xref: /petsc/src/dm/impls/plex/plexpartition.c (revision 7de78196c56adc1717a53efbf1d173bcdf642ecd)

#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__ "DMPlexCreatePartitionerGraph"
/*@C
  DMPlexCreatePartitionerGraph - Create a CSR graph of point connections for the partitioner

  Input Parameters:
+ dm      - The mesh DM dm
- height  - Height of the strata from which to construct the graph

  Output Parameter:
+ numVertices - Number of vertices in the graph
- offsets     - Point offsets in the graph
- adjacency   - Point connectivity in the graph

  The user can control the definition of adjacency for the mesh using DMPlexGetAdjacencyUseCone() and
  DMPlexSetAdjacencyUseClosure(). They should choose the combination appropriate for the function
  representation on the mesh.

  Level: developer

.seealso: PetscPartitionerGetType(), PetscPartitionerCreate(), DMPlexSetAdjacencyUseCone(), DMPlexSetAdjacencyUseClosure()
@*/
PetscErrorCode DMPlexCreatePartitionerGraph(DM dm, PetscInt height, PetscInt *numVertices, PetscInt **offsets, PetscInt **adjacency)
{
  PetscInt       p, pStart, pEnd, a, adjSize, idx, size, nroots;
  PetscInt      *adj = NULL, *vOffsets = NULL, *graph = NULL;
  IS             cellNumbering;
  const PetscInt *cellNum;
  PetscBool      useCone, useClosure;
  PetscSection   section;
  PetscSegBuffer adjBuffer;
  PetscSF        sfPoint;
  PetscMPIInt    rank;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, height, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = DMGetPointSF(dm, &sfPoint);CHKERRQ(ierr);
  ierr = PetscSFGetGraph(sfPoint, &nroots, NULL, NULL, NULL);CHKERRQ(ierr);
  /* Build adjacency graph via a section/segbuffer */
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject) dm), &section);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(section, pStart, pEnd);CHKERRQ(ierr);
  ierr = PetscSegBufferCreate(sizeof(PetscInt),1000,&adjBuffer);CHKERRQ(ierr);
  /* Always use FVM adjacency to create partitioner graph */
  ierr = DMPlexGetAdjacencyUseCone(dm, &useCone);CHKERRQ(ierr);
  ierr = DMPlexGetAdjacencyUseClosure(dm, &useClosure);CHKERRQ(ierr);
  ierr = DMPlexSetAdjacencyUseCone(dm, PETSC_TRUE);CHKERRQ(ierr);
  ierr = DMPlexSetAdjacencyUseClosure(dm, PETSC_FALSE);CHKERRQ(ierr);
  if (nroots > 0) {
    ierr = DMPlexGetCellNumbering(dm, &cellNumbering);CHKERRQ(ierr);
    ierr = ISGetIndices(cellNumbering, &cellNum);CHKERRQ(ierr);
  }
  for (*numVertices = 0, p = pStart; p < pEnd; p++) {
    /* Skip non-owned cells in parallel (ParMetis expects no overlap) */
    if (nroots > 0) {if (cellNum[p] < 0) continue;}
    adjSize = PETSC_DETERMINE;
    ierr = DMPlexGetAdjacency(dm, p, &adjSize, &adj);CHKERRQ(ierr);
    for (a = 0; a < adjSize; ++a) {
      const PetscInt point = adj[a];
      if (point != p && pStart <= point && point < pEnd) {
        PetscInt *PETSC_RESTRICT pBuf;
        ierr = PetscSectionAddDof(section, p, 1);CHKERRQ(ierr);
        ierr = PetscSegBufferGetInts(adjBuffer, 1, &pBuf);CHKERRQ(ierr);
        *pBuf = point;
      }
    }
    (*numVertices)++;
  }
  ierr = DMPlexSetAdjacencyUseCone(dm, useCone);CHKERRQ(ierr);
  ierr = DMPlexSetAdjacencyUseClosure(dm, useClosure);CHKERRQ(ierr);
  /* Derive CSR graph from section/segbuffer */
  ierr = PetscSectionSetUp(section);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(section, &size);CHKERRQ(ierr);
  ierr = PetscMalloc1(*numVertices+1, &vOffsets);CHKERRQ(ierr);
  for (idx = 0, p = pStart; p < pEnd; p++) {
    if (nroots > 0) {if (cellNum[p] < 0) continue;}
    ierr = PetscSectionGetOffset(section, p, &(vOffsets[idx++]));CHKERRQ(ierr);
  }
  vOffsets[*numVertices] = size;
  if (offsets) *offsets = vOffsets;
  ierr = PetscSegBufferExtractAlloc(adjBuffer, &graph);CHKERRQ(ierr);
  if (nroots > 0) {
    ISLocalToGlobalMapping ltogCells;
    PetscInt n, size, *cells_arr;
    /* In parallel, apply a global cell numbering to the graph */
    ierr = ISRestoreIndices(cellNumbering, &cellNum);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingCreateIS(cellNumbering, &ltogCells);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingGetSize(ltogCells, &size);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingGetIndices(ltogCells, (const PetscInt**)&cells_arr);CHKERRQ(ierr);
    /* Convert to positive global cell numbers */
    for (n=0; n<size; n++) {if (cells_arr[n] < 0) cells_arr[n] = -(cells_arr[n]+1);}
    ierr = ISLocalToGlobalMappingRestoreIndices(ltogCells, (const PetscInt**)&cells_arr);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingApplyBlock(ltogCells, vOffsets[*numVertices], graph, graph);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingDestroy(&ltogCells);CHKERRQ(ierr);
  }
  if (adjacency) *adjacency = graph;
  /* Clean up */
  ierr = PetscSegBufferDestroy(&adjBuffer);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&section);CHKERRQ(ierr);
  ierr = PetscFree(adj);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#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 = DMPlexCreatePartitionerGraph(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 PART

  Input Parameters:
+ part     - The PetscPartitioner
. numProcs - The number of partitions
. sizes    - array of size numProcs (or NULL) providing the number of points in each partition
- points   - array of size sum(sizes) (may be NULL iff sizes is NULL) providing the partition each point belongs to

  Level: developer

  Notes:

    It is safe to free the sizes and points arrays after use in this routine.

.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

  Note: This gets a borrowed reference, so the user should not destroy this PetscPartitioner.

.seealso DMPlexDistribute(), DMPlexSetPartitioner(), 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__ "DMPlexSetPartitioner"
/*@
  DMPlexSetPartitioner - Set the mesh partitioner

  logically collective on dm and part

  Input Parameters:
+ dm - The DM
- part - The partitioner

  Level: developer

  Note: Any existing PetscPartitioner will be destroyed.

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

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(part, PETSCPARTITIONER_CLASSID, 2);
  ierr = PetscObjectReference((PetscObject)part);CHKERRQ(ierr);
  ierr = PetscPartitionerDestroy(&mesh->partitioner);CHKERRQ(ierr);
  mesh->partitioner = part;
  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, 0, 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     rank, numProcs;
  PetscInt        n, numRemote, p, numPoints, pStart, pEnd, idx = 0;
  PetscSFNode    *remotePoints;
  IS              remoteRootIS;
  const PetscInt *remoteRoots;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject) dm), &rank);CHKERRQ(ierr);
  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);
  /* Put owned points first */
  ierr = DMLabelGetStratumSize(label, rank, &numPoints);CHKERRQ(ierr);
  if (numPoints > 0) {
    ierr = DMLabelGetStratumIS(label, rank, &remoteRootIS);CHKERRQ(ierr);
    ierr = ISGetIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
    for (p = 0; p < numPoints; p++) {
      remotePoints[idx].index = remoteRoots[p];
      remotePoints[idx].rank = rank;
      idx++;
    }
    ierr = ISRestoreIndices(remoteRootIS, &remoteRoots);CHKERRQ(ierr);
    ierr = ISDestroy(&remoteRootIS);CHKERRQ(ierr);
  }
  /* Now add remote points */
  for (n = 0; n < numProcs; ++n) {
    ierr = DMLabelGetStratumSize(label, n, &numPoints);CHKERRQ(ierr);
    if (numPoints <= 0 || n == rank) 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);
}