impls/mpi/pbvec.c

/*
   This file contains routines for Parallel vector operations.
 */
#include <petscsys.h>
#include <../src/vec/vec/impls/mpi/pvecimpl.h> /*I  "petscvec.h"   I*/

PETSC_INTERN PetscErrorCode VecView_MPI_Draw(Vec, PetscViewer);

PetscErrorCode VecPlaceArray_MPI(Vec vin, const PetscScalar *a)
{
  Vec_MPI *v = (Vec_MPI *)vin->data;

  PetscFunctionBegin;
  PetscCheck(!v->unplacedarray, PETSC_COMM_SELF, PETSC_ERR_ARG_WRONGSTATE, "VecPlaceArray() was already called on this vector, without a call to VecResetArray()");
  v->unplacedarray = v->array; /* save previous array so reset can bring it back */
  v->array         = (PetscScalar *)a;
  if (v->localrep) PetscCall(VecPlaceArray(v->localrep, a));
  PetscFunctionReturn(PETSC_SUCCESS);
}

// Duplicate a vector with the provided array on host (if not NULL) for the new vector.
// In that case, the array should be long enough to take into account ghost points if any.
// If array is NULL, the routine will allocate memory itself.
PetscErrorCode VecDuplicateWithArray_MPI(Vec win, const PetscScalar *array, Vec *v)
{
  Vec_MPI *vw, *w = (Vec_MPI *)win->data;

  PetscFunctionBegin;
  PetscCall(VecCreateWithLayout_Private(win->map, v));

  PetscCall(VecCreate_MPI_Private(*v, PETSC_TRUE, w->nghost, array)); // array could be NULL
  vw           = (Vec_MPI *)(*v)->data;
  (*v)->ops[0] = win->ops[0];

  /* save local representation of the parallel vector (and scatter) if it exists */
  if (w->localrep) {
    PetscScalar *arr = ((Vec_MPI *)(*v)->data)->array;

    PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, win->map->bs, win->map->n + w->nghost, arr, &vw->localrep));
    vw->localrep->ops[0] = w->localrep->ops[0];

    vw->localupdate = w->localupdate;
    if (vw->localupdate) PetscCall(PetscObjectReference((PetscObject)vw->localupdate));

    vw->ghost = w->ghost;
    if (vw->ghost) PetscCall(PetscObjectReference((PetscObject)vw->ghost));
  }

  /* New vector should inherit stashing property of parent */
  (*v)->stash.donotstash   = win->stash.donotstash;
  (*v)->stash.ignorenegidx = win->stash.ignorenegidx;

  PetscCall(PetscObjectListDuplicate(((PetscObject)win)->olist, &((PetscObject)*v)->olist));
  PetscCall(PetscFunctionListDuplicate(((PetscObject)win)->qlist, &((PetscObject)*v)->qlist));

  (*v)->stash.bs  = win->stash.bs;
  (*v)->bstash.bs = win->bstash.bs;
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecDuplicate_MPI(Vec win, Vec *v)
{
  PetscFunctionBegin;
  PetscCall(VecDuplicateWithArray_MPI(win, NULL, v));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecDuplicateVecs_MPI_GEMV(Vec w, PetscInt m, Vec *V[])
{
  Vec_MPI *wmpi = (Vec_MPI *)w->data;

  PetscFunctionBegin;
  // Currently only do GEMV for vectors without ghosts. Note w might be a VECMPI subclass object.
  // This routine relies on the duplicate operation being VecDuplicate_MPI. If not, bail out to the default.
  if (wmpi->localrep || w->ops->duplicate != VecDuplicate_MPI) {
    w->ops->duplicatevecs = VecDuplicateVecs_Default;
    PetscCall(VecDuplicateVecs(w, m, V));
  } else {
    PetscScalar *array;
    PetscInt64   lda; // use 64-bit as we will do "m * lda"

    PetscCall(PetscMalloc1(m, V));
    VecGetLocalSizeAligned(w, 64, &lda); // get in lda the 64-bytes aligned local size

    PetscCall(PetscCalloc1(m * lda, &array));
    for (PetscInt i = 0; i < m; i++) {
      Vec v;
      PetscCall(VecCreateMPIWithLayoutAndArray_Private(w->map, PetscSafePointerPlusOffset(array, i * lda), &v));
      PetscCall(VecSetType(v, ((PetscObject)w)->type_name));
      PetscCall(PetscObjectListDuplicate(((PetscObject)w)->olist, &((PetscObject)v)->olist));
      PetscCall(PetscFunctionListDuplicate(((PetscObject)w)->qlist, &((PetscObject)v)->qlist));
      v->ops[0]             = w->ops[0];
      v->stash.donotstash   = w->stash.donotstash;
      v->stash.ignorenegidx = w->stash.ignorenegidx;
      v->stash.bs           = w->stash.bs;
      v->bstash.bs          = w->bstash.bs;
      (*V)[i]               = v;
    }
    // So when the first vector is destroyed it will destroy the array
    if (m) ((Vec_MPI *)(*V)[0]->data)->array_allocated = array;
    // disable replacearray of the first vector, as freeing its memory also frees others in the group.
    // But replacearray of others is ok, as they don't own their array.
    if (m > 1) (*V)[0]->ops->replacearray = VecReplaceArray_Default_GEMV_Error;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecSetOption_MPI(Vec V, VecOption op, PetscBool flag)
{
  Vec_MPI *v = (Vec_MPI *)V->data;

  PetscFunctionBegin;
  switch (op) {
  case VEC_IGNORE_OFF_PROC_ENTRIES:
    V->stash.donotstash = flag;
    break;
  case VEC_IGNORE_NEGATIVE_INDICES:
    V->stash.ignorenegidx = flag;
    break;
  case VEC_SUBSET_OFF_PROC_ENTRIES:
    v->assembly_subset = flag;              /* See the same logic in MatAssembly wrt MAT_SUBSET_OFF_PROC_ENTRIES */
    if (!v->assembly_subset) {              /* User indicates "do not reuse the communication pattern" */
      PetscCall(VecAssemblyReset_MPI(V));   /* Reset existing pattern to free memory */
      v->first_assembly_done = PETSC_FALSE; /* Mark the first assembly is not done */
    }
    break;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecResetArray_MPI(Vec vin)
{
  Vec_MPI *v = (Vec_MPI *)vin->data;

  PetscFunctionBegin;
  v->array         = v->unplacedarray;
  v->unplacedarray = NULL;
  if (v->localrep) PetscCall(VecResetArray(v->localrep));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecAssemblySend_MPI_Private(MPI_Comm comm, const PetscMPIInt tag[], PetscMPIInt rankid, PetscMPIInt rank, void *sdata, MPI_Request req[], void *ctx)
{
  Vec                X   = (Vec)ctx;
  Vec_MPI           *x   = (Vec_MPI *)X->data;
  VecAssemblyHeader *hdr = (VecAssemblyHeader *)sdata;
  PetscInt           bs  = X->map->bs;

  PetscFunctionBegin;
  /* x->first_assembly_done indicates we are reusing a communication network. In that case, some
     messages can be empty, but we have to send them this time if we sent them before because the
     receiver is expecting them.
   */
  if (hdr->count || (x->first_assembly_done && x->sendptrs[rankid].ints)) {
    PetscCallMPI(MPIU_Isend(x->sendptrs[rankid].ints, hdr->count, MPIU_INT, rank, tag[0], comm, &req[0]));
    PetscCallMPI(MPIU_Isend(x->sendptrs[rankid].scalars, hdr->count, MPIU_SCALAR, rank, tag[1], comm, &req[1]));
  }
  if (hdr->bcount || (x->first_assembly_done && x->sendptrs[rankid].intb)) {
    PetscCallMPI(MPIU_Isend(x->sendptrs[rankid].intb, hdr->bcount, MPIU_INT, rank, tag[2], comm, &req[2]));
    PetscCallMPI(MPIU_Isend(x->sendptrs[rankid].scalarb, hdr->bcount * bs, MPIU_SCALAR, rank, tag[3], comm, &req[3]));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecAssemblyRecv_MPI_Private(MPI_Comm comm, const PetscMPIInt tag[], PetscMPIInt rank, void *rdata, MPI_Request req[], void *ctx)
{
  Vec                X   = (Vec)ctx;
  Vec_MPI           *x   = (Vec_MPI *)X->data;
  VecAssemblyHeader *hdr = (VecAssemblyHeader *)rdata;
  PetscInt           bs  = X->map->bs;
  VecAssemblyFrame  *frame;

  PetscFunctionBegin;
  PetscCall(PetscSegBufferGet(x->segrecvframe, 1, &frame));

  if (hdr->count) {
    PetscCall(PetscSegBufferGet(x->segrecvint, hdr->count, &frame->ints));
    PetscCallMPI(MPIU_Irecv(frame->ints, hdr->count, MPIU_INT, rank, tag[0], comm, &req[0]));
    PetscCall(PetscSegBufferGet(x->segrecvscalar, hdr->count, &frame->scalars));
    PetscCallMPI(MPIU_Irecv(frame->scalars, hdr->count, MPIU_SCALAR, rank, tag[1], comm, &req[1]));
    frame->pendings = 2;
  } else {
    frame->ints     = NULL;
    frame->scalars  = NULL;
    frame->pendings = 0;
  }

  if (hdr->bcount) {
    PetscCall(PetscSegBufferGet(x->segrecvint, hdr->bcount, &frame->intb));
    PetscCallMPI(MPIU_Irecv(frame->intb, hdr->bcount, MPIU_INT, rank, tag[2], comm, &req[2]));
    PetscCall(PetscSegBufferGet(x->segrecvscalar, hdr->bcount * bs, &frame->scalarb));
    PetscCallMPI(MPIU_Irecv(frame->scalarb, hdr->bcount * bs, MPIU_SCALAR, rank, tag[3], comm, &req[3]));
    frame->pendingb = 2;
  } else {
    frame->intb     = NULL;
    frame->scalarb  = NULL;
    frame->pendingb = 0;
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecAssemblyBegin_MPI_BTS(Vec X)
{
  Vec_MPI    *x = (Vec_MPI *)X->data;
  MPI_Comm    comm;
  PetscMPIInt i;
  PetscInt    j, jb, bs;

  PetscFunctionBegin;
  if (X->stash.donotstash) PetscFunctionReturn(PETSC_SUCCESS);

  PetscCall(PetscObjectGetComm((PetscObject)X, &comm));
  PetscCall(VecGetBlockSize(X, &bs));
  if (PetscDefined(USE_DEBUG)) {
    InsertMode addv;

    PetscCallMPI(MPIU_Allreduce((PetscEnum *)&X->stash.insertmode, (PetscEnum *)&addv, 1, MPIU_ENUM, MPI_BOR, comm));
    PetscCheck(addv != (ADD_VALUES | INSERT_VALUES), comm, PETSC_ERR_ARG_NOTSAMETYPE, "Some processors inserted values while others added");
  }
  X->bstash.insertmode = X->stash.insertmode; /* Block stash implicitly tracks InsertMode of scalar stash */

  PetscCall(VecStashSortCompress_Private(&X->stash));
  PetscCall(VecStashSortCompress_Private(&X->bstash));

  if (!x->sendranks) {
    PetscMPIInt nowners, bnowners, *owners, *bowners;
    PetscInt    ntmp;

    PetscCall(VecStashGetOwnerList_Private(&X->stash, X->map, &nowners, &owners));
    PetscCall(VecStashGetOwnerList_Private(&X->bstash, X->map, &bnowners, &bowners));
    PetscCall(PetscMergeMPIIntArray(nowners, owners, bnowners, bowners, &ntmp, &x->sendranks));
    PetscCall(PetscMPIIntCast(ntmp, &x->nsendranks));
    PetscCall(PetscFree(owners));
    PetscCall(PetscFree(bowners));
    PetscCall(PetscMalloc1(x->nsendranks, &x->sendhdr));
    PetscCall(PetscCalloc1(x->nsendranks, &x->sendptrs));
  }
  for (i = 0, j = 0, jb = 0; i < x->nsendranks; i++) {
    PetscMPIInt rank = x->sendranks[i];

    x->sendhdr[i].insertmode = X->stash.insertmode;
    /* Initialize pointers for non-empty stashes the first time around.  Subsequent assemblies with
     * VEC_SUBSET_OFF_PROC_ENTRIES will leave the old pointers (dangling because the stash has been collected) when
     * there is nothing new to send, so that size-zero messages get sent instead. */
    x->sendhdr[i].count = 0;
    if (X->stash.n) {
      x->sendptrs[i].ints    = &X->stash.idx[j];
      x->sendptrs[i].scalars = &X->stash.array[j];
      for (; j < X->stash.n && X->stash.idx[j] < X->map->range[rank + 1]; j++) x->sendhdr[i].count++;
    }
    x->sendhdr[i].bcount = 0;
    if (X->bstash.n) {
      x->sendptrs[i].intb    = &X->bstash.idx[jb];
      x->sendptrs[i].scalarb = &X->bstash.array[jb * bs];
      for (; jb < X->bstash.n && X->bstash.idx[jb] * bs < X->map->range[rank + 1]; jb++) x->sendhdr[i].bcount++;
    }
  }

  if (!x->segrecvint) PetscCall(PetscSegBufferCreate(sizeof(PetscInt), 1000, &x->segrecvint));
  if (!x->segrecvscalar) PetscCall(PetscSegBufferCreate(sizeof(PetscScalar), 1000, &x->segrecvscalar));
  if (!x->segrecvframe) PetscCall(PetscSegBufferCreate(sizeof(VecAssemblyFrame), 50, &x->segrecvframe));
  if (x->first_assembly_done) { /* this is not the first assembly */
    PetscMPIInt tag[4];
    for (i = 0; i < 4; i++) PetscCall(PetscCommGetNewTag(comm, &tag[i]));
    for (i = 0; i < x->nsendranks; i++) PetscCall(VecAssemblySend_MPI_Private(comm, tag, i, x->sendranks[i], x->sendhdr + i, x->sendreqs + 4 * i, X));
    for (i = 0; i < x->nrecvranks; i++) PetscCall(VecAssemblyRecv_MPI_Private(comm, tag, x->recvranks[i], x->recvhdr + i, x->recvreqs + 4 * i, X));
    x->use_status = PETSC_TRUE;
  } else { /* First time assembly */
    PetscCall(PetscCommBuildTwoSidedFReq(comm, 3, MPIU_INT, x->nsendranks, x->sendranks, (PetscInt *)x->sendhdr, &x->nrecvranks, &x->recvranks, &x->recvhdr, 4, &x->sendreqs, &x->recvreqs, VecAssemblySend_MPI_Private, VecAssemblyRecv_MPI_Private, X));
    x->use_status = PETSC_FALSE;
  }

  /* The first_assembly_done flag is only meaningful when x->assembly_subset is set.
     This line says when assembly_subset is set, then we mark that the first assembly is done.
   */
  x->first_assembly_done = x->assembly_subset;

  {
    PetscInt nstash, reallocs;
    PetscCall(VecStashGetInfo_Private(&X->stash, &nstash, &reallocs));
    PetscCall(PetscInfo(X, "Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
    PetscCall(VecStashGetInfo_Private(&X->bstash, &nstash, &reallocs));
    PetscCall(PetscInfo(X, "Block-Stash has %" PetscInt_FMT " entries, uses %" PetscInt_FMT " mallocs.\n", nstash, reallocs));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecAssemblyEnd_MPI_BTS(Vec X)
{
  Vec_MPI          *x  = (Vec_MPI *)X->data;
  PetscInt          bs = X->map->bs;
  PetscMPIInt       npending, *some_indices, r;
  MPI_Status       *some_statuses;
  PetscScalar      *xarray;
  VecAssemblyFrame *frame;

  PetscFunctionBegin;
  if (X->stash.donotstash) {
    X->stash.insertmode  = NOT_SET_VALUES;
    X->bstash.insertmode = NOT_SET_VALUES;
    PetscFunctionReturn(PETSC_SUCCESS);
  }

  PetscCheck(x->segrecvframe, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Missing segrecvframe! Probably you forgot to call VecAssemblyBegin() first");
  PetscCall(VecGetArray(X, &xarray));
  PetscCall(PetscSegBufferExtractInPlace(x->segrecvframe, &frame));
  PetscCall(PetscMalloc2(4 * x->nrecvranks, &some_indices, (x->use_status ? (size_t)4 * x->nrecvranks : 0), &some_statuses));
  for (r = 0, npending = 0; r < x->nrecvranks; r++) npending += frame[r].pendings + frame[r].pendingb;
  while (npending > 0) {
    PetscMPIInt ndone = 0, ii;
    /* Filling MPI_Status fields requires some resources from the MPI library.  We skip it on the first assembly, or
     * when VEC_SUBSET_OFF_PROC_ENTRIES has not been set, because we could exchange exact sizes in the initial
     * rendezvous.  When the rendezvous is elided, however, we use MPI_Status to get actual message lengths, so that
     * subsequent assembly can set a proper subset of the values. */
    PetscCallMPI(MPI_Waitsome(4 * x->nrecvranks, x->recvreqs, &ndone, some_indices, x->use_status ? some_statuses : MPI_STATUSES_IGNORE));
    for (ii = 0; ii < ndone; ii++) {
      PetscInt     i     = some_indices[ii] / 4, j, k;
      InsertMode   imode = (InsertMode)x->recvhdr[i].insertmode;
      PetscInt    *recvint;
      PetscScalar *recvscalar;
      PetscBool    intmsg   = (PetscBool)(some_indices[ii] % 2 == 0);
      PetscBool    blockmsg = (PetscBool)((some_indices[ii] % 4) / 2 == 1);

      npending--;
      if (!blockmsg) { /* Scalar stash */
        PetscMPIInt count;

        if (--frame[i].pendings > 0) continue;
        if (x->use_status) {
          PetscCallMPI(MPI_Get_count(&some_statuses[ii], intmsg ? MPIU_INT : MPIU_SCALAR, &count));
        } else {
          PetscCall(PetscMPIIntCast(x->recvhdr[i].count, &count));
        }
        for (j = 0, recvint = frame[i].ints, recvscalar = frame[i].scalars; j < count; j++, recvint++) {
          PetscInt loc = *recvint - X->map->rstart;

          PetscCheck(*recvint >= X->map->rstart && X->map->rend > *recvint, PETSC_COMM_SELF, PETSC_ERR_PLIB, "Received vector entry %" PetscInt_FMT " out of local range [%" PetscInt_FMT ",%" PetscInt_FMT ")]", *recvint, X->map->rstart, X->map->rend);
          switch (imode) {
          case ADD_VALUES:
            xarray[loc] += *recvscalar++;
            break;
          case INSERT_VALUES:
            xarray[loc] = *recvscalar++;
            break;
          default:
            SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Insert mode not supported 0x%x", imode);
          }
        }
      } else { /* Block stash */
        PetscMPIInt count;
        if (--frame[i].pendingb > 0) continue;
        if (x->use_status) {
          PetscCallMPI(MPI_Get_count(&some_statuses[ii], intmsg ? MPIU_INT : MPIU_SCALAR, &count));
          if (!intmsg) count /= bs; /* Convert from number of scalars to number of blocks */
        } else {
          PetscCall(PetscMPIIntCast(x->recvhdr[i].bcount, &count));
        }
        for (j = 0, recvint = frame[i].intb, recvscalar = frame[i].scalarb; j < count; j++, recvint++) {
          PetscInt loc = (*recvint) * bs - X->map->rstart;
          switch (imode) {
          case ADD_VALUES:
            for (k = loc; k < loc + bs; k++) xarray[k] += *recvscalar++;
            break;
          case INSERT_VALUES:
            for (k = loc; k < loc + bs; k++) xarray[k] = *recvscalar++;
            break;
          default:
            SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "Insert mode not supported 0x%x", imode);
          }
        }
      }
    }
  }
  PetscCall(VecRestoreArray(X, &xarray));
  PetscCallMPI(MPI_Waitall(4 * x->nsendranks, x->sendreqs, MPI_STATUSES_IGNORE));
  PetscCall(PetscFree2(some_indices, some_statuses));
  if (x->assembly_subset) {
    PetscCall(PetscSegBufferExtractInPlace(x->segrecvint, NULL));
    PetscCall(PetscSegBufferExtractInPlace(x->segrecvscalar, NULL));
  } else {
    PetscCall(VecAssemblyReset_MPI(X));
  }

  X->stash.insertmode  = NOT_SET_VALUES;
  X->bstash.insertmode = NOT_SET_VALUES;
  PetscCall(VecStashScatterEnd_Private(&X->stash));
  PetscCall(VecStashScatterEnd_Private(&X->bstash));
  PetscFunctionReturn(PETSC_SUCCESS);
}

PetscErrorCode VecAssemblyReset_MPI(Vec X)
{
  Vec_MPI *x = (Vec_MPI *)X->data;

  PetscFunctionBegin;
  PetscCall(PetscFree(x->sendreqs));
  PetscCall(PetscFree(x->recvreqs));
  PetscCall(PetscFree(x->sendranks));
  PetscCall(PetscFree(x->recvranks));
  PetscCall(PetscFree(x->sendhdr));
  PetscCall(PetscFree(x->recvhdr));
  PetscCall(PetscFree(x->sendptrs));
  PetscCall(PetscSegBufferDestroy(&x->segrecvint));
  PetscCall(PetscSegBufferDestroy(&x->segrecvscalar));
  PetscCall(PetscSegBufferDestroy(&x->segrecvframe));
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecSetFromOptions_MPI(Vec X, PetscOptionItems PetscOptionsObject)
{
#if !defined(PETSC_HAVE_MPIUNI)
  PetscBool flg = PETSC_FALSE, set;

  PetscFunctionBegin;
  PetscOptionsHeadBegin(PetscOptionsObject, "VecMPI Options");
  PetscCall(PetscOptionsBool("-vec_assembly_legacy", "Use MPI 1 version of assembly", "", flg, &flg, &set));
  if (set) {
    X->ops->assemblybegin = flg ? VecAssemblyBegin_MPI : VecAssemblyBegin_MPI_BTS;
    X->ops->assemblyend   = flg ? VecAssemblyEnd_MPI : VecAssemblyEnd_MPI_BTS;
  }
  PetscOptionsHeadEnd();
#else
  PetscFunctionBegin;
  X->ops->assemblybegin = VecAssemblyBegin_MPI;
  X->ops->assemblyend   = VecAssemblyEnd_MPI;
#endif
  PetscFunctionReturn(PETSC_SUCCESS);
}

static PetscErrorCode VecGetLocalToGlobalMapping_MPI_VecGhost(Vec X, ISLocalToGlobalMapping *ltg)
{
  PetscInt       *indices, n, nghost, rstart, i;
  IS              ghostis;
  const PetscInt *ghostidx;

  PetscFunctionBegin;
  *ltg = X->map->mapping;
  if (X->map->mapping) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(VecGhostGetGhostIS(X, &ghostis));
  if (!ghostis) PetscFunctionReturn(PETSC_SUCCESS);
  PetscCall(ISGetLocalSize(ghostis, &nghost));
  PetscCall(VecGetLocalSize(X, &n));
  PetscCall(ISGetIndices(ghostis, &ghostidx));
  /* set local to global mapping for ghosted vector */
  PetscCall(PetscMalloc1(n + nghost, &indices));
  PetscCall(VecGetOwnershipRange(X, &rstart, NULL));
  for (i = 0; i < n; i++) indices[i] = rstart + i;
  PetscCall(PetscArraycpy(indices + n, ghostidx, nghost));
  PetscCall(ISRestoreIndices(ghostis, &ghostidx));
  PetscCall(ISLocalToGlobalMappingCreate(PETSC_COMM_SELF, 1, n + nghost, indices, PETSC_OWN_POINTER, &X->map->mapping));
  *ltg = X->map->mapping;
  PetscFunctionReturn(PETSC_SUCCESS);
}

static struct _VecOps DvOps = {
  PetscDesignatedInitializer(duplicate, VecDuplicate_MPI), /* 1 */
  PetscDesignatedInitializer(duplicatevecs, VecDuplicateVecs_Default),
  PetscDesignatedInitializer(destroyvecs, VecDestroyVecs_Default),
  PetscDesignatedInitializer(dot, VecDot_MPI),
  PetscDesignatedInitializer(mdot, VecMDot_MPI),
  PetscDesignatedInitializer(norm, VecNorm_MPI),
  PetscDesignatedInitializer(tdot, VecTDot_MPI),
  PetscDesignatedInitializer(mtdot, VecMTDot_MPI),
  PetscDesignatedInitializer(scale, VecScale_Seq),
  PetscDesignatedInitializer(copy, VecCopy_Seq), /* 10 */
  PetscDesignatedInitializer(set, VecSet_Seq),
  PetscDesignatedInitializer(swap, VecSwap_Seq),
  PetscDesignatedInitializer(axpy, VecAXPY_Seq),
  PetscDesignatedInitializer(axpby, VecAXPBY_Seq),
  PetscDesignatedInitializer(maxpy, VecMAXPY_Seq),
  PetscDesignatedInitializer(aypx, VecAYPX_Seq),
  PetscDesignatedInitializer(waxpy, VecWAXPY_Seq),
  PetscDesignatedInitializer(axpbypcz, VecAXPBYPCZ_Seq),
  PetscDesignatedInitializer(pointwisemult, VecPointwiseMult_Seq),
  PetscDesignatedInitializer(pointwisedivide, VecPointwiseDivide_Seq),
  PetscDesignatedInitializer(setvalues, VecSetValues_MPI), /* 20 */
  PetscDesignatedInitializer(assemblybegin, VecAssemblyBegin_MPI_BTS),
  PetscDesignatedInitializer(assemblyend, VecAssemblyEnd_MPI_BTS),
  PetscDesignatedInitializer(getarray, NULL),
  PetscDesignatedInitializer(getsize, VecGetSize_MPI),
  PetscDesignatedInitializer(getlocalsize, VecGetSize_Seq),
  PetscDesignatedInitializer(restorearray, NULL),
  PetscDesignatedInitializer(max, VecMax_MPI),
  PetscDesignatedInitializer(min, VecMin_MPI),
  PetscDesignatedInitializer(setrandom, VecSetRandom_Seq),
  PetscDesignatedInitializer(setoption, VecSetOption_MPI),
  PetscDesignatedInitializer(setvaluesblocked, VecSetValuesBlocked_MPI),
  PetscDesignatedInitializer(destroy, VecDestroy_MPI),
  PetscDesignatedInitializer(view, VecView_MPI),
  PetscDesignatedInitializer(placearray, VecPlaceArray_MPI),
  PetscDesignatedInitializer(replacearray, VecReplaceArray_Seq),
  PetscDesignatedInitializer(dot_local, VecDot_Seq),
  PetscDesignatedInitializer(tdot_local, VecTDot_Seq),
  PetscDesignatedInitializer(norm_local, VecNorm_Seq),
  PetscDesignatedInitializer(mdot_local, VecMDot_Seq),
  PetscDesignatedInitializer(mtdot_local, VecMTDot_Seq),
  PetscDesignatedInitializer(load, VecLoad_Default),
  PetscDesignatedInitializer(reciprocal, VecReciprocal_Default),
  PetscDesignatedInitializer(conjugate, VecConjugate_Seq),
  PetscDesignatedInitializer(setlocaltoglobalmapping, NULL),
  PetscDesignatedInitializer(getlocaltoglobalmapping, VecGetLocalToGlobalMapping_MPI_VecGhost),
  PetscDesignatedInitializer(setvalueslocal, NULL),
  PetscDesignatedInitializer(resetarray, VecResetArray_MPI),
  PetscDesignatedInitializer(setfromoptions, VecSetFromOptions_MPI), /*set from options */
  PetscDesignatedInitializer(maxpointwisedivide, VecMaxPointwiseDivide_Seq),
  PetscDesignatedInitializer(pointwisemax, VecPointwiseMax_Seq),
  PetscDesignatedInitializer(pointwisemaxabs, VecPointwiseMaxAbs_Seq),
  PetscDesignatedInitializer(pointwisemin, VecPointwiseMin_Seq),
  PetscDesignatedInitializer(getvalues, VecGetValues_MPI),
  PetscDesignatedInitializer(sqrt, NULL),
  PetscDesignatedInitializer(abs, NULL),
  PetscDesignatedInitializer(exp, NULL),
  PetscDesignatedInitializer(log, NULL),
  PetscDesignatedInitializer(shift, NULL),
  PetscDesignatedInitializer(create, NULL), /* really? */
  PetscDesignatedInitializer(stridegather, VecStrideGather_Default),
  PetscDesignatedInitializer(stridescatter, VecStrideScatter_Default),
  PetscDesignatedInitializer(dotnorm2, NULL),
  PetscDesignatedInitializer(getsubvector, NULL),
  PetscDesignatedInitializer(restoresubvector, NULL),
  PetscDesignatedInitializer(getarrayread, NULL),
  PetscDesignatedInitializer(restorearrayread, NULL),
  PetscDesignatedInitializer(stridesubsetgather, VecStrideSubSetGather_Default),
  PetscDesignatedInitializer(stridesubsetscatter, VecStrideSubSetScatter_Default),
  PetscDesignatedInitializer(viewnative, VecView_MPI),
  PetscDesignatedInitializer(loadnative, NULL),
  PetscDesignatedInitializer(createlocalvector, NULL),
  PetscDesignatedInitializer(getlocalvector, NULL),
  PetscDesignatedInitializer(restorelocalvector, NULL),
  PetscDesignatedInitializer(getlocalvectorread, NULL),
  PetscDesignatedInitializer(restorelocalvectorread, NULL),
  PetscDesignatedInitializer(bindtocpu, NULL),
  PetscDesignatedInitializer(getarraywrite, NULL),
  PetscDesignatedInitializer(restorearraywrite, NULL),
  PetscDesignatedInitializer(getarrayandmemtype, NULL),
  PetscDesignatedInitializer(restorearrayandmemtype, NULL),
  PetscDesignatedInitializer(getarrayreadandmemtype, NULL),
  PetscDesignatedInitializer(restorearrayreadandmemtype, NULL),
  PetscDesignatedInitializer(getarraywriteandmemtype, NULL),
  PetscDesignatedInitializer(restorearraywriteandmemtype, NULL),
  PetscDesignatedInitializer(concatenate, NULL),
  PetscDesignatedInitializer(sum, NULL),
  PetscDesignatedInitializer(setpreallocationcoo, VecSetPreallocationCOO_MPI),
  PetscDesignatedInitializer(setvaluescoo, VecSetValuesCOO_MPI),
  PetscDesignatedInitializer(errorwnorm, NULL),
  PetscDesignatedInitializer(maxpby, NULL),
};

/*
    VecCreate_MPI_Private - Basic create routine called by VecCreate_MPI() (i.e. VecCreateMPI()),
    VecCreateMPIWithArray(), VecCreate_Shared() (i.e. VecCreateShared()), VecCreateGhost(),
    VecDuplicate_MPI(), VecCreateGhostWithArray(), VecDuplicate_MPI(), and VecDuplicate_Shared()

    If alloc is true and array is NULL then this routine allocates the space, otherwise
    no space is allocated.
*/
PetscErrorCode VecCreate_MPI_Private(Vec v, PetscBool alloc, PetscInt nghost, const PetscScalar array[])
{
  Vec_MPI  *s;
  PetscBool mdot_use_gemv  = PETSC_TRUE;
  PetscBool maxpy_use_gemv = PETSC_FALSE; // default is false as we saw bad performance with vendors' GEMV with tall skinny matrices.

  PetscFunctionBegin;
  PetscCall(PetscNew(&s));
  v->data   = (void *)s;
  v->ops[0] = DvOps;

  PetscCall(PetscOptionsGetBool(NULL, NULL, "-vec_mdot_use_gemv", &mdot_use_gemv, NULL));
  PetscCall(PetscOptionsGetBool(NULL, NULL, "-vec_maxpy_use_gemv", &maxpy_use_gemv, NULL));

  // allocate multiple vectors together
  if (mdot_use_gemv || maxpy_use_gemv) v->ops[0].duplicatevecs = VecDuplicateVecs_MPI_GEMV;

  if (mdot_use_gemv) {
    v->ops[0].mdot        = VecMDot_MPI_GEMV;
    v->ops[0].mdot_local  = VecMDot_Seq_GEMV;
    v->ops[0].mtdot       = VecMTDot_MPI_GEMV;
    v->ops[0].mtdot_local = VecMTDot_Seq_GEMV;
  }
  if (maxpy_use_gemv) v->ops[0].maxpy = VecMAXPY_Seq_GEMV;

  s->nghost      = nghost;
  v->petscnative = PETSC_TRUE;
  if (array) v->offloadmask = PETSC_OFFLOAD_CPU;

  PetscCall(PetscLayoutSetUp(v->map));

  s->array           = (PetscScalar *)array;
  s->array_allocated = NULL;
  if (alloc && !array) {
    PetscInt n = v->map->n + nghost;
    PetscCall(PetscCalloc1(n, &s->array));
    s->array_allocated = s->array;
    PetscCall(PetscObjectComposedDataSetReal((PetscObject)v, NormIds[NORM_2], 0));
    PetscCall(PetscObjectComposedDataSetReal((PetscObject)v, NormIds[NORM_1], 0));
    PetscCall(PetscObjectComposedDataSetReal((PetscObject)v, NormIds[NORM_INFINITY], 0));
  }

  /* By default parallel vectors do not have local representation */
  s->localrep    = NULL;
  s->localupdate = NULL;
  s->ghost       = NULL;

  v->stash.insertmode  = NOT_SET_VALUES;
  v->bstash.insertmode = NOT_SET_VALUES;
  /* create the stashes. The block-size for bstash is set later when
     VecSetValuesBlocked is called.
  */
  PetscCall(VecStashCreate_Private(PetscObjectComm((PetscObject)v), 1, &v->stash));
  PetscCall(VecStashCreate_Private(PetscObjectComm((PetscObject)v), v->map->bs, &v->bstash));

#if defined(PETSC_HAVE_MATLAB)
  PetscCall(PetscObjectComposeFunction((PetscObject)v, "PetscMatlabEnginePut_C", VecMatlabEnginePut_Default));
  PetscCall(PetscObjectComposeFunction((PetscObject)v, "PetscMatlabEngineGet_C", VecMatlabEngineGet_Default));
#endif
  PetscCall(PetscObjectChangeTypeName((PetscObject)v, VECMPI));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*
  Create a VECMPI with the given layout and array

  Collective

  Input Parameter:
+ map   - the layout
- array - the array on host

  Output Parameter:
. V  - The vector object
*/
PetscErrorCode VecCreateMPIWithLayoutAndArray_Private(PetscLayout map, const PetscScalar array[], Vec *V)
{
  PetscFunctionBegin;
  PetscCall(VecCreateWithLayout_Private(map, V));
  PetscCall(VecCreate_MPI_Private(*V, PETSC_FALSE, 0, array));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
   VECMPI - VECMPI = "mpi" - The basic parallel vector

   Options Database Key:
. -vec_type mpi - sets the vector type to `VECMPI` during a call to `VecSetFromOptions()`

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecType`, `VecCreate()`, `VecSetType()`, `VecSetFromOptions()`, `VecCreateMPIWithArray()`, `VECMPI`, `VecType`, `VecCreateMPI()`, `VecCreateMPI()`
M*/

PetscErrorCode VecCreate_MPI(Vec vv)
{
  PetscFunctionBegin;
  PetscCall(VecCreate_MPI_Private(vv, PETSC_TRUE, 0, NULL));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*MC
   VECSTANDARD = "standard" - A `VECSEQ` on one process and `VECMPI` on more than one process

   Options Database Key:
. -vec_type standard - sets a vector type to standard on calls to `VecSetFromOptions()`

  Level: beginner

.seealso: [](ch_vectors), `Vec`, `VecType`, `VecCreateSeq()`, `VecCreateMPI()`
M*/

PETSC_EXTERN PetscErrorCode VecCreate_Standard(Vec v)
{
  PetscMPIInt size;

  PetscFunctionBegin;
  PetscCallMPI(MPI_Comm_size(PetscObjectComm((PetscObject)v), &size));
  if (size == 1) {
    PetscCall(VecSetType(v, VECSEQ));
  } else {
    PetscCall(VecSetType(v, VECMPI));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecCreateMPIWithArray - Creates a parallel, array-style vector,
  where the user provides the array space to store the vector values.

  Collective

  Input Parameters:
+ comm  - the MPI communicator to use
. bs    - block size, same meaning as `VecSetBlockSize()`
. n     - local vector length, cannot be `PETSC_DECIDE`
. N     - global vector length (or `PETSC_DETERMINE` to have calculated)
- array - the user provided array to store the vector values

  Output Parameter:
. vv - the vector

  Level: intermediate

  Notes:
  Use `VecDuplicate()` or `VecDuplicateVecs()` to form additional vectors of the
  same type as an existing vector.

  If the user-provided array is `NULL`, then `VecPlaceArray()` can be used
  at a later stage to SET the array for storing the vector values.

  PETSc does NOT free `array` when the vector is destroyed via `VecDestroy()`.

  The user should not free `array` until the vector is destroyed.

.seealso: [](ch_vectors), `Vec`, `VecType`, `VecCreateSeqWithArray()`, `VecCreate()`, `VecDuplicate()`, `VecDuplicateVecs()`, `VecCreateGhost()`,
          `VecCreateMPI()`, `VecCreateGhostWithArray()`, `VecPlaceArray()`
@*/
PetscErrorCode VecCreateMPIWithArray(MPI_Comm comm, PetscInt bs, PetscInt n, PetscInt N, const PetscScalar array[], Vec *vv)
{
  PetscFunctionBegin;
  PetscCheck(n != PETSC_DECIDE, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must set local size of vector");
  PetscCall(PetscSplitOwnership(comm, &n, &N));
  PetscCall(VecCreate(comm, vv));
  PetscCall(VecSetSizes(*vv, n, N));
  PetscCall(VecSetBlockSize(*vv, bs));
  PetscCall(VecCreate_MPI_Private(*vv, PETSC_FALSE, 0, array));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecCreateGhostWithArray - Creates a parallel vector with ghost padding on each processor;
  the caller allocates the array space.

  Collective

  Input Parameters:
+ comm   - the MPI communicator to use
. n      - local vector length
. N      - global vector length (or `PETSC_DETERMINE` to have calculated if `n` is given)
. nghost - number of local ghost points
. ghosts - global indices of ghost points (or `NULL` if not needed), these do not need to be in increasing order (sorted)
- array  - the space to store the vector values (as long as n + nghost)

  Output Parameter:
. vv - the global vector representation (without ghost points as part of vector)

  Level: advanced

  Notes:
  Use `VecGhostGetLocalForm()` to access the local, ghosted representation
  of the vector.

  This also automatically sets the `ISLocalToGlobalMapping()` for this vector.

.seealso: [](ch_vectors), `Vec`, `VecType`, `VecCreate()`, `VecGhostGetLocalForm()`, `VecGhostRestoreLocalForm()`,
          `VecCreateGhost()`, `VecCreateSeqWithArray()`, `VecCreateMPIWithArray()`,
          `VecCreateGhostBlock()`, `VecCreateGhostBlockWithArray()`, `VecMPISetGhost()`
@*/
PetscErrorCode VecCreateGhostWithArray(MPI_Comm comm, PetscInt n, PetscInt N, PetscInt nghost, const PetscInt ghosts[], const PetscScalar array[], Vec *vv)
{
  Vec_MPI     *w;
  PetscScalar *larray;
  IS           from, to;

  PetscFunctionBegin;
  *vv = NULL;
  PetscCheck(nghost != PETSC_DECIDE, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must set local ghost size");
  PetscCheck(nghost >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Ghost length must be >= 0");
  PetscCall(PetscSplitOwnership(comm, &n, &N));
  /* Create global representation */
  PetscCall(VecCreate(comm, vv));
  PetscCall(VecSetSizes(*vv, n, N));
  PetscCall(VecCreate_MPI_Private(*vv, PETSC_TRUE, nghost, array));
  w = (Vec_MPI *)(*vv)->data;
  /* Create local representation */
  PetscCall(VecGetArray(*vv, &larray));
  PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, n + nghost, larray, &w->localrep));
  PetscCall(VecRestoreArray(*vv, &larray));

  /*
       Create scatter context for scattering (updating) ghost values
  */
  PetscCall(ISCreateGeneral(comm, nghost, ghosts, PETSC_COPY_VALUES, &from));
  PetscCall(ISCreateStride(PETSC_COMM_SELF, nghost, n, 1, &to));
  PetscCall(VecScatterCreate(*vv, from, w->localrep, to, &w->localupdate));
  PetscCall(ISDestroy(&to));

  w->ghost                            = from;
  (*vv)->ops->getlocaltoglobalmapping = VecGetLocalToGlobalMapping_MPI_VecGhost;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecGhostGetGhostIS - Return ghosting indices of a ghost vector

  Input Parameters:
. X - ghost vector

  Output Parameter:
. ghost - ghosting indices

  Level: beginner

.seealso: `VecCreateGhostWithArray()`, `VecCreateMPIWithArray()`
@*/
PetscErrorCode VecGhostGetGhostIS(Vec X, IS *ghost)
{
  Vec_MPI  *w;
  PetscBool flg;

  PetscFunctionBegin;
  PetscValidType(X, 1);
  PetscAssertPointer(ghost, 2);
  PetscCall(PetscObjectTypeCompare((PetscObject)X, VECMPI, &flg));
  PetscCheck(flg, PetscObjectComm((PetscObject)X), PETSC_ERR_ARG_WRONGSTATE, "VecGhostGetGhostIS was not supported for vec type %s", ((PetscObject)X)->type_name);
  w      = (Vec_MPI *)X->data;
  *ghost = w->ghost;
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecCreateGhost - Creates a parallel vector with ghost padding on each processor.

  Collective

  Input Parameters:
+ comm   - the MPI communicator to use
. n      - local vector length
. N      - global vector length (or `PETSC_DETERMINE` to have calculated if `n` is given)
. nghost - number of local ghost points
- ghosts - global indices of ghost points, these do not need to be in increasing order (sorted)

  Output Parameter:
. vv - the global vector representation (without ghost points as part of vector)

  Level: advanced

  Notes:
  Use `VecGhostGetLocalForm()` to access the local, ghosted representation
  of the vector.

  This also automatically sets the `ISLocalToGlobalMapping()` for this vector.

.seealso: [](ch_vectors), `Vec`, `VecType`, `VecCreateSeq()`, `VecCreate()`, `VecDuplicate()`, `VecDuplicateVecs()`, `VecCreateMPI()`,
          `VecGhostGetLocalForm()`, `VecGhostRestoreLocalForm()`, `VecGhostUpdateBegin()`,
          `VecCreateGhostWithArray()`, `VecCreateMPIWithArray()`, `VecGhostUpdateEnd()`,
          `VecCreateGhostBlock()`, `VecCreateGhostBlockWithArray()`, `VecMPISetGhost()`

@*/
PetscErrorCode VecCreateGhost(MPI_Comm comm, PetscInt n, PetscInt N, PetscInt nghost, const PetscInt ghosts[], Vec *vv)
{
  PetscFunctionBegin;
  PetscCall(VecCreateGhostWithArray(comm, n, N, nghost, ghosts, NULL, vv));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecMPISetGhost - Sets the ghost points for an MPI ghost vector

  Collective

  Input Parameters:
+ vv     - the MPI vector
. nghost - number of local ghost points
- ghosts - global indices of ghost points, these do not need to be in increasing order (sorted)

  Level: advanced

  Notes:
  Use `VecGhostGetLocalForm()` to access the local, ghosted representation
  of the vector.

  This also automatically sets the `ISLocalToGlobalMapping()` for this vector.

  You must call this AFTER you have set the type of the vector (with` VecSetType()`) and the size (with `VecSetSizes()`).

.seealso: [](ch_vectors), `Vec`, `VecType`, `VecCreateSeq()`, `VecCreate()`, `VecDuplicate()`, `VecDuplicateVecs()`, `VecCreateMPI()`,
          `VecGhostGetLocalForm()`, `VecGhostRestoreLocalForm()`, `VecGhostUpdateBegin()`,
          `VecCreateGhostWithArray()`, `VecCreateMPIWithArray()`, `VecGhostUpdateEnd()`,
          `VecCreateGhostBlock()`, `VecCreateGhostBlockWithArray()`
@*/
PetscErrorCode VecMPISetGhost(Vec vv, PetscInt nghost, const PetscInt ghosts[])
{
  PetscBool flg;

  PetscFunctionBegin;
  PetscCall(PetscObjectTypeCompare((PetscObject)vv, VECMPI, &flg));
  /* if already fully existent VECMPI then basically destroy it and rebuild with ghosting */
  if (flg) {
    PetscInt     n, N;
    Vec_MPI     *w;
    PetscScalar *larray;
    IS           from, to;
    MPI_Comm     comm;

    PetscCall(PetscObjectGetComm((PetscObject)vv, &comm));
    n = vv->map->n;
    N = vv->map->N;
    PetscUseTypeMethod(vv, destroy);
    PetscCall(VecSetSizes(vv, n, N));
    PetscCall(VecCreate_MPI_Private(vv, PETSC_TRUE, nghost, NULL));
    w = (Vec_MPI *)vv->data;
    /* Create local representation */
    PetscCall(VecGetArray(vv, &larray));
    PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, 1, n + nghost, larray, &w->localrep));
    PetscCall(VecRestoreArray(vv, &larray));

    /*
     Create scatter context for scattering (updating) ghost values
     */
    PetscCall(ISCreateGeneral(comm, nghost, ghosts, PETSC_COPY_VALUES, &from));
    PetscCall(ISCreateStride(PETSC_COMM_SELF, nghost, n, 1, &to));
    PetscCall(VecScatterCreate(vv, from, w->localrep, to, &w->localupdate));
    PetscCall(ISDestroy(&to));

    w->ghost                         = from;
    vv->ops->getlocaltoglobalmapping = VecGetLocalToGlobalMapping_MPI_VecGhost;
  } else {
    PetscCheck(vv->ops->create != VecCreate_MPI, PetscObjectComm((PetscObject)vv), PETSC_ERR_ARG_WRONGSTATE, "Must set local or global size before setting ghosting");
    PetscCheck(((PetscObject)vv)->type_name, PetscObjectComm((PetscObject)vv), PETSC_ERR_ARG_WRONGSTATE, "Must set type to VECMPI before ghosting");
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecCreateGhostBlockWithArray - Creates a parallel vector with ghost padding on each processor;
  the caller allocates the array space. Indices in the ghost region are based on blocks.

  Collective

  Input Parameters:
+ comm   - the MPI communicator to use
. bs     - block size
. n      - local vector length
. N      - global vector length (or `PETSC_DETERMINE` to have calculated if `n` is given)
. nghost - number of local ghost blocks
. ghosts - global indices of ghost blocks (or `NULL` if not needed), counts are by block not by index, these do not need to be in increasing order (sorted)
- array  - the space to store the vector values (as long as `n + nghost*bs`)

  Output Parameter:
. vv - the global vector representation (without ghost points as part of vector)

  Level: advanced

  Notes:
  Use `VecGhostGetLocalForm()` to access the local, ghosted representation
  of the vector.

  n is the local vector size (total local size not the number of blocks) while nghost
  is the number of blocks in the ghost portion, i.e. the number of elements in the ghost
  portion is bs*nghost

.seealso: [](ch_vectors), `Vec`, `VecType`, `VecCreate()`, `VecGhostGetLocalForm()`, `VecGhostRestoreLocalForm()`,
          `VecCreateGhost()`, `VecCreateSeqWithArray()`, `VecCreateMPIWithArray()`,
          `VecCreateGhostWithArray()`, `VecCreateGhostBlock()`
@*/
PetscErrorCode VecCreateGhostBlockWithArray(MPI_Comm comm, PetscInt bs, PetscInt n, PetscInt N, PetscInt nghost, const PetscInt ghosts[], const PetscScalar array[], Vec *vv)
{
  Vec_MPI               *w;
  PetscScalar           *larray;
  IS                     from, to;
  ISLocalToGlobalMapping ltog;
  PetscInt               rstart, i, nb, *indices;

  PetscFunctionBegin;
  *vv = NULL;

  PetscCheck(n != PETSC_DECIDE, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must set local size");
  PetscCheck(nghost != PETSC_DECIDE, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Must set local ghost size");
  PetscCheck(nghost >= 0, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Ghost length must be >= 0");
  PetscCheck(n % bs == 0, PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Local size must be a multiple of block size");
  PetscCall(PetscSplitOwnership(comm, &n, &N));
  /* Create global representation */
  PetscCall(VecCreate(comm, vv));
  PetscCall(VecSetSizes(*vv, n, N));
  PetscCall(VecSetBlockSize(*vv, bs));
  PetscCall(VecCreate_MPI_Private(*vv, PETSC_TRUE, nghost * bs, array));
  w = (Vec_MPI *)(*vv)->data;
  /* Create local representation */
  PetscCall(VecGetArray(*vv, &larray));
  PetscCall(VecCreateSeqWithArray(PETSC_COMM_SELF, bs, n + bs * nghost, larray, &w->localrep));
  PetscCall(VecRestoreArray(*vv, &larray));

  /*
       Create scatter context for scattering (updating) ghost values
  */
  PetscCall(ISCreateBlock(comm, bs, nghost, ghosts, PETSC_COPY_VALUES, &from));
  PetscCall(ISCreateStride(PETSC_COMM_SELF, bs * nghost, n, 1, &to));
  PetscCall(VecScatterCreate(*vv, from, w->localrep, to, &w->localupdate));
  PetscCall(ISDestroy(&to));
  PetscCall(ISDestroy(&from));

  /* set local to global mapping for ghosted vector */
  nb = n / bs;
  PetscCall(PetscMalloc1(nb + nghost, &indices));
  PetscCall(VecGetOwnershipRange(*vv, &rstart, NULL));
  rstart = rstart / bs;

  for (i = 0; i < nb; i++) indices[i] = rstart + i;
  for (i = 0; i < nghost; i++) indices[nb + i] = ghosts[i];

  PetscCall(ISLocalToGlobalMappingCreate(comm, bs, nb + nghost, indices, PETSC_OWN_POINTER, &ltog));
  PetscCall(VecSetLocalToGlobalMapping(*vv, ltog));
  PetscCall(ISLocalToGlobalMappingDestroy(&ltog));
  PetscFunctionReturn(PETSC_SUCCESS);
}

/*@
  VecCreateGhostBlock - Creates a parallel vector with ghost padding on each processor.
  The indicing of the ghost points is done with blocks.

  Collective

  Input Parameters:
+ comm   - the MPI communicator to use
. bs     - the block size
. n      - local vector length
. N      - global vector length (or `PETSC_DETERMINE` to have calculated if `n` is given)
. nghost - number of local ghost blocks
- ghosts - global indices of ghost blocks, counts are by block, not by individual index, these do not need to be in increasing order (sorted)

  Output Parameter:
. vv - the global vector representation (without ghost points as part of vector)

  Level: advanced

  Notes:
  Use `VecGhostGetLocalForm()` to access the local, ghosted representation
  of the vector.

  `n` is the local vector size (total local size not the number of blocks) while `nghost`
  is the number of blocks in the ghost portion, i.e. the number of elements in the ghost
  portion is `bs*nghost`

.seealso: [](ch_vectors), `Vec`, `VecType`, `VecCreateSeq()`, `VecCreate()`, `VecDuplicate()`, `VecDuplicateVecs()`, `VecCreateMPI()`,
          `VecGhostGetLocalForm()`, `VecGhostRestoreLocalForm()`,
          `VecCreateGhostWithArray()`, `VecCreateMPIWithArray()`, `VecCreateGhostBlockWithArray()`
@*/
PetscErrorCode VecCreateGhostBlock(MPI_Comm comm, PetscInt bs, PetscInt n, PetscInt N, PetscInt nghost, const PetscInt ghosts[], Vec *vv)
{
  PetscFunctionBegin;
  PetscCall(VecCreateGhostBlockWithArray(comm, bs, n, N, nghost, ghosts, NULL, vv));
  PetscFunctionReturn(PETSC_SUCCESS);
}