void AlgPTScotch<Adapter>::partition(
  const RCP<PartitioningSolution<Adapter> > &solution
)
{
  HELLO;

  size_t numGlobalParts = solution->getTargetGlobalNumberOfParts();

  SCOTCH_Num partnbr=0;
  TPL_Traits<SCOTCH_Num, size_t>::ASSIGN_TPL_T(partnbr, numGlobalParts, env);

#ifdef HAVE_ZOLTAN2_MPI
  int ierr = 0;
  int me = problemComm->getRank();

  const SCOTCH_Num  baseval = 0;  // Base value for array indexing.
                                  // GraphModel returns GNOs from base 0.

  SCOTCH_Strat stratstr;          // Strategy string
                                  // TODO:  Set from parameters
  SCOTCH_stratInit(&stratstr);

  // Allocate and initialize PTScotch Graph data structure.
  SCOTCH_Dgraph *gr = SCOTCH_dgraphAlloc();  // Scotch distributed graph
  ierr = SCOTCH_dgraphInit(gr, mpicomm);

  env->globalInputAssertion(__FILE__, __LINE__, "SCOTCH_dgraphInit", 
    !ierr, BASIC_ASSERTION, problemComm);

  // Get vertex info
  ArrayView<const gno_t> vtxID;
  ArrayView<StridedData<lno_t, scalar_t> > xyz;
  ArrayView<StridedData<lno_t, scalar_t> > vwgts;
  size_t nVtx = model->getVertexList(vtxID, xyz, vwgts);
  SCOTCH_Num vertlocnbr=0;
  TPL_Traits<SCOTCH_Num, size_t>::ASSIGN_TPL_T(vertlocnbr, nVtx, env);
  SCOTCH_Num vertlocmax = vertlocnbr; // Assumes no holes in global nums.

  // Get edge info
  ArrayView<const gno_t> edgeIds;
  ArrayView<const int>   procIds;
  ArrayView<const lno_t> offsets;
  ArrayView<StridedData<lno_t, scalar_t> > ewgts;

  size_t nEdge = model->getEdgeList(edgeIds, procIds, offsets, ewgts);

  SCOTCH_Num edgelocnbr=0;
  TPL_Traits<SCOTCH_Num, size_t>::ASSIGN_TPL_T(edgelocnbr, nEdge, env);
  const SCOTCH_Num edgelocsize = edgelocnbr;  // Assumes adj array is compact.

  SCOTCH_Num *vertloctab;  // starting adj/vtx
  TPL_Traits<SCOTCH_Num, lno_t>::ASSIGN_TPL_T_ARRAY(&vertloctab, offsets, env);

  SCOTCH_Num *edgeloctab;  // adjacencies
  TPL_Traits<SCOTCH_Num, gno_t>::ASSIGN_TPL_T_ARRAY(&edgeloctab, edgeIds, env);

  // We don't use these arrays, but we need them as arguments to Scotch.
  SCOTCH_Num *vendloctab = NULL;  // Assume consecutive storage for adj
  SCOTCH_Num *vlblloctab = NULL;  // Vertex label array
  SCOTCH_Num *edgegsttab = NULL;  // Array for ghost vertices

  // Get weight info.
  SCOTCH_Num *velotab = NULL;  // Vertex weights
  SCOTCH_Num *edlotab = NULL;  // Edge weights

  int nVwgts = model->getNumWeightsPerVertex();
  int nEwgts = model->getNumWeightsPerEdge();
  if (nVwgts > 1 && me == 0) {
    std::cerr << "Warning:  NumWeightsPerVertex is " << nVwgts 
              << " but Scotch allows only one weight. "
              << " Zoltan2 will use only the first weight per vertex."
              << std::endl;
  }
  if (nEwgts > 1 && me == 0) {
    std::cerr << "Warning:  NumWeightsPerEdge is " << nEwgts 
              << " but Scotch allows only one weight. "
              << " Zoltan2 will use only the first weight per edge."
              << std::endl;
  }

  if (nVwgts) {
    velotab = new SCOTCH_Num[nVtx+1];  // +1 since Scotch wants all procs 
                                       // to have non-NULL arrays
    scale_weights(nVtx, vwgts[0], velotab);
  }

  if (nEwgts) {
    edlotab = new SCOTCH_Num[nEdge+1];  // +1 since Scotch wants all procs 
                                         // to have non-NULL arrays
    scale_weights(nEdge, ewgts[0], edlotab);
  }

  // Build PTScotch distributed data structure
  ierr = SCOTCH_dgraphBuild(gr, baseval, vertlocnbr, vertlocmax,
                            vertloctab, vendloctab, velotab, vlblloctab,
                            edgelocnbr, edgelocsize,
                            edgeloctab, edgegsttab, edlotab);

  env->globalInputAssertion(__FILE__, __LINE__, "SCOTCH_dgraphBuild", 
    !ierr, BASIC_ASSERTION, problemComm);

  // Create array for Scotch to return results in.
  ArrayRCP<part_t> partList(new part_t[nVtx], 0, nVtx,true);
  SCOTCH_Num *partloctab = NULL;
  if (nVtx && (sizeof(SCOTCH_Num) == sizeof(part_t))) {
    // Can write directly into the solution's memory
    partloctab = (SCOTCH_Num *) partList.getRawPtr();
  }
  else {
    // Can't use solution memory directly; will have to copy later.
    // Note:  Scotch does not like NULL arrays, so add 1 to always have non-null.
    //        ParMETIS has this same "feature."  See Zoltan bug 4299.
    partloctab = new SCOTCH_Num[nVtx+1];
  }

  // Get target part sizes
  float *partsizes = new float[numGlobalParts];
  if (!solution->criteriaHasUniformPartSizes(0))
    for (size_t i=0; i<numGlobalParts; i++)
      partsizes[i] = solution->getCriteriaPartSize(0, i);
  else
    for (size_t i=0; i<numGlobalParts; i++)
      partsizes[i] = 1.0 / float(numGlobalParts);

  // Allocate and initialize PTScotch target architecture data structure
  SCOTCH_Arch archdat;
  SCOTCH_archInit(&archdat);

  SCOTCH_Num velosum = 0;
  SCOTCH_dgraphSize (gr, &velosum, NULL, NULL, NULL);
  SCOTCH_Num *goalsizes = new SCOTCH_Num[partnbr];
  // TODO: The goalsizes are set as in Zoltan; not sure it is correct there 
  // or here.
  // It appears velosum is global NUMBER of vertices, not global total 
  // vertex weight.  I think we should use the latter.
  // Fix this when we add vertex weights.
  for (SCOTCH_Num i = 0; i < partnbr; i++)
    goalsizes[i] = SCOTCH_Num(ceil(velosum * partsizes[i]));
  delete [] partsizes;

  SCOTCH_archCmpltw(&archdat, partnbr, goalsizes);

  // Call partitioning; result returned in partloctab.
  ierr = SCOTCH_dgraphMap(gr, &archdat, &stratstr, partloctab);

  env->globalInputAssertion(__FILE__, __LINE__, "SCOTCH_dgraphMap", 
    !ierr, BASIC_ASSERTION, problemComm);

  SCOTCH_archExit(&archdat);
  delete [] goalsizes;

  // TODO - metrics

#ifdef SHOW_ZOLTAN2_SCOTCH_MEMORY
  int me = env->comm_->getRank();
#endif

#ifdef HAVE_SCOTCH_ZOLTAN2_GETMEMORYMAX
  if (me == 0){
    size_t scotchBytes = SCOTCH_getMemoryMax();
    std::cout << "Rank " << me << ": Maximum bytes used by Scotch: ";
    std::cout << scotchBytes << std::endl;
  }
#endif

  // Clean up PTScotch
  SCOTCH_dgraphExit(gr);
  free(gr);
  SCOTCH_stratExit(&stratstr);

  // Load answer into the solution.

  if ((sizeof(SCOTCH_Num) != sizeof(part_t)) || (nVtx == 0)) {
    for (size_t i = 0; i < nVtx; i++) partList[i] = partloctab[i];
    delete [] partloctab;
  }

  solution->setParts(partList);

  env->memory("Zoltan2-Scotch: After creating solution");

  // Clean up copies made due to differing data sizes.
  TPL_Traits<SCOTCH_Num, lno_t>::DELETE_TPL_T_ARRAY(&vertloctab);
  TPL_Traits<SCOTCH_Num, gno_t>::DELETE_TPL_T_ARRAY(&edgeloctab);

  if (nVwgts) delete [] velotab;
  if (nEwgts) delete [] edlotab;

#else // DO NOT HAVE_MPI

  // TODO:  Handle serial case with calls to Scotch.
  // TODO:  For now, assign everything to rank 0 and assume only one part.
  // TODO:  Can probably use the code above for loading solution,
  // TODO:  instead of duplicating it here.
  // TODO
  // TODO:  Actual logic should call Scotch when number of processes == 1.
  ArrayView<const gno_t> vtxID;
  ArrayView<StridedData<lno_t, scalar_t> > xyz;
  ArrayView<StridedData<lno_t, scalar_t> > vwgts;
  size_t nVtx = model->getVertexList(vtxID, xyz, vwgts);

  ArrayRCP<part_t> partList(new part_t[nVtx], 0, nVtx, true);
  for (size_t i = 0; i < nVtx; i++) partList[i] = 0;

  solution->setParts(partList);

#endif // DO NOT HAVE_MPI
}
Beispiel #2
0
static PetscErrorCode MatPartitioningApply_PTScotch_Private(MatPartitioning part, PetscBool useND, IS *partitioning)
{
  MPI_Comm                 pcomm,comm;
  MatPartitioning_PTScotch *scotch = (MatPartitioning_PTScotch*)part->data;
  PetscErrorCode           ierr;
  PetscMPIInt              rank;
  Mat                      mat  = part->adj;
  Mat_MPIAdj               *adj = (Mat_MPIAdj*)mat->data;
  PetscBool                flg,distributed;
  PetscBool                proc_weight_flg;
  PetscInt                 i,j,p,bs=1,nold;
  PetscInt                 *NDorder = NULL;
  PetscReal                *vwgttab,deltval;
  SCOTCH_Num               *locals,*velotab,*veloloctab,*edloloctab,vertlocnbr,edgelocnbr,nparts=part->n;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)part,&pcomm);CHKERRQ(ierr);
  /* Duplicate the communicator to be sure that PTSCOTCH attribute caching does not interfere with PETSc. */
  ierr = MPI_Comm_dup(pcomm,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)mat,MATMPIADJ,&flg);CHKERRQ(ierr);
  if (!flg) {
    /* bs indicates if the converted matrix is "reduced" from the original and hence the
       resulting partition results need to be stretched to match the original matrix */
    nold = mat->rmap->n;
    ierr = MatConvert(mat,MATMPIADJ,MAT_INITIAL_MATRIX,&mat);CHKERRQ(ierr);
    if (mat->rmap->n > 0) bs = nold/mat->rmap->n;
    adj  = (Mat_MPIAdj*)mat->data;
  }

  proc_weight_flg = PETSC_TRUE;
  ierr = PetscOptionsGetBool(NULL, NULL, "-mat_partitioning_ptscotch_proc_weight", &proc_weight_flg, NULL);CHKERRQ(ierr);

  ierr = PetscMalloc1(mat->rmap->n+1,&locals);CHKERRQ(ierr);

  if (useND) {
#if defined(PETSC_HAVE_SCOTCH_PARMETIS_V3_NODEND)
    PetscInt    *sizes, *seps, log2size, subd, *level, base = 0;
    PetscMPIInt size;

    ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
    log2size = PetscLog2Real(size);
    subd = PetscPowInt(2,log2size);
    if (subd != size) SETERRQ(comm,PETSC_ERR_SUP,"Only power of 2 communicator sizes");
    ierr = PetscMalloc1(mat->rmap->n,&NDorder);CHKERRQ(ierr);
    ierr = PetscMalloc3(2*size,&sizes,4*size,&seps,size,&level);CHKERRQ(ierr);
    SCOTCH_ParMETIS_V3_NodeND(mat->rmap->range,adj->i,adj->j,&base,NULL,NDorder,sizes,&comm);
    ierr = MatPartitioningSizesToSep_Private(subd,sizes,seps,level);CHKERRQ(ierr);
    for (i=0;i<mat->rmap->n;i++) {
      PetscInt loc;

      ierr = PetscFindInt(NDorder[i],2*subd,seps,&loc);CHKERRQ(ierr);
      if (loc < 0) {
        loc = -(loc+1);
        if (loc%2) { /* part of subdomain */
          locals[i] = loc/2;
        } else {
          ierr = PetscFindInt(NDorder[i],2*(subd-1),seps+2*subd,&loc);CHKERRQ(ierr);
          loc = loc < 0 ? -(loc+1)/2 : loc/2;
          locals[i] = level[loc];
        }
      } else locals[i] = loc/2;
    }
    ierr = PetscFree3(sizes,seps,level);CHKERRQ(ierr);
#else
    SETERRQ(pcomm,PETSC_ERR_SUP,"Need libptscotchparmetis.a compiled with -DSCOTCH_METIS_PREFIX");
#endif
  } else {
    velotab = NULL;
    if (proc_weight_flg) {
      ierr = PetscMalloc1(nparts,&vwgttab);CHKERRQ(ierr);
      ierr = PetscMalloc1(nparts,&velotab);CHKERRQ(ierr);
      for (j=0; j<nparts; j++) {
        if (part->part_weights) vwgttab[j] = part->part_weights[j]*nparts;
        else vwgttab[j] = 1.0;
      }
      for (i=0; i<nparts; i++) {
        deltval = PetscAbsReal(vwgttab[i]-PetscFloorReal(vwgttab[i]+0.5));
        if (deltval>0.01) {
          for (j=0; j<nparts; j++) vwgttab[j] /= deltval;
        }
      }
      for (i=0; i<nparts; i++) velotab[i] = (SCOTCH_Num)(vwgttab[i] + 0.5);
      ierr = PetscFree(vwgttab);CHKERRQ(ierr);
    }

    vertlocnbr = mat->rmap->range[rank+1] - mat->rmap->range[rank];
    edgelocnbr = adj->i[vertlocnbr];
    veloloctab = part->vertex_weights;
    edloloctab = adj->values;

    /* detect whether all vertices are located at the same process in original graph */
    for (p = 0; !mat->rmap->range[p+1] && p < nparts; ++p);
    distributed = (mat->rmap->range[p+1] == mat->rmap->N) ? PETSC_FALSE : PETSC_TRUE;

    if (distributed) {
      SCOTCH_Arch              archdat;
      SCOTCH_Dgraph            grafdat;
      SCOTCH_Dmapping          mappdat;
      SCOTCH_Strat             stradat;

      ierr = SCOTCH_dgraphInit(&grafdat,comm);CHKERRQ(ierr);
      ierr = SCOTCH_dgraphBuild(&grafdat,0,vertlocnbr,vertlocnbr,adj->i,adj->i+1,veloloctab,
                                NULL,edgelocnbr,edgelocnbr,adj->j,NULL,edloloctab);CHKERRQ(ierr);

#if defined(PETSC_USE_DEBUG)
      ierr = SCOTCH_dgraphCheck(&grafdat);CHKERRQ(ierr);
#endif

      ierr = SCOTCH_archInit(&archdat);CHKERRQ(ierr);
      ierr = SCOTCH_stratInit(&stradat);CHKERRQ(ierr);
      ierr = SCOTCH_stratDgraphMapBuild(&stradat,scotch->strategy,nparts,nparts,scotch->imbalance);CHKERRQ(ierr);

      if (velotab) {
        ierr = SCOTCH_archCmpltw(&archdat,nparts,velotab);CHKERRQ(ierr);
      } else {
        ierr = SCOTCH_archCmplt( &archdat,nparts);CHKERRQ(ierr);
      }
      ierr = SCOTCH_dgraphMapInit(&grafdat,&mappdat,&archdat,locals);CHKERRQ(ierr);
      ierr = SCOTCH_dgraphMapCompute(&grafdat,&mappdat,&stradat);CHKERRQ(ierr);

      SCOTCH_dgraphMapExit(&grafdat,&mappdat);
      SCOTCH_archExit(&archdat);
      SCOTCH_stratExit(&stradat);
      SCOTCH_dgraphExit(&grafdat);

    } else if (rank == p) {
      SCOTCH_Graph   grafdat;
      SCOTCH_Strat   stradat;

      ierr = SCOTCH_graphInit(&grafdat);CHKERRQ(ierr);
      ierr = SCOTCH_graphBuild(&grafdat,0,vertlocnbr,adj->i,adj->i+1,veloloctab,NULL,edgelocnbr,adj->j,edloloctab);CHKERRQ(ierr);

#if defined(PETSC_USE_DEBUG)
      ierr = SCOTCH_graphCheck(&grafdat);CHKERRQ(ierr);
#endif

      ierr = SCOTCH_stratInit(&stradat);CHKERRQ(ierr);
      ierr = SCOTCH_stratGraphMapBuild(&stradat,scotch->strategy,nparts,scotch->imbalance);CHKERRQ(ierr);

      ierr = SCOTCH_graphPart(&grafdat,nparts,&stradat,locals);CHKERRQ(ierr);

      SCOTCH_stratExit(&stradat);
      SCOTCH_graphExit(&grafdat);
    }

    ierr = PetscFree(velotab);CHKERRQ(ierr);
  }
  ierr = MPI_Comm_free(&comm);CHKERRQ(ierr);

  if (bs > 1) {
    PetscInt *newlocals;
    ierr = PetscMalloc1(bs*mat->rmap->n,&newlocals);CHKERRQ(ierr);
    for (i=0;i<mat->rmap->n;i++) {
      for (j=0;j<bs;j++) {
        newlocals[bs*i+j] = locals[i];
      }
    }
    ierr = PetscFree(locals);CHKERRQ(ierr);
    ierr = ISCreateGeneral(pcomm,bs*mat->rmap->n,newlocals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
  } else {
    ierr = ISCreateGeneral(pcomm,mat->rmap->n,locals,PETSC_OWN_POINTER,partitioning);CHKERRQ(ierr);
  }
  if (useND) {
    IS ndis;

    if (bs > 1) {
      ierr = ISCreateBlock(pcomm,bs,mat->rmap->n,NDorder,PETSC_OWN_POINTER,&ndis);CHKERRQ(ierr);
    } else {
      ierr = ISCreateGeneral(pcomm,mat->rmap->n,NDorder,PETSC_OWN_POINTER,&ndis);CHKERRQ(ierr);
    }
    ierr = ISSetPermutation(ndis);CHKERRQ(ierr);
    ierr = PetscObjectCompose((PetscObject)(*partitioning),"_petsc_matpartitioning_ndorder",(PetscObject)ndis);CHKERRQ(ierr);
    ierr = ISDestroy(&ndis);CHKERRQ(ierr);
  }

  if (!flg) {
    ierr = MatDestroy(&mat);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}
void
METISNAMEU(ParMETIS_V3_PartKway) (
const SCOTCH_Num * const    vtxdist,
SCOTCH_Num * const          xadj,
SCOTCH_Num * const          adjncy,
SCOTCH_Num * const          vwgt,
SCOTCH_Num * const          adjwgt,
const SCOTCH_Num * const    wgtflag,
const SCOTCH_Num * const    numflag,
const SCOTCH_Num * const    ncon,                 /* Not used */
const SCOTCH_Num * const    nparts,
const float * const         tpwgts,
const float * const         ubvec,                /* Not used */
const SCOTCH_Num * const    options,              /* Not used */
SCOTCH_Num * const          edgecut,
SCOTCH_Num * const          part,
MPI_Comm *                  comm)
{
  MPI_Comm            proccomm;
  int                 procglbnbr;
  int                 proclocnum;
  SCOTCH_Num          baseval;
  SCOTCH_Arch         archdat;
  SCOTCH_Dgraph       grafdat;                    /* Scotch distributed graph object to interface with libScotch   */
  SCOTCH_Dmapping     mappdat;                    /* Scotch distributed mapping object to interface with libScotch */
  SCOTCH_Strat        stradat;
  SCOTCH_Num          vertlocnbr;
  SCOTCH_Num *        veloloctab;
  SCOTCH_Num          edgelocnbr;
  SCOTCH_Num *        edloloctab;
  SCOTCH_Num *        velotab;
  double *            vwgttab;
  SCOTCH_Num          i;

  if ((vwgttab = malloc (*nparts * sizeof (double))) == NULL)
    return;
  if ((velotab = malloc (*nparts * sizeof (SCOTCH_Num))) == NULL) {
    free (vwgttab);
    return;
  }
  for (i = 0; i < *nparts; i ++)
    vwgttab[i] = (double) tpwgts[i] * (double) (*nparts);
  for (i = 0; i < *nparts; i ++) {
    double deltval;
    deltval = fabs (vwgttab[i] - floor (vwgttab[i] + 0.5));
    if (deltval > 0.01) {
      SCOTCH_Num          j;

      deltval = 1.0 / deltval;
      for (j = 0; j < *nparts; j ++)
        vwgttab[j] *= deltval;
    }
  }
  for (i = 0; i < *nparts; i ++)
    velotab[i] = (SCOTCH_Num) (vwgttab[i] + 0.5);

  proccomm = *comm;
  if (SCOTCH_dgraphInit (&grafdat, proccomm) != 0)
    return;

  MPI_Comm_size (proccomm, &procglbnbr);
  MPI_Comm_rank (proccomm, &proclocnum);
  baseval    = *numflag;
  vertlocnbr = vtxdist[proclocnum + 1] - vtxdist[proclocnum];
  edgelocnbr = xadj[vertlocnbr] - baseval;
  veloloctab = ((vwgt   != NULL) && ((*wgtflag & 2) != 0)) ? vwgt   : NULL;
  edloloctab = ((adjwgt != NULL) && ((*wgtflag & 1) != 0)) ? adjwgt : NULL;

  if (SCOTCH_dgraphBuild (&grafdat, baseval,
                          vertlocnbr, vertlocnbr, xadj, xadj + 1, veloloctab, NULL,
                          edgelocnbr, edgelocnbr, adjncy, NULL, edloloctab) == 0) {
    SCOTCH_stratInit (&stradat);
#ifdef SCOTCH_DEBUG_ALL
    if (SCOTCH_dgraphCheck (&grafdat) == 0)       /* TRICK: next instruction called only if graph is consistent */
#endif /* SCOTCH_DEBUG_ALL */
    {
      SCOTCH_archInit (&archdat);

      if ((SCOTCH_archCmpltw (&archdat, *nparts, velotab) == 0) &&
          (SCOTCH_dgraphMapInit (&grafdat, &mappdat, &archdat, part) == 0)) {
        SCOTCH_dgraphMapCompute (&grafdat, &mappdat, &stradat);

        SCOTCH_dgraphMapExit (&grafdat, &mappdat);
      }
      SCOTCH_archExit (&archdat);
    }
    SCOTCH_stratExit (&stradat);
  }
  SCOTCH_dgraphExit (&grafdat);

  *edgecut = 0;                                   /* TODO : compute real edge cut for people who might want it */

  free (vwgttab);
  free (velotab);

  if (baseval != 0) {                             /* MeTiS part array is based, Scotch is not */
    SCOTCH_Num          vertlocnum;

    for (vertlocnum = 0; vertlocnum < vertlocnbr; vertlocnum ++)
      part[vertlocnum] += baseval;
  }
}
void AlgPTScotch(
  const RCP<const Environment> &env,        // parameters & app comm
  const RCP<const Comm<int> > &problemComm, // problem comm
#ifdef HAVE_ZOLTAN2_MPI
  MPI_Comm mpicomm,
#endif
  const RCP<GraphModel<typename Adapter::base_adapter_t> > &model, // the graph
  RCP<PartitioningSolution<Adapter> > &solution
)
{
  HELLO;

  typedef typename Adapter::lno_t lno_t;
  typedef typename Adapter::gno_t gno_t;
  typedef typename Adapter::scalar_t scalar_t;

  int ierr = 0;

  size_t numGlobalParts = solution->getTargetGlobalNumberOfParts();

  SCOTCH_Num partnbr;
  SCOTCH_Num_Traits<size_t>::ASSIGN_TO_SCOTCH_NUM(partnbr, numGlobalParts, env);

#ifdef HAVE_ZOLTAN2_MPI

  const SCOTCH_Num  baseval = 0;  // Base value for array indexing.
                                  // GraphModel returns GNOs from base 0.

  SCOTCH_Strat stratstr;          // Strategy string
                                  // TODO:  Set from parameters
  SCOTCH_stratInit(&stratstr);

  // Allocate & initialize PTScotch data structure.
  SCOTCH_Dgraph *gr = SCOTCH_dgraphAlloc();  // Scotch distributed graph
  ierr = SCOTCH_dgraphInit(gr, mpicomm);

  env->globalInputAssertion(__FILE__, __LINE__, "SCOTCH_dgraphInit", 
    !ierr, BASIC_ASSERTION, problemComm);

  // Get vertex info
  ArrayView<const gno_t> vtxID;
  ArrayView<StridedData<lno_t, scalar_t> > xyz;
  ArrayView<StridedData<lno_t, scalar_t> > vtxWt;
  size_t nVtx = model->getVertexList(vtxID, xyz, vtxWt);
  SCOTCH_Num vertlocnbr;
  SCOTCH_Num_Traits<size_t>::ASSIGN_TO_SCOTCH_NUM(vertlocnbr, nVtx, env);
  SCOTCH_Num vertlocmax = vertlocnbr; // Assumes no holes in global nums.

  // Get edge info
  ArrayView<const gno_t> edgeIds;
  ArrayView<const int>   procIds;
  ArrayView<const lno_t> offsets;
  ArrayView<StridedData<lno_t, scalar_t> > ewgts;

  size_t nEdges = model->getEdgeList(edgeIds, procIds, offsets, ewgts);

  SCOTCH_Num edgelocnbr;
  SCOTCH_Num_Traits<size_t>::ASSIGN_TO_SCOTCH_NUM(edgelocnbr, nEdges, env);
  const SCOTCH_Num edgelocsize = edgelocnbr;  // Assumes adj array is compact.

  SCOTCH_Num *vertloctab;  // starting adj/vtx
  SCOTCH_Num_Traits<lno_t>::ASSIGN_SCOTCH_NUM_ARRAY(&vertloctab, offsets, env);

  SCOTCH_Num *edgeloctab;  // adjacencies
  SCOTCH_Num_Traits<gno_t>::ASSIGN_SCOTCH_NUM_ARRAY(&edgeloctab, edgeIds, env);

  // We don't use these arrays, but we need them as arguments to Scotch.
  SCOTCH_Num *vendloctab = NULL;  // Assume consecutive storage for adj
  SCOTCH_Num *vlblloctab = NULL;  // Vertex label array
  SCOTCH_Num *edgegsttab = NULL;  // Array for ghost vertices

  // Get weight info.
  // TODO:  Actually get the weights; for now, not using weights.
  SCOTCH_Num *veloloctab = NULL;  // Vertex weights
  SCOTCH_Num *edloloctab = NULL;  // Edge weights
  //TODO int vwtdim = model->getVertexWeightDim();
  //TODO int ewtdim = model->getEdgeWeightDim();
  //TODO if (vwtdim) veloloctab = new SCOTCH_Num[nVtx];
  //TODO if (ewtdim) edloloctab = new SCOTCH_Num[nEdges];
  //TODO scale weights to SCOTCH_Nums.

  // Build PTScotch distributed data structure
  ierr = SCOTCH_dgraphBuild(gr, baseval, vertlocnbr, vertlocmax,
                            vertloctab, vendloctab, veloloctab, vlblloctab,
                            edgelocnbr, edgelocsize,
                            edgeloctab, edgegsttab, edloloctab);

  env->globalInputAssertion(__FILE__, __LINE__, "SCOTCH_dgraphBuild", 
    !ierr, BASIC_ASSERTION, problemComm);

  // Create array for Scotch to return results in.
  ArrayRCP<partId_t> partList(new partId_t [nVtx], 0, nVtx,true);
  SCOTCH_Num *partloctab = NULL;
  if (nVtx && (sizeof(SCOTCH_Num) == sizeof(partId_t))) {
    // Can write directly into the solution's memory
    partloctab = (SCOTCH_Num *) partList.getRawPtr();
  }
  else {
    // Can't use solution memory directly; will have to copy later.
    // Note:  Scotch does not like NULL arrays, so add 1 to always have non-null.
    //        ParMETIS has this same "feature."  See Zoltan bug 4299.
    partloctab = new SCOTCH_Num[nVtx+1];
  }


  // Call partitioning; result returned in partloctab.
  // TODO:  Use SCOTCH_dgraphMap so can include a machine model in partitioning

  ierr = SCOTCH_dgraphPart(gr, partnbr, &stratstr, partloctab);

  env->globalInputAssertion(__FILE__, __LINE__, "SCOTCH_dgraphPart", 
    !ierr, BASIC_ASSERTION, problemComm);

  // TODO - metrics

#ifdef SHOW_ZOLTAN2_SCOTCH_MEMORY
  int me = env->comm_->getRank();
#endif

#ifdef HAVE_SCOTCH_ZOLTAN2_GETMEMORYMAX
  if (me == 0){
    size_t scotchBytes = SCOTCH_getMemoryMax();
    std::cout << "Rank " << me << ": Maximum bytes used by Scotch: ";
    std::cout << scotchBytes << std::endl;
  }
#endif

  // Clean up PTScotch
  SCOTCH_dgraphExit(gr);
  delete gr;
  SCOTCH_stratExit(&stratstr);

  // Load answer into the solution.

  if ((sizeof(SCOTCH_Num) != sizeof(partId_t)) || (nVtx == 0)) {
    for (size_t i = 0; i < nVtx; i++) partList[i] = partloctab[i];
    delete [] partloctab;
  }

  ArrayRCP<const gno_t> gnos = arcpFromArrayView(vtxID);

  solution->setParts(gnos, partList, true);

  env->memory("Zoltan2-Scotch: After creating solution");

  //if (me == 0) cout << " done." << endl;
  // Clean up Zoltan2
  //TODO if (vwtdim) delete [] velotab;
  //TODO if (ewtdim) delete [] edlotab;

  // Clean up copies made due to differing data sizes.
  SCOTCH_Num_Traits<lno_t>::DELETE_SCOTCH_NUM_ARRAY(&vertloctab);
  SCOTCH_Num_Traits<gno_t>::DELETE_SCOTCH_NUM_ARRAY(&edgeloctab);

#else // DO NOT HAVE_MPI

  // TODO:  Handle serial case with calls to Scotch.
  // TODO:  For now, assign everything to rank 0 and assume only one part.
  // TODO:  Can probably use the code above for loading solution,
  // TODO:  instead of duplicating it here.
  // TODO
  // TODO:  Actual logic should call Scotch when number of processes == 1.
  ArrayView<const gno_t> vtxID;
  ArrayView<StridedData<lno_t, scalar_t> > xyz;
  ArrayView<StridedData<lno_t, scalar_t> > vtxWt;
  size_t nVtx = model->getVertexList(vtxID, xyz, vtxWt);

  for (size_t i = 0; i < nVtx; i++) partList[i] = 0;


#endif // DO NOT HAVE_MPI
}
// Call scotch with options from dictionary.
Foam::label Foam::ptscotchDecomp::decompose
(
    const fileName& meshPath,
    const List<int>& adjncy,
    const List<int>& xadj,
    const scalarField& cWeights,

    List<int>& finalDecomp
) const
{
    if (debug)
    {
        Pout<< "ptscotchDecomp : entering with xadj:" << xadj.size() << endl;
    }

    // Dump graph
    if (decompositionDict_.found("ptscotchCoeffs"))
    {
        const dictionary& scotchCoeffs =
            decompositionDict_.subDict("ptscotchCoeffs");

        if (scotchCoeffs.lookupOrDefault("writeGraph", false))
        {
            OFstream str
            (
               meshPath + "_" + Foam::name(Pstream::myProcNo()) + ".dgr"
            );

            Pout<< "Dumping Scotch graph file to " << str.name() << endl
                << "Use this in combination with dgpart." << endl;

            globalIndex globalCells(xadj.size()-1);

            // Distributed graph file (.grf)
            label version = 2;
            str << version << nl;
            // Number of files (procglbnbr)
            str << Pstream::nProcs();
            // My file number (procloc)
            str << ' ' << Pstream::myProcNo() << nl;

            // Total number of vertices (vertglbnbr)
            str << globalCells.size();
            // Total number of connections (edgeglbnbr)
            str << ' ' << returnReduce(xadj[xadj.size()-1], sumOp<label>())
                << nl;
            // Local number of vertices (vertlocnbr)
            str << xadj.size()-1;
            // Local number of connections (edgelocnbr)
            str << ' ' << xadj[xadj.size()-1] << nl;
            // Numbering starts from 0
            label baseval = 0;
            // 100*hasVertlabels+10*hasEdgeWeights+1*hasVertWeighs
            str << baseval << ' ' << "000" << nl;
            for (label cellI = 0; cellI < xadj.size()-1; cellI++)
            {
                label start = xadj[cellI];
                label end = xadj[cellI+1];
                str << end-start;

                for (label i = start; i < end; i++)
                {
                    str << ' ' << adjncy[i];
                }
                str << nl;
            }
        }
    }

    // Strategy
    // ~~~~~~~~

    // Default.
    SCOTCH_Strat stradat;
    check(SCOTCH_stratInit(&stradat), "SCOTCH_stratInit");

    if (decompositionDict_.found("scotchCoeffs"))
    {
        const dictionary& scotchCoeffs =
            decompositionDict_.subDict("scotchCoeffs");


        string strategy;
        if (scotchCoeffs.readIfPresent("strategy", strategy))
        {
            if (debug)
            {
                Info<< "ptscotchDecomp : Using strategy " << strategy << endl;
            }
            SCOTCH_stratDgraphMap(&stradat, strategy.c_str());
            //fprintf(stdout, "S\tStrat=");
            //SCOTCH_stratSave(&stradat, stdout);
            //fprintf(stdout, "\n");
        }
    }


    // Graph
    // ~~~~~

    List<int> velotab;


    // Check for externally provided cellweights and if so initialise weights
    scalar minWeights = gMin(cWeights);
    if (cWeights.size() > 0)
    {
        if (minWeights <= 0)
        {
            WarningIn
            (
                "ptscotchDecomp::decompose(..)"
            )   << "Illegal minimum weight " << minWeights
                << endl;
        }

        if (cWeights.size() != xadj.size()-1)
        {
            FatalErrorIn
            (
                "ptscotchDecomp::decompose(..)"
            )   << "Number of cell weights " << cWeights.size()
                << " does not equal number of cells " << xadj.size()-1
                << exit(FatalError);
        }

        // Convert to integers.
        velotab.setSize(cWeights.size());
        forAll(velotab, i)
        {
            velotab[i] = int(cWeights[i]/minWeights);
        }
    }



    if (debug)
    {
        Pout<< "SCOTCH_dgraphInit" << endl;
    }
    SCOTCH_Dgraph grafdat;
    check(SCOTCH_dgraphInit(&grafdat, MPI_COMM_WORLD), "SCOTCH_dgraphInit");


    if (debug)
    {
        Pout<< "SCOTCH_dgraphBuild with:" << nl
            << "xadj.size()-1   : " << xadj.size()-1 << nl
            << "xadj            : " << long(xadj.begin()) << nl
            << "velotab         : " << long(velotab.begin()) << nl
            << "adjncy.size()   : " << adjncy.size() << nl
            << "adjncy          : " << long(adjncy.begin()) << nl
            << endl;
    }

    check
    (
        SCOTCH_dgraphBuild
        (
            &grafdat,               // grafdat
            0,                      // baseval, c-style numbering
            xadj.size()-1,          // vertlocnbr, nCells
            xadj.size()-1,          // vertlocmax
            const_cast<SCOTCH_Num*>(xadj.begin()),
                                    // vertloctab, start index per cell into
                                    // adjncy
            const_cast<SCOTCH_Num*>(&xadj[1]),// vendloctab, end index  ,,

            const_cast<SCOTCH_Num*>(velotab.begin()),// veloloctab, vtx weights
            NULL,                   // vlblloctab

            adjncy.size(),          // edgelocnbr, number of arcs
            adjncy.size(),          // edgelocsiz
            const_cast<SCOTCH_Num*>(adjncy.begin()),         // edgeloctab
            NULL,                   // edgegsttab
            NULL                    // edlotab, edge weights
        ),
        "SCOTCH_dgraphBuild"
    );


    if (debug)
    {
        Pout<< "SCOTCH_dgraphCheck" << endl;
    }
    check(SCOTCH_dgraphCheck(&grafdat), "SCOTCH_dgraphCheck");


    // Architecture
    // ~~~~~~~~~~~~
    // (fully connected network topology since using switch)

    if (debug)
    {
        Pout<< "SCOTCH_archInit" << endl;
    }
    SCOTCH_Arch archdat;
    check(SCOTCH_archInit(&archdat), "SCOTCH_archInit");

    List<label> processorWeights;
    if (decompositionDict_.found("scotchCoeffs"))
    {
        const dictionary& scotchCoeffs =
            decompositionDict_.subDict("scotchCoeffs");

        scotchCoeffs.readIfPresent("processorWeights", processorWeights);
    }
    if (processorWeights.size())
    {
        if (debug)
        {
            Info<< "ptscotchDecomp : Using procesor weights "
                << processorWeights
                << endl;
        }
        check
        (
            SCOTCH_archCmpltw(&archdat, nProcessors_, processorWeights.begin()),
            "SCOTCH_archCmpltw"
        );
    }
    else
    {
        if (debug)
        {
            Pout<< "SCOTCH_archCmplt" << endl;
        }
        check
        (
            SCOTCH_archCmplt(&archdat, nProcessors_),
            "SCOTCH_archCmplt"
        );
    }


    //SCOTCH_Mapping mapdat;
    //SCOTCH_dgraphMapInit(&grafdat, &mapdat, &archdat, NULL);
    //SCOTCH_dgraphMapCompute(&grafdat, &mapdat, &stradat); /*Perform mapping*/
    //SCOTCHdgraphMapExit(&grafdat, &mapdat);


    // Hack:switch off fpu error trapping
#   ifdef LINUX_GNUC
    int oldExcepts = fedisableexcept
    (
        FE_DIVBYZERO
      | FE_INVALID
      | FE_OVERFLOW
    );
#   endif

    if (debug)
    {
        Pout<< "SCOTCH_dgraphMap" << endl;
    }
    finalDecomp.setSize(xadj.size()-1);
    finalDecomp = 0;
    check
    (
        SCOTCH_dgraphMap
        (
            &grafdat,
            &archdat,
            &stradat,           // const SCOTCH_Strat *
            finalDecomp.begin() // parttab
        ),
        "SCOTCH_graphMap"
    );

#   ifdef LINUX_GNUC
    feenableexcept(oldExcepts);
#   endif



    //finalDecomp.setSize(xadj.size()-1);
    //check
    //(
    //    SCOTCH_dgraphPart
    //    (
    //        &grafdat,
    //        nProcessors_,       // partnbr
    //        &stradat,           // const SCOTCH_Strat *
    //        finalDecomp.begin() // parttab
    //    ),
    //    "SCOTCH_graphPart"
    //);

    if (debug)
    {
        Pout<< "SCOTCH_dgraphExit" << endl;
    }
    // Release storage for graph
    SCOTCH_dgraphExit(&grafdat);
    // Release storage for strategy
    SCOTCH_stratExit(&stradat);
    // Release storage for network topology
    SCOTCH_archExit(&archdat);

    return 0;
}
void
METISNAMEU(ParMETIS_V3_NodeND) (
const int * const           vtxdist,
int * const                 xadj,
int * const                 adjncy,
const int * const           numflag,
const int * const           options,              /* Not used */
int * const                 order,
int * const                 sizes,                /* Of size twice the number of processors ; not used */
MPI_Comm *                  comm)
{
  MPI_Comm            proccomm;
  int                 procglbnbr;
  int                 proclocnum;
  SCOTCH_Num          baseval;
  SCOTCH_Dgraph       grafdat;                    /* Scotch distributed graph object to interface with libScotch    */
  SCOTCH_Dordering    ordedat;                    /* Scotch distributed ordering object to interface with libScotch */
  SCOTCH_Strat        stradat;
  SCOTCH_Num          vertlocnbr;
  SCOTCH_Num          edgelocnbr;

  if (sizeof (SCOTCH_Num) != sizeof (int)) {
    SCOTCH_errorPrint ("ParMETIS_V3_NodeND (as of SCOTCH): SCOTCH_Num type should equate to int");
    return;
  }

  proccomm = *comm;
  if (SCOTCH_dgraphInit (&grafdat, proccomm) != 0)
    return;

  MPI_Comm_size (proccomm, &procglbnbr);
  MPI_Comm_rank (proccomm, &proclocnum);
  baseval    = *numflag;
  vertlocnbr = vtxdist[proclocnum + 1] - vtxdist[proclocnum];
  edgelocnbr = xadj[vertlocnbr] - baseval;

  if (sizes != NULL)
    memSet (sizes, ~0, (2 * procglbnbr - 1) * sizeof (int)); /* Array not used if procglbnbr is not a power of 2 or if error */

  if (SCOTCH_dgraphBuild (&grafdat, baseval,
                          vertlocnbr, vertlocnbr, xadj, xadj + 1, NULL, NULL,
                          edgelocnbr, edgelocnbr, adjncy, NULL, NULL) == 0) {
    SCOTCH_stratInit (&stradat);
#ifdef SCOTCH_DEBUG_ALL
    if (SCOTCH_dgraphCheck (&grafdat) == 0)       /* TRICK: next instruction called only if graph is consistent */
#endif /* SCOTCH_DEBUG_ALL */
    {
      if (SCOTCH_dgraphOrderInit (&grafdat, &ordedat) == 0) {
        int                 levlmax;
        int                 bitsnbr;
        SCOTCH_Num          proctmp;

        SCOTCH_dgraphOrderCompute (&grafdat, &ordedat, &stradat);
        SCOTCH_dgraphOrderPerm    (&grafdat, &ordedat, order);

        for (levlmax = -1, bitsnbr = 0, proctmp = procglbnbr; /* Count number of bits set to 1 in procglbnbr */
             proctmp != 0; levlmax ++, proctmp >>= 1)
          bitsnbr += proctmp & 1;

        if (bitsnbr == 1) {
          SCOTCH_Num          cblkglbnbr;

          if ((cblkglbnbr = SCOTCH_dgraphOrderCblkDist (&grafdat, &ordedat)) >= 0) {
            SCOTCH_Num *        treeglbtab;
            SCOTCH_Num *        sizeglbtab;
            SCOTCH_Num *        sepaglbtab;

            if (memAllocGroup ((void **) (void *)
                               &treeglbtab, (size_t) (cblkglbnbr * sizeof (SCOTCH_Num)),
                               &sizeglbtab, (size_t) (cblkglbnbr * sizeof (SCOTCH_Num)),
                               &sepaglbtab, (size_t) (cblkglbnbr * sizeof (SCOTCH_Num) * 3), NULL) != NULL) {
              if (SCOTCH_dgraphOrderTreeDist (&grafdat, &ordedat, treeglbtab, sizeglbtab) == 0) {
                SCOTCH_Num          rootnum;
                SCOTCH_Num          cblknum;

                memSet (sepaglbtab, ~0, cblkglbnbr * sizeof (SCOTCH_Num) * 3);
                
                for (rootnum = -1, cblknum = 0; cblknum < cblkglbnbr; cblknum ++) {
                  SCOTCH_Num          fathnum;

                  fathnum = treeglbtab[cblknum] - baseval; /* Use un-based indices  */
                  if (fathnum < 0) {              /* If father index indicates root */
                    if (rootnum != -1) {          /* If another root already found  */
                      rootnum = -1;               /* Indicate an error              */
                      break;
                    }
                    rootnum = cblknum;            /* Record index of root node */
                  }
                  else {
                    int                 i;

                    for (i = 0; i < 3; i ++) {
                      int                 j;

                      j = 3 * fathnum + i;        /* Slot number of prospective son  */
                      if (sepaglbtab[j] < 0) {    /* If potentially empty slot found */
                        if (sepaglbtab[j] == -1)  /* If we don't have too many sons  */
                          sepaglbtab[j] = cblknum; /* Add link to son in slot        */
                        break;
                      }
                    }
                    if (i == 3) {                 /* If no empty slot found             */
                      sepaglbtab[3 * fathnum] = -2; /* Indicate there are too many sons */
                      break;
                    }
                  }
                }

                if ((rootnum >= 0) && (sizes != NULL)) { /* If no error above, go on processing separator tree  */
                  memSet (sizes, 0, (2 * procglbnbr - 1) * sizeof (int)); /* Set array of sizes to 0 by default */
                  _SCOTCH_ParMETIS_V3_NodeNDTree (sizes + (2 * procglbnbr - 1), sizeglbtab, sepaglbtab, levlmax, 0, rootnum, 1);
                }
              }

              memFree (treeglbtab);               /* Free group leader */
            }
          }
        }

        SCOTCH_dgraphOrderExit (&grafdat, &ordedat);
      }
    }
/*
**
*/

FORTRAN (                                       \
SCOTCHFDGRAPHBUILD, scotchfdgraphbuild, (       \
SCOTCH_Dgraph * const       grafptr,            \
const SCOTCH_Num * const    baseptr,            \
const SCOTCH_Num * const    vertlocptr,         \
const SCOTCH_Num * const    vertlocmpt,         \
SCOTCH_Num * const          vertloctab,         \
SCOTCH_Num * const          vendloctab,         \
SCOTCH_Num * const          veloloctab,         \
SCOTCH_Num * const          vlblloctab,         \
const SCOTCH_Num * const    edgelocptr,         \
const SCOTCH_Num * const    edgelocptz,         \
SCOTCH_Num * const          edgeloctab,         \
SCOTCH_Num * const          edgegsttab,         \
SCOTCH_Num * const          edloloctab,         \
int * const                 revaptr),           \
(grafptr, baseptr, vertlocptr, vertlocmpt,      \
 vertloctab, vendloctab, veloloctab,            \
 vlblloctab, edgelocptr, edgelocptz,            \
 edgeloctab, edgegsttab, edloloctab,            \
 revaptr))
{
  *revaptr = SCOTCH_dgraphBuild (grafptr, *baseptr, *vertlocptr, *vertlocmpt, vertloctab,
                                 vendloctab, veloloctab, vlblloctab,
                                 *edgelocptr, *edgelocptz, edgeloctab, edgegsttab, edloloctab);
}