impls/plex/plexpartition.c

#include <petsc-private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/

PetscClassId PETSCPARTITIONER_CLASSID = 0;

PetscFunctionList PetscPartitionerList              = NULL;
PetscBool         PetscPartitionerRegisterAllCalled = PETSC_FALSE;

PetscBool ChacoPartitionercite = PETSC_FALSE;
const char ChacoPartitionerCitation[] = "@inproceedings{Chaco95,\n"
                               "  author    = {Bruce Hendrickson and Robert Leland},\n"
                               "  title     = {A multilevel algorithm for partitioning graphs},\n"
                               "  booktitle = {Supercomputing '95: Proceedings of the 1995 ACM/IEEE Conference on Supercomputing (CDROM)},"
                               "  isbn      = {0-89791-816-9},\n"
                               "  pages     = {28},\n"
                               "  doi       = {http://doi.acm.org/10.1145/224170.224228},\n"
                               "  publisher = {ACM Press},\n"
                               "  address   = {New York},\n"
                               "  year      = {1995}\n}\n";

PetscBool ParMetisPartitionercite = PETSC_FALSE;
const char ParMetisPartitionerCitation[] = "@article{KarypisKumar98,\n"
                               "  author  = {George Karypis and Vipin Kumar},\n"
                               "  title   = {A Parallel Algorithm for Multilevel Graph Partitioning and Sparse Matrix Ordering},\n"
                               "  journal = {Journal of Parallel and Distributed Computing},\n"
                               "  volume  = {48},\n"
                               "  pages   = {71--85},\n"
                               "  year    = {1998}\n}\n";

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateNeighborCSR"
PetscErrorCode DMPlexCreateNeighborCSR(DM dm, PetscInt cellHeight, PetscInt *numVertices, PetscInt **offsets, PetscInt **adjacency)
{
  const PetscInt maxFaceCases = 30;
  PetscInt       numFaceCases = 0;
  PetscInt       numFaceVertices[30]; /* maxFaceCases, C89 sucks sucks sucks */
  PetscInt      *off, *adj;
  PetscInt      *neighborCells = NULL;
  PetscInt       dim, cellDim, depth = 0, faceDepth, cStart, cEnd, c, numCells, cell;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* For parallel partitioning, I think you have to communicate supports */
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  cellDim = dim - cellHeight;
  ierr = DMPlexGetDepth(dm, &depth);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
  if (cEnd - cStart == 0) {
    if (numVertices) *numVertices = 0;
    if (offsets)   *offsets   = NULL;
    if (adjacency) *adjacency = NULL;
    PetscFunctionReturn(0);
  }
  numCells  = cEnd - cStart;
  faceDepth = depth - cellHeight;
  if (dim == depth) {
    PetscInt f, fStart, fEnd;

    ierr = PetscCalloc1(numCells+1, &off);CHKERRQ(ierr);
    /* Count neighboring cells */
    ierr = DMPlexGetHeightStratum(dm, cellHeight+1, &fStart, &fEnd);CHKERRQ(ierr);
    for (f = fStart; f < fEnd; ++f) {
      const PetscInt *support;
      PetscInt        supportSize;
      ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
      ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
      if (supportSize == 2) {
        PetscInt numChildren;

        ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
        if (!numChildren) {
          ++off[support[0]-cStart+1];
          ++off[support[1]-cStart+1];
        }
      }
    }
    /* Prefix sum */
    for (c = 1; c <= numCells; ++c) off[c] += off[c-1];
    if (adjacency) {
      PetscInt *tmp;

      ierr = PetscMalloc1(off[numCells], &adj);CHKERRQ(ierr);
      ierr = PetscMalloc1((numCells+1), &tmp);CHKERRQ(ierr);
      ierr = PetscMemcpy(tmp, off, (numCells+1) * sizeof(PetscInt));CHKERRQ(ierr);
      /* Get neighboring cells */
      for (f = fStart; f < fEnd; ++f) {
        const PetscInt *support;
        PetscInt        supportSize;
        ierr = DMPlexGetSupportSize(dm, f, &supportSize);CHKERRQ(ierr);
        ierr = DMPlexGetSupport(dm, f, &support);CHKERRQ(ierr);
        if (supportSize == 2) {
          PetscInt numChildren;

          ierr = DMPlexGetTreeChildren(dm,f,&numChildren,NULL);CHKERRQ(ierr);
          if (!numChildren) {
            adj[tmp[support[0]-cStart]++] = support[1];
            adj[tmp[support[1]-cStart]++] = support[0];
          }
        }
      }
#if defined(PETSC_USE_DEBUG)
      for (c = 0; c < cEnd-cStart; ++c) if (tmp[c] != off[c+1]) SETERRQ3(PETSC_COMM_SELF, PETSC_ERR_PLIB, "Offset %d != %d for cell %d", tmp[c], off[c], c+cStart);
#endif
      ierr = PetscFree(tmp);CHKERRQ(ierr);
    }
    if (numVertices) *numVertices = numCells;
    if (offsets)   *offsets   = off;
    if (adjacency) *adjacency = adj;
    PetscFunctionReturn(0);
  }
  /* Setup face recognition */
  if (faceDepth == 1) {
    PetscInt cornersSeen[30] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}; /* Could use PetscBT */

    for (c = cStart; c < cEnd; ++c) {
      PetscInt corners;

      ierr = DMPlexGetConeSize(dm, c, &corners);CHKERRQ(ierr);
      if (!cornersSeen[corners]) {
        PetscInt nFV;

        if (numFaceCases >= maxFaceCases) SETERRQ(PetscObjectComm((PetscObject)dm), PETSC_ERR_PLIB, "Exceeded maximum number of face recognition cases");
        cornersSeen[corners] = 1;

        ierr = DMPlexGetNumFaceVertices(dm, cellDim, corners, &nFV);CHKERRQ(ierr);

        numFaceVertices[numFaceCases++] = nFV;
      }
    }
  }
  ierr = PetscCalloc1(numCells+1, &off);CHKERRQ(ierr);
  /* Count neighboring cells */
  for (cell = cStart; cell < cEnd; ++cell) {
    PetscInt numNeighbors = PETSC_DETERMINE, n;

    ierr = DMPlexGetAdjacency_Internal(dm, cell, PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, &numNeighbors, &neighborCells);CHKERRQ(ierr);
    /* Get meet with each cell, and check with recognizer (could optimize to check each pair only once) */
    for (n = 0; n < numNeighbors; ++n) {
      PetscInt        cellPair[2];
      PetscBool       found    = faceDepth > 1 ? PETSC_TRUE : PETSC_FALSE;
      PetscInt        meetSize = 0;
      const PetscInt *meet    = NULL;

      cellPair[0] = cell; cellPair[1] = neighborCells[n];
      if (cellPair[0] == cellPair[1]) continue;
      if (!found) {
        ierr = DMPlexGetMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
        if (meetSize) {
          PetscInt f;

          for (f = 0; f < numFaceCases; ++f) {
            if (numFaceVertices[f] == meetSize) {
              found = PETSC_TRUE;
              break;
            }
          }
        }
        ierr = DMPlexRestoreMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
      }
      if (found) ++off[cell-cStart+1];
    }
  }
  /* Prefix sum */
  for (cell = 1; cell <= numCells; ++cell) off[cell] += off[cell-1];

  if (adjacency) {
    ierr = PetscMalloc1(off[numCells], &adj);CHKERRQ(ierr);
    /* Get neighboring cells */
    for (cell = cStart; cell < cEnd; ++cell) {
      PetscInt numNeighbors = PETSC_DETERMINE, n;
      PetscInt cellOffset   = 0;

      ierr = DMPlexGetAdjacency_Internal(dm, cell, PETSC_TRUE, PETSC_FALSE, PETSC_FALSE, &numNeighbors, &neighborCells);CHKERRQ(ierr);
      /* Get meet with each cell, and check with recognizer (could optimize to check each pair only once) */
      for (n = 0; n < numNeighbors; ++n) {
        PetscInt        cellPair[2];
        PetscBool       found    = faceDepth > 1 ? PETSC_TRUE : PETSC_FALSE;
        PetscInt        meetSize = 0;
        const PetscInt *meet    = NULL;

        cellPair[0] = cell; cellPair[1] = neighborCells[n];
        if (cellPair[0] == cellPair[1]) continue;
        if (!found) {
          ierr = DMPlexGetMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
          if (meetSize) {
            PetscInt f;

            for (f = 0; f < numFaceCases; ++f) {
              if (numFaceVertices[f] == meetSize) {
                found = PETSC_TRUE;
                break;
              }
            }
          }
          ierr = DMPlexRestoreMeet(dm, 2, cellPair, &meetSize, &meet);CHKERRQ(ierr);
        }
        if (found) {
          adj[off[cell-cStart]+cellOffset] = neighborCells[n];
          ++cellOffset;
        }
      }
    }
  }
  ierr = PetscFree(neighborCells);CHKERRQ(ierr);
  if (numVertices) *numVertices = numCells;
  if (offsets)   *offsets   = off;
  if (adjacency) *adjacency = adj;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexEnlargePartition"
/* Expand the partition by BFS on the adjacency graph */
PetscErrorCode DMPlexEnlargePartition(DM dm, const PetscInt start[], const PetscInt adjacency[], PetscSection origPartSection, IS origPartition, PetscSection partSection, IS *partition)
{
  PetscHashI      h;
  const PetscInt *points;
  PetscInt      **tmpPoints, *newPoints, totPoints = 0;
  PetscInt        pStart, pEnd, part, q;
  PetscBool       useCone;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscHashICreate(h);
  ierr = PetscSectionGetChart(origPartSection, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(partSection, pStart, pEnd);CHKERRQ(ierr);
  ierr = ISGetIndices(origPartition, &points);CHKERRQ(ierr);
  ierr = PetscMalloc1((pEnd - pStart), &tmpPoints);CHKERRQ(ierr);
  ierr = DMPlexGetAdjacencyUseCone(dm, &useCone);CHKERRQ(ierr);
  ierr = DMPlexSetAdjacencyUseCone(dm, PETSC_TRUE);CHKERRQ(ierr);
  for (part = pStart; part < pEnd; ++part) {
    PetscInt *adj = NULL;
    PetscInt  numPoints, nP, numNewPoints, off, p, n = 0;

    PetscHashIClear(h);
    ierr = PetscSectionGetDof(origPartSection, part, &numPoints);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(origPartSection, part, &off);CHKERRQ(ierr);
    /* Add all existing points to h */
    for (p = 0; p < numPoints; ++p) {
      const PetscInt point = points[off+p];
      PetscHashIAdd(h, point, 1);
    }
    PetscHashISize(h, nP);
    if (nP != numPoints) SETERRQ2(PetscObjectComm((PetscObject)dm), PETSC_ERR_ARG_WRONG, "Invalid partition has %d points, but only %d were unique", numPoints, nP);
    /* Add all points in next BFS level */
    for (p = 0; p < numPoints; ++p) {
      const PetscInt point   = points[off+p];
      PetscInt       adjSize = PETSC_DETERMINE, a;

      ierr = DMPlexGetAdjacency(dm, point, &adjSize, &adj);CHKERRQ(ierr);
      for (a = 0; a < adjSize; ++a) PetscHashIAdd(h, adj[a], 1);
    }
    PetscHashISize(h, numNewPoints);
    ierr = PetscSectionSetDof(partSection, part, numNewPoints);CHKERRQ(ierr);
    ierr = PetscMalloc1(numNewPoints, &tmpPoints[part]);CHKERRQ(ierr);
    ierr = PetscHashIGetKeys(h, &n, tmpPoints[part]);CHKERRQ(ierr);
    ierr = PetscFree(adj);CHKERRQ(ierr);
    totPoints += numNewPoints;
  }
  ierr = DMPlexSetAdjacencyUseCone(dm, useCone);CHKERRQ(ierr);
  ierr = ISRestoreIndices(origPartition, &points);CHKERRQ(ierr);
  PetscHashIDestroy(h);
  ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
  ierr = PetscMalloc1(totPoints, &newPoints);CHKERRQ(ierr);
  for (part = pStart, q = 0; part < pEnd; ++part) {
    PetscInt numPoints, p;

    ierr = PetscSectionGetDof(partSection, part, &numPoints);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p, ++q) newPoints[q] = tmpPoints[part][p];
    ierr = PetscFree(tmpPoints[part]);CHKERRQ(ierr);
  }
  ierr = PetscFree(tmpPoints);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), totPoints, newPoints, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerRegister"
/*@C
  PetscPartitionerRegister - Adds a new PetscPartitioner implementation

  Not Collective

  Input Parameters:
+ name        - The name of a new user-defined creation routine
- create_func - The creation routine itself

  Notes:
  PetscPartitionerRegister() may be called multiple times to add several user-defined PetscPartitioners

  Sample usage:
.vb
    PetscPartitionerRegister("my_part", MyPetscPartitionerCreate);
.ve

  Then, your PetscPartitioner type can be chosen with the procedural interface via
.vb
    PetscPartitionerCreate(MPI_Comm, PetscPartitioner *);
    PetscPartitionerSetType(PetscPartitioner, "my_part");
.ve
   or at runtime via the option
.vb
    -petscpartitioner_type my_part
.ve

  Level: advanced

.keywords: PetscPartitioner, register
.seealso: PetscPartitionerRegisterAll(), PetscPartitionerRegisterDestroy()

@*/
PetscErrorCode PetscPartitionerRegister(const char sname[], PetscErrorCode (*function)(PetscPartitioner))
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscFunctionListAdd(&PetscPartitionerList, sname, function);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerSetType"
/*@C
  PetscPartitionerSetType - Builds a particular PetscPartitioner

  Collective on PetscPartitioner

  Input Parameters:
+ part - The PetscPartitioner object
- name - The kind of partitioner

  Options Database Key:
. -petscpartitioner_type <type> - Sets the PetscPartitioner type; use -help for a list of available types

  Level: intermediate

.keywords: PetscPartitioner, set, type
.seealso: PetscPartitionerGetType(), PetscPartitionerCreate()
@*/
PetscErrorCode PetscPartitionerSetType(PetscPartitioner part, PetscPartitionerType name)
{
  PetscErrorCode (*r)(PetscPartitioner);
  PetscBool      match;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  ierr = PetscObjectTypeCompare((PetscObject) part, name, &match);CHKERRQ(ierr);
  if (match) PetscFunctionReturn(0);

  if (!PetscPartitionerRegisterAllCalled) {ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);}
  ierr = PetscFunctionListFind(PetscPartitionerList, name, &r);CHKERRQ(ierr);
  if (!r) SETERRQ1(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_UNKNOWN_TYPE, "Unknown PetscPartitioner type: %s", name);

  if (part->ops->destroy) {
    ierr              = (*part->ops->destroy)(part);CHKERRQ(ierr);
    part->ops->destroy = NULL;
  }
  ierr = (*r)(part);CHKERRQ(ierr);
  ierr = PetscObjectChangeTypeName((PetscObject) part, name);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerGetType"
/*@C
  PetscPartitionerGetType - Gets the PetscPartitioner type name (as a string) from the object.

  Not Collective

  Input Parameter:
. part - The PetscPartitioner

  Output Parameter:
. name - The PetscPartitioner type name

  Level: intermediate

.keywords: PetscPartitioner, get, type, name
.seealso: PetscPartitionerSetType(), PetscPartitionerCreate()
@*/
PetscErrorCode PetscPartitionerGetType(PetscPartitioner part, PetscPartitionerType *name)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  PetscValidPointer(name, 2);
  if (!PetscPartitionerRegisterAllCalled) {ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);}
  *name = ((PetscObject) part)->type_name;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerView"
/*@C
  PetscPartitionerView - Views a PetscPartitioner

  Collective on PetscPartitioner

  Input Parameter:
+ part - the PetscPartitioner object to view
- v    - the viewer

  Level: developer

.seealso: PetscPartitionerDestroy()
@*/
PetscErrorCode PetscPartitionerView(PetscPartitioner part, PetscViewer v)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  if (!v) {ierr = PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject) part), &v);CHKERRQ(ierr);}
  if (part->ops->view) {ierr = (*part->ops->view)(part, v);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerViewFromOptions"
/*
  PetscPartitionerViewFromOptions - Processes command line options to determine if/how a PetscPartitioner is to be viewed.

  Collective on PetscPartitioner

  Input Parameters:
+ part   - the PetscPartitioner
. prefix - prefix to use for viewing, or NULL
- optionname - option to activate viewing

  Level: intermediate

.keywords: PetscPartitioner, view, options, database
.seealso: VecViewFromOptions(), MatViewFromOptions()
*/
PetscErrorCode PetscPartitionerViewFromOptions(PetscPartitioner part, const char prefix[], const char optionname[])
{
  PetscViewer       viewer;
  PetscViewerFormat format;
  PetscBool         flg;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  if (prefix) {ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject) part), prefix,                       optionname, &viewer, &format, &flg);CHKERRQ(ierr);}
  else        {ierr = PetscOptionsGetViewer(PetscObjectComm((PetscObject) part), ((PetscObject) part)->prefix, optionname, &viewer, &format, &flg);CHKERRQ(ierr);}
  if (flg) {
    ierr = PetscViewerPushFormat(viewer, format);CHKERRQ(ierr);
    ierr = PetscPartitionerView(part, viewer);CHKERRQ(ierr);
    ierr = PetscViewerPopFormat(viewer);CHKERRQ(ierr);
    ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}
#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerSetTypeFromOptions_Internal"
PetscErrorCode PetscPartitionerSetTypeFromOptions_Internal(PetscPartitioner part)
{
  const char    *defaultType;
  char           name[256];
  PetscBool      flg;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  if (!((PetscObject) part)->type_name) defaultType = PETSCPARTITIONERCHACO;
  else                                  defaultType = ((PetscObject) part)->type_name;
  if (!PetscPartitionerRegisterAllCalled) {ierr = PetscPartitionerRegisterAll();CHKERRQ(ierr);}

  ierr = PetscObjectOptionsBegin((PetscObject) part);CHKERRQ(ierr);
  ierr = PetscOptionsFList("-petscpartitioner_type", "Graph partitioner", "PetscPartitionerSetType", PetscPartitionerList, defaultType, name, 256, &flg);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscPartitionerSetType(part, name);CHKERRQ(ierr);
  } else if (!((PetscObject) part)->type_name) {
    ierr = PetscPartitionerSetType(part, defaultType);CHKERRQ(ierr);
  }
  ierr = PetscOptionsEnd();CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerSetFromOptions"
/*@
  PetscPartitionerSetFromOptions - sets parameters in a PetscPartitioner from the options database

  Collective on PetscPartitioner

  Input Parameter:
. part - the PetscPartitioner object to set options for

  Level: developer

.seealso: PetscPartitionerView()
@*/
PetscErrorCode PetscPartitionerSetFromOptions(PetscPartitioner part)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  ierr = PetscPartitionerSetTypeFromOptions_Internal(part);CHKERRQ(ierr);

  ierr = PetscObjectOptionsBegin((PetscObject) part);CHKERRQ(ierr);
  if (part->ops->setfromoptions) {ierr = (*part->ops->setfromoptions)(part);CHKERRQ(ierr);}
  /* process any options handlers added with PetscObjectAddOptionsHandler() */
  ierr = PetscObjectProcessOptionsHandlers((PetscObject) part);CHKERRQ(ierr);
  ierr = PetscOptionsEnd();CHKERRQ(ierr);
  ierr = PetscPartitionerViewFromOptions(part, NULL, "-petscpartitioner_view");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerSetUp"
/*@C
  PetscPartitionerSetUp - Construct data structures for the PetscPartitioner

  Collective on PetscPartitioner

  Input Parameter:
. part - the PetscPartitioner object to setup

  Level: developer

.seealso: PetscPartitionerView(), PetscPartitionerDestroy()
@*/
PetscErrorCode PetscPartitionerSetUp(PetscPartitioner part)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  if (part->ops->setup) {ierr = (*part->ops->setup)(part);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerDestroy"
/*@
  PetscPartitionerDestroy - Destroys a PetscPartitioner object

  Collective on PetscPartitioner

  Input Parameter:
. part - the PetscPartitioner object to destroy

  Level: developer

.seealso: PetscPartitionerView()
@*/
PetscErrorCode PetscPartitionerDestroy(PetscPartitioner *part)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (!*part) PetscFunctionReturn(0);
  PetscValidHeaderSpecific((*part), PETSCPARTITIONER_CLASSID, 1);

  if (--((PetscObject)(*part))->refct > 0) {*part = 0; PetscFunctionReturn(0);}
  ((PetscObject) (*part))->refct = 0;

  if ((*part)->ops->destroy) {ierr = (*(*part)->ops->destroy)(*part);CHKERRQ(ierr);}
  ierr = PetscHeaderDestroy(part);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerCreate"
/*@
  PetscPartitionerCreate - Creates an empty PetscPartitioner object. The type can then be set with PetscPartitionerSetType().

  Collective on MPI_Comm

  Input Parameter:
. comm - The communicator for the PetscPartitioner object

  Output Parameter:
. part - The PetscPartitioner object

  Level: beginner

.seealso: PetscPartitionerSetType(), PETSCPARTITIONERCHACO, PETSCPARTITIONERPARMETIS, PETSCPARTITIONERSHELL
@*/
PetscErrorCode PetscPartitionerCreate(MPI_Comm comm, PetscPartitioner *part)
{
  PetscPartitioner p;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  PetscValidPointer(part, 2);
  *part = NULL;
  ierr = PetscFVInitializePackage();CHKERRQ(ierr);

  ierr = PetscHeaderCreate(p, _p_PetscPartitioner, struct _PetscPartitionerOps, PETSCPARTITIONER_CLASSID, "PetscPartitioner", "Graph Partitioner", "PetscPartitioner", comm, PetscPartitionerDestroy, PetscPartitionerView);CHKERRQ(ierr);
  ierr = PetscMemzero(p->ops, sizeof(struct _PetscPartitionerOps));CHKERRQ(ierr);

  *part = p;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerPartition"
/*@
  PetscPartitionerPartition - Create a non-overlapping partition of the cells in the mesh

  Collective on DM

  Input Parameters:
+ part    - The PetscPartitioner
- dm      - The mesh DM

  Output Parameters:
+ partSection     - The PetscSection giving the division of points by partition
- partition       - The list of points by partition

  Note: Instead of cells, points at a given height can be partitioned by calling PetscPartitionerSetPointHeight()

  Level: developer

.seealso DMPlexDistribute(), PetscPartitionerSetPointHeight(), PetscPartitionerCreate()
@*/
PetscErrorCode PetscPartitionerPartition(PetscPartitioner part, DM dm, PetscSection partSection, IS *partition)
{
  PetscMPIInt    size;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  PetscValidHeaderSpecific(dm, DM_CLASSID, 2);
  PetscValidHeaderSpecific(partSection, PETSC_SECTION_CLASSID, 4);
  PetscValidPointer(partition, 5);
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject) part), &size);CHKERRQ(ierr);
  if (size == 1) {
    PetscInt *points;
    PetscInt  cStart, cEnd, c;

    ierr = DMPlexGetHeightStratum(dm, part->height, &cStart, &cEnd);CHKERRQ(ierr);
    ierr = PetscSectionSetChart(partSection, 0, size);CHKERRQ(ierr);
    ierr = PetscSectionSetDof(partSection, 0, cEnd-cStart);CHKERRQ(ierr);
    ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
    ierr = PetscMalloc1(cEnd-cStart, &points);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; ++c) points[c] = c;
    ierr = ISCreateGeneral(PetscObjectComm((PetscObject) part), cEnd-cStart, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (part->height == 0) {
    PetscInt  numVertices;
    PetscInt *start     = NULL;
    PetscInt *adjacency = NULL;

    ierr = DMPlexCreateNeighborCSR(dm, 0, &numVertices, &start, &adjacency);CHKERRQ(ierr);
    if (!part->ops->partition) SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_WRONGSTATE, "PetscPartitioner has no type");
    ierr = (*part->ops->partition)(part, dm, size, numVertices, start, adjacency, partSection, partition);CHKERRQ(ierr);
    ierr = PetscFree(start);CHKERRQ(ierr);
    ierr = PetscFree(adjacency);CHKERRQ(ierr);
  } else SETERRQ1(PetscObjectComm((PetscObject) part), PETSC_ERR_ARG_OUTOFRANGE, "Invalid height %D for points to partition", part->height);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerDestroy_Shell"
PetscErrorCode PetscPartitionerDestroy_Shell(PetscPartitioner part)
{
  PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
  PetscErrorCode          ierr;

  PetscFunctionBegin;
  ierr = PetscSectionDestroy(&p->section);CHKERRQ(ierr);
  ierr = ISDestroy(&p->partition);CHKERRQ(ierr);
  ierr = PetscFree(p);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerView_Shell_Ascii"
PetscErrorCode PetscPartitionerView_Shell_Ascii(PetscPartitioner part, PetscViewer viewer)
{
  PetscViewerFormat format;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = PetscViewerGetFormat(viewer, &format);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer, "Shell Graph Partitioner:\n");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerView_Shell"
PetscErrorCode PetscPartitionerView_Shell(PetscPartitioner part, PetscViewer viewer)
{
  PetscBool      iascii;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
  if (iascii) {ierr = PetscPartitionerView_Shell_Ascii(part, viewer);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerPartition_Shell"
PetscErrorCode PetscPartitionerPartition_Shell(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
{
  PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
  PetscInt                np;
  PetscErrorCode          ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetChart(p->section, NULL, &np);CHKERRQ(ierr);
  if (nparts != np) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of requested partitions %d != configured partitions %d", nparts, np);
  ierr = ISGetLocalSize(p->partition, &np);CHKERRQ(ierr);
  if (numVertices != np) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Number of input vertices %d != configured vertices %d", numVertices, np);
  ierr = PetscSectionCopy(p->section, partSection);CHKERRQ(ierr);
  *partition = p->partition;
  ierr = PetscObjectReference((PetscObject) p->partition);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerInitialize_Shell"
PetscErrorCode PetscPartitionerInitialize_Shell(PetscPartitioner part)
{
  PetscFunctionBegin;
  part->ops->view      = PetscPartitionerView_Shell;
  part->ops->destroy   = PetscPartitionerDestroy_Shell;
  part->ops->partition = PetscPartitionerPartition_Shell;
  PetscFunctionReturn(0);
}

/*MC
  PETSCPARTITIONERSHELL = "shell" - A PetscPartitioner object

  Level: intermediate

.seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
M*/

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerCreate_Shell"
PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Shell(PetscPartitioner part)
{
  PetscPartitioner_Shell *p;
  PetscErrorCode          ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
  part->data = p;

  ierr = PetscPartitionerInitialize_Shell(part);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerShellSetPartition"
/*@C
  PetscPartitionerShellSetPartition - Set an artifical partition for a mesh

  Collective on DM

  Input Parameters:
+ part    - The PetscPartitioner
. dm      - The mesh DM
- enlarge - Expand each partition with neighbors

  Level: developer

.seealso DMPlexDistribute(), PetscPartitionerCreate()
@*/
PetscErrorCode PetscPartitionerShellSetPartition(PetscPartitioner part, PetscInt numProcs, const PetscInt sizes[], const PetscInt points[])
{
  PetscPartitioner_Shell *p = (PetscPartitioner_Shell *) part->data;
  PetscInt                proc, numPoints;
  PetscErrorCode          ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  if (sizes) {PetscValidPointer(sizes, 3);}
  if (sizes) {PetscValidPointer(points, 4);}
  ierr = PetscSectionDestroy(&p->section);CHKERRQ(ierr);
  ierr = ISDestroy(&p->partition);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject) part), &p->section);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(p->section, 0, numProcs);CHKERRQ(ierr);
  if (sizes) {
    for (proc = 0; proc < numProcs; ++proc) {
      ierr = PetscSectionSetDof(p->section, proc, sizes[proc]);CHKERRQ(ierr);
    }
  }
  ierr = PetscSectionSetUp(p->section);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(p->section, &numPoints);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject) part), numPoints, points, PETSC_COPY_VALUES, &p->partition);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerDestroy_Chaco"
PetscErrorCode PetscPartitionerDestroy_Chaco(PetscPartitioner part)
{
  PetscPartitioner_Chaco *p = (PetscPartitioner_Chaco *) part->data;
  PetscErrorCode          ierr;

  PetscFunctionBegin;
  ierr = PetscFree(p);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerView_Chaco_Ascii"
PetscErrorCode PetscPartitionerView_Chaco_Ascii(PetscPartitioner part, PetscViewer viewer)
{
  PetscViewerFormat format;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = PetscViewerGetFormat(viewer, &format);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer, "Chaco Graph Partitioner:\n");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerView_Chaco"
PetscErrorCode PetscPartitionerView_Chaco(PetscPartitioner part, PetscViewer viewer)
{
  PetscBool      iascii;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
  if (iascii) {ierr = PetscPartitionerView_Chaco_Ascii(part, viewer);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_CHACO)
#if defined(PETSC_HAVE_UNISTD_H)
#include <unistd.h>
#endif
/* Chaco does not have an include file */
PETSC_EXTERN int interface(int nvtxs, int *start, int *adjacency, int *vwgts,
                       float *ewgts, float *x, float *y, float *z, char *outassignname,
                       char *outfilename, short *assignment, int architecture, int ndims_tot,
                       int mesh_dims[3], double *goal, int global_method, int local_method,
                       int rqi_flag, int vmax, int ndims, double eigtol, long seed);

extern int FREE_GRAPH;
#endif

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerPartition_Chaco"
PetscErrorCode PetscPartitionerPartition_Chaco(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
{
#if defined(PETSC_HAVE_CHACO)
  enum {DEFAULT_METHOD = 1, INERTIAL_METHOD = 3};
  MPI_Comm       comm;
  int            nvtxs          = numVertices; /* number of vertices in full graph */
  int           *vwgts          = NULL;   /* weights for all vertices */
  float         *ewgts          = NULL;   /* weights for all edges */
  float         *x              = NULL, *y = NULL, *z = NULL; /* coordinates for inertial method */
  char          *outassignname  = NULL;   /*  name of assignment output file */
  char          *outfilename    = NULL;   /* output file name */
  int            architecture   = 1;      /* 0 => hypercube, d => d-dimensional mesh */
  int            ndims_tot      = 0;      /* total number of cube dimensions to divide */
  int            mesh_dims[3];            /* dimensions of mesh of processors */
  double        *goal          = NULL;    /* desired set sizes for each set */
  int            global_method = 1;       /* global partitioning algorithm */
  int            local_method  = 1;       /* local partitioning algorithm */
  int            rqi_flag      = 0;       /* should I use RQI/Symmlq eigensolver? */
  int            vmax          = 200;     /* how many vertices to coarsen down to? */
  int            ndims         = 1;       /* number of eigenvectors (2^d sets) */
  double         eigtol        = 0.001;   /* tolerance on eigenvectors */
  long           seed          = 123636512; /* for random graph mutations */
  short int     *assignment;              /* Output partition */
  int            fd_stdout, fd_pipe[2];
  PetscInt      *points;
  int            i, v, p;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  if (!numVertices) {
    ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
    ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
    ierr = ISCreateGeneral(comm, 0, NULL, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  FREE_GRAPH = 0;                         /* Do not let Chaco free my memory */
  for (i = 0; i < start[numVertices]; ++i) ++adjacency[i];

  if (global_method == INERTIAL_METHOD) {
    /* manager.createCellCoordinates(nvtxs, &x, &y, &z); */
    SETERRQ(comm, PETSC_ERR_SUP, "Inertial partitioning not yet supported");
  }
  mesh_dims[0] = nparts;
  mesh_dims[1] = 1;
  mesh_dims[2] = 1;
  ierr = PetscMalloc1(nvtxs, &assignment);CHKERRQ(ierr);
  /* Chaco outputs to stdout. We redirect this to a buffer. */
  /* TODO: check error codes for UNIX calls */
#if defined(PETSC_HAVE_UNISTD_H)
  {
    int piperet;
    piperet = pipe(fd_pipe);
    if (piperet) SETERRQ(comm,PETSC_ERR_SYS,"Could not create pipe");
    fd_stdout = dup(1);
    close(1);
    dup2(fd_pipe[1], 1);
  }
#endif
  ierr = interface(nvtxs, (int*) start, (int*) adjacency, vwgts, ewgts, x, y, z, outassignname, outfilename,
                   assignment, architecture, ndims_tot, mesh_dims, goal, global_method, local_method, rqi_flag,
                   vmax, ndims, eigtol, seed);
#if defined(PETSC_HAVE_UNISTD_H)
  {
    char msgLog[10000];
    int  count;

    fflush(stdout);
    count = read(fd_pipe[0], msgLog, (10000-1)*sizeof(char));
    if (count < 0) count = 0;
    msgLog[count] = 0;
    close(1);
    dup2(fd_stdout, 1);
    close(fd_stdout);
    close(fd_pipe[0]);
    close(fd_pipe[1]);
    if (ierr) SETERRQ1(comm, PETSC_ERR_LIB, "Error in Chaco library: %s", msgLog);
  }
#endif
  /* Convert to PetscSection+IS */
  ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
  for (v = 0; v < nvtxs; ++v) {
    ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
  ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
  for (p = 0, i = 0; p < nparts; ++p) {
    for (v = 0; v < nvtxs; ++v) {
      if (assignment[v] == p) points[i++] = v;
    }
  }
  if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
  ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
  if (global_method == INERTIAL_METHOD) {
    /* manager.destroyCellCoordinates(nvtxs, &x, &y, &z); */
  }
  ierr = PetscFree(assignment);CHKERRQ(ierr);
  for (i = 0; i < start[numVertices]; ++i) --adjacency[i];
  PetscFunctionReturn(0);
#else
  SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-chaco.");
#endif
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerInitialize_Chaco"
PetscErrorCode PetscPartitionerInitialize_Chaco(PetscPartitioner part)
{
  PetscFunctionBegin;
  part->ops->view      = PetscPartitionerView_Chaco;
  part->ops->destroy   = PetscPartitionerDestroy_Chaco;
  part->ops->partition = PetscPartitionerPartition_Chaco;
  PetscFunctionReturn(0);
}

/*MC
  PETSCPARTITIONERCHACO = "chaco" - A PetscPartitioner object using the Chaco library

  Level: intermediate

.seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
M*/

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerCreate_Chaco"
PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_Chaco(PetscPartitioner part)
{
  PetscPartitioner_Chaco *p;
  PetscErrorCode          ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
  part->data = p;

  ierr = PetscPartitionerInitialize_Chaco(part);CHKERRQ(ierr);
  ierr = PetscCitationsRegister(ChacoPartitionerCitation, &ChacoPartitionercite);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerDestroy_ParMetis"
PetscErrorCode PetscPartitionerDestroy_ParMetis(PetscPartitioner part)
{
  PetscPartitioner_ParMetis *p = (PetscPartitioner_ParMetis *) part->data;
  PetscErrorCode             ierr;

  PetscFunctionBegin;
  ierr = PetscFree(p);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerView_ParMetis_Ascii"
PetscErrorCode PetscPartitionerView_ParMetis_Ascii(PetscPartitioner part, PetscViewer viewer)
{
  PetscViewerFormat format;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = PetscViewerGetFormat(viewer, &format);CHKERRQ(ierr);
  ierr = PetscViewerASCIIPrintf(viewer, "ParMetis Graph Partitioner:\n");CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerView_ParMetis"
PetscErrorCode PetscPartitionerView_ParMetis(PetscPartitioner part, PetscViewer viewer)
{
  PetscBool      iascii;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  PetscValidHeaderSpecific(viewer, PETSC_VIEWER_CLASSID, 2);
  ierr = PetscObjectTypeCompare((PetscObject) viewer, PETSCVIEWERASCII, &iascii);CHKERRQ(ierr);
  if (iascii) {ierr = PetscPartitionerView_ParMetis_Ascii(part, viewer);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}

#if defined(PETSC_HAVE_PARMETIS)
#include <parmetis.h>
#endif

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerPartition_ParMetis"
PetscErrorCode PetscPartitionerPartition_ParMetis(PetscPartitioner part, DM dm, PetscInt nparts, PetscInt numVertices, PetscInt start[], PetscInt adjacency[], PetscSection partSection, IS *partition)
{
#if defined(PETSC_HAVE_PARMETIS)
  MPI_Comm       comm;
  PetscInt       nvtxs      = numVertices; /* The number of vertices in full graph */
  PetscInt      *vtxdist;                  /* Distribution of vertices across processes */
  PetscInt      *xadj       = start;       /* Start of edge list for each vertex */
  PetscInt      *adjncy     = adjacency;   /* Edge lists for all vertices */
  PetscInt      *vwgt       = NULL;        /* Vertex weights */
  PetscInt      *adjwgt     = NULL;        /* Edge weights */
  PetscInt       wgtflag    = 0;           /* Indicates which weights are present */
  PetscInt       numflag    = 0;           /* Indicates initial offset (0 or 1) */
  PetscInt       ncon       = 1;           /* The number of weights per vertex */
  PetscReal     *tpwgts;                   /* The fraction of vertex weights assigned to each partition */
  PetscReal     *ubvec;                    /* The balance intolerance for vertex weights */
  PetscInt       options[5];               /* Options */
  /* Outputs */
  PetscInt       edgeCut;                  /* The number of edges cut by the partition */
  PetscInt      *assignment, *points;
  PetscMPIInt    rank, p, v, i;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject) part, &comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  options[0] = 0; /* Use all defaults */
  /* Calculate vertex distribution */
  ierr = PetscMalloc4(nparts+1,&vtxdist,nparts*ncon,&tpwgts,ncon,&ubvec,nvtxs,&assignment);CHKERRQ(ierr);
  vtxdist[0] = 0;
  ierr = MPI_Allgather(&nvtxs, 1, MPIU_INT, &vtxdist[1], 1, MPIU_INT, comm);CHKERRQ(ierr);
  for (p = 2; p <= nparts; ++p) {
    vtxdist[p] += vtxdist[p-1];
  }
  /* Calculate weights */
  for (p = 0; p < nparts; ++p) {
    tpwgts[p] = 1.0/nparts;
  }
  ubvec[0] = 1.05;

  if (nparts == 1) {
    ierr = PetscMemzero(assignment, nvtxs * sizeof(PetscInt));
  } else {
    if (vtxdist[1] == vtxdist[nparts]) {
      if (!rank) {
        PetscStackPush("METIS_PartGraphKway");
        ierr = METIS_PartGraphKway(&nvtxs, &ncon, xadj, adjncy, vwgt, NULL, adjwgt, &nparts, tpwgts, ubvec, NULL, &edgeCut, assignment);
        PetscStackPop;
        if (ierr != METIS_OK) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in METIS_PartGraphKway()");
      }
    } else {
      PetscStackPush("ParMETIS_V3_PartKway");
      ierr = ParMETIS_V3_PartKway(vtxdist, xadj, adjncy, vwgt, adjwgt, &wgtflag, &numflag, &ncon, &nparts, tpwgts, ubvec, options, &edgeCut, assignment, &comm);
      PetscStackPop;
      if (ierr != METIS_OK) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_LIB, "Error in ParMETIS_V3_PartKway()");
    }
  }
  /* Convert to PetscSection+IS */
  ierr = PetscSectionSetChart(partSection, 0, nparts);CHKERRQ(ierr);
  for (v = 0; v < nvtxs; ++v) {ierr = PetscSectionAddDof(partSection, assignment[v], 1);CHKERRQ(ierr);}
  ierr = PetscSectionSetUp(partSection);CHKERRQ(ierr);
  ierr = PetscMalloc1(nvtxs, &points);CHKERRQ(ierr);
  for (p = 0, i = 0; p < nparts; ++p) {
    for (v = 0; v < nvtxs; ++v) {
      if (assignment[v] == p) points[i++] = v;
    }
  }
  if (i != nvtxs) SETERRQ2(comm, PETSC_ERR_PLIB, "Number of points %D should be %D", i, nvtxs);
  ierr = ISCreateGeneral(comm, nvtxs, points, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
  ierr = PetscFree4(vtxdist,tpwgts,ubvec,assignment);CHKERRQ(ierr);
#else
  SETERRQ(PetscObjectComm((PetscObject) part), PETSC_ERR_SUP, "Mesh partitioning needs external package support.\nPlease reconfigure with --download-parmetis.");
#endif
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerInitialize_ParMetis"
PetscErrorCode PetscPartitionerInitialize_ParMetis(PetscPartitioner part)
{
  PetscFunctionBegin;
  part->ops->view      = PetscPartitionerView_ParMetis;
  part->ops->destroy   = PetscPartitionerDestroy_ParMetis;
  part->ops->partition = PetscPartitionerPartition_ParMetis;
  PetscFunctionReturn(0);
}

/*MC
  PETSCPARTITIONERPARMETIS = "parmetis" - A PetscPartitioner object using the ParMetis library

  Level: intermediate

.seealso: PetscPartitionerType, PetscPartitionerCreate(), PetscPartitionerSetType()
M*/

#undef __FUNCT__
#define __FUNCT__ "PetscPartitionerCreate_ParMetis"
PETSC_EXTERN PetscErrorCode PetscPartitionerCreate_ParMetis(PetscPartitioner part)
{
  PetscPartitioner_ParMetis *p;
  PetscErrorCode          ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 1);
  ierr       = PetscNewLog(part, &p);CHKERRQ(ierr);
  part->data = p;

  ierr = PetscPartitionerInitialize_ParMetis(part);CHKERRQ(ierr);
  ierr = PetscCitationsRegister(ParMetisPartitionerCitation, &ParMetisPartitionercite);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetPartitioner"
/*@
  DMPlexGetPartitioner - Get the mesh partitioner

  Not collective

  Input Parameter:
. dm - The DM

  Output Parameter:
. part - The PetscPartitioner

  Level: developer

.seealso DMPlexDistribute(), PetscPartitionerCreate()
@*/
PetscErrorCode DMPlexGetPartitioner(DM dm, PetscPartitioner *part)
{
  DM_Plex *mesh = (DM_Plex *) dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidPointer(part, 2);
  *part = mesh->partitioner;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexMarkTreeClosure"
static PetscErrorCode DMPlexMarkTreeClosure(DM dm, PetscSegBuffer segpart, PetscBT bt, PetscInt point, PetscInt *partSize)
{
  PetscInt       parent, closureSize, *closure = NULL, i, pStart, pEnd;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
  if (parent == point) PetscFunctionReturn(0);
  ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
  for (i = 0; i < closureSize; i++) {
    PetscInt cpoint = closure[2*i];

    if (!PetscBTLookupSet(bt,cpoint-pStart)) {
      PetscInt *PETSC_RESTRICT pt;
      (*partSize)++;
      ierr = PetscSegBufferGetInts(segpart,1,&pt);CHKERRQ(ierr);
      *pt = cpoint;
    }
    ierr = DMPlexMarkTreeClosure(dm,segpart,bt,cpoint,partSize);CHKERRQ(ierr);
  }
  ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreatePartitionClosure"
PetscErrorCode DMPlexCreatePartitionClosure(DM dm, PetscSection pointSection, IS pointPartition, PetscSection *section, IS *partition)
{
  /* const PetscInt  height = 0; */
  const PetscInt *partArray;
  PetscInt       *allPoints, *packPoints;
  PetscInt        rStart, rEnd, rank, pStart, pEnd, newSize;
  PetscErrorCode  ierr;
  PetscBT         bt;
  PetscSegBuffer  segpack,segpart;

  PetscFunctionBegin;
  ierr = PetscSectionGetChart(pointSection, &rStart, &rEnd);CHKERRQ(ierr);
  ierr = ISGetIndices(pointPartition, &partArray);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm), section);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*section, rStart, rEnd);CHKERRQ(ierr);
  ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = PetscBTCreate(pEnd-pStart,&bt);CHKERRQ(ierr);
  ierr = PetscSegBufferCreate(sizeof(PetscInt),1000,&segpack);CHKERRQ(ierr);
  ierr = PetscSegBufferCreate(sizeof(PetscInt),1000,&segpart);CHKERRQ(ierr);
  for (rank = rStart; rank < rEnd; ++rank) {
    PetscInt partSize = 0, numPoints, offset, p, *PETSC_RESTRICT placePoints;

    ierr = PetscSectionGetDof(pointSection, rank, &numPoints);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(pointSection, rank, &offset);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      PetscInt  point   = partArray[offset+p], closureSize, c;
      PetscInt *closure = NULL;

      /* TODO Include support for height > 0 case */
      ierr = DMPlexGetTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      for (c=0; c<closureSize; c++) {
        PetscInt cpoint = closure[c*2];
        if (!PetscBTLookupSet(bt,cpoint-pStart)) {
          PetscInt *PETSC_RESTRICT pt;
          partSize++;
          ierr = PetscSegBufferGetInts(segpart,1,&pt);CHKERRQ(ierr);
          *pt = cpoint;
        }
        ierr = DMPlexMarkTreeClosure(dm,segpart,bt,cpoint,&partSize);CHKERRQ(ierr);
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, point, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetDof(*section, rank, partSize);CHKERRQ(ierr);
    ierr = PetscSegBufferGetInts(segpack,partSize,&placePoints);CHKERRQ(ierr);
    ierr = PetscSegBufferExtractTo(segpart,placePoints);CHKERRQ(ierr);
    ierr = PetscSortInt(partSize,placePoints);CHKERRQ(ierr);
    for (p=0; p<partSize; p++) {ierr = PetscBTClear(bt,placePoints[p]-pStart);CHKERRQ(ierr);}
  }
  ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
  ierr = PetscSegBufferDestroy(&segpart);CHKERRQ(ierr);

  ierr = PetscSectionSetUp(*section);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(*section, &newSize);CHKERRQ(ierr);
  ierr = PetscMalloc1(newSize, &allPoints);CHKERRQ(ierr);

  ierr = PetscSegBufferExtractInPlace(segpack,&packPoints);CHKERRQ(ierr);
  for (rank = rStart; rank < rEnd; ++rank) {
    PetscInt numPoints, offset;

    ierr = PetscSectionGetDof(*section, rank, &numPoints);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(*section, rank, &offset);CHKERRQ(ierr);
    ierr = PetscMemcpy(&allPoints[offset], packPoints, numPoints * sizeof(PetscInt));CHKERRQ(ierr);
    packPoints += numPoints;
  }

  ierr = PetscSegBufferDestroy(&segpack);CHKERRQ(ierr);
  ierr = ISRestoreIndices(pointPartition, &partArray);CHKERRQ(ierr);
  ierr = ISCreateGeneral(PetscObjectComm((PetscObject)dm), newSize, allPoints, PETSC_OWN_POINTER, partition);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexPartitionLabelClosure"
/*@
  DMPlexPartitionLabelClosure - Add the closure of all points to the partition label

  Input Parameters:
+ dm     - The DM
- label  - DMLabel assinging ranks to remote roots

  Level: developer

.seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
@*/
PetscErrorCode DMPlexPartitionLabelClosure(DM dm, DMLabel label)
{
  IS              rankIS,   pointIS;
  const PetscInt *ranks,   *points;
  PetscInt        numRanks, numPoints, r, p, c, closureSize;
  PetscInt       *closure = NULL;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
  ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
  ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
  for (r = 0; r < numRanks; ++r) {
    const PetscInt rank = ranks[r];

    ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
    ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
    ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      ierr = DMPlexGetTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      for (c = 0; c < closureSize*2; c += 2) {ierr = DMLabelSetValue(label, closure[c], rank);CHKERRQ(ierr);}
    }
    ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
    ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
  }
  if (closure) {ierr = DMPlexRestoreTransitiveClosure(dm, points[p], PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);}
  ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
  ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexPartitionLabelAdjacency"
/*@
  DMPlexPartitionLabelAdjacency - Add one level of adjacent points to the partition label

  Input Parameters:
+ dm     - The DM
- label  - DMLabel assinging ranks to remote roots

  Level: developer

.seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
@*/
PetscErrorCode DMPlexPartitionLabelAdjacency(DM dm, DMLabel label)
{
  IS              rankIS,   pointIS;
  const PetscInt *ranks,   *points;
  PetscInt        numRanks, numPoints, r, p, a, adjSize;
  PetscInt       *adj = NULL;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = DMLabelGetValueIS(label, &rankIS);CHKERRQ(ierr);
  ierr = ISGetLocalSize(rankIS, &numRanks);CHKERRQ(ierr);
  ierr = ISGetIndices(rankIS, &ranks);CHKERRQ(ierr);
  for (r = 0; r < numRanks; ++r) {
    const PetscInt rank = ranks[r];

    ierr = DMLabelGetStratumIS(label, rank, &pointIS);CHKERRQ(ierr);
    ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
    ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      adjSize = PETSC_DETERMINE;
      ierr = DMPlexGetAdjacency(dm, points[p], &adjSize, &adj);CHKERRQ(ierr);
      for (a = 0; a < adjSize; ++a) {ierr = DMLabelSetValue(label, adj[a], rank);CHKERRQ(ierr);}
    }
    ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
    ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(rankIS, &ranks);CHKERRQ(ierr);
  ierr = ISDestroy(&rankIS);CHKERRQ(ierr);
  ierr = PetscFree(adj);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexPartitionLabelInvert"
/*@
  DMPlexPartitionLabelInvert - Create a partition label of remote roots from a local root label

  Input Parameters:
+ dm        - The DM
. rootLabel - DMLabel assinging ranks to local roots
. processSF - A star forest mapping into the local index on each remote rank

  Output Parameter:
- leafLabel - DMLabel assinging ranks to remote roots

  Note: The rootLabel defines a send pattern by mapping local points to remote target ranks. The
  resulting leafLabel is a receiver mapping of remote roots to their parent rank.

  Level: developer

.seealso: DMPlexPartitionLabelCreateSF, DMPlexDistribute(), DMPlexCreateOverlap
@*/
PetscErrorCode DMPlexPartitionLabelInvert(DM dm, DMLabel rootLabel, PetscSF processSF, DMLabel leafLabel)
{
  MPI_Comm           comm;
  PetscMPIInt        rank, numProcs;
  PetscInt           p, n, numNeighbors, size, l, nleaves;
  PetscSF            sfPoint;
  PetscSFNode       *rootPoints, *leafPoints;
  PetscSection       rootSection, leafSection;
  const PetscSFNode *remote;
  const PetscInt    *local, *neighbors;
  IS                 valueIS;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject) dm, &comm);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);
  ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);

  /* Convert to (point, rank) and use actual owners */
  ierr = PetscSectionCreate(comm, &rootSection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(rootSection, 0, numProcs);CHKERRQ(ierr);
  ierr = DMLabelGetValueIS(rootLabel, &valueIS);CHKERRQ(ierr);
  ierr = ISGetLocalSize(valueIS, &numNeighbors);CHKERRQ(ierr);
  ierr = ISGetIndices(valueIS, &neighbors);CHKERRQ(ierr);
  for (n = 0; n < numNeighbors; ++n) {
    PetscInt numPoints;

    ierr = DMLabelGetStratumSize(rootLabel, neighbors[n], &numPoints);CHKERRQ(ierr);
    ierr = PetscSectionAddDof(rootSection, neighbors[n], numPoints);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(rootSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(rootSection, &size);CHKERRQ(ierr);
  ierr = PetscMalloc1(size, &rootPoints);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sfPoint, NULL, &nleaves, &local, &remote);CHKERRQ(ierr);
  for (n = 0; n < numNeighbors; ++n) {
    IS              pointIS;
    const PetscInt *points;
    PetscInt        off, numPoints, p;

    ierr = PetscSectionGetOffset(rootSection, neighbors[n], &off);CHKERRQ(ierr);
    ierr = DMLabelGetStratumIS(rootLabel, neighbors[n], &pointIS);CHKERRQ(ierr);
    ierr = ISGetLocalSize(pointIS, &numPoints);CHKERRQ(ierr);
    ierr = ISGetIndices(pointIS, &points);CHKERRQ(ierr);
    for (p = 0; p < numPoints; ++p) {
      if (local) {ierr = PetscFindInt(points[p], nleaves, local, &l);CHKERRQ(ierr);}
      else       {l = -1;}
      if (l >= 0) {rootPoints[off+p] = remote[l];}
      else        {rootPoints[off+p].index = points[p]; rootPoints[off+p].rank = rank;}
    }
    ierr = ISRestoreIndices(pointIS, &points);CHKERRQ(ierr);
    ierr = ISDestroy(&pointIS);CHKERRQ(ierr);
  }
  ierr = ISRestoreIndices(valueIS, &neighbors);CHKERRQ(ierr);
  ierr = ISDestroy(&valueIS);CHKERRQ(ierr);
  /* Communicate overlap */
  ierr = PetscSectionCreate(comm, &leafSection);CHKERRQ(ierr);
  ierr = DMPlexDistributeData(dm, processSF, rootSection, MPIU_2INT, rootPoints, leafSection, (void**) &leafPoints);CHKERRQ(ierr);
  /* Filter remote contributions (ovLeafPoints) into the overlapSF */
  ierr = PetscSectionGetStorageSize(leafSection, &size);CHKERRQ(ierr);
  for (p = 0; p < size; p++) {
    ierr = DMLabelSetValue(leafLabel, leafPoints[p].index, leafPoints[p].rank);CHKERRQ(ierr);
  }
  ierr = PetscFree(rootPoints);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&rootSection);CHKERRQ(ierr);
  ierr = PetscFree(leafPoints);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&leafSection);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexPartitionLabelCreateSF"
/*@
  DMPlexPartitionLabelCreateSF - Create a star forest from a label that assigns ranks to points

  Input Parameters:
+ dm    - The DM
. label - DMLabel assinging ranks to remote roots

  Output Parameter:
- sf    - The star forest communication context encapsulating the defined mapping

  Note: The incoming label is a receiver mapping of remote points to their parent rank.

  Level: developer

.seealso: DMPlexDistribute(), DMPlexCreateOverlap
@*/
PetscErrorCode DMPlexPartitionLabelCreateSF(DM dm, DMLabel label, PetscSF *sf)
{
  PetscMPIInt    numProcs;
  PetscInt       n, idx, numRemote, p, numPoints, pStart, pEnd;
  PetscSFNode   *remotePoints;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(PetscObjectComm((PetscObject) dm), &numProcs);CHKERRQ(ierr);

  for (numRemote = 0, n = 0; n < numProcs; ++n) {
    ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
    numRemote += numPoints;
  }
  ierr = PetscMalloc1(numRemote, &remotePoints);CHKERRQ(ierr);
  for (idx = 0, n = 0; n < numProcs; ++n) {
    IS remoteRootIS;
    const PetscInt *remoteRoots;
    ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
    if (numPoints <= 0) continue;
    ierr = DMLabelGetStratumIS(label, n, &remoteRootIS);CHKERRQ(ierr);
    ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
    for (p = 0; p < numPoints; p++) {
      remotePoints[idx].index = remoteRoots[p];
      remotePoints[idx].rank = n;
      idx++;
    }
    ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
    ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
  }
  ierr = PetscSFCreate(PetscObjectComm((PetscObject) dm), sf);CHKERRQ(ierr);
  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSFSetGraph(*sf, pEnd-pStart, numRemote, NULL, PETSC_OWN_POINTER, remotePoints, PETSC_OWN_POINTER);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}