PetscAbsScalar(va[i]) < PetscAbsScalar(vb[i])) {
    2179:       vv[i] = vb[i];
    2180:       if (idx) idx[i] = a->garray[idxb[i]];
    2181:     } else {
    2182:       vv[i] = va[i];
    2183:       if (idx && PetscAbsScalar(va[i]) == PetscAbsScalar(vb[i]) && idxb[i] != -1 && idx[i] > a->garray[idxb[i]]) idx[i] = a->garray[idxb[i]];
    2184:     }
    2185:   }
    2186:   PetscCall(VecRestoreArrayWrite(v, &vv));
    2187:   PetscCall(VecRestoreArrayRead(vA, &va));
    2188:   PetscCall(VecRestoreArrayRead(vB, &vb));
    2189:   PetscCall(PetscFree(idxb));
    2190:   PetscCall(VecDestroy(&vA));
    2191:   PetscCall(VecDestroy(&vB));
    2192:   PetscFunctionReturn(PETSC_SUCCESS);
    2193: }

    2195: static PetscErrorCode MatGetRowSumAbs_MPIAIJ(Mat A, Vec v)
    2196: {
    2197:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    2198:   Vec         vB, vA;

    2200:   PetscFunctionBegin;
    2201:   PetscCall(MatCreateVecs(a->A, NULL, &vA));
    2202:   PetscCall(MatGetRowSumAbs(a->A, vA));
    2203:   PetscCall(MatCreateVecs(a->B, NULL, &vB));
    2204:   PetscCall(MatGetRowSumAbs(a->B, vB));
    2205:   PetscCall(VecAXPY(vA, 1.0, vB));
    2206:   PetscCall(VecDestroy(&vB));
    2207:   PetscCall(VecCopy(vA, v));
    2208:   PetscCall(VecDestroy(&vA));
    2209:   PetscFunctionReturn(PETSC_SUCCESS);
    2210: }

    2212: static PetscErrorCode MatGetRowMinAbs_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2213: {
    2214:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2215:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2216:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2217:   PetscInt          *cmap = mat->garray;
    2218:   PetscInt          *diagIdx, *offdiagIdx;
    2219:   Vec                diagV, offdiagV;
    2220:   PetscScalar       *a, *diagA, *offdiagA;
    2221:   const PetscScalar *ba, *bav;
    2222:   PetscInt           r, j, col, ncols, *bi, *bj;
    2223:   Mat                B = mat->B;
    2224:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2226:   PetscFunctionBegin;
    2227:   /* When a process holds entire A and other processes have no entry */
    2228:   if (A->cmap->N == n) {
    2229:     PetscCall(VecGetArrayWrite(v, &diagA));
    2230:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2231:     PetscCall(MatGetRowMinAbs(mat->A, diagV, idx));
    2232:     PetscCall(VecDestroy(&diagV));
    2233:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2234:     PetscFunctionReturn(PETSC_SUCCESS);
    2235:   } else if (n == 0) {
    2236:     if (m) {
    2237:       PetscCall(VecGetArrayWrite(v, &a));
    2238:       for (r = 0; r < m; r++) {
    2239:         a[r] = 0.0;
    2240:         if (idx) idx[r] = -1;
    2241:       }
    2242:       PetscCall(VecRestoreArrayWrite(v, &a));
    2243:     }
    2244:     PetscFunctionReturn(PETSC_SUCCESS);
    2245:   }

    2247:   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
    2248:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2249:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2250:   PetscCall(MatGetRowMinAbs(mat->A, diagV, diagIdx));

    2252:   /* Get offdiagIdx[] for implicit 0.0 */
    2253:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2254:   ba = bav;
    2255:   bi = b->i;
    2256:   bj = b->j;
    2257:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2258:   for (r = 0; r < m; r++) {
    2259:     ncols = bi[r + 1] - bi[r];
    2260:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2261:       offdiagA[r]   = *ba;
    2262:       offdiagIdx[r] = cmap[0];
    2263:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2264:       offdiagA[r] = 0.0;

    2266:       /* Find first hole in the cmap */
    2267:       for (j = 0; j < ncols; j++) {
    2268:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2269:         if (col > j && j < cstart) {
    2270:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2271:           break;
    2272:         } else if (col > j + n && j >= cstart) {
    2273:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2274:           break;
    2275:         }
    2276:       }
    2277:       if (j == ncols && ncols < A->cmap->N - n) {
    2278:         /* a hole is outside compressed Bcols */
    2279:         if (ncols == 0) {
    2280:           if (cstart) {
    2281:             offdiagIdx[r] = 0;
    2282:           } else offdiagIdx[r] = cend;
    2283:         } else { /* ncols > 0 */
    2284:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2285:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2286:         }
    2287:       }
    2288:     }

    2290:     for (j = 0; j < ncols; j++) {
    2291:       if (PetscAbsScalar(offdiagA[r]) > PetscAbsScalar(*ba)) {
    2292:         offdiagA[r]   = *ba;
    2293:         offdiagIdx[r] = cmap[*bj];
    2294:       }
    2295:       ba++;
    2296:       bj++;
    2297:     }
    2298:   }

    2300:   PetscCall(VecGetArrayWrite(v, &a));
    2301:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2302:   for (r = 0; r < m; ++r) {
    2303:     if (PetscAbsScalar(diagA[r]) < PetscAbsScalar(offdiagA[r])) {
    2304:       a[r] = diagA[r];
    2305:       if (idx) idx[r] = cstart + diagIdx[r];
    2306:     } else if (PetscAbsScalar(diagA[r]) == PetscAbsScalar(offdiagA[r])) {
    2307:       a[r] = diagA[r];
    2308:       if (idx) {
    2309:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2310:           idx[r] = cstart + diagIdx[r];
    2311:         } else idx[r] = offdiagIdx[r];
    2312:       }
    2313:     } else {
    2314:       a[r] = offdiagA[r];
    2315:       if (idx) idx[r] = offdiagIdx[r];
    2316:     }
    2317:   }
    2318:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2319:   PetscCall(VecRestoreArrayWrite(v, &a));
    2320:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2321:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2322:   PetscCall(VecDestroy(&diagV));
    2323:   PetscCall(VecDestroy(&offdiagV));
    2324:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2325:   PetscFunctionReturn(PETSC_SUCCESS);
    2326: }

    2328: static PetscErrorCode MatGetRowMin_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2329: {
    2330:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2331:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2332:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2333:   PetscInt          *cmap = mat->garray;
    2334:   PetscInt          *diagIdx, *offdiagIdx;
    2335:   Vec                diagV, offdiagV;
    2336:   PetscScalar       *a, *diagA, *offdiagA;
    2337:   const PetscScalar *ba, *bav;
    2338:   PetscInt           r, j, col, ncols, *bi, *bj;
    2339:   Mat                B = mat->B;
    2340:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2342:   PetscFunctionBegin;
    2343:   /* When a process holds entire A and other processes have no entry */
    2344:   if (A->cmap->N == n) {
    2345:     PetscCall(VecGetArrayWrite(v, &diagA));
    2346:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2347:     PetscCall(MatGetRowMin(mat->A, diagV, idx));
    2348:     PetscCall(VecDestroy(&diagV));
    2349:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2350:     PetscFunctionReturn(PETSC_SUCCESS);
    2351:   } else if (n == 0) {
    2352:     if (m) {
    2353:       PetscCall(VecGetArrayWrite(v, &a));
    2354:       for (r = 0; r < m; r++) {
    2355:         a[r] = PETSC_MAX_REAL;
    2356:         if (idx) idx[r] = -1;
    2357:       }
    2358:       PetscCall(VecRestoreArrayWrite(v, &a));
    2359:     }
    2360:     PetscFunctionReturn(PETSC_SUCCESS);
    2361:   }

    2363:   PetscCall(PetscCalloc2(m, &diagIdx, m, &offdiagIdx));
    2364:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2365:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2366:   PetscCall(MatGetRowMin(mat->A, diagV, diagIdx));

    2368:   /* Get offdiagIdx[] for implicit 0.0 */
    2369:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2370:   ba = bav;
    2371:   bi = b->i;
    2372:   bj = b->j;
    2373:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2374:   for (r = 0; r < m; r++) {
    2375:     ncols = bi[r + 1] - bi[r];
    2376:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2377:       offdiagA[r]   = *ba;
    2378:       offdiagIdx[r] = cmap[0];
    2379:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2380:       offdiagA[r] = 0.0;

    2382:       /* Find first hole in the cmap */
    2383:       for (j = 0; j < ncols; j++) {
    2384:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2385:         if (col > j && j < cstart) {
    2386:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2387:           break;
    2388:         } else if (col > j + n && j >= cstart) {
    2389:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2390:           break;
    2391:         }
    2392:       }
    2393:       if (j == ncols && ncols < A->cmap->N - n) {
    2394:         /* a hole is outside compressed Bcols */
    2395:         if (ncols == 0) {
    2396:           if (cstart) {
    2397:             offdiagIdx[r] = 0;
    2398:           } else offdiagIdx[r] = cend;
    2399:         } else { /* ncols > 0 */
    2400:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2401:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2402:         }
    2403:       }
    2404:     }

    2406:     for (j = 0; j < ncols; j++) {
    2407:       if (PetscRealPart(offdiagA[r]) > PetscRealPart(*ba)) {
    2408:         offdiagA[r]   = *ba;
    2409:         offdiagIdx[r] = cmap[*bj];
    2410:       }
    2411:       ba++;
    2412:       bj++;
    2413:     }
    2414:   }

    2416:   PetscCall(VecGetArrayWrite(v, &a));
    2417:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2418:   for (r = 0; r < m; ++r) {
    2419:     if (PetscRealPart(diagA[r]) < PetscRealPart(offdiagA[r])) {
    2420:       a[r] = diagA[r];
    2421:       if (idx) idx[r] = cstart + diagIdx[r];
    2422:     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
    2423:       a[r] = diagA[r];
    2424:       if (idx) {
    2425:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2426:           idx[r] = cstart + diagIdx[r];
    2427:         } else idx[r] = offdiagIdx[r];
    2428:       }
    2429:     } else {
    2430:       a[r] = offdiagA[r];
    2431:       if (idx) idx[r] = offdiagIdx[r];
    2432:     }
    2433:   }
    2434:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2435:   PetscCall(VecRestoreArrayWrite(v, &a));
    2436:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2437:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2438:   PetscCall(VecDestroy(&diagV));
    2439:   PetscCall(VecDestroy(&offdiagV));
    2440:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2441:   PetscFunctionReturn(PETSC_SUCCESS);
    2442: }

    2444: static PetscErrorCode MatGetRowMax_MPIAIJ(Mat A, Vec v, PetscInt idx[])
    2445: {
    2446:   Mat_MPIAIJ        *mat = (Mat_MPIAIJ *)A->data;
    2447:   PetscInt           m = A->rmap->n, n = A->cmap->n;
    2448:   PetscInt           cstart = A->cmap->rstart, cend = A->cmap->rend;
    2449:   PetscInt          *cmap = mat->garray;
    2450:   PetscInt          *diagIdx, *offdiagIdx;
    2451:   Vec                diagV, offdiagV;
    2452:   PetscScalar       *a, *diagA, *offdiagA;
    2453:   const PetscScalar *ba, *bav;
    2454:   PetscInt           r, j, col, ncols, *bi, *bj;
    2455:   Mat                B = mat->B;
    2456:   Mat_SeqAIJ        *b = (Mat_SeqAIJ *)B->data;

    2458:   PetscFunctionBegin;
    2459:   /* When a process holds entire A and other processes have no entry */
    2460:   if (A->cmap->N == n) {
    2461:     PetscCall(VecGetArrayWrite(v, &diagA));
    2462:     PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, m, diagA, &diagV));
    2463:     PetscCall(MatGetRowMax(mat->A, diagV, idx));
    2464:     PetscCall(VecDestroy(&diagV));
    2465:     PetscCall(VecRestoreArrayWrite(v, &diagA));
    2466:     PetscFunctionReturn(PETSC_SUCCESS);
    2467:   } else if (n == 0) {
    2468:     if (m) {
    2469:       PetscCall(VecGetArrayWrite(v, &a));
    2470:       for (r = 0; r < m; r++) {
    2471:         a[r] = PETSC_MIN_REAL;
    2472:         if (idx) idx[r] = -1;
    2473:       }
    2474:       PetscCall(VecRestoreArrayWrite(v, &a));
    2475:     }
    2476:     PetscFunctionReturn(PETSC_SUCCESS);
    2477:   }

    2479:   PetscCall(PetscMalloc2(m, &diagIdx, m, &offdiagIdx));
    2480:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &diagV));
    2481:   PetscCall(VecCreateSeq(PETSC_COMM_SELF, m, &offdiagV));
    2482:   PetscCall(MatGetRowMax(mat->A, diagV, diagIdx));

    2484:   /* Get offdiagIdx[] for implicit 0.0 */
    2485:   PetscCall(MatSeqAIJGetArrayRead(B, &bav));
    2486:   ba = bav;
    2487:   bi = b->i;
    2488:   bj = b->j;
    2489:   PetscCall(VecGetArrayWrite(offdiagV, &offdiagA));
    2490:   for (r = 0; r < m; r++) {
    2491:     ncols = bi[r + 1] - bi[r];
    2492:     if (ncols == A->cmap->N - n) { /* Brow is dense */
    2493:       offdiagA[r]   = *ba;
    2494:       offdiagIdx[r] = cmap[0];
    2495:     } else { /* Brow is sparse so already KNOW maximum is 0.0 or higher */
    2496:       offdiagA[r] = 0.0;

    2498:       /* Find first hole in the cmap */
    2499:       for (j = 0; j < ncols; j++) {
    2500:         col = cmap[bj[j]]; /* global column number = cmap[B column number] */
    2501:         if (col > j && j < cstart) {
    2502:           offdiagIdx[r] = j; /* global column number of first implicit 0.0 */
    2503:           break;
    2504:         } else if (col > j + n && j >= cstart) {
    2505:           offdiagIdx[r] = j + n; /* global column number of first implicit 0.0 */
    2506:           break;
    2507:         }
    2508:       }
    2509:       if (j == ncols && ncols < A->cmap->N - n) {
    2510:         /* a hole is outside compressed Bcols */
    2511:         if (ncols == 0) {
    2512:           if (cstart) {
    2513:             offdiagIdx[r] = 0;
    2514:           } else offdiagIdx[r] = cend;
    2515:         } else { /* ncols > 0 */
    2516:           offdiagIdx[r] = cmap[ncols - 1] + 1;
    2517:           if (offdiagIdx[r] == cstart) offdiagIdx[r] += n;
    2518:         }
    2519:       }
    2520:     }

    2522:     for (j = 0; j < ncols; j++) {
    2523:       if (PetscRealPart(offdiagA[r]) < PetscRealPart(*ba)) {
    2524:         offdiagA[r]   = *ba;
    2525:         offdiagIdx[r] = cmap[*bj];
    2526:       }
    2527:       ba++;
    2528:       bj++;
    2529:     }
    2530:   }

    2532:   PetscCall(VecGetArrayWrite(v, &a));
    2533:   PetscCall(VecGetArrayRead(diagV, (const PetscScalar **)&diagA));
    2534:   for (r = 0; r < m; ++r) {
    2535:     if (PetscRealPart(diagA[r]) > PetscRealPart(offdiagA[r])) {
    2536:       a[r] = diagA[r];
    2537:       if (idx) idx[r] = cstart + diagIdx[r];
    2538:     } else if (PetscRealPart(diagA[r]) == PetscRealPart(offdiagA[r])) {
    2539:       a[r] = diagA[r];
    2540:       if (idx) {
    2541:         if (cstart + diagIdx[r] <= offdiagIdx[r]) {
    2542:           idx[r] = cstart + diagIdx[r];
    2543:         } else idx[r] = offdiagIdx[r];
    2544:       }
    2545:     } else {
    2546:       a[r] = offdiagA[r];
    2547:       if (idx) idx[r] = offdiagIdx[r];
    2548:     }
    2549:   }
    2550:   PetscCall(MatSeqAIJRestoreArrayRead(B, &bav));
    2551:   PetscCall(VecRestoreArrayWrite(v, &a));
    2552:   PetscCall(VecRestoreArrayRead(diagV, (const PetscScalar **)&diagA));
    2553:   PetscCall(VecRestoreArrayWrite(offdiagV, &offdiagA));
    2554:   PetscCall(VecDestroy(&diagV));
    2555:   PetscCall(VecDestroy(&offdiagV));
    2556:   PetscCall(PetscFree2(diagIdx, offdiagIdx));
    2557:   PetscFunctionReturn(PETSC_SUCCESS);
    2558: }

    2560: PetscErrorCode MatGetSeqNonzeroStructure_MPIAIJ(Mat mat, Mat *newmat)
    2561: {
    2562:   Mat *dummy;

    2564:   PetscFunctionBegin;
    2565:   PetscCall(MatCreateSubMatrix_MPIAIJ_All(mat, MAT_DO_NOT_GET_VALUES, MAT_INITIAL_MATRIX, &dummy));
    2566:   *newmat = *dummy;
    2567:   PetscCall(PetscFree(dummy));
    2568:   PetscFunctionReturn(PETSC_SUCCESS);
    2569: }

    2571: static PetscErrorCode MatInvertBlockDiagonal_MPIAIJ(Mat A, const PetscScalar **values)
    2572: {
    2573:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2575:   PetscFunctionBegin;
    2576:   PetscCall(MatInvertBlockDiagonal(a->A, values));
    2577:   A->factorerrortype = a->A->factorerrortype;
    2578:   PetscFunctionReturn(PETSC_SUCCESS);
    2579: }

    2581: static PetscErrorCode MatSetRandom_MPIAIJ(Mat x, PetscRandom rctx)
    2582: {
    2583:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)x->data;

    2585:   PetscFunctionBegin;
    2586:   PetscCheck(x->assembled || x->preallocated, PetscObjectComm((PetscObject)x), PETSC_ERR_ARG_WRONGSTATE, "MatSetRandom on an unassembled and unpreallocated MATMPIAIJ is not allowed");
    2587:   PetscCall(MatSetRandom(aij->A, rctx));
    2588:   if (x->assembled) {
    2589:     PetscCall(MatSetRandom(aij->B, rctx));
    2590:   } else {
    2591:     PetscCall(MatSetRandomSkipColumnRange_SeqAIJ_Private(aij->B, x->cmap->rstart, x->cmap->rend, rctx));
    2592:   }
    2593:   PetscCall(MatAssemblyBegin(x, MAT_FINAL_ASSEMBLY));
    2594:   PetscCall(MatAssemblyEnd(x, MAT_FINAL_ASSEMBLY));
    2595:   PetscFunctionReturn(PETSC_SUCCESS);
    2596: }

    2598: static PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ(Mat A, PetscBool sc)
    2599: {
    2600:   PetscFunctionBegin;
    2601:   if (sc) A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ_Scalable;
    2602:   else A->ops->increaseoverlap = MatIncreaseOverlap_MPIAIJ;
    2603:   PetscFunctionReturn(PETSC_SUCCESS);
    2604: }

    2606: /*@
    2607:   MatMPIAIJGetNumberNonzeros - gets the number of nonzeros in the matrix on this MPI rank

    2609:   Not Collective

    2611:   Input Parameter:
    2612: . A - the matrix

    2614:   Output Parameter:
    2615: . nz - the number of nonzeros

    2617:   Level: advanced

    2619: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
    2620: @*/
    2621: PetscErrorCode MatMPIAIJGetNumberNonzeros(Mat A, PetscCount *nz)
    2622: {
    2623:   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)A->data;
    2624:   Mat_SeqAIJ *aaij = (Mat_SeqAIJ *)maij->A->data, *baij = (Mat_SeqAIJ *)maij->B->data;
    2625:   PetscBool   isaij;

    2627:   PetscFunctionBegin;
    2628:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)A, MATMPIAIJ, &isaij));
    2629:   PetscCheck(isaij, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Not for type %s", ((PetscObject)A)->type_name);
    2630:   *nz = aaij->i[A->rmap->n] + baij->i[A->rmap->n];
    2631:   PetscFunctionReturn(PETSC_SUCCESS);
    2632: }

    2634: /*@
    2635:   MatMPIAIJSetUseScalableIncreaseOverlap - Determine if the matrix uses a scalable algorithm to compute the overlap

    2637:   Collective

    2639:   Input Parameters:
    2640: + A  - the matrix
    2641: - sc - `PETSC_TRUE` indicates use the scalable algorithm (default is not to use the scalable algorithm)

    2643:   Level: advanced

    2645: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`
    2646: @*/
    2647: PetscErrorCode MatMPIAIJSetUseScalableIncreaseOverlap(Mat A, PetscBool sc)
    2648: {
    2649:   PetscFunctionBegin;
    2650:   PetscTryMethod(A, "MatMPIAIJSetUseScalableIncreaseOverlap_C", (Mat, PetscBool), (A, sc));
    2651:   PetscFunctionReturn(PETSC_SUCCESS);
    2652: }

    2654: PetscErrorCode MatSetFromOptions_MPIAIJ(Mat A, PetscOptionItems *PetscOptionsObject)
    2655: {
    2656:   PetscBool sc = PETSC_FALSE, flg;

    2658:   PetscFunctionBegin;
    2659:   PetscOptionsHeadBegin(PetscOptionsObject, "MPIAIJ options");
    2660:   if (A->ops->increaseoverlap == MatIncreaseOverlap_MPIAIJ_Scalable) sc = PETSC_TRUE;
    2661:   PetscCall(PetscOptionsBool("-mat_increase_overlap_scalable", "Use a scalable algorithm to compute the overlap", "MatIncreaseOverlap", sc, &sc, &flg));
    2662:   if (flg) PetscCall(MatMPIAIJSetUseScalableIncreaseOverlap(A, sc));
    2663:   PetscOptionsHeadEnd();
    2664:   PetscFunctionReturn(PETSC_SUCCESS);
    2665: }

    2667: static PetscErrorCode MatShift_MPIAIJ(Mat Y, PetscScalar a)
    2668: {
    2669:   Mat_MPIAIJ *maij = (Mat_MPIAIJ *)Y->data;
    2670:   Mat_SeqAIJ *aij  = (Mat_SeqAIJ *)maij->A->data;

    2672:   PetscFunctionBegin;
    2673:   if (!Y->preallocated) {
    2674:     PetscCall(MatMPIAIJSetPreallocation(Y, 1, NULL, 0, NULL));
    2675:   } else if (!aij->nz) { /* It does not matter if diagonals of Y only partially lie in maij->A. We just need an estimated preallocation. */
    2676:     PetscInt nonew = aij->nonew;
    2677:     PetscCall(MatSeqAIJSetPreallocation(maij->A, 1, NULL));
    2678:     aij->nonew = nonew;
    2679:   }
    2680:   PetscCall(MatShift_Basic(Y, a));
    2681:   PetscFunctionReturn(PETSC_SUCCESS);
    2682: }

    2684: static PetscErrorCode MatMissingDiagonal_MPIAIJ(Mat A, PetscBool *missing, PetscInt *d)
    2685: {
    2686:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2688:   PetscFunctionBegin;
    2689:   PetscCheck(A->rmap->n == A->cmap->n, PETSC_COMM_SELF, PETSC_ERR_SUP, "Only works for square matrices");
    2690:   PetscCall(MatMissingDiagonal(a->A, missing, d));
    2691:   if (d) {
    2692:     PetscInt rstart;
    2693:     PetscCall(MatGetOwnershipRange(A, &rstart, NULL));
    2694:     *d += rstart;
    2695:   }
    2696:   PetscFunctionReturn(PETSC_SUCCESS);
    2697: }

    2699: static PetscErrorCode MatInvertVariableBlockDiagonal_MPIAIJ(Mat A, PetscInt nblocks, const PetscInt *bsizes, PetscScalar *diag)
    2700: {
    2701:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2703:   PetscFunctionBegin;
    2704:   PetscCall(MatInvertVariableBlockDiagonal(a->A, nblocks, bsizes, diag));
    2705:   PetscFunctionReturn(PETSC_SUCCESS);
    2706: }

    2708: static PetscErrorCode MatEliminateZeros_MPIAIJ(Mat A, PetscBool keep)
    2709: {
    2710:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;

    2712:   PetscFunctionBegin;
    2713:   PetscCall(MatEliminateZeros_SeqAIJ(a->A, keep));        // possibly keep zero diagonal coefficients
    2714:   PetscCall(MatEliminateZeros_SeqAIJ(a->B, PETSC_FALSE)); // never keep zero diagonal coefficients
    2715:   PetscFunctionReturn(PETSC_SUCCESS);
    2716: }

    2718: static struct _MatOps MatOps_Values = {MatSetValues_MPIAIJ,
    2719:                                        MatGetRow_MPIAIJ,
    2720:                                        MatRestoreRow_MPIAIJ,
    2721:                                        MatMult_MPIAIJ,
    2722:                                        /* 4*/ MatMultAdd_MPIAIJ,
    2723:                                        MatMultTranspose_MPIAIJ,
    2724:                                        MatMultTransposeAdd_MPIAIJ,
    2725:                                        NULL,
    2726:                                        NULL,
    2727:                                        NULL,
    2728:                                        /*10*/ NULL,
    2729:                                        NULL,
    2730:                                        NULL,
    2731:                                        MatSOR_MPIAIJ,
    2732:                                        MatTranspose_MPIAIJ,
    2733:                                        /*15*/ MatGetInfo_MPIAIJ,
    2734:                                        MatEqual_MPIAIJ,
    2735:                                        MatGetDiagonal_MPIAIJ,
    2736:                                        MatDiagonalScale_MPIAIJ,
    2737:                                        MatNorm_MPIAIJ,
    2738:                                        /*20*/ MatAssemblyBegin_MPIAIJ,
    2739:                                        MatAssemblyEnd_MPIAIJ,
    2740:                                        MatSetOption_MPIAIJ,
    2741:                                        MatZeroEntries_MPIAIJ,
    2742:                                        /*24*/ MatZeroRows_MPIAIJ,
    2743:                                        NULL,
    2744:                                        NULL,
    2745:                                        NULL,
    2746:                                        NULL,
    2747:                                        /*29*/ MatSetUp_MPI_Hash,
    2748:                                        NULL,
    2749:                                        NULL,
    2750:                                        MatGetDiagonalBlock_MPIAIJ,
    2751:                                        NULL,
    2752:                                        /*34*/ MatDuplicate_MPIAIJ,
    2753:                                        NULL,
    2754:                                        NULL,
    2755:                                        NULL,
    2756:                                        NULL,
    2757:                                        /*39*/ MatAXPY_MPIAIJ,
    2758:                                        MatCreateSubMatrices_MPIAIJ,
    2759:                                        MatIncreaseOverlap_MPIAIJ,
    2760:                                        MatGetValues_MPIAIJ,
    2761:                                        MatCopy_MPIAIJ,
    2762:                                        /*44*/ MatGetRowMax_MPIAIJ,
    2763:                                        MatScale_MPIAIJ,
    2764:                                        MatShift_MPIAIJ,
    2765:                                        MatDiagonalSet_MPIAIJ,
    2766:                                        MatZeroRowsColumns_MPIAIJ,
    2767:                                        /*49*/ MatSetRandom_MPIAIJ,
    2768:                                        MatGetRowIJ_MPIAIJ,
    2769:                                        MatRestoreRowIJ_MPIAIJ,
    2770:                                        NULL,
    2771:                                        NULL,
    2772:                                        /*54*/ MatFDColoringCreate_MPIXAIJ,
    2773:                                        NULL,
    2774:                                        MatSetUnfactored_MPIAIJ,
    2775:                                        MatPermute_MPIAIJ,
    2776:                                        NULL,
    2777:                                        /*59*/ MatCreateSubMatrix_MPIAIJ,
    2778:                                        MatDestroy_MPIAIJ,
    2779:                                        MatView_MPIAIJ,
    2780:                                        NULL,
    2781:                                        NULL,
    2782:                                        /*64*/ NULL,
    2783:                                        MatMatMatMultNumeric_MPIAIJ_MPIAIJ_MPIAIJ,
    2784:                                        NULL,
    2785:                                        NULL,
    2786:                                        NULL,
    2787:                                        /*69*/ MatGetRowMaxAbs_MPIAIJ,
    2788:                                        MatGetRowMinAbs_MPIAIJ,
    2789:                                        NULL,
    2790:                                        NULL,
    2791:                                        NULL,
    2792:                                        NULL,
    2793:                                        /*75*/ MatFDColoringApply_AIJ,
    2794:                                        MatSetFromOptions_MPIAIJ,
    2795:                                        NULL,
    2796:                                        NULL,
    2797:                                        MatFindZeroDiagonals_MPIAIJ,
    2798:                                        /*80*/ NULL,
    2799:                                        NULL,
    2800:                                        NULL,
    2801:                                        /*83*/ MatLoad_MPIAIJ,
    2802:                                        NULL,
    2803:                                        NULL,
    2804:                                        NULL,
    2805:                                        NULL,
    2806:                                        NULL,
    2807:                                        /*89*/ NULL,
    2808:                                        NULL,
    2809:                                        MatMatMultNumeric_MPIAIJ_MPIAIJ,
    2810:                                        NULL,
    2811:                                        NULL,
    2812:                                        /*94*/ MatPtAPNumeric_MPIAIJ_MPIAIJ,
    2813:                                        NULL,
    2814:                                        NULL,
    2815:                                        NULL,
    2816:                                        MatBindToCPU_MPIAIJ,
    2817:                                        /*99*/ MatProductSetFromOptions_MPIAIJ,
    2818:                                        NULL,
    2819:                                        NULL,
    2820:                                        MatConjugate_MPIAIJ,
    2821:                                        NULL,
    2822:                                        /*104*/ MatSetValuesRow_MPIAIJ,
    2823:                                        MatRealPart_MPIAIJ,
    2824:                                        MatImaginaryPart_MPIAIJ,
    2825:                                        NULL,
    2826:                                        NULL,
    2827:                                        /*109*/ NULL,
    2828:                                        NULL,
    2829:                                        MatGetRowMin_MPIAIJ,
    2830:                                        NULL,
    2831:                                        MatMissingDiagonal_MPIAIJ,
    2832:                                        /*114*/ MatGetSeqNonzeroStructure_MPIAIJ,
    2833:                                        NULL,
    2834:                                        MatGetGhosts_MPIAIJ,
    2835:                                        NULL,
    2836:                                        NULL,
    2837:                                        /*119*/ MatMultDiagonalBlock_MPIAIJ,
    2838:                                        NULL,
    2839:                                        NULL,
    2840:                                        NULL,
    2841:                                        MatGetMultiProcBlock_MPIAIJ,
    2842:                                        /*124*/ MatFindNonzeroRows_MPIAIJ,
    2843:                                        MatGetColumnReductions_MPIAIJ,
    2844:                                        MatInvertBlockDiagonal_MPIAIJ,
    2845:                                        MatInvertVariableBlockDiagonal_MPIAIJ,
    2846:                                        MatCreateSubMatricesMPI_MPIAIJ,
    2847:                                        /*129*/ NULL,
    2848:                                        NULL,
    2849:                                        NULL,
    2850:                                        MatTransposeMatMultNumeric_MPIAIJ_MPIAIJ,
    2851:                                        NULL,
    2852:                                        /*134*/ NULL,
    2853:                                        NULL,
    2854:                                        NULL,
    2855:                                        NULL,
    2856:                                        NULL,
    2857:                                        /*139*/ MatSetBlockSizes_MPIAIJ,
    2858:                                        NULL,
    2859:                                        NULL,
    2860:                                        MatFDColoringSetUp_MPIXAIJ,
    2861:                                        MatFindOffBlockDiagonalEntries_MPIAIJ,
    2862:                                        MatCreateMPIMatConcatenateSeqMat_MPIAIJ,
    2863:                                        /*145*/ NULL,
    2864:                                        NULL,
    2865:                                        NULL,
    2866:                                        MatCreateGraph_Simple_AIJ,
    2867:                                        NULL,
    2868:                                        /*150*/ NULL,
    2869:                                        MatEliminateZeros_MPIAIJ,
    2870:                                        MatGetRowSumAbs_MPIAIJ,
    2871:                                        NULL,
    2872:                                        NULL,
    2873:                                        NULL};

    2875: static PetscErrorCode MatStoreValues_MPIAIJ(Mat mat)
    2876: {
    2877:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2879:   PetscFunctionBegin;
    2880:   PetscCall(MatStoreValues(aij->A));
    2881:   PetscCall(MatStoreValues(aij->B));
    2882:   PetscFunctionReturn(PETSC_SUCCESS);
    2883: }

    2885: static PetscErrorCode MatRetrieveValues_MPIAIJ(Mat mat)
    2886: {
    2887:   Mat_MPIAIJ *aij = (Mat_MPIAIJ *)mat->data;

    2889:   PetscFunctionBegin;
    2890:   PetscCall(MatRetrieveValues(aij->A));
    2891:   PetscCall(MatRetrieveValues(aij->B));
    2892:   PetscFunctionReturn(PETSC_SUCCESS);
    2893: }

    2895: PetscErrorCode MatMPIAIJSetPreallocation_MPIAIJ(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
    2896: {
    2897:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
    2898:   PetscMPIInt size;

    2900:   PetscFunctionBegin;
    2901:   if (B->hash_active) {
    2902:     B->ops[0]      = b->cops;
    2903:     B->hash_active = PETSC_FALSE;
    2904:   }
    2905:   PetscCall(PetscLayoutSetUp(B->rmap));
    2906:   PetscCall(PetscLayoutSetUp(B->cmap));

    2908: #if defined(PETSC_USE_CTABLE)
    2909:   PetscCall(PetscHMapIDestroy(&b->colmap));
    2910: #else
    2911:   PetscCall(PetscFree(b->colmap));
    2912: #endif
    2913:   PetscCall(PetscFree(b->garray));
    2914:   PetscCall(VecDestroy(&b->lvec));
    2915:   PetscCall(VecScatterDestroy(&b->Mvctx));

    2917:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

    2919:   MatSeqXAIJGetOptions_Private(b->B);
    2920:   PetscCall(MatDestroy(&b->B));
    2921:   PetscCall(MatCreate(PETSC_COMM_SELF, &b->B));
    2922:   PetscCall(MatSetSizes(b->B, B->rmap->n, size > 1 ? B->cmap->N : 0, B->rmap->n, size > 1 ? B->cmap->N : 0));
    2923:   PetscCall(MatSetBlockSizesFromMats(b->B, B, B));
    2924:   PetscCall(MatSetType(b->B, MATSEQAIJ));
    2925:   MatSeqXAIJRestoreOptions_Private(b->B);

    2927:   MatSeqXAIJGetOptions_Private(b->A);
    2928:   PetscCall(MatDestroy(&b->A));
    2929:   PetscCall(MatCreate(PETSC_COMM_SELF, &b->A));
    2930:   PetscCall(MatSetSizes(b->A, B->rmap->n, B->cmap->n, B->rmap->n, B->cmap->n));
    2931:   PetscCall(MatSetBlockSizesFromMats(b->A, B, B));
    2932:   PetscCall(MatSetType(b->A, MATSEQAIJ));
    2933:   MatSeqXAIJRestoreOptions_Private(b->A);

    2935:   PetscCall(MatSeqAIJSetPreallocation(b->A, d_nz, d_nnz));
    2936:   PetscCall(MatSeqAIJSetPreallocation(b->B, o_nz, o_nnz));
    2937:   B->preallocated  = PETSC_TRUE;
    2938:   B->was_assembled = PETSC_FALSE;
    2939:   B->assembled     = PETSC_FALSE;
    2940:   PetscFunctionReturn(PETSC_SUCCESS);
    2941: }

    2943: static PetscErrorCode MatResetPreallocation_MPIAIJ(Mat B)
    2944: {
    2945:   Mat_MPIAIJ *b = (Mat_MPIAIJ *)B->data;
    2946:   PetscBool   ondiagreset, offdiagreset, memoryreset;

    2948:   PetscFunctionBegin;
    2950:   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()");
    2951:   if (B->num_ass == 0) PetscFunctionReturn(PETSC_SUCCESS);

    2953:   PetscCall(MatResetPreallocation_SeqAIJ_Private(b->A, &ondiagreset));
    2954:   PetscCall(MatResetPreallocation_SeqAIJ_Private(b->B, &offdiagreset));
    2955:   memoryreset = (PetscBool)(ondiagreset || offdiagreset);
    2956:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &memoryreset, 1, MPIU_BOOL, MPI_LOR, PetscObjectComm((PetscObject)B)));
    2957:   if (!memoryreset) PetscFunctionReturn(PETSC_SUCCESS);

    2959:   PetscCall(PetscLayoutSetUp(B->rmap));
    2960:   PetscCall(PetscLayoutSetUp(B->cmap));
    2961:   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");
    2962:   PetscCall(MatDisAssemble_MPIAIJ(B, PETSC_TRUE));
    2963:   PetscCall(VecScatterDestroy(&b->Mvctx));

    2965:   B->preallocated  = PETSC_TRUE;
    2966:   B->was_assembled = PETSC_FALSE;
    2967:   B->assembled     = PETSC_FALSE;
    2968:   /* Log that the state of this object has changed; this will help guarantee that preconditioners get re-setup */
    2969:   PetscCall(PetscObjectStateIncrease((PetscObject)B));
    2970:   PetscFunctionReturn(PETSC_SUCCESS);
    2971: }

    2973: PetscErrorCode MatDuplicate_MPIAIJ(Mat matin, MatDuplicateOption cpvalues, Mat *newmat)
    2974: {
    2975:   Mat         mat;
    2976:   Mat_MPIAIJ *a, *oldmat = (Mat_MPIAIJ *)matin->data;

    2978:   PetscFunctionBegin;
    2979:   *newmat = NULL;
    2980:   PetscCall(MatCreate(PetscObjectComm((PetscObject)matin), &mat));
    2981:   PetscCall(MatSetSizes(mat, matin->rmap->n, matin->cmap->n, matin->rmap->N, matin->cmap->N));
    2982:   PetscCall(MatSetBlockSizesFromMats(mat, matin, matin));
    2983:   PetscCall(MatSetType(mat, ((PetscObject)matin)->type_name));
    2984:   a = (Mat_MPIAIJ *)mat->data;

    2986:   mat->factortype = matin->factortype;
    2987:   mat->assembled  = matin->assembled;
    2988:   mat->insertmode = NOT_SET_VALUES;

    2990:   a->size         = oldmat->size;
    2991:   a->rank         = oldmat->rank;
    2992:   a->donotstash   = oldmat->donotstash;
    2993:   a->roworiented  = oldmat->roworiented;
    2994:   a->rowindices   = NULL;
    2995:   a->rowvalues    = NULL;
    2996:   a->getrowactive = PETSC_FALSE;

    2998:   PetscCall(PetscLayoutReference(matin->rmap, &mat->rmap));
    2999:   PetscCall(PetscLayoutReference(matin->cmap, &mat->cmap));
    3000:   if (matin->hash_active) {
    3001:     PetscCall(MatSetUp(mat));
    3002:   } else {
    3003:     mat->preallocated = matin->preallocated;
    3004:     if (oldmat->colmap) {
    3005: #if defined(PETSC_USE_CTABLE)
    3006:       PetscCall(PetscHMapIDuplicate(oldmat->colmap, &a->colmap));
    3007: #else
    3008:       PetscCall(PetscMalloc1(mat->cmap->N, &a->colmap));
    3009:       PetscCall(PetscArraycpy(a->colmap, oldmat->colmap, mat->cmap->N));
    3010: #endif
    3011:     } else a->colmap = NULL;
    3012:     if (oldmat->garray) {
    3013:       PetscInt len;
    3014:       len = oldmat->B->cmap->n;
    3015:       PetscCall(PetscMalloc1(len + 1, &a->garray));
    3016:       if (len) PetscCall(PetscArraycpy(a->garray, oldmat->garray, len));
    3017:     } else a->garray = NULL;

    3019:     /* It may happen MatDuplicate is called with a non-assembled matrix
    3020:       In fact, MatDuplicate only requires the matrix to be preallocated
    3021:       This may happen inside a DMCreateMatrix_Shell */
    3022:     if (oldmat->lvec) PetscCall(VecDuplicate(oldmat->lvec, &a->lvec));
    3023:     if (oldmat->Mvctx) {
    3024:       a->Mvctx = oldmat->Mvctx;
    3025:       PetscCall(PetscObjectReference((PetscObject)oldmat->Mvctx));
    3026:     }
    3027:     PetscCall(MatDuplicate(oldmat->A, cpvalues, &a->A));
    3028:     PetscCall(MatDuplicate(oldmat->B, cpvalues, &a->B));
    3029:   }
    3030:   PetscCall(PetscFunctionListDuplicate(((PetscObject)matin)->qlist, &((PetscObject)mat)->qlist));
    3031:   *newmat = mat;
    3032:   PetscFunctionReturn(PETSC_SUCCESS);
    3033: }

    3035: PetscErrorCode MatLoad_MPIAIJ(Mat newMat, PetscViewer viewer)
    3036: {
    3037:   PetscBool isbinary, ishdf5;

    3039:   PetscFunctionBegin;
    3042:   /* force binary viewer to load .info file if it has not yet done so */
    3043:   PetscCall(PetscViewerSetUp(viewer));
    3044:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERBINARY, &isbinary));
    3045:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERHDF5, &ishdf5));
    3046:   if (isbinary) {
    3047:     PetscCall(MatLoad_MPIAIJ_Binary(newMat, viewer));
    3048:   } else if (ishdf5) {
    3049: #if defined(PETSC_HAVE_HDF5)
    3050:     PetscCall(MatLoad_AIJ_HDF5(newMat, viewer));
    3051: #else
    3052:     SETERRQ(PetscObjectComm((PetscObject)newMat), PETSC_ERR_SUP, "HDF5 not supported in this build.\nPlease reconfigure using --download-hdf5");
    3053: #endif
    3054:   } else {
    3055:     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);
    3056:   }
    3057:   PetscFunctionReturn(PETSC_SUCCESS);
    3058: }

    3060: PetscErrorCode MatLoad_MPIAIJ_Binary(Mat mat, PetscViewer viewer)
    3061: {
    3062:   PetscInt     header[4], M, N, m, nz, rows, cols, sum, i;
    3063:   PetscInt    *rowidxs, *colidxs;
    3064:   PetscScalar *matvals;

    3066:   PetscFunctionBegin;
    3067:   PetscCall(PetscViewerSetUp(viewer));

    3069:   /* read in matrix header */
    3070:   PetscCall(PetscViewerBinaryRead(viewer, header, 4, NULL, PETSC_INT));
    3071:   PetscCheck(header[0] == MAT_FILE_CLASSID, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Not a matrix object in file");
    3072:   M  = header[1];
    3073:   N  = header[2];
    3074:   nz = header[3];
    3075:   PetscCheck(M >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix row size (%" PetscInt_FMT ") in file is negative", M);
    3076:   PetscCheck(N >= 0, PetscObjectComm((PetscObject)viewer), PETSC_ERR_FILE_UNEXPECTED, "Matrix column size (%" PetscInt_FMT ") in file is negative", N);
    3077:   PetscCheck(nz >= 0, PETSC_COMM_SELF, PETSC_ERR_FILE_UNEXPECTED, "Matrix stored in special format on disk, cannot load as MPIAIJ");

    3079:   /* set block sizes from the viewer's .info file */
    3080:   PetscCall(MatLoad_Binary_BlockSizes(mat, viewer));
    3081:   /* set global sizes if not set already */
    3082:   if (mat->rmap->N < 0) mat->rmap->N = M;
    3083:   if (mat->cmap->N < 0) mat->cmap->N = N;
    3084:   PetscCall(PetscLayoutSetUp(mat->rmap));
    3085:   PetscCall(PetscLayoutSetUp(mat->cmap));

    3087:   /* check if the matrix sizes are correct */
    3088:   PetscCall(MatGetSize(mat, &rows, &cols));
    3089:   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);

    3091:   /* read in row lengths and build row indices */
    3092:   PetscCall(MatGetLocalSize(mat, &m, NULL));
    3093:   PetscCall(PetscMalloc1(m + 1, &rowidxs));
    3094:   PetscCall(PetscViewerBinaryReadAll(viewer, rowidxs + 1, m, PETSC_DECIDE, M, PETSC_INT));
    3095:   rowidxs[0] = 0;
    3096:   for (i = 0; i < m; i++) rowidxs[i + 1] += rowidxs[i];
    3097:   if (nz != PETSC_INT_MAX) {
    3098:     PetscCallMPI(MPIU_Allreduce(&rowidxs[m], &sum, 1, MPIU_INT, MPI_SUM, PetscObjectComm((PetscObject)viewer)));
    3099:     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);
    3100:   }

    3102:   /* read in column indices and matrix values */
    3103:   PetscCall(PetscMalloc2(rowidxs[m], &colidxs, rowidxs[m], &matvals));
    3104:   PetscCall(PetscViewerBinaryReadAll(viewer, colidxs, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_INT));
    3105:   PetscCall(PetscViewerBinaryReadAll(viewer, matvals, rowidxs[m], PETSC_DETERMINE, PETSC_DETERMINE, PETSC_SCALAR));
    3106:   /* store matrix indices and values */
    3107:   PetscCall(MatMPIAIJSetPreallocationCSR(mat, rowidxs, colidxs, matvals));
    3108:   PetscCall(PetscFree(rowidxs));
    3109:   PetscCall(PetscFree2(colidxs, matvals));
    3110:   PetscFunctionReturn(PETSC_SUCCESS);
    3111: }

    3113: /* Not scalable because of ISAllGather() unless getting all columns. */
    3114: static PetscErrorCode ISGetSeqIS_Private(Mat mat, IS iscol, IS *isseq)
    3115: {
    3116:   IS          iscol_local;
    3117:   PetscBool   isstride;
    3118:   PetscMPIInt gisstride = 0;

    3120:   PetscFunctionBegin;
    3121:   /* check if we are grabbing all columns*/
    3122:   PetscCall(PetscObjectTypeCompare((PetscObject)iscol, ISSTRIDE, &isstride));

    3124:   if (isstride) {
    3125:     PetscInt start, len, mstart, mlen;
    3126:     PetscCall(ISStrideGetInfo(iscol, &start, NULL));
    3127:     PetscCall(ISGetLocalSize(iscol, &len));
    3128:     PetscCall(MatGetOwnershipRangeColumn(mat, &mstart, &mlen));
    3129:     if (mstart == start && mlen - mstart == len) gisstride = 1;
    3130:   }

    3132:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &gisstride, 1, MPI_INT, MPI_MIN, PetscObjectComm((PetscObject)mat)));
    3133:   if (gisstride) {
    3134:     PetscInt N;
    3135:     PetscCall(MatGetSize(mat, NULL, &N));
    3136:     PetscCall(ISCreateStride(PETSC_COMM_SELF, N, 0, 1, &iscol_local));
    3137:     PetscCall(ISSetIdentity(iscol_local));
    3138:     PetscCall(PetscInfo(mat, "Optimizing for obtaining all columns of the matrix; skipping ISAllGather()\n"));
    3139:   } else {
    3140:     PetscInt cbs;
    3141:     PetscCall(ISGetBlockSize(iscol, &cbs));
    3142:     PetscCall(ISAllGather(iscol, &iscol_local));
    3143:     PetscCall(ISSetBlockSize(iscol_local, cbs));
    3144:   }

    3146:   *isseq = iscol_local;
    3147:   PetscFunctionReturn(PETSC_SUCCESS);
    3148: }

    3150: /*
    3151:  Used by MatCreateSubMatrix_MPIAIJ_SameRowColDist() to avoid ISAllGather() and global size of iscol_local
    3152:  (see MatCreateSubMatrix_MPIAIJ_nonscalable)

    3154:  Input Parameters:
    3155: +   mat - matrix
    3156: .   isrow - parallel row index set; its local indices are a subset of local columns of `mat`,
    3157:            i.e., mat->rstart <= isrow[i] < mat->rend
    3158: -   iscol - parallel column index set; its local indices are a subset of local columns of `mat`,
    3159:            i.e., mat->cstart <= iscol[i] < mat->cend

    3161:  Output Parameters:
    3162: +   isrow_d - sequential row index set for retrieving mat->A
    3163: .   iscol_d - sequential  column index set for retrieving mat->A
    3164: .   iscol_o - sequential column index set for retrieving mat->B
    3165: -   garray - column map; garray[i] indicates global location of iscol_o[i] in `iscol`
    3166:  */
    3167: static PetscErrorCode ISGetSeqIS_SameColDist_Private(Mat mat, IS isrow, IS iscol, IS *isrow_d, IS *iscol_d, IS *iscol_o, const PetscInt *garray[])
    3168: {
    3169:   Vec             x, cmap;
    3170:   const PetscInt *is_idx;
    3171:   PetscScalar    *xarray, *cmaparray;
    3172:   PetscInt        ncols, isstart, *idx, m, rstart, *cmap1, count;
    3173:   Mat_MPIAIJ     *a    = (Mat_MPIAIJ *)mat->data;
    3174:   Mat             B    = a->B;
    3175:   Vec             lvec = a->lvec, lcmap;
    3176:   PetscInt        i, cstart, cend, Bn = B->cmap->N;
    3177:   MPI_Comm        comm;
    3178:   VecScatter      Mvctx = a->Mvctx;

    3180:   PetscFunctionBegin;
    3181:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3182:   PetscCall(ISGetLocalSize(iscol, &ncols));

    3184:   /* (1) iscol is a sub-column vector of mat, pad it with '-1.' to form a full vector x */
    3185:   PetscCall(MatCreateVecs(mat, &x, NULL));
    3186:   PetscCall(VecSet(x, -1.0));
    3187:   PetscCall(VecDuplicate(x, &cmap));
    3188:   PetscCall(VecSet(cmap, -1.0));

    3190:   /* Get start indices */
    3191:   PetscCallMPI(MPI_Scan(&ncols, &isstart, 1, MPIU_INT, MPI_SUM, comm));
    3192:   isstart -= ncols;
    3193:   PetscCall(MatGetOwnershipRangeColumn(mat, &cstart, &cend));

    3195:   PetscCall(ISGetIndices(iscol, &is_idx));
    3196:   PetscCall(VecGetArray(x, &xarray));
    3197:   PetscCall(VecGetArray(cmap, &cmaparray));
    3198:   PetscCall(PetscMalloc1(ncols, &idx));
    3199:   for (i = 0; i < ncols; i++) {
    3200:     xarray[is_idx[i] - cstart]    = (PetscScalar)is_idx[i];
    3201:     cmaparray[is_idx[i] - cstart] = i + isstart;        /* global index of iscol[i] */
    3202:     idx[i]                        = is_idx[i] - cstart; /* local index of iscol[i]  */
    3203:   }
    3204:   PetscCall(VecRestoreArray(x, &xarray));
    3205:   PetscCall(VecRestoreArray(cmap, &cmaparray));
    3206:   PetscCall(ISRestoreIndices(iscol, &is_idx));

    3208:   /* Get iscol_d */
    3209:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, iscol_d));
    3210:   PetscCall(ISGetBlockSize(iscol, &i));
    3211:   PetscCall(ISSetBlockSize(*iscol_d, i));

    3213:   /* Get isrow_d */
    3214:   PetscCall(ISGetLocalSize(isrow, &m));
    3215:   rstart = mat->rmap->rstart;
    3216:   PetscCall(PetscMalloc1(m, &idx));
    3217:   PetscCall(ISGetIndices(isrow, &is_idx));
    3218:   for (i = 0; i < m; i++) idx[i] = is_idx[i] - rstart;
    3219:   PetscCall(ISRestoreIndices(isrow, &is_idx));

    3221:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, m, idx, PETSC_OWN_POINTER, isrow_d));
    3222:   PetscCall(ISGetBlockSize(isrow, &i));
    3223:   PetscCall(ISSetBlockSize(*isrow_d, i));

    3225:   /* (2) Scatter x and cmap using aij->Mvctx to get their off-process portions (see MatMult_MPIAIJ) */
    3226:   PetscCall(VecScatterBegin(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));
    3227:   PetscCall(VecScatterEnd(Mvctx, x, lvec, INSERT_VALUES, SCATTER_FORWARD));

    3229:   PetscCall(VecDuplicate(lvec, &lcmap));

    3231:   PetscCall(VecScatterBegin(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));
    3232:   PetscCall(VecScatterEnd(Mvctx, cmap, lcmap, INSERT_VALUES, SCATTER_FORWARD));

    3234:   /* (3) create sequential iscol_o (a subset of iscol) and isgarray */
    3235:   /* off-process column indices */
    3236:   count = 0;
    3237:   PetscCall(PetscMalloc1(Bn, &idx));
    3238:   PetscCall(PetscMalloc1(Bn, &cmap1));

    3240:   PetscCall(VecGetArray(lvec, &xarray));
    3241:   PetscCall(VecGetArray(lcmap, &cmaparray));
    3242:   for (i = 0; i < Bn; i++) {
    3243:     if (PetscRealPart(xarray[i]) > -1.0) {
    3244:       idx[count]   = i;                                     /* local column index in off-diagonal part B */
    3245:       cmap1[count] = (PetscInt)PetscRealPart(cmaparray[i]); /* column index in submat */
    3246:       count++;
    3247:     }
    3248:   }
    3249:   PetscCall(VecRestoreArray(lvec, &xarray));
    3250:   PetscCall(VecRestoreArray(lcmap, &cmaparray));

    3252:   PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_COPY_VALUES, iscol_o));
    3253:   /* cannot ensure iscol_o has same blocksize as iscol! */

    3255:   PetscCall(PetscFree(idx));
    3256:   *garray = cmap1;

    3258:   PetscCall(VecDestroy(&x));
    3259:   PetscCall(VecDestroy(&cmap));
    3260:   PetscCall(VecDestroy(&lcmap));
    3261:   PetscFunctionReturn(PETSC_SUCCESS);
    3262: }

    3264: /* isrow and iscol have same processor distribution as mat, output *submat is a submatrix of local mat */
    3265: PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowColDist(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *submat)
    3266: {
    3267:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)mat->data, *asub;
    3268:   Mat         M = NULL;
    3269:   MPI_Comm    comm;
    3270:   IS          iscol_d, isrow_d, iscol_o;
    3271:   Mat         Asub = NULL, Bsub = NULL;
    3272:   PetscInt    n;

    3274:   PetscFunctionBegin;
    3275:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));

    3277:   if (call == MAT_REUSE_MATRIX) {
    3278:     /* Retrieve isrow_d, iscol_d and iscol_o from submat */
    3279:     PetscCall(PetscObjectQuery((PetscObject)*submat, "isrow_d", (PetscObject *)&isrow_d));
    3280:     PetscCheck(isrow_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "isrow_d passed in was not used before, cannot reuse");

    3282:     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_d", (PetscObject *)&iscol_d));
    3283:     PetscCheck(iscol_d, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_d passed in was not used before, cannot reuse");

    3285:     PetscCall(PetscObjectQuery((PetscObject)*submat, "iscol_o", (PetscObject *)&iscol_o));
    3286:     PetscCheck(iscol_o, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "iscol_o passed in was not used before, cannot reuse");

    3288:     /* Update diagonal and off-diagonal portions of submat */
    3289:     asub = (Mat_MPIAIJ *)(*submat)->data;
    3290:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->A));
    3291:     PetscCall(ISGetLocalSize(iscol_o, &n));
    3292:     if (n) PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_REUSE_MATRIX, &asub->B));
    3293:     PetscCall(MatAssemblyBegin(*submat, MAT_FINAL_ASSEMBLY));
    3294:     PetscCall(MatAssemblyEnd(*submat, MAT_FINAL_ASSEMBLY));

    3296:   } else { /* call == MAT_INITIAL_MATRIX) */
    3297:     const PetscInt *garray;
    3298:     PetscInt        BsubN;

    3300:     /* Create isrow_d, iscol_d, iscol_o and isgarray (replace isgarray with array?) */
    3301:     PetscCall(ISGetSeqIS_SameColDist_Private(mat, isrow, iscol, &isrow_d, &iscol_d, &iscol_o, &garray));

    3303:     /* Create local submatrices Asub and Bsub */
    3304:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->A, isrow_d, iscol_d, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Asub));
    3305:     PetscCall(MatCreateSubMatrix_SeqAIJ(a->B, isrow_d, iscol_o, PETSC_DECIDE, MAT_INITIAL_MATRIX, &Bsub));

    3307:     /* Create submatrix M */
    3308:     PetscCall(MatCreateMPIAIJWithSeqAIJ(comm, Asub, Bsub, garray, &M));

    3310:     /* If Bsub has empty columns, compress iscol_o such that it will retrieve condensed Bsub from a->B during reuse */
    3311:     asub = (Mat_MPIAIJ *)M->data;

    3313:     PetscCall(ISGetLocalSize(iscol_o, &BsubN));
    3314:     n = asub->B->cmap->N;
    3315:     if (BsubN > n) {
    3316:       /* This case can be tested using ~petsc/src/tao/bound/tutorials/runplate2_3 */
    3317:       const PetscInt *idx;
    3318:       PetscInt        i, j, *idx_new, *subgarray = asub->garray;
    3319:       PetscCall(PetscInfo(M, "submatrix Bn %" PetscInt_FMT " != BsubN %" PetscInt_FMT ", update iscol_o\n", n, BsubN));

    3321:       PetscCall(PetscMalloc1(n, &idx_new));
    3322:       j = 0;
    3323:       PetscCall(ISGetIndices(iscol_o, &idx));
    3324:       for (i = 0; i < n; i++) {
    3325:         if (j >= BsubN) break;
    3326:         while (subgarray[i] > garray[j]) j++;

    3328:         if (subgarray[i] == garray[j]) {
    3329:           idx_new[i] = idx[j++];
    3330:         } 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]);
    3331:       }
    3332:       PetscCall(ISRestoreIndices(iscol_o, &idx));

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

    3337:     } else if (BsubN < n) {
    3338:       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);
    3339:     }

    3341:     PetscCall(PetscFree(garray));
    3342:     *submat = M;

    3344:     /* Save isrow_d, iscol_d and iscol_o used in processor for next request */
    3345:     PetscCall(PetscObjectCompose((PetscObject)M, "isrow_d", (PetscObject)isrow_d));
    3346:     PetscCall(ISDestroy(&isrow_d));

    3348:     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_d", (PetscObject)iscol_d));
    3349:     PetscCall(ISDestroy(&iscol_d));

    3351:     PetscCall(PetscObjectCompose((PetscObject)M, "iscol_o", (PetscObject)iscol_o));
    3352:     PetscCall(ISDestroy(&iscol_o));
    3353:   }
    3354:   PetscFunctionReturn(PETSC_SUCCESS);
    3355: }

    3357: PetscErrorCode MatCreateSubMatrix_MPIAIJ(Mat mat, IS isrow, IS iscol, MatReuse call, Mat *newmat)
    3358: {
    3359:   IS        iscol_local = NULL, isrow_d;
    3360:   PetscInt  csize;
    3361:   PetscInt  n, i, j, start, end;
    3362:   PetscBool sameRowDist = PETSC_FALSE, sameDist[2], tsameDist[2];
    3363:   MPI_Comm  comm;

    3365:   PetscFunctionBegin;
    3366:   /* If isrow has same processor distribution as mat,
    3367:      call MatCreateSubMatrix_MPIAIJ_SameRowDist() to avoid using a hash table with global size of iscol */
    3368:   if (call == MAT_REUSE_MATRIX) {
    3369:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "isrow_d", (PetscObject *)&isrow_d));
    3370:     if (isrow_d) {
    3371:       sameRowDist  = PETSC_TRUE;
    3372:       tsameDist[1] = PETSC_TRUE; /* sameColDist */
    3373:     } else {
    3374:       PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_local));
    3375:       if (iscol_local) {
    3376:         sameRowDist  = PETSC_TRUE;
    3377:         tsameDist[1] = PETSC_FALSE; /* !sameColDist */
    3378:       }
    3379:     }
    3380:   } else {
    3381:     /* Check if isrow has same processor distribution as mat */
    3382:     sameDist[0] = PETSC_FALSE;
    3383:     PetscCall(ISGetLocalSize(isrow, &n));
    3384:     if (!n) {
    3385:       sameDist[0] = PETSC_TRUE;
    3386:     } else {
    3387:       PetscCall(ISGetMinMax(isrow, &i, &j));
    3388:       PetscCall(MatGetOwnershipRange(mat, &start, &end));
    3389:       if (i >= start && j < end) sameDist[0] = PETSC_TRUE;
    3390:     }

    3392:     /* Check if iscol has same processor distribution as mat */
    3393:     sameDist[1] = PETSC_FALSE;
    3394:     PetscCall(ISGetLocalSize(iscol, &n));
    3395:     if (!n) {
    3396:       sameDist[1] = PETSC_TRUE;
    3397:     } else {
    3398:       PetscCall(ISGetMinMax(iscol, &i, &j));
    3399:       PetscCall(MatGetOwnershipRangeColumn(mat, &start, &end));
    3400:       if (i >= start && j < end) sameDist[1] = PETSC_TRUE;
    3401:     }

    3403:     PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3404:     PetscCallMPI(MPIU_Allreduce(&sameDist, &tsameDist, 2, MPIU_BOOL, MPI_LAND, comm));
    3405:     sameRowDist = tsameDist[0];
    3406:   }

    3408:   if (sameRowDist) {
    3409:     if (tsameDist[1]) { /* sameRowDist & sameColDist */
    3410:       /* isrow and iscol have same processor distribution as mat */
    3411:       PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowColDist(mat, isrow, iscol, call, newmat));
    3412:       PetscFunctionReturn(PETSC_SUCCESS);
    3413:     } else { /* sameRowDist */
    3414:       /* isrow has same processor distribution as mat */
    3415:       if (call == MAT_INITIAL_MATRIX) {
    3416:         PetscBool sorted;
    3417:         PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
    3418:         PetscCall(ISGetLocalSize(iscol_local, &n)); /* local size of iscol_local = global columns of newmat */
    3419:         PetscCall(ISGetSize(iscol, &i));
    3420:         PetscCheck(n == i, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "n %" PetscInt_FMT " != size of iscol %" PetscInt_FMT, n, i);

    3422:         PetscCall(ISSorted(iscol_local, &sorted));
    3423:         if (sorted) {
    3424:           /* MatCreateSubMatrix_MPIAIJ_SameRowDist() requires iscol_local be sorted; it can have duplicate indices */
    3425:           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, iscol_local, MAT_INITIAL_MATRIX, newmat));
    3426:           PetscFunctionReturn(PETSC_SUCCESS);
    3427:         }
    3428:       } else { /* call == MAT_REUSE_MATRIX */
    3429:         IS iscol_sub;
    3430:         PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
    3431:         if (iscol_sub) {
    3432:           PetscCall(MatCreateSubMatrix_MPIAIJ_SameRowDist(mat, isrow, iscol, NULL, call, newmat));
    3433:           PetscFunctionReturn(PETSC_SUCCESS);
    3434:         }
    3435:       }
    3436:     }
    3437:   }

    3439:   /* General case: iscol -> iscol_local which has global size of iscol */
    3440:   if (call == MAT_REUSE_MATRIX) {
    3441:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "ISAllGather", (PetscObject *)&iscol_local));
    3442:     PetscCheck(iscol_local, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    3443:   } else {
    3444:     if (!iscol_local) PetscCall(ISGetSeqIS_Private(mat, iscol, &iscol_local));
    3445:   }

    3447:   PetscCall(ISGetLocalSize(iscol, &csize));
    3448:   PetscCall(MatCreateSubMatrix_MPIAIJ_nonscalable(mat, isrow, iscol_local, csize, call, newmat));

    3450:   if (call == MAT_INITIAL_MATRIX) {
    3451:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    3452:     PetscCall(ISDestroy(&iscol_local));
    3453:   }
    3454:   PetscFunctionReturn(PETSC_SUCCESS);
    3455: }

    3457: /*@C
    3458:   MatCreateMPIAIJWithSeqAIJ - creates a `MATMPIAIJ` matrix using `MATSEQAIJ` matrices that contain the "diagonal"
    3459:   and "off-diagonal" part of the matrix in CSR format.

    3461:   Collective

    3463:   Input Parameters:
    3464: + comm   - MPI communicator
    3465: . A      - "diagonal" portion of matrix
    3466: . B      - "off-diagonal" portion of matrix, may have empty columns, will be destroyed by this routine
    3467: - garray - global index of `B` columns

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

    3472:   Level: advanced

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

    3477:   `A` becomes part of output mat, `B` is destroyed by this routine. The user cannot use `A` and `B` anymore.

    3479: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MATSEQAIJ`, `MatCreateMPIAIJWithSplitArrays()`
    3480: @*/
    3481: PetscErrorCode MatCreateMPIAIJWithSeqAIJ(MPI_Comm comm, Mat A, Mat B, const PetscInt garray[], Mat *mat)
    3482: {
    3483:   Mat_MPIAIJ        *maij;
    3484:   Mat_SeqAIJ        *b  = (Mat_SeqAIJ *)B->data, *bnew;
    3485:   PetscInt          *oi = b->i, *oj = b->j, i, nz, col;
    3486:   const PetscScalar *oa;
    3487:   Mat                Bnew;
    3488:   PetscInt           m, n, N;
    3489:   MatType            mpi_mat_type;

    3491:   PetscFunctionBegin;
    3492:   PetscCall(MatCreate(comm, mat));
    3493:   PetscCall(MatGetSize(A, &m, &n));
    3494:   PetscCheck(m == B->rmap->N, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Am %" PetscInt_FMT " != Bm %" PetscInt_FMT, m, B->rmap->N);
    3495:   PetscCheck(PetscAbs(A->rmap->bs) == PetscAbs(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);
    3496:   /* remove check below; When B is created using iscol_o from ISGetSeqIS_SameColDist_Private(), its bs may not be same as A */
    3497:   /* PetscCheck(A->cmap->bs == B->cmap->bs,PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"A column bs %" PetscInt_FMT " != B column bs %" PetscInt_FMT,A->cmap->bs,B->cmap->bs); */

    3499:   /* Get global columns of mat */
    3500:   PetscCallMPI(MPIU_Allreduce(&n, &N, 1, MPIU_INT, MPI_SUM, comm));

    3502:   PetscCall(MatSetSizes(*mat, m, n, PETSC_DECIDE, N));
    3503:   /* Determine the type of MPI matrix that should be created from the type of matrix A, which holds the "diagonal" portion. */
    3504:   PetscCall(MatGetMPIMatType_Private(A, &mpi_mat_type));
    3505:   PetscCall(MatSetType(*mat, mpi_mat_type));

    3507:   if (A->rmap->bs > 1 || A->cmap->bs > 1) PetscCall(MatSetBlockSizes(*mat, A->rmap->bs, A->cmap->bs));
    3508:   maij = (Mat_MPIAIJ *)(*mat)->data;

    3510:   (*mat)->preallocated = PETSC_TRUE;

    3512:   PetscCall(PetscLayoutSetUp((*mat)->rmap));
    3513:   PetscCall(PetscLayoutSetUp((*mat)->cmap));

    3515:   /* Set A as diagonal portion of *mat */
    3516:   maij->A = A;

    3518:   nz = oi[m];
    3519:   for (i = 0; i < nz; i++) {
    3520:     col   = oj[i];
    3521:     oj[i] = garray[col];
    3522:   }

    3524:   /* Set Bnew as off-diagonal portion of *mat */
    3525:   PetscCall(MatSeqAIJGetArrayRead(B, &oa));
    3526:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, N, oi, oj, (PetscScalar *)oa, &Bnew));
    3527:   PetscCall(MatSeqAIJRestoreArrayRead(B, &oa));
    3528:   bnew        = (Mat_SeqAIJ *)Bnew->data;
    3529:   bnew->maxnz = b->maxnz; /* allocated nonzeros of B */
    3530:   maij->B     = Bnew;

    3532:   PetscCheck(B->rmap->N == Bnew->rmap->N, PETSC_COMM_SELF, PETSC_ERR_PLIB, "BN %" PetscInt_FMT " != BnewN %" PetscInt_FMT, B->rmap->N, Bnew->rmap->N);

    3534:   b->free_a  = PETSC_FALSE;
    3535:   b->free_ij = PETSC_FALSE;
    3536:   PetscCall(MatDestroy(&B));

    3538:   bnew->free_a  = PETSC_TRUE;
    3539:   bnew->free_ij = PETSC_TRUE;

    3541:   /* condense columns of maij->B */
    3542:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    3543:   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
    3544:   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
    3545:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    3546:   PetscCall(MatSetOption(*mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    3547:   PetscFunctionReturn(PETSC_SUCCESS);
    3548: }

    3550: extern PetscErrorCode MatCreateSubMatrices_MPIAIJ_SingleIS_Local(Mat, PetscInt, const IS[], const IS[], MatReuse, PetscBool, Mat *);

    3552: PetscErrorCode MatCreateSubMatrix_MPIAIJ_SameRowDist(Mat mat, IS isrow, IS iscol, IS iscol_local, MatReuse call, Mat *newmat)
    3553: {
    3554:   PetscInt        i, m, n, rstart, row, rend, nz, j, bs, cbs;
    3555:   PetscInt       *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
    3556:   Mat_MPIAIJ     *a = (Mat_MPIAIJ *)mat->data;
    3557:   Mat             M, Msub, B = a->B;
    3558:   MatScalar      *aa;
    3559:   Mat_SeqAIJ     *aij;
    3560:   PetscInt       *garray = a->garray, *colsub, Ncols;
    3561:   PetscInt        count, Bn = B->cmap->N, cstart = mat->cmap->rstart, cend = mat->cmap->rend;
    3562:   IS              iscol_sub, iscmap;
    3563:   const PetscInt *is_idx, *cmap;
    3564:   PetscBool       allcolumns = PETSC_FALSE;
    3565:   MPI_Comm        comm;

    3567:   PetscFunctionBegin;
    3568:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3569:   if (call == MAT_REUSE_MATRIX) {
    3570:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubIScol", (PetscObject *)&iscol_sub));
    3571:     PetscCheck(iscol_sub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "SubIScol passed in was not used before, cannot reuse");
    3572:     PetscCall(ISGetLocalSize(iscol_sub, &count));

    3574:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "Subcmap", (PetscObject *)&iscmap));
    3575:     PetscCheck(iscmap, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Subcmap passed in was not used before, cannot reuse");

    3577:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Msub));
    3578:     PetscCheck(Msub, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");

    3580:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_REUSE_MATRIX, PETSC_FALSE, &Msub));

    3582:   } else { /* call == MAT_INITIAL_MATRIX) */
    3583:     PetscBool flg;

    3585:     PetscCall(ISGetLocalSize(iscol, &n));
    3586:     PetscCall(ISGetSize(iscol, &Ncols));

    3588:     /* (1) iscol -> nonscalable iscol_local */
    3589:     /* Check for special case: each processor gets entire matrix columns */
    3590:     PetscCall(ISIdentity(iscol_local, &flg));
    3591:     if (flg && n == mat->cmap->N) allcolumns = PETSC_TRUE;
    3592:     PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));
    3593:     if (allcolumns) {
    3594:       iscol_sub = iscol_local;
    3595:       PetscCall(PetscObjectReference((PetscObject)iscol_local));
    3596:       PetscCall(ISCreateStride(PETSC_COMM_SELF, n, 0, 1, &iscmap));

    3598:     } else {
    3599:       /* (2) iscol_local -> iscol_sub and iscmap. Implementation below requires iscol_local be sorted, it can have duplicate indices */
    3600:       PetscInt *idx, *cmap1, k;
    3601:       PetscCall(PetscMalloc1(Ncols, &idx));
    3602:       PetscCall(PetscMalloc1(Ncols, &cmap1));
    3603:       PetscCall(ISGetIndices(iscol_local, &is_idx));
    3604:       count = 0;
    3605:       k     = 0;
    3606:       for (i = 0; i < Ncols; i++) {
    3607:         j = is_idx[i];
    3608:         if (j >= cstart && j < cend) {
    3609:           /* diagonal part of mat */
    3610:           idx[count]     = j;
    3611:           cmap1[count++] = i; /* column index in submat */
    3612:         } else if (Bn) {
    3613:           /* off-diagonal part of mat */
    3614:           if (j == garray[k]) {
    3615:             idx[count]     = j;
    3616:             cmap1[count++] = i; /* column index in submat */
    3617:           } else if (j > garray[k]) {
    3618:             while (j > garray[k] && k < Bn - 1) k++;
    3619:             if (j == garray[k]) {
    3620:               idx[count]     = j;
    3621:               cmap1[count++] = i; /* column index in submat */
    3622:             }
    3623:           }
    3624:         }
    3625:       }
    3626:       PetscCall(ISRestoreIndices(iscol_local, &is_idx));

    3628:       PetscCall(ISCreateGeneral(PETSC_COMM_SELF, count, idx, PETSC_OWN_POINTER, &iscol_sub));
    3629:       PetscCall(ISGetBlockSize(iscol, &cbs));
    3630:       PetscCall(ISSetBlockSize(iscol_sub, cbs));

    3632:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)iscol_local), count, cmap1, PETSC_OWN_POINTER, &iscmap));
    3633:     }

    3635:     /* (3) Create sequential Msub */
    3636:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol_sub, MAT_INITIAL_MATRIX, allcolumns, &Msub));
    3637:   }

    3639:   PetscCall(ISGetLocalSize(iscol_sub, &count));
    3640:   aij = (Mat_SeqAIJ *)Msub->data;
    3641:   ii  = aij->i;
    3642:   PetscCall(ISGetIndices(iscmap, &cmap));

    3644:   /*
    3645:       m - number of local rows
    3646:       Ncols - number of columns (same on all processors)
    3647:       rstart - first row in new global matrix generated
    3648:   */
    3649:   PetscCall(MatGetSize(Msub, &m, NULL));

    3651:   if (call == MAT_INITIAL_MATRIX) {
    3652:     /* (4) Create parallel newmat */
    3653:     PetscMPIInt rank, size;
    3654:     PetscInt    csize;

    3656:     PetscCallMPI(MPI_Comm_size(comm, &size));
    3657:     PetscCallMPI(MPI_Comm_rank(comm, &rank));

    3659:     /*
    3660:         Determine the number of non-zeros in the diagonal and off-diagonal
    3661:         portions of the matrix in order to do correct preallocation
    3662:     */

    3664:     /* first get start and end of "diagonal" columns */
    3665:     PetscCall(ISGetLocalSize(iscol, &csize));
    3666:     if (csize == PETSC_DECIDE) {
    3667:       PetscCall(ISGetSize(isrow, &mglobal));
    3668:       if (mglobal == Ncols) { /* square matrix */
    3669:         nlocal = m;
    3670:       } else {
    3671:         nlocal = Ncols / size + ((Ncols % size) > rank);
    3672:       }
    3673:     } else {
    3674:       nlocal = csize;
    3675:     }
    3676:     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    3677:     rstart = rend - nlocal;
    3678:     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);

    3680:     /* next, compute all the lengths */
    3681:     jj = aij->j;
    3682:     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
    3683:     olens = dlens + m;
    3684:     for (i = 0; i < m; i++) {
    3685:       jend = ii[i + 1] - ii[i];
    3686:       olen = 0;
    3687:       dlen = 0;
    3688:       for (j = 0; j < jend; j++) {
    3689:         if (cmap[*jj] < rstart || cmap[*jj] >= rend) olen++;
    3690:         else dlen++;
    3691:         jj++;
    3692:       }
    3693:       olens[i] = olen;
    3694:       dlens[i] = dlen;
    3695:     }

    3697:     PetscCall(ISGetBlockSize(isrow, &bs));
    3698:     PetscCall(ISGetBlockSize(iscol, &cbs));

    3700:     PetscCall(MatCreate(comm, &M));
    3701:     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, Ncols));
    3702:     PetscCall(MatSetBlockSizes(M, bs, cbs));
    3703:     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
    3704:     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
    3705:     PetscCall(PetscFree(dlens));

    3707:   } else { /* call == MAT_REUSE_MATRIX */
    3708:     M = *newmat;
    3709:     PetscCall(MatGetLocalSize(M, &i, NULL));
    3710:     PetscCheck(i == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    3711:     PetscCall(MatZeroEntries(M));
    3712:     /*
    3713:          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
    3714:        rather than the slower MatSetValues().
    3715:     */
    3716:     M->was_assembled = PETSC_TRUE;
    3717:     M->assembled     = PETSC_FALSE;
    3718:   }

    3720:   /* (5) Set values of Msub to *newmat */
    3721:   PetscCall(PetscMalloc1(count, &colsub));
    3722:   PetscCall(MatGetOwnershipRange(M, &rstart, NULL));

    3724:   jj = aij->j;
    3725:   PetscCall(MatSeqAIJGetArrayRead(Msub, (const PetscScalar **)&aa));
    3726:   for (i = 0; i < m; i++) {
    3727:     row = rstart + i;
    3728:     nz  = ii[i + 1] - ii[i];
    3729:     for (j = 0; j < nz; j++) colsub[j] = cmap[jj[j]];
    3730:     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, colsub, aa, INSERT_VALUES));
    3731:     jj += nz;
    3732:     aa += nz;
    3733:   }
    3734:   PetscCall(MatSeqAIJRestoreArrayRead(Msub, (const PetscScalar **)&aa));
    3735:   PetscCall(ISRestoreIndices(iscmap, &cmap));

    3737:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
    3738:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));

    3740:   PetscCall(PetscFree(colsub));

    3742:   /* save Msub, iscol_sub and iscmap used in processor for next request */
    3743:   if (call == MAT_INITIAL_MATRIX) {
    3744:     *newmat = M;
    3745:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "SubMatrix", (PetscObject)Msub));
    3746:     PetscCall(MatDestroy(&Msub));

    3748:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "SubIScol", (PetscObject)iscol_sub));
    3749:     PetscCall(ISDestroy(&iscol_sub));

    3751:     PetscCall(PetscObjectCompose((PetscObject)*newmat, "Subcmap", (PetscObject)iscmap));
    3752:     PetscCall(ISDestroy(&iscmap));

    3754:     if (iscol_local) {
    3755:       PetscCall(PetscObjectCompose((PetscObject)*newmat, "ISAllGather", (PetscObject)iscol_local));
    3756:       PetscCall(ISDestroy(&iscol_local));
    3757:     }
    3758:   }
    3759:   PetscFunctionReturn(PETSC_SUCCESS);
    3760: }

    3762: /*
    3763:     Not great since it makes two copies of the submatrix, first an SeqAIJ
    3764:   in local and then by concatenating the local matrices the end result.
    3765:   Writing it directly would be much like MatCreateSubMatrices_MPIAIJ()

    3767:   This requires a sequential iscol with all indices.
    3768: */
    3769: PetscErrorCode MatCreateSubMatrix_MPIAIJ_nonscalable(Mat mat, IS isrow, IS iscol, PetscInt csize, MatReuse call, Mat *newmat)
    3770: {
    3771:   PetscMPIInt rank, size;
    3772:   PetscInt    i, m, n, rstart, row, rend, nz, *cwork, j, bs, cbs;
    3773:   PetscInt   *ii, *jj, nlocal, *dlens, *olens, dlen, olen, jend, mglobal;
    3774:   Mat         M, Mreuse;
    3775:   MatScalar  *aa, *vwork;
    3776:   MPI_Comm    comm;
    3777:   Mat_SeqAIJ *aij;
    3778:   PetscBool   colflag, allcolumns = PETSC_FALSE;

    3780:   PetscFunctionBegin;
    3781:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    3782:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    3783:   PetscCallMPI(MPI_Comm_size(comm, &size));

    3785:   /* Check for special case: each processor gets entire matrix columns */
    3786:   PetscCall(ISIdentity(iscol, &colflag));
    3787:   PetscCall(ISGetLocalSize(iscol, &n));
    3788:   if (colflag && n == mat->cmap->N) allcolumns = PETSC_TRUE;
    3789:   PetscCallMPI(MPIU_Allreduce(MPI_IN_PLACE, &allcolumns, 1, MPIU_BOOL, MPI_LAND, PetscObjectComm((PetscObject)mat)));

    3791:   if (call == MAT_REUSE_MATRIX) {
    3792:     PetscCall(PetscObjectQuery((PetscObject)*newmat, "SubMatrix", (PetscObject *)&Mreuse));
    3793:     PetscCheck(Mreuse, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Submatrix passed in was not used before, cannot reuse");
    3794:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_REUSE_MATRIX, allcolumns, &Mreuse));
    3795:   } else {
    3796:     PetscCall(MatCreateSubMatrices_MPIAIJ_SingleIS_Local(mat, 1, &isrow, &iscol, MAT_INITIAL_MATRIX, allcolumns, &Mreuse));
    3797:   }

    3799:   /*
    3800:       m - number of local rows
    3801:       n - number of columns (same on all processors)
    3802:       rstart - first row in new global matrix generated
    3803:   */
    3804:   PetscCall(MatGetSize(Mreuse, &m, &n));
    3805:   PetscCall(MatGetBlockSizes(Mreuse, &bs, &cbs));
    3806:   if (call == MAT_INITIAL_MATRIX) {
    3807:     aij = (Mat_SeqAIJ *)Mreuse->data;
    3808:     ii  = aij->i;
    3809:     jj  = aij->j;

    3811:     /*
    3812:         Determine the number of non-zeros in the diagonal and off-diagonal
    3813:         portions of the matrix in order to do correct preallocation
    3814:     */

    3816:     /* first get start and end of "diagonal" columns */
    3817:     if (csize == PETSC_DECIDE) {
    3818:       PetscCall(ISGetSize(isrow, &mglobal));
    3819:       if (mglobal == n) { /* square matrix */
    3820:         nlocal = m;
    3821:       } else {
    3822:         nlocal = n / size + ((n % size) > rank);
    3823:       }
    3824:     } else {
    3825:       nlocal = csize;
    3826:     }
    3827:     PetscCallMPI(MPI_Scan(&nlocal, &rend, 1, MPIU_INT, MPI_SUM, comm));
    3828:     rstart = rend - nlocal;
    3829:     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);

    3831:     /* next, compute all the lengths */
    3832:     PetscCall(PetscMalloc1(2 * m + 1, &dlens));
    3833:     olens = dlens + m;
    3834:     for (i = 0; i < m; i++) {
    3835:       jend = ii[i + 1] - ii[i];
    3836:       olen = 0;
    3837:       dlen = 0;
    3838:       for (j = 0; j < jend; j++) {
    3839:         if (*jj < rstart || *jj >= rend) olen++;
    3840:         else dlen++;
    3841:         jj++;
    3842:       }
    3843:       olens[i] = olen;
    3844:       dlens[i] = dlen;
    3845:     }
    3846:     PetscCall(MatCreate(comm, &M));
    3847:     PetscCall(MatSetSizes(M, m, nlocal, PETSC_DECIDE, n));
    3848:     PetscCall(MatSetBlockSizes(M, bs, cbs));
    3849:     PetscCall(MatSetType(M, ((PetscObject)mat)->type_name));
    3850:     PetscCall(MatMPIAIJSetPreallocation(M, 0, dlens, 0, olens));
    3851:     PetscCall(PetscFree(dlens));
    3852:   } else {
    3853:     PetscInt ml, nl;

    3855:     M = *newmat;
    3856:     PetscCall(MatGetLocalSize(M, &ml, &nl));
    3857:     PetscCheck(ml == m, PETSC_COMM_SELF, PETSC_ERR_ARG_SIZ, "Previous matrix must be same size/layout as request");
    3858:     PetscCall(MatZeroEntries(M));
    3859:     /*
    3860:          The next two lines are needed so we may call MatSetValues_MPIAIJ() below directly,
    3861:        rather than the slower MatSetValues().
    3862:     */
    3863:     M->was_assembled = PETSC_TRUE;
    3864:     M->assembled     = PETSC_FALSE;
    3865:   }
    3866:   PetscCall(MatGetOwnershipRange(M, &rstart, &rend));
    3867:   aij = (Mat_SeqAIJ *)Mreuse->data;
    3868:   ii  = aij->i;
    3869:   jj  = aij->j;

    3871:   /* trigger copy to CPU if needed */
    3872:   PetscCall(MatSeqAIJGetArrayRead(Mreuse, (const PetscScalar **)&aa));
    3873:   for (i = 0; i < m; i++) {
    3874:     row   = rstart + i;
    3875:     nz    = ii[i + 1] - ii[i];
    3876:     cwork = jj;
    3877:     jj    = PetscSafePointerPlusOffset(jj, nz);
    3878:     vwork = aa;
    3879:     aa    = PetscSafePointerPlusOffset(aa, nz);
    3880:     PetscCall(MatSetValues_MPIAIJ(M, 1, &row, nz, cwork, vwork, INSERT_VALUES));
    3881:   }
    3882:   PetscCall(MatSeqAIJRestoreArrayRead(Mreuse, (const PetscScalar **)&aa));

    3884:   PetscCall(MatAssemblyBegin(M, MAT_FINAL_ASSEMBLY));
    3885:   PetscCall(MatAssemblyEnd(M, MAT_FINAL_ASSEMBLY));
    3886:   *newmat = M;

    3888:   /* save submatrix used in processor for next request */
    3889:   if (call == MAT_INITIAL_MATRIX) {
    3890:     PetscCall(PetscObjectCompose((PetscObject)M, "SubMatrix", (PetscObject)Mreuse));
    3891:     PetscCall(MatDestroy(&Mreuse));
    3892:   }
    3893:   PetscFunctionReturn(PETSC_SUCCESS);
    3894: }

    3896: static PetscErrorCode MatMPIAIJSetPreallocationCSR_MPIAIJ(Mat B, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
    3897: {
    3898:   PetscInt        m, cstart, cend, j, nnz, i, d, *ld;
    3899:   PetscInt       *d_nnz, *o_nnz, nnz_max = 0, rstart, ii, irstart;
    3900:   const PetscInt *JJ;
    3901:   PetscBool       nooffprocentries;
    3902:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)B->data;

    3904:   PetscFunctionBegin;
    3905:   PetscCall(PetscLayoutSetUp(B->rmap));
    3906:   PetscCall(PetscLayoutSetUp(B->cmap));
    3907:   m       = B->rmap->n;
    3908:   cstart  = B->cmap->rstart;
    3909:   cend    = B->cmap->rend;
    3910:   rstart  = B->rmap->rstart;
    3911:   irstart = Ii[0];

    3913:   PetscCall(PetscCalloc2(m, &d_nnz, m, &o_nnz));

    3915:   if (PetscDefined(USE_DEBUG)) {
    3916:     for (i = 0; i < m; i++) {
    3917:       nnz = Ii[i + 1] - Ii[i];
    3918:       JJ  = PetscSafePointerPlusOffset(J, Ii[i] - irstart);
    3919:       PetscCheck(nnz >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Local row %" PetscInt_FMT " has a negative %" PetscInt_FMT " number of columns", i, nnz);
    3920:       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]);
    3921:       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);
    3922:     }
    3923:   }

    3925:   for (i = 0; i < m; i++) {
    3926:     nnz     = Ii[i + 1] - Ii[i];
    3927:     JJ      = PetscSafePointerPlusOffset(J, Ii[i] - irstart);
    3928:     nnz_max = PetscMax(nnz_max, nnz);
    3929:     d       = 0;
    3930:     for (j = 0; j < nnz; j++) {
    3931:       if (cstart <= JJ[j] && JJ[j] < cend) d++;
    3932:     }
    3933:     d_nnz[i] = d;
    3934:     o_nnz[i] = nnz - d;
    3935:   }
    3936:   PetscCall(MatMPIAIJSetPreallocation(B, 0, d_nnz, 0, o_nnz));
    3937:   PetscCall(PetscFree2(d_nnz, o_nnz));

    3939:   for (i = 0; i < m; i++) {
    3940:     ii = i + rstart;
    3941:     PetscCall(MatSetValues_MPIAIJ(B, 1, &ii, Ii[i + 1] - Ii[i], PetscSafePointerPlusOffset(J, Ii[i] - irstart), PetscSafePointerPlusOffset(v, Ii[i] - irstart), INSERT_VALUES));
    3942:   }
    3943:   nooffprocentries    = B->nooffprocentries;
    3944:   B->nooffprocentries = PETSC_TRUE;
    3945:   PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
    3946:   PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
    3947:   B->nooffprocentries = nooffprocentries;

    3949:   /* count number of entries below block diagonal */
    3950:   PetscCall(PetscFree(Aij->ld));
    3951:   PetscCall(PetscCalloc1(m, &ld));
    3952:   Aij->ld = ld;
    3953:   for (i = 0; i < m; i++) {
    3954:     nnz = Ii[i + 1] - Ii[i];
    3955:     j   = 0;
    3956:     while (j < nnz && J[j] < cstart) j++;
    3957:     ld[i] = j;
    3958:     if (J) J += nnz;
    3959:   }

    3961:   PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    3962:   PetscFunctionReturn(PETSC_SUCCESS);
    3963: }

    3965: /*@
    3966:   MatMPIAIJSetPreallocationCSR - Allocates memory for a sparse parallel matrix in `MATAIJ` format
    3967:   (the default parallel PETSc format).

    3969:   Collective

    3971:   Input Parameters:
    3972: + B - the matrix
    3973: . i - the indices into `j` for the start of each local row (indices start with zero)
    3974: . j - the column indices for each local row (indices start with zero)
    3975: - v - optional values in the matrix

    3977:   Level: developer

    3979:   Notes:
    3980:   The `i`, `j`, and `v` arrays ARE copied by this routine into the internal format used by PETSc;
    3981:   thus you CANNOT change the matrix entries by changing the values of `v` after you have
    3982:   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

    3984:   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

    3986:   A convenience routine for this functionality is `MatCreateMPIAIJWithArrays()`.

    3988:   You can update the matrix with new numerical values using `MatUpdateMPIAIJWithArrays()` after this call if the column indices in `j` are sorted.

    3990:   If you do **not** use `MatUpdateMPIAIJWithArrays()`, the column indices in `j` do not need to be sorted. If you will use
    3991:   `MatUpdateMPIAIJWithArrays()`, the column indices **must** be sorted.

    3993:   The format which is used for the sparse matrix input, is equivalent to a
    3994:   row-major ordering.. i.e for the following matrix, the input data expected is
    3995:   as shown
    3996: .vb
    3997:         1 0 0
    3998:         2 0 3     P0
    3999:        -------
    4000:         4 5 6     P1

    4002:      Process0 [P0] rows_owned=[0,1]
    4003:         i =  {0,1,3}  [size = nrow+1  = 2+1]
    4004:         j =  {0,0,2}  [size = 3]
    4005:         v =  {1,2,3}  [size = 3]

    4007:      Process1 [P1] rows_owned=[2]
    4008:         i =  {0,3}    [size = nrow+1  = 1+1]
    4009:         j =  {0,1,2}  [size = 3]
    4010:         v =  {4,5,6}  [size = 3]
    4011: .ve

    4013: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatCreateAIJ()`,
    4014:           `MatCreateSeqAIJWithArrays()`, `MatCreateMPIAIJWithSplitArrays()`, `MatCreateMPIAIJWithArrays()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4015: @*/
    4016: PetscErrorCode MatMPIAIJSetPreallocationCSR(Mat B, const PetscInt i[], const PetscInt j[], const PetscScalar v[])
    4017: {
    4018:   PetscFunctionBegin;
    4019:   PetscTryMethod(B, "MatMPIAIJSetPreallocationCSR_C", (Mat, const PetscInt[], const PetscInt[], const PetscScalar[]), (B, i, j, v));
    4020:   PetscFunctionReturn(PETSC_SUCCESS);
    4021: }

    4023: /*@
    4024:   MatMPIAIJSetPreallocation - Preallocates memory for a sparse parallel matrix in `MATMPIAIJ` format
    4025:   (the default parallel PETSc format).  For good matrix assembly performance
    4026:   the user should preallocate the matrix storage by setting the parameters
    4027:   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).

    4029:   Collective

    4031:   Input Parameters:
    4032: + B     - the matrix
    4033: . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
    4034:            (same value is used for all local rows)
    4035: . d_nnz - array containing the number of nonzeros in the various rows of the
    4036:            DIAGONAL portion of the local submatrix (possibly different for each row)
    4037:            or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `d_nz` is used to specify the nonzero structure.
    4038:            The size of this array is equal to the number of local rows, i.e 'm'.
    4039:            For matrices that will be factored, you must leave room for (and set)
    4040:            the diagonal entry even if it is zero.
    4041: . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
    4042:            submatrix (same value is used for all local rows).
    4043: - o_nnz - array containing the number of nonzeros in the various rows of the
    4044:            OFF-DIAGONAL portion of the local submatrix (possibly different for
    4045:            each row) or `NULL` (`PETSC_NULL_INTEGER` in Fortran), if `o_nz` is used to specify the nonzero
    4046:            structure. The size of this array is equal to the number
    4047:            of local rows, i.e 'm'.

    4049:   Example Usage:
    4050:   Consider the following 8x8 matrix with 34 non-zero values, that is
    4051:   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
    4052:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    4053:   as follows

    4055: .vb
    4056:             1  2  0  |  0  3  0  |  0  4
    4057:     Proc0   0  5  6  |  7  0  0  |  8  0
    4058:             9  0 10  | 11  0  0  | 12  0
    4059:     -------------------------------------
    4060:            13  0 14  | 15 16 17  |  0  0
    4061:     Proc1   0 18  0  | 19 20 21  |  0  0
    4062:             0  0  0  | 22 23  0  | 24  0
    4063:     -------------------------------------
    4064:     Proc2  25 26 27  |  0  0 28  | 29  0
    4065:            30  0  0  | 31 32 33  |  0 34
    4066: .ve

    4068:   This can be represented as a collection of submatrices as
    4069: .vb
    4070:       A B C
    4071:       D E F
    4072:       G H I
    4073: .ve

    4075:   Where the submatrices A,B,C are owned by proc0, D,E,F are
    4076:   owned by proc1, G,H,I are owned by proc2.

    4078:   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4079:   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4080:   The 'M','N' parameters are 8,8, and have the same values on all procs.

    4082:   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
    4083:   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
    4084:   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
    4085:   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
    4086:   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
    4087:   matrix, and [DF] as another `MATSEQAIJ` matrix.

    4089:   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
    4090:   allocated for every row of the local DIAGONAL submatrix, and `o_nz`
    4091:   storage locations are allocated for every row of the OFF-DIAGONAL submatrix.
    4092:   One way to choose `d_nz` and `o_nz` is to use the maximum number of nonzeros over
    4093:   the local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
    4094:   In this case, the values of `d_nz`, `o_nz` are
    4095: .vb
    4096:      proc0  dnz = 2, o_nz = 2
    4097:      proc1  dnz = 3, o_nz = 2
    4098:      proc2  dnz = 1, o_nz = 4
    4099: .ve
    4100:   We are allocating `m`*(`d_nz`+`o_nz`) storage locations for every proc. This
    4101:   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
    4102:   for proc3. i.e we are using 12+15+10=37 storage locations to store
    4103:   34 values.

    4105:   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
    4106:   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
    4107:   In the above case the values for `d_nnz`, `o_nnz` are
    4108: .vb
    4109:      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
    4110:      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
    4111:      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
    4112: .ve
    4113:   Here the space allocated is sum of all the above values i.e 34, and
    4114:   hence pre-allocation is perfect.

    4116:   Level: intermediate

    4118:   Notes:
    4119:   If the *_nnz parameter is given then the *_nz parameter is ignored

    4121:   The `MATAIJ` format, also called compressed row storage (CSR), is compatible with standard Fortran
    4122:   storage.  The stored row and column indices begin with zero.
    4123:   See [Sparse Matrices](sec_matsparse) for details.

    4125:   The parallel matrix is partitioned such that the first m0 rows belong to
    4126:   process 0, the next m1 rows belong to process 1, the next m2 rows belong
    4127:   to process 2 etc.. where m0,m1,m2... are the input parameter 'm'.

    4129:   The DIAGONAL portion of the local submatrix of a processor can be defined
    4130:   as the submatrix which is obtained by extraction the part corresponding to
    4131:   the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the
    4132:   first row that belongs to the processor, r2 is the last row belonging to
    4133:   the this processor, and c1-c2 is range of indices of the local part of a
    4134:   vector suitable for applying the matrix to.  This is an mxn matrix.  In the
    4135:   common case of a square matrix, the row and column ranges are the same and
    4136:   the DIAGONAL part is also square. The remaining portion of the local
    4137:   submatrix (mxN) constitute the OFF-DIAGONAL portion.

    4139:   If `o_nnz` and `d_nnz` are specified, then `o_nz` and `d_nz` are ignored.

    4141:   You can call `MatGetInfo()` to get information on how effective the preallocation was;
    4142:   for example the fields mallocs,nz_allocated,nz_used,nz_unneeded;
    4143:   You can also run with the option `-info` and look for messages with the string
    4144:   malloc in them to see if additional memory allocation was needed.

    4146: .seealso: [](ch_matrices), `Mat`, [Sparse Matrices](sec_matsparse), `MATMPIAIJ`, `MATAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatCreateAIJ()`, `MatMPIAIJSetPreallocationCSR()`,
    4147:           `MatGetInfo()`, `PetscSplitOwnership()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4148: @*/
    4149: PetscErrorCode MatMPIAIJSetPreallocation(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])
    4150: {
    4151:   PetscFunctionBegin;
    4154:   PetscTryMethod(B, "MatMPIAIJSetPreallocation_C", (Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[]), (B, d_nz, d_nnz, o_nz, o_nnz));
    4155:   PetscFunctionReturn(PETSC_SUCCESS);
    4156: }

    4158: /*@
    4159:   MatCreateMPIAIJWithArrays - creates a `MATMPIAIJ` matrix using arrays that contain in standard
    4160:   CSR format for the local rows.

    4162:   Collective

    4164:   Input Parameters:
    4165: + comm - MPI communicator
    4166: . m    - number of local rows (Cannot be `PETSC_DECIDE`)
    4167: . n    - This value should be the same as the local size used in creating the
    4168:          x vector for the matrix-vector product $ y = Ax$. (or `PETSC_DECIDE` to have
    4169:          calculated if `N` is given) For square matrices n is almost always `m`.
    4170: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    4171: . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    4172: . 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
    4173: . j    - global column indices
    4174: - a    - optional matrix values

    4176:   Output Parameter:
    4177: . mat - the matrix

    4179:   Level: intermediate

    4181:   Notes:
    4182:   The `i`, `j`, and `a` arrays ARE copied by this routine into the internal format used by PETSc;
    4183:   thus you CANNOT change the matrix entries by changing the values of `a[]` after you have
    4184:   called this routine. Use `MatCreateMPIAIJWithSplitArrays()` to avoid needing to copy the arrays.

    4186:   The `i` and `j` indices are 0 based, and `i` indices are indices corresponding to the local `j` array.

    4188:   Once you have created the matrix you can update it with new numerical values using `MatUpdateMPIAIJWithArray()`

    4190:   If you do **not** use `MatUpdateMPIAIJWithArray()`, the column indices in `j` do not need to be sorted. If you will use
    4191:   `MatUpdateMPIAIJWithArrays()`, the column indices **must** be sorted.

    4193:   The format which is used for the sparse matrix input, is equivalent to a
    4194:   row-major ordering, i.e., for the following matrix, the input data expected is
    4195:   as shown
    4196: .vb
    4197:         1 0 0
    4198:         2 0 3     P0
    4199:        -------
    4200:         4 5 6     P1

    4202:      Process0 [P0] rows_owned=[0,1]
    4203:         i =  {0,1,3}  [size = nrow+1  = 2+1]
    4204:         j =  {0,0,2}  [size = 3]
    4205:         v =  {1,2,3}  [size = 3]

    4207:      Process1 [P1] rows_owned=[2]
    4208:         i =  {0,3}    [size = nrow+1  = 1+1]
    4209:         j =  {0,1,2}  [size = 3]
    4210:         v =  {4,5,6}  [size = 3]
    4211: .ve

    4213: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4214:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4215: @*/
    4216: PetscErrorCode MatCreateMPIAIJWithArrays(MPI_Comm comm, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt i[], const PetscInt j[], const PetscScalar a[], Mat *mat)
    4217: {
    4218:   PetscFunctionBegin;
    4219:   PetscCheck(!i || !i[0], PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    4220:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    4221:   PetscCall(MatCreate(comm, mat));
    4222:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    4223:   /* PetscCall(MatSetBlockSizes(M,bs,cbs)); */
    4224:   PetscCall(MatSetType(*mat, MATMPIAIJ));
    4225:   PetscCall(MatMPIAIJSetPreallocationCSR(*mat, i, j, a));
    4226:   PetscFunctionReturn(PETSC_SUCCESS);
    4227: }

    4229: /*@
    4230:   MatUpdateMPIAIJWithArrays - updates a `MATMPIAIJ` matrix using arrays that contain in standard
    4231:   CSR format for the local rows. Only the numerical values are updated the other arrays must be identical to what was passed
    4232:   from `MatCreateMPIAIJWithArrays()`

    4234:   Deprecated: Use `MatUpdateMPIAIJWithArray()`

    4236:   Collective

    4238:   Input Parameters:
    4239: + mat - the matrix
    4240: . m   - number of local rows (Cannot be `PETSC_DECIDE`)
    4241: . n   - This value should be the same as the local size used in creating the
    4242:        x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
    4243:        calculated if N is given) For square matrices n is almost always m.
    4244: . M   - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
    4245: . N   - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
    4246: . Ii  - row indices; that is Ii[0] = 0, Ii[row] = Ii[row-1] + number of elements in that row of the matrix
    4247: . J   - column indices
    4248: - v   - matrix values

    4250:   Level: deprecated

    4252: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4253:           `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArray()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4254: @*/
    4255: PetscErrorCode MatUpdateMPIAIJWithArrays(Mat mat, PetscInt m, PetscInt n, PetscInt M, PetscInt N, const PetscInt Ii[], const PetscInt J[], const PetscScalar v[])
    4256: {
    4257:   PetscInt        nnz, i;
    4258:   PetscBool       nooffprocentries;
    4259:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
    4260:   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
    4261:   PetscScalar    *ad, *ao;
    4262:   PetscInt        ldi, Iii, md;
    4263:   const PetscInt *Adi = Ad->i;
    4264:   PetscInt       *ld  = Aij->ld;

    4266:   PetscFunctionBegin;
    4267:   PetscCheck(Ii[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    4268:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    4269:   PetscCheck(m == mat->rmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of rows cannot change from call to MatUpdateMPIAIJWithArrays()");
    4270:   PetscCheck(n == mat->cmap->n, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Local number of columns cannot change from call to MatUpdateMPIAIJWithArrays()");

    4272:   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
    4273:   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));

    4275:   for (i = 0; i < m; i++) {
    4276:     if (PetscDefined(USE_DEBUG)) {
    4277:       for (PetscInt j = Ii[i] + 1; j < Ii[i + 1]; ++j) {
    4278:         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);
    4279:         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);
    4280:       }
    4281:     }
    4282:     nnz = Ii[i + 1] - Ii[i];
    4283:     Iii = Ii[i];
    4284:     ldi = ld[i];
    4285:     md  = Adi[i + 1] - Adi[i];
    4286:     PetscCall(PetscArraycpy(ao, v + Iii, ldi));
    4287:     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
    4288:     PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
    4289:     ad += md;
    4290:     ao += nnz - md;
    4291:   }
    4292:   nooffprocentries      = mat->nooffprocentries;
    4293:   mat->nooffprocentries = PETSC_TRUE;
    4294:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
    4295:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
    4296:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
    4297:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
    4298:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    4299:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    4300:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    4301:   mat->nooffprocentries = nooffprocentries;
    4302:   PetscFunctionReturn(PETSC_SUCCESS);
    4303: }

    4305: /*@
    4306:   MatUpdateMPIAIJWithArray - updates an `MATMPIAIJ` matrix using an array that contains the nonzero values

    4308:   Collective

    4310:   Input Parameters:
    4311: + mat - the matrix
    4312: - v   - matrix values, stored by row

    4314:   Level: intermediate

    4316:   Notes:
    4317:   The matrix must have been obtained with `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()`

    4319:   The column indices in the call to `MatCreateMPIAIJWithArrays()` or `MatMPIAIJSetPreallocationCSR()` must have been sorted for this call to work correctly

    4321: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4322:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithSplitArrays()`, `MatUpdateMPIAIJWithArrays()`, `MatSetPreallocationCOO()`, `MatSetValuesCOO()`
    4323: @*/
    4324: PetscErrorCode MatUpdateMPIAIJWithArray(Mat mat, const PetscScalar v[])
    4325: {
    4326:   PetscInt        nnz, i, m;
    4327:   PetscBool       nooffprocentries;
    4328:   Mat_MPIAIJ     *Aij = (Mat_MPIAIJ *)mat->data;
    4329:   Mat_SeqAIJ     *Ad  = (Mat_SeqAIJ *)Aij->A->data;
    4330:   Mat_SeqAIJ     *Ao  = (Mat_SeqAIJ *)Aij->B->data;
    4331:   PetscScalar    *ad, *ao;
    4332:   const PetscInt *Adi = Ad->i, *Adj = Ao->i;
    4333:   PetscInt        ldi, Iii, md;
    4334:   PetscInt       *ld = Aij->ld;

    4336:   PetscFunctionBegin;
    4337:   m = mat->rmap->n;

    4339:   PetscCall(MatSeqAIJGetArrayWrite(Aij->A, &ad));
    4340:   PetscCall(MatSeqAIJGetArrayWrite(Aij->B, &ao));
    4341:   Iii = 0;
    4342:   for (i = 0; i < m; i++) {
    4343:     nnz = Adi[i + 1] - Adi[i] + Adj[i + 1] - Adj[i];
    4344:     ldi = ld[i];
    4345:     md  = Adi[i + 1] - Adi[i];
    4346:     PetscCall(PetscArraycpy(ad, v + Iii + ldi, md));
    4347:     ad += md;
    4348:     if (ao) {
    4349:       PetscCall(PetscArraycpy(ao, v + Iii, ldi));
    4350:       PetscCall(PetscArraycpy(ao + ldi, v + Iii + ldi + md, nnz - ldi - md));
    4351:       ao += nnz - md;
    4352:     }
    4353:     Iii += nnz;
    4354:   }
    4355:   nooffprocentries      = mat->nooffprocentries;
    4356:   mat->nooffprocentries = PETSC_TRUE;
    4357:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->A, &ad));
    4358:   PetscCall(MatSeqAIJRestoreArrayWrite(Aij->B, &ao));
    4359:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->A));
    4360:   PetscCall(PetscObjectStateIncrease((PetscObject)Aij->B));
    4361:   PetscCall(PetscObjectStateIncrease((PetscObject)mat));
    4362:   PetscCall(MatAssemblyBegin(mat, MAT_FINAL_ASSEMBLY));
    4363:   PetscCall(MatAssemblyEnd(mat, MAT_FINAL_ASSEMBLY));
    4364:   mat->nooffprocentries = nooffprocentries;
    4365:   PetscFunctionReturn(PETSC_SUCCESS);
    4366: }

    4368: /*@
    4369:   MatCreateAIJ - Creates a sparse parallel matrix in `MATAIJ` format
    4370:   (the default parallel PETSc format).  For good matrix assembly performance
    4371:   the user should preallocate the matrix storage by setting the parameters
    4372:   `d_nz` (or `d_nnz`) and `o_nz` (or `o_nnz`).

    4374:   Collective

    4376:   Input Parameters:
    4377: + comm  - MPI communicator
    4378: . m     - number of local rows (or `PETSC_DECIDE` to have calculated if M is given)
    4379:           This value should be the same as the local size used in creating the
    4380:           y vector for the matrix-vector product y = Ax.
    4381: . n     - This value should be the same as the local size used in creating the
    4382:           x vector for the matrix-vector product y = Ax. (or `PETSC_DECIDE` to have
    4383:           calculated if N is given) For square matrices n is almost always m.
    4384: . M     - number of global rows (or `PETSC_DETERMINE` to have calculated if m is given)
    4385: . N     - number of global columns (or `PETSC_DETERMINE` to have calculated if n is given)
    4386: . d_nz  - number of nonzeros per row in DIAGONAL portion of local submatrix
    4387:           (same value is used for all local rows)
    4388: . d_nnz - array containing the number of nonzeros in the various rows of the
    4389:           DIAGONAL portion of the local submatrix (possibly different for each row)
    4390:           or `NULL`, if `d_nz` is used to specify the nonzero structure.
    4391:           The size of this array is equal to the number of local rows, i.e 'm'.
    4392: . o_nz  - number of nonzeros per row in the OFF-DIAGONAL portion of local
    4393:           submatrix (same value is used for all local rows).
    4394: - o_nnz - array containing the number of nonzeros in the various rows of the
    4395:           OFF-DIAGONAL portion of the local submatrix (possibly different for
    4396:           each row) or `NULL`, if `o_nz` is used to specify the nonzero
    4397:           structure. The size of this array is equal to the number
    4398:           of local rows, i.e 'm'.

    4400:   Output Parameter:
    4401: . A - the matrix

    4403:   Options Database Keys:
    4404: + -mat_no_inode                     - Do not use inodes
    4405: . -mat_inode_limit <limit>          - Sets inode limit (max limit=5)
    4406: - -matmult_vecscatter_view <viewer> - View the vecscatter (i.e., communication pattern) used in `MatMult()` of sparse parallel matrices.
    4407:                                       See viewer types in manual of `MatView()`. Of them, ascii_matlab, draw or binary cause the `VecScatter`
    4408:                                       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.

    4410:   Level: intermediate

    4412:   Notes:
    4413:   It is recommended that one use `MatCreateFromOptions()` or the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
    4414:   MatXXXXSetPreallocation() paradigm instead of this routine directly.
    4415:   [MatXXXXSetPreallocation() is, for example, `MatSeqAIJSetPreallocation()`]

    4417:   If the *_nnz parameter is given then the *_nz parameter is ignored

    4419:   The `m`,`n`,`M`,`N` parameters specify the size of the matrix, and its partitioning across
    4420:   processors, while `d_nz`,`d_nnz`,`o_nz`,`o_nnz` parameters specify the approximate
    4421:   storage requirements for this matrix.

    4423:   If `PETSC_DECIDE` or  `PETSC_DETERMINE` is used for a particular argument on one
    4424:   processor than it must be used on all processors that share the object for
    4425:   that argument.

    4427:   If `m` and `n` are not `PETSC_DECIDE`, then the values determine the `PetscLayout` of the matrix and the ranges returned by
    4428:   `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`, and `MatGetOwnershipRangesColumn()`.

    4430:   The user MUST specify either the local or global matrix dimensions
    4431:   (possibly both).

    4433:   The parallel matrix is partitioned across processors such that the
    4434:   first `m0` rows belong to process 0, the next `m1` rows belong to
    4435:   process 1, the next `m2` rows belong to process 2, etc., where
    4436:   `m0`, `m1`, `m2`... are the input parameter `m` on each MPI process. I.e., each MPI process stores
    4437:   values corresponding to [m x N] submatrix.

    4439:   The columns are logically partitioned with the n0 columns belonging
    4440:   to 0th partition, the next n1 columns belonging to the next
    4441:   partition etc.. where n0,n1,n2... are the input parameter 'n'.

    4443:   The DIAGONAL portion of the local submatrix on any given processor
    4444:   is the submatrix corresponding to the rows and columns m,n
    4445:   corresponding to the given processor. i.e diagonal matrix on
    4446:   process 0 is [m0 x n0], diagonal matrix on process 1 is [m1 x n1]
    4447:   etc. The remaining portion of the local submatrix [m x (N-n)]
    4448:   constitute the OFF-DIAGONAL portion. The example below better
    4449:   illustrates this concept. The two matrices, the DIAGONAL portion and
    4450:   the OFF-DIAGONAL portion are each stored as `MATSEQAIJ` matrices.

    4452:   For a square global matrix we define each processor's diagonal portion
    4453:   to be its local rows and the corresponding columns (a square submatrix);
    4454:   each processor's off-diagonal portion encompasses the remainder of the
    4455:   local matrix (a rectangular submatrix).

    4457:   If `o_nnz`, `d_nnz` are specified, then `o_nz`, and `d_nz` are ignored.

    4459:   When calling this routine with a single process communicator, a matrix of
    4460:   type `MATSEQAIJ` is returned.  If a matrix of type `MATMPIAIJ` is desired for this
    4461:   type of communicator, use the construction mechanism
    4462: .vb
    4463:   MatCreate(..., &A);
    4464:   MatSetType(A, MATMPIAIJ);
    4465:   MatSetSizes(A, m, n, M, N);
    4466:   MatMPIAIJSetPreallocation(A, ...);
    4467: .ve

    4469:   By default, this format uses inodes (identical nodes) when possible.
    4470:   We search for consecutive rows with the same nonzero structure, thereby
    4471:   reusing matrix information to achieve increased efficiency.

    4473:   Example Usage:
    4474:   Consider the following 8x8 matrix with 34 non-zero values, that is
    4475:   assembled across 3 processors. Lets assume that proc0 owns 3 rows,
    4476:   proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown
    4477:   as follows

    4479: .vb
    4480:             1  2  0  |  0  3  0  |  0  4
    4481:     Proc0   0  5  6  |  7  0  0  |  8  0
    4482:             9  0 10  | 11  0  0  | 12  0
    4483:     -------------------------------------
    4484:            13  0 14  | 15 16 17  |  0  0
    4485:     Proc1   0 18  0  | 19 20 21  |  0  0
    4486:             0  0  0  | 22 23  0  | 24  0
    4487:     -------------------------------------
    4488:     Proc2  25 26 27  |  0  0 28  | 29  0
    4489:            30  0  0  | 31 32 33  |  0 34
    4490: .ve

    4492:   This can be represented as a collection of submatrices as

    4494: .vb
    4495:       A B C
    4496:       D E F
    4497:       G H I
    4498: .ve

    4500:   Where the submatrices A,B,C are owned by proc0, D,E,F are
    4501:   owned by proc1, G,H,I are owned by proc2.

    4503:   The 'm' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4504:   The 'n' parameters for proc0,proc1,proc2 are 3,3,2 respectively.
    4505:   The 'M','N' parameters are 8,8, and have the same values on all procs.

    4507:   The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are
    4508:   submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices
    4509:   corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively.
    4510:   Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL
    4511:   part as `MATSEQAIJ` matrices. For example, proc1 will store [E] as a `MATSEQAIJ`
    4512:   matrix, and [DF] as another SeqAIJ matrix.

    4514:   When `d_nz`, `o_nz` parameters are specified, `d_nz` storage elements are
    4515:   allocated for every row of the local DIAGONAL submatrix, and `o_nz`
    4516:   storage locations are allocated for every row of the OFF-DIAGONAL submatrix.
    4517:   One way to choose `d_nz` and `o_nz` is to use the maximum number of nonzeros over
    4518:   the local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices.
    4519:   In this case, the values of `d_nz`,`o_nz` are
    4520: .vb
    4521:      proc0  dnz = 2, o_nz = 2
    4522:      proc1  dnz = 3, o_nz = 2
    4523:      proc2  dnz = 1, o_nz = 4
    4524: .ve
    4525:   We are allocating m*(`d_nz`+`o_nz`) storage locations for every proc. This
    4526:   translates to 3*(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10
    4527:   for proc3. i.e we are using 12+15+10=37 storage locations to store
    4528:   34 values.

    4530:   When `d_nnz`, `o_nnz` parameters are specified, the storage is specified
    4531:   for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices.
    4532:   In the above case the values for d_nnz,o_nnz are
    4533: .vb
    4534:      proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
    4535:      proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
    4536:      proc2 d_nnz = [1,1]   and o_nnz = [4,4]
    4537: .ve
    4538:   Here the space allocated is sum of all the above values i.e 34, and
    4539:   hence pre-allocation is perfect.

    4541: .seealso: [](ch_matrices), `Mat`, [Sparse Matrix Creation](sec_matsparse), `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    4542:           `MATMPIAIJ`, `MatCreateMPIAIJWithArrays()`, `MatGetOwnershipRange()`, `MatGetOwnershipRanges()`, `MatGetOwnershipRangeColumn()`,
    4543:           `MatGetOwnershipRangesColumn()`, `PetscLayout`
    4544: @*/
    4545: 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)
    4546: {
    4547:   PetscMPIInt size;

    4549:   PetscFunctionBegin;
    4550:   PetscCall(MatCreate(comm, A));
    4551:   PetscCall(MatSetSizes(*A, m, n, M, N));
    4552:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4553:   if (size > 1) {
    4554:     PetscCall(MatSetType(*A, MATMPIAIJ));
    4555:     PetscCall(MatMPIAIJSetPreallocation(*A, d_nz, d_nnz, o_nz, o_nnz));
    4556:   } else {
    4557:     PetscCall(MatSetType(*A, MATSEQAIJ));
    4558:     PetscCall(MatSeqAIJSetPreallocation(*A, d_nz, d_nnz));
    4559:   }
    4560:   PetscFunctionReturn(PETSC_SUCCESS);
    4561: }

    4563: /*MC
    4564:     MatMPIAIJGetSeqAIJF90 - Returns the local pieces of this distributed matrix

    4566:     Synopsis:
    4567:     MatMPIAIJGetSeqAIJF90(Mat A, Mat Ad, Mat Ao, {PetscInt, pointer :: colmap(:)},integer ierr)

    4569:     Not Collective

    4571:     Input Parameter:
    4572: .   A - the `MATMPIAIJ` matrix

    4574:     Output Parameters:
    4575: +   Ad - the diagonal portion of the matrix
    4576: .   Ao - the off-diagonal portion of the matrix
    4577: .   colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix
    4578: -   ierr - error code

    4580:      Level: advanced

    4582:     Note:
    4583:     Use  `MatMPIAIJRestoreSeqAIJF90()` when you no longer need access to the matrices and `colmap`

    4585: .seealso: [](ch_matrices), `Mat`, [](sec_fortranarrays), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetSeqAIJ()`, `MatMPIAIJRestoreSeqAIJF90()`
    4586: M*/

    4588: /*MC
    4589:     MatMPIAIJRestoreSeqAIJF90 - call after `MatMPIAIJGetSeqAIJF90()` when you no longer need access to the matrices and `colmap`

    4591:     Synopsis:
    4592:     MatMPIAIJRestoreSeqAIJF90(Mat A, Mat Ad, Mat Ao, {PetscInt, pointer :: colmap(:)},integer ierr)

    4594:     Not Collective

    4596:     Input Parameters:
    4597: +   A - the `MATMPIAIJ` matrix
    4598: .   Ad - the diagonal portion of the matrix
    4599: .   Ao - the off-diagonal portion of the matrix
    4600: .   colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix
    4601: -   ierr - error code

    4603:      Level: advanced

    4605: .seealso: [](ch_matrices), `Mat`, [](sec_fortranarrays), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetSeqAIJ()`, `MatMPIAIJGetSeqAIJF90()`
    4606: M*/

    4608: /*@C
    4609:   MatMPIAIJGetSeqAIJ - Returns the local pieces of this distributed matrix

    4611:   Not Collective

    4613:   Input Parameter:
    4614: . A - The `MATMPIAIJ` matrix

    4616:   Output Parameters:
    4617: + Ad     - The local diagonal block as a `MATSEQAIJ` matrix
    4618: . Ao     - The local off-diagonal block as a `MATSEQAIJ` matrix
    4619: - colmap - An array mapping local column numbers of `Ao` to global column numbers of the parallel matrix

    4621:   Level: intermediate

    4623:   Note:
    4624:   The rows in `Ad` and `Ao` are in [0, Nr), where Nr is the number of local rows on this process. The columns
    4625:   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
    4626:   the number of nonzero columns in the local off-diagonal piece of the matrix `A`. The array colmap maps these
    4627:   local column numbers to global column numbers in the original matrix.

    4629:   Fortran Notes:
    4630:   `MatMPIAIJGetSeqAIJ()` Fortran binding is deprecated (since PETSc 3.19), use `MatMPIAIJGetSeqAIJF90()`

    4632: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatMPIAIJGetSeqAIJF90()`, `MatMPIAIJRestoreSeqAIJF90()`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`, `MatCreateAIJ()`, `MATSEQAIJ`
    4633: @*/
    4634: PetscErrorCode MatMPIAIJGetSeqAIJ(Mat A, Mat *Ad, Mat *Ao, const PetscInt *colmap[])
    4635: {
    4636:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    4637:   PetscBool   flg;

    4639:   PetscFunctionBegin;
    4640:   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &flg));
    4641:   PetscCheck(flg, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "This function requires a MATMPIAIJ matrix as input");
    4642:   if (Ad) *Ad = a->A;
    4643:   if (Ao) *Ao = a->B;
    4644:   if (colmap) *colmap = a->garray;
    4645:   PetscFunctionReturn(PETSC_SUCCESS);
    4646: }

    4648: PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm comm, Mat inmat, PetscInt n, MatReuse scall, Mat *outmat)
    4649: {
    4650:   PetscInt     m, N, i, rstart, nnz, Ii;
    4651:   PetscInt    *indx;
    4652:   PetscScalar *values;
    4653:   MatType      rootType;

    4655:   PetscFunctionBegin;
    4656:   PetscCall(MatGetSize(inmat, &m, &N));
    4657:   if (scall == MAT_INITIAL_MATRIX) { /* symbolic phase */
    4658:     PetscInt *dnz, *onz, sum, bs, cbs;

    4660:     if (n == PETSC_DECIDE) PetscCall(PetscSplitOwnership(comm, &n, &N));
    4661:     /* Check sum(n) = N */
    4662:     PetscCallMPI(MPIU_Allreduce(&n, &sum, 1, MPIU_INT, MPI_SUM, comm));
    4663:     PetscCheck(sum == N, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Sum of local columns %" PetscInt_FMT " != global columns %" PetscInt_FMT, sum, N);

    4665:     PetscCallMPI(MPI_Scan(&m, &rstart, 1, MPIU_INT, MPI_SUM, comm));
    4666:     rstart -= m;

    4668:     MatPreallocateBegin(comm, m, n, dnz, onz);
    4669:     for (i = 0; i < m; i++) {
    4670:       PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
    4671:       PetscCall(MatPreallocateSet(i + rstart, nnz, indx, dnz, onz));
    4672:       PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, NULL));
    4673:     }

    4675:     PetscCall(MatCreate(comm, outmat));
    4676:     PetscCall(MatSetSizes(*outmat, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    4677:     PetscCall(MatGetBlockSizes(inmat, &bs, &cbs));
    4678:     PetscCall(MatSetBlockSizes(*outmat, bs, cbs));
    4679:     PetscCall(MatGetRootType_Private(inmat, &rootType));
    4680:     PetscCall(MatSetType(*outmat, rootType));
    4681:     PetscCall(MatSeqAIJSetPreallocation(*outmat, 0, dnz));
    4682:     PetscCall(MatMPIAIJSetPreallocation(*outmat, 0, dnz, 0, onz));
    4683:     MatPreallocateEnd(dnz, onz);
    4684:     PetscCall(MatSetOption(*outmat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    4685:   }

    4687:   /* numeric phase */
    4688:   PetscCall(MatGetOwnershipRange(*outmat, &rstart, NULL));
    4689:   for (i = 0; i < m; i++) {
    4690:     PetscCall(MatGetRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
    4691:     Ii = i + rstart;
    4692:     PetscCall(MatSetValues(*outmat, 1, &Ii, nnz, indx, values, INSERT_VALUES));
    4693:     PetscCall(MatRestoreRow_SeqAIJ(inmat, i, &nnz, &indx, &values));
    4694:   }
    4695:   PetscCall(MatAssemblyBegin(*outmat, MAT_FINAL_ASSEMBLY));
    4696:   PetscCall(MatAssemblyEnd(*outmat, MAT_FINAL_ASSEMBLY));
    4697:   PetscFunctionReturn(PETSC_SUCCESS);
    4698: }

    4700: static PetscErrorCode MatDestroy_MPIAIJ_SeqsToMPI(void *data)
    4701: {
    4702:   Mat_Merge_SeqsToMPI *merge = (Mat_Merge_SeqsToMPI *)data;

    4704:   PetscFunctionBegin;
    4705:   if (!merge) PetscFunctionReturn(PETSC_SUCCESS);
    4706:   PetscCall(PetscFree(merge->id_r));
    4707:   PetscCall(PetscFree(merge->len_s));
    4708:   PetscCall(PetscFree(merge->len_r));
    4709:   PetscCall(PetscFree(merge->bi));
    4710:   PetscCall(PetscFree(merge->bj));
    4711:   PetscCall(PetscFree(merge->buf_ri[0]));
    4712:   PetscCall(PetscFree(merge->buf_ri));
    4713:   PetscCall(PetscFree(merge->buf_rj[0]));
    4714:   PetscCall(PetscFree(merge->buf_rj));
    4715:   PetscCall(PetscFree(merge->coi));
    4716:   PetscCall(PetscFree(merge->coj));
    4717:   PetscCall(PetscFree(merge->owners_co));
    4718:   PetscCall(PetscLayoutDestroy(&merge->rowmap));
    4719:   PetscCall(PetscFree(merge));
    4720:   PetscFunctionReturn(PETSC_SUCCESS);
    4721: }

    4723: #include <../src/mat/utils/freespace.h>
    4724: #include <petscbt.h>

    4726: PetscErrorCode MatCreateMPIAIJSumSeqAIJNumeric(Mat seqmat, Mat mpimat)
    4727: {
    4728:   MPI_Comm             comm;
    4729:   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)seqmat->data;
    4730:   PetscMPIInt          size, rank, taga, *len_s;
    4731:   PetscInt             N = mpimat->cmap->N, i, j, *owners, *ai = a->i, *aj, m;
    4732:   PetscMPIInt          proc, k;
    4733:   PetscInt           **buf_ri, **buf_rj;
    4734:   PetscInt             anzi, *bj_i, *bi, *bj, arow, bnzi, nextaj;
    4735:   PetscInt             nrows, **buf_ri_k, **nextrow, **nextai;
    4736:   MPI_Request         *s_waits, *r_waits;
    4737:   MPI_Status          *status;
    4738:   const MatScalar     *aa, *a_a;
    4739:   MatScalar          **abuf_r, *ba_i;
    4740:   Mat_Merge_SeqsToMPI *merge;
    4741:   PetscContainer       container;

    4743:   PetscFunctionBegin;
    4744:   PetscCall(PetscObjectGetComm((PetscObject)mpimat, &comm));
    4745:   PetscCall(PetscLogEventBegin(MAT_Seqstompinum, seqmat, 0, 0, 0));

    4747:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4748:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    4750:   PetscCall(PetscObjectQuery((PetscObject)mpimat, "MatMergeSeqsToMPI", (PetscObject *)&container));
    4751:   PetscCheck(container, PetscObjectComm((PetscObject)mpimat), PETSC_ERR_PLIB, "Mat not created from MatCreateMPIAIJSumSeqAIJSymbolic");
    4752:   PetscCall(PetscContainerGetPointer(container, (void **)&merge));
    4753:   PetscCall(MatSeqAIJGetArrayRead(seqmat, &a_a));
    4754:   aa = a_a;

    4756:   bi     = merge->bi;
    4757:   bj     = merge->bj;
    4758:   buf_ri = merge->buf_ri;
    4759:   buf_rj = merge->buf_rj;

    4761:   PetscCall(PetscMalloc1(size, &status));
    4762:   owners = merge->rowmap->range;
    4763:   len_s  = merge->len_s;

    4765:   /* send and recv matrix values */
    4766:   PetscCall(PetscObjectGetNewTag((PetscObject)mpimat, &taga));
    4767:   PetscCall(PetscPostIrecvScalar(comm, taga, merge->nrecv, merge->id_r, merge->len_r, &abuf_r, &r_waits));

    4769:   PetscCall(PetscMalloc1(merge->nsend + 1, &s_waits));
    4770:   for (proc = 0, k = 0; proc < size; proc++) {
    4771:     if (!len_s[proc]) continue;
    4772:     i = owners[proc];
    4773:     PetscCallMPI(MPIU_Isend(aa + ai[i], len_s[proc], MPIU_MATSCALAR, proc, taga, comm, s_waits + k));
    4774:     k++;
    4775:   }

    4777:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, r_waits, status));
    4778:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, s_waits, status));
    4779:   PetscCall(PetscFree(status));

    4781:   PetscCall(PetscFree(s_waits));
    4782:   PetscCall(PetscFree(r_waits));

    4784:   /* insert mat values of mpimat */
    4785:   PetscCall(PetscMalloc1(N, &ba_i));
    4786:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));

    4788:   for (k = 0; k < merge->nrecv; k++) {
    4789:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    4790:     nrows       = *buf_ri_k[k];
    4791:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    4792:     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    4793:   }

    4795:   /* set values of ba */
    4796:   m = merge->rowmap->n;
    4797:   for (i = 0; i < m; i++) {
    4798:     arow = owners[rank] + i;
    4799:     bj_i = bj + bi[i]; /* col indices of the i-th row of mpimat */
    4800:     bnzi = bi[i + 1] - bi[i];
    4801:     PetscCall(PetscArrayzero(ba_i, bnzi));

    4803:     /* add local non-zero vals of this proc's seqmat into ba */
    4804:     anzi   = ai[arow + 1] - ai[arow];
    4805:     aj     = a->j + ai[arow];
    4806:     aa     = a_a + ai[arow];
    4807:     nextaj = 0;
    4808:     for (j = 0; nextaj < anzi; j++) {
    4809:       if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
    4810:         ba_i[j] += aa[nextaj++];
    4811:       }
    4812:     }

    4814:     /* add received vals into ba */
    4815:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    4816:       /* i-th row */
    4817:       if (i == *nextrow[k]) {
    4818:         anzi   = *(nextai[k] + 1) - *nextai[k];
    4819:         aj     = buf_rj[k] + *nextai[k];
    4820:         aa     = abuf_r[k] + *nextai[k];
    4821:         nextaj = 0;
    4822:         for (j = 0; nextaj < anzi; j++) {
    4823:           if (*(bj_i + j) == aj[nextaj]) { /* bcol == acol */
    4824:             ba_i[j] += aa[nextaj++];
    4825:           }
    4826:         }
    4827:         nextrow[k]++;
    4828:         nextai[k]++;
    4829:       }
    4830:     }
    4831:     PetscCall(MatSetValues(mpimat, 1, &arow, bnzi, bj_i, ba_i, INSERT_VALUES));
    4832:   }
    4833:   PetscCall(MatSeqAIJRestoreArrayRead(seqmat, &a_a));
    4834:   PetscCall(MatAssemblyBegin(mpimat, MAT_FINAL_ASSEMBLY));
    4835:   PetscCall(MatAssemblyEnd(mpimat, MAT_FINAL_ASSEMBLY));

    4837:   PetscCall(PetscFree(abuf_r[0]));
    4838:   PetscCall(PetscFree(abuf_r));
    4839:   PetscCall(PetscFree(ba_i));
    4840:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));
    4841:   PetscCall(PetscLogEventEnd(MAT_Seqstompinum, seqmat, 0, 0, 0));
    4842:   PetscFunctionReturn(PETSC_SUCCESS);
    4843: }

    4845: PetscErrorCode MatCreateMPIAIJSumSeqAIJSymbolic(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, Mat *mpimat)
    4846: {
    4847:   Mat                  B_mpi;
    4848:   Mat_SeqAIJ          *a = (Mat_SeqAIJ *)seqmat->data;
    4849:   PetscMPIInt          size, rank, tagi, tagj, *len_s, *len_si, *len_ri;
    4850:   PetscInt           **buf_rj, **buf_ri, **buf_ri_k;
    4851:   PetscInt             M = seqmat->rmap->n, N = seqmat->cmap->n, i, *owners, *ai = a->i, *aj = a->j;
    4852:   PetscInt             len, *dnz, *onz, bs, cbs;
    4853:   PetscInt             k, anzi, *bi, *bj, *lnk, nlnk, arow, bnzi;
    4854:   PetscInt             nrows, *buf_s, *buf_si, *buf_si_i, **nextrow, **nextai;
    4855:   MPI_Request         *si_waits, *sj_waits, *ri_waits, *rj_waits;
    4856:   MPI_Status          *status;
    4857:   PetscFreeSpaceList   free_space = NULL, current_space = NULL;
    4858:   PetscBT              lnkbt;
    4859:   Mat_Merge_SeqsToMPI *merge;
    4860:   PetscContainer       container;

    4862:   PetscFunctionBegin;
    4863:   PetscCall(PetscLogEventBegin(MAT_Seqstompisym, seqmat, 0, 0, 0));

    4865:   /* make sure it is a PETSc comm */
    4866:   PetscCall(PetscCommDuplicate(comm, &comm, NULL));
    4867:   PetscCallMPI(MPI_Comm_size(comm, &size));
    4868:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    4870:   PetscCall(PetscNew(&merge));
    4871:   PetscCall(PetscMalloc1(size, &status));

    4873:   /* determine row ownership */
    4874:   PetscCall(PetscLayoutCreate(comm, &merge->rowmap));
    4875:   PetscCall(PetscLayoutSetLocalSize(merge->rowmap, m));
    4876:   PetscCall(PetscLayoutSetSize(merge->rowmap, M));
    4877:   PetscCall(PetscLayoutSetBlockSize(merge->rowmap, 1));
    4878:   PetscCall(PetscLayoutSetUp(merge->rowmap));
    4879:   PetscCall(PetscMalloc1(size, &len_si));
    4880:   PetscCall(PetscMalloc1(size, &merge->len_s));

    4882:   m      = merge->rowmap->n;
    4883:   owners = merge->rowmap->range;

    4885:   /* determine the number of messages to send, their lengths */
    4886:   len_s = merge->len_s;

    4888:   len          = 0; /* length of buf_si[] */
    4889:   merge->nsend = 0;
    4890:   for (PetscMPIInt proc = 0; proc < size; proc++) {
    4891:     len_si[proc] = 0;
    4892:     if (proc == rank) {
    4893:       len_s[proc] = 0;
    4894:     } else {
    4895:       PetscCall(PetscMPIIntCast(owners[proc + 1] - owners[proc] + 1, &len_si[proc]));
    4896:       PetscCall(PetscMPIIntCast(ai[owners[proc + 1]] - ai[owners[proc]], &len_s[proc])); /* num of rows to be sent to [proc] */
    4897:     }
    4898:     if (len_s[proc]) {
    4899:       merge->nsend++;
    4900:       nrows = 0;
    4901:       for (i = owners[proc]; i < owners[proc + 1]; i++) {
    4902:         if (ai[i + 1] > ai[i]) nrows++;
    4903:       }
    4904:       PetscCall(PetscMPIIntCast(2 * (nrows + 1), &len_si[proc]));
    4905:       len += len_si[proc];
    4906:     }
    4907:   }

    4909:   /* determine the number and length of messages to receive for ij-structure */
    4910:   PetscCall(PetscGatherNumberOfMessages(comm, NULL, len_s, &merge->nrecv));
    4911:   PetscCall(PetscGatherMessageLengths2(comm, merge->nsend, merge->nrecv, len_s, len_si, &merge->id_r, &merge->len_r, &len_ri));

    4913:   /* post the Irecv of j-structure */
    4914:   PetscCall(PetscCommGetNewTag(comm, &tagj));
    4915:   PetscCall(PetscPostIrecvInt(comm, tagj, merge->nrecv, merge->id_r, merge->len_r, &buf_rj, &rj_waits));

    4917:   /* post the Isend of j-structure */
    4918:   PetscCall(PetscMalloc2(merge->nsend, &si_waits, merge->nsend, &sj_waits));

    4920:   for (PetscMPIInt proc = 0, k = 0; proc < size; proc++) {
    4921:     if (!len_s[proc]) continue;
    4922:     i = owners[proc];
    4923:     PetscCallMPI(MPIU_Isend(aj + ai[i], len_s[proc], MPIU_INT, proc, tagj, comm, sj_waits + k));
    4924:     k++;
    4925:   }

    4927:   /* receives and sends of j-structure are complete */
    4928:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, rj_waits, status));
    4929:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, sj_waits, status));

    4931:   /* send and recv i-structure */
    4932:   PetscCall(PetscCommGetNewTag(comm, &tagi));
    4933:   PetscCall(PetscPostIrecvInt(comm, tagi, merge->nrecv, merge->id_r, len_ri, &buf_ri, &ri_waits));

    4935:   PetscCall(PetscMalloc1(len + 1, &buf_s));
    4936:   buf_si = buf_s; /* points to the beginning of k-th msg to be sent */
    4937:   for (PetscMPIInt proc = 0, k = 0; proc < size; proc++) {
    4938:     if (!len_s[proc]) continue;
    4939:     /* form outgoing message for i-structure:
    4940:          buf_si[0]:                 nrows to be sent
    4941:                [1:nrows]:           row index (global)
    4942:                [nrows+1:2*nrows+1]: i-structure index
    4943:     */
    4944:     nrows       = len_si[proc] / 2 - 1;
    4945:     buf_si_i    = buf_si + nrows + 1;
    4946:     buf_si[0]   = nrows;
    4947:     buf_si_i[0] = 0;
    4948:     nrows       = 0;
    4949:     for (i = owners[proc]; i < owners[proc + 1]; i++) {
    4950:       anzi = ai[i + 1] - ai[i];
    4951:       if (anzi) {
    4952:         buf_si_i[nrows + 1] = buf_si_i[nrows] + anzi; /* i-structure */
    4953:         buf_si[nrows + 1]   = i - owners[proc];       /* local row index */
    4954:         nrows++;
    4955:       }
    4956:     }
    4957:     PetscCallMPI(MPIU_Isend(buf_si, len_si[proc], MPIU_INT, proc, tagi, comm, si_waits + k));
    4958:     k++;
    4959:     buf_si += len_si[proc];
    4960:   }

    4962:   if (merge->nrecv) PetscCallMPI(MPI_Waitall(merge->nrecv, ri_waits, status));
    4963:   if (merge->nsend) PetscCallMPI(MPI_Waitall(merge->nsend, si_waits, status));

    4965:   PetscCall(PetscInfo(seqmat, "nsend: %d, nrecv: %d\n", merge->nsend, merge->nrecv));
    4966:   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]));

    4968:   PetscCall(PetscFree(len_si));
    4969:   PetscCall(PetscFree(len_ri));
    4970:   PetscCall(PetscFree(rj_waits));
    4971:   PetscCall(PetscFree2(si_waits, sj_waits));
    4972:   PetscCall(PetscFree(ri_waits));
    4973:   PetscCall(PetscFree(buf_s));
    4974:   PetscCall(PetscFree(status));

    4976:   /* compute a local seq matrix in each processor */
    4977:   /* allocate bi array and free space for accumulating nonzero column info */
    4978:   PetscCall(PetscMalloc1(m + 1, &bi));
    4979:   bi[0] = 0;

    4981:   /* create and initialize a linked list */
    4982:   nlnk = N + 1;
    4983:   PetscCall(PetscLLCreate(N, N, nlnk, lnk, lnkbt));

    4985:   /* initial FreeSpace size is 2*(num of local nnz(seqmat)) */
    4986:   len = ai[owners[rank + 1]] - ai[owners[rank]];
    4987:   PetscCall(PetscFreeSpaceGet(PetscIntMultTruncate(2, len) + 1, &free_space));

    4989:   current_space = free_space;

    4991:   /* determine symbolic info for each local row */
    4992:   PetscCall(PetscMalloc3(merge->nrecv, &buf_ri_k, merge->nrecv, &nextrow, merge->nrecv, &nextai));

    4994:   for (k = 0; k < merge->nrecv; k++) {
    4995:     buf_ri_k[k] = buf_ri[k]; /* beginning of k-th recved i-structure */
    4996:     nrows       = *buf_ri_k[k];
    4997:     nextrow[k]  = buf_ri_k[k] + 1;           /* next row number of k-th recved i-structure */
    4998:     nextai[k]   = buf_ri_k[k] + (nrows + 1); /* points to the next i-structure of k-th recved i-structure  */
    4999:   }

    5001:   MatPreallocateBegin(comm, m, n, dnz, onz);
    5002:   len = 0;
    5003:   for (i = 0; i < m; i++) {
    5004:     bnzi = 0;
    5005:     /* add local non-zero cols of this proc's seqmat into lnk */
    5006:     arow = owners[rank] + i;
    5007:     anzi = ai[arow + 1] - ai[arow];
    5008:     aj   = a->j + ai[arow];
    5009:     PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
    5010:     bnzi += nlnk;
    5011:     /* add received col data into lnk */
    5012:     for (k = 0; k < merge->nrecv; k++) { /* k-th received message */
    5013:       if (i == *nextrow[k]) {            /* i-th row */
    5014:         anzi = *(nextai[k] + 1) - *nextai[k];
    5015:         aj   = buf_rj[k] + *nextai[k];
    5016:         PetscCall(PetscLLAddSorted(anzi, aj, N, &nlnk, lnk, lnkbt));
    5017:         bnzi += nlnk;
    5018:         nextrow[k]++;
    5019:         nextai[k]++;
    5020:       }
    5021:     }
    5022:     if (len < bnzi) len = bnzi; /* =max(bnzi) */

    5024:     /* if free space is not available, make more free space */
    5025:     if (current_space->local_remaining < bnzi) PetscCall(PetscFreeSpaceGet(PetscIntSumTruncate(bnzi, current_space->total_array_size), &current_space));
    5026:     /* copy data into free space, then initialize lnk */
    5027:     PetscCall(PetscLLClean(N, N, bnzi, lnk, current_space->array, lnkbt));
    5028:     PetscCall(MatPreallocateSet(i + owners[rank], bnzi, current_space->array, dnz, onz));

    5030:     current_space->array += bnzi;
    5031:     current_space->local_used += bnzi;
    5032:     current_space->local_remaining -= bnzi;

    5034:     bi[i + 1] = bi[i] + bnzi;
    5035:   }

    5037:   PetscCall(PetscFree3(buf_ri_k, nextrow, nextai));

    5039:   PetscCall(PetscMalloc1(bi[m] + 1, &bj));
    5040:   PetscCall(PetscFreeSpaceContiguous(&free_space, bj));
    5041:   PetscCall(PetscLLDestroy(lnk, lnkbt));

    5043:   /* create symbolic parallel matrix B_mpi */
    5044:   PetscCall(MatGetBlockSizes(seqmat, &bs, &cbs));
    5045:   PetscCall(MatCreate(comm, &B_mpi));
    5046:   if (n == PETSC_DECIDE) {
    5047:     PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, N));
    5048:   } else {
    5049:     PetscCall(MatSetSizes(B_mpi, m, n, PETSC_DETERMINE, PETSC_DETERMINE));
    5050:   }
    5051:   PetscCall(MatSetBlockSizes(B_mpi, bs, cbs));
    5052:   PetscCall(MatSetType(B_mpi, MATMPIAIJ));
    5053:   PetscCall(MatMPIAIJSetPreallocation(B_mpi, 0, dnz, 0, onz));
    5054:   MatPreallocateEnd(dnz, onz);
    5055:   PetscCall(MatSetOption(B_mpi, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE));

    5057:   /* B_mpi is not ready for use - assembly will be done by MatCreateMPIAIJSumSeqAIJNumeric() */
    5058:   B_mpi->assembled = PETSC_FALSE;
    5059:   merge->bi        = bi;
    5060:   merge->bj        = bj;
    5061:   merge->buf_ri    = buf_ri;
    5062:   merge->buf_rj    = buf_rj;
    5063:   merge->coi       = NULL;
    5064:   merge->coj       = NULL;
    5065:   merge->owners_co = NULL;

    5067:   PetscCall(PetscCommDestroy(&comm));

    5069:   /* attach the supporting struct to B_mpi for reuse */
    5070:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    5071:   PetscCall(PetscContainerSetPointer(container, merge));
    5072:   PetscCall(PetscContainerSetUserDestroy(container, MatDestroy_MPIAIJ_SeqsToMPI));
    5073:   PetscCall(PetscObjectCompose((PetscObject)B_mpi, "MatMergeSeqsToMPI", (PetscObject)container));
    5074:   PetscCall(PetscContainerDestroy(&container));
    5075:   *mpimat = B_mpi;

    5077:   PetscCall(PetscLogEventEnd(MAT_Seqstompisym, seqmat, 0, 0, 0));
    5078:   PetscFunctionReturn(PETSC_SUCCESS);
    5079: }

    5081: /*@
    5082:   MatCreateMPIAIJSumSeqAIJ - Creates a `MATMPIAIJ` matrix by adding sequential
    5083:   matrices from each processor

    5085:   Collective

    5087:   Input Parameters:
    5088: + comm   - the communicators the parallel matrix will live on
    5089: . seqmat - the input sequential matrices
    5090: . m      - number of local rows (or `PETSC_DECIDE`)
    5091: . n      - number of local columns (or `PETSC_DECIDE`)
    5092: - scall  - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5094:   Output Parameter:
    5095: . mpimat - the parallel matrix generated

    5097:   Level: advanced

    5099:   Note:
    5100:   The dimensions of the sequential matrix in each processor MUST be the same.
    5101:   The input seqmat is included into the container "Mat_Merge_SeqsToMPI", and will be
    5102:   destroyed when `mpimat` is destroyed. Call `PetscObjectQuery()` to access `seqmat`.

    5104: .seealso: [](ch_matrices), `Mat`, `MatCreateAIJ()`
    5105: @*/
    5106: PetscErrorCode MatCreateMPIAIJSumSeqAIJ(MPI_Comm comm, Mat seqmat, PetscInt m, PetscInt n, MatReuse scall, Mat *mpimat)
    5107: {
    5108:   PetscMPIInt size;

    5110:   PetscFunctionBegin;
    5111:   PetscCallMPI(MPI_Comm_size(comm, &size));
    5112:   if (size == 1) {
    5113:     PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
    5114:     if (scall == MAT_INITIAL_MATRIX) {
    5115:       PetscCall(MatDuplicate(seqmat, MAT_COPY_VALUES, mpimat));
    5116:     } else {
    5117:       PetscCall(MatCopy(seqmat, *mpimat, SAME_NONZERO_PATTERN));
    5118:     }
    5119:     PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
    5120:     PetscFunctionReturn(PETSC_SUCCESS);
    5121:   }
    5122:   PetscCall(PetscLogEventBegin(MAT_Seqstompi, seqmat, 0, 0, 0));
    5123:   if (scall == MAT_INITIAL_MATRIX) PetscCall(MatCreateMPIAIJSumSeqAIJSymbolic(comm, seqmat, m, n, mpimat));
    5124:   PetscCall(MatCreateMPIAIJSumSeqAIJNumeric(seqmat, *mpimat));
    5125:   PetscCall(PetscLogEventEnd(MAT_Seqstompi, seqmat, 0, 0, 0));
    5126:   PetscFunctionReturn(PETSC_SUCCESS);
    5127: }

    5129: /*@
    5130:   MatAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATAIJ` matrix.

    5132:   Not Collective

    5134:   Input Parameter:
    5135: . A - the matrix

    5137:   Output Parameter:
    5138: . A_loc - the local sequential matrix generated

    5140:   Level: developer

    5142:   Notes:
    5143:   The matrix is created by taking `A`'s local rows and putting them into a sequential matrix
    5144:   with `mlocal` rows and `n` columns. Where `mlocal` is obtained with `MatGetLocalSize()` and
    5145:   `n` is the global column count obtained with `MatGetSize()`

    5147:   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.

    5149:   For parallel matrices this creates an entirely new matrix. If the matrix is sequential it merely increases the reference count.

    5151:   Destroy the matrix with `MatDestroy()`

    5153: .seealso: [](ch_matrices), `Mat`, `MatMPIAIJGetLocalMat()`
    5154: @*/
    5155: PetscErrorCode MatAIJGetLocalMat(Mat A, Mat *A_loc)
    5156: {
    5157:   PetscBool mpi;

    5159:   PetscFunctionBegin;
    5160:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &mpi));
    5161:   if (mpi) {
    5162:     PetscCall(MatMPIAIJGetLocalMat(A, MAT_INITIAL_MATRIX, A_loc));
    5163:   } else {
    5164:     *A_loc = A;
    5165:     PetscCall(PetscObjectReference((PetscObject)*A_loc));
    5166:   }
    5167:   PetscFunctionReturn(PETSC_SUCCESS);
    5168: }

    5170: /*@
    5171:   MatMPIAIJGetLocalMat - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix.

    5173:   Not Collective

    5175:   Input Parameters:
    5176: + A     - the matrix
    5177: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5179:   Output Parameter:
    5180: . A_loc - the local sequential matrix generated

    5182:   Level: developer

    5184:   Notes:
    5185:   The matrix is created by taking all `A`'s local rows and putting them into a sequential
    5186:   matrix with `mlocal` rows and `n` columns.`mlocal` is the row count obtained with
    5187:   `MatGetLocalSize()` and `n` is the global column count obtained with `MatGetSize()`.

    5189:   In other words combines the two parts of a parallel `MATMPIAIJ` matrix on each process to a single matrix.

    5191:   When `A` is sequential and `MAT_INITIAL_MATRIX` is requested, the matrix returned is the diagonal part of `A` (which contains the entire matrix),
    5192:   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
    5193:   then `MatCopy`(Adiag,*`A_loc`,`SAME_NONZERO_PATTERN`) is called to fill `A_loc`. Thus one can preallocate the appropriate sequential matrix `A_loc`
    5194:   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.

    5196: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMatCondensed()`, `MatMPIAIJGetLocalMatMerge()`
    5197: @*/
    5198: PetscErrorCode MatMPIAIJGetLocalMat(Mat A, MatReuse scall, Mat *A_loc)
    5199: {
    5200:   Mat_MPIAIJ        *mpimat = (Mat_MPIAIJ *)A->data;
    5201:   Mat_SeqAIJ        *mat, *a, *b;
    5202:   PetscInt          *ai, *aj, *bi, *bj, *cmap = mpimat->garray;
    5203:   const PetscScalar *aa, *ba, *aav, *bav;
    5204:   PetscScalar       *ca, *cam;
    5205:   PetscMPIInt        size;
    5206:   PetscInt           am = A->rmap->n, i, j, k, cstart = A->cmap->rstart;
    5207:   PetscInt          *ci, *cj, col, ncols_d, ncols_o, jo;
    5208:   PetscBool          match;

    5210:   PetscFunctionBegin;
    5211:   PetscCall(PetscStrbeginswith(((PetscObject)A)->type_name, MATMPIAIJ, &match));
    5212:   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
    5213:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    5214:   if (size == 1) {
    5215:     if (scall == MAT_INITIAL_MATRIX) {
    5216:       PetscCall(PetscObjectReference((PetscObject)mpimat->A));
    5217:       *A_loc = mpimat->A;
    5218:     } else if (scall == MAT_REUSE_MATRIX) {
    5219:       PetscCall(MatCopy(mpimat->A, *A_loc, SAME_NONZERO_PATTERN));
    5220:     }
    5221:     PetscFunctionReturn(PETSC_SUCCESS);
    5222:   }

    5224:   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
    5225:   a  = (Mat_SeqAIJ *)mpimat->A->data;
    5226:   b  = (Mat_SeqAIJ *)mpimat->B->data;
    5227:   ai = a->i;
    5228:   aj = a->j;
    5229:   bi = b->i;
    5230:   bj = b->j;
    5231:   PetscCall(MatSeqAIJGetArrayRead(mpimat->A, &aav));
    5232:   PetscCall(MatSeqAIJGetArrayRead(mpimat->B, &bav));
    5233:   aa = aav;
    5234:   ba = bav;
    5235:   if (scall == MAT_INITIAL_MATRIX) {
    5236:     PetscCall(PetscMalloc1(1 + am, &ci));
    5237:     ci[0] = 0;
    5238:     for (i = 0; i < am; i++) ci[i + 1] = ci[i] + (ai[i + 1] - ai[i]) + (bi[i + 1] - bi[i]);
    5239:     PetscCall(PetscMalloc1(1 + ci[am], &cj));
    5240:     PetscCall(PetscMalloc1(1 + ci[am], &ca));
    5241:     k = 0;
    5242:     for (i = 0; i < am; i++) {
    5243:       ncols_o = bi[i + 1] - bi[i];
    5244:       ncols_d = ai[i + 1] - ai[i];
    5245:       /* off-diagonal portion of A */
    5246:       for (jo = 0; jo < ncols_o; jo++) {
    5247:         col = cmap[*bj];
    5248:         if (col >= cstart) break;
    5249:         cj[k] = col;
    5250:         bj++;
    5251:         ca[k++] = *ba++;
    5252:       }
    5253:       /* diagonal portion of A */
    5254:       for (j = 0; j < ncols_d; j++) {
    5255:         cj[k]   = cstart + *aj++;
    5256:         ca[k++] = *aa++;
    5257:       }
    5258:       /* off-diagonal portion of A */
    5259:       for (j = jo; j < ncols_o; j++) {
    5260:         cj[k]   = cmap[*bj++];
    5261:         ca[k++] = *ba++;
    5262:       }
    5263:     }
    5264:     /* put together the new matrix */
    5265:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, A->cmap->N, ci, cj, ca, A_loc));
    5266:     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5267:     /* Since these are PETSc arrays, change flags to free them as necessary. */
    5268:     mat          = (Mat_SeqAIJ *)(*A_loc)->data;
    5269:     mat->free_a  = PETSC_TRUE;
    5270:     mat->free_ij = PETSC_TRUE;
    5271:     mat->nonew   = 0;
    5272:   } else if (scall == MAT_REUSE_MATRIX) {
    5273:     mat = (Mat_SeqAIJ *)(*A_loc)->data;
    5274:     ci  = mat->i;
    5275:     cj  = mat->j;
    5276:     PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &cam));
    5277:     for (i = 0; i < am; i++) {
    5278:       /* off-diagonal portion of A */
    5279:       ncols_o = bi[i + 1] - bi[i];
    5280:       for (jo = 0; jo < ncols_o; jo++) {
    5281:         col = cmap[*bj];
    5282:         if (col >= cstart) break;
    5283:         *cam++ = *ba++;
    5284:         bj++;
    5285:       }
    5286:       /* diagonal portion of A */
    5287:       ncols_d = ai[i + 1] - ai[i];
    5288:       for (j = 0; j < ncols_d; j++) *cam++ = *aa++;
    5289:       /* off-diagonal portion of A */
    5290:       for (j = jo; j < ncols_o; j++) {
    5291:         *cam++ = *ba++;
    5292:         bj++;
    5293:       }
    5294:     }
    5295:     PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &cam));
    5296:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
    5297:   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->A, &aav));
    5298:   PetscCall(MatSeqAIJRestoreArrayRead(mpimat->B, &bav));
    5299:   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
    5300:   PetscFunctionReturn(PETSC_SUCCESS);
    5301: }

    5303: /*@
    5304:   MatMPIAIJGetLocalMatMerge - Creates a `MATSEQAIJ` from a `MATMPIAIJ` matrix by taking all its local rows and putting them into a sequential matrix with
    5305:   mlocal rows and n columns. Where n is the sum of the number of columns of the diagonal and off-diagonal part

    5307:   Not Collective

    5309:   Input Parameters:
    5310: + A     - the matrix
    5311: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5313:   Output Parameters:
    5314: + glob  - sequential `IS` with global indices associated with the columns of the local sequential matrix generated (can be `NULL`)
    5315: - A_loc - the local sequential matrix generated

    5317:   Level: developer

    5319:   Note:
    5320:   This is different from `MatMPIAIJGetLocalMat()` since the first columns in the returning matrix are those associated with the diagonal
    5321:   part, then those associated with the off-diagonal part (in its local ordering)

    5323: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`, `MatMPIAIJGetLocalMatCondensed()`
    5324: @*/
    5325: PetscErrorCode MatMPIAIJGetLocalMatMerge(Mat A, MatReuse scall, IS *glob, Mat *A_loc)
    5326: {
    5327:   Mat             Ao, Ad;
    5328:   const PetscInt *cmap;
    5329:   PetscMPIInt     size;
    5330:   PetscErrorCode (*f)(Mat, MatReuse, IS *, Mat *);

    5332:   PetscFunctionBegin;
    5333:   PetscCall(MatMPIAIJGetSeqAIJ(A, &Ad, &Ao, &cmap));
    5334:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)A), &size));
    5335:   if (size == 1) {
    5336:     if (scall == MAT_INITIAL_MATRIX) {
    5337:       PetscCall(PetscObjectReference((PetscObject)Ad));
    5338:       *A_loc = Ad;
    5339:     } else if (scall == MAT_REUSE_MATRIX) {
    5340:       PetscCall(MatCopy(Ad, *A_loc, SAME_NONZERO_PATTERN));
    5341:     }
    5342:     if (glob) PetscCall(ISCreateStride(PetscObjectComm((PetscObject)Ad), Ad->cmap->n, Ad->cmap->rstart, 1, glob));
    5343:     PetscFunctionReturn(PETSC_SUCCESS);
    5344:   }
    5345:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatMPIAIJGetLocalMatMerge_C", &f));
    5346:   PetscCall(PetscLogEventBegin(MAT_Getlocalmat, A, 0, 0, 0));
    5347:   if (f) {
    5348:     PetscCall((*f)(A, scall, glob, A_loc));
    5349:   } else {
    5350:     Mat_SeqAIJ        *a = (Mat_SeqAIJ *)Ad->data;
    5351:     Mat_SeqAIJ        *b = (Mat_SeqAIJ *)Ao->data;
    5352:     Mat_SeqAIJ        *c;
    5353:     PetscInt          *ai = a->i, *aj = a->j;
    5354:     PetscInt          *bi = b->i, *bj = b->j;
    5355:     PetscInt          *ci, *cj;
    5356:     const PetscScalar *aa, *ba;
    5357:     PetscScalar       *ca;
    5358:     PetscInt           i, j, am, dn, on;

    5360:     PetscCall(MatGetLocalSize(Ad, &am, &dn));
    5361:     PetscCall(MatGetLocalSize(Ao, NULL, &on));
    5362:     PetscCall(MatSeqAIJGetArrayRead(Ad, &aa));
    5363:     PetscCall(MatSeqAIJGetArrayRead(Ao, &ba));
    5364:     if (scall == MAT_INITIAL_MATRIX) {
    5365:       PetscInt k;
    5366:       PetscCall(PetscMalloc1(1 + am, &ci));
    5367:       PetscCall(PetscMalloc1(ai[am] + bi[am], &cj));
    5368:       PetscCall(PetscMalloc1(ai[am] + bi[am], &ca));
    5369:       ci[0] = 0;
    5370:       for (i = 0, k = 0; i < am; i++) {
    5371:         const PetscInt ncols_o = bi[i + 1] - bi[i];
    5372:         const PetscInt ncols_d = ai[i + 1] - ai[i];
    5373:         ci[i + 1]              = ci[i] + ncols_o + ncols_d;
    5374:         /* diagonal portion of A */
    5375:         for (j = 0; j < ncols_d; j++, k++) {
    5376:           cj[k] = *aj++;
    5377:           ca[k] = *aa++;
    5378:         }
    5379:         /* off-diagonal portion of A */
    5380:         for (j = 0; j < ncols_o; j++, k++) {
    5381:           cj[k] = dn + *bj++;
    5382:           ca[k] = *ba++;
    5383:         }
    5384:       }
    5385:       /* put together the new matrix */
    5386:       PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, am, dn + on, ci, cj, ca, A_loc));
    5387:       /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    5388:       /* Since these are PETSc arrays, change flags to free them as necessary. */
    5389:       c          = (Mat_SeqAIJ *)(*A_loc)->data;
    5390:       c->free_a  = PETSC_TRUE;
    5391:       c->free_ij = PETSC_TRUE;
    5392:       c->nonew   = 0;
    5393:       PetscCall(MatSetType(*A_loc, ((PetscObject)Ad)->type_name));
    5394:     } else if (scall == MAT_REUSE_MATRIX) {
    5395:       PetscCall(MatSeqAIJGetArrayWrite(*A_loc, &ca));
    5396:       for (i = 0; i < am; i++) {
    5397:         const PetscInt ncols_d = ai[i + 1] - ai[i];
    5398:         const PetscInt ncols_o = bi[i + 1] - bi[i];
    5399:         /* diagonal portion of A */
    5400:         for (j = 0; j < ncols_d; j++) *ca++ = *aa++;
    5401:         /* off-diagonal portion of A */
    5402:         for (j = 0; j < ncols_o; j++) *ca++ = *ba++;
    5403:       }
    5404:       PetscCall(MatSeqAIJRestoreArrayWrite(*A_loc, &ca));
    5405:     } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONG, "Invalid MatReuse %d", (int)scall);
    5406:     PetscCall(MatSeqAIJRestoreArrayRead(Ad, &aa));
    5407:     PetscCall(MatSeqAIJRestoreArrayRead(Ao, &aa));
    5408:     if (glob) {
    5409:       PetscInt cst, *gidx;

    5411:       PetscCall(MatGetOwnershipRangeColumn(A, &cst, NULL));
    5412:       PetscCall(PetscMalloc1(dn + on, &gidx));
    5413:       for (i = 0; i < dn; i++) gidx[i] = cst + i;
    5414:       for (i = 0; i < on; i++) gidx[i + dn] = cmap[i];
    5415:       PetscCall(ISCreateGeneral(PetscObjectComm((PetscObject)Ad), dn + on, gidx, PETSC_OWN_POINTER, glob));
    5416:     }
    5417:   }
    5418:   PetscCall(PetscLogEventEnd(MAT_Getlocalmat, A, 0, 0, 0));
    5419:   PetscFunctionReturn(PETSC_SUCCESS);
    5420: }

    5422: /*@C
    5423:   MatMPIAIJGetLocalMatCondensed - Creates a `MATSEQAIJ` matrix from an `MATMPIAIJ` matrix by taking all its local rows and NON-ZERO columns

    5425:   Not Collective

    5427:   Input Parameters:
    5428: + A     - the matrix
    5429: . scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
    5430: . row   - index set of rows to extract (or `NULL`)
    5431: - col   - index set of columns to extract (or `NULL`)

    5433:   Output Parameter:
    5434: . A_loc - the local sequential matrix generated

    5436:   Level: developer

    5438: .seealso: [](ch_matrices), `Mat`, `MATMPIAIJ`, `MatGetOwnershipRange()`, `MatMPIAIJGetLocalMat()`
    5439: @*/
    5440: PetscErrorCode MatMPIAIJGetLocalMatCondensed(Mat A, MatReuse scall, IS *row, IS *col, Mat *A_loc)
    5441: {
    5442:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    5443:   PetscInt    i, start, end, ncols, nzA, nzB, *cmap, imark, *idx;
    5444:   IS          isrowa, iscola;
    5445:   Mat        *aloc;
    5446:   PetscBool   match;

    5448:   PetscFunctionBegin;
    5449:   PetscCall(PetscObjectTypeCompare((PetscObject)A, MATMPIAIJ, &match));
    5450:   PetscCheck(match, PetscObjectComm((PetscObject)A), PETSC_ERR_SUP, "Requires MATMPIAIJ matrix as input");
    5451:   PetscCall(PetscLogEventBegin(MAT_Getlocalmatcondensed, A, 0, 0, 0));
    5452:   if (!row) {
    5453:     start = A->rmap->rstart;
    5454:     end   = A->rmap->rend;
    5455:     PetscCall(ISCreateStride(PETSC_COMM_SELF, end - start, start, 1, &isrowa));
    5456:   } else {
    5457:     isrowa = *row;
    5458:   }
    5459:   if (!col) {
    5460:     start = A->cmap->rstart;
    5461:     cmap  = a->garray;
    5462:     nzA   = a->A->cmap->n;
    5463:     nzB   = a->B->cmap->n;
    5464:     PetscCall(PetscMalloc1(nzA + nzB, &idx));
    5465:     ncols = 0;
    5466:     for (i = 0; i < nzB; i++) {
    5467:       if (cmap[i] < start) idx[ncols++] = cmap[i];
    5468:       else break;
    5469:     }
    5470:     imark = i;
    5471:     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;
    5472:     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i];
    5473:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &iscola));
    5474:   } else {
    5475:     iscola = *col;
    5476:   }
    5477:   if (scall != MAT_INITIAL_MATRIX) {
    5478:     PetscCall(PetscMalloc1(1, &aloc));
    5479:     aloc[0] = *A_loc;
    5480:   }
    5481:   PetscCall(MatCreateSubMatrices(A, 1, &isrowa, &iscola, scall, &aloc));
    5482:   if (!col) { /* attach global id of condensed columns */
    5483:     PetscCall(PetscObjectCompose((PetscObject)aloc[0], "_petsc_GetLocalMatCondensed_iscol", (PetscObject)iscola));
    5484:   }
    5485:   *A_loc = aloc[0];
    5486:   PetscCall(PetscFree(aloc));
    5487:   if (!row) PetscCall(ISDestroy(&isrowa));
    5488:   if (!col) PetscCall(ISDestroy(&iscola));
    5489:   PetscCall(PetscLogEventEnd(MAT_Getlocalmatcondensed, A, 0, 0, 0));
    5490:   PetscFunctionReturn(PETSC_SUCCESS);
    5491: }

    5493: /*
    5494:  * Create a sequential AIJ matrix based on row indices. a whole column is extracted once a row is matched.
    5495:  * Row could be local or remote.The routine is designed to be scalable in memory so that nothing is based
    5496:  * on a global size.
    5497:  * */
    5498: static PetscErrorCode MatCreateSeqSubMatrixWithRows_Private(Mat P, IS rows, Mat *P_oth)
    5499: {
    5500:   Mat_MPIAIJ            *p  = (Mat_MPIAIJ *)P->data;
    5501:   Mat_SeqAIJ            *pd = (Mat_SeqAIJ *)p->A->data, *po = (Mat_SeqAIJ *)p->B->data, *p_oth;
    5502:   PetscInt               plocalsize, nrows, *ilocal, *oilocal, i, lidx, *nrcols, *nlcols, ncol;
    5503:   PetscMPIInt            owner;
    5504:   PetscSFNode           *iremote, *oiremote;
    5505:   const PetscInt        *lrowindices;
    5506:   PetscSF                sf, osf;
    5507:   PetscInt               pcstart, *roffsets, *loffsets, *pnnz, j;
    5508:   PetscInt               ontotalcols, dntotalcols, ntotalcols, nout;
    5509:   MPI_Comm               comm;
    5510:   ISLocalToGlobalMapping mapping;
    5511:   const PetscScalar     *pd_a, *po_a;

    5513:   PetscFunctionBegin;
    5514:   PetscCall(PetscObjectGetComm((PetscObject)P, &comm));
    5515:   /* plocalsize is the number of roots
    5516:    * nrows is the number of leaves
    5517:    * */
    5518:   PetscCall(MatGetLocalSize(P, &plocalsize, NULL));
    5519:   PetscCall(ISGetLocalSize(rows, &nrows));
    5520:   PetscCall(PetscCalloc1(nrows, &iremote));
    5521:   PetscCall(ISGetIndices(rows, &lrowindices));
    5522:   for (i = 0; i < nrows; i++) {
    5523:     /* Find a remote index and an owner for a row
    5524:      * The row could be local or remote
    5525:      * */
    5526:     owner = 0;
    5527:     lidx  = 0;
    5528:     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, &lidx));
    5529:     iremote[i].index = lidx;
    5530:     iremote[i].rank  = owner;
    5531:   }
    5532:   /* Create SF to communicate how many nonzero columns for each row */
    5533:   PetscCall(PetscSFCreate(comm, &sf));
    5534:   /* SF will figure out the number of nonzero columns for each row, and their
    5535:    * offsets
    5536:    * */
    5537:   PetscCall(PetscSFSetGraph(sf, plocalsize, nrows, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    5538:   PetscCall(PetscSFSetFromOptions(sf));
    5539:   PetscCall(PetscSFSetUp(sf));

    5541:   PetscCall(PetscCalloc1(2 * (plocalsize + 1), &roffsets));
    5542:   PetscCall(PetscCalloc1(2 * plocalsize, &nrcols));
    5543:   PetscCall(PetscCalloc1(nrows, &pnnz));
    5544:   roffsets[0] = 0;
    5545:   roffsets[1] = 0;
    5546:   for (i = 0; i < plocalsize; i++) {
    5547:     /* diagonal */
    5548:     nrcols[i * 2 + 0] = pd->i[i + 1] - pd->i[i];
    5549:     /* off-diagonal */
    5550:     nrcols[i * 2 + 1] = po->i[i + 1] - po->i[i];
    5551:     /* compute offsets so that we relative location for each row */
    5552:     roffsets[(i + 1) * 2 + 0] = roffsets[i * 2 + 0] + nrcols[i * 2 + 0];
    5553:     roffsets[(i + 1) * 2 + 1] = roffsets[i * 2 + 1] + nrcols[i * 2 + 1];
    5554:   }
    5555:   PetscCall(PetscCalloc1(2 * nrows, &nlcols));
    5556:   PetscCall(PetscCalloc1(2 * nrows, &loffsets));
    5557:   /* 'r' means root, and 'l' means leaf */
    5558:   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
    5559:   PetscCall(PetscSFBcastBegin(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
    5560:   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, nrcols, nlcols, MPI_REPLACE));
    5561:   PetscCall(PetscSFBcastEnd(sf, MPIU_2INT, roffsets, loffsets, MPI_REPLACE));
    5562:   PetscCall(PetscSFDestroy(&sf));
    5563:   PetscCall(PetscFree(roffsets));
    5564:   PetscCall(PetscFree(nrcols));
    5565:   dntotalcols = 0;
    5566:   ontotalcols = 0;
    5567:   ncol        = 0;
    5568:   for (i = 0; i < nrows; i++) {
    5569:     pnnz[i] = nlcols[i * 2 + 0] + nlcols[i * 2 + 1];
    5570:     ncol    = PetscMax(pnnz[i], ncol);
    5571:     /* diagonal */
    5572:     dntotalcols += nlcols[i * 2 + 0];
    5573:     /* off-diagonal */
    5574:     ontotalcols += nlcols[i * 2 + 1];
    5575:   }
    5576:   /* We do not need to figure the right number of columns
    5577:    * since all the calculations will be done by going through the raw data
    5578:    * */
    5579:   PetscCall(MatCreateSeqAIJ(PETSC_COMM_SELF, nrows, ncol, 0, pnnz, P_oth));
    5580:   PetscCall(MatSetUp(*P_oth));
    5581:   PetscCall(PetscFree(pnnz));
    5582:   p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
    5583:   /* diagonal */
    5584:   PetscCall(PetscCalloc1(dntotalcols, &iremote));
    5585:   /* off-diagonal */
    5586:   PetscCall(PetscCalloc1(ontotalcols, &oiremote));
    5587:   /* diagonal */
    5588:   PetscCall(PetscCalloc1(dntotalcols, &ilocal));
    5589:   /* off-diagonal */
    5590:   PetscCall(PetscCalloc1(ontotalcols, &oilocal));
    5591:   dntotalcols = 0;
    5592:   ontotalcols = 0;
    5593:   ntotalcols  = 0;
    5594:   for (i = 0; i < nrows; i++) {
    5595:     owner = 0;
    5596:     PetscCall(PetscLayoutFindOwnerIndex(P->rmap, lrowindices[i], &owner, NULL));
    5597:     /* Set iremote for diag matrix */
    5598:     for (j = 0; j < nlcols[i * 2 + 0]; j++) {
    5599:       iremote[dntotalcols].index = loffsets[i * 2 + 0] + j;
    5600:       iremote[dntotalcols].rank  = owner;
    5601:       /* P_oth is seqAIJ so that ilocal need to point to the first part of memory */
    5602:       ilocal[dntotalcols++] = ntotalcols++;
    5603:     }
    5604:     /* off-diagonal */
    5605:     for (j = 0; j < nlcols[i * 2 + 1]; j++) {
    5606:       oiremote[ontotalcols].index = loffsets[i * 2 + 1] + j;
    5607:       oiremote[ontotalcols].rank  = owner;
    5608:       oilocal[ontotalcols++]      = ntotalcols++;
    5609:     }
    5610:   }
    5611:   PetscCall(ISRestoreIndices(rows, &lrowindices));
    5612:   PetscCall(PetscFree(loffsets));
    5613:   PetscCall(PetscFree(nlcols));
    5614:   PetscCall(PetscSFCreate(comm, &sf));
    5615:   /* P serves as roots and P_oth is leaves
    5616:    * Diag matrix
    5617:    * */
    5618:   PetscCall(PetscSFSetGraph(sf, pd->i[plocalsize], dntotalcols, ilocal, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    5619:   PetscCall(PetscSFSetFromOptions(sf));
    5620:   PetscCall(PetscSFSetUp(sf));

    5622:   PetscCall(PetscSFCreate(comm, &osf));
    5623:   /* off-diagonal */
    5624:   PetscCall(PetscSFSetGraph(osf, po->i[plocalsize], ontotalcols, oilocal, PETSC_OWN_POINTER, oiremote, PETSC_OWN_POINTER));
    5625:   PetscCall(PetscSFSetFromOptions(osf));
    5626:   PetscCall(PetscSFSetUp(osf));
    5627:   PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
    5628:   PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
    5629:   /* operate on the matrix internal data to save memory */
    5630:   PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5631:   PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5632:   PetscCall(MatGetOwnershipRangeColumn(P, &pcstart, NULL));
    5633:   /* Convert to global indices for diag matrix */
    5634:   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] += pcstart;
    5635:   PetscCall(PetscSFBcastBegin(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
    5636:   /* We want P_oth store global indices */
    5637:   PetscCall(ISLocalToGlobalMappingCreate(comm, 1, p->B->cmap->n, p->garray, PETSC_COPY_VALUES, &mapping));
    5638:   /* Use memory scalable approach */
    5639:   PetscCall(ISLocalToGlobalMappingSetType(mapping, ISLOCALTOGLOBALMAPPINGHASH));
    5640:   PetscCall(ISLocalToGlobalMappingApply(mapping, po->i[plocalsize], po->j, po->j));
    5641:   PetscCall(PetscSFBcastBegin(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
    5642:   PetscCall(PetscSFBcastEnd(sf, MPIU_INT, pd->j, p_oth->j, MPI_REPLACE));
    5643:   /* Convert back to local indices */
    5644:   for (i = 0; i < pd->i[plocalsize]; i++) pd->j[i] -= pcstart;
    5645:   PetscCall(PetscSFBcastEnd(osf, MPIU_INT, po->j, p_oth->j, MPI_REPLACE));
    5646:   nout = 0;
    5647:   PetscCall(ISGlobalToLocalMappingApply(mapping, IS_GTOLM_DROP, po->i[plocalsize], po->j, &nout, po->j));
    5648:   PetscCheck(nout == po->i[plocalsize], comm, PETSC_ERR_ARG_INCOMP, "n %" PetscInt_FMT " does not equal to nout %" PetscInt_FMT " ", po->i[plocalsize], nout);
    5649:   PetscCall(ISLocalToGlobalMappingDestroy(&mapping));
    5650:   /* Exchange values */
    5651:   PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5652:   PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5653:   PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
    5654:   PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
    5655:   /* Stop PETSc from shrinking memory */
    5656:   for (i = 0; i < nrows; i++) p_oth->ilen[i] = p_oth->imax[i];
    5657:   PetscCall(MatAssemblyBegin(*P_oth, MAT_FINAL_ASSEMBLY));
    5658:   PetscCall(MatAssemblyEnd(*P_oth, MAT_FINAL_ASSEMBLY));
    5659:   /* Attach PetscSF objects to P_oth so that we can reuse it later */
    5660:   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "diagsf", (PetscObject)sf));
    5661:   PetscCall(PetscObjectCompose((PetscObject)*P_oth, "offdiagsf", (PetscObject)osf));
    5662:   PetscCall(PetscSFDestroy(&sf));
    5663:   PetscCall(PetscSFDestroy(&osf));
    5664:   PetscFunctionReturn(PETSC_SUCCESS);
    5665: }

    5667: /*
    5668:  * Creates a SeqAIJ matrix by taking rows of B that equal to nonzero columns of local A
    5669:  * This supports MPIAIJ and MAIJ
    5670:  * */
    5671: PetscErrorCode MatGetBrowsOfAcols_MPIXAIJ(Mat A, Mat P, PetscInt dof, MatReuse reuse, Mat *P_oth)
    5672: {
    5673:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data, *p = (Mat_MPIAIJ *)P->data;
    5674:   Mat_SeqAIJ *p_oth;
    5675:   IS          rows, map;
    5676:   PetscHMapI  hamp;
    5677:   PetscInt    i, htsize, *rowindices, off, *mapping, key, count;
    5678:   MPI_Comm    comm;
    5679:   PetscSF     sf, osf;
    5680:   PetscBool   has;

    5682:   PetscFunctionBegin;
    5683:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    5684:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, P, 0, 0));
    5685:   /* If it is the first time, create an index set of off-diag nonzero columns of A,
    5686:    *  and then create a submatrix (that often is an overlapping matrix)
    5687:    * */
    5688:   if (reuse == MAT_INITIAL_MATRIX) {
    5689:     /* Use a hash table to figure out unique keys */
    5690:     PetscCall(PetscHMapICreateWithSize(a->B->cmap->n, &hamp));
    5691:     PetscCall(PetscCalloc1(a->B->cmap->n, &mapping));
    5692:     count = 0;
    5693:     /* Assume that  a->g is sorted, otherwise the following does not make sense */
    5694:     for (i = 0; i < a->B->cmap->n; i++) {
    5695:       key = a->garray[i] / dof;
    5696:       PetscCall(PetscHMapIHas(hamp, key, &has));
    5697:       if (!has) {
    5698:         mapping[i] = count;
    5699:         PetscCall(PetscHMapISet(hamp, key, count++));
    5700:       } else {
    5701:         /* Current 'i' has the same value the previous step */
    5702:         mapping[i] = count - 1;
    5703:       }
    5704:     }
    5705:     PetscCall(ISCreateGeneral(comm, a->B->cmap->n, mapping, PETSC_OWN_POINTER, &map));
    5706:     PetscCall(PetscHMapIGetSize(hamp, &htsize));
    5707:     PetscCheck(htsize == count, comm, PETSC_ERR_ARG_INCOMP, " Size of hash map %" PetscInt_FMT " is inconsistent with count %" PetscInt_FMT, htsize, count);
    5708:     PetscCall(PetscCalloc1(htsize, &rowindices));
    5709:     off = 0;
    5710:     PetscCall(PetscHMapIGetKeys(hamp, &off, rowindices));
    5711:     PetscCall(PetscHMapIDestroy(&hamp));
    5712:     PetscCall(PetscSortInt(htsize, rowindices));
    5713:     PetscCall(ISCreateGeneral(comm, htsize, rowindices, PETSC_OWN_POINTER, &rows));
    5714:     /* In case, the matrix was already created but users want to recreate the matrix */
    5715:     PetscCall(MatDestroy(P_oth));
    5716:     PetscCall(MatCreateSeqSubMatrixWithRows_Private(P, rows, P_oth));
    5717:     PetscCall(PetscObjectCompose((PetscObject)*P_oth, "aoffdiagtopothmapping", (PetscObject)map));
    5718:     PetscCall(ISDestroy(&map));
    5719:     PetscCall(ISDestroy(&rows));
    5720:   } else if (reuse == MAT_REUSE_MATRIX) {
    5721:     /* If matrix was already created, we simply update values using SF objects
    5722:      * that as attached to the matrix earlier.
    5723:      */
    5724:     const PetscScalar *pd_a, *po_a;

    5726:     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "diagsf", (PetscObject *)&sf));
    5727:     PetscCall(PetscObjectQuery((PetscObject)*P_oth, "offdiagsf", (PetscObject *)&osf));
    5728:     PetscCheck(sf && osf, comm, PETSC_ERR_ARG_NULL, "Matrix is not initialized yet");
    5729:     p_oth = (Mat_SeqAIJ *)(*P_oth)->data;
    5730:     /* Update values in place */
    5731:     PetscCall(MatSeqAIJGetArrayRead(p->A, &pd_a));
    5732:     PetscCall(MatSeqAIJGetArrayRead(p->B, &po_a));
    5733:     PetscCall(PetscSFBcastBegin(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5734:     PetscCall(PetscSFBcastBegin(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5735:     PetscCall(PetscSFBcastEnd(sf, MPIU_SCALAR, pd_a, p_oth->a, MPI_REPLACE));
    5736:     PetscCall(PetscSFBcastEnd(osf, MPIU_SCALAR, po_a, p_oth->a, MPI_REPLACE));
    5737:     PetscCall(MatSeqAIJRestoreArrayRead(p->A, &pd_a));
    5738:     PetscCall(MatSeqAIJRestoreArrayRead(p->B, &po_a));
    5739:   } else SETERRQ(comm, PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown reuse type");
    5740:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, P, 0, 0));
    5741:   PetscFunctionReturn(PETSC_SUCCESS);
    5742: }

    5744: /*@C
    5745:   MatGetBrowsOfAcols - Returns `IS` that contain rows of `B` that equal to nonzero columns of local `A`

    5747:   Collective

    5749:   Input Parameters:
    5750: + A     - the first matrix in `MATMPIAIJ` format
    5751: . B     - the second matrix in `MATMPIAIJ` format
    5752: - scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5754:   Output Parameters:
    5755: + rowb  - On input index sets of rows of B to extract (or `NULL`), modified on output
    5756: . colb  - On input index sets of columns of B to extract (or `NULL`), modified on output
    5757: - B_seq - the sequential matrix generated

    5759:   Level: developer

    5761: .seealso: `Mat`, `MATMPIAIJ`, `IS`, `MatReuse`
    5762: @*/
    5763: PetscErrorCode MatGetBrowsOfAcols(Mat A, Mat B, MatReuse scall, IS *rowb, IS *colb, Mat *B_seq)
    5764: {
    5765:   Mat_MPIAIJ *a = (Mat_MPIAIJ *)A->data;
    5766:   PetscInt   *idx, i, start, ncols, nzA, nzB, *cmap, imark;
    5767:   IS          isrowb, iscolb;
    5768:   Mat        *bseq = NULL;

    5770:   PetscFunctionBegin;
    5771:   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 ")",
    5772:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    5773:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAcols, A, B, 0, 0));

    5775:   if (scall == MAT_INITIAL_MATRIX) {
    5776:     start = A->cmap->rstart;
    5777:     cmap  = a->garray;
    5778:     nzA   = a->A->cmap->n;
    5779:     nzB   = a->B->cmap->n;
    5780:     PetscCall(PetscMalloc1(nzA + nzB, &idx));
    5781:     ncols = 0;
    5782:     for (i = 0; i < nzB; i++) { /* row < local row index */
    5783:       if (cmap[i] < start) idx[ncols++] = cmap[i];
    5784:       else break;
    5785:     }
    5786:     imark = i;
    5787:     for (i = 0; i < nzA; i++) idx[ncols++] = start + i;   /* local rows */
    5788:     for (i = imark; i < nzB; i++) idx[ncols++] = cmap[i]; /* row > local row index */
    5789:     PetscCall(ISCreateGeneral(PETSC_COMM_SELF, ncols, idx, PETSC_OWN_POINTER, &isrowb));
    5790:     PetscCall(ISCreateStride(PETSC_COMM_SELF, B->cmap->N, 0, 1, &iscolb));
    5791:   } else {
    5792:     PetscCheck(rowb && colb, PETSC_COMM_SELF, PETSC_ERR_SUP, "IS rowb and colb must be provided for MAT_REUSE_MATRIX");
    5793:     isrowb = *rowb;
    5794:     iscolb = *colb;
    5795:     PetscCall(PetscMalloc1(1, &bseq));
    5796:     bseq[0] = *B_seq;
    5797:   }
    5798:   PetscCall(MatCreateSubMatrices(B, 1, &isrowb, &iscolb, scall, &bseq));
    5799:   *B_seq = bseq[0];
    5800:   PetscCall(PetscFree(bseq));
    5801:   if (!rowb) {
    5802:     PetscCall(ISDestroy(&isrowb));
    5803:   } else {
    5804:     *rowb = isrowb;
    5805:   }
    5806:   if (!colb) {
    5807:     PetscCall(ISDestroy(&iscolb));
    5808:   } else {
    5809:     *colb = iscolb;
    5810:   }
    5811:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAcols, A, B, 0, 0));
    5812:   PetscFunctionReturn(PETSC_SUCCESS);
    5813: }

    5815: /*
    5816:     MatGetBrowsOfAoCols_MPIAIJ - Creates a `MATSEQAIJ` matrix by taking rows of B that equal to nonzero columns
    5817:     of the OFF-DIAGONAL portion of local A

    5819:     Collective

    5821:    Input Parameters:
    5822: +    A,B - the matrices in `MATMPIAIJ` format
    5823: -    scall - either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`

    5825:    Output Parameter:
    5826: +    startsj_s - starting point in B's sending j-arrays, saved for MAT_REUSE (or NULL)
    5827: .    startsj_r - starting point in B's receiving j-arrays, saved for MAT_REUSE (or NULL)
    5828: .    bufa_ptr - array for sending matrix values, saved for MAT_REUSE (or NULL)
    5829: -    B_oth - the sequential matrix generated with size aBn=a->B->cmap->n by B->cmap->N

    5831:     Developer Note:
    5832:     This directly accesses information inside the VecScatter associated with the matrix-vector product
    5833:      for this matrix. This is not desirable..

    5835:     Level: developer

    5837: */

    5839: PetscErrorCode MatGetBrowsOfAoCols_MPIAIJ(Mat A, Mat B, MatReuse scall, PetscInt **startsj_s, PetscInt **startsj_r, MatScalar **bufa_ptr, Mat *B_oth)
    5840: {
    5841:   Mat_MPIAIJ        *a = (Mat_MPIAIJ *)A->data;
    5842:   VecScatter         ctx;
    5843:   MPI_Comm           comm;
    5844:   const PetscMPIInt *rprocs, *sprocs;
    5845:   PetscMPIInt        nrecvs, nsends;
    5846:   const PetscInt    *srow, *rstarts, *sstarts;
    5847:   PetscInt          *rowlen, *bufj, *bufJ, ncols = 0, aBn = a->B->cmap->n, row, *b_othi, *b_othj, *rvalues = NULL, *svalues = NULL, *cols, sbs, rbs;
    5848:   PetscInt           i, j, k = 0, l, ll, nrows, *rstartsj = NULL, *sstartsj, len;
    5849:   PetscScalar       *b_otha, *bufa, *bufA, *vals = NULL;
    5850:   MPI_Request       *reqs = NULL, *rwaits = NULL, *swaits = NULL;
    5851:   PetscMPIInt        size, tag, rank, nreqs;

    5853:   PetscFunctionBegin;
    5854:   PetscCall(PetscObjectGetComm((PetscObject)A, &comm));
    5855:   PetscCallMPI(MPI_Comm_size(comm, &size));

    5857:   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 ")",
    5858:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    5859:   PetscCall(PetscLogEventBegin(MAT_GetBrowsOfAocols, A, B, 0, 0));
    5860:   PetscCallMPI(MPI_Comm_rank(comm, &rank));

    5862:   if (size == 1) {
    5863:     startsj_s = NULL;
    5864:     bufa_ptr  = NULL;
    5865:     *B_oth    = NULL;
    5866:     PetscFunctionReturn(PETSC_SUCCESS);
    5867:   }

    5869:   ctx = a->Mvctx;
    5870:   tag = ((PetscObject)ctx)->tag;

    5872:   PetscCall(VecScatterGetRemote_Private(ctx, PETSC_TRUE /*send*/, &nsends, &sstarts, &srow, &sprocs, &sbs));
    5873:   /* rprocs[] must be ordered so that indices received from them are ordered in rvalues[], which is key to algorithms used in this subroutine */
    5874:   PetscCall(VecScatterGetRemoteOrdered_Private(ctx, PETSC_FALSE /*recv*/, &nrecvs, &rstarts, NULL /*indices not needed*/, &rprocs, &rbs));
    5875:   PetscCall(PetscMPIIntCast(nsends + nrecvs, &nreqs));
    5876:   PetscCall(PetscMalloc1(nreqs, &reqs));
    5877:   rwaits = reqs;
    5878:   swaits = PetscSafePointerPlusOffset(reqs, nrecvs);

    5880:   if (!startsj_s || !bufa_ptr) scall = MAT_INITIAL_MATRIX;
    5881:   if (scall == MAT_INITIAL_MATRIX) {
    5882:     /* i-array */
    5883:     /*  post receives */
    5884:     if (nrecvs) PetscCall(PetscMalloc1(rbs * (rstarts[nrecvs] - rstarts[0]), &rvalues)); /* rstarts can be NULL when nrecvs=0 */
    5885:     for (i = 0; i < nrecvs; i++) {
    5886:       rowlen = rvalues + rstarts[i] * rbs;
    5887:       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of indices to be received */
    5888:       PetscCallMPI(MPIU_Irecv(rowlen, nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
    5889:     }

    5891:     /* pack the outgoing message */
    5892:     PetscCall(PetscMalloc2(nsends + 1, &sstartsj, nrecvs + 1, &rstartsj));

    5894:     sstartsj[0] = 0;
    5895:     rstartsj[0] = 0;
    5896:     len         = 0; /* total length of j or a array to be sent */
    5897:     if (nsends) {
    5898:       k = sstarts[0]; /* ATTENTION: sstarts[0] and rstarts[0] are not necessarily zero */
    5899:       PetscCall(PetscMalloc1(sbs * (sstarts[nsends] - sstarts[0]), &svalues));
    5900:     }
    5901:     for (i = 0; i < nsends; i++) {
    5902:       rowlen = svalues + (sstarts[i] - sstarts[0]) * sbs;
    5903:       nrows  = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5904:       for (j = 0; j < nrows; j++) {
    5905:         row = srow[k] + B->rmap->range[rank]; /* global row idx */
    5906:         for (l = 0; l < sbs; l++) {
    5907:           PetscCall(MatGetRow_MPIAIJ(B, row + l, &ncols, NULL, NULL)); /* rowlength */

    5909:           rowlen[j * sbs + l] = ncols;

    5911:           len += ncols;
    5912:           PetscCall(MatRestoreRow_MPIAIJ(B, row + l, &ncols, NULL, NULL));
    5913:         }
    5914:         k++;
    5915:       }
    5916:       PetscCallMPI(MPIU_Isend(rowlen, nrows * sbs, MPIU_INT, sprocs[i], tag, comm, swaits + i));

    5918:       sstartsj[i + 1] = len; /* starting point of (i+1)-th outgoing msg in bufj and bufa */
    5919:     }
    5920:     /* recvs and sends of i-array are completed */
    5921:     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5922:     PetscCall(PetscFree(svalues));

    5924:     /* allocate buffers for sending j and a arrays */
    5925:     PetscCall(PetscMalloc1(len + 1, &bufj));
    5926:     PetscCall(PetscMalloc1(len + 1, &bufa));

    5928:     /* create i-array of B_oth */
    5929:     PetscCall(PetscMalloc1(aBn + 2, &b_othi));

    5931:     b_othi[0] = 0;
    5932:     len       = 0; /* total length of j or a array to be received */
    5933:     k         = 0;
    5934:     for (i = 0; i < nrecvs; i++) {
    5935:       rowlen = rvalues + (rstarts[i] - rstarts[0]) * rbs;
    5936:       nrows  = (rstarts[i + 1] - rstarts[i]) * rbs; /* num of rows to be received */
    5937:       for (j = 0; j < nrows; j++) {
    5938:         b_othi[k + 1] = b_othi[k] + rowlen[j];
    5939:         PetscCall(PetscIntSumError(rowlen[j], len, &len));
    5940:         k++;
    5941:       }
    5942:       rstartsj[i + 1] = len; /* starting point of (i+1)-th incoming msg in bufj and bufa */
    5943:     }
    5944:     PetscCall(PetscFree(rvalues));

    5946:     /* allocate space for j and a arrays of B_oth */
    5947:     PetscCall(PetscMalloc1(b_othi[aBn] + 1, &b_othj));
    5948:     PetscCall(PetscMalloc1(b_othi[aBn] + 1, &b_otha));

    5950:     /* j-array */
    5951:     /*  post receives of j-array */
    5952:     for (i = 0; i < nrecvs; i++) {
    5953:       nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
    5954:       PetscCallMPI(MPIU_Irecv(b_othj + rstartsj[i], nrows, MPIU_INT, rprocs[i], tag, comm, rwaits + i));
    5955:     }

    5957:     /* pack the outgoing message j-array */
    5958:     if (nsends) k = sstarts[0];
    5959:     for (i = 0; i < nsends; i++) {
    5960:       nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5961:       bufJ  = bufj + sstartsj[i];
    5962:       for (j = 0; j < nrows; j++) {
    5963:         row = srow[k++] + B->rmap->range[rank]; /* global row idx */
    5964:         for (ll = 0; ll < sbs; ll++) {
    5965:           PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
    5966:           for (l = 0; l < ncols; l++) *bufJ++ = cols[l];
    5967:           PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, &cols, NULL));
    5968:         }
    5969:       }
    5970:       PetscCallMPI(MPIU_Isend(bufj + sstartsj[i], sstartsj[i + 1] - sstartsj[i], MPIU_INT, sprocs[i], tag, comm, swaits + i));
    5971:     }

    5973:     /* recvs and sends of j-array are completed */
    5974:     if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    5975:   } else if (scall == MAT_REUSE_MATRIX) {
    5976:     sstartsj = *startsj_s;
    5977:     rstartsj = *startsj_r;
    5978:     bufa     = *bufa_ptr;
    5979:     PetscCall(MatSeqAIJGetArrayWrite(*B_oth, &b_otha));
    5980:   } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Matrix P does not possess an object container");

    5982:   /* a-array */
    5983:   /*  post receives of a-array */
    5984:   for (i = 0; i < nrecvs; i++) {
    5985:     nrows = rstartsj[i + 1] - rstartsj[i]; /* length of the msg received */
    5986:     PetscCallMPI(MPIU_Irecv(b_otha + rstartsj[i], nrows, MPIU_SCALAR, rprocs[i], tag, comm, rwaits + i));
    5987:   }

    5989:   /* pack the outgoing message a-array */
    5990:   if (nsends) k = sstarts[0];
    5991:   for (i = 0; i < nsends; i++) {
    5992:     nrows = sstarts[i + 1] - sstarts[i]; /* num of block rows */
    5993:     bufA  = bufa + sstartsj[i];
    5994:     for (j = 0; j < nrows; j++) {
    5995:       row = srow[k++] + B->rmap->range[rank]; /* global row idx */
    5996:       for (ll = 0; ll < sbs; ll++) {
    5997:         PetscCall(MatGetRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
    5998:         for (l = 0; l < ncols; l++) *bufA++ = vals[l];
    5999:         PetscCall(MatRestoreRow_MPIAIJ(B, row + ll, &ncols, NULL, &vals));
    6000:       }
    6001:     }
    6002:     PetscCallMPI(MPIU_Isend(bufa + sstartsj[i], sstartsj[i + 1] - sstartsj[i], MPIU_SCALAR, sprocs[i], tag, comm, swaits + i));
    6003:   }
    6004:   /* recvs and sends of a-array are completed */
    6005:   if (nreqs) PetscCallMPI(MPI_Waitall(nreqs, reqs, MPI_STATUSES_IGNORE));
    6006:   PetscCall(PetscFree(reqs));

    6008:   if (scall == MAT_INITIAL_MATRIX) {
    6009:     Mat_SeqAIJ *b_oth;

    6011:     /* put together the new matrix */
    6012:     PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, aBn, B->cmap->N, b_othi, b_othj, b_otha, B_oth));

    6014:     /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
    6015:     /* Since these are PETSc arrays, change flags to free them as necessary. */
    6016:     b_oth          = (Mat_SeqAIJ *)(*B_oth)->data;
    6017:     b_oth->free_a  = PETSC_TRUE;
    6018:     b_oth->free_ij = PETSC_TRUE;
    6019:     b_oth->nonew   = 0;

    6021:     PetscCall(PetscFree(bufj));
    6022:     if (!startsj_s || !bufa_ptr) {
    6023:       PetscCall(PetscFree2(sstartsj, rstartsj));
    6024:       PetscCall(PetscFree(bufa_ptr));
    6025:     } else {
    6026:       *startsj_s = sstartsj;
    6027:       *startsj_r = rstartsj;
    6028:       *bufa_ptr  = bufa;
    6029:     }
    6030:   } else if (scall == MAT_REUSE_MATRIX) {
    6031:     PetscCall(MatSeqAIJRestoreArrayWrite(*B_oth, &b_otha));
    6032:   }

    6034:   PetscCall(VecScatterRestoreRemote_Private(ctx, PETSC_TRUE, &nsends, &sstarts, &srow, &sprocs, &sbs));
    6035:   PetscCall(VecScatterRestoreRemoteOrdered_Private(ctx, PETSC_FALSE, &nrecvs, &rstarts, NULL, &rprocs, &rbs));
    6036:   PetscCall(PetscLogEventEnd(MAT_GetBrowsOfAocols, A, B, 0, 0));
    6037:   PetscFunctionReturn(PETSC_SUCCESS);
    6038: }

    6040: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCRL(Mat, MatType, MatReuse, Mat *);
    6041: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJPERM(Mat, MatType, MatReuse, Mat *);
    6042: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJSELL(Mat, MatType, MatReuse, Mat *);
    6043: #if defined(PETSC_HAVE_MKL_SPARSE)
    6044: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJMKL(Mat, MatType, MatReuse, Mat *);
    6045: #endif
    6046: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIBAIJ(Mat, MatType, MatReuse, Mat *);
    6047: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISBAIJ(Mat, MatType, MatReuse, Mat *);
    6048: #if defined(PETSC_HAVE_ELEMENTAL)
    6049: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
    6050: #endif
    6051: #if defined(PETSC_HAVE_SCALAPACK)
    6052: PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
    6053: #endif
    6054: #if defined(PETSC_HAVE_HYPRE)
    6055: PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat, MatType, MatReuse, Mat *);
    6056: #endif
    6057: #if defined(PETSC_HAVE_CUDA)
    6058: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJCUSPARSE(Mat, MatType, MatReuse, Mat *);
    6059: #endif
    6060: #if defined(PETSC_HAVE_HIP)
    6061: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJHIPSPARSE(Mat, MatType, MatReuse, Mat *);
    6062: #endif
    6063: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    6064: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPIAIJKokkos(Mat, MatType, MatReuse, Mat *);
    6065: #endif
    6066: PETSC_INTERN PetscErrorCode MatConvert_MPIAIJ_MPISELL(Mat, MatType, MatReuse, Mat *);
    6067: PETSC_INTERN PetscErrorCode MatConvert_XAIJ_IS(Mat, MatType, MatReuse, Mat *);
    6068: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_IS_XAIJ(Mat);

    6070: /*
    6071:     Computes (B'*A')' since computing B*A directly is untenable

    6073:                n                       p                          p
    6074:         [             ]       [             ]         [                 ]
    6075:       m [      A      ]  *  n [       B     ]   =   m [         C       ]
    6076:         [             ]       [             ]         [                 ]

    6078: */
    6079: static PetscErrorCode MatMatMultNumeric_MPIDense_MPIAIJ(Mat A, Mat B, Mat C)
    6080: {
    6081:   Mat At, Bt, Ct;

    6083:   PetscFunctionBegin;
    6084:   PetscCall(MatTranspose(A, MAT_INITIAL_MATRIX, &At));
    6085:   PetscCall(MatTranspose(B, MAT_INITIAL_MATRIX, &Bt));
    6086:   PetscCall(MatMatMult(Bt, At, MAT_INITIAL_MATRIX, PETSC_CURRENT, &Ct));
    6087:   PetscCall(MatDestroy(&At));
    6088:   PetscCall(MatDestroy(&Bt));
    6089:   PetscCall(MatTransposeSetPrecursor(Ct, C));
    6090:   PetscCall(MatTranspose(Ct, MAT_REUSE_MATRIX, &C));
    6091:   PetscCall(MatDestroy(&Ct));
    6092:   PetscFunctionReturn(PETSC_SUCCESS);
    6093: }

    6095: static PetscErrorCode MatMatMultSymbolic_MPIDense_MPIAIJ(Mat A, Mat B, PetscReal fill, Mat C)
    6096: {
    6097:   PetscBool cisdense;

    6099:   PetscFunctionBegin;
    6100:   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);
    6101:   PetscCall(MatSetSizes(C, A->rmap->n, B->cmap->n, A->rmap->N, B->cmap->N));
    6102:   PetscCall(MatSetBlockSizesFromMats(C, A, B));
    6103:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &cisdense, MATMPIDENSE, MATMPIDENSECUDA, MATMPIDENSEHIP, ""));
    6104:   if (!cisdense) PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    6105:   PetscCall(MatSetUp(C));

    6107:   C->ops->matmultnumeric = MatMatMultNumeric_MPIDense_MPIAIJ;
    6108:   PetscFunctionReturn(PETSC_SUCCESS);
    6109: }

    6111: static PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ_AB(Mat C)
    6112: {
    6113:   Mat_Product *product = C->product;
    6114:   Mat          A = product->A, B = product->B;

    6116:   PetscFunctionBegin;
    6117:   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 ")",
    6118:              A->cmap->rstart, A->cmap->rend, B->rmap->rstart, B->rmap->rend);
    6119:   C->ops->matmultsymbolic = MatMatMultSymbolic_MPIDense_MPIAIJ;
    6120:   C->ops->productsymbolic = MatProductSymbolic_AB;
    6121:   PetscFunctionReturn(PETSC_SUCCESS);
    6122: }

    6124: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_MPIDense_MPIAIJ(Mat C)
    6125: {
    6126:   Mat_Product *product = C->product;

    6128:   PetscFunctionBegin;
    6129:   if (product->type == MATPRODUCT_AB) PetscCall(MatProductSetFromOptions_MPIDense_MPIAIJ_AB(C));
    6130:   PetscFunctionReturn(PETSC_SUCCESS);
    6131: }

    6133: /*
    6134:    Merge two sets of sorted nonzeros and return a CSR for the merged (sequential) matrix

    6136:   Input Parameters:

    6138:     j1,rowBegin1,rowEnd1,jmap1: describe the first set of nonzeros (Set1)
    6139:     j2,rowBegin2,rowEnd2,jmap2: describe the second set of nonzeros (Set2)

    6141:     mat: both sets' nonzeros are on m rows, where m is the number of local rows of the matrix mat

    6143:     For Set1, j1[] contains column indices of the nonzeros.
    6144:     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
    6145:     respectively (note rowEnd1[k] is not necessarily equal to rwoBegin1[k+1]). Indices in this range of j1[] are sorted,
    6146:     but might have repeats. jmap1[t+1] - jmap1[t] is the number of repeats for the t-th unique nonzero in Set1.

    6148:     Similar for Set2.

    6150:     This routine merges the two sets of nonzeros row by row and removes repeats.

    6152:   Output Parameters: (memory is allocated by the caller)

    6154:     i[],j[]: the CSR of the merged matrix, which has m rows.
    6155:     imap1[]: the k-th unique nonzero in Set1 (k=0,1,...) corresponds to imap1[k]-th unique nonzero in the merged matrix.
    6156:     imap2[]: similar to imap1[], but for Set2.
    6157:     Note we order nonzeros row-by-row and from left to right.
    6158: */
    6159: 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[])
    6160: {
    6161:   PetscInt   r, m; /* Row index of mat */
    6162:   PetscCount t, t1, t2, b1, e1, b2, e2;

    6164:   PetscFunctionBegin;
    6165:   PetscCall(MatGetLocalSize(mat, &m, NULL));
    6166:   t1 = t2 = t = 0; /* Count unique nonzeros of in Set1, Set1 and the merged respectively */
    6167:   i[0]        = 0;
    6168:   for (r = 0; r < m; r++) { /* Do row by row merging */
    6169:     b1 = rowBegin1[r];
    6170:     e1 = rowEnd1[r];
    6171:     b2 = rowBegin2[r];
    6172:     e2 = rowEnd2[r];
    6173:     while (b1 < e1 && b2 < e2) {
    6174:       if (j1[b1] == j2[b2]) { /* Same column index and hence same nonzero */
    6175:         j[t]      = j1[b1];
    6176:         imap1[t1] = t;
    6177:         imap2[t2] = t;
    6178:         b1 += jmap1[t1 + 1] - jmap1[t1]; /* Jump to next unique local nonzero */
    6179:         b2 += jmap2[t2 + 1] - jmap2[t2]; /* Jump to next unique remote nonzero */
    6180:         t1++;
    6181:         t2++;
    6182:         t++;
    6183:       } else if (j1[b1] < j2[b2]) {
    6184:         j[t]      = j1[b1];
    6185:         imap1[t1] = t;
    6186:         b1 += jmap1[t1 + 1] - jmap1[t1];
    6187:         t1++;
    6188:         t++;
    6189:       } else {
    6190:         j[t]      = j2[b2];
    6191:         imap2[t2] = t;
    6192:         b2 += jmap2[t2 + 1] - jmap2[t2];
    6193:         t2++;
    6194:         t++;
    6195:       }
    6196:     }
    6197:     /* Merge the remaining in either j1[] or j2[] */
    6198:     while (b1 < e1) {
    6199:       j[t]      = j1[b1];
    6200:       imap1[t1] = t;
    6201:       b1 += jmap1[t1 + 1] - jmap1[t1];
    6202:       t1++;
    6203:       t++;
    6204:     }
    6205:     while (b2 < e2) {
    6206:       j[t]      = j2[b2];
    6207:       imap2[t2] = t;
    6208:       b2 += jmap2[t2 + 1] - jmap2[t2];
    6209:       t2++;
    6210:       t++;
    6211:     }
    6212:     PetscCall(PetscIntCast(t, i + r + 1));
    6213:   }
    6214:   PetscFunctionReturn(PETSC_SUCCESS);
    6215: }

    6217: /*
    6218:   Split nonzeros in a block of local rows into two subsets: those in the diagonal block and those in the off-diagonal block

    6220:   Input Parameters:
    6221:     mat: an MPI matrix that provides row and column layout information for splitting. Let's say its number of local rows is m.
    6222:     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[]
    6223:       respectively, along with a permutation array perm[]. Length of the i[],j[],perm[] arrays is n.

    6225:       i[] is already sorted, but within a row, j[] is not sorted and might have repeats.
    6226:       i[] might contain negative indices at the beginning, which means the corresponding entries should be ignored in the splitting.

    6228:   Output Parameters:
    6229:     j[],perm[]: the routine needs to sort j[] within each row along with perm[].
    6230:     rowBegin[],rowMid[],rowEnd[]: of length m, and the memory is preallocated and zeroed by the caller.
    6231:       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,
    6232:       and [rowMid[r],rowEnd[r]) point to begin/end entries of row r of the off-diagonal block.

    6234:     Aperm[],Ajmap[],Atot,Annz: Arrays are allocated by this routine.
    6235:       Atot: number of entries belonging to the diagonal block.
    6236:       Annz: number of unique nonzeros belonging to the diagonal block.
    6237:       Aperm[Atot] stores values from perm[] for entries belonging to the diagonal block. Length of Aperm[] is Atot, though it may also count
    6238:         repeats (i.e., same 'i,j' pair).
    6239:       Ajmap[Annz+1] stores the number of repeats of each unique entry belonging to the diagonal block. More precisely, Ajmap[t+1] - Ajmap[t]
    6240:         is the number of repeats for the t-th unique entry in the diagonal block. Ajmap[0] is always 0.

    6242:       Atot: number of entries belonging to the diagonal block
    6243:       Annz: number of unique nonzeros belonging to the diagonal block.

    6245:     Bperm[], Bjmap[], Btot, Bnnz are similar but for the off-diagonal block.

    6247:     Aperm[],Bperm[],Ajmap[] and Bjmap[] are allocated separately by this routine with PetscMalloc1().
    6248: */
    6249: 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_)
    6250: {
    6251:   PetscInt    cstart, cend, rstart, rend, row, col;
    6252:   PetscCount  Atot = 0, Btot = 0; /* Total number of nonzeros in the diagonal and off-diagonal blocks */
    6253:   PetscCount  Annz = 0, Bnnz = 0; /* Number of unique nonzeros in the diagonal and off-diagonal blocks */
    6254:   PetscCount  k, m, p, q, r, s, mid;
    6255:   PetscCount *Aperm, *Bperm, *Ajmap, *Bjmap;

    6257:   PetscFunctionBegin;
    6258:   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
    6259:   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
    6260:   m = rend - rstart;

    6262:   /* Skip negative rows */
    6263:   for (k = 0; k < n; k++)
    6264:     if (i[k] >= 0) break;

    6266:   /* Process [k,n): sort and partition each local row into diag and offdiag portions,
    6267:      fill rowBegin[], rowMid[], rowEnd[], and count Atot, Btot, Annz, Bnnz.
    6268:   */
    6269:   while (k < n) {
    6270:     row = i[k];
    6271:     /* Entries in [k,s) are in one row. Shift diagonal block col indices so that diag is ahead of offdiag after sorting the row */
    6272:     for (s = k; s < n; s++)
    6273:       if (i[s] != row) break;

    6275:     /* Shift diag columns to range of [-PETSC_INT_MAX, -1] */
    6276:     for (p = k; p < s; p++) {
    6277:       if (j[p] >= cstart && j[p] < cend) j[p] -= PETSC_INT_MAX;
    6278:       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]);
    6279:     }
    6280:     PetscCall(PetscSortIntWithCountArray(s - k, j + k, perm + k));
    6281:     PetscCall(PetscSortedIntUpperBound(j, k, s, -1, &mid)); /* Separate [k,s) into [k,mid) for diag and [mid,s) for offdiag */
    6282:     rowBegin[row - rstart] = k;
    6283:     rowMid[row - rstart]   = mid;
    6284:     rowEnd[row - rstart]   = s;

    6286:     /* Count nonzeros of this diag/offdiag row, which might have repeats */
    6287:     Atot += mid - k;
    6288:     Btot += s - mid;

    6290:     /* Count unique nonzeros of this diag row */
    6291:     for (p = k; p < mid;) {
    6292:       col = j[p];
    6293:       do {
    6294:         j[p] += PETSC_INT_MAX; /* Revert the modified diagonal indices */
    6295:         p++;
    6296:       } while (p < mid && j[p] == col);
    6297:       Annz++;
    6298:     }

    6300:     /* Count unique nonzeros of this offdiag row */
    6301:     for (p = mid; p < s;) {
    6302:       col = j[p];
    6303:       do {
    6304:         p++;
    6305:       } while (p < s && j[p] == col);
    6306:       Bnnz++;
    6307:     }
    6308:     k = s;
    6309:   }

    6311:   /* Allocation according to Atot, Btot, Annz, Bnnz */
    6312:   PetscCall(PetscMalloc1(Atot, &Aperm));
    6313:   PetscCall(PetscMalloc1(Btot, &Bperm));
    6314:   PetscCall(PetscMalloc1(Annz + 1, &Ajmap));
    6315:   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap));

    6317:   /* Re-scan indices and copy diag/offdiag permutation indices to Aperm, Bperm and also fill Ajmap and Bjmap */
    6318:   Ajmap[0] = Bjmap[0] = Atot = Btot = Annz = Bnnz = 0;
    6319:   for (r = 0; r < m; r++) {
    6320:     k   = rowBegin[r];
    6321:     mid = rowMid[r];
    6322:     s   = rowEnd[r];
    6323:     PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(Aperm, Atot), PetscSafePointerPlusOffset(perm, k), mid - k));
    6324:     PetscCall(PetscArraycpy(PetscSafePointerPlusOffset(Bperm, Btot), PetscSafePointerPlusOffset(perm, mid), s - mid));
    6325:     Atot += mid - k;
    6326:     Btot += s - mid;

    6328:     /* Scan column indices in this row and find out how many repeats each unique nonzero has */
    6329:     for (p = k; p < mid;) {
    6330:       col = j[p];
    6331:       q   = p;
    6332:       do {
    6333:         p++;
    6334:       } while (p < mid && j[p] == col);
    6335:       Ajmap[Annz + 1] = Ajmap[Annz] + (p - q);
    6336:       Annz++;
    6337:     }

    6339:     for (p = mid; p < s;) {
    6340:       col = j[p];
    6341:       q   = p;
    6342:       do {
    6343:         p++;
    6344:       } while (p < s && j[p] == col);
    6345:       Bjmap[Bnnz + 1] = Bjmap[Bnnz] + (p - q);
    6346:       Bnnz++;
    6347:     }
    6348:   }
    6349:   /* Output */
    6350:   *Aperm_ = Aperm;
    6351:   *Annz_  = Annz;
    6352:   *Atot_  = Atot;
    6353:   *Ajmap_ = Ajmap;
    6354:   *Bperm_ = Bperm;
    6355:   *Bnnz_  = Bnnz;
    6356:   *Btot_  = Btot;
    6357:   *Bjmap_ = Bjmap;
    6358:   PetscFunctionReturn(PETSC_SUCCESS);
    6359: }

    6361: /*
    6362:   Expand the jmap[] array to make a new one in view of nonzeros in the merged matrix

    6364:   Input Parameters:
    6365:     nnz1: number of unique nonzeros in a set that was used to produce imap[], jmap[]
    6366:     nnz:  number of unique nonzeros in the merged matrix
    6367:     imap[nnz1]: i-th nonzero in the set is the imap[i]-th nonzero in the merged matrix
    6368:     jmap[nnz1+1]: i-th nonzero in the set has jmap[i+1] - jmap[i] repeats in the set

    6370:   Output Parameter: (memory is allocated by the caller)
    6371:     jmap_new[nnz+1]: i-th nonzero in the merged matrix has jmap_new[i+1] - jmap_new[i] repeats in the set

    6373:   Example:
    6374:     nnz1 = 4
    6375:     nnz  = 6
    6376:     imap = [1,3,4,5]
    6377:     jmap = [0,3,5,6,7]
    6378:    then,
    6379:     jmap_new = [0,0,3,3,5,6,7]
    6380: */
    6381: static PetscErrorCode ExpandJmap_Internal(PetscCount nnz1, PetscCount nnz, const PetscCount imap[], const PetscCount jmap[], PetscCount jmap_new[])
    6382: {
    6383:   PetscCount k, p;

    6385:   PetscFunctionBegin;
    6386:   jmap_new[0] = 0;
    6387:   p           = nnz;                /* p loops over jmap_new[] backwards */
    6388:   for (k = nnz1 - 1; k >= 0; k--) { /* k loops over imap[] */
    6389:     for (; p > imap[k]; p--) jmap_new[p] = jmap[k + 1];
    6390:   }
    6391:   for (; p >= 0; p--) jmap_new[p] = jmap[0];
    6392:   PetscFunctionReturn(PETSC_SUCCESS);
    6393: }

    6395: static PetscErrorCode MatCOOStructDestroy_MPIAIJ(void *data)
    6396: {
    6397:   MatCOOStruct_MPIAIJ *coo = (MatCOOStruct_MPIAIJ *)data;

    6399:   PetscFunctionBegin;
    6400:   PetscCall(PetscSFDestroy(&coo->sf));
    6401:   PetscCall(PetscFree(coo->Aperm1));
    6402:   PetscCall(PetscFree(coo->Bperm1));
    6403:   PetscCall(PetscFree(coo->Ajmap1));
    6404:   PetscCall(PetscFree(coo->Bjmap1));
    6405:   PetscCall(PetscFree(coo->Aimap2));
    6406:   PetscCall(PetscFree(coo->Bimap2));
    6407:   PetscCall(PetscFree(coo->Aperm2));
    6408:   PetscCall(PetscFree(coo->Bperm2));
    6409:   PetscCall(PetscFree(coo->Ajmap2));
    6410:   PetscCall(PetscFree(coo->Bjmap2));
    6411:   PetscCall(PetscFree(coo->Cperm1));
    6412:   PetscCall(PetscFree2(coo->sendbuf, coo->recvbuf));
    6413:   PetscCall(PetscFree(coo));
    6414:   PetscFunctionReturn(PETSC_SUCCESS);
    6415: }

    6417: PetscErrorCode MatSetPreallocationCOO_MPIAIJ(Mat mat, PetscCount coo_n, PetscInt coo_i[], PetscInt coo_j[])
    6418: {
    6419:   MPI_Comm             comm;
    6420:   PetscMPIInt          rank, size;
    6421:   PetscInt             m, n, M, N, rstart, rend, cstart, cend; /* Sizes, indices of row/col, therefore with type PetscInt */
    6422:   PetscCount           k, p, q, rem;                           /* Loop variables over coo arrays */
    6423:   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
    6424:   PetscContainer       container;
    6425:   MatCOOStruct_MPIAIJ *coo;

    6427:   PetscFunctionBegin;
    6428:   PetscCall(PetscFree(mpiaij->garray));
    6429:   PetscCall(VecDestroy(&mpiaij->lvec));
    6430: #if defined(PETSC_USE_CTABLE)
    6431:   PetscCall(PetscHMapIDestroy(&mpiaij->colmap));
    6432: #else
    6433:   PetscCall(PetscFree(mpiaij->colmap));
    6434: #endif
    6435:   PetscCall(VecScatterDestroy(&mpiaij->Mvctx));
    6436:   mat->assembled     = PETSC_FALSE;
    6437:   mat->was_assembled = PETSC_FALSE;

    6439:   PetscCall(PetscObjectGetComm((PetscObject)mat, &comm));
    6440:   PetscCallMPI(MPI_Comm_size(comm, &size));
    6441:   PetscCallMPI(MPI_Comm_rank(comm, &rank));
    6442:   PetscCall(PetscLayoutSetUp(mat->rmap));
    6443:   PetscCall(PetscLayoutSetUp(mat->cmap));
    6444:   PetscCall(PetscLayoutGetRange(mat->rmap, &rstart, &rend));
    6445:   PetscCall(PetscLayoutGetRange(mat->cmap, &cstart, &cend));
    6446:   PetscCall(MatGetLocalSize(mat, &m, &n));
    6447:   PetscCall(MatGetSize(mat, &M, &N));

    6449:   /* Sort (i,j) by row along with a permutation array, so that the to-be-ignored */
    6450:   /* entries come first, then local rows, then remote rows.                     */
    6451:   PetscCount n1 = coo_n, *perm1;
    6452:   PetscInt  *i1 = coo_i, *j1 = coo_j;

    6454:   PetscCall(PetscMalloc1(n1, &perm1));
    6455:   for (k = 0; k < n1; k++) perm1[k] = k;

    6457:   /* Manipulate indices so that entries with negative row or col indices will have smallest
    6458:      row indices, local entries will have greater but negative row indices, and remote entries
    6459:      will have positive row indices.
    6460:   */
    6461:   for (k = 0; k < n1; k++) {
    6462:     if (i1[k] < 0 || j1[k] < 0) i1[k] = PETSC_INT_MIN;                /* e.g., -2^31, minimal to move them ahead */
    6463:     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] */
    6464:     else {
    6465:       PetscCheck(!mat->nooffprocentries, PETSC_COMM_SELF, PETSC_ERR_USER_INPUT, "MAT_NO_OFF_PROC_ENTRIES is set but insert to remote rows");
    6466:       if (mpiaij->donotstash) i1[k] = PETSC_INT_MIN; /* Ignore offproc entries as if they had negative indices */
    6467:     }
    6468:   }

    6470:   /* Sort by row; after that, [0,k) have ignored entries, [k,rem) have local rows and [rem,n1) have remote rows */
    6471:   PetscCall(PetscSortIntWithIntCountArrayPair(n1, i1, j1, perm1));

    6473:   /* Advance k to the first entry we need to take care of */
    6474:   for (k = 0; k < n1; k++)
    6475:     if (i1[k] > PETSC_INT_MIN) break;
    6476:   PetscCount i1start = k;

    6478:   PetscCall(PetscSortedIntUpperBound(i1, k, n1, rend - 1 - PETSC_INT_MAX, &rem)); /* rem is upper bound of the last local row */
    6479:   for (; k < rem; k++) i1[k] += PETSC_INT_MAX;                                    /* Revert row indices of local rows*/

    6481:   /*           Send remote rows to their owner                                  */
    6482:   /* Find which rows should be sent to which remote ranks*/
    6483:   PetscInt        nsend = 0; /* Number of MPI ranks to send data to */
    6484:   PetscMPIInt    *sendto;    /* [nsend], storing remote ranks */
    6485:   PetscInt       *nentries;  /* [nsend], storing number of entries sent to remote ranks; Assume PetscInt is big enough for this count, and error if not */
    6486:   const PetscInt *ranges;
    6487:   PetscInt        maxNsend = size >= 128 ? 128 : size; /* Assume max 128 neighbors; realloc when needed */

    6489:   PetscCall(PetscLayoutGetRanges(mat->rmap, &ranges));
    6490:   PetscCall(PetscMalloc2(maxNsend, &sendto, maxNsend, &nentries));
    6491:   for (k = rem; k < n1;) {
    6492:     PetscMPIInt owner;
    6493:     PetscInt    firstRow, lastRow;

    6495:     /* Locate a row range */
    6496:     firstRow = i1[k]; /* first row of this owner */
    6497:     PetscCall(PetscLayoutFindOwner(mat->rmap, firstRow, &owner));
    6498:     lastRow = ranges[owner + 1] - 1; /* last row of this owner */

    6500:     /* Find the first index 'p' in [k,n) with i[p] belonging to next owner */
    6501:     PetscCall(PetscSortedIntUpperBound(i1, k, n1, lastRow, &p));

    6503:     /* All entries in [k,p) belong to this remote owner */
    6504:     if (nsend >= maxNsend) { /* Double the remote ranks arrays if not long enough */
    6505:       PetscMPIInt *sendto2;
    6506:       PetscInt    *nentries2;
    6507:       PetscInt     maxNsend2 = (maxNsend <= size / 2) ? maxNsend * 2 : size;

    6509:       PetscCall(PetscMalloc2(maxNsend2, &sendto2, maxNsend2, &nentries2));
    6510:       PetscCall(PetscArraycpy(sendto2, sendto, maxNsend));
    6511:       PetscCall(PetscArraycpy(nentries2, nentries2, maxNsend + 1));
    6512:       PetscCall(PetscFree2(sendto, nentries2));
    6513:       sendto   = sendto2;
    6514:       nentries = nentries2;
    6515:       maxNsend = maxNsend2;
    6516:     }
    6517:     sendto[nsend] = owner;
    6518:     PetscCall(PetscIntCast(p - k, &nentries[nsend]));
    6519:     nsend++;
    6520:     k = p;
    6521:   }

    6523:   /* Build 1st SF to know offsets on remote to send data */
    6524:   PetscSF      sf1;
    6525:   PetscInt     nroots = 1, nroots2 = 0;
    6526:   PetscInt     nleaves = nsend, nleaves2 = 0;
    6527:   PetscInt    *offsets;
    6528:   PetscSFNode *iremote;

    6530:   PetscCall(PetscSFCreate(comm, &sf1));
    6531:   PetscCall(PetscMalloc1(nsend, &iremote));
    6532:   PetscCall(PetscMalloc1(nsend, &offsets));
    6533:   for (k = 0; k < nsend; k++) {
    6534:     iremote[k].rank  = sendto[k];
    6535:     iremote[k].index = 0;
    6536:     nleaves2 += nentries[k];
    6537:     PetscCheck(nleaves2 >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF leaves is too large for PetscInt");
    6538:   }
    6539:   PetscCall(PetscSFSetGraph(sf1, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));
    6540:   PetscCall(PetscSFFetchAndOpWithMemTypeBegin(sf1, MPIU_INT, PETSC_MEMTYPE_HOST, &nroots2 /*rootdata*/, PETSC_MEMTYPE_HOST, nentries /*leafdata*/, PETSC_MEMTYPE_HOST, offsets /*leafupdate*/, MPI_SUM));
    6541:   PetscCall(PetscSFFetchAndOpEnd(sf1, MPIU_INT, &nroots2, nentries, offsets, MPI_SUM)); /* Would nroots2 overflow, we check offsets[] below */
    6542:   PetscCall(PetscSFDestroy(&sf1));
    6543:   PetscAssert(nleaves2 == n1 - rem, PETSC_COMM_SELF, PETSC_ERR_PLIB, "nleaves2 %" PetscInt_FMT " != number of remote entries %" PetscCount_FMT, nleaves2, n1 - rem);

    6545:   /* Build 2nd SF to send remote COOs to their owner */
    6546:   PetscSF sf2;
    6547:   nroots  = nroots2;
    6548:   nleaves = nleaves2;
    6549:   PetscCall(PetscSFCreate(comm, &sf2));
    6550:   PetscCall(PetscSFSetFromOptions(sf2));
    6551:   PetscCall(PetscMalloc1(nleaves, &iremote));
    6552:   p = 0;
    6553:   for (k = 0; k < nsend; k++) {
    6554:     PetscCheck(offsets[k] >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of SF roots is too large for PetscInt");
    6555:     for (q = 0; q < nentries[k]; q++, p++) {
    6556:       iremote[p].rank = sendto[k];
    6557:       PetscCall(PetscIntCast(offsets[k] + q, &iremote[p].index));
    6558:     }
    6559:   }
    6560:   PetscCall(PetscSFSetGraph(sf2, nroots, nleaves, NULL, PETSC_OWN_POINTER, iremote, PETSC_OWN_POINTER));

    6562:   /* Send the remote COOs to their owner */
    6563:   PetscInt    n2 = nroots, *i2, *j2; /* Buffers for received COOs from other ranks, along with a permutation array */
    6564:   PetscCount *perm2;                 /* Though PetscInt is enough for remote entries, we use PetscCount here as we want to reuse MatSplitEntries_Internal() */
    6565:   PetscCall(PetscMalloc3(n2, &i2, n2, &j2, n2, &perm2));
    6566:   PetscAssert(rem == 0 || i1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6567:   PetscAssert(rem == 0 || j1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6568:   PetscInt *i1prem = PetscSafePointerPlusOffset(i1, rem);
    6569:   PetscInt *j1prem = PetscSafePointerPlusOffset(j1, rem);
    6570:   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, i1prem, PETSC_MEMTYPE_HOST, i2, MPI_REPLACE));
    6571:   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, i1prem, i2, MPI_REPLACE));
    6572:   PetscCall(PetscSFReduceWithMemTypeBegin(sf2, MPIU_INT, PETSC_MEMTYPE_HOST, j1prem, PETSC_MEMTYPE_HOST, j2, MPI_REPLACE));
    6573:   PetscCall(PetscSFReduceEnd(sf2, MPIU_INT, j1prem, j2, MPI_REPLACE));

    6575:   PetscCall(PetscFree(offsets));
    6576:   PetscCall(PetscFree2(sendto, nentries));

    6578:   /* Sort received COOs by row along with the permutation array     */
    6579:   for (k = 0; k < n2; k++) perm2[k] = k;
    6580:   PetscCall(PetscSortIntWithIntCountArrayPair(n2, i2, j2, perm2));

    6582:   /* sf2 only sends contiguous leafdata to contiguous rootdata. We record the permutation which will be used to fill leafdata */
    6583:   PetscCount *Cperm1;
    6584:   PetscAssert(rem == 0 || perm1 != NULL, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Cannot add nonzero offset to null");
    6585:   PetscCount *perm1prem = PetscSafePointerPlusOffset(perm1, rem);
    6586:   PetscCall(PetscMalloc1(nleaves, &Cperm1));
    6587:   PetscCall(PetscArraycpy(Cperm1, perm1prem, nleaves));

    6589:   /* Support for HYPRE matrices, kind of a hack.
    6590:      Swap min column with diagonal so that diagonal values will go first */
    6591:   PetscBool hypre;
    6592:   PetscCall(PetscStrcmp("_internal_COO_mat_for_hypre", ((PetscObject)mat)->name, &hypre));
    6593:   if (hypre) {
    6594:     PetscInt *minj;
    6595:     PetscBT   hasdiag;

    6597:     PetscCall(PetscBTCreate(m, &hasdiag));
    6598:     PetscCall(PetscMalloc1(m, &minj));
    6599:     for (k = 0; k < m; k++) minj[k] = PETSC_INT_MAX;
    6600:     for (k = i1start; k < rem; k++) {
    6601:       if (j1[k] < cstart || j1[k] >= cend) continue;
    6602:       const PetscInt rindex = i1[k] - rstart;
    6603:       if ((j1[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
    6604:       minj[rindex] = PetscMin(minj[rindex], j1[k]);
    6605:     }
    6606:     for (k = 0; k < n2; k++) {
    6607:       if (j2[k] < cstart || j2[k] >= cend) continue;
    6608:       const PetscInt rindex = i2[k] - rstart;
    6609:       if ((j2[k] - cstart) == rindex) PetscCall(PetscBTSet(hasdiag, rindex));
    6610:       minj[rindex] = PetscMin(minj[rindex], j2[k]);
    6611:     }
    6612:     for (k = i1start; k < rem; k++) {
    6613:       const PetscInt rindex = i1[k] - rstart;
    6614:       if (j1[k] < cstart || j1[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
    6615:       if (j1[k] == minj[rindex]) j1[k] = i1[k] + (cstart - rstart);
    6616:       else if ((j1[k] - cstart) == rindex) j1[k] = minj[rindex];
    6617:     }
    6618:     for (k = 0; k < n2; k++) {
    6619:       const PetscInt rindex = i2[k] - rstart;
    6620:       if (j2[k] < cstart || j2[k] >= cend || !PetscBTLookup(hasdiag, rindex)) continue;
    6621:       if (j2[k] == minj[rindex]) j2[k] = i2[k] + (cstart - rstart);
    6622:       else if ((j2[k] - cstart) == rindex) j2[k] = minj[rindex];
    6623:     }
    6624:     PetscCall(PetscBTDestroy(&hasdiag));
    6625:     PetscCall(PetscFree(minj));
    6626:   }

    6628:   /* Split local COOs and received COOs into diag/offdiag portions */
    6629:   PetscCount *rowBegin1, *rowMid1, *rowEnd1;
    6630:   PetscCount *Ajmap1, *Aperm1, *Bjmap1, *Bperm1;
    6631:   PetscCount  Annz1, Bnnz1, Atot1, Btot1;
    6632:   PetscCount *rowBegin2, *rowMid2, *rowEnd2;
    6633:   PetscCount *Ajmap2, *Aperm2, *Bjmap2, *Bperm2;
    6634:   PetscCount  Annz2, Bnnz2, Atot2, Btot2;

    6636:   PetscCall(PetscCalloc3(m, &rowBegin1, m, &rowMid1, m, &rowEnd1));
    6637:   PetscCall(PetscCalloc3(m, &rowBegin2, m, &rowMid2, m, &rowEnd2));
    6638:   PetscCall(MatSplitEntries_Internal(mat, rem, i1, j1, perm1, rowBegin1, rowMid1, rowEnd1, &Atot1, &Aperm1, &Annz1, &Ajmap1, &Btot1, &Bperm1, &Bnnz1, &Bjmap1));
    6639:   PetscCall(MatSplitEntries_Internal(mat, n2, i2, j2, perm2, rowBegin2, rowMid2, rowEnd2, &Atot2, &Aperm2, &Annz2, &Ajmap2, &Btot2, &Bperm2, &Bnnz2, &Bjmap2));

    6641:   /* Merge local COOs with received COOs: diag with diag, offdiag with offdiag */
    6642:   PetscInt *Ai, *Bi;
    6643:   PetscInt *Aj, *Bj;

    6645:   PetscCall(PetscMalloc1(m + 1, &Ai));
    6646:   PetscCall(PetscMalloc1(m + 1, &Bi));
    6647:   PetscCall(PetscMalloc1(Annz1 + Annz2, &Aj)); /* Since local and remote entries might have dups, we might allocate excess memory */
    6648:   PetscCall(PetscMalloc1(Bnnz1 + Bnnz2, &Bj));

    6650:   PetscCount *Aimap1, *Bimap1, *Aimap2, *Bimap2;
    6651:   PetscCall(PetscMalloc1(Annz1, &Aimap1));
    6652:   PetscCall(PetscMalloc1(Bnnz1, &Bimap1));
    6653:   PetscCall(PetscMalloc1(Annz2, &Aimap2));
    6654:   PetscCall(PetscMalloc1(Bnnz2, &Bimap2));

    6656:   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowBegin1, rowMid1, rowBegin2, rowMid2, Ajmap1, Ajmap2, Aimap1, Aimap2, Ai, Aj));
    6657:   PetscCall(MatMergeEntries_Internal(mat, j1, j2, rowMid1, rowEnd1, rowMid2, rowEnd2, Bjmap1, Bjmap2, Bimap1, Bimap2, Bi, Bj));

    6659:   /* Expand Ajmap1/Bjmap1 to make them based off nonzeros in A/B, since we     */
    6660:   /* expect nonzeros in A/B most likely have local contributing entries        */
    6661:   PetscInt    Annz = Ai[m];
    6662:   PetscInt    Bnnz = Bi[m];
    6663:   PetscCount *Ajmap1_new, *Bjmap1_new;

    6665:   PetscCall(PetscMalloc1(Annz + 1, &Ajmap1_new));
    6666:   PetscCall(PetscMalloc1(Bnnz + 1, &Bjmap1_new));

    6668:   PetscCall(ExpandJmap_Internal(Annz1, Annz, Aimap1, Ajmap1, Ajmap1_new));
    6669:   PetscCall(ExpandJmap_Internal(Bnnz1, Bnnz, Bimap1, Bjmap1, Bjmap1_new));

    6671:   PetscCall(PetscFree(Aimap1));
    6672:   PetscCall(PetscFree(Ajmap1));
    6673:   PetscCall(PetscFree(Bimap1));
    6674:   PetscCall(PetscFree(Bjmap1));
    6675:   PetscCall(PetscFree3(rowBegin1, rowMid1, rowEnd1));
    6676:   PetscCall(PetscFree3(rowBegin2, rowMid2, rowEnd2));
    6677:   PetscCall(PetscFree(perm1));
    6678:   PetscCall(PetscFree3(i2, j2, perm2));

    6680:   Ajmap1 = Ajmap1_new;
    6681:   Bjmap1 = Bjmap1_new;

    6683:   /* Reallocate Aj, Bj once we know actual numbers of unique nonzeros in A and B */
    6684:   if (Annz < Annz1 + Annz2) {
    6685:     PetscInt *Aj_new;
    6686:     PetscCall(PetscMalloc1(Annz, &Aj_new));
    6687:     PetscCall(PetscArraycpy(Aj_new, Aj, Annz));
    6688:     PetscCall(PetscFree(Aj));
    6689:     Aj = Aj_new;
    6690:   }

    6692:   if (Bnnz < Bnnz1 + Bnnz2) {
    6693:     PetscInt *Bj_new;
    6694:     PetscCall(PetscMalloc1(Bnnz, &Bj_new));
    6695:     PetscCall(PetscArraycpy(Bj_new, Bj, Bnnz));
    6696:     PetscCall(PetscFree(Bj));
    6697:     Bj = Bj_new;
    6698:   }

    6700:   /* Create new submatrices for on-process and off-process coupling                  */
    6701:   PetscScalar     *Aa, *Ba;
    6702:   MatType          rtype;
    6703:   Mat_SeqAIJ      *a, *b;
    6704:   PetscObjectState state;
    6705:   PetscCall(PetscCalloc1(Annz, &Aa)); /* Zero matrix on device */
    6706:   PetscCall(PetscCalloc1(Bnnz, &Ba));
    6707:   /* make Aj[] local, i.e, based off the start column of the diagonal portion */
    6708:   if (cstart) {
    6709:     for (k = 0; k < Annz; k++) Aj[k] -= cstart;
    6710:   }

    6712:   PetscCall(MatGetRootType_Private(mat, &rtype));

    6714:   MatSeqXAIJGetOptions_Private(mpiaij->A);
    6715:   PetscCall(MatDestroy(&mpiaij->A));
    6716:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, Ai, Aj, Aa, &mpiaij->A));
    6717:   PetscCall(MatSetBlockSizesFromMats(mpiaij->A, mat, mat));
    6718:   MatSeqXAIJRestoreOptions_Private(mpiaij->A);

    6720:   MatSeqXAIJGetOptions_Private(mpiaij->B);
    6721:   PetscCall(MatDestroy(&mpiaij->B));
    6722:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, mat->cmap->N, Bi, Bj, Ba, &mpiaij->B));
    6723:   PetscCall(MatSetBlockSizesFromMats(mpiaij->B, mat, mat));
    6724:   MatSeqXAIJRestoreOptions_Private(mpiaij->B);

    6726:   PetscCall(MatSetUpMultiply_MPIAIJ(mat));
    6727:   mat->was_assembled = PETSC_TRUE; // was_assembled in effect means the Mvctx is built; doing so avoids redundant MatSetUpMultiply_MPIAIJ
    6728:   state              = mpiaij->A->nonzerostate + mpiaij->B->nonzerostate;
    6729:   PetscCallMPI(MPIU_Allreduce(&state, &mat->nonzerostate, 1, MPIU_INT64, MPI_SUM, PetscObjectComm((PetscObject)mat)));

    6731:   a          = (Mat_SeqAIJ *)mpiaij->A->data;
    6732:   b          = (Mat_SeqAIJ *)mpiaij->B->data;
    6733:   a->free_a  = PETSC_TRUE;
    6734:   a->free_ij = PETSC_TRUE;
    6735:   b->free_a  = PETSC_TRUE;
    6736:   b->free_ij = PETSC_TRUE;
    6737:   a->maxnz   = a->nz;
    6738:   b->maxnz   = b->nz;

    6740:   /* conversion must happen AFTER multiply setup */
    6741:   PetscCall(MatConvert(mpiaij->A, rtype, MAT_INPLACE_MATRIX, &mpiaij->A));
    6742:   PetscCall(MatConvert(mpiaij->B, rtype, MAT_INPLACE_MATRIX, &mpiaij->B));
    6743:   PetscCall(VecDestroy(&mpiaij->lvec));
    6744:   PetscCall(MatCreateVecs(mpiaij->B, &mpiaij->lvec, NULL));

    6746:   // Put the COO struct in a container and then attach that to the matrix
    6747:   PetscCall(PetscMalloc1(1, &coo));
    6748:   coo->n       = coo_n;
    6749:   coo->sf      = sf2;
    6750:   coo->sendlen = nleaves;
    6751:   coo->recvlen = nroots;
    6752:   coo->Annz    = Annz;
    6753:   coo->Bnnz    = Bnnz;
    6754:   coo->Annz2   = Annz2;
    6755:   coo->Bnnz2   = Bnnz2;
    6756:   coo->Atot1   = Atot1;
    6757:   coo->Atot2   = Atot2;
    6758:   coo->Btot1   = Btot1;
    6759:   coo->Btot2   = Btot2;
    6760:   coo->Ajmap1  = Ajmap1;
    6761:   coo->Aperm1  = Aperm1;
    6762:   coo->Bjmap1  = Bjmap1;
    6763:   coo->Bperm1  = Bperm1;
    6764:   coo->Aimap2  = Aimap2;
    6765:   coo->Ajmap2  = Ajmap2;
    6766:   coo->Aperm2  = Aperm2;
    6767:   coo->Bimap2  = Bimap2;
    6768:   coo->Bjmap2  = Bjmap2;
    6769:   coo->Bperm2  = Bperm2;
    6770:   coo->Cperm1  = Cperm1;
    6771:   // Allocate in preallocation. If not used, it has zero cost on host
    6772:   PetscCall(PetscMalloc2(coo->sendlen, &coo->sendbuf, coo->recvlen, &coo->recvbuf));
    6773:   PetscCall(PetscContainerCreate(PETSC_COMM_SELF, &container));
    6774:   PetscCall(PetscContainerSetPointer(container, coo));
    6775:   PetscCall(PetscContainerSetUserDestroy(container, MatCOOStructDestroy_MPIAIJ));
    6776:   PetscCall(PetscObjectCompose((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject)container));
    6777:   PetscCall(PetscContainerDestroy(&container));
    6778:   PetscFunctionReturn(PETSC_SUCCESS);
    6779: }

    6781: static PetscErrorCode MatSetValuesCOO_MPIAIJ(Mat mat, const PetscScalar v[], InsertMode imode)
    6782: {
    6783:   Mat_MPIAIJ          *mpiaij = (Mat_MPIAIJ *)mat->data;
    6784:   Mat                  A = mpiaij->A, B = mpiaij->B;
    6785:   PetscScalar         *Aa, *Ba;
    6786:   PetscScalar         *sendbuf, *recvbuf;
    6787:   const PetscCount    *Ajmap1, *Ajmap2, *Aimap2;
    6788:   const PetscCount    *Bjmap1, *Bjmap2, *Bimap2;
    6789:   const PetscCount    *Aperm1, *Aperm2, *Bperm1, *Bperm2;
    6790:   const PetscCount    *Cperm1;
    6791:   PetscContainer       container;
    6792:   MatCOOStruct_MPIAIJ *coo;

    6794:   PetscFunctionBegin;
    6795:   PetscCall(PetscObjectQuery((PetscObject)mat, "__PETSc_MatCOOStruct_Host", (PetscObject *)&container));
    6796:   PetscCheck(container, PetscObjectComm((PetscObject)mat), PETSC_ERR_PLIB, "Not found MatCOOStruct on this matrix");
    6797:   PetscCall(PetscContainerGetPointer(container, (void **)&coo));
    6798:   sendbuf = coo->sendbuf;
    6799:   recvbuf = coo->recvbuf;
    6800:   Ajmap1  = coo->Ajmap1;
    6801:   Ajmap2  = coo->Ajmap2;
    6802:   Aimap2  = coo->Aimap2;
    6803:   Bjmap1  = coo->Bjmap1;
    6804:   Bjmap2  = coo->Bjmap2;
    6805:   Bimap2  = coo->Bimap2;
    6806:   Aperm1  = coo->Aperm1;
    6807:   Aperm2  = coo->Aperm2;
    6808:   Bperm1  = coo->Bperm1;
    6809:   Bperm2  = coo->Bperm2;
    6810:   Cperm1  = coo->Cperm1;

    6812:   PetscCall(MatSeqAIJGetArray(A, &Aa)); /* Might read and write matrix values */
    6813:   PetscCall(MatSeqAIJGetArray(B, &Ba));

    6815:   /* Pack entries to be sent to remote */
    6816:   for (PetscCount i = 0; i < coo->sendlen; i++) sendbuf[i] = v[Cperm1[i]];

    6818:   /* Send remote entries to their owner and overlap the communication with local computation */
    6819:   PetscCall(PetscSFReduceWithMemTypeBegin(coo->sf, MPIU_SCALAR, PETSC_MEMTYPE_HOST, sendbuf, PETSC_MEMTYPE_HOST, recvbuf, MPI_REPLACE));
    6820:   /* Add local entries to A and B */
    6821:   for (PetscCount i = 0; i < coo->Annz; i++) { /* All nonzeros in A are either zero'ed or added with a value (i.e., initialized) */
    6822:     PetscScalar sum = 0.0;                     /* Do partial summation first to improve numerical stability */
    6823:     for (PetscCount k = Ajmap1[i]; k < Ajmap1[i + 1]; k++) sum += v[Aperm1[k]];
    6824:     Aa[i] = (imode == INSERT_VALUES ? 0.0 : Aa[i]) + sum;
    6825:   }
    6826:   for (PetscCount i = 0; i < coo->Bnnz; i++) {
    6827:     PetscScalar sum = 0.0;
    6828:     for (PetscCount k = Bjmap1[i]; k < Bjmap1[i + 1]; k++) sum += v[Bperm1[k]];
    6829:     Ba[i] = (imode == INSERT_VALUES ? 0.0 : Ba[i]) + sum;
    6830:   }
    6831:   PetscCall(PetscSFReduceEnd(coo->sf, MPIU_SCALAR, sendbuf, recvbuf, MPI_REPLACE));

    6833:   /* Add received remote entries to A and B */
    6834:   for (PetscCount i = 0; i < coo->Annz2; i++) {
    6835:     for (PetscCount k = Ajmap2[i]; k < Ajmap2[i + 1]; k++) Aa[Aimap2[i]] += recvbuf[Aperm2[k]];
    6836:   }
    6837:   for (PetscCount i = 0; i < coo->Bnnz2; i++) {
    6838:     for (PetscCount k = Bjmap2[i]; k < Bjmap2[i + 1]; k++) Ba[Bimap2[i]] += recvbuf[Bperm2[k]];
    6839:   }
    6840:   PetscCall(MatSeqAIJRestoreArray(A, &Aa));
    6841:   PetscCall(MatSeqAIJRestoreArray(B, &Ba));
    6842:   PetscFunctionReturn(PETSC_SUCCESS);
    6843: }

    6845: /*MC
    6846:    MATMPIAIJ - MATMPIAIJ = "mpiaij" - A matrix type to be used for parallel sparse matrices.

    6848:    Options Database Keys:
    6849: . -mat_type mpiaij - sets the matrix type to `MATMPIAIJ` during a call to `MatSetFromOptions()`

    6851:    Level: beginner

    6853:    Notes:
    6854:    `MatSetValues()` may be called for this matrix type with a `NULL` argument for the numerical values,
    6855:     in this case the values associated with the rows and columns one passes in are set to zero
    6856:     in the matrix

    6858:     `MatSetOptions`(,`MAT_STRUCTURE_ONLY`,`PETSC_TRUE`) may be called for this matrix type. In this no
    6859:     space is allocated for the nonzero entries and any entries passed with `MatSetValues()` are ignored

    6861: .seealso: [](ch_matrices), `Mat`, `MATSEQAIJ`, `MATAIJ`, `MatCreateAIJ()`
    6862: M*/
    6863: PETSC_EXTERN PetscErrorCode MatCreate_MPIAIJ(Mat B)
    6864: {
    6865:   Mat_MPIAIJ *b;
    6866:   PetscMPIInt size;

    6868:   PetscFunctionBegin;
    6869:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)B), &size));

    6871:   PetscCall(PetscNew(&b));
    6872:   B->data       = (void *)b;
    6873:   B->ops[0]     = MatOps_Values;
    6874:   B->assembled  = PETSC_FALSE;
    6875:   B->insertmode = NOT_SET_VALUES;
    6876:   b->size       = size;

    6878:   PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)B), &b->rank));

    6880:   /* build cache for off array entries formed */
    6881:   PetscCall(MatStashCreate_Private(PetscObjectComm((PetscObject)B), 1, &B->stash));

    6883:   b->donotstash  = PETSC_FALSE;
    6884:   b->colmap      = NULL;
    6885:   b->garray      = NULL;
    6886:   b->roworiented = PETSC_TRUE;

    6888:   /* stuff used for matrix vector multiply */
    6889:   b->lvec  = NULL;
    6890:   b->Mvctx = NULL;

    6892:   /* stuff for MatGetRow() */
    6893:   b->rowindices   = NULL;
    6894:   b->rowvalues    = NULL;
    6895:   b->getrowactive = PETSC_FALSE;

    6897:   /* flexible pointer used in CUSPARSE classes */
    6898:   b->spptr = NULL;

    6900:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetUseScalableIncreaseOverlap_C", MatMPIAIJSetUseScalableIncreaseOverlap_MPIAIJ));
    6901:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatStoreValues_C", MatStoreValues_MPIAIJ));
    6902:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatRetrieveValues_C", MatRetrieveValues_MPIAIJ));
    6903:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatIsTranspose_C", MatIsTranspose_MPIAIJ));
    6904:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocation_C", MatMPIAIJSetPreallocation_MPIAIJ));
    6905:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatResetPreallocation_C", MatResetPreallocation_MPIAIJ));
    6906:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatMPIAIJSetPreallocationCSR_C", MatMPIAIJSetPreallocationCSR_MPIAIJ));
    6907:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatDiagonalScaleLocal_C", MatDiagonalScaleLocal_MPIAIJ));
    6908:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijperm_C", MatConvert_MPIAIJ_MPIAIJPERM));
    6909:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijsell_C", MatConvert_MPIAIJ_MPIAIJSELL));
    6910: #if defined(PETSC_HAVE_CUDA)
    6911:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcusparse_C", MatConvert_MPIAIJ_MPIAIJCUSPARSE));
    6912: #endif
    6913: #if defined(PETSC_HAVE_HIP)
    6914:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijhipsparse_C", MatConvert_MPIAIJ_MPIAIJHIPSPARSE));
    6915: #endif
    6916: #if defined(PETSC_HAVE_KOKKOS_KERNELS)
    6917:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijkokkos_C", MatConvert_MPIAIJ_MPIAIJKokkos));
    6918: #endif
    6919: #if defined(PETSC_HAVE_MKL_SPARSE)
    6920:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijmkl_C", MatConvert_MPIAIJ_MPIAIJMKL));
    6921: #endif
    6922:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpiaijcrl_C", MatConvert_MPIAIJ_MPIAIJCRL));
    6923:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpibaij_C", MatConvert_MPIAIJ_MPIBAIJ));
    6924:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisbaij_C", MatConvert_MPIAIJ_MPISBAIJ));
    6925:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpidense_C", MatConvert_MPIAIJ_MPIDense));
    6926: #if defined(PETSC_HAVE_ELEMENTAL)
    6927:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_elemental_C", MatConvert_MPIAIJ_Elemental));
    6928: #endif
    6929: #if defined(PETSC_HAVE_SCALAPACK)
    6930:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_scalapack_C", MatConvert_AIJ_ScaLAPACK));
    6931: #endif
    6932:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_is_C", MatConvert_XAIJ_IS));
    6933:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_mpisell_C", MatConvert_MPIAIJ_MPISELL));
    6934: #if defined(PETSC_HAVE_HYPRE)
    6935:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatConvert_mpiaij_hypre_C", MatConvert_AIJ_HYPRE));
    6936:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_transpose_mpiaij_mpiaij_C", MatProductSetFromOptions_Transpose_AIJ_AIJ));
    6937: #endif
    6938:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_is_mpiaij_C", MatProductSetFromOptions_IS_XAIJ));
    6939:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatProductSetFromOptions_mpiaij_mpiaij_C", MatProductSetFromOptions_MPIAIJ));
    6940:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetPreallocationCOO_C", MatSetPreallocationCOO_MPIAIJ));
    6941:   PetscCall(PetscObjectComposeFunction((PetscObject)B, "MatSetValuesCOO_C", MatSetValuesCOO_MPIAIJ));
    6942:   PetscCall(PetscObjectChangeTypeName((PetscObject)B, MATMPIAIJ));
    6943:   PetscFunctionReturn(PETSC_SUCCESS);
    6944: }

    6946: /*@
    6947:   MatCreateMPIAIJWithSplitArrays - creates a `MATMPIAIJ` matrix using arrays that contain the "diagonal"
    6948:   and "off-diagonal" part of the matrix in CSR format.

    6950:   Collective

    6952:   Input Parameters:
    6953: + comm - MPI communicator
    6954: . m    - number of local rows (Cannot be `PETSC_DECIDE`)
    6955: . n    - This value should be the same as the local size used in creating the
    6956:          x vector for the matrix-vector product $y = Ax$. (or `PETSC_DECIDE` to have
    6957:          calculated if `N` is given) For square matrices `n` is almost always `m`.
    6958: . M    - number of global rows (or `PETSC_DETERMINE` to have calculated if `m` is given)
    6959: . N    - number of global columns (or `PETSC_DETERMINE` to have calculated if `n` is given)
    6960: . 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
    6961: . j    - column indices, which must be local, i.e., based off the start column of the diagonal portion
    6962: . a    - matrix values
    6963: . 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
    6964: . oj   - column indices, which must be global, representing global columns in the `MATMPIAIJ` matrix
    6965: - oa   - matrix values

    6967:   Output Parameter:
    6968: . mat - the matrix

    6970:   Level: advanced

    6972:   Notes:
    6973:   The `i`, `j`, and `a` arrays ARE NOT copied by this routine into the internal format used by PETSc (even in Fortran). The user
    6974:   must free the arrays once the matrix has been destroyed and not before.

    6976:   The `i` and `j` indices are 0 based

    6978:   See `MatCreateAIJ()` for the definition of "diagonal" and "off-diagonal" portion of the matrix

    6980:   This sets local rows and cannot be used to set off-processor values.

    6982:   Use of this routine is discouraged because it is inflexible and cumbersome to use. It is extremely rare that a
    6983:   legacy application natively assembles into exactly this split format. The code to do so is nontrivial and does
    6984:   not easily support in-place reassembly. It is recommended to use MatSetValues() (or a variant thereof) because
    6985:   the resulting assembly is easier to implement, will work with any matrix format, and the user does not have to
    6986:   keep track of the underlying array. Use `MatSetOption`(A,`MAT_NO_OFF_PROC_ENTRIES`,`PETSC_TRUE`) to disable all
    6987:   communication if it is known that only local entries will be set.

    6989: .seealso: [](ch_matrices), `Mat`, `MatCreate()`, `MatCreateSeqAIJ()`, `MatSetValues()`, `MatMPIAIJSetPreallocation()`, `MatMPIAIJSetPreallocationCSR()`,
    6990:           `MATMPIAIJ`, `MatCreateAIJ()`, `MatCreateMPIAIJWithArrays()`
    6991: @*/
    6992: 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)
    6993: {
    6994:   Mat_MPIAIJ *maij;

    6996:   PetscFunctionBegin;
    6997:   PetscCheck(m >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "local number of rows (m) cannot be PETSC_DECIDE, or negative");
    6998:   PetscCheck(i[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "i (row indices) must start with 0");
    6999:   PetscCheck(oi[0] == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "oi (row indices) must start with 0");
    7000:   PetscCall(MatCreate(comm, mat));
    7001:   PetscCall(MatSetSizes(*mat, m, n, M, N));
    7002:   PetscCall(MatSetType(*mat, MATMPIAIJ));
    7003:   maij = (Mat_MPIAIJ *)(*mat)->data;

    7005:   (*mat)->preallocated = PETSC_TRUE;

    7007:   PetscCall(PetscLayoutSetUp((*mat)->rmap));
    7008:   PetscCall(PetscLayoutSetUp((*mat)->cmap));

    7010:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, n, i, j, a, &maij->A));
    7011:   PetscCall(MatCreateSeqAIJWithArrays(PETSC_COMM_SELF, m, (*mat)->cmap->N, oi, oj, oa, &maij->B));

    7013:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_TRUE));
    7014:   PetscCall(MatAssemblyBegin(*mat, MAT_FINAL_ASSEMBLY));
    7015:   PetscCall(MatAssemblyEnd(*mat, MAT_FINAL_ASSEMBLY));
    7016:   PetscCall(MatSetOption(*mat, MAT_NO_OFF_PROC_ENTRIES, PETSC_FALSE));
    7017:   PetscCall(MatSetOption(*mat, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_TRUE));
    7018:   PetscFunctionReturn(PETSC_SUCCESS);
    7019: }

    7021: typedef struct {
    7022:   Mat       *mp;    /* intermediate products */
    7023:   PetscBool *mptmp; /* is the intermediate product temporary ? */
    7024:   PetscInt   cp;    /* number of intermediate products */

    7026:   /* support for MatGetBrowsOfAoCols_MPIAIJ for P_oth */
    7027:   PetscInt    *startsj_s, *startsj_r;
    7028:   PetscScalar *bufa;
    7029:   Mat          P_oth;

    7031:   /* may take advantage of merging product->B */
    7032:   Mat Bloc; /* B-local by merging diag and off-diag */

    7034:   /* cusparse does not have support to split between symbolic and numeric phases.
    7035:      When api_user is true, we don't need to update the numerical values
    7036:      of the temporary storage */
    7037:   PetscBool reusesym;

    7039:   /* support for COO values insertion */
    7040:   PetscScalar *coo_v, *coo_w; /* store on-process and off-process COO scalars, and used as MPI recv/send buffers respectively */
    7041:   PetscInt   **own;           /* own[i] points to address of on-process COO indices for Mat mp[i] */
    7042:   PetscInt   **off;           /* off[i] points to address of off-process COO indices for Mat mp[i] */
    7043:   PetscBool    hasoffproc;    /* if true, have off-process values insertion (i.e. AtB or PtAP) */
    7044:   PetscSF      sf;            /* used for non-local values insertion and memory malloc */
    7045:   PetscMemType mtype;

    7047:   /* customization */
    7048:   PetscBool abmerge;
    7049:   PetscBool P_oth_bind;
    7050: } MatMatMPIAIJBACKEND;

    7052: static PetscErrorCode MatDestroy_MatMatMPIAIJBACKEND(void *data)
    7053: {
    7054:   MatMatMPIAIJBACKEND *mmdata = (MatMatMPIAIJBACKEND *)data;
    7055:   PetscInt             i;

    7057:   PetscFunctionBegin;
    7058:   PetscCall(PetscFree2(mmdata->startsj_s, mmdata->startsj_r));
    7059:   PetscCall(PetscFree(mmdata->bufa));
    7060:   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_v));
    7061:   PetscCall(PetscSFFree(mmdata->sf, mmdata->mtype, mmdata->coo_w));
    7062:   PetscCall(MatDestroy(&mmdata->P_oth));
    7063:   PetscCall(MatDestroy(&mmdata->Bloc));
    7064:   PetscCall(PetscSFDestroy(&mmdata->sf));
    7065:   for (i = 0; i < mmdata->cp; i++) PetscCall(MatDestroy(&mmdata->mp[i]));
    7066:   PetscCall(PetscFree2(mmdata->mp, mmdata->mptmp));
    7067:   PetscCall(PetscFree(mmdata->own[0]));
    7068:   PetscCall(PetscFree(mmdata->own));
    7069:   PetscCall(PetscFree(mmdata->off[0]));
    7070:   PetscCall(PetscFree(mmdata->off));
    7071:   PetscCall(PetscFree(mmdata));
    7072:   PetscFunctionReturn(PETSC_SUCCESS);
    7073: }

    7075: /* Copy selected n entries with indices in idx[] of A to v[].
    7076:    If idx is NULL, copy the whole data array of A to v[]
    7077:  */
    7078: static PetscErrorCode MatSeqAIJCopySubArray(Mat A, PetscInt n, const PetscInt idx[], PetscScalar v[])
    7079: {
    7080:   PetscErrorCode (*f)(Mat, PetscInt, const PetscInt[], PetscScalar[]);

    7082:   PetscFunctionBegin;
    7083:   PetscCall(PetscObjectQueryFunction((PetscObject)A, "MatSeqAIJCopySubArray_C", &f));
    7084:   if (f) {
    7085:     PetscCall((*f)(A, n, idx, v));
    7086:   } else {
    7087:     const PetscScalar *vv;

    7089:     PetscCall(MatSeqAIJGetArrayRead(A, &vv));
    7090:     if (n && idx) {
    7091:       PetscScalar    *w  = v;
    7092:       const PetscInt *oi = idx;
    7093:       PetscInt        j;

    7095:       for (j = 0; j < n; j++) *w++ = vv[*oi++];
    7096:     } else {
    7097:       PetscCall(PetscArraycpy(v, vv, n));
    7098:     }
    7099:     PetscCall(MatSeqAIJRestoreArrayRead(A, &vv));
    7100:   }
    7101:   PetscFunctionReturn(PETSC_SUCCESS);
    7102: }

    7104: static PetscErrorCode MatProductNumeric_MPIAIJBACKEND(Mat C)
    7105: {
    7106:   MatMatMPIAIJBACKEND *mmdata;
    7107:   PetscInt             i, n_d, n_o;

    7109:   PetscFunctionBegin;
    7110:   MatCheckProduct(C, 1);
    7111:   PetscCheck(C->product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data empty");
    7112:   mmdata = (MatMatMPIAIJBACKEND *)C->product->data;
    7113:   if (!mmdata->reusesym) { /* update temporary matrices */
    7114:     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));
    7115:     if (mmdata->Bloc) PetscCall(MatMPIAIJGetLocalMatMerge(C->product->B, MAT_REUSE_MATRIX, NULL, &mmdata->Bloc));
    7116:   }
    7117:   mmdata->reusesym = PETSC_FALSE;

    7119:   for (i = 0; i < mmdata->cp; i++) {
    7120:     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]);
    7121:     PetscCall((*mmdata->mp[i]->ops->productnumeric)(mmdata->mp[i]));
    7122:   }
    7123:   for (i = 0, n_d = 0, n_o = 0; i < mmdata->cp; i++) {
    7124:     PetscInt noff;

    7126:     PetscCall(PetscIntCast(mmdata->off[i + 1] - mmdata->off[i], &noff));
    7127:     if (mmdata->mptmp[i]) continue;
    7128:     if (noff) {
    7129:       PetscInt nown;

    7131:       PetscCall(PetscIntCast(mmdata->own[i + 1] - mmdata->own[i], &nown));
    7132:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], noff, mmdata->off[i], mmdata->coo_w + n_o));
    7133:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], nown, mmdata->own[i], mmdata->coo_v + n_d));
    7134:       n_o += noff;
    7135:       n_d += nown;
    7136:     } else {
    7137:       Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mmdata->mp[i]->data;

    7139:       PetscCall(MatSeqAIJCopySubArray(mmdata->mp[i], mm->nz, NULL, mmdata->coo_v + n_d));
    7140:       n_d += mm->nz;
    7141:     }
    7142:   }
    7143:   if (mmdata->hasoffproc) { /* offprocess insertion */
    7144:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
    7145:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_SCALAR, mmdata->coo_w, mmdata->coo_v + n_d));
    7146:   }
    7147:   PetscCall(MatSetValuesCOO(C, mmdata->coo_v, INSERT_VALUES));
    7148:   PetscFunctionReturn(PETSC_SUCCESS);
    7149: }

    7151: /* Support for Pt * A, A * P, or Pt * A * P */
    7152: #define MAX_NUMBER_INTERMEDIATE 4
    7153: PetscErrorCode MatProductSymbolic_MPIAIJBACKEND(Mat C)
    7154: {
    7155:   Mat_Product           *product = C->product;
    7156:   Mat                    A, P, mp[MAX_NUMBER_INTERMEDIATE]; /* A, P and a series of intermediate matrices */
    7157:   Mat_MPIAIJ            *a, *p;
    7158:   MatMatMPIAIJBACKEND   *mmdata;
    7159:   ISLocalToGlobalMapping P_oth_l2g = NULL;
    7160:   IS                     glob      = NULL;
    7161:   const char            *prefix;
    7162:   char                   pprefix[256];
    7163:   const PetscInt        *globidx, *P_oth_idx;
    7164:   PetscInt               i, j, cp, m, n, M, N, *coo_i, *coo_j;
    7165:   PetscCount             ncoo, ncoo_d, ncoo_o, ncoo_oown;
    7166:   PetscInt               cmapt[MAX_NUMBER_INTERMEDIATE], rmapt[MAX_NUMBER_INTERMEDIATE]; /* col/row map type for each Mat in mp[]. */
    7167:                                                                                          /* type-0: consecutive, start from 0; type-1: consecutive with */
    7168:                                                                                          /* a base offset; type-2: sparse with a local to global map table */
    7169:   const PetscInt *cmapa[MAX_NUMBER_INTERMEDIATE], *rmapa[MAX_NUMBER_INTERMEDIATE];       /* col/row local to global map array (table) for type-2 map type */

    7171:   MatProductType ptype;
    7172:   PetscBool      mptmp[MAX_NUMBER_INTERMEDIATE], hasoffproc = PETSC_FALSE, iscuda, iship, iskokk;
    7173:   PetscMPIInt    size;

    7175:   PetscFunctionBegin;
    7176:   MatCheckProduct(C, 1);
    7177:   PetscCheck(!product->data, PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Product data not empty");
    7178:   ptype = product->type;
    7179:   if (product->A->symmetric == PETSC_BOOL3_TRUE && ptype == MATPRODUCT_AtB) {
    7180:     ptype                                          = MATPRODUCT_AB;
    7181:     product->symbolic_used_the_fact_A_is_symmetric = PETSC_TRUE;
    7182:   }
    7183:   switch (ptype) {
    7184:   case MATPRODUCT_AB:
    7185:     A          = product->A;
    7186:     P          = product->B;
    7187:     m          = A->rmap->n;
    7188:     n          = P->cmap->n;
    7189:     M          = A->rmap->N;
    7190:     N          = P->cmap->N;
    7191:     hasoffproc = PETSC_FALSE; /* will not scatter mat product values to other processes */
    7192:     break;
    7193:   case MATPRODUCT_AtB:
    7194:     P          = product->A;
    7195:     A          = product->B;
    7196:     m          = P->cmap->n;
    7197:     n          = A->cmap->n;
    7198:     M          = P->cmap->N;
    7199:     N          = A->cmap->N;
    7200:     hasoffproc = PETSC_TRUE;
    7201:     break;
    7202:   case MATPRODUCT_PtAP:
    7203:     A          = product->A;
    7204:     P          = product->B;
    7205:     m          = P->cmap->n;
    7206:     n          = P->cmap->n;
    7207:     M          = P->cmap->N;
    7208:     N          = P->cmap->N;
    7209:     hasoffproc = PETSC_TRUE;
    7210:     break;
    7211:   default:
    7212:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
    7213:   }
    7214:   PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)C), &size));
    7215:   if (size == 1) hasoffproc = PETSC_FALSE;

    7217:   /* defaults */
    7218:   for (i = 0; i < MAX_NUMBER_INTERMEDIATE; i++) {
    7219:     mp[i]    = NULL;
    7220:     mptmp[i] = PETSC_FALSE;
    7221:     rmapt[i] = -1;
    7222:     cmapt[i] = -1;
    7223:     rmapa[i] = NULL;
    7224:     cmapa[i] = NULL;
    7225:   }

    7227:   /* customization */
    7228:   PetscCall(PetscNew(&mmdata));
    7229:   mmdata->reusesym = product->api_user;
    7230:   if (ptype == MATPRODUCT_AB) {
    7231:     if (product->api_user) {
    7232:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatMatMult", "Mat");
    7233:       PetscCall(PetscOptionsBool("-matmatmult_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
    7234:       PetscCall(PetscOptionsBool("-matmatmult_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7235:       PetscOptionsEnd();
    7236:     } else {
    7237:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_AB", "Mat");
    7238:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_mergeB", "Merge product->B local matrices", "MatMatMult", mmdata->abmerge, &mmdata->abmerge, NULL));
    7239:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7240:       PetscOptionsEnd();
    7241:     }
    7242:   } else if (ptype == MATPRODUCT_PtAP) {
    7243:     if (product->api_user) {
    7244:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatPtAP", "Mat");
    7245:       PetscCall(PetscOptionsBool("-matptap_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7246:       PetscOptionsEnd();
    7247:     } else {
    7248:       PetscOptionsBegin(PetscObjectComm((PetscObject)C), ((PetscObject)C)->prefix, "MatProduct_PtAP", "Mat");
    7249:       PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_pothbind", "Bind P_oth to CPU", "MatBindToCPU", mmdata->P_oth_bind, &mmdata->P_oth_bind, NULL));
    7250:       PetscOptionsEnd();
    7251:     }
    7252:   }
    7253:   a = (Mat_MPIAIJ *)A->data;
    7254:   p = (Mat_MPIAIJ *)P->data;
    7255:   PetscCall(MatSetSizes(C, m, n, M, N));
    7256:   PetscCall(PetscLayoutSetUp(C->rmap));
    7257:   PetscCall(PetscLayoutSetUp(C->cmap));
    7258:   PetscCall(MatSetType(C, ((PetscObject)A)->type_name));
    7259:   PetscCall(MatGetOptionsPrefix(C, &prefix));

    7261:   cp = 0;
    7262:   switch (ptype) {
    7263:   case MATPRODUCT_AB: /* A * P */
    7264:     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));

    7266:     /* A_diag * P_local (merged or not) */
    7267:     if (mmdata->abmerge) { /* P's diagonal and off-diag blocks are merged to one matrix, then multiplied by A_diag */
    7268:       /* P is product->B */
    7269:       PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7270:       PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
    7271:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7272:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7273:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7274:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7275:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7276:       mp[cp]->product->api_user = product->api_user;
    7277:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7278:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7279:       PetscCall(ISGetIndices(glob, &globidx));
    7280:       rmapt[cp] = 1;
    7281:       cmapt[cp] = 2;
    7282:       cmapa[cp] = globidx;
    7283:       mptmp[cp] = PETSC_FALSE;
    7284:       cp++;
    7285:     } else { /* A_diag * P_diag and A_diag * P_off */
    7286:       PetscCall(MatProductCreate(a->A, p->A, NULL, &mp[cp]));
    7287:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7288:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7289:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7290:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7291:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7292:       mp[cp]->product->api_user = product->api_user;
    7293:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7294:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7295:       rmapt[cp] = 1;
    7296:       cmapt[cp] = 1;
    7297:       mptmp[cp] = PETSC_FALSE;
    7298:       cp++;
    7299:       PetscCall(MatProductCreate(a->A, p->B, NULL, &mp[cp]));
    7300:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7301:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7302:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7303:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7304:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7305:       mp[cp]->product->api_user = product->api_user;
    7306:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7307:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7308:       rmapt[cp] = 1;
    7309:       cmapt[cp] = 2;
    7310:       cmapa[cp] = p->garray;
    7311:       mptmp[cp] = PETSC_FALSE;
    7312:       cp++;
    7313:     }

    7315:     /* A_off * P_other */
    7316:     if (mmdata->P_oth) {
    7317:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g)); /* make P_oth use local col ids */
    7318:       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
    7319:       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)a->B)->type_name));
    7320:       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
    7321:       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
    7322:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7323:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7324:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7325:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7326:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7327:       mp[cp]->product->api_user = product->api_user;
    7328:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7329:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7330:       rmapt[cp] = 1;
    7331:       cmapt[cp] = 2;
    7332:       cmapa[cp] = P_oth_idx;
    7333:       mptmp[cp] = PETSC_FALSE;
    7334:       cp++;
    7335:     }
    7336:     break;

    7338:   case MATPRODUCT_AtB: /* (P^t * A): P_diag * A_loc + P_off * A_loc */
    7339:     /* A is product->B */
    7340:     PetscCall(MatMPIAIJGetLocalMatMerge(A, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7341:     if (A == P) { /* when A==P, we can take advantage of the already merged mmdata->Bloc */
    7342:       PetscCall(MatProductCreate(mmdata->Bloc, mmdata->Bloc, NULL, &mp[cp]));
    7343:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7344:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7345:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7346:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7347:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7348:       mp[cp]->product->api_user = product->api_user;
    7349:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7350:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7351:       PetscCall(ISGetIndices(glob, &globidx));
    7352:       rmapt[cp] = 2;
    7353:       rmapa[cp] = globidx;
    7354:       cmapt[cp] = 2;
    7355:       cmapa[cp] = globidx;
    7356:       mptmp[cp] = PETSC_FALSE;
    7357:       cp++;
    7358:     } else {
    7359:       PetscCall(MatProductCreate(p->A, mmdata->Bloc, NULL, &mp[cp]));
    7360:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7361:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7362:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7363:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7364:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7365:       mp[cp]->product->api_user = product->api_user;
    7366:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7367:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7368:       PetscCall(ISGetIndices(glob, &globidx));
    7369:       rmapt[cp] = 1;
    7370:       cmapt[cp] = 2;
    7371:       cmapa[cp] = globidx;
    7372:       mptmp[cp] = PETSC_FALSE;
    7373:       cp++;
    7374:       PetscCall(MatProductCreate(p->B, mmdata->Bloc, NULL, &mp[cp]));
    7375:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7376:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7377:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7378:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7379:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7380:       mp[cp]->product->api_user = product->api_user;
    7381:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7382:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7383:       rmapt[cp] = 2;
    7384:       rmapa[cp] = p->garray;
    7385:       cmapt[cp] = 2;
    7386:       cmapa[cp] = globidx;
    7387:       mptmp[cp] = PETSC_FALSE;
    7388:       cp++;
    7389:     }
    7390:     break;
    7391:   case MATPRODUCT_PtAP:
    7392:     PetscCall(MatGetBrowsOfAoCols_MPIAIJ(A, P, MAT_INITIAL_MATRIX, &mmdata->startsj_s, &mmdata->startsj_r, &mmdata->bufa, &mmdata->P_oth));
    7393:     /* P is product->B */
    7394:     PetscCall(MatMPIAIJGetLocalMatMerge(P, MAT_INITIAL_MATRIX, &glob, &mmdata->Bloc));
    7395:     PetscCall(MatProductCreate(a->A, mmdata->Bloc, NULL, &mp[cp]));
    7396:     PetscCall(MatProductSetType(mp[cp], MATPRODUCT_PtAP));
    7397:     PetscCall(MatProductSetFill(mp[cp], product->fill));
    7398:     PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7399:     PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7400:     PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7401:     mp[cp]->product->api_user = product->api_user;
    7402:     PetscCall(MatProductSetFromOptions(mp[cp]));
    7403:     PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7404:     PetscCall(ISGetIndices(glob, &globidx));
    7405:     rmapt[cp] = 2;
    7406:     rmapa[cp] = globidx;
    7407:     cmapt[cp] = 2;
    7408:     cmapa[cp] = globidx;
    7409:     mptmp[cp] = PETSC_FALSE;
    7410:     cp++;
    7411:     if (mmdata->P_oth) {
    7412:       PetscCall(MatSeqAIJCompactOutExtraColumns_SeqAIJ(mmdata->P_oth, &P_oth_l2g));
    7413:       PetscCall(ISLocalToGlobalMappingGetIndices(P_oth_l2g, &P_oth_idx));
    7414:       PetscCall(MatSetType(mmdata->P_oth, ((PetscObject)a->B)->type_name));
    7415:       PetscCall(MatBindToCPU(mmdata->P_oth, mmdata->P_oth_bind));
    7416:       PetscCall(MatProductCreate(a->B, mmdata->P_oth, NULL, &mp[cp]));
    7417:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AB));
    7418:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7419:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7420:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7421:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7422:       mp[cp]->product->api_user = product->api_user;
    7423:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7424:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7425:       mptmp[cp] = PETSC_TRUE;
    7426:       cp++;
    7427:       PetscCall(MatProductCreate(mmdata->Bloc, mp[1], NULL, &mp[cp]));
    7428:       PetscCall(MatProductSetType(mp[cp], MATPRODUCT_AtB));
    7429:       PetscCall(MatProductSetFill(mp[cp], product->fill));
    7430:       PetscCall(PetscSNPrintf(pprefix, sizeof(pprefix), "backend_p%" PetscInt_FMT "_", cp));
    7431:       PetscCall(MatSetOptionsPrefix(mp[cp], prefix));
    7432:       PetscCall(MatAppendOptionsPrefix(mp[cp], pprefix));
    7433:       mp[cp]->product->api_user = product->api_user;
    7434:       PetscCall(MatProductSetFromOptions(mp[cp]));
    7435:       PetscCall((*mp[cp]->ops->productsymbolic)(mp[cp]));
    7436:       rmapt[cp] = 2;
    7437:       rmapa[cp] = globidx;
    7438:       cmapt[cp] = 2;
    7439:       cmapa[cp] = P_oth_idx;
    7440:       mptmp[cp] = PETSC_FALSE;
    7441:       cp++;
    7442:     }
    7443:     break;
    7444:   default:
    7445:     SETERRQ(PetscObjectComm((PetscObject)C), PETSC_ERR_PLIB, "Not for product type %s", MatProductTypes[ptype]);
    7446:   }
    7447:   /* sanity check */
    7448:   if (size > 1)
    7449:     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);

    7451:   PetscCall(PetscMalloc2(cp, &mmdata->mp, cp, &mmdata->mptmp));
    7452:   for (i = 0; i < cp; i++) {
    7453:     mmdata->mp[i]    = mp[i];
    7454:     mmdata->mptmp[i] = mptmp[i];
    7455:   }
    7456:   mmdata->cp             = cp;
    7457:   C->product->data       = mmdata;
    7458:   C->product->destroy    = MatDestroy_MatMatMPIAIJBACKEND;
    7459:   C->ops->productnumeric = MatProductNumeric_MPIAIJBACKEND;

    7461:   /* memory type */
    7462:   mmdata->mtype = PETSC_MEMTYPE_HOST;
    7463:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iscuda, MATSEQAIJCUSPARSE, MATMPIAIJCUSPARSE, ""));
    7464:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iship, MATSEQAIJHIPSPARSE, MATMPIAIJHIPSPARSE, ""));
    7465:   PetscCall(PetscObjectTypeCompareAny((PetscObject)C, &iskokk, MATSEQAIJKOKKOS, MATMPIAIJKOKKOS, ""));
    7466:   if (iscuda) mmdata->mtype = PETSC_MEMTYPE_CUDA;
    7467:   else if (iship) mmdata->mtype = PETSC_MEMTYPE_HIP;
    7468:   else if (iskokk) mmdata->mtype = PETSC_MEMTYPE_KOKKOS;

    7470:   /* prepare coo coordinates for values insertion */

    7472:   /* count total nonzeros of those intermediate seqaij Mats
    7473:     ncoo_d:    # of nonzeros of matrices that do not have offproc entries
    7474:     ncoo_o:    # of nonzeros (of matrices that might have offproc entries) that will be inserted to remote procs
    7475:     ncoo_oown: # of nonzeros (of matrices that might have offproc entries) that will be inserted locally
    7476:   */
    7477:   for (cp = 0, ncoo_d = 0, ncoo_o = 0, ncoo_oown = 0; cp < mmdata->cp; cp++) {
    7478:     Mat_SeqAIJ *mm = (Mat_SeqAIJ *)mp[cp]->data;
    7479:     if (mptmp[cp]) continue;
    7480:     if (rmapt[cp] == 2 && hasoffproc) { /* the rows need to be scatter to all processes (might include self) */
    7481:       const PetscInt *rmap = rmapa[cp];
    7482:       const PetscInt  mr   = mp[cp]->rmap->n;
    7483:       const PetscInt  rs   = C->rmap->rstart;
    7484:       const PetscInt  re   = C->rmap->rend;
    7485:       const PetscInt *ii   = mm->i;
    7486:       for (i = 0; i < mr; i++) {
    7487:         const PetscInt gr = rmap[i];
    7488:         const PetscInt nz = ii[i + 1] - ii[i];
    7489:         if (gr < rs || gr >= re) ncoo_o += nz; /* this row is offproc */
    7490:         else ncoo_oown += nz;                  /* this row is local */
    7491:       }
    7492:     } else ncoo_d += mm->nz;
    7493:   }

    7495:   /*
    7496:     ncoo: total number of nonzeros (including those inserted by remote procs) belonging to this proc

    7498:     ncoo = ncoo_d + ncoo_oown + ncoo2, which ncoo2 is number of nonzeros inserted to me by other procs.

    7500:     off[0] points to a big index array, which is shared by off[1,2,...]. Similarly, for own[0].

    7502:     off[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert to others
    7503:     own[p]: points to the segment for matrix mp[p], storing location of nonzeros that mp[p] will insert locally
    7504:     so, off[p+1]-off[p] is the number of nonzeros that mp[p] will send to others.

    7506:     coo_i/j/v[]: [ncoo] row/col/val of nonzeros belonging to this proc.
    7507:     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.
    7508:   */
    7509:   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->off)); /* +1 to make a csr-like data structure */
    7510:   PetscCall(PetscCalloc1(mmdata->cp + 1, &mmdata->own));

    7512:   /* gather (i,j) of nonzeros inserted by remote procs */
    7513:   if (hasoffproc) {
    7514:     PetscSF  msf;
    7515:     PetscInt ncoo2, *coo_i2, *coo_j2;

    7517:     PetscCall(PetscMalloc1(ncoo_o, &mmdata->off[0]));
    7518:     PetscCall(PetscMalloc1(ncoo_oown, &mmdata->own[0]));
    7519:     PetscCall(PetscMalloc2(ncoo_o, &coo_i, ncoo_o, &coo_j)); /* to collect (i,j) of entries to be sent to others */

    7521:     for (cp = 0, ncoo_o = 0; cp < mmdata->cp; cp++) {
    7522:       Mat_SeqAIJ *mm     = (Mat_SeqAIJ *)mp[cp]->data;
    7523:       PetscInt   *idxoff = mmdata->off[cp];
    7524:       PetscInt   *idxown = mmdata->own[cp];
    7525:       if (!mptmp[cp] && rmapt[cp] == 2) { /* row map is sparse */
    7526:         const PetscInt *rmap = rmapa[cp];
    7527:         const PetscInt *cmap = cmapa[cp];
    7528:         const PetscInt *ii   = mm->i;
    7529:         PetscInt       *coi  = coo_i + ncoo_o;
    7530:         PetscInt       *coj  = coo_j + ncoo_o;
    7531:         const PetscInt  mr   = mp[cp]->rmap->n;
    7532:         const PetscInt  rs   = C->rmap->rstart;
    7533:         const PetscInt  re   = C->rmap->rend;
    7534:         const PetscInt  cs   = C->cmap->rstart;
    7535:         for (i = 0; i < mr; i++) {
    7536:           const PetscInt *jj = mm->j + ii[i];
    7537:           const PetscInt  gr = rmap[i];
    7538:           const PetscInt  nz = ii[i + 1] - ii[i];
    7539:           if (gr < rs || gr >= re) { /* this is an offproc row */
    7540:             for (j = ii[i]; j < ii[i + 1]; j++) {
    7541:               *coi++    = gr;
    7542:               *idxoff++ = j;
    7543:             }
    7544:             if (!cmapt[cp]) { /* already global */
    7545:               for (j = 0; j < nz; j++) *coj++ = jj[j];
    7546:             } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
    7547:               for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
    7548:             } else { /* offdiag */
    7549:               for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
    7550:             }
    7551:             ncoo_o += nz;
    7552:           } else { /* this is a local row */
    7553:             for (j = ii[i]; j < ii[i + 1]; j++) *idxown++ = j;
    7554:           }
    7555:         }
    7556:       }
    7557:       mmdata->off[cp + 1] = idxoff;
    7558:       mmdata->own[cp + 1] = idxown;
    7559:     }

    7561:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
    7562:     PetscInt incoo_o;
    7563:     PetscCall(PetscIntCast(ncoo_o, &incoo_o));
    7564:     PetscCall(PetscSFSetGraphLayout(mmdata->sf, C->rmap, incoo_o /*nleaves*/, NULL /*ilocal*/, PETSC_OWN_POINTER, coo_i));
    7565:     PetscCall(PetscSFGetMultiSF(mmdata->sf, &msf));
    7566:     PetscCall(PetscSFGetGraph(msf, &ncoo2 /*nroots*/, NULL, NULL, NULL));
    7567:     ncoo = ncoo_d + ncoo_oown + ncoo2;
    7568:     PetscCall(PetscMalloc2(ncoo, &coo_i2, ncoo, &coo_j2));
    7569:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown)); /* put (i,j) of remote nonzeros at back */
    7570:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_i, coo_i2 + ncoo_d + ncoo_oown));
    7571:     PetscCall(PetscSFGatherBegin(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
    7572:     PetscCall(PetscSFGatherEnd(mmdata->sf, MPIU_INT, coo_j, coo_j2 + ncoo_d + ncoo_oown));
    7573:     PetscCall(PetscFree2(coo_i, coo_j));
    7574:     /* allocate MPI send buffer to collect nonzero values to be sent to remote procs */
    7575:     PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo_o * sizeof(PetscScalar), (void **)&mmdata->coo_w));
    7576:     coo_i = coo_i2;
    7577:     coo_j = coo_j2;
    7578:   } else { /* no offproc values insertion */
    7579:     ncoo = ncoo_d;
    7580:     PetscCall(PetscMalloc2(ncoo, &coo_i, ncoo, &coo_j));

    7582:     PetscCall(PetscSFCreate(PetscObjectComm((PetscObject)C), &mmdata->sf));
    7583:     PetscCall(PetscSFSetGraph(mmdata->sf, 0, 0, NULL, PETSC_OWN_POINTER, NULL, PETSC_OWN_POINTER));
    7584:     PetscCall(PetscSFSetUp(mmdata->sf));
    7585:   }
    7586:   mmdata->hasoffproc = hasoffproc;

    7588:   /* gather (i,j) of nonzeros inserted locally */
    7589:   for (cp = 0, ncoo_d = 0; cp < mmdata->cp; cp++) {
    7590:     Mat_SeqAIJ     *mm   = (Mat_SeqAIJ *)mp[cp]->data;
    7591:     PetscInt       *coi  = coo_i + ncoo_d;
    7592:     PetscInt       *coj  = coo_j + ncoo_d;
    7593:     const PetscInt *jj   = mm->j;
    7594:     const PetscInt *ii   = mm->i;
    7595:     const PetscInt *cmap = cmapa[cp];
    7596:     const PetscInt *rmap = rmapa[cp];
    7597:     const PetscInt  mr   = mp[cp]->rmap->n;
    7598:     const PetscInt  rs   = C->rmap->rstart;
    7599:     const PetscInt  re   = C->rmap->rend;
    7600:     const PetscInt  cs   = C->cmap->rstart;

    7602:     if (mptmp[cp]) continue;
    7603:     if (rmapt[cp] == 1) { /* consecutive rows */
    7604:       /* fill coo_i */
    7605:       for (i = 0; i < mr; i++) {
    7606:         const PetscInt gr = i + rs;
    7607:         for (j = ii[i]; j < ii[i + 1]; j++) coi[j] = gr;
    7608:       }
    7609:       /* fill coo_j */
    7610:       if (!cmapt[cp]) { /* type-0, already global */
    7611:         PetscCall(PetscArraycpy(coj, jj, mm->nz));
    7612:       } else if (cmapt[cp] == 1) {                        /* type-1, local to global for consecutive columns of C */
    7613:         for (j = 0; j < mm->nz; j++) coj[j] = jj[j] + cs; /* lid + col start */
    7614:       } else {                                            /* type-2, local to global for sparse columns */
    7615:         for (j = 0; j < mm->nz; j++) coj[j] = cmap[jj[j]];
    7616:       }
    7617:       ncoo_d += mm->nz;
    7618:     } else if (rmapt[cp] == 2) { /* sparse rows */
    7619:       for (i = 0; i < mr; i++) {
    7620:         const PetscInt *jj = mm->j + ii[i];
    7621:         const PetscInt  gr = rmap[i];
    7622:         const PetscInt  nz = ii[i + 1] - ii[i];
    7623:         if (gr >= rs && gr < re) { /* local rows */
    7624:           for (j = ii[i]; j < ii[i + 1]; j++) *coi++ = gr;
    7625:           if (!cmapt[cp]) { /* type-0, already global */
    7626:             for (j = 0; j < nz; j++) *coj++ = jj[j];
    7627:           } else if (cmapt[cp] == 1) { /* local to global for owned columns of C */
    7628:             for (j = 0; j < nz; j++) *coj++ = jj[j] + cs;
    7629:           } else { /* type-2, local to global for sparse columns */
    7630:             for (j = 0; j < nz; j++) *coj++ = cmap[jj[j]];
    7631:           }
    7632:           ncoo_d += nz;
    7633:         }
    7634:       }
    7635:     }
    7636:   }
    7637:   if (glob) PetscCall(ISRestoreIndices(glob, &globidx));
    7638:   PetscCall(ISDestroy(&glob));
    7639:   if (P_oth_l2g) PetscCall(ISLocalToGlobalMappingRestoreIndices(P_oth_l2g, &P_oth_idx));
    7640:   PetscCall(ISLocalToGlobalMappingDestroy(&P_oth_l2g));
    7641:   /* allocate an array to store all nonzeros (inserted locally or remotely) belonging to this proc */
    7642:   PetscCall(PetscSFMalloc(mmdata->sf, mmdata->mtype, ncoo * sizeof(PetscScalar), (void **)&mmdata->coo_v));

    7644:   /* preallocate with COO data */
    7645:   PetscCall(MatSetPreallocationCOO(C, ncoo, coo_i, coo_j));
    7646:   PetscCall(PetscFree2(coo_i, coo_j));
    7647:   PetscFunctionReturn(PETSC_SUCCESS);
    7648: }

    7650: PetscErrorCode MatProductSetFromOptions_MPIAIJBACKEND(Mat mat)
    7651: {
    7652:   Mat_Product *product = mat->product;
    7653: #if defined(PETSC_HAVE_DEVICE)
    7654:   PetscBool match  = PETSC_FALSE;
    7655:   PetscBool usecpu = PETSC_FALSE;
    7656: #else
    7657:   PetscBool match = PETSC_TRUE;
    7658: #endif

    7660:   PetscFunctionBegin;
    7661:   MatCheckProduct(mat, 1);
    7662: #if defined(PETSC_HAVE_DEVICE)
    7663:   if (!product->A->boundtocpu && !product->B->boundtocpu) PetscCall(PetscObjectTypeCompare((PetscObject)product->B, ((PetscObject)product->A)->type_name, &match));
    7664:   if (match) { /* we can always fallback to the CPU if requested */
    7665:     switch (product->type) {
    7666:     case MATPRODUCT_AB:
    7667:       if (product->api_user) {
    7668:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatMatMult", "Mat");
    7669:         PetscCall(PetscOptionsBool("-matmatmult_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
    7670:         PetscOptionsEnd();
    7671:       } else {
    7672:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AB", "Mat");
    7673:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatMatMult", usecpu, &usecpu, NULL));
    7674:         PetscOptionsEnd();
    7675:       }
    7676:       break;
    7677:     case MATPRODUCT_AtB:
    7678:       if (product->api_user) {
    7679:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatTransposeMatMult", "Mat");
    7680:         PetscCall(PetscOptionsBool("-mattransposematmult_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
    7681:         PetscOptionsEnd();
    7682:       } else {
    7683:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_AtB", "Mat");
    7684:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatTransposeMatMult", usecpu, &usecpu, NULL));
    7685:         PetscOptionsEnd();
    7686:       }
    7687:       break;
    7688:     case MATPRODUCT_PtAP:
    7689:       if (product->api_user) {
    7690:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatPtAP", "Mat");
    7691:         PetscCall(PetscOptionsBool("-matptap_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
    7692:         PetscOptionsEnd();
    7693:       } else {
    7694:         PetscOptionsBegin(PetscObjectComm((PetscObject)mat), ((PetscObject)mat)->prefix, "MatProduct_PtAP", "Mat");
    7695:         PetscCall(PetscOptionsBool("-mat_product_algorithm_backend_cpu", "Use CPU code", "MatPtAP", usecpu, &usecpu, NULL));
    7696:         PetscOptionsEnd();
    7697:       }
    7698:       break;
    7699:     default:
    7700:       break;
    7701:     }
    7702:     match = (PetscBool)!usecpu;
    7703:   }
    7704: #endif
    7705:   if (match) {
    7706:     switch (product->type) {
    7707:     case MATPRODUCT_AB:
    7708:     case MATPRODUCT_AtB:
    7709:     case MATPRODUCT_PtAP:
    7710:       mat->ops->productsymbolic = MatProductSymbolic_MPIAIJBACKEND;
    7711:       break;
    7712:     default:
    7713:       break;
    7714:     }
    7715:   }
    7716:   /* fallback to MPIAIJ ops */
    7717:   if (!mat->ops->productsymbolic) PetscCall(MatProductSetFromOptions_MPIAIJ(mat));
    7718:   PetscFunctionReturn(PETSC_SUCCESS);
    7719: }

    7721: /*
    7722:    Produces a set of block column indices of the matrix row, one for each block represented in the original row

    7724:    n - the number of block indices in cc[]
    7725:    cc - the block indices (must be large enough to contain the indices)
    7726: */
    7727: static inline PetscErrorCode MatCollapseRow(Mat Amat, PetscInt row, PetscInt bs, PetscInt *n, PetscInt *cc)
    7728: {
    7729:   PetscInt        cnt = -1, nidx, j;
    7730:   const PetscInt *idx;

    7732:   PetscFunctionBegin;
    7733:   PetscCall(MatGetRow(Amat, row, &nidx, &idx, NULL));
    7734:   if (nidx) {
    7735:     cnt     = 0;
    7736:     cc[cnt] = idx[0] / bs;
    7737:     for (j = 1; j < nidx; j++) {
    7738:       if (cc[cnt] < idx[j] / bs) cc[++cnt] = idx[j] / bs;
    7739:     }
    7740:   }
    7741:   PetscCall(MatRestoreRow(Amat, row, &nidx, &idx, NULL));
    7742:   *n = cnt + 1;
    7743:   PetscFunctionReturn(PETSC_SUCCESS);
    7744: }

    7746: /*
    7747:     Produces a set of block column indices of the matrix block row, one for each block represented in the original set of rows

    7749:     ncollapsed - the number of block indices
    7750:     collapsed - the block indices (must be large enough to contain the indices)
    7751: */
    7752: static inline PetscErrorCode MatCollapseRows(Mat Amat, PetscInt start, PetscInt bs, PetscInt *w0, PetscInt *w1, PetscInt *w2, PetscInt *ncollapsed, PetscInt **collapsed)
    7753: {
    7754:   PetscInt i, nprev, *cprev = w0, ncur = 0, *ccur = w1, *merged = w2, *cprevtmp;

    7756:   PetscFunctionBegin;
    7757:   PetscCall(MatCollapseRow(Amat, start, bs, &nprev, cprev));
    7758:   for (i = start + 1; i < start + bs; i++) {
    7759:     PetscCall(MatCollapseRow(Amat, i, bs, &ncur, ccur));
    7760:     PetscCall(PetscMergeIntArray(nprev, cprev, ncur, ccur, &nprev, &merged));
    7761:     cprevtmp = cprev;
    7762:     cprev    = merged;
    7763:     merged   = cprevtmp;
    7764:   }
    7765:   *ncollapsed = nprev;
    7766:   if (collapsed) *collapsed = cprev;
    7767:   PetscFunctionReturn(PETSC_SUCCESS);
    7768: }

    7770: /*
    7771:  MatCreateGraph_Simple_AIJ - create simple scalar matrix (graph) from potentially blocked matrix

    7773:  Input Parameter:
    7774:  . Amat - matrix
    7775:  - symmetrize - make the result symmetric
    7776:  + scale - scale with diagonal

    7778:  Output Parameter:
    7779:  . a_Gmat - output scalar graph >= 0

    7781: */
    7782: PETSC_INTERN PetscErrorCode MatCreateGraph_Simple_AIJ(Mat Amat, PetscBool symmetrize, PetscBool scale, PetscReal filter, PetscInt index_size, PetscInt index[], Mat *a_Gmat)
    7783: {
    7784:   PetscInt  Istart, Iend, Ii, jj, kk, ncols, nloc, NN, MM, bs;
    7785:   MPI_Comm  comm;
    7786:   Mat       Gmat;
    7787:   PetscBool ismpiaij, isseqaij;
    7788:   Mat       a, b, c;
    7789:   MatType   jtype;

    7791:   PetscFunctionBegin;
    7792:   PetscCall(PetscObjectGetComm((PetscObject)Amat, &comm));
    7793:   PetscCall(MatGetOwnershipRange(Amat, &Istart, &Iend));
    7794:   PetscCall(MatGetSize(Amat, &MM, &NN));
    7795:   PetscCall(MatGetBlockSize(Amat, &bs));
    7796:   nloc = (Iend - Istart) / bs;

    7798:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATSEQAIJ, &isseqaij));
    7799:   PetscCall(PetscObjectBaseTypeCompare((PetscObject)Amat, MATMPIAIJ, &ismpiaij));
    7800:   PetscCheck(isseqaij || ismpiaij, comm, PETSC_ERR_USER, "Require (MPI)AIJ matrix type");

    7802:   /* TODO GPU: these calls are potentially expensive if matrices are large and we want to use the GPU */
    7803:   /* A solution consists in providing a new API, MatAIJGetCollapsedAIJ, and each class can provide a fast
    7804:      implementation */
    7805:   if (bs > 1) {
    7806:     PetscCall(MatGetType(Amat, &jtype));
    7807:     PetscCall(MatCreate(comm, &Gmat));
    7808:     PetscCall(MatSetType(Gmat, jtype));
    7809:     PetscCall(MatSetSizes(Gmat, nloc, nloc, PETSC_DETERMINE, PETSC_DETERMINE));
    7810:     PetscCall(MatSetBlockSizes(Gmat, 1, 1));
    7811:     if (isseqaij || ((Mat_MPIAIJ *)Amat->data)->garray) {
    7812:       PetscInt  *d_nnz, *o_nnz;
    7813:       MatScalar *aa, val, *AA;
    7814:       PetscInt  *aj, *ai, *AJ, nc, nmax = 0;

    7816:       if (isseqaij) {
    7817:         a = Amat;
    7818:         b = NULL;
    7819:       } else {
    7820:         Mat_MPIAIJ *d = (Mat_MPIAIJ *)Amat->data;
    7821:         a             = d->A;
    7822:         b             = d->B;
    7823:       }
    7824:       PetscCall(PetscInfo(Amat, "New bs>1 Graph. nloc=%" PetscInt_FMT "\n", nloc));
    7825:       PetscCall(PetscMalloc2(nloc, &d_nnz, (isseqaij ? 0 : nloc), &o_nnz));
    7826:       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
    7827:         PetscInt       *nnz = (c == a) ? d_nnz : o_nnz;
    7828:         const PetscInt *cols1, *cols2;

    7830:         for (PetscInt brow = 0, nc1, nc2, ok = 1; brow < nloc * bs; brow += bs) { // block rows
    7831:           PetscCall(MatGetRow(c, brow, &nc2, &cols2, NULL));
    7832:           nnz[brow / bs] = nc2 / bs;
    7833:           if (nc2 % bs) ok = 0;
    7834:           if (nnz[brow / bs] > nmax) nmax = nnz[brow / bs];
    7835:           for (PetscInt ii = 1; ii < bs; ii++) { // check for non-dense blocks
    7836:             PetscCall(MatGetRow(c, brow + ii, &nc1, &cols1, NULL));
    7837:             if (nc1 != nc2) ok = 0;
    7838:             else {
    7839:               for (PetscInt jj = 0; jj < nc1 && ok == 1; jj++) {
    7840:                 if (cols1[jj] != cols2[jj]) ok = 0;
    7841:                 if (cols1[jj] % bs != jj % bs) ok = 0;
    7842:               }
    7843:             }
    7844:             PetscCall(MatRestoreRow(c, brow + ii, &nc1, &cols1, NULL));
    7845:           }
    7846:           PetscCall(MatRestoreRow(c, brow, &nc2, &cols2, NULL));
    7847:           if (!ok) {
    7848:             PetscCall(PetscFree2(d_nnz, o_nnz));
    7849:             PetscCall(PetscInfo(Amat, "Found sparse blocks - revert to slow method\n"));
    7850:             goto old_bs;
    7851:           }
    7852:         }
    7853:       }
    7854:       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
    7855:       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
    7856:       PetscCall(PetscFree2(d_nnz, o_nnz));
    7857:       PetscCall(PetscMalloc2(nmax, &AA, nmax, &AJ));
    7858:       // diag
    7859:       for (PetscInt brow = 0, n, grow; brow < nloc * bs; brow += bs) { // block rows
    7860:         Mat_SeqAIJ *aseq = (Mat_SeqAIJ *)a->data;

    7862:         ai = aseq->i;
    7863:         n  = ai[brow + 1] - ai[brow];
    7864:         aj = aseq->j + ai[brow];
    7865:         for (PetscInt k = 0; k < n; k += bs) {   // block columns
    7866:           AJ[k / bs] = aj[k] / bs + Istart / bs; // diag starts at (Istart,Istart)
    7867:           val        = 0;
    7868:           if (index_size == 0) {
    7869:             for (PetscInt ii = 0; ii < bs; ii++) { // rows in block
    7870:               aa = aseq->a + ai[brow + ii] + k;
    7871:               for (PetscInt jj = 0; jj < bs; jj++) {    // columns in block
    7872:                 val += PetscAbs(PetscRealPart(aa[jj])); // a sort of norm
    7873:               }
    7874:             }
    7875:           } else {                                            // use (index,index) value if provided
    7876:             for (PetscInt iii = 0; iii < index_size; iii++) { // rows in block
    7877:               PetscInt ii = index[iii];
    7878:               aa          = aseq->a + ai[brow + ii] + k;
    7879:               for (PetscInt jjj = 0; jjj < index_size; jjj++) { // columns in block
    7880:                 PetscInt jj = index[jjj];
    7881:                 val += PetscAbs(PetscRealPart(aa[jj]));
    7882:               }
    7883:             }
    7884:           }
    7885:           PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%d) >= nmax (%d)", (int)(k / bs), (int)nmax);
    7886:           AA[k / bs] = val;
    7887:         }
    7888:         grow = Istart / bs + brow / bs;
    7889:         PetscCall(MatSetValues(Gmat, 1, &grow, n / bs, AJ, AA, ADD_VALUES));
    7890:       }
    7891:       // off-diag
    7892:       if (ismpiaij) {
    7893:         Mat_MPIAIJ        *aij = (Mat_MPIAIJ *)Amat->data;
    7894:         const PetscScalar *vals;
    7895:         const PetscInt    *cols, *garray = aij->garray;

    7897:         PetscCheck(garray, PETSC_COMM_SELF, PETSC_ERR_USER, "No garray ?");
    7898:         for (PetscInt brow = 0, grow; brow < nloc * bs; brow += bs) { // block rows
    7899:           PetscCall(MatGetRow(b, brow, &ncols, &cols, NULL));
    7900:           for (PetscInt k = 0, cidx = 0; k < ncols; k += bs, cidx++) {
    7901:             PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs >= nmax");
    7902:             AA[k / bs] = 0;
    7903:             AJ[cidx]   = garray[cols[k]] / bs;
    7904:           }
    7905:           nc = ncols / bs;
    7906:           PetscCall(MatRestoreRow(b, brow, &ncols, &cols, NULL));
    7907:           if (index_size == 0) {
    7908:             for (PetscInt ii = 0; ii < bs; ii++) { // rows in block
    7909:               PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
    7910:               for (PetscInt k = 0; k < ncols; k += bs) {
    7911:                 for (PetscInt jj = 0; jj < bs; jj++) { // cols in block
    7912:                   PetscAssert(k / bs < nmax, comm, PETSC_ERR_USER, "k / bs (%d) >= nmax (%d)", (int)(k / bs), (int)nmax);
    7913:                   AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
    7914:                 }
    7915:               }
    7916:               PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
    7917:             }
    7918:           } else {                                            // use (index,index) value if provided
    7919:             for (PetscInt iii = 0; iii < index_size; iii++) { // rows in block
    7920:               PetscInt ii = index[iii];
    7921:               PetscCall(MatGetRow(b, brow + ii, &ncols, &cols, &vals));
    7922:               for (PetscInt k = 0; k < ncols; k += bs) {
    7923:                 for (PetscInt jjj = 0; jjj < index_size; jjj++) { // cols in block
    7924:                   PetscInt jj = index[jjj];
    7925:                   AA[k / bs] += PetscAbs(PetscRealPart(vals[k + jj]));
    7926:                 }
    7927:               }
    7928:               PetscCall(MatRestoreRow(b, brow + ii, &ncols, &cols, &vals));
    7929:             }
    7930:           }
    7931:           grow = Istart / bs + brow / bs;
    7932:           PetscCall(MatSetValues(Gmat, 1, &grow, nc, AJ, AA, ADD_VALUES));
    7933:         }
    7934:       }
    7935:       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
    7936:       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
    7937:       PetscCall(PetscFree2(AA, AJ));
    7938:     } else {
    7939:       const PetscScalar *vals;
    7940:       const PetscInt    *idx;
    7941:       PetscInt          *d_nnz, *o_nnz, *w0, *w1, *w2;
    7942:     old_bs:
    7943:       /*
    7944:        Determine the preallocation needed for the scalar matrix derived from the vector matrix.
    7945:        */
    7946:       PetscCall(PetscInfo(Amat, "OLD bs>1 CreateGraph\n"));
    7947:       PetscCall(PetscMalloc2(nloc, &d_nnz, (isseqaij ? 0 : nloc), &o_nnz));
    7948:       if (isseqaij) {
    7949:         PetscInt max_d_nnz;

    7951:         /*
    7952:          Determine exact preallocation count for (sequential) scalar matrix
    7953:          */
    7954:         PetscCall(MatSeqAIJGetMaxRowNonzeros(Amat, &max_d_nnz));
    7955:         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
    7956:         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
    7957:         for (Ii = 0, jj = 0; Ii < Iend; Ii += bs, jj++) PetscCall(MatCollapseRows(Amat, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
    7958:         PetscCall(PetscFree3(w0, w1, w2));
    7959:       } else if (ismpiaij) {
    7960:         Mat             Daij, Oaij;
    7961:         const PetscInt *garray;
    7962:         PetscInt        max_d_nnz;

    7964:         PetscCall(MatMPIAIJGetSeqAIJ(Amat, &Daij, &Oaij, &garray));
    7965:         /*
    7966:          Determine exact preallocation count for diagonal block portion of scalar matrix
    7967:          */
    7968:         PetscCall(MatSeqAIJGetMaxRowNonzeros(Daij, &max_d_nnz));
    7969:         max_d_nnz = PetscMin(nloc, bs * max_d_nnz);
    7970:         PetscCall(PetscMalloc3(max_d_nnz, &w0, max_d_nnz, &w1, max_d_nnz, &w2));
    7971:         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) PetscCall(MatCollapseRows(Daij, Ii, bs, w0, w1, w2, &d_nnz[jj], NULL));
    7972:         PetscCall(PetscFree3(w0, w1, w2));
    7973:         /*
    7974:          Over estimate (usually grossly over), preallocation count for off-diagonal portion of scalar matrix
    7975:          */
    7976:         for (Ii = 0, jj = 0; Ii < Iend - Istart; Ii += bs, jj++) {
    7977:           o_nnz[jj] = 0;
    7978:           for (kk = 0; kk < bs; kk++) { /* rows that get collapsed to a single row */
    7979:             PetscCall(MatGetRow(Oaij, Ii + kk, &ncols, NULL, NULL));
    7980:             o_nnz[jj] += ncols;
    7981:             PetscCall(MatRestoreRow(Oaij, Ii + kk, &ncols, NULL, NULL));
    7982:           }
    7983:           if (o_nnz[jj] > (NN / bs - nloc)) o_nnz[jj] = NN / bs - nloc;
    7984:         }
    7985:       } else SETERRQ(comm, PETSC_ERR_USER, "Require AIJ matrix type");
    7986:       /* get scalar copy (norms) of matrix */
    7987:       PetscCall(MatSeqAIJSetPreallocation(Gmat, 0, d_nnz));
    7988:       PetscCall(MatMPIAIJSetPreallocation(Gmat, 0, d_nnz, 0, o_nnz));
    7989:       PetscCall(PetscFree2(d_nnz, o_nnz));
    7990:       for (Ii = Istart; Ii < Iend; Ii++) {
    7991:         PetscInt dest_row = Ii / bs;

    7993:         PetscCall(MatGetRow(Amat, Ii, &ncols, &idx, &vals));
    7994:         for (jj = 0; jj < ncols; jj++) {
    7995:           PetscInt    dest_col = idx[jj] / bs;
    7996:           PetscScalar sv       = PetscAbs(PetscRealPart(vals[jj]));

    7998:           PetscCall(MatSetValues(Gmat, 1, &dest_row, 1, &dest_col, &sv, ADD_VALUES));
    7999:         }
    8000:         PetscCall(MatRestoreRow(Amat, Ii, &ncols, &idx, &vals));
    8001:       }
    8002:       PetscCall(MatAssemblyBegin(Gmat, MAT_FINAL_ASSEMBLY));
    8003:       PetscCall(MatAssemblyEnd(Gmat, MAT_FINAL_ASSEMBLY));
    8004:     }
    8005:   } else {
    8006:     if (symmetrize || filter >= 0 || scale) PetscCall(MatDuplicate(Amat, MAT_COPY_VALUES, &Gmat));
    8007:     else {
    8008:       Gmat = Amat;
    8009:       PetscCall(PetscObjectReference((PetscObject)Gmat));
    8010:     }
    8011:     if (isseqaij) {
    8012:       a = Gmat;
    8013:       b = NULL;
    8014:     } else {
    8015:       Mat_MPIAIJ *d = (Mat_MPIAIJ *)Gmat->data;
    8016:       a             = d->A;
    8017:       b             = d->B;
    8018:     }
    8019:     if (filter >= 0 || scale) {
    8020:       /* take absolute value of each entry */
    8021:       for (c = a, kk = 0; c && kk < 2; c = b, kk++) {
    8022:         MatInfo      info;
    8023:         PetscScalar *avals;

    8025:         PetscCall(MatGetInfo(c, MAT_LOCAL, &info));
    8026:         PetscCall(MatSeqAIJGetArray(c, &avals));
    8027:         for (int jj = 0; jj < info.nz_used; jj++) avals[jj] = PetscAbsScalar(avals[jj]);
    8028:         PetscCall(MatSeqAIJRestoreArray(c, &avals));
    8029:       }
    8030:     }
    8031:   }
    8032:   if (symmetrize) {
    8033:     PetscBool isset, issym;

    8035:     PetscCall(MatIsSymmetricKnown(Amat, &isset, &issym));
    8036:     if (!isset || !issym) {
    8037:       Mat matTrans;

    8039:       PetscCall(MatTranspose(Gmat, MAT_INITIAL_MATRIX, &matTrans));
    8040:       PetscCall(MatAXPY(Gmat, 1.0, matTrans, Gmat->structurally_symmetric == PETSC_BOOL3_TRUE ? SAME_NONZERO_PATTERN : DIFFERENT_NONZERO_PATTERN));
    8041:       PetscCall(MatDestroy(&matTrans));
    8042:     }
    8043:     PetscCall(MatSetOption(Gmat, MAT_SYMMETRIC, PETSC_TRUE));
    8044:   } else if (Amat != Gmat) PetscCall(MatPropagateSymmetryOptions(Amat, Gmat));
    8045:   if (scale) {
    8046:     /* scale c for all diagonal values = 1 or -1 */
    8047:     Vec diag;

    8049:     PetscCall(MatCreateVecs(Gmat, &diag, NULL));
    8050:     PetscCall(MatGetDiagonal(Gmat, diag));
    8051:     PetscCall(VecReciprocal(diag));
    8052:     PetscCall(VecSqrtAbs(diag));
    8053:     PetscCall(MatDiagonalScale(Gmat, diag, diag));
    8054:     PetscCall(VecDestroy(&diag));
    8055:   }
    8056:   PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_graph_view"));
    8057:   if (filter >= 0) {
    8058:     PetscCall(MatFilter(Gmat, filter, PETSC_TRUE, PETSC_TRUE));
    8059:     PetscCall(MatViewFromOptions(Gmat, NULL, "-mat_filter_graph_view"));
    8060:   }
    8061:   *a_Gmat = Gmat;
    8062:   PetscFunctionReturn(PETSC_SUCCESS);
    8063: }

    8065: /*
    8066:     Special version for direct calls from Fortran
    8067: */

    8069: /* Change these macros so can be used in void function */
    8070: /* Identical to PetscCallVoid, except it assigns to *_ierr */
    8071: #undef PetscCall
    8072: #define PetscCall(...) \
    8073:   do { \
    8074:     PetscErrorCode ierr_msv_mpiaij = __VA_ARGS__; \
    8075:     if (PetscUnlikely(ierr_msv_mpiaij)) { \
    8076:       *_ierr = PetscError(PETSC_COMM_SELF, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr_msv_mpiaij, PETSC_ERROR_REPEAT, " "); \
    8077:       return; \
    8078:     } \
    8079:   } while (0)

    8081: #undef SETERRQ
    8082: #define SETERRQ(comm, ierr, ...) \
    8083:   do { \
    8084:     *_ierr = PetscError(comm, __LINE__, PETSC_FUNCTION_NAME, __FILE__, ierr, PETSC_ERROR_INITIAL, __VA_ARGS__); \
    8085:     return; \
    8086:   } while (0)

    8088: #if defined(PETSC_HAVE_FORTRAN_CAPS)
    8089:   #define matsetvaluesmpiaij_ MATSETVALUESMPIAIJ
    8090: #elif !defined(PETSC_HAVE_FORTRAN_UNDERSCORE)
    8091:   #define matsetvaluesmpiaij_ matsetvaluesmpiaij
    8092: #else
    8093: #endif
    8094: PETSC_EXTERN void matsetvaluesmpiaij_(Mat *mmat, PetscInt *mm, const PetscInt im[], PetscInt *mn, const PetscInt in[], const PetscScalar v[], InsertMode *maddv, PetscErrorCode *_ierr)
    8095: {
    8096:   Mat         mat = *mmat;
    8097:   PetscInt    m = *mm, n = *mn;
    8098:   InsertMode  addv = *maddv;
    8099:   Mat_MPIAIJ *aij  = (Mat_MPIAIJ *)mat->data;
    8100:   PetscScalar value;

    8102:   MatCheckPreallocated(mat, 1);
    8103:   if (mat->insertmode == NOT_SET_VALUES) mat->insertmode = addv;
    8104:   else PetscCheck(mat->insertmode == addv, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "Cannot mix add values and insert values");
    8105:   {
    8106:     PetscInt  i, j, rstart = mat->rmap->rstart, rend = mat->rmap->rend;
    8107:     PetscInt  cstart = mat->cmap->rstart, cend = mat->cmap->rend, row, col;
    8108:     PetscBool roworiented = aij->roworiented;

    8110:     /* Some Variables required in the macro */
    8111:     Mat         A     = aij->A;
    8112:     Mat_SeqAIJ *a     = (Mat_SeqAIJ *)A->data;
    8113:     PetscInt   *aimax = a->imax, *ai = a->i, *ailen = a->ilen, *aj = a->j;
    8114:     MatScalar  *aa;
    8115:     PetscBool   ignorezeroentries = ((a->ignorezeroentries && (addv == ADD_VALUES)) ? PETSC_TRUE : PETSC_FALSE);
    8116:     Mat         B                 = aij->B;
    8117:     Mat_SeqAIJ *b                 = (Mat_SeqAIJ *)B->data;
    8118:     PetscInt   *bimax = b->imax, *bi = b->i, *bilen = b->ilen, *bj = b->j, bm = aij->B->rmap->n, am = aij->A->rmap->n;
    8119:     MatScalar  *ba;
    8120:     /* This variable below is only for the PETSC_HAVE_VIENNACL or PETSC_HAVE_CUDA cases, but we define it in all cases because we
    8121:      * cannot use "#if defined" inside a macro. */
    8122:     PETSC_UNUSED PetscBool inserted = PETSC_FALSE;

    8124:     PetscInt  *rp1, *rp2, ii, nrow1, nrow2, _i, rmax1, rmax2, N, low1, high1, low2, high2, t, lastcol1, lastcol2;
    8125:     PetscInt   nonew = a->nonew;
    8126:     MatScalar *ap1, *ap2;

    8128:     PetscFunctionBegin;
    8129:     PetscCall(MatSeqAIJGetArray(A, &aa));
    8130:     PetscCall(MatSeqAIJGetArray(B, &ba));
    8131:     for (i = 0; i < m; i++) {
    8132:       if (im[i] < 0) continue;
    8133:       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);
    8134:       if (im[i] >= rstart && im[i] < rend) {
    8135:         row      = im[i] - rstart;
    8136:         lastcol1 = -1;
    8137:         rp1      = aj + ai[row];
    8138:         ap1      = aa + ai[row];
    8139:         rmax1    = aimax[row];
    8140:         nrow1    = ailen[row];
    8141:         low1     = 0;
    8142:         high1    = nrow1;
    8143:         lastcol2 = -1;
    8144:         rp2      = bj + bi[row];
    8145:         ap2      = ba + bi[row];
    8146:         rmax2    = bimax[row];
    8147:         nrow2    = bilen[row];
    8148:         low2     = 0;
    8149:         high2    = nrow2;

    8151:         for (j = 0; j < n; j++) {
    8152:           if (roworiented) value = v[i * n + j];
    8153:           else value = v[i + j * m];
    8154:           if (ignorezeroentries && value == 0.0 && (addv == ADD_VALUES) && im[i] != in[j]) continue;
    8155:           if (in[j] >= cstart && in[j] < cend) {
    8156:             col = in[j] - cstart;
    8157:             MatSetValues_SeqAIJ_A_Private(row, col, value, addv, im[i], in[j]);
    8158:           } else if (in[j] < 0) continue;
    8159:           else if (PetscUnlikelyDebug(in[j] >= mat->cmap->N)) {
    8160:             SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Column too large: col %" PetscInt_FMT " max %" PetscInt_FMT, in[j], mat->cmap->N - 1);
    8161:           } else {
    8162:             if (mat->was_assembled) {
    8163:               if (!aij->colmap) PetscCall(MatCreateColmap_MPIAIJ_Private(mat));
    8164: #if defined(PETSC_USE_CTABLE)
    8165:               PetscCall(PetscHMapIGetWithDefault(aij->colmap, in[j] + 1, 0, &col));
    8166:               col--;
    8167: #else
    8168:               col = aij->colmap[in[j]] - 1;
    8169: #endif
    8170:               if (col < 0 && !((Mat_SeqAIJ *)aij->A->data)->nonew) {
    8171:                 PetscCall(MatDisAssemble_MPIAIJ(mat, PETSC_FALSE));
    8172:                 col = in[j];
    8173:                 /* Reinitialize the variables required by MatSetValues_SeqAIJ_B_Private() */
    8174:                 B        = aij->B;
    8175:                 b        = (Mat_SeqAIJ *)B->data;
    8176:                 bimax    = b->imax;
    8177:                 bi       = b->i;
    8178:                 bilen    = b->ilen;
    8179:                 bj       = b->j;
    8180:                 rp2      = bj + bi[row];
    8181:                 ap2      = ba + bi[row];
    8182:                 rmax2    = bimax[row];
    8183:                 nrow2    = bilen[row];
    8184:                 low2     = 0;
    8185:                 high2    = nrow2;
    8186:                 bm       = aij->B->rmap->n;
    8187:                 ba       = b->a;
    8188:                 inserted = PETSC_FALSE;
    8189:               }
    8190:             } else col = in[j];
    8191:             MatSetValues_SeqAIJ_B_Private(row, col, value, addv, im[i], in[j]);
    8192:           }
    8193:         }
    8194:       } else if (!aij->donotstash) {
    8195:         if (roworiented) {
    8196:           PetscCall(MatStashValuesRow_Private(&mat->stash, im[i], n, in, v + i * n, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    8197:         } else {
    8198:           PetscCall(MatStashValuesCol_Private(&mat->stash, im[i], n, in, v + i, m, (PetscBool)(ignorezeroentries && (addv == ADD_VALUES))));
    8199:         }
    8200:       }
    8201:     }
    8202:     PetscCall(MatSeqAIJRestoreArray(A, &aa));
    8203:     PetscCall(MatSeqAIJRestoreArray(B, &ba));
    8204:   }
    8205:   PetscFunctionReturnVoid();
    8206: }

    8208: /* Undefining these here since they were redefined from their original definition above! No
    8209:  * other PETSc functions should be defined past this point, as it is impossible to recover the
    8210:  * original definitions */
    8211: #undef PetscCall
    8212: #undef SETERRQ