xref: /petsc/src/dm/impls/plex/plextree.c (revision b3a4bf2af0e854253e55ab20a7ec10e7afe3fb75)

#include <petsc/private/dmpleximpl.h>   /*I      "petscdmplex.h"   I*/
#include <../src/sys/utils/hash.h>
#include <petsc/private/isimpl.h>
#include <petsc/private/petscfeimpl.h>
#include <petscsf.h>
#include <petscds.h>

/** hierarchy routines */

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetReferenceTree"
/*@
  DMPlexSetReferenceTree - set the reference tree for hierarchically non-conforming meshes.

  Not collective

  Input Parameters:
+ dm - The DMPlex object
- ref - The reference tree DMPlex object

  Level: intermediate

.seealso: DMPlexGetReferenceTree(), DMPlexCreateDefaultReferenceTree()
@*/
PetscErrorCode DMPlexSetReferenceTree(DM dm, DM ref)
{
  DM_Plex        *mesh = (DM_Plex *)dm->data;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (ref) {PetscValidHeaderSpecific(ref, DM_CLASSID, 2);}
  ierr = PetscObjectReference((PetscObject)ref);CHKERRQ(ierr);
  ierr = DMDestroy(&mesh->referenceTree);CHKERRQ(ierr);
  mesh->referenceTree = ref;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetReferenceTree"
/*@
  DMPlexGetReferenceTree - get the reference tree for hierarchically non-conforming meshes.

  Not collective

  Input Parameters:
. dm - The DMPlex object

  Output Parameters
. ref - The reference tree DMPlex object

  Level: intermediate

.seealso: DMPlexSetReferenceTree(), DMPlexCreateDefaultReferenceTree()
@*/
PetscErrorCode DMPlexGetReferenceTree(DM dm, DM *ref)
{
  DM_Plex        *mesh = (DM_Plex *)dm->data;

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

#undef __FUNCT__
#define __FUNCT__ "DMPlexReferenceTreeGetChildSymmetry_Default"
static PetscErrorCode DMPlexReferenceTreeGetChildSymmetry_Default(DM dm, PetscInt parent, PetscInt parentOrientA, PetscInt childOrientA, PetscInt childA, PetscInt parentOrientB, PetscInt *childOrientB, PetscInt *childB)
{
  PetscInt       coneSize, dStart, dEnd, dim, ABswap, oAvert, oBvert, ABswapVert;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (parentOrientA == parentOrientB) {
    if (childOrientB) *childOrientB = childOrientA;
    if (childB) *childB = childA;
    PetscFunctionReturn(0);
  }
  for (dim = 0; dim < 3; dim++) {
    ierr = DMPlexGetDepthStratum(dm,dim,&dStart,&dEnd);CHKERRQ(ierr);
    if (parent >= dStart && parent <= dEnd) {
      break;
    }
  }
  if (dim > 2) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot perform child symmetry for %d-cells",dim);
  if (!dim) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"A vertex has no children");
  if (childA < dStart || childA >= dEnd) {
    /* this is a lower-dimensional child: bootstrap */
    PetscInt size, i, sA = -1, sB, sOrientB, sConeSize;
    const PetscInt *supp, *coneA, *coneB, *oA, *oB;

    ierr = DMPlexGetSupportSize(dm,childA,&size);CHKERRQ(ierr);
    ierr = DMPlexGetSupport(dm,childA,&supp);CHKERRQ(ierr);

    /* find a point sA in supp(childA) that has the same parent */
    for (i = 0; i < size; i++) {
      PetscInt sParent;

      sA   = supp[i];
      if (sA == parent) continue;
      ierr = DMPlexGetTreeParent(dm,sA,&sParent,NULL);CHKERRQ(ierr);
      if (sParent == parent) {
        break;
      }
    }
    if (i == size) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"could not find support in children");
    /* find out which point sB is in an equivalent position to sA under
     * parentOrientB */
    ierr = DMPlexReferenceTreeGetChildSymmetry_Default(dm,parent,parentOrientA,0,sA,parentOrientB,&sOrientB,&sB);CHKERRQ(ierr);
    ierr = DMPlexGetConeSize(dm,sA,&sConeSize);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm,sA,&coneA);CHKERRQ(ierr);
    ierr = DMPlexGetCone(dm,sB,&coneB);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(dm,sA,&oA);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(dm,sB,&oB);CHKERRQ(ierr);
    /* step through the cone of sA in natural order */
    for (i = 0; i < sConeSize; i++) {
      if (coneA[i] == childA) {
        /* if childA is at position i in coneA,
         * then we want the point that is at sOrientB*i in coneB */
        PetscInt j = (sOrientB >= 0) ? ((sOrientB + i) % sConeSize) : ((sConeSize -(sOrientB+1) - i) % sConeSize);
        if (childB) *childB = coneB[j];
        if (childOrientB) {
          PetscInt oBtrue;

          ierr          = DMPlexGetConeSize(dm,childA,&coneSize);CHKERRQ(ierr);
          /* compose sOrientB and oB[j] */
          if (coneSize != 0 && coneSize != 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Expected a vertex or an edge");
          /* we may have to flip an edge */
          oBtrue        = coneSize ? ((sOrientB >= 0) ? oB[j] : -(oB[j] + 2)) : 0;
          ABswap        = DihedralSwap(coneSize,oA[i],oBtrue);CHKERRQ(ierr);
          *childOrientB = DihedralCompose(coneSize,childOrientA,ABswap);
        }
        break;
      }
    }
    if (i == sConeSize) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"support cone mismatch");
    PetscFunctionReturn(0);
  }
  /* get the cone size and symmetry swap */
  ierr   = DMPlexGetConeSize(dm,parent,&coneSize);CHKERRQ(ierr);
  ABswap = DihedralSwap(coneSize, parentOrientA, parentOrientB);
  if (dim == 2) {
    /* orientations refer to cones: we want them to refer to vertices:
     * if it's a rotation, they are the same, but if the order is reversed, a
     * permutation that puts side i first does *not* put vertex i first */
    oAvert     = (parentOrientA >= 0) ? parentOrientA : -((-parentOrientA % coneSize) + 1);
    oBvert     = (parentOrientB >= 0) ? parentOrientB : -((-parentOrientB % coneSize) + 1);
    ABswapVert = DihedralSwap(coneSize, oAvert, oBvert);
  } else {
    ABswapVert = ABswap;
  }
  if (childB) {
    /* assume that each child corresponds to a vertex, in the same order */
    PetscInt p, posA = -1, numChildren, i;
    const PetscInt *children;

    /* count which position the child is in */
    ierr = DMPlexGetTreeChildren(dm,parent,&numChildren,&children);CHKERRQ(ierr);
    for (i = 0; i < numChildren; i++) {
      p = children[i];
      if (p == childA) {
        posA = i;
        break;
      }
    }
    if (posA >= coneSize) {
      /* this is the triangle in the middle of a uniformly refined triangle: it
       * is invariant */
      if (dim != 2 || posA != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Expected a middle triangle, got something else");
      *childB = childA;
    }
    else {
      /* figure out position B by applying ABswapVert */
      PetscInt posB;

      posB = (ABswapVert >= 0) ? ((ABswapVert + posA) % coneSize) : ((coneSize -(ABswapVert + 1) - posA) % coneSize);
      if (childB) *childB = children[posB];
    }
  }
  if (childOrientB) *childOrientB = DihedralCompose(coneSize,childOrientA,ABswap);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexReferenceTreeGetChildSymmetry"
/*@
  DMPlexReferenceTreeGetChildSymmetry - Given a reference tree, transform a childid and orientation from one parent frame to another

  Input Parameters:
+ dm - the reference tree DMPlex object
. parent - the parent point
. parentOrientA - the reference orientation for describing the parent
. childOrientA - the reference orientation for describing the child
. childA - the reference childID for describing the child
- parentOrientB - the new orientation for describing the parent

  Output Parameters:
+ childOrientB - if not NULL, set to the new oreintation for describing the child
. childB - if not NULL, the new childID for describing the child

  Level: developer

.seealso: DMPlexGetReferenceTree(), DMPlexSetReferenceTree(), DMPlexSetTree()
@*/
PetscErrorCode DMPlexReferenceTreeGetChildSymmetry(DM dm, PetscInt parent, PetscInt parentOrientA, PetscInt childOrientA, PetscInt childA, PetscInt parentOrientB, PetscInt *childOrientB, PetscInt *childB)
{
  DM_Plex        *mesh = (DM_Plex *)dm->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (!mesh->getchildsymmetry) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"DMPlexReferenceTreeGetChildSymmetry not implemented");
  ierr = mesh->getchildsymmetry(dm,parent,parentOrientA,childOrientA,childA,parentOrientB,childOrientB,childB);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

static PetscErrorCode DMPlexSetTree_Internal(DM,PetscSection,PetscInt*,PetscInt*,PetscBool,PetscBool);

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateReferenceTree_Union"
PetscErrorCode DMPlexCreateReferenceTree_Union(DM K, DM Kref, const char *labelName, DM *ref)
{
  MPI_Comm       comm;
  PetscInt       dim, p, pStart, pEnd, pRefStart, pRefEnd, d, offset, parentSize, *parents, *childIDs;
  PetscInt      *permvals, *unionCones, *coneSizes, *unionOrientations, numUnionPoints, *numDimPoints, numCones, numVerts;
  DMLabel        identity, identityRef;
  PetscSection   unionSection, unionConeSection, parentSection;
  PetscScalar   *unionCoords;
  IS             perm;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  comm = PetscObjectComm((PetscObject)K);
  ierr = DMGetDimension(K, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetChart(K, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = DMGetLabel(K, labelName, &identity);CHKERRQ(ierr);
  ierr = DMGetLabel(Kref, labelName, &identityRef);CHKERRQ(ierr);
  ierr = DMPlexGetChart(Kref, &pRefStart, &pRefEnd);CHKERRQ(ierr);
  ierr = PetscSectionCreate(comm, &unionSection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(unionSection, 0, (pEnd - pStart) + (pRefEnd - pRefStart));CHKERRQ(ierr);
  /* count points that will go in the union */
  for (p = pStart; p < pEnd; p++) {
    ierr = PetscSectionSetDof(unionSection, p - pStart, 1);CHKERRQ(ierr);
  }
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt q, qSize;
    ierr = DMLabelGetValue(identityRef, p, &q);CHKERRQ(ierr);
    ierr = DMLabelGetStratumSize(identityRef, q, &qSize);CHKERRQ(ierr);
    if (qSize > 1) {
      ierr = PetscSectionSetDof(unionSection, p - pRefStart + (pEnd - pStart), 1);CHKERRQ(ierr);
    }
  }
  ierr = PetscMalloc1(pEnd - pStart + pRefEnd - pRefStart,&permvals);CHKERRQ(ierr);
  offset = 0;
  /* stratify points in the union by topological dimension */
  for (d = 0; d <= dim; d++) {
    PetscInt cStart, cEnd, c;

    ierr = DMPlexGetHeightStratum(K, d, &cStart, &cEnd);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; c++) {
      permvals[offset++] = c;
    }

    ierr = DMPlexGetHeightStratum(Kref, d, &cStart, &cEnd);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; c++) {
      permvals[offset++] = c + (pEnd - pStart);
    }
  }
  ierr = ISCreateGeneral(comm, (pEnd - pStart) + (pRefEnd - pRefStart), permvals, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);
  ierr = PetscSectionSetPermutation(unionSection,perm);CHKERRQ(ierr);
  ierr = PetscSectionSetUp(unionSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(unionSection,&numUnionPoints);CHKERRQ(ierr);
  ierr = PetscMalloc2(numUnionPoints,&coneSizes,dim+1,&numDimPoints);CHKERRQ(ierr);
  /* count dimension points */
  for (d = 0; d <= dim; d++) {
    PetscInt cStart, cOff, cOff2;
    ierr = DMPlexGetHeightStratum(K,d,&cStart,NULL);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(unionSection,cStart-pStart,&cOff);CHKERRQ(ierr);
    if (d < dim) {
      ierr = DMPlexGetHeightStratum(K,d+1,&cStart,NULL);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(unionSection,cStart-pStart,&cOff2);CHKERRQ(ierr);
    }
    else {
      cOff2 = numUnionPoints;
    }
    numDimPoints[dim - d] = cOff2 - cOff;
  }
  ierr = PetscSectionCreate(comm, &unionConeSection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(unionConeSection, 0, numUnionPoints);CHKERRQ(ierr);
  /* count the cones in the union */
  for (p = pStart; p < pEnd; p++) {
    PetscInt dof, uOff;

    ierr = DMPlexGetConeSize(K, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(unionSection, p - pStart,&uOff);CHKERRQ(ierr);
    ierr = PetscSectionSetDof(unionConeSection, uOff, dof);CHKERRQ(ierr);
    coneSizes[uOff] = dof;
  }
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt dof, uDof, uOff;

    ierr = DMPlexGetConeSize(Kref, p, &dof);CHKERRQ(ierr);
    ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
    if (uDof) {
      ierr = PetscSectionSetDof(unionConeSection, uOff, dof);CHKERRQ(ierr);
      coneSizes[uOff] = dof;
    }
  }
  ierr = PetscSectionSetUp(unionConeSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(unionConeSection,&numCones);CHKERRQ(ierr);
  ierr = PetscMalloc2(numCones,&unionCones,numCones,&unionOrientations);CHKERRQ(ierr);
  /* write the cones in the union */
  for (p = pStart; p < pEnd; p++) {
    PetscInt dof, uOff, c, cOff;
    const PetscInt *cone, *orientation;

    ierr = DMPlexGetConeSize(K, p, &dof);CHKERRQ(ierr);
    ierr = DMPlexGetCone(K, p, &cone);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(K, p, &orientation);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(unionSection, p - pStart,&uOff);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(unionConeSection,uOff,&cOff);CHKERRQ(ierr);
    for (c = 0; c < dof; c++) {
      PetscInt e, eOff;
      e                           = cone[c];
      ierr                        = PetscSectionGetOffset(unionSection, e - pStart, &eOff);CHKERRQ(ierr);
      unionCones[cOff + c]        = eOff;
      unionOrientations[cOff + c] = orientation[c];
    }
  }
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt dof, uDof, uOff, c, cOff;
    const PetscInt *cone, *orientation;

    ierr = DMPlexGetConeSize(Kref, p, &dof);CHKERRQ(ierr);
    ierr = DMPlexGetCone(Kref, p, &cone);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientation(Kref, p, &orientation);CHKERRQ(ierr);
    ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
    if (uDof) {
      ierr = PetscSectionGetOffset(unionConeSection,uOff,&cOff);CHKERRQ(ierr);
      for (c = 0; c < dof; c++) {
        PetscInt e, eOff, eDof;

        e    = cone[c];
        ierr = PetscSectionGetDof(unionSection, e - pRefStart + (pEnd - pStart),&eDof);CHKERRQ(ierr);
        if (eDof) {
          ierr = PetscSectionGetOffset(unionSection, e - pRefStart + (pEnd - pStart), &eOff);CHKERRQ(ierr);
        }
        else {
          ierr = DMLabelGetValue(identityRef, e, &e);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(unionSection, e - pStart, &eOff);CHKERRQ(ierr);
        }
        unionCones[cOff + c]        = eOff;
        unionOrientations[cOff + c] = orientation[c];
      }
    }
  }
  /* get the coordinates */
  {
    PetscInt vStart, vEnd, vRefStart, vRefEnd, v, vDof, vOff;
    PetscSection KcoordsSec, KrefCoordsSec;
    Vec      KcoordsVec, KrefCoordsVec;
    PetscScalar *Kcoords;

    DMGetCoordinateSection(K, &KcoordsSec);CHKERRQ(ierr);
    DMGetCoordinatesLocal(K, &KcoordsVec);CHKERRQ(ierr);
    DMGetCoordinateSection(Kref, &KrefCoordsSec);CHKERRQ(ierr);
    DMGetCoordinatesLocal(Kref, &KrefCoordsVec);CHKERRQ(ierr);

    numVerts = numDimPoints[0];
    ierr     = PetscMalloc1(numVerts * dim,&unionCoords);CHKERRQ(ierr);
    ierr     = DMPlexGetDepthStratum(K,0,&vStart,&vEnd);CHKERRQ(ierr);

    offset = 0;
    for (v = vStart; v < vEnd; v++) {
      ierr = PetscSectionGetOffset(unionSection,v - pStart,&vOff);CHKERRQ(ierr);
      ierr = VecGetValuesSection(KcoordsVec, KcoordsSec, v, &Kcoords);CHKERRQ(ierr);
      for (d = 0; d < dim; d++) {
        unionCoords[offset * dim + d] = Kcoords[d];
      }
      offset++;
    }
    ierr = DMPlexGetDepthStratum(Kref,0,&vRefStart,&vRefEnd);CHKERRQ(ierr);
    for (v = vRefStart; v < vRefEnd; v++) {
      ierr = PetscSectionGetDof(unionSection,v - pRefStart + (pEnd - pStart),&vDof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(unionSection,v - pRefStart + (pEnd - pStart),&vOff);CHKERRQ(ierr);
      ierr = VecGetValuesSection(KrefCoordsVec, KrefCoordsSec, v, &Kcoords);CHKERRQ(ierr);
      if (vDof) {
        for (d = 0; d < dim; d++) {
          unionCoords[offset * dim + d] = Kcoords[d];
        }
        offset++;
      }
    }
  }
  ierr = DMCreate(comm,ref);CHKERRQ(ierr);
  ierr = DMSetType(*ref,DMPLEX);CHKERRQ(ierr);
  ierr = DMSetDimension(*ref,dim);CHKERRQ(ierr);
  ierr = DMPlexCreateFromDAG(*ref,dim,numDimPoints,coneSizes,unionCones,unionOrientations,unionCoords);CHKERRQ(ierr);
  /* set the tree */
  ierr = PetscSectionCreate(comm,&parentSection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(parentSection,0,numUnionPoints);CHKERRQ(ierr);
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt uDof, uOff;

    ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
    if (uDof) {
      PetscSectionSetDof(parentSection,uOff,1);CHKERRQ(ierr);
    }
  }
  ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(parentSection,&parentSize);CHKERRQ(ierr);
  ierr = PetscMalloc2(parentSize,&parents,parentSize,&childIDs);CHKERRQ(ierr);
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt uDof, uOff;

    ierr = PetscSectionGetDof(unionSection, p - pRefStart + (pEnd - pStart),&uDof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(unionSection, p - pRefStart + (pEnd - pStart),&uOff);CHKERRQ(ierr);
    if (uDof) {
      PetscInt pOff, parent, parentU;
      PetscSectionGetOffset(parentSection,uOff,&pOff);CHKERRQ(ierr);
      DMLabelGetValue(identityRef,p,&parent);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(unionSection, parent - pStart,&parentU);CHKERRQ(ierr);
      parents[pOff] = parentU;
      childIDs[pOff] = uOff;
    }
  }
  ierr = DMPlexSetTree_Internal(*ref,parentSection,parents,childIDs,PETSC_TRUE,PETSC_FALSE);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);
  ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);

  /* clean up */
  ierr = PetscSectionDestroy(&unionSection);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&unionConeSection);CHKERRQ(ierr);
  ierr = ISDestroy(&perm);CHKERRQ(ierr);
  ierr = PetscFree(unionCoords);CHKERRQ(ierr);
  ierr = PetscFree2(unionCones,unionOrientations);CHKERRQ(ierr);
  ierr = PetscFree2(coneSizes,numDimPoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateDefaultReferenceTree"
/*@
  DMPlexCreateDefaultReferenceTree - create a reference tree for isotropic hierarchical mesh refinement.

  Collective on comm

  Input Parameters:
+ comm    - the MPI communicator
. dim     - the spatial dimension
- simplex - Flag for simplex, otherwise use a tensor-product cell

  Output Parameters:
. ref     - the reference tree DMPlex object

  Level: intermediate

.keywords: reference cell
.seealso: DMPlexSetReferenceTree(), DMPlexGetReferenceTree()
@*/
PetscErrorCode DMPlexCreateDefaultReferenceTree(MPI_Comm comm, PetscInt dim, PetscBool simplex, DM *ref)
{
  DM_Plex       *mesh;
  DM             K, Kref;
  PetscInt       p, pStart, pEnd;
  DMLabel        identity;
  PetscErrorCode ierr;

  PetscFunctionBegin;
#if 1
  comm = PETSC_COMM_SELF;
#endif
  /* create a reference element */
  ierr = DMPlexCreateReferenceCell(comm, dim, simplex, &K);CHKERRQ(ierr);
  ierr = DMCreateLabel(K, "identity");CHKERRQ(ierr);
  ierr = DMGetLabel(K, "identity", &identity);CHKERRQ(ierr);
  ierr = DMPlexGetChart(K, &pStart, &pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; p++) {
    ierr = DMLabelSetValue(identity, p, p);CHKERRQ(ierr);
  }
  /* refine it */
  ierr = DMRefine(K,comm,&Kref);CHKERRQ(ierr);

  /* the reference tree is the union of these two, without duplicating
   * points that appear in both */
  ierr = DMPlexCreateReferenceTree_Union(K, Kref, "identity", ref);CHKERRQ(ierr);
  mesh = (DM_Plex *) (*ref)->data;
  mesh->getchildsymmetry = DMPlexReferenceTreeGetChildSymmetry_Default;
  ierr = DMDestroy(&K);CHKERRQ(ierr);
  ierr = DMDestroy(&Kref);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexTreeSymmetrize"
static PetscErrorCode DMPlexTreeSymmetrize(DM dm)
{
  DM_Plex        *mesh = (DM_Plex *)dm->data;
  PetscSection   childSec, pSec;
  PetscInt       p, pSize, cSize, parMax = PETSC_MIN_INT, parMin = PETSC_MAX_INT;
  PetscInt       *offsets, *children, pStart, pEnd;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = PetscSectionDestroy(&mesh->childSection);CHKERRQ(ierr);
  ierr = PetscFree(mesh->children);CHKERRQ(ierr);
  pSec = mesh->parentSection;
  if (!pSec) PetscFunctionReturn(0);
  ierr = PetscSectionGetStorageSize(pSec,&pSize);CHKERRQ(ierr);
  for (p = 0; p < pSize; p++) {
    PetscInt par = mesh->parents[p];

    parMax = PetscMax(parMax,par+1);
    parMin = PetscMin(parMin,par);
  }
  if (parMin > parMax) {
    parMin = -1;
    parMax = -1;
  }
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)pSec),&childSec);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(childSec,parMin,parMax);CHKERRQ(ierr);
  for (p = 0; p < pSize; p++) {
    PetscInt par = mesh->parents[p];

    ierr = PetscSectionAddDof(childSec,par,1);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(childSec);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(childSec,&cSize);CHKERRQ(ierr);
  ierr = PetscMalloc1(cSize,&children);CHKERRQ(ierr);
  ierr = PetscCalloc1(parMax-parMin,&offsets);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(pSec,&pStart,&pEnd);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; p++) {
    PetscInt dof, off, i;

    ierr = PetscSectionGetDof(pSec,p,&dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(pSec,p,&off);CHKERRQ(ierr);
    for (i = 0; i < dof; i++) {
      PetscInt par = mesh->parents[off + i], cOff;

      ierr = PetscSectionGetOffset(childSec,par,&cOff);CHKERRQ(ierr);
      children[cOff + offsets[par-parMin]++] = p;
    }
  }
  mesh->childSection = childSec;
  mesh->children = children;
  ierr = PetscFree(offsets);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "AnchorsFlatten"
static PetscErrorCode AnchorsFlatten (PetscSection section, IS is, PetscSection *sectionNew, IS *isNew)
{
  PetscInt       pStart, pEnd, size, sizeNew, i, p, *valsNew = NULL;
  const PetscInt *vals;
  PetscSection   secNew;
  PetscBool      anyNew, globalAnyNew;
  PetscBool      compress;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSectionGetChart(section,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = ISGetLocalSize(is,&size);CHKERRQ(ierr);
  ierr = ISGetIndices(is,&vals);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),&secNew);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(secNew,pStart,pEnd);CHKERRQ(ierr);
  for (i = 0; i < size; i++) {
    PetscInt dof;

    p = vals[i];
    if (p < pStart || p >= pEnd) continue;
    ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
    if (dof) break;
  }
  if (i == size) {
    ierr     = PetscSectionSetUp(secNew);CHKERRQ(ierr);
    anyNew   = PETSC_FALSE;
    compress = PETSC_FALSE;
    sizeNew  = 0;
  }
  else {
    anyNew = PETSC_TRUE;
    for (p = pStart; p < pEnd; p++) {
      PetscInt dof, off;

      ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
      for (i = 0; i < dof; i++) {
        PetscInt q = vals[off + i], qDof = 0;

        if (q >= pStart && q < pEnd) {
          ierr = PetscSectionGetDof(section, q, &qDof);CHKERRQ(ierr);
        }
        if (qDof) {
          ierr = PetscSectionAddDof(secNew, p, qDof);CHKERRQ(ierr);
        }
        else {
          ierr = PetscSectionAddDof(secNew, p, 1);CHKERRQ(ierr);
        }
      }
    }
    ierr = PetscSectionSetUp(secNew);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(secNew,&sizeNew);CHKERRQ(ierr);
    ierr = PetscMalloc1(sizeNew,&valsNew);CHKERRQ(ierr);
    compress = PETSC_FALSE;
    for (p = pStart; p < pEnd; p++) {
      PetscInt dof, off, count, offNew, dofNew;

      ierr  = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
      ierr  = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
      ierr  = PetscSectionGetDof(secNew, p, &dofNew);CHKERRQ(ierr);
      ierr  = PetscSectionGetOffset(secNew, p, &offNew);CHKERRQ(ierr);
      count = 0;
      for (i = 0; i < dof; i++) {
        PetscInt q = vals[off + i], qDof = 0, qOff = 0, j;

        if (q >= pStart && q < pEnd) {
          ierr = PetscSectionGetDof(section, q, &qDof);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(section, q, &qOff);CHKERRQ(ierr);
        }
        if (qDof) {
          PetscInt oldCount = count;

          for (j = 0; j < qDof; j++) {
            PetscInt k, r = vals[qOff + j];

            for (k = 0; k < oldCount; k++) {
              if (valsNew[offNew + k] == r) {
                break;
              }
            }
            if (k == oldCount) {
              valsNew[offNew + count++] = r;
            }
          }
        }
        else {
          PetscInt k, oldCount = count;

          for (k = 0; k < oldCount; k++) {
            if (valsNew[offNew + k] == q) {
              break;
            }
          }
          if (k == oldCount) {
            valsNew[offNew + count++] = q;
          }
        }
      }
      if (count < dofNew) {
        ierr = PetscSectionSetDof(secNew, p, count);CHKERRQ(ierr);
        compress = PETSC_TRUE;
      }
    }
  }
  ierr = ISRestoreIndices(is,&vals);CHKERRQ(ierr);
  ierr = MPIU_Allreduce(&anyNew,&globalAnyNew,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)secNew));CHKERRQ(ierr);
  if (!globalAnyNew) {
    ierr = PetscSectionDestroy(&secNew);CHKERRQ(ierr);
    *sectionNew = NULL;
    *isNew = NULL;
  }
  else {
    PetscBool globalCompress;

    ierr = MPIU_Allreduce(&compress,&globalCompress,1,MPIU_BOOL,MPI_LOR,PetscObjectComm((PetscObject)secNew));CHKERRQ(ierr);
    if (compress) {
      PetscSection secComp;
      PetscInt *valsComp = NULL;

      ierr = PetscSectionCreate(PetscObjectComm((PetscObject)section),&secComp);CHKERRQ(ierr);
      ierr = PetscSectionSetChart(secComp,pStart,pEnd);CHKERRQ(ierr);
      for (p = pStart; p < pEnd; p++) {
        PetscInt dof;

        ierr = PetscSectionGetDof(secNew, p, &dof);CHKERRQ(ierr);
        ierr = PetscSectionSetDof(secComp, p, dof);CHKERRQ(ierr);
      }
      ierr = PetscSectionSetUp(secComp);CHKERRQ(ierr);
      ierr = PetscSectionGetStorageSize(secComp,&sizeNew);CHKERRQ(ierr);
      ierr = PetscMalloc1(sizeNew,&valsComp);CHKERRQ(ierr);
      for (p = pStart; p < pEnd; p++) {
        PetscInt dof, off, offNew, j;

        ierr = PetscSectionGetDof(secNew, p, &dof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(secNew, p, &off);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(secComp, p, &offNew);CHKERRQ(ierr);
        for (j = 0; j < dof; j++) {
          valsComp[offNew + j] = valsNew[off + j];
        }
      }
      ierr    = PetscSectionDestroy(&secNew);CHKERRQ(ierr);
      secNew  = secComp;
      ierr    = PetscFree(valsNew);CHKERRQ(ierr);
      valsNew = valsComp;
    }
    ierr = ISCreateGeneral(PetscObjectComm((PetscObject)is),sizeNew,valsNew,PETSC_OWN_POINTER,isNew);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexCreateAnchors_Tree"
static PetscErrorCode DMPlexCreateAnchors_Tree(DM dm)
{
  PetscInt       p, pStart, pEnd, *anchors, size;
  PetscInt       aMin = PETSC_MAX_INT, aMax = PETSC_MIN_INT;
  PetscSection   aSec;
  DMLabel        canonLabel;
  IS             aIS;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = DMGetLabel(dm,"canonical",&canonLabel);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; p++) {
    PetscInt parent;

    if (canonLabel) {
      PetscInt canon;

      ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
      if (p != canon) continue;
    }
    ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
    if (parent != p) {
      aMin = PetscMin(aMin,p);
      aMax = PetscMax(aMax,p+1);
    }
  }
  if (aMin > aMax) {
    aMin = -1;
    aMax = -1;
  }
  ierr = PetscSectionCreate(PETSC_COMM_SELF,&aSec);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(aSec,aMin,aMax);CHKERRQ(ierr);
  for (p = aMin; p < aMax; p++) {
    PetscInt parent, ancestor = p;

    if (canonLabel) {
      PetscInt canon;

      ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
      if (p != canon) continue;
    }
    ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
    while (parent != ancestor) {
      ancestor = parent;
      ierr     = DMPlexGetTreeParent(dm,ancestor,&parent,NULL);CHKERRQ(ierr);
    }
    if (ancestor != p) {
      PetscInt closureSize, *closure = NULL;

      ierr = DMPlexGetTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      ierr = PetscSectionSetDof(aSec,p,closureSize);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
    }
  }
  ierr = PetscSectionSetUp(aSec);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(aSec,&size);CHKERRQ(ierr);
  ierr = PetscMalloc1(size,&anchors);CHKERRQ(ierr);
  for (p = aMin; p < aMax; p++) {
    PetscInt parent, ancestor = p;

    if (canonLabel) {
      PetscInt canon;

      ierr = DMLabelGetValue(canonLabel,p,&canon);CHKERRQ(ierr);
      if (p != canon) continue;
    }
    ierr = DMPlexGetTreeParent(dm,p,&parent,NULL);CHKERRQ(ierr);
    while (parent != ancestor) {
      ancestor = parent;
      ierr     = DMPlexGetTreeParent(dm,ancestor,&parent,NULL);CHKERRQ(ierr);
    }
    if (ancestor != p) {
      PetscInt j, closureSize, *closure = NULL, aOff;

      ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);

      ierr = DMPlexGetTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      for (j = 0; j < closureSize; j++) {
        anchors[aOff + j] = closure[2*j];
      }
      ierr = DMPlexRestoreTransitiveClosure(dm,ancestor,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
    }
  }
  ierr = ISCreateGeneral(PETSC_COMM_SELF,size,anchors,PETSC_OWN_POINTER,&aIS);CHKERRQ(ierr);
  {
    PetscSection aSecNew = aSec;
    IS           aISNew  = aIS;

    ierr = PetscObjectReference((PetscObject)aSec);CHKERRQ(ierr);
    ierr = PetscObjectReference((PetscObject)aIS);CHKERRQ(ierr);
    while (aSecNew) {
      ierr    = PetscSectionDestroy(&aSec);CHKERRQ(ierr);
      ierr    = ISDestroy(&aIS);CHKERRQ(ierr);
      aSec    = aSecNew;
      aIS     = aISNew;
      aSecNew = NULL;
      aISNew  = NULL;
      ierr    = AnchorsFlatten(aSec,aIS,&aSecNew,&aISNew);CHKERRQ(ierr);
    }
  }
  ierr = DMPlexSetAnchors(dm,aSec,aIS);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&aSec);CHKERRQ(ierr);
  ierr = ISDestroy(&aIS);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetTrueSupportSize"
static PetscErrorCode DMPlexGetTrueSupportSize(DM dm,PetscInt p,PetscInt *dof,PetscInt *numTrueSupp)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (numTrueSupp[p] == -1) {
    PetscInt i, alldof;
    const PetscInt *supp;
    PetscInt count = 0;

    ierr = DMPlexGetSupportSize(dm,p,&alldof);CHKERRQ(ierr);
    ierr = DMPlexGetSupport(dm,p,&supp);CHKERRQ(ierr);
    for (i = 0; i < alldof; i++) {
      PetscInt q = supp[i], numCones, j;
      const PetscInt *cone;

      ierr = DMPlexGetConeSize(dm,q,&numCones);CHKERRQ(ierr);
      ierr = DMPlexGetCone(dm,q,&cone);CHKERRQ(ierr);
      for (j = 0; j < numCones; j++) {
        if (cone[j] == p) break;
      }
      if (j < numCones) count++;
    }
    numTrueSupp[p] = count;
  }
  *dof = numTrueSupp[p];
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexTreeExchangeSupports"
static PetscErrorCode DMPlexTreeExchangeSupports(DM dm)
{
  DM_Plex *mesh = (DM_Plex *)dm->data;
  PetscSection newSupportSection;
  PetscInt newSize, *newSupports, pStart, pEnd, p, d, depth;
  PetscInt *numTrueSupp;
  PetscInt *offsets;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  /* symmetrize the hierarchy */
  ierr = DMPlexGetDepth(dm,&depth);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)(mesh->supportSection)),&newSupportSection);CHKERRQ(ierr);
  ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(newSupportSection,pStart,pEnd);CHKERRQ(ierr);
  ierr = PetscCalloc1(pEnd,&offsets);CHKERRQ(ierr);
  ierr = PetscMalloc1(pEnd,&numTrueSupp);CHKERRQ(ierr);
  for (p = 0; p < pEnd; p++) numTrueSupp[p] = -1;
  /* if a point is in the (true) support of q, it should be in the support of
   * parent(q) */
  for (d = 0; d <= depth; d++) {
    ierr = DMPlexGetHeightStratum(dm,d,&pStart,&pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      PetscInt dof, q, qdof, parent;

      ierr = DMPlexGetTrueSupportSize(dm,p,&dof,numTrueSupp);CHKERRQ(ierr);
      ierr = PetscSectionAddDof(newSupportSection, p, dof);CHKERRQ(ierr);
      q    = p;
      ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
      while (parent != q && parent >= pStart && parent < pEnd) {
        q = parent;

        ierr = DMPlexGetTrueSupportSize(dm,q,&qdof,numTrueSupp);CHKERRQ(ierr);
        ierr = PetscSectionAddDof(newSupportSection,p,qdof);CHKERRQ(ierr);
        ierr = PetscSectionAddDof(newSupportSection,q,dof);CHKERRQ(ierr);
        ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
      }
    }
  }
  ierr = PetscSectionSetUp(newSupportSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(newSupportSection,&newSize);CHKERRQ(ierr);
  ierr = PetscMalloc1(newSize,&newSupports);CHKERRQ(ierr);
  for (d = 0; d <= depth; d++) {
    ierr = DMPlexGetHeightStratum(dm,d,&pStart,&pEnd);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; p++) {
      PetscInt dof, off, q, qdof, qoff, newDof, newOff, newqOff, i, parent;

      ierr = PetscSectionGetDof(mesh->supportSection, p, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(mesh->supportSection, p, &off);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(newSupportSection, p, &newDof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(newSupportSection, p, &newOff);CHKERRQ(ierr);
      for (i = 0; i < dof; i++) {
        PetscInt numCones, j;
        const PetscInt *cone;
        PetscInt q = mesh->supports[off + i];

        ierr = DMPlexGetConeSize(dm,q,&numCones);CHKERRQ(ierr);
        ierr = DMPlexGetCone(dm,q,&cone);CHKERRQ(ierr);
        for (j = 0; j < numCones; j++) {
          if (cone[j] == p) break;
        }
        if (j < numCones) newSupports[newOff+offsets[p]++] = q;
      }
      mesh->maxSupportSize = PetscMax(mesh->maxSupportSize,newDof);

      q    = p;
      ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
      while (parent != q && parent >= pStart && parent < pEnd) {
        q = parent;
        ierr = PetscSectionGetDof(mesh->supportSection, q, &qdof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(mesh->supportSection, q, &qoff);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(newSupportSection, q, &newqOff);CHKERRQ(ierr);
        for (i = 0; i < qdof; i++) {
          PetscInt numCones, j;
          const PetscInt *cone;
          PetscInt r = mesh->supports[qoff + i];

          ierr = DMPlexGetConeSize(dm,r,&numCones);CHKERRQ(ierr);
          ierr = DMPlexGetCone(dm,r,&cone);CHKERRQ(ierr);
          for (j = 0; j < numCones; j++) {
            if (cone[j] == q) break;
          }
          if (j < numCones) newSupports[newOff+offsets[p]++] = r;
        }
        for (i = 0; i < dof; i++) {
          PetscInt numCones, j;
          const PetscInt *cone;
          PetscInt r = mesh->supports[off + i];

          ierr = DMPlexGetConeSize(dm,r,&numCones);CHKERRQ(ierr);
          ierr = DMPlexGetCone(dm,r,&cone);CHKERRQ(ierr);
          for (j = 0; j < numCones; j++) {
            if (cone[j] == p) break;
          }
          if (j < numCones) newSupports[newqOff+offsets[q]++] = r;
        }
        ierr = DMPlexGetTreeParent(dm,q,&parent,NULL);CHKERRQ(ierr);
      }
    }
  }
  ierr = PetscSectionDestroy(&mesh->supportSection);CHKERRQ(ierr);
  mesh->supportSection = newSupportSection;
  ierr = PetscFree(mesh->supports);CHKERRQ(ierr);
  mesh->supports = newSupports;
  ierr = PetscFree(offsets);CHKERRQ(ierr);
  ierr = PetscFree(numTrueSupp);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_Direct(DM,PetscSection,PetscSection,Mat);
static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_FromReference(DM,PetscSection,PetscSection,Mat);

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetTree_Internal"
static PetscErrorCode DMPlexSetTree_Internal(DM dm, PetscSection parentSection, PetscInt *parents, PetscInt *childIDs, PetscBool computeCanonical, PetscBool exchangeSupports)
{
  DM_Plex       *mesh = (DM_Plex *)dm->data;
  DM             refTree;
  PetscInt       size;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  PetscValidHeaderSpecific(parentSection, PETSC_SECTION_CLASSID, 2);
  ierr = PetscObjectReference((PetscObject)parentSection);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&mesh->parentSection);CHKERRQ(ierr);
  mesh->parentSection = parentSection;
  ierr = PetscSectionGetStorageSize(parentSection,&size);CHKERRQ(ierr);
  if (parents != mesh->parents) {
    ierr = PetscFree(mesh->parents);CHKERRQ(ierr);
    ierr = PetscMalloc1(size,&mesh->parents);CHKERRQ(ierr);
    ierr = PetscMemcpy(mesh->parents, parents, size * sizeof(*parents));CHKERRQ(ierr);
  }
  if (childIDs != mesh->childIDs) {
    ierr = PetscFree(mesh->childIDs);CHKERRQ(ierr);
    ierr = PetscMalloc1(size,&mesh->childIDs);CHKERRQ(ierr);
    ierr = PetscMemcpy(mesh->childIDs, childIDs, size * sizeof(*childIDs));CHKERRQ(ierr);
  }
  ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
  if (refTree) {
    DMLabel canonLabel;

    ierr = DMGetLabel(refTree,"canonical",&canonLabel);CHKERRQ(ierr);
    if (canonLabel) {
      PetscInt i;

      for (i = 0; i < size; i++) {
        PetscInt canon;
        ierr = DMLabelGetValue(canonLabel, mesh->childIDs[i], &canon);CHKERRQ(ierr);
        if (canon >= 0) {
          mesh->childIDs[i] = canon;
        }
      }
    }
    mesh->computeanchormatrix = DMPlexComputeAnchorMatrix_Tree_FromReference;
  }
  else {
    mesh->computeanchormatrix = DMPlexComputeAnchorMatrix_Tree_Direct;
  }
  ierr = DMPlexTreeSymmetrize(dm);CHKERRQ(ierr);
  if (computeCanonical) {
    PetscInt d, dim;

    /* add the canonical label */
    ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
    ierr = DMCreateLabel(dm,"canonical");CHKERRQ(ierr);
    for (d = 0; d <= dim; d++) {
      PetscInt p, dStart, dEnd, canon = -1, cNumChildren;
      const PetscInt *cChildren;

      ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
      for (p = dStart; p < dEnd; p++) {
        ierr = DMPlexGetTreeChildren(dm,p,&cNumChildren,&cChildren);CHKERRQ(ierr);
        if (cNumChildren) {
          canon = p;
          break;
        }
      }
      if (canon == -1) continue;
      for (p = dStart; p < dEnd; p++) {
        PetscInt numChildren, i;
        const PetscInt *children;

        ierr = DMPlexGetTreeChildren(dm,p,&numChildren,&children);CHKERRQ(ierr);
        if (numChildren) {
          if (numChildren != cNumChildren) SETERRQ2(PetscObjectComm((PetscObject)dm),PETSC_ERR_PLIB,"All parent points in a stratum should have the same number of children: %d != %d", numChildren, cNumChildren);
          ierr = DMSetLabelValue(dm,"canonical",p,canon);CHKERRQ(ierr);
          for (i = 0; i < numChildren; i++) {
            ierr = DMSetLabelValue(dm,"canonical",children[i],cChildren[i]);CHKERRQ(ierr);
          }
        }
      }
    }
  }
  if (exchangeSupports) {
    ierr = DMPlexTreeExchangeSupports(dm);CHKERRQ(ierr);
  }
  mesh->createanchors = DMPlexCreateAnchors_Tree;
  /* reset anchors */
  ierr = DMPlexSetAnchors(dm,NULL,NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexSetTree"
/*@
  DMPlexSetTree - set the tree that describes the hierarchy of non-conforming mesh points.  This routine also creates
  the point-to-point constraints determined by the tree: a point is constained to the points in the closure of its
  tree root.

  Collective on dm

  Input Parameters:
+ dm - the DMPlex object
. parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
                  offset indexes the parent and childID list; the reference count of parentSection is incremented
. parents - a list of the point parents; copied, can be destroyed
- childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
             the child corresponds to the point in the reference tree with index childIDs; copied, can be destroyed

  Level: intermediate

.seealso: DMPlexGetTree(), DMPlexSetReferenceTree(), DMPlexSetAnchors(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
@*/
PetscErrorCode DMPlexSetTree(DM dm, PetscSection parentSection, PetscInt parents[], PetscInt childIDs[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexSetTree_Internal(dm,parentSection,parents,childIDs,PETSC_FALSE,PETSC_TRUE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetTree"
/*@
  DMPlexGetTree - get the tree that describes the hierarchy of non-conforming mesh points.
  Collective on dm

  Input Parameters:
. dm - the DMPlex object

  Output Parameters:
+ parentSection - a section describing the tree: a point has a parent if it has 1 dof in the section; the section
                  offset indexes the parent and childID list
. parents - a list of the point parents
. childIDs - identifies the relationship of the child point to the parent point; if there is a reference tree, then
             the child corresponds to the point in the reference tree with index childID
. childSection - the inverse of the parent section
- children - a list of the point children

  Level: intermediate

.seealso: DMPlexSetTree(), DMPlexSetReferenceTree(), DMPlexSetAnchors(), DMPlexGetTreeParent(), DMPlexGetTreeChildren()
@*/
PetscErrorCode DMPlexGetTree(DM dm, PetscSection *parentSection, PetscInt *parents[], PetscInt *childIDs[], PetscSection *childSection, PetscInt *children[])
{
  DM_Plex        *mesh = (DM_Plex *)dm->data;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  if (parentSection) *parentSection = mesh->parentSection;
  if (parents)       *parents       = mesh->parents;
  if (childIDs)      *childIDs      = mesh->childIDs;
  if (childSection)  *childSection  = mesh->childSection;
  if (children)      *children      = mesh->children;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetTreeParent"
/*@
  DMPlexGetTreeParent - get the parent of a point in the tree describing the point hierarchy (not the Sieve DAG)

  Input Parameters:
+ dm - the DMPlex object
- point - the query point

  Output Parameters:
+ parent - if not NULL, set to the parent of the point, or the point itself if the point does not have a parent
- childID - if not NULL, set to the child ID of the point with respect to its parent, or 0 if the point
            does not have a parent

  Level: intermediate

.seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeChildren()
@*/
PetscErrorCode DMPlexGetTreeParent(DM dm, PetscInt point, PetscInt *parent, PetscInt *childID)
{
  DM_Plex       *mesh = (DM_Plex *)dm->data;
  PetscSection   pSec;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  pSec = mesh->parentSection;
  if (pSec && point >= pSec->pStart && point < pSec->pEnd) {
    PetscInt dof;

    ierr = PetscSectionGetDof (pSec, point, &dof);CHKERRQ(ierr);
    if (dof) {
      PetscInt off;

      ierr = PetscSectionGetOffset (pSec, point, &off);CHKERRQ(ierr);
      if (parent)  *parent = mesh->parents[off];
      if (childID) *childID = mesh->childIDs[off];
      PetscFunctionReturn(0);
    }
  }
  if (parent) {
    *parent = point;
  }
  if (childID) {
    *childID = 0;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexGetTreeChildren"
/*@C
  DMPlexGetTreeChildren - get the children of a point in the tree describing the point hierarchy (not the Sieve DAG)

  Input Parameters:
+ dm - the DMPlex object
- point - the query point

  Output Parameters:
+ numChildren - if not NULL, set to the number of children
- children - if not NULL, set to a list children, or set to NULL if the point has no children

  Level: intermediate

  Fortran Notes:
  Since it returns an array, this routine is only available in Fortran 90, and you must
  include petsc.h90 in your code.

.seealso: DMPlexSetTree(), DMPlexGetTree(), DMPlexGetTreeParent()
@*/
PetscErrorCode DMPlexGetTreeChildren(DM dm, PetscInt point, PetscInt *numChildren, const PetscInt *children[])
{
  DM_Plex       *mesh = (DM_Plex *)dm->data;
  PetscSection   childSec;
  PetscInt       dof = 0;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  childSec = mesh->childSection;
  if (childSec && point >= childSec->pStart && point < childSec->pEnd) {
    ierr = PetscSectionGetDof (childSec, point, &dof);CHKERRQ(ierr);
  }
  if (numChildren) *numChildren = dof;
  if (children) {
    if (dof) {
      PetscInt off;

      ierr = PetscSectionGetOffset (childSec, point, &off);CHKERRQ(ierr);
      *children = &mesh->children[off];
    }
    else {
      *children = NULL;
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "EvaluateBasis"
static PetscErrorCode EvaluateBasis(PetscSpace space, PetscInt nFunctionals, PetscInt nPoints, const PetscInt *pointsPerFn, const PetscReal *points, const PetscReal *weights, PetscReal *work, Mat basisAtPoints)
{
  PetscInt       i, j, k, offset, qPoints;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscSpaceEvaluate(space,nPoints,points,work,NULL,NULL);CHKERRQ(ierr);
  for (i = 0, offset = 0; i < nFunctionals; i++) {
    qPoints = pointsPerFn[i];
    for (j = 0; j < nFunctionals; j++) {
      PetscScalar val = 0.;

      for (k = 0; k < qPoints; k++) {
        val += work[(offset + k) * nFunctionals + j] * weights[k];
      }
      ierr = MatSetValue(basisAtPoints,j,i,val,INSERT_VALUES);CHKERRQ(ierr);
    }
    offset += qPoints;
  }
  ierr = MatAssemblyBegin(basisAtPoints,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(basisAtPoints,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeAnchorMatrix_Tree_Direct"
static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_Direct(DM dm, PetscSection section, PetscSection cSec, Mat cMat)
{
  PetscDS        ds;
  PetscInt       spdim;
  PetscInt       numFields, f, c, cStart, cEnd, pStart, pEnd, conStart, conEnd;
  const PetscInt *anchors;
  PetscSection   aSec;
  PetscReal      *v0, *v0parent, *vtmp, *J, *Jparent, *invJparent, detJ, detJparent;
  IS             aIS;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm,0,&cStart,&cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetAnchors(dm,&aSec,&aIS);CHKERRQ(ierr);
  ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(cSec,&conStart,&conEnd);CHKERRQ(ierr);
  ierr = DMGetDimension(dm,&spdim);CHKERRQ(ierr);
  ierr = PetscMalloc6(spdim,&v0,spdim,&v0parent,spdim,&vtmp,spdim*spdim,&J,spdim*spdim,&Jparent,spdim*spdim,&invJparent);CHKERRQ(ierr);

  for (f = 0; f < numFields; f++) {
    PetscObject disc;
    PetscClassId id;
    PetscSpace     bspace;
    PetscDualSpace dspace;
    PetscInt i, j, k, nPoints, offset;
    PetscInt fSize, fComp;
    PetscReal *weights, *pointsRef, *pointsReal, *work;
    PetscInt  *sizes;
    Mat Amat, Bmat, Xmat;

    ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
    ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
    if (id == PETSCFE_CLASSID) {
      PetscFE fe = (PetscFE) disc;

      ierr = PetscFEGetBasisSpace(fe,&bspace);CHKERRQ(ierr);
      ierr = PetscFEGetDualSpace(fe,&dspace);CHKERRQ(ierr);
      ierr = PetscDualSpaceGetDimension(dspace,&fSize);CHKERRQ(ierr);
      ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
    }
    else if (id == PETSCFV_CLASSID) {
      PetscFV fv = (PetscFV) disc;

      ierr = PetscSpaceCreate(PetscObjectComm((PetscObject)fv),&bspace);CHKERRQ(ierr);
      ierr = PetscSpaceSetType(bspace,PETSCSPACEPOLYNOMIAL);CHKERRQ(ierr);
      ierr = PetscSpaceSetOrder(bspace,0);CHKERRQ(ierr);
      ierr = PetscSpacePolynomialSetNumVariables(bspace,spdim);CHKERRQ(ierr);
      ierr = PetscSpaceSetUp(bspace);CHKERRQ(ierr);
      ierr = PetscFVGetDualSpace(fv,&dspace);CHKERRQ(ierr);
      ierr = PetscDualSpaceGetDimension(dspace,&fSize);CHKERRQ(ierr);
      ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
    }
    else SETERRQ1(PetscObjectComm(disc),PETSC_ERR_ARG_UNKNOWN_TYPE, "PetscDS discretization id %d not recognized.", id);

    ierr = MatCreate(PETSC_COMM_SELF,&Amat);CHKERRQ(ierr);
    ierr = MatSetSizes(Amat,fSize,fSize,fSize,fSize);CHKERRQ(ierr);
    ierr = MatSetType(Amat,MATSEQDENSE);CHKERRQ(ierr);
    ierr = MatSetUp(Amat);CHKERRQ(ierr);
    ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Bmat);CHKERRQ(ierr);
    ierr = MatDuplicate(Amat,MAT_DO_NOT_COPY_VALUES,&Xmat);CHKERRQ(ierr);
    nPoints = 0;
    for (i = 0; i < fSize; i++) {
      PetscInt        qPoints;
      PetscQuadrature quad;

      ierr = PetscDualSpaceGetFunctional(dspace,i,&quad);CHKERRQ(ierr);
      ierr = PetscQuadratureGetData(quad,NULL,&qPoints,NULL,NULL);CHKERRQ(ierr);
      nPoints += qPoints;
    }
    ierr = PetscMalloc5(fSize,&sizes,nPoints,&weights,spdim*nPoints,&pointsRef,spdim*nPoints,&pointsReal,fSize*nPoints,&work);CHKERRQ(ierr);
    offset = 0;
    for (i = 0; i < fSize; i++) {
      PetscInt        qPoints;
      const PetscReal    *p, *w;
      PetscQuadrature quad;

      ierr = PetscDualSpaceGetFunctional(dspace,i,&quad);CHKERRQ(ierr);
      ierr = PetscQuadratureGetData(quad,NULL,&qPoints,&p,&w);CHKERRQ(ierr);
      ierr = PetscMemcpy(weights+offset,w,qPoints*sizeof(*w));CHKERRQ(ierr);
      ierr = PetscMemcpy(pointsRef+spdim*offset,p,spdim*qPoints*sizeof(*p));CHKERRQ(ierr);
      sizes[i] = qPoints;
      offset  += qPoints;
    }
    ierr = EvaluateBasis(bspace,fSize,nPoints,sizes,pointsRef,weights,work,Amat);CHKERRQ(ierr);
    ierr = MatLUFactor(Amat,NULL,NULL,NULL);CHKERRQ(ierr);
    for (c = cStart; c < cEnd; c++) {
      PetscInt parent;
      PetscInt closureSize, closureSizeP, *closure = NULL, *closureP = NULL;
      PetscInt *childOffsets, *parentOffsets;

      ierr = DMPlexGetTreeParent(dm,c,&parent,NULL);CHKERRQ(ierr);
      if (parent == c) continue;
      ierr = DMPlexGetTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      for (i = 0; i < closureSize; i++) {
        PetscInt p = closure[2*i];
        PetscInt conDof;

        if (p < conStart || p >= conEnd) continue;
        if (numFields > 1) {
          ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
        }
        else {
          ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
        }
        if (conDof) break;
      }
      if (i == closureSize) {
        ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
        continue;
      }

      ierr = DMPlexComputeCellGeometryFEM(dm, c, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
      ierr = DMPlexComputeCellGeometryFEM(dm, parent, NULL, v0parent, Jparent, invJparent, &detJparent);CHKERRQ(ierr);
      for (i = 0; i < nPoints; i++) {
        CoordinatesRefToReal(spdim, spdim, v0, J, &pointsRef[i*spdim],vtmp);
        CoordinatesRealToRef(spdim, spdim, v0parent, invJparent, vtmp, &pointsReal[i*spdim]);
      }
      ierr = EvaluateBasis(bspace,fSize,nPoints,sizes,pointsReal,weights,work,Bmat);CHKERRQ(ierr);
      ierr = MatMatSolve(Amat,Bmat,Xmat);CHKERRQ(ierr);
      ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
      ierr = PetscMalloc2(closureSize+1,&childOffsets,closureSizeP+1,&parentOffsets);CHKERRQ(ierr);
      childOffsets[0] = 0;
      for (i = 0; i < closureSize; i++) {
        PetscInt p = closure[2*i];
        PetscInt dof;

        if (numFields > 1) {
          ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
        }
        else {
          ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
        }
        childOffsets[i+1]=childOffsets[i]+dof / fComp;
      }
      parentOffsets[0] = 0;
      for (i = 0; i < closureSizeP; i++) {
        PetscInt p = closureP[2*i];
        PetscInt dof;

        if (numFields > 1) {
          ierr = PetscSectionGetFieldDof(section,p,f,&dof);CHKERRQ(ierr);
        }
        else {
          ierr = PetscSectionGetDof(section,p,&dof);CHKERRQ(ierr);
        }
        parentOffsets[i+1]=parentOffsets[i]+dof / fComp;
      }
      for (i = 0; i < closureSize; i++) {
        PetscInt conDof, conOff, aDof, aOff;
        PetscInt p = closure[2*i];
        PetscInt o = closure[2*i+1];

        if (p < conStart || p >= conEnd) continue;
        if (numFields > 1) {
          ierr = PetscSectionGetFieldDof(cSec,p,f,&conDof);CHKERRQ(ierr);
          ierr = PetscSectionGetFieldOffset(cSec,p,f,&conOff);CHKERRQ(ierr);
        }
        else {
          ierr = PetscSectionGetDof(cSec,p,&conDof);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(cSec,p,&conOff);CHKERRQ(ierr);
        }
        if (!conDof) continue;
        ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
        for (k = 0; k < aDof; k++) {
          PetscInt a = anchors[aOff + k];
          PetscInt aSecDof, aSecOff;

          if (numFields > 1) {
            ierr = PetscSectionGetFieldDof(section,a,f,&aSecDof);CHKERRQ(ierr);
            ierr = PetscSectionGetFieldOffset(section,a,f,&aSecOff);CHKERRQ(ierr);
          }
          else {
            ierr = PetscSectionGetDof(section,a,&aSecDof);CHKERRQ(ierr);
            ierr = PetscSectionGetOffset(section,a,&aSecOff);CHKERRQ(ierr);
          }
          if (!aSecDof) continue;

          for (j = 0; j < closureSizeP; j++) {
            PetscInt q = closureP[2*j];
            PetscInt oq = closureP[2*j+1];

            if (q == a) {
              PetscInt r, s, t;

              for (r = childOffsets[i]; r < childOffsets[i+1]; r++) {
                for (s = parentOffsets[j]; s < parentOffsets[j+1]; s++) {
                  PetscScalar val;
                  PetscInt insertCol, insertRow;

                  ierr = MatGetValue(Xmat,s,r,&val);CHKERRQ(ierr);
                  if (o >= 0) {
                    insertRow = conOff + fComp * (r - childOffsets[i]);
                  }
                  else {
                    insertRow = conOff + fComp * (childOffsets[i + 1] - 1 - r);
                  }
                  if (oq >= 0) {
                    insertCol = aSecOff + fComp * (s - parentOffsets[j]);
                  }
                  else {
                    insertCol = aSecOff + fComp * (parentOffsets[j + 1] - 1 - s);
                  }
                  for (t = 0; t < fComp; t++) {
                    ierr = MatSetValue(cMat,insertRow + t,insertCol + t,val,INSERT_VALUES);CHKERRQ(ierr);
                  }
                }
              }
            }
          }
        }
      }
      ierr = PetscFree2(childOffsets,parentOffsets);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(dm,c,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSizeP,&closureP);CHKERRQ(ierr);
    }
    ierr = MatDestroy(&Amat);CHKERRQ(ierr);
    ierr = MatDestroy(&Bmat);CHKERRQ(ierr);
    ierr = MatDestroy(&Xmat);CHKERRQ(ierr);
    ierr = PetscFree5(sizes,weights,pointsRef,pointsReal,work);CHKERRQ(ierr);
    if (id == PETSCFV_CLASSID) {
      ierr = PetscSpaceDestroy(&bspace);CHKERRQ(ierr);
    }
  }
  ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscFree6(v0,v0parent,vtmp,J,Jparent,invJparent);CHKERRQ(ierr);
  ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexReferenceTreeGetChildrenMatrices"
static PetscErrorCode DMPlexReferenceTreeGetChildrenMatrices(DM refTree, PetscScalar ****childrenMats, PetscInt ***childrenN)
{
  Mat            refCmat;
  PetscDS        ds;
  PetscInt       numFields, f, pRefStart, pRefEnd, p, *rows, *cols, maxDof, maxAnDof, **refPointFieldN;
  PetscScalar    ***refPointFieldMats;
  PetscSection   refConSec, refAnSec, refSection;
  IS             refAnIS;
  const PetscInt *refAnchors;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
  ierr = DMGetDefaultConstraints(refTree,&refConSec,&refCmat);CHKERRQ(ierr);
  ierr = DMPlexGetAnchors(refTree,&refAnSec,&refAnIS);CHKERRQ(ierr);
  ierr = ISGetIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
  ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldMats);CHKERRQ(ierr);
  ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldN);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
  ierr = PetscMalloc1(maxDof,&rows);CHKERRQ(ierr);
  ierr = PetscMalloc1(maxDof*maxAnDof,&cols);CHKERRQ(ierr);
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt parent, closureSize, *closure = NULL, pDof;

    ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
    ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
    if (!pDof || parent == p) continue;

    ierr = PetscMalloc1(numFields,&refPointFieldMats[p-pRefStart]);CHKERRQ(ierr);
    ierr = PetscCalloc1(numFields,&refPointFieldN[p-pRefStart]);CHKERRQ(ierr);
    ierr = DMPlexGetTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
    for (f = 0; f < numFields; f++) {
      PetscInt cDof, cOff, numCols, r, i, fComp;
      PetscObject disc;
      PetscClassId id;
      PetscFE fe = NULL;
      PetscFV fv = NULL;

      ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
      if (id == PETSCFE_CLASSID) {
        fe = (PetscFE) disc;
        ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
      }
      else if (id == PETSCFV_CLASSID) {
        fv = (PetscFV) disc;
        ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
      }
      else SETERRQ1(PetscObjectComm(disc),PETSC_ERR_ARG_UNKNOWN_TYPE, "PetscDS discretization id %d not recognized.", id);

      if (numFields > 1) {
        ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
        ierr = PetscSectionGetFieldOffset(refConSec,p,f,&cOff);CHKERRQ(ierr);
      }
      else {
        ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(refConSec,p,&cOff);CHKERRQ(ierr);
      }

      for (r = 0; r < cDof; r++) {
        rows[r] = cOff + r;
      }
      numCols = 0;
      for (i = 0; i < closureSize; i++) {
        PetscInt q = closure[2*i];
        PetscInt o = closure[2*i+1];
        PetscInt aDof, aOff, j;

        if (numFields > 1) {
          ierr = PetscSectionGetFieldDof(refSection,q,f,&aDof);CHKERRQ(ierr);
          ierr = PetscSectionGetFieldOffset(refSection,q,f,&aOff);CHKERRQ(ierr);
        }
        else {
          ierr = PetscSectionGetDof(refSection,q,&aDof);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(refSection,q,&aOff);CHKERRQ(ierr);
        }

        for (j = 0; j < aDof; j++) {
          PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
          PetscInt comp = (j % fComp);

          cols[numCols++] = aOff + node * fComp + comp;
        }
      }
      refPointFieldN[p-pRefStart][f] = numCols;
      ierr = PetscMalloc1(cDof*numCols,&refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
      ierr = MatGetValues(refCmat,cDof,rows,numCols,cols,refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
    }
    ierr = DMPlexRestoreTransitiveClosure(refTree,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
  }
  *childrenMats = refPointFieldMats;
  *childrenN = refPointFieldN;
  ierr = ISRestoreIndices(refAnIS,&refAnchors);CHKERRQ(ierr);
  ierr = PetscFree(rows);CHKERRQ(ierr);
  ierr = PetscFree(cols);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexReferenceTreeRestoreChildrenMatrices"
static PetscErrorCode DMPlexReferenceTreeRestoreChildrenMatrices(DM refTree, PetscScalar ****childrenMats, PetscInt ***childrenN)
{
  PetscDS        ds;
  PetscInt       **refPointFieldN;
  PetscScalar    ***refPointFieldMats;
  PetscInt       numFields, pRefStart, pRefEnd, p, f;
  PetscSection   refConSec;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  refPointFieldN = *childrenN;
  *childrenN = NULL;
  refPointFieldMats = *childrenMats;
  *childrenMats = NULL;
  ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
  ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt parent, pDof;

    ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
    ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
    if (!pDof || parent == p) continue;

    for (f = 0; f < numFields; f++) {
      PetscInt cDof;

      if (numFields > 1) {
        ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
      }
      else {
        ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
      }

      ierr = PetscFree(refPointFieldMats[p - pRefStart][f]);CHKERRQ(ierr);
    }
    ierr = PetscFree(refPointFieldMats[p - pRefStart]);CHKERRQ(ierr);
    ierr = PetscFree(refPointFieldN[p - pRefStart]);CHKERRQ(ierr);
  }
  ierr = PetscFree(refPointFieldMats);CHKERRQ(ierr);
  ierr = PetscFree(refPointFieldN);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeAnchorMatrix_Tree_FromReference"
static PetscErrorCode DMPlexComputeAnchorMatrix_Tree_FromReference(DM dm, PetscSection section, PetscSection conSec, Mat cMat)
{
  DM             refTree;
  PetscDS        ds;
  Mat            refCmat;
  PetscInt       numFields, f, pRefStart, pRefEnd, p, maxDof, maxAnDof, *perm, *iperm, pStart, pEnd, conStart, conEnd, **refPointFieldN;
  PetscScalar ***refPointFieldMats, *pointWork;
  PetscSection   refConSec, refAnSec, anSec;
  IS             refAnIS, anIS;
  const PetscInt *anchors;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm, DM_CLASSID, 1);
  ierr = DMGetDS(dm,&ds);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
  ierr = DMPlexGetReferenceTree(dm,&refTree);CHKERRQ(ierr);
  ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
  ierr = DMGetDefaultConstraints(refTree,&refConSec,&refCmat);CHKERRQ(ierr);
  ierr = DMPlexGetAnchors(refTree,&refAnSec,&refAnIS);CHKERRQ(ierr);
  ierr = DMPlexGetAnchors(dm,&anSec,&anIS);CHKERRQ(ierr);
  ierr = ISGetIndices(anIS,&anchors);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(conSec,&conStart,&conEnd);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(refAnSec,&maxAnDof);CHKERRQ(ierr);
  ierr = PetscMalloc1(maxDof*maxDof*maxAnDof,&pointWork);CHKERRQ(ierr);

  /* step 1: get submats for every constrained point in the reference tree */
  ierr = DMPlexReferenceTreeGetChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);

  /* step 2: compute the preorder */
  ierr = DMPlexGetChart(dm,&pStart,&pEnd);CHKERRQ(ierr);
  ierr = PetscMalloc2(pEnd-pStart,&perm,pEnd-pStart,&iperm);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; p++) {
    perm[p - pStart] = p;
    iperm[p - pStart] = p-pStart;
  }
  for (p = 0; p < pEnd - pStart;) {
    PetscInt point = perm[p];
    PetscInt parent;

    ierr = DMPlexGetTreeParent(dm,point,&parent,NULL);CHKERRQ(ierr);
    if (parent == point) {
      p++;
    }
    else {
      PetscInt size, closureSize, *closure = NULL, i;

      ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      for (i = 0; i < closureSize; i++) {
        PetscInt q = closure[2*i];
        if (iperm[q-pStart] > iperm[point-pStart]) {
          /* swap */
          perm[p]               = q;
          perm[iperm[q-pStart]] = point;
          iperm[point-pStart]   = iperm[q-pStart];
          iperm[q-pStart]       = p;
          break;
        }
      }
      size = closureSize;
      ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      if (i == size) {
        p++;
      }
    }
  }

  /* step 3: fill the constraint matrix */
  /* we are going to use a preorder progressive fill strategy.  Mat doesn't
   * allow progressive fill without assembly, so we are going to set up the
   * values outside of the Mat first.
   */
  {
    PetscInt nRows, row, nnz;
    PetscBool done;
    const PetscInt *ia, *ja;
    PetscScalar *vals;

    ierr = MatGetRowIJ(cMat,0,PETSC_FALSE,PETSC_FALSE,&nRows,&ia,&ja,&done);CHKERRQ(ierr);
    if (!done) SETERRQ(PetscObjectComm((PetscObject)cMat),PETSC_ERR_PLIB,"Could not get RowIJ of constraint matrix");
    nnz  = ia[nRows];
    /* malloc and then zero rows right before we fill them: this way valgrind
     * can tell if we are doing progressive fill in the wrong order */
    ierr = PetscMalloc1(nnz,&vals);CHKERRQ(ierr);
    for (p = 0; p < pEnd - pStart; p++) {
      PetscInt parent, childid, closureSize, *closure = NULL;
      PetscInt point = perm[p], pointDof;

      ierr = DMPlexGetTreeParent(dm,point,&parent,&childid);CHKERRQ(ierr);
      if ((point < conStart) || (point >= conEnd) || (parent == point)) continue;
      ierr = PetscSectionGetDof(conSec,point,&pointDof);CHKERRQ(ierr);
      if (!pointDof) continue;
      ierr = DMPlexGetTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      for (f = 0; f < numFields; f++) {
        PetscInt cDof, cOff, numCols, numFillCols, i, r, fComp = -1, matOffset, offset;
        PetscScalar *pointMat;
        PetscObject disc;
        PetscClassId id;
        PetscFE fe = NULL;
        PetscFV fv = NULL;

        ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
        ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
        if (id == PETSCFE_CLASSID) {
          fe = (PetscFE) disc;
          ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
        }
        else if (id == PETSCFV_CLASSID) {
          fv = (PetscFV) disc;
          ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
        }
        else {
          SETERRQ(PetscObjectComm((PetscObject)disc),PETSC_ERR_SUP,"Unsupported discretization");
        }

        if (numFields > 1) {
          ierr = PetscSectionGetFieldDof(conSec,point,f,&cDof);CHKERRQ(ierr);
          ierr = PetscSectionGetFieldOffset(conSec,point,f,&cOff);CHKERRQ(ierr);
        }
        else {
          ierr = PetscSectionGetDof(conSec,point,&cDof);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(conSec,point,&cOff);CHKERRQ(ierr);
        }
        if (!cDof) continue;

        /* make sure that every row for this point is the same size */
#if defined(PETSC_USE_DEBUG)
        for (r = 0; r < cDof; r++) {
          if (cDof > 1 && r) {
            if ((ia[cOff+r+1]-ia[cOff+r]) != (ia[cOff+r]-ia[cOff+r-1])) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Two point rows have different nnz: %D vs. %D", (ia[cOff+r+1]-ia[cOff+r]), (ia[cOff+r]-ia[cOff+r-1]));
          }
        }
#endif
        /* zero rows */
        for (i = ia[cOff] ; i< ia[cOff+cDof];i++) {
          vals[i] = 0.;
        }
        matOffset = ia[cOff];
        numFillCols = ia[cOff+1] - matOffset;
        pointMat = refPointFieldMats[childid-pRefStart][f];
        numCols = refPointFieldN[childid-pRefStart][f];
        offset = 0;
        for (i = 0; i < closureSize; i++) {
          PetscInt q = closure[2*i];
          PetscInt o = closure[2*i+1];
          PetscInt aDof, aOff, j, k, qConDof, qConOff;

          qConDof = qConOff = 0;
          if (numFields > 1) {
            ierr = PetscSectionGetFieldDof(section,q,f,&aDof);CHKERRQ(ierr);
            ierr = PetscSectionGetFieldOffset(section,q,f,&aOff);CHKERRQ(ierr);
            if (q >= conStart && q < conEnd) {
              ierr = PetscSectionGetFieldDof(conSec,q,f,&qConDof);CHKERRQ(ierr);
              ierr = PetscSectionGetFieldOffset(conSec,q,f,&qConOff);CHKERRQ(ierr);
            }
          }
          else {
            ierr = PetscSectionGetDof(section,q,&aDof);CHKERRQ(ierr);
            ierr = PetscSectionGetOffset(section,q,&aOff);CHKERRQ(ierr);
            if (q >= conStart && q < conEnd) {
              ierr = PetscSectionGetDof(conSec,q,&qConDof);CHKERRQ(ierr);
              ierr = PetscSectionGetOffset(conSec,q,&qConOff);CHKERRQ(ierr);
            }
          }
          if (!aDof) continue;
          if (qConDof) {
            /* this point has anchors: its rows of the matrix should already
             * be filled, thanks to preordering */
            /* first multiply into pointWork, then set in matrix */
            PetscInt aMatOffset = ia[qConOff];
            PetscInt aNumFillCols = ia[qConOff + 1] - aMatOffset;
            for (r = 0; r < cDof; r++) {
              for (j = 0; j < aNumFillCols; j++) {
                PetscScalar inVal = 0;
                for (k = 0; k < aDof; k++) {
                  PetscInt node = (o >= 0) ? (k / fComp) : ((aDof - 1 - k) / fComp);
                  PetscInt comp = (k % fComp);
                  PetscInt col  = node * fComp + comp;

                  inVal += pointMat[r * numCols + offset + col] * vals[aMatOffset + aNumFillCols * k + j];
                }
                pointWork[r * aNumFillCols + j] = inVal;
              }
            }
            /* assume that the columns are sorted, spend less time searching */
            for (j = 0, k = 0; j < aNumFillCols; j++) {
              PetscInt col = ja[aMatOffset + j];
              for (;k < numFillCols; k++) {
                if (ja[matOffset + k] == col) {
                  break;
                }
              }
              if (k == numFillCols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"No nonzero space for (%d, %d)", cOff, col);
              for (r = 0; r < cDof; r++) {
                vals[matOffset + numFillCols * r + k] = pointWork[r * aNumFillCols + j];
              }
            }
          }
          else {
            /* find where to put this portion of pointMat into the matrix */
            for (k = 0; k < numFillCols; k++) {
              if (ja[matOffset + k] == aOff) {
                break;
              }
            }
            if (k == numFillCols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"No nonzero space for (%d, %d)", cOff, aOff);
            for (j = 0; j < aDof; j++) {
              PetscInt node = (o >= 0) ? (j / fComp) : ((aDof - 1 - j) / fComp);
              PetscInt comp = (j % fComp);
              PetscInt col  = node * fComp + comp;
              for (r = 0; r < cDof; r++) {
                vals[matOffset + numFillCols * r + k + col] += pointMat[r * numCols + offset + col];
              }
            }
          }
          offset += aDof;
        }
      }
      ierr = DMPlexRestoreTransitiveClosure(dm,parent,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
    }
    for (row = 0; row < nRows; row++) {
      ierr = MatSetValues(cMat,1,&row,ia[row+1]-ia[row],&ja[ia[row]],&vals[ia[row]],INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = MatRestoreRowIJ(cMat,0,PETSC_FALSE,PETSC_FALSE,&nRows,&ia,&ja,&done);CHKERRQ(ierr);
    if (!done) SETERRQ(PetscObjectComm((PetscObject)cMat),PETSC_ERR_PLIB,"Could not restore RowIJ of constraint matrix");
    ierr = MatAssemblyBegin(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(cMat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = PetscFree(vals);CHKERRQ(ierr);
  }

  /* clean up */
  ierr = ISRestoreIndices(anIS,&anchors);CHKERRQ(ierr);
  ierr = PetscFree2(perm,iperm);CHKERRQ(ierr);
  ierr = PetscFree(pointWork);CHKERRQ(ierr);
  ierr = DMPlexReferenceTreeRestoreChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexTreeRefineCell"
/* refine a single cell on rank 0: this is not intended to provide good local refinement, only to create an example of
 * a non-conforming mesh.  Local refinement comes later */
PetscErrorCode DMPlexTreeRefineCell (DM dm, PetscInt cell, DM *ncdm)
{
  DM K;
  PetscMPIInt rank;
  PetscInt dim, *pNewStart, *pNewEnd, *pNewCount, *pOldStart, *pOldEnd, offset, d, pStart, pEnd;
  PetscInt numNewCones, *newConeSizes, *newCones, *newOrientations;
  PetscInt *Kembedding;
  PetscInt *cellClosure=NULL, nc;
  PetscScalar *newVertexCoords;
  PetscInt numPointsWithParents, *parents, *childIDs, *perm, *iperm, *preOrient, pOffset;
  PetscSection parentSection;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)dm),&rank);CHKERRQ(ierr);
  ierr = DMGetDimension(dm,&dim);CHKERRQ(ierr);
  ierr = DMPlexCreate(PetscObjectComm((PetscObject)dm), ncdm);CHKERRQ(ierr);
  ierr = DMSetDimension(*ncdm,dim);CHKERRQ(ierr);

  ierr = DMPlexGetChart(dm, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&parentSection);CHKERRQ(ierr);
  ierr = DMPlexGetReferenceTree(dm,&K);CHKERRQ(ierr);
  if (!rank) {
    /* compute the new charts */
    ierr = PetscMalloc5(dim+1,&pNewCount,dim+1,&pNewStart,dim+1,&pNewEnd,dim+1,&pOldStart,dim+1,&pOldEnd);CHKERRQ(ierr);
    offset = 0;
    for (d = 0; d <= dim; d++) {
      PetscInt pOldCount, kStart, kEnd, k;

      pNewStart[d] = offset;
      ierr = DMPlexGetHeightStratum(dm,d,&pOldStart[d],&pOldEnd[d]);CHKERRQ(ierr);
      ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
      pOldCount = pOldEnd[d] - pOldStart[d];
      /* adding the new points */
      pNewCount[d] = pOldCount + kEnd - kStart;
      if (!d) {
        /* removing the cell */
        pNewCount[d]--;
      }
      for (k = kStart; k < kEnd; k++) {
        PetscInt parent;
        ierr = DMPlexGetTreeParent(K,k,&parent,NULL);CHKERRQ(ierr);
        if (parent == k) {
          /* avoid double counting points that won't actually be new */
          pNewCount[d]--;
        }
      }
      pNewEnd[d] = pNewStart[d] + pNewCount[d];
      offset = pNewEnd[d];

    }
    if (cell < pOldStart[0] || cell >= pOldEnd[0]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"%d not in cell range [%d, %d)", cell, pOldStart[0], pOldEnd[0]);
    /* get the current closure of the cell that we are removing */
    ierr = DMPlexGetTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);

    ierr = PetscMalloc1(pNewEnd[dim],&newConeSizes);CHKERRQ(ierr);
    {
      PetscInt kStart, kEnd, k, closureSizeK, *closureK = NULL, j;

      ierr = DMPlexGetChart(K,&kStart,&kEnd);CHKERRQ(ierr);
      ierr = PetscMalloc4(kEnd-kStart,&Kembedding,kEnd-kStart,&perm,kEnd-kStart,&iperm,kEnd-kStart,&preOrient);CHKERRQ(ierr);

      for (k = kStart; k < kEnd; k++) {
        perm[k - kStart] = k;
        iperm [k - kStart] = k - kStart;
        preOrient[k - kStart] = 0;
      }

      ierr = DMPlexGetTransitiveClosure(K,0,PETSC_TRUE,&closureSizeK,&closureK);CHKERRQ(ierr);
      for (j = 1; j < closureSizeK; j++) {
        PetscInt parentOrientA = closureK[2*j+1];
        PetscInt parentOrientB = cellClosure[2*j+1];
        PetscInt p, q;

        p = closureK[2*j];
        q = cellClosure[2*j];
        for (d = 0; d <= dim; d++) {
          if (q >= pOldStart[d] && q < pOldEnd[d]) {
            Kembedding[p] = (q - pOldStart[d]) + pNewStart[d];
          }
        }
        if (parentOrientA != parentOrientB) {
          PetscInt numChildren, i;
          const PetscInt *children;

          ierr = DMPlexGetTreeChildren(K,p,&numChildren,&children);CHKERRQ(ierr);
          for (i = 0; i < numChildren; i++) {
            PetscInt kPerm, oPerm;

            k    = children[i];
            ierr = DMPlexReferenceTreeGetChildSymmetry(K,p,parentOrientA,0,k,parentOrientB,&oPerm,&kPerm);CHKERRQ(ierr);
            /* perm = what refTree position I'm in */
            perm[kPerm-kStart]      = k;
            /* iperm = who is at this position */
            iperm[k-kStart]         = kPerm-kStart;
            preOrient[kPerm-kStart] = oPerm;
          }
        }
      }
      ierr = DMPlexRestoreTransitiveClosure(K,0,PETSC_TRUE,&closureSizeK,&closureK);CHKERRQ(ierr);
    }
    ierr = PetscSectionSetChart(parentSection,0,pNewEnd[dim]);CHKERRQ(ierr);
    offset = 0;
    numNewCones = 0;
    for (d = 0; d <= dim; d++) {
      PetscInt kStart, kEnd, k;
      PetscInt p;
      PetscInt size;

      for (p = pOldStart[d]; p < pOldEnd[d]; p++) {
        /* skip cell 0 */
        if (p == cell) continue;
        /* old cones to new cones */
        ierr = DMPlexGetConeSize(dm,p,&size);CHKERRQ(ierr);
        newConeSizes[offset++] = size;
        numNewCones += size;
      }

      ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
      for (k = kStart; k < kEnd; k++) {
        PetscInt kParent;

        ierr = DMPlexGetTreeParent(K,k,&kParent,NULL);CHKERRQ(ierr);
        if (kParent != k) {
          Kembedding[k] = offset;
          ierr = DMPlexGetConeSize(K,k,&size);CHKERRQ(ierr);
          newConeSizes[offset++] = size;
          numNewCones += size;
          if (kParent != 0) {
            ierr = PetscSectionSetDof(parentSection,Kembedding[k],1);CHKERRQ(ierr);
          }
        }
      }
    }

    ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(parentSection,&numPointsWithParents);CHKERRQ(ierr);
    ierr = PetscMalloc2(numNewCones,&newCones,numNewCones,&newOrientations);CHKERRQ(ierr);
    ierr = PetscMalloc2(numPointsWithParents,&parents,numPointsWithParents,&childIDs);CHKERRQ(ierr);

    /* fill new cones */
    offset = 0;
    for (d = 0; d <= dim; d++) {
      PetscInt kStart, kEnd, k, l;
      PetscInt p;
      PetscInt size;
      const PetscInt *cone, *orientation;

      for (p = pOldStart[d]; p < pOldEnd[d]; p++) {
        /* skip cell 0 */
        if (p == cell) continue;
        /* old cones to new cones */
        ierr = DMPlexGetConeSize(dm,p,&size);CHKERRQ(ierr);
        ierr = DMPlexGetCone(dm,p,&cone);CHKERRQ(ierr);
        ierr = DMPlexGetConeOrientation(dm,p,&orientation);CHKERRQ(ierr);
        for (l = 0; l < size; l++) {
          newCones[offset]          = (cone[l] - pOldStart[d + 1]) + pNewStart[d + 1];
          newOrientations[offset++] = orientation[l];
        }
      }

      ierr = DMPlexGetHeightStratum(K,d,&kStart,&kEnd);CHKERRQ(ierr);
      for (k = kStart; k < kEnd; k++) {
        PetscInt kPerm = perm[k], kParent;
        PetscInt preO  = preOrient[k];

        ierr = DMPlexGetTreeParent(K,k,&kParent,NULL);CHKERRQ(ierr);
        if (kParent != k) {
          /* embed new cones */
          ierr = DMPlexGetConeSize(K,k,&size);CHKERRQ(ierr);
          ierr = DMPlexGetCone(K,kPerm,&cone);CHKERRQ(ierr);
          ierr = DMPlexGetConeOrientation(K,kPerm,&orientation);CHKERRQ(ierr);
          for (l = 0; l < size; l++) {
            PetscInt q, m = (preO >= 0) ? ((preO + l) % size) : ((size -(preO + 1) - l) % size);
            PetscInt newO, lSize, oTrue;

            q                         = iperm[cone[m]];
            newCones[offset]          = Kembedding[q];
            ierr                      = DMPlexGetConeSize(K,q,&lSize);CHKERRQ(ierr);
            oTrue                     = orientation[m];
            oTrue                     = ((!lSize) || (preOrient[k] >= 0)) ? oTrue : -(oTrue + 2);
            newO                      = DihedralCompose(lSize,oTrue,preOrient[q]);
            newOrientations[offset++] = newO;
          }
          if (kParent != 0) {
            PetscInt newPoint = Kembedding[kParent];
            ierr              = PetscSectionGetOffset(parentSection,Kembedding[k],&pOffset);CHKERRQ(ierr);
            parents[pOffset]  = newPoint;
            childIDs[pOffset] = k;
          }
        }
      }
    }

    ierr = PetscMalloc1(dim*(pNewEnd[dim]-pNewStart[dim]),&newVertexCoords);CHKERRQ(ierr);

    /* fill coordinates */
    offset = 0;
    {
      PetscInt kStart, kEnd, l;
      PetscSection vSection;
      PetscInt v;
      Vec coords;
      PetscScalar *coordvals;
      PetscInt dof, off;
      PetscReal v0[3], J[9], detJ;

#if defined(PETSC_USE_DEBUG)
      {
        PetscInt k;
        ierr = DMPlexGetHeightStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
        for (k = kStart; k < kEnd; k++) {
          ierr = DMPlexComputeCellGeometryFEM(K, k, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
          if (detJ <= 0.) SETERRQ1 (PETSC_COMM_SELF,PETSC_ERR_PLIB,"reference tree cell %d has bad determinant",k);
        }
      }
#endif
      ierr = DMPlexComputeCellGeometryFEM(dm, cell, NULL, v0, J, NULL, &detJ);CHKERRQ(ierr);
      ierr = DMGetCoordinateSection(dm,&vSection);CHKERRQ(ierr);
      ierr = DMGetCoordinatesLocal(dm,&coords);CHKERRQ(ierr);
      ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
      for (v = pOldStart[dim]; v < pOldEnd[dim]; v++) {

        ierr = PetscSectionGetDof(vSection,v,&dof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(vSection,v,&off);CHKERRQ(ierr);
        for (l = 0; l < dof; l++) {
          newVertexCoords[offset++] = coordvals[off + l];
        }
      }
      ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);

      ierr = DMGetCoordinateSection(K,&vSection);CHKERRQ(ierr);
      ierr = DMGetCoordinatesLocal(K,&coords);CHKERRQ(ierr);
      ierr = VecGetArray(coords,&coordvals);CHKERRQ(ierr);
      ierr = DMPlexGetDepthStratum(K,0,&kStart,&kEnd);CHKERRQ(ierr);
      for (v = kStart; v < kEnd; v++) {
        PetscReal coord[3], newCoord[3];
        PetscInt  vPerm = perm[v];
        PetscInt  kParent;

        ierr = DMPlexGetTreeParent(K,v,&kParent,NULL);CHKERRQ(ierr);
        if (kParent != v) {
          /* this is a new vertex */
          ierr = PetscSectionGetOffset(vSection,vPerm,&off);CHKERRQ(ierr);
          for (l = 0; l < dim; ++l) coord[l] = PetscRealPart(coordvals[off+l]);
          CoordinatesRefToReal(dim, dim, v0, J, coord, newCoord);CHKERRQ(ierr);
          for (l = 0; l < dim; ++l) newVertexCoords[offset+l] = newCoord[l];
          offset += dim;
        }
      }
      ierr = VecRestoreArray(coords,&coordvals);CHKERRQ(ierr);
    }

    /* need to reverse the order of pNewCount: vertices first, cells last */
    for (d = 0; d < (dim + 1) / 2; d++) {
      PetscInt tmp;

      tmp = pNewCount[d];
      pNewCount[d] = pNewCount[dim - d];
      pNewCount[dim - d] = tmp;
    }

    ierr = DMPlexCreateFromDAG(*ncdm,dim,pNewCount,newConeSizes,newCones,newOrientations,newVertexCoords);CHKERRQ(ierr);
    ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
    ierr = DMPlexSetTree(*ncdm,parentSection,parents,childIDs);CHKERRQ(ierr);

    /* clean up */
    ierr = DMPlexRestoreTransitiveClosure(dm,cell,PETSC_TRUE,&nc,&cellClosure);CHKERRQ(ierr);
    ierr = PetscFree5(pNewCount,pNewStart,pNewEnd,pOldStart,pOldEnd);CHKERRQ(ierr);
    ierr = PetscFree(newConeSizes);CHKERRQ(ierr);
    ierr = PetscFree2(newCones,newOrientations);CHKERRQ(ierr);
    ierr = PetscFree(newVertexCoords);CHKERRQ(ierr);
    ierr = PetscFree2(parents,childIDs);CHKERRQ(ierr);
    ierr = PetscFree4(Kembedding,perm,iperm,preOrient);CHKERRQ(ierr);
  }
  else {
    PetscInt    p, counts[4];
    PetscInt    *coneSizes, *cones, *orientations;
    Vec         coordVec;
    PetscScalar *coords;

    for (d = 0; d <= dim; d++) {
      PetscInt dStart, dEnd;

      ierr = DMPlexGetDepthStratum(dm,d,&dStart,&dEnd);CHKERRQ(ierr);
      counts[d] = dEnd - dStart;
    }
    ierr = PetscMalloc1(pEnd-pStart,&coneSizes);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; p++) {
      ierr = DMPlexGetConeSize(dm,p,&coneSizes[p-pStart]);CHKERRQ(ierr);
    }
    ierr = DMPlexGetCones(dm, &cones);CHKERRQ(ierr);
    ierr = DMPlexGetConeOrientations(dm, &orientations);CHKERRQ(ierr);
    ierr = DMGetCoordinatesLocal(dm,&coordVec);CHKERRQ(ierr);
    ierr = VecGetArray(coordVec,&coords);CHKERRQ(ierr);

    ierr = PetscSectionSetChart(parentSection,pStart,pEnd);CHKERRQ(ierr);
    ierr = PetscSectionSetUp(parentSection);CHKERRQ(ierr);
    ierr = DMPlexCreateFromDAG(*ncdm,dim,counts,coneSizes,cones,orientations,NULL);CHKERRQ(ierr);
    ierr = DMPlexSetReferenceTree(*ncdm,K);CHKERRQ(ierr);
    ierr = DMPlexSetTree(*ncdm,parentSection,NULL,NULL);CHKERRQ(ierr);
    ierr = VecRestoreArray(coordVec,&coords);CHKERRQ(ierr);
  }
  ierr = PetscSectionDestroy(&parentSection);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeInterpolatorTree"
PetscErrorCode DMPlexComputeInterpolatorTree(DM coarse, DM fine, PetscSF coarseToFine, PetscInt *childIds, Mat mat)
{
  PetscSF        coarseToFineEmbedded;
  PetscSection   globalCoarse, globalFine;
  PetscSection   localCoarse, localFine;
  PetscSection   aSec, cSec;
  PetscSection   rootIndicesSec, rootMatricesSec;
  PetscSection   leafIndicesSec, leafMatricesSec;
  PetscInt       *rootIndices, *leafIndices;
  PetscScalar    *rootMatrices, *leafMatrices;
  IS             aIS;
  const PetscInt *anchors;
  Mat            cMat;
  PetscInt       numFields;
  PetscInt       pStartC, pEndC, pStartF, pEndF, p;
  PetscInt       aStart, aEnd, cStart, cEnd;
  PetscInt       *maxChildIds;
  PetscInt       *offsets, *newOffsets, *offsetsCopy, *newOffsetsCopy, *rowOffsets, *numD, *numO;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
  ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
  { /* winnow fine points that don't have global dofs out of the sf */
    PetscInt dof, cdof, numPointsWithDofs, offset, *pointsWithDofs, nleaves, l;
    const PetscInt *leaves;

    ierr = PetscSFGetGraph(coarseToFine,NULL,&nleaves,&leaves,NULL);CHKERRQ(ierr);
    for (l = 0, numPointsWithDofs = 0; l < nleaves; l++) {
      p = leaves ? leaves[l] : l;
      ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
      if ((dof - cdof) > 0) {
        numPointsWithDofs++;
      }
    }
    ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
    for (l = 0, offset = 0; l < nleaves; l++) {
      p = leaves ? leaves[l] : l;
      ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
      if ((dof - cdof) > 0) {
        pointsWithDofs[offset++] = l;
      }
    }
    ierr = PetscSFCreateEmbeddedLeafSF(coarseToFine, numPointsWithDofs, pointsWithDofs, &coarseToFineEmbedded);CHKERRQ(ierr);
    ierr = PetscFree(pointsWithDofs);CHKERRQ(ierr);
  }
  /* communicate back to the coarse mesh which coarse points have children (that may require interpolation) */
  ierr = PetscMalloc1(pEndC-pStartC,&maxChildIds);CHKERRQ(ierr);
  for (p = pStartC; p < pEndC; p++) {
    maxChildIds[p - pStartC] = -2;
  }
  ierr = PetscSFReduceBegin(coarseToFineEmbedded,MPIU_INT,childIds,maxChildIds,MPIU_MAX);CHKERRQ(ierr);
  ierr = PetscSFReduceEnd(coarseToFineEmbedded,MPIU_INT,childIds,maxChildIds,MPIU_MAX);CHKERRQ(ierr);

  ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);

  ierr = DMPlexGetAnchors(coarse,&aSec,&aIS);CHKERRQ(ierr);
  ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(aSec,&aStart,&aEnd);CHKERRQ(ierr);

  ierr = DMGetDefaultConstraints(coarse,&cSec,&cMat);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(cSec,&cStart,&cEnd);CHKERRQ(ierr);

  /* create sections that will send to children the indices and matrices they will need to construct the interpolator */
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootIndicesSec);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootMatricesSec);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(rootIndicesSec,pStartC,pEndC);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(rootMatricesSec,pStartC,pEndC);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(localCoarse,&numFields);CHKERRQ(ierr);
  {
    PetscInt maxFields = PetscMax(1,numFields) + 1;
    ierr = PetscMalloc7(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&newOffsets,maxFields,&newOffsetsCopy,maxFields,&rowOffsets,maxFields,&numD,maxFields,&numO);CHKERRQ(ierr);
  }

  for (p = pStartC; p < pEndC; p++) { /* count the sizes of the indices and matrices */
    PetscInt dof, matSize   = 0;
    PetscInt aDof           = 0;
    PetscInt cDof           = 0;
    PetscInt maxChildId     = maxChildIds[p - pStartC];
    PetscInt numRowIndices  = 0;
    PetscInt numColIndices  = 0;
    PetscInt f;

    ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
    if (dof < 0) {
      dof = -(dof + 1);
    }
    if (p >= aStart && p < aEnd) {
      ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
    }
    if (p >= cStart && p < cEnd) {
      ierr = PetscSectionGetDof(cSec,p,&cDof);CHKERRQ(ierr);
    }
    for (f = 0; f <= numFields; f++) offsets[f] = 0;
    for (f = 0; f <= numFields; f++) newOffsets[f] = 0;
    if (maxChildId >= 0) { /* this point has children (with dofs) that will need to be interpolated from the closure of p */
      PetscInt *closure = NULL, closureSize, cl;

      ierr = DMPlexGetTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      for (cl = 0; cl < closureSize; cl++) { /* get the closure */
        PetscInt c = closure[2 * cl], clDof;

        ierr = PetscSectionGetDof(localCoarse,c,&clDof);CHKERRQ(ierr);
        numRowIndices += clDof;
        for (f = 0; f < numFields; f++) {
          ierr = PetscSectionGetFieldDof(localCoarse,c,f,&clDof);CHKERRQ(ierr);
          offsets[f + 1] += clDof;
        }
      }
      for (f = 0; f < numFields; f++) {
        offsets[f + 1]   += offsets[f];
        newOffsets[f + 1] = offsets[f + 1];
      }
      /* get the number of indices needed and their field offsets */
      ierr = DMPlexAnchorsModifyMat(coarse,localCoarse,closureSize,numRowIndices,closure,NULL,NULL,&numColIndices,NULL,NULL,newOffsets,PETSC_FALSE);CHKERRQ(ierr);
      ierr = DMPlexRestoreTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      if (!numColIndices) { /* there are no hanging constraint modifications, so the matrix is just the identity: do not send it */
        numColIndices = numRowIndices;
        matSize = 0;
      }
      else if (numFields) { /* we send one submat for each field: sum their sizes */
        matSize = 0;
        for (f = 0; f < numFields; f++) {
          PetscInt numRow, numCol;

          numRow = offsets[f + 1] - offsets[f];
          numCol = newOffsets[f + 1] - newOffsets[f];
          matSize += numRow * numCol;
        }
      }
      else {
        matSize = numRowIndices * numColIndices;
      }
    } else if (maxChildId == -1) {
      if (cDof > 0) { /* this point's dofs are interpolated via cMat: get the submatrix of cMat */
        PetscInt aOff, a;

        ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
        for (f = 0; f < numFields; f++) {
          PetscInt fDof;

          ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
          offsets[f+1] = fDof;
        }
        for (a = 0; a < aDof; a++) {
          PetscInt anchor = anchors[a + aOff], aLocalDof;

          ierr = PetscSectionGetDof(localCoarse,anchor,&aLocalDof);CHKERRQ(ierr);
          numColIndices += aLocalDof;
          for (f = 0; f < numFields; f++) {
            PetscInt fDof;

            ierr = PetscSectionGetFieldDof(localCoarse,anchor,f,&fDof);CHKERRQ(ierr);
            newOffsets[f+1] += fDof;
          }
        }
        if (numFields) {
          matSize = 0;
          for (f = 0; f < numFields; f++) {
            matSize += offsets[f+1] * newOffsets[f+1];
          }
        }
        else {
          matSize = numColIndices * dof;
        }
      }
      else { /* no children, and no constraints on dofs: just get the global indices */
        numColIndices = dof;
        matSize       = 0;
      }
    }
    /* we will pack the column indices with the field offsets */
    ierr = PetscSectionSetDof(rootIndicesSec,p,numColIndices ? numColIndices+2*numFields : 0);CHKERRQ(ierr);
    ierr = PetscSectionSetDof(rootMatricesSec,p,matSize);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(rootIndicesSec);CHKERRQ(ierr);
  ierr = PetscSectionSetUp(rootMatricesSec);CHKERRQ(ierr);
  {
    PetscInt numRootIndices, numRootMatrices;

    ierr = PetscSectionGetStorageSize(rootIndicesSec,&numRootIndices);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(rootMatricesSec,&numRootMatrices);CHKERRQ(ierr);
    ierr = PetscMalloc2(numRootIndices,&rootIndices,numRootMatrices,&rootMatrices);CHKERRQ(ierr);
    for (p = pStartC; p < pEndC; p++) {
      PetscInt    numRowIndices, numColIndices, matSize, dof;
      PetscInt    pIndOff, pMatOff, f;
      PetscInt    *pInd;
      PetscInt    maxChildId = maxChildIds[p - pStartC];
      PetscScalar *pMat = NULL;

      ierr = PetscSectionGetDof(rootIndicesSec,p,&numColIndices);CHKERRQ(ierr);
      if (!numColIndices) {
        continue;
      }
      for (f = 0; f <= numFields; f++) {
        offsets[f]        = 0;
        newOffsets[f]     = 0;
        offsetsCopy[f]    = 0;
        newOffsetsCopy[f] = 0;
      }
      numColIndices -= 2 * numFields;
      ierr = PetscSectionGetOffset(rootIndicesSec,p,&pIndOff);CHKERRQ(ierr);
      pInd = &(rootIndices[pIndOff]);
      ierr = PetscSectionGetDof(rootMatricesSec,p,&matSize);CHKERRQ(ierr);
      if (matSize) {
        ierr = PetscSectionGetOffset(rootMatricesSec,p,&pMatOff);CHKERRQ(ierr);
        pMat = &rootMatrices[pMatOff];
      }
      ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
      if (dof < 0) {
        dof = -(dof + 1);
      }
      if (maxChildId >= 0) { /* build an identity matrix, apply matrix constraints on the right */
        PetscInt i, j;
        PetscInt numRowIndices = matSize / numColIndices;

        if (!numRowIndices) { /* don't need to calculate the mat, just the indices */
          PetscInt numIndices, *indices;
          ierr = DMPlexGetClosureIndices(coarse,localCoarse,globalCoarse,p,&numIndices,&indices,offsets);CHKERRQ(ierr);
          if (numIndices != numColIndices) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"mismatching constraint indices calculations");
          for (i = 0; i < numColIndices; i++) {
            pInd[i] = indices[i];
          }
          for (i = 0; i < numFields; i++) {
            pInd[numColIndices + i]             = offsets[i+1];
            pInd[numColIndices + numFields + i] = offsets[i+1];
          }
          ierr = DMPlexRestoreClosureIndices(coarse,localCoarse,globalCoarse,p,&numIndices,&indices,offsets);CHKERRQ(ierr);
        }
        else {
          PetscInt closureSize, *closure = NULL, cl;
          PetscScalar *pMatIn, *pMatModified;
          PetscInt numPoints,*points;

          ierr = DMGetWorkArray(coarse,numRowIndices * numRowIndices,PETSC_SCALAR,&pMatIn);CHKERRQ(ierr);
          for (i = 0; i < numRowIndices; i++) { /* initialize to the identity */
            for (j = 0; j < numRowIndices; j++) {
              pMatIn[i * numRowIndices + j] = (i == j) ? 1. : 0.;
            }
          }
          ierr = DMPlexGetTransitiveClosure(coarse, p, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
          if (numFields) {
            for (cl = 0; cl < closureSize; cl++) {
              PetscInt c = closure[2 * cl];

              for (f = 0; f < numFields; f++) {
                PetscInt fDof;

                ierr = PetscSectionGetFieldDof(localCoarse,c,f,&fDof);CHKERRQ(ierr);
                offsets[f + 1] += fDof;
              }
            }
            for (f = 0; f < numFields; f++) {
              offsets[f + 1]   += offsets[f];
              newOffsets[f + 1] = offsets[f + 1];
            }
          }
          /* apply hanging node constraints on the right, get the new points and the new offsets */
          ierr = DMPlexAnchorsModifyMat(coarse,localCoarse,closureSize,numRowIndices,closure,pMatIn,&numPoints,NULL,&points,&pMatModified,newOffsets,PETSC_FALSE);CHKERRQ(ierr);
          if (!numFields) {
            for (i = 0; i < numRowIndices * numColIndices; i++) {
              pMat[i] = pMatModified[i];
            }
          }
          else {
            PetscInt i, j, count;
            for (f = 0, count = 0; f < numFields; f++) {
              for (i = offsets[f]; i < offsets[f+1]; i++) {
                for (j = newOffsets[f]; j < newOffsets[f+1]; j++, count++) {
                  pMat[count] = pMatModified[i * numColIndices + j];
                }
              }
            }
          }
          ierr = DMRestoreWorkArray(coarse,numRowIndices * numColIndices,PETSC_SCALAR,&pMatModified);CHKERRQ(ierr);
          ierr = DMPlexRestoreTransitiveClosure(coarse, p, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
          ierr = DMRestoreWorkArray(coarse,numRowIndices * numColIndices,PETSC_SCALAR,&pMatIn);CHKERRQ(ierr);
          if (numFields) {
            for (f = 0; f < numFields; f++) {
              pInd[numColIndices + f]             = offsets[f+1];
              pInd[numColIndices + numFields + f] = newOffsets[f+1];
            }
            for (cl = 0; cl < numPoints*2; cl += 2) {
              PetscInt o = points[cl+1], globalOff, c = points[cl];
              ierr = PetscSectionGetOffset(globalCoarse, c, &globalOff);CHKERRQ(ierr);
              DMPlexGetIndicesPointFields_Internal(localCoarse, c, globalOff < 0 ? -(globalOff+1) : globalOff, newOffsets, PETSC_FALSE, o, pInd);
            }
          } else {
            for (cl = 0; cl < numPoints*2; cl += 2) {
              PetscInt o = points[cl+1], c = points[cl], globalOff;
              ierr = PetscSectionGetOffset(globalCoarse, c, &globalOff);CHKERRQ(ierr);
              DMPlexGetIndicesPoint_Internal(localCoarse, c, globalOff < 0 ? -(globalOff+1) : globalOff, newOffsets, PETSC_FALSE, o, pInd);
            }
          }
          ierr = DMRestoreWorkArray(coarse,numPoints,PETSC_SCALAR,&points);CHKERRQ(ierr);
        }
      }
      else if (matSize) {
        PetscInt cOff;
        PetscInt *rowIndices, *colIndices, a, aDof, aOff;

        numRowIndices = matSize / numColIndices;
        if (numRowIndices != dof) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Miscounted dofs");
        ierr = DMGetWorkArray(coarse,numRowIndices,PETSC_INT,&rowIndices);CHKERRQ(ierr);
        ierr = DMGetWorkArray(coarse,numColIndices,PETSC_INT,&colIndices);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(cSec,p,&cOff);CHKERRQ(ierr);
        ierr = PetscSectionGetDof(aSec,p,&aDof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(aSec,p,&aOff);CHKERRQ(ierr);
        if (numFields) {
          for (f = 0; f < numFields; f++) {
            PetscInt fDof;

            ierr = PetscSectionGetFieldDof(cSec,p,f,&fDof);CHKERRQ(ierr);
            offsets[f + 1] = fDof;
            for (a = 0; a < aDof; a++) {
              PetscInt anchor = anchors[a + aOff];
              ierr = PetscSectionGetFieldDof(localCoarse,anchor,f,&fDof);CHKERRQ(ierr);
              newOffsets[f + 1] += fDof;
            }
          }
          for (f = 0; f < numFields; f++) {
            offsets[f + 1]       += offsets[f];
            offsetsCopy[f + 1]    = offsets[f + 1];
            newOffsets[f + 1]    += newOffsets[f];
            newOffsetsCopy[f + 1] = newOffsets[f + 1];
          }
          DMPlexGetIndicesPointFields_Internal(cSec,p,cOff,offsetsCopy,PETSC_TRUE,0,rowIndices);CHKERRQ(ierr);
          for (a = 0; a < aDof; a++) {
            PetscInt anchor = anchors[a + aOff], lOff;
            ierr = PetscSectionGetOffset(localCoarse,anchor,&lOff);CHKERRQ(ierr);
            DMPlexGetIndicesPointFields_Internal(localCoarse,anchor,lOff,newOffsetsCopy,PETSC_TRUE,0,colIndices);CHKERRQ(ierr);
          }
        }
        else {
          DMPlexGetIndicesPoint_Internal(cSec,p,cOff,offsetsCopy,PETSC_TRUE,0,rowIndices);CHKERRQ(ierr);
          for (a = 0; a < aDof; a++) {
            PetscInt anchor = anchors[a + aOff], lOff;
            ierr = PetscSectionGetOffset(localCoarse,anchor,&lOff);CHKERRQ(ierr);
            DMPlexGetIndicesPoint_Internal(localCoarse,anchor,lOff,newOffsetsCopy,PETSC_TRUE,0,colIndices);CHKERRQ(ierr);
          }
        }
        if (numFields) {
          PetscInt count, a;

          for (f = 0, count = 0; f < numFields; f++) {
            PetscInt iSize = offsets[f + 1] - offsets[f];
            PetscInt jSize = newOffsets[f + 1] - newOffsets[f];
            ierr = MatGetValues(cMat,iSize,&rowIndices[offsets[f]],jSize,&colIndices[newOffsets[f]],&pMat[count]);CHKERRQ(ierr);
            count += iSize * jSize;
            pInd[numColIndices + f]             = offsets[f+1];
            pInd[numColIndices + numFields + f] = newOffsets[f+1];
          }
          for (a = 0; a < aDof; a++) {
            PetscInt anchor = anchors[a + aOff];
            PetscInt gOff;
            ierr = PetscSectionGetOffset(globalCoarse,anchor,&gOff);CHKERRQ(ierr);
            DMPlexGetIndicesPointFields_Internal(localCoarse,anchor,gOff < 0 ? -(gOff + 1) : gOff,newOffsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
          }
        }
        else {
          PetscInt a;
          ierr = MatGetValues(cMat,numRowIndices,rowIndices,numColIndices,colIndices,pMat);CHKERRQ(ierr);
          for (a = 0; a < aDof; a++) {
            PetscInt anchor = anchors[a + aOff];
            PetscInt gOff;
            ierr = PetscSectionGetOffset(globalCoarse,anchor,&gOff);CHKERRQ(ierr);
            DMPlexGetIndicesPoint_Internal(localCoarse,anchor,gOff < 0 ? -(gOff + 1) : gOff,newOffsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
          }
        }
        ierr = DMRestoreWorkArray(coarse,numColIndices,PETSC_INT,&colIndices);CHKERRQ(ierr);
        ierr = DMRestoreWorkArray(coarse,numRowIndices,PETSC_INT,&rowIndices);CHKERRQ(ierr);
      }
      else {
        PetscInt gOff;

        ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);
        if (numFields) {
          for (f = 0; f < numFields; f++) {
            PetscInt fDof;
            ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
            offsets[f + 1] = fDof + offsets[f];
          }
          for (f = 0; f < numFields; f++) {
            pInd[numColIndices + f]             = offsets[f+1];
            pInd[numColIndices + numFields + f] = offsets[f+1];
          }
          DMPlexGetIndicesPointFields_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
        }
        else {
          DMPlexGetIndicesPoint_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
        }
      }
    }
    ierr = PetscFree(maxChildIds);CHKERRQ(ierr);
  }
  {
    PetscSF  indicesSF, matricesSF;
    PetscInt *remoteOffsetsIndices, *remoteOffsetsMatrices, numLeafIndices, numLeafMatrices;

    ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafIndicesSec);CHKERRQ(ierr);
    ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafMatricesSec);CHKERRQ(ierr);
    ierr = PetscSFDistributeSection(coarseToFineEmbedded,rootIndicesSec,&remoteOffsetsIndices,leafIndicesSec);CHKERRQ(ierr);
    ierr = PetscSFDistributeSection(coarseToFineEmbedded,rootMatricesSec,&remoteOffsetsMatrices,leafMatricesSec);CHKERRQ(ierr);
    ierr = PetscSFCreateSectionSF(coarseToFineEmbedded,rootIndicesSec,remoteOffsetsIndices,leafIndicesSec,&indicesSF);CHKERRQ(ierr);
    ierr = PetscSFCreateSectionSF(coarseToFineEmbedded,rootMatricesSec,remoteOffsetsMatrices,leafMatricesSec,&matricesSF);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
    ierr = PetscFree(remoteOffsetsIndices);CHKERRQ(ierr);
    ierr = PetscFree(remoteOffsetsMatrices);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(leafIndicesSec,&numLeafIndices);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(leafMatricesSec,&numLeafMatrices);CHKERRQ(ierr);
    ierr = PetscMalloc2(numLeafIndices,&leafIndices,numLeafMatrices,&leafMatrices);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(indicesSF,MPIU_INT,rootIndices,leafIndices);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(matricesSF,MPIU_SCALAR,rootMatrices,leafMatrices);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(indicesSF,MPIU_INT,rootIndices,leafIndices);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(matricesSF,MPIU_SCALAR,rootMatrices,leafMatrices);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&matricesSF);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&indicesSF);CHKERRQ(ierr);
    ierr = PetscFree2(rootIndices,rootMatrices);CHKERRQ(ierr);
    ierr = PetscSectionDestroy(&rootIndicesSec);CHKERRQ(ierr);
    ierr = PetscSectionDestroy(&rootMatricesSec);CHKERRQ(ierr);
  }
  /* count to preallocate */
  ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
  {
    PetscInt    nGlobal;
    PetscInt    *dnnz, *onnz;
    PetscLayout rowMap, colMap;
    PetscInt    rowStart, rowEnd, colStart, colEnd;
    PetscInt    maxDof;
    PetscInt    *rowIndices;
    DM           refTree;
    PetscInt     **refPointFieldN;
    PetscScalar  ***refPointFieldMats;
    PetscSection refConSec, refAnSec;
    PetscInt     pRefStart,pRefEnd,maxConDof,maxColumns,leafStart,leafEnd;
    PetscScalar  *pointWork;

    ierr = PetscSectionGetConstrainedStorageSize(globalFine,&nGlobal);CHKERRQ(ierr);
    ierr = PetscCalloc2(nGlobal,&dnnz,nGlobal,&onnz);CHKERRQ(ierr);
    ierr = MatGetLayouts(mat,&rowMap,&colMap);CHKERRQ(ierr);
    ierr = PetscLayoutSetUp(rowMap);CHKERRQ(ierr);
    ierr = PetscLayoutSetUp(colMap);CHKERRQ(ierr);
    ierr = PetscLayoutGetRange(rowMap,&rowStart,&rowEnd);CHKERRQ(ierr);
    ierr = PetscLayoutGetRange(colMap,&colStart,&colEnd);CHKERRQ(ierr);
    ierr = PetscSectionGetMaxDof(globalFine,&maxDof);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(leafIndicesSec,&leafStart,&leafEnd);CHKERRQ(ierr);
    ierr = DMGetWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
    for (p = leafStart; p < leafEnd; p++) {
      PetscInt    gDof, gcDof, gOff;
      PetscInt    numColIndices, pIndOff, *pInd;
      PetscInt    matSize;
      PetscInt    i;

      ierr = PetscSectionGetDof(globalFine,p,&gDof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&gcDof);CHKERRQ(ierr);
      if ((gDof - gcDof) <= 0) {
        continue;
      }
      ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
      if (gOff < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"I though having global dofs meant a non-negative offset");
      if ((gOff < rowStart) || ((gOff + gDof - gcDof) > rowEnd)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"I thought the row map would constrain the global dofs");
      ierr = PetscSectionGetDof(leafIndicesSec,p,&numColIndices);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(leafIndicesSec,p,&pIndOff);CHKERRQ(ierr);
      numColIndices -= 2 * numFields;
      if (numColIndices <= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"global fine dof with no dofs to interpolate from");
      pInd = &leafIndices[pIndOff];
      offsets[0]        = 0;
      offsetsCopy[0]    = 0;
      newOffsets[0]     = 0;
      newOffsetsCopy[0] = 0;
      if (numFields) {
        PetscInt f;
        for (f = 0; f < numFields; f++) {
          PetscInt rowDof;

          ierr = PetscSectionGetFieldDof(localFine,p,f,&rowDof);CHKERRQ(ierr);
          offsets[f + 1]        = offsets[f] + rowDof;
          offsetsCopy[f + 1]    = offsets[f + 1];
          newOffsets[f + 1]     = pInd[numColIndices + numFields + f];
          numD[f] = 0;
          numO[f] = 0;
        }
        ierr = DMPlexGetIndicesPointFields_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
        for (f = 0; f < numFields; f++) {
          PetscInt colOffset    = newOffsets[f];
          PetscInt numFieldCols = newOffsets[f + 1] - newOffsets[f];

          for (i = 0; i < numFieldCols; i++) {
            PetscInt gInd = pInd[i + colOffset];

            if (gInd >= colStart && gInd < colEnd) {
              numD[f]++;
            }
            else if (gInd >= 0) { /* negative means non-entry */
              numO[f]++;
            }
          }
        }
      }
      else {
        ierr = DMPlexGetIndicesPoint_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
        numD[0] = 0;
        numO[0] = 0;
        for (i = 0; i < numColIndices; i++) {
          PetscInt gInd = pInd[i];

          if (gInd >= colStart && gInd < colEnd) {
            numD[0]++;
          }
          else if (gInd >= 0) { /* negative means non-entry */
            numO[0]++;
          }
        }
      }
      ierr = PetscSectionGetDof(leafMatricesSec,p,&matSize);CHKERRQ(ierr);
      if (!matSize) { /* incoming matrix is identity */
        PetscInt childId;

        childId = childIds[p-pStartF];
        if (childId < 0) { /* no child interpolation: one nnz per */
          if (numFields) {
            PetscInt f;
            for (f = 0; f < numFields; f++) {
              PetscInt numRows = offsets[f+1] - offsets[f], row;
              for (row = 0; row < numRows; row++) {
                PetscInt gIndCoarse = pInd[newOffsets[f] + row];
                PetscInt gIndFine   = rowIndices[offsets[f] + row];
                if (gIndCoarse >= colStart && gIndCoarse < colEnd) { /* local */
                  if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
                  dnnz[gIndFine - rowStart] = 1;
                }
                else if (gIndCoarse >= 0) { /* remote */
                  if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
                  onnz[gIndFine - rowStart] = 1;
                }
                else { /* constrained */
                  if (gIndFine >= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
                }
              }
            }
          }
          else {
            PetscInt i;
            for (i = 0; i < gDof; i++) {
              PetscInt gIndCoarse = pInd[i];
              PetscInt gIndFine   = rowIndices[i];
              if (gIndCoarse >= colStart && gIndCoarse < colEnd) { /* local */
                if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
                dnnz[gIndFine - rowStart] = 1;
              }
              else if (gIndCoarse >= 0) { /* remote */
                if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
                onnz[gIndFine - rowStart] = 1;
              }
              else { /* constrained */
                if (gIndFine >= 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
              }
            }
          }
        }
        else { /* interpolate from all */
          if (numFields) {
            PetscInt f;
            for (f = 0; f < numFields; f++) {
              PetscInt numRows = offsets[f+1] - offsets[f], row;
              for (row = 0; row < numRows; row++) {
                PetscInt gIndFine = rowIndices[offsets[f] + row];
                if (gIndFine >= 0) {
                  if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
                  dnnz[gIndFine - rowStart] = numD[f];
                  onnz[gIndFine - rowStart] = numO[f];
                }
              }
            }
          }
          else {
            PetscInt i;
            for (i = 0; i < gDof; i++) {
              PetscInt gIndFine = rowIndices[i];
              if (gIndFine >= 0) {
                if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
                dnnz[gIndFine - rowStart] = numD[0];
                onnz[gIndFine - rowStart] = numO[0];
              }
            }
          }
        }
      }
      else { /* interpolate from all */
        if (numFields) {
          PetscInt f;
          for (f = 0; f < numFields; f++) {
            PetscInt numRows = offsets[f+1] - offsets[f], row;
            for (row = 0; row < numRows; row++) {
              PetscInt gIndFine = rowIndices[offsets[f] + row];
              if (gIndFine >= 0) {
                if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
                dnnz[gIndFine - rowStart] = numD[f];
                onnz[gIndFine - rowStart] = numO[f];
              }
            }
          }
        }
        else { /* every dof get a full row */
          PetscInt i;
          for (i = 0; i < gDof; i++) {
            PetscInt gIndFine = rowIndices[i];
            if (gIndFine >= 0) {
              if (gIndFine < rowStart || gIndFine >= rowEnd) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Mismatched number of constrained dofs");
              dnnz[gIndFine - rowStart] = numD[0];
              onnz[gIndFine - rowStart] = numO[0];
            }
          }
        }
      }
    }
    ierr = MatXAIJSetPreallocation(mat,1,dnnz,onnz,NULL,NULL);CHKERRQ(ierr);
    ierr = PetscFree2(dnnz,onnz);CHKERRQ(ierr);

    ierr = DMPlexGetReferenceTree(fine,&refTree);CHKERRQ(ierr);
    ierr = DMPlexReferenceTreeGetChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
    ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
    ierr = DMPlexGetAnchors(refTree,&refAnSec,NULL);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
    ierr = PetscSectionGetMaxDof(refConSec,&maxConDof);CHKERRQ(ierr);
    ierr = PetscSectionGetMaxDof(leafIndicesSec,&maxColumns);CHKERRQ(ierr);
    ierr = PetscMalloc1(maxConDof*maxColumns,&pointWork);CHKERRQ(ierr);
    for (p = leafStart; p < leafEnd; p++) {
      PetscInt    gDof, gcDof, gOff;
      PetscInt    numColIndices, pIndOff, *pInd;
      PetscInt    matSize;
      PetscInt    childId;


      ierr = PetscSectionGetDof(globalFine,p,&gDof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&gcDof);CHKERRQ(ierr);
      if ((gDof - gcDof) <= 0) {
        continue;
      }
      childId = childIds[p-pStartF];
      ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(leafIndicesSec,p,&numColIndices);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(leafIndicesSec,p,&pIndOff);CHKERRQ(ierr);
      numColIndices -= 2 * numFields;
      pInd = &leafIndices[pIndOff];
      offsets[0]        = 0;
      offsetsCopy[0]    = 0;
      newOffsets[0]     = 0;
      newOffsetsCopy[0] = 0;
      rowOffsets[0]     = 0;
      if (numFields) {
        PetscInt f;
        for (f = 0; f < numFields; f++) {
          PetscInt rowDof;

          ierr = PetscSectionGetFieldDof(localFine,p,f,&rowDof);CHKERRQ(ierr);
          offsets[f + 1]     = offsets[f] + rowDof;
          offsetsCopy[f + 1] = offsets[f + 1];
          rowOffsets[f + 1]  = pInd[numColIndices + f];
          newOffsets[f + 1]  = pInd[numColIndices + numFields + f];
        }
        ierr = DMPlexGetIndicesPointFields_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
      }
      else {
        ierr = DMPlexGetIndicesPoint_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
      }
      ierr = PetscSectionGetDof(leafMatricesSec,p,&matSize);CHKERRQ(ierr);
      if (!matSize) { /* incoming matrix is identity */
        if (childId < 0) { /* no child interpolation: scatter */
          if (numFields) {
            PetscInt f;
            for (f = 0; f < numFields; f++) {
              PetscInt numRows = offsets[f+1] - offsets[f], row;
              for (row = 0; row < numRows; row++) {
                ierr = MatSetValue(mat,rowIndices[offsets[f]+row],pInd[newOffsets[f]+row],1.,INSERT_VALUES);CHKERRQ(ierr);
              }
            }
          }
          else {
            PetscInt numRows = gDof, row;
            for (row = 0; row < numRows; row++) {
              ierr = MatSetValue(mat,rowIndices[row],pInd[row],1.,INSERT_VALUES);CHKERRQ(ierr);
            }
          }
        }
        else { /* interpolate from all */
          if (numFields) {
            PetscInt f;
            for (f = 0; f < numFields; f++) {
              PetscInt numRows = offsets[f+1] - offsets[f];
              PetscInt numCols = newOffsets[f + 1] - newOffsets[f];
              ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],refPointFieldMats[childId - pRefStart][f],INSERT_VALUES);CHKERRQ(ierr);
            }
          }
          else {
            ierr = MatSetValues(mat,gDof,rowIndices,numColIndices,pInd,refPointFieldMats[childId - pRefStart][0],INSERT_VALUES);CHKERRQ(ierr);
          }
        }
      }
      else { /* interpolate from all */
        PetscInt    pMatOff;
        PetscScalar *pMat;

        ierr = PetscSectionGetOffset(leafMatricesSec,p,&pMatOff);CHKERRQ(ierr);
        pMat = &leafMatrices[pMatOff];
        if (childId < 0) { /* copy the incoming matrix */
          if (numFields) {
            PetscInt f, count;
            for (f = 0, count = 0; f < numFields; f++) {
              PetscInt numRows = offsets[f+1]-offsets[f];
              PetscInt numCols = newOffsets[f+1]-newOffsets[f];
              PetscInt numInRows = rowOffsets[f+1]-rowOffsets[f];
              PetscScalar *inMat = &pMat[count];

              ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],inMat,INSERT_VALUES);CHKERRQ(ierr);
              count += numCols * numInRows;
            }
          }
          else {
            ierr = MatSetValues(mat,gDof,rowIndices,numColIndices,pInd,pMat,INSERT_VALUES);CHKERRQ(ierr);
          }
        }
        else { /* multiply the incoming matrix by the child interpolation */
          if (numFields) {
            PetscInt f, count;
            for (f = 0, count = 0; f < numFields; f++) {
              PetscInt numRows = offsets[f+1]-offsets[f];
              PetscInt numCols = newOffsets[f+1]-newOffsets[f];
              PetscInt numInRows = rowOffsets[f+1]-rowOffsets[f];
              PetscScalar *inMat = &pMat[count];
              PetscInt i, j, k;
              if (refPointFieldN[childId - pRefStart][f] != numInRows) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Point constraint matrix multiply dimension mismatch");
              for (i = 0; i < numRows; i++) {
                for (j = 0; j < numCols; j++) {
                  PetscScalar val = 0.;
                  for (k = 0; k < numInRows; k++) {
                    val += refPointFieldMats[childId - pRefStart][f][i * numInRows + k] * inMat[k * numCols + j];
                  }
                  pointWork[i * numCols + j] = val;
                }
              }
              ierr = MatSetValues(mat,numRows,&rowIndices[offsets[f]],numCols,&pInd[newOffsets[f]],pointWork,INSERT_VALUES);CHKERRQ(ierr);
              count += numCols * numInRows;
            }
          }
          else { /* every dof gets a full row */
            PetscInt numRows   = gDof;
            PetscInt numCols   = numColIndices;
            PetscInt numInRows = matSize / numColIndices;
            PetscInt i, j, k;
            if (refPointFieldN[childId - pRefStart][0] != numInRows) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Point constraint matrix multiply dimension mismatch");
            for (i = 0; i < numRows; i++) {
              for (j = 0; j < numCols; j++) {
                PetscScalar val = 0.;
                for (k = 0; k < numInRows; k++) {
                  val += refPointFieldMats[childId - pRefStart][0][i * numInRows + k] * pMat[k * numCols + j];
                }
                pointWork[i * numCols + j] = val;
              }
            }
            ierr = MatSetValues(mat,numRows,rowIndices,numCols,pInd,pointWork,INSERT_VALUES);CHKERRQ(ierr);
          }
        }
      }
    }
    ierr = DMPlexReferenceTreeRestoreChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
    ierr = DMRestoreWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
    ierr = PetscFree(pointWork);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&leafIndicesSec);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&leafMatricesSec);CHKERRQ(ierr);
  ierr = PetscFree2(leafIndices,leafMatrices);CHKERRQ(ierr);
  ierr = PetscFree7(offsets,offsetsCopy,newOffsets,newOffsetsCopy,rowOffsets,numD,numO);CHKERRQ(ierr);
  ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeInjectorReferenceTree"
/*
 * Assuming a nodal basis (w.r.t. the dual basis) basis:
 *
 * for each coarse dof \phi^c_i:
 *   for each quadrature point (w_l,x_l) in the dual basis definition of \phi^c_i:
 *     for each fine dof \phi^f_j;
 *       a_{i,j} = 0;
 *       for each fine dof \phi^f_k:
 *         a_{i,j} += interp_{i,k} * \phi^f_k(x_l) * \phi^f_j(x_l) * w_l
 *                    [^^^ this is = \phi^c_i ^^^]
 */
PetscErrorCode DMPlexComputeInjectorReferenceTree(DM refTree, Mat *inj)
{
  PetscDS        ds;
  PetscSection   section, cSection;
  DMLabel        canonical, depth;
  Mat            cMat, mat;
  PetscInt       *nnz;
  PetscInt       f, dim, numFields, numSecFields, p, pStart, pEnd, cStart, cEnd;
  PetscInt       m, n;
  PetscScalar    *pointScalar;
  PetscReal      *v0, *v0parent, *vtmp, *J, *Jparent, *invJ, *pointRef, detJ, detJparent;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetDefaultSection(refTree,&section);CHKERRQ(ierr);
  ierr = DMGetDimension(refTree, &dim);CHKERRQ(ierr);
  ierr = PetscMalloc6(dim,&v0,dim,&v0parent,dim,&vtmp,dim*dim,&J,dim*dim,&Jparent,dim*dim,&invJ);CHKERRQ(ierr);
  ierr = PetscMalloc2(dim,&pointScalar,dim,&pointRef);CHKERRQ(ierr);
  ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(section,&numSecFields);CHKERRQ(ierr);
  ierr = DMGetLabel(refTree,"canonical",&canonical);CHKERRQ(ierr);
  ierr = DMGetLabel(refTree,"depth",&depth);CHKERRQ(ierr);
  ierr = DMGetDefaultConstraints(refTree,&cSection,&cMat);CHKERRQ(ierr);
  ierr = DMPlexGetChart(refTree, &pStart, &pEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(refTree, 0, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = MatGetSize(cMat,&n,&m);CHKERRQ(ierr); /* the injector has transpose sizes from the constraint matrix */
  /* Step 1: compute non-zero pattern.  A proper subset of constraint matrix non-zero */
  ierr = PetscCalloc1(m,&nnz);CHKERRQ(ierr);
  for (p = pStart; p < pEnd; p++) { /* a point will have non-zeros if it is canonical, it has dofs, and its children have dofs */
    const PetscInt *children;
    PetscInt numChildren;
    PetscInt i, numChildDof, numSelfDof;

    if (canonical) {
      PetscInt pCanonical;
      ierr = DMLabelGetValue(canonical,p,&pCanonical);CHKERRQ(ierr);
      if (p != pCanonical) continue;
    }
    ierr = DMPlexGetTreeChildren(refTree,p,&numChildren,&children);CHKERRQ(ierr);
    if (!numChildren) continue;
    for (i = 0, numChildDof = 0; i < numChildren; i++) {
      PetscInt child = children[i];
      PetscInt dof;

      ierr = PetscSectionGetDof(section,child,&dof);CHKERRQ(ierr);
      numChildDof += dof;
    }
    ierr = PetscSectionGetDof(section,p,&numSelfDof);CHKERRQ(ierr);
    if (!numChildDof || !numSelfDof) continue;
    for (f = 0; f < numFields; f++) {
      PetscInt selfOff;

      if (numSecFields) { /* count the dofs for just this field */
        for (i = 0, numChildDof = 0; i < numChildren; i++) {
          PetscInt child = children[i];
          PetscInt dof;

          ierr = PetscSectionGetFieldDof(section,child,f,&dof);CHKERRQ(ierr);
          numChildDof += dof;
        }
        ierr = PetscSectionGetFieldDof(section,p,f,&numSelfDof);CHKERRQ(ierr);
        ierr = PetscSectionGetFieldOffset(section,p,f,&selfOff);CHKERRQ(ierr);
      }
      else {
        ierr = PetscSectionGetOffset(section,p,&selfOff);CHKERRQ(ierr);
      }
      for (i = 0; i < numSelfDof; i++) {
        nnz[selfOff + i] = numChildDof;
      }
    }
  }
  ierr = MatCreateAIJ(PETSC_COMM_SELF,m,n,m,n,-1,nnz,-1,NULL,&mat);CHKERRQ(ierr);
  ierr = PetscFree(nnz);CHKERRQ(ierr);
  /* Setp 2: compute entries */
  for (p = pStart; p < pEnd; p++) {
    const PetscInt *children;
    PetscInt numChildren;
    PetscInt i, numChildDof, numSelfDof;

    /* same conditions about when entries occur */
    if (canonical) {
      PetscInt pCanonical;
      ierr = DMLabelGetValue(canonical,p,&pCanonical);CHKERRQ(ierr);
      if (p != pCanonical) continue;
    }
    ierr = DMPlexGetTreeChildren(refTree,p,&numChildren,&children);CHKERRQ(ierr);
    if (!numChildren) continue;
    for (i = 0, numChildDof = 0; i < numChildren; i++) {
      PetscInt child = children[i];
      PetscInt dof;

      ierr = PetscSectionGetDof(section,child,&dof);CHKERRQ(ierr);
      numChildDof += dof;
    }
    ierr = PetscSectionGetDof(section,p,&numSelfDof);CHKERRQ(ierr);
    if (!numChildDof || !numSelfDof) continue;

    for (f = 0; f < numFields; f++) {
      PetscInt       selfOff, fComp, numSelfShapes, numChildShapes, parentCell;
      PetscInt       cellShapeOff;
      PetscObject    disc;
      PetscDualSpace dsp;
      PetscClassId   classId;
      PetscScalar    *pointMat;
      PetscInt       *matRows, *matCols;
      PetscInt       pO = PETSC_MIN_INT;
      const PetscInt *depthNumDof;

      if (numSecFields) {
        for (i = 0, numChildDof = 0; i < numChildren; i++) {
          PetscInt child = children[i];
          PetscInt dof;

          ierr = PetscSectionGetFieldDof(section,child,f,&dof);CHKERRQ(ierr);
          numChildDof += dof;
        }
        ierr = PetscSectionGetFieldDof(section,p,f,&numSelfDof);CHKERRQ(ierr);
        ierr = PetscSectionGetFieldOffset(section,p,f,&selfOff);CHKERRQ(ierr);
        ierr = PetscSectionGetFieldComponents(section,f,&fComp);CHKERRQ(ierr);
      }
      else {
        ierr = PetscSectionGetOffset(section,p,&selfOff);CHKERRQ(ierr);
        fComp = 1;
      }
      numSelfShapes  = numSelfDof  / fComp;
      numChildShapes = numChildDof / fComp;

      /* find a cell whose closure contains p */
      if (p >= cStart && p < cEnd) {
        parentCell = p;
      }
      else {
        PetscInt *star = NULL;
        PetscInt numStar;

        parentCell = -1;
        ierr = DMPlexGetTransitiveClosure(refTree,p,PETSC_FALSE,&numStar,&star);CHKERRQ(ierr);
        for (i = numStar - 1; i >= 0; i--) {
          PetscInt c = star[2 * i];

          if (c >= cStart && c < cEnd) {
            parentCell = c;
            break;
          }
        }
        ierr = DMPlexRestoreTransitiveClosure(refTree,p,PETSC_FALSE,&numStar,&star);CHKERRQ(ierr);
      }
      /* determine the offset of p's shape functions withing parentCell's shape functions */
      ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(disc,&classId);CHKERRQ(ierr);
      if (classId == PETSCFE_CLASSID) {
        ierr = PetscFEGetDualSpace((PetscFE)disc,&dsp);CHKERRQ(ierr);
      }
      else if (classId == PETSCFV_CLASSID) {
        ierr = PetscFVGetDualSpace((PetscFV)disc,&dsp);CHKERRQ(ierr);
      }
      else {
        SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Unsupported discretization object");CHKERRQ(ierr);
      }
      ierr = PetscDualSpaceGetNumDof(dsp,&depthNumDof);CHKERRQ(ierr);
      {
        PetscInt *closure = NULL;
        PetscInt numClosure;

        ierr = DMPlexGetTransitiveClosure(refTree,parentCell,PETSC_TRUE,&numClosure,&closure);CHKERRQ(ierr);
        for (i = 0, cellShapeOff = 0; i < numClosure; i++) {
          PetscInt point = closure[2 * i], pointDepth;

          pO = closure[2 * i + 1];
          if (point == p) break;
          ierr = DMLabelGetValue(depth,point,&pointDepth);CHKERRQ(ierr);
          cellShapeOff += depthNumDof[pointDepth];
        }
        ierr = DMPlexRestoreTransitiveClosure(refTree,parentCell,PETSC_TRUE,&numClosure,&closure);CHKERRQ(ierr);
      }

      ierr = DMGetWorkArray(refTree, numSelfShapes * numChildShapes, PETSC_SCALAR,&pointMat);CHKERRQ(ierr);
      ierr = DMGetWorkArray(refTree, numSelfShapes + numChildShapes, PETSC_INT,&matRows);CHKERRQ(ierr);
      matCols = matRows + numSelfShapes;
      for (i = 0; i < numSelfShapes; i++) {
        matRows[i] = selfOff + i * fComp;
      }
      {
        PetscInt colOff = 0;

        for (i = 0; i < numChildren; i++) {
          PetscInt child = children[i];
          PetscInt dof, off, j;

          if (numSecFields) {
            ierr = PetscSectionGetFieldDof(cSection,child,f,&dof);CHKERRQ(ierr);
            ierr = PetscSectionGetFieldOffset(cSection,child,f,&off);CHKERRQ(ierr);
          }
          else {
            ierr = PetscSectionGetDof(cSection,child,&dof);CHKERRQ(ierr);
            ierr = PetscSectionGetOffset(cSection,child,&off);CHKERRQ(ierr);
          }

          for (j = 0; j < dof / fComp; j++) {
            matCols[colOff++] = off + j * fComp;
          }
        }
      }
      if (classId == PETSCFE_CLASSID) {
        PetscFE        fe = (PetscFE) disc;
        PetscInt       fSize;

        ierr = PetscFEGetDualSpace(fe,&dsp);CHKERRQ(ierr);
        ierr = PetscDualSpaceGetDimension(dsp,&fSize);CHKERRQ(ierr);
        for (i = 0; i < numSelfShapes; i++) { /* for every shape function */
          PetscQuadrature q;
          PetscInt        dim, numPoints, j, k;
          const PetscReal *points;
          const PetscReal *weights;
          PetscInt        *closure = NULL;
          PetscInt        numClosure;
          PetscInt        parentCellShapeDof = cellShapeOff + (pO < 0 ? (numSelfShapes - 1 - i) : i);
          PetscReal       *Bparent;

          ierr = PetscDualSpaceGetFunctional(dsp,parentCellShapeDof,&q);CHKERRQ(ierr);
          ierr = PetscQuadratureGetData(q,&dim,&numPoints,&points,&weights);CHKERRQ(ierr);
          ierr = PetscFEGetTabulation(fe,numPoints,points,&Bparent,NULL,NULL);CHKERRQ(ierr); /* I'm expecting a nodal basis: weights[:]' * Bparent[:,cellShapeDof] = 1. */
          for (k = 0; k < numChildShapes; k++) {
            pointMat[numChildShapes * i + k] = 0.;
          }
          for (j = 0; j < numPoints; j++) {
            PetscInt          childCell = -1;
            PetscReal         parentValAtPoint;
            const PetscReal   *pointReal = &points[dim * j];
            const PetscScalar *point;
            PetscReal         *Bchild;
            PetscInt          childCellShapeOff, pointMatOff;
#if defined(PETSC_USE_COMPLEX)
            PetscInt          d;

            for (d = 0; d < dim; d++) {
              pointScalar[d] = points[dim * j + d];
            }
            point = pointScalar;
#else
            point = pointReal;
#endif

            parentValAtPoint = Bparent[(fSize * j + parentCellShapeDof) * fComp];

            for (k = 0; k < numChildren; k++) { /* locate the point in a child's star cell*/
              PetscInt child = children[k];
              PetscInt *star = NULL;
              PetscInt numStar, s;

              ierr = DMPlexGetTransitiveClosure(refTree,child,PETSC_FALSE,&numStar,&star);CHKERRQ(ierr);
              for (s = numStar - 1; s >= 0; s--) {
                PetscInt c = star[2 * s];

                if (c < cStart || c >= cEnd) continue;
                ierr = DMPlexLocatePoint_Internal(refTree,dim,point,c,&childCell);CHKERRQ(ierr);
                if (childCell >= 0) break;
              }
              ierr = DMPlexRestoreTransitiveClosure(refTree,child,PETSC_FALSE,&numStar,&star);CHKERRQ(ierr);
              if (childCell >= 0) break;
            }
            if (childCell < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Could not locate quadrature point");CHKERRQ(ierr);
            ierr = DMPlexComputeCellGeometryFEM(refTree, childCell, NULL, v0, J, invJ, &detJ);CHKERRQ(ierr);
            ierr = DMPlexComputeCellGeometryFEM(refTree, parentCell, NULL, v0parent, Jparent, NULL, &detJparent);CHKERRQ(ierr);
            CoordinatesRefToReal(dim, dim, v0parent, Jparent, pointReal, vtmp);
            CoordinatesRealToRef(dim, dim, v0, invJ, vtmp, pointRef);

            ierr = PetscFEGetTabulation(fe,1,pointRef,&Bchild,NULL,NULL);CHKERRQ(ierr);
            ierr = DMPlexGetTransitiveClosure(refTree,childCell,PETSC_TRUE,&numClosure,&closure);CHKERRQ(ierr);
            for (k = 0, pointMatOff = 0; k < numChildren; k++) { /* point is located in cell => child dofs support at point are in closure of cell */
              PetscInt child = children[k], childDepth, childDof, childO = PETSC_MIN_INT;
              PetscInt l;

              ierr = DMLabelGetValue(depth,child,&childDepth);CHKERRQ(ierr);
              childDof = depthNumDof[childDepth];
              for (l = 0, childCellShapeOff = 0; l < numClosure; l++) {
                PetscInt point = closure[2 * l];
                PetscInt pointDepth;

                childO = closure[2 * l + 1];
                if (point == child) break;
                ierr = DMLabelGetValue(depth,point,&pointDepth);CHKERRQ(ierr);
                childCellShapeOff += depthNumDof[pointDepth];
              }
              if (l == numClosure) {
                pointMatOff += childDof;
                continue; /* child is not in the closure of the cell: has nothing to contribute to this point */
              }
              for (l = 0; l < childDof; l++) {
                PetscInt    childCellDof    = childCellShapeOff + (childO ? (childDof - 1 - l) : l);
                PetscReal   childValAtPoint = Bchild[childCellDof * fComp];

                pointMat[i * numChildShapes + pointMatOff + l] += weights[j] * parentValAtPoint * childValAtPoint;
              }
              pointMatOff += childDof;
            }
            ierr = DMPlexRestoreTransitiveClosure(refTree,childCell,PETSC_TRUE,&numClosure,&closure);CHKERRQ(ierr);
            ierr = PetscFERestoreTabulation(fe,1,pointRef,&Bchild,NULL,NULL);CHKERRQ(ierr);
          }
          ierr = PetscFERestoreTabulation(fe,numPoints,points,&Bparent,NULL,NULL);CHKERRQ(ierr);
        }
      }
      else { /* just the volume-weighted averages of the children */
        PetscInt  childShapeOff;
        PetscReal parentVol;

        ierr = DMPlexComputeCellGeometryFVM(refTree, p, &parentVol, NULL, NULL);CHKERRQ(ierr);
        for (i = 0, childShapeOff = 0; i < numChildren; i++) {
          PetscInt  child = children[i];
          PetscReal childVol;

          if (child < cStart || child >= cEnd) continue;
          ierr = DMPlexComputeCellGeometryFVM(refTree, child, &childVol, NULL, NULL);CHKERRQ(ierr);
          pointMat[childShapeOff] = childVol / parentVol;
          childShapeOff++;
        }
      }
      /* Insert pointMat into mat */
      for (i = 0; i < fComp; i++) {
        PetscInt j;
        ierr = MatSetValues(mat,numSelfShapes,matRows,numChildShapes,matCols,pointMat,INSERT_VALUES);CHKERRQ(ierr);

        for (j = 0; j < numSelfShapes; j++) {
          matRows[j]++;
        }
        for (j = 0; j < numChildShapes; j++) {
          matCols[j]++;
        }
      }
      ierr = DMRestoreWorkArray(refTree, numSelfShapes + numChildShapes, PETSC_INT,&matRows);CHKERRQ(ierr);
      ierr = DMRestoreWorkArray(refTree, numSelfShapes * numChildShapes, PETSC_SCALAR,&pointMat);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree6(v0,v0parent,vtmp,J,Jparent,invJ);CHKERRQ(ierr);
  ierr = PetscFree2(pointScalar,pointRef);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  *inj = mat;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexReferenceTreeGetChildrenMatrices_Injection"
static PetscErrorCode DMPlexReferenceTreeGetChildrenMatrices_Injection(DM refTree, Mat inj, PetscScalar ****childrenMats)
{
  PetscDS        ds;
  PetscInt       numFields, f, pRefStart, pRefEnd, p, *rows, *cols, maxDof;
  PetscScalar    ***refPointFieldMats;
  PetscSection   refConSec, refSection;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
  ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
  ierr = PetscMalloc1(pRefEnd-pRefStart,&refPointFieldMats);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(refConSec,&maxDof);CHKERRQ(ierr);
  ierr = PetscMalloc1(maxDof,&rows);CHKERRQ(ierr);
  ierr = PetscMalloc1(maxDof*maxDof,&cols);CHKERRQ(ierr);
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt parent, pDof, parentDof;

    ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
    ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
    ierr = PetscSectionGetDof(refSection,parent,&parentDof);CHKERRQ(ierr);
    if (!pDof || !parentDof || parent == p) continue;

    ierr = PetscMalloc1(numFields,&refPointFieldMats[p-pRefStart]);CHKERRQ(ierr);
    for (f = 0; f < numFields; f++) {
      PetscInt cDof, cOff, numCols, r, fComp;
      PetscObject disc;
      PetscClassId id;
      PetscFE fe = NULL;
      PetscFV fv = NULL;

      ierr = PetscDSGetDiscretization(ds,f,&disc);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(disc,&id);CHKERRQ(ierr);
      if (id == PETSCFE_CLASSID) {
        fe = (PetscFE) disc;
        ierr = PetscFEGetNumComponents(fe,&fComp);CHKERRQ(ierr);
      }
      else if (id == PETSCFV_CLASSID) {
        fv = (PetscFV) disc;
        ierr = PetscFVGetNumComponents(fv,&fComp);CHKERRQ(ierr);
      }
      else SETERRQ1(PetscObjectComm(disc),PETSC_ERR_ARG_UNKNOWN_TYPE, "PetscDS discretization id %d not recognized.", id);

      if (numFields > 1) {
        ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
        ierr = PetscSectionGetFieldOffset(refConSec,p,f,&cOff);CHKERRQ(ierr);
      }
      else {
        ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(refConSec,p,&cOff);CHKERRQ(ierr);
      }

      for (r = 0; r < cDof; r++) {
        rows[r] = cOff + r;
      }
      numCols = 0;
      {
        PetscInt aDof, aOff, j;

        if (numFields > 1) {
          ierr = PetscSectionGetFieldDof(refSection,parent,f,&aDof);CHKERRQ(ierr);
          ierr = PetscSectionGetFieldOffset(refSection,parent,f,&aOff);CHKERRQ(ierr);
        }
        else {
          ierr = PetscSectionGetDof(refSection,parent,&aDof);CHKERRQ(ierr);
          ierr = PetscSectionGetOffset(refSection,parent,&aOff);CHKERRQ(ierr);
        }

        for (j = 0; j < aDof; j++) {
          cols[numCols++] = aOff + j;
        }
      }
      ierr = PetscMalloc1(cDof*numCols,&refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
      /* transpose of constraint matrix */
      ierr = MatGetValues(inj,numCols,cols,cDof,rows,refPointFieldMats[p-pRefStart][f]);CHKERRQ(ierr);
    }
  }
  *childrenMats = refPointFieldMats;
  ierr = PetscFree(rows);CHKERRQ(ierr);
  ierr = PetscFree(cols);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexReferenceTreeRestoreChildrenMatrices_Injection"
static PetscErrorCode DMPlexReferenceTreeRestoreChildrenMatrices_Injection(DM refTree, Mat inj, PetscScalar ****childrenMats)
{
  PetscDS        ds;
  PetscScalar    ***refPointFieldMats;
  PetscInt       numFields, pRefStart, pRefEnd, p, f;
  PetscSection   refConSec, refSection;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  refPointFieldMats = *childrenMats;
  *childrenMats = NULL;
  ierr = DMGetDS(refTree,&ds);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(refTree,&refSection);CHKERRQ(ierr);
  ierr = PetscDSGetNumFields(ds,&numFields);CHKERRQ(ierr);
  ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
  for (p = pRefStart; p < pRefEnd; p++) {
    PetscInt parent, pDof, parentDof;

    ierr = DMPlexGetTreeParent(refTree,p,&parent,NULL);CHKERRQ(ierr);
    ierr = PetscSectionGetDof(refConSec,p,&pDof);CHKERRQ(ierr);
    ierr = PetscSectionGetDof(refSection,parent,&parentDof);CHKERRQ(ierr);
    if (!pDof || !parentDof || parent == p) continue;

    for (f = 0; f < numFields; f++) {
      PetscInt cDof;

      if (numFields > 1) {
        ierr = PetscSectionGetFieldDof(refConSec,p,f,&cDof);CHKERRQ(ierr);
      }
      else {
        ierr = PetscSectionGetDof(refConSec,p,&cDof);CHKERRQ(ierr);
      }

      ierr = PetscFree(refPointFieldMats[p - pRefStart][f]);CHKERRQ(ierr);
    }
    ierr = PetscFree(refPointFieldMats[p - pRefStart]);CHKERRQ(ierr);
  }
  ierr = PetscFree(refPointFieldMats);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexReferenceTreeGetInjector"
static PetscErrorCode DMPlexReferenceTreeGetInjector(DM refTree,Mat *injRef)
{
  Mat            cMatRef;
  PetscObject    injRefObj;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMGetDefaultConstraints(refTree,NULL,&cMatRef);CHKERRQ(ierr);
  ierr = PetscObjectQuery((PetscObject)cMatRef,"DMPlexComputeInjectorTree_refTree",&injRefObj);CHKERRQ(ierr);
  *injRef = (Mat) injRefObj;
  if (!*injRef) {
    ierr = DMPlexComputeInjectorReferenceTree(refTree,injRef);CHKERRQ(ierr);
    ierr = PetscObjectCompose((PetscObject)cMatRef,"DMPlexComputeInjectorTree_refTree",(PetscObject)*injRef);CHKERRQ(ierr);
    /* there is now a reference in cMatRef, which should be the only one for symmetry with the above case */
    ierr = PetscObjectDereference((PetscObject)*injRef);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexTransferInjectorTree"
static PetscErrorCode DMPlexTransferInjectorTree(DM coarse, DM fine, PetscSF coarseToFine, const PetscInt *childIds, Vec fineVec, PetscInt numFields, PetscInt *offsets, PetscSection *rootMultiSec, PetscSection *multiLeafSec, PetscInt **gatheredIndices, PetscScalar **gatheredValues)
{
  PetscInt       pStartF, pEndF, pStartC, pEndC, p, maxDof, numMulti;
  PetscSection   globalCoarse, globalFine;
  PetscSection   localCoarse, localFine, leafIndicesSec;
  PetscSection   multiRootSec, rootIndicesSec;
  PetscInt       *leafInds, *rootInds = NULL;
  const PetscInt *rootDegrees;
  PetscScalar    *leafVals = NULL, *rootVals = NULL;
  PetscSF        coarseToFineEmbedded;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
  ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafIndicesSec);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(leafIndicesSec,pStartF, pEndF);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(localFine,&maxDof);CHKERRQ(ierr);
  { /* winnow fine points that don't have global dofs out of the sf */
    PetscInt l, nleaves, dof, cdof, numPointsWithDofs, offset, *pointsWithDofs, numIndices;
    const PetscInt *leaves;

    ierr = PetscSFGetGraph(coarseToFine,NULL,&nleaves,&leaves,NULL);CHKERRQ(ierr);
    for (l = 0, numPointsWithDofs = 0; l < nleaves; l++) {
      p    = leaves ? leaves[l] : l;
      ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
      if ((dof - cdof) > 0) {
        numPointsWithDofs++;

        ierr = PetscSectionGetDof(localFine,p,&dof);CHKERRQ(ierr);
        ierr = PetscSectionSetDof(leafIndicesSec,p,dof + 1);CHKERRQ(ierr);
      }
    }
    ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
    ierr = PetscSectionSetUp(leafIndicesSec);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(leafIndicesSec,&numIndices);CHKERRQ(ierr);
    ierr = PetscMalloc1(gatheredIndices ? numIndices : (maxDof + 1),&leafInds);CHKERRQ(ierr);
    if (gatheredValues)  {ierr = PetscMalloc1(numIndices,&leafVals);CHKERRQ(ierr);}
    for (l = 0, offset = 0; l < nleaves; l++) {
      p    = leaves ? leaves[l] : l;
      ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
      if ((dof - cdof) > 0) {
        PetscInt    off, gOff;
        PetscInt    *pInd;
        PetscScalar *pVal = NULL;

        pointsWithDofs[offset++] = l;

        ierr = PetscSectionGetOffset(leafIndicesSec,p,&off);CHKERRQ(ierr);

        pInd = gatheredIndices ? (&leafInds[off + 1]) : leafInds;
        if (gatheredValues) {
          PetscInt i;

          pVal = &leafVals[off + 1];
          for (i = 0; i < dof; i++) pVal[i] = 0.;
        }
        ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);

        offsets[0] = 0;
        if (numFields) {
          PetscInt f;

          for (f = 0; f < numFields; f++) {
            PetscInt fDof;
            ierr = PetscSectionGetFieldDof(localFine,p,f,&fDof);CHKERRQ(ierr);
            offsets[f + 1] = fDof + offsets[f];
          }
          DMPlexGetIndicesPointFields_Internal(localFine,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
        }
        else {
          DMPlexGetIndicesPoint_Internal(localFine,p,gOff < 0 ? -(gOff + 1) : gOff,offsets,PETSC_FALSE,0,pInd);CHKERRQ(ierr);
        }
        if (gatheredValues) {ierr = VecGetValues(fineVec,dof,pInd,pVal);CHKERRQ(ierr);}
      }
    }
    ierr = PetscSFCreateEmbeddedLeafSF(coarseToFine, numPointsWithDofs, pointsWithDofs, &coarseToFineEmbedded);CHKERRQ(ierr);
    ierr = PetscFree(pointsWithDofs);CHKERRQ(ierr);
  }

  ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);

  { /* there may be the case where an sf root has a parent: broadcast parents back to children */
    MPI_Datatype threeInt;
    PetscMPIInt  rank;
    PetscInt     (*parentNodeAndIdCoarse)[3];
    PetscInt     (*parentNodeAndIdFine)[3];
    PetscInt     p, nleaves, nleavesToParents;
    PetscSF      pointSF, sfToParents;
    const PetscInt *ilocal;
    const PetscSFNode *iremote;
    PetscSFNode  *iremoteToParents;
    PetscInt     *ilocalToParents;

    ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)coarse),&rank);CHKERRQ(ierr);
    ierr = MPI_Type_contiguous(3,MPIU_INT,&threeInt);CHKERRQ(ierr);
    ierr = MPI_Type_commit(&threeInt);CHKERRQ(ierr);
    ierr = PetscMalloc2(pEndC-pStartC,&parentNodeAndIdCoarse,pEndF-pStartF,&parentNodeAndIdFine);CHKERRQ(ierr);
    ierr = DMGetPointSF(coarse,&pointSF);CHKERRQ(ierr);
    ierr = PetscSFGetGraph(pointSF,NULL,&nleaves,&ilocal,&iremote);CHKERRQ(ierr);
    for (p = pStartC; p < pEndC; p++) {
      PetscInt parent, childId;
      ierr = DMPlexGetTreeParent(coarse,p,&parent,&childId);CHKERRQ(ierr);
      parentNodeAndIdCoarse[p - pStartC][0] = rank;
      parentNodeAndIdCoarse[p - pStartC][1] = parent - pStartC;
      parentNodeAndIdCoarse[p - pStartC][2] = (p == parent) ? -1 : childId;
      if (nleaves > 0) {
        PetscInt leaf = -1;

        if (ilocal) {
          ierr  = PetscFindInt(parent,nleaves,ilocal,&leaf);CHKERRQ(ierr);
        }
        else {
          leaf = p - pStartC;
        }
        if (leaf >= 0) {
          parentNodeAndIdCoarse[p - pStartC][0] = iremote[leaf].rank;
          parentNodeAndIdCoarse[p - pStartC][1] = iremote[leaf].index;
        }
      }
    }
    for (p = pStartF; p < pEndF; p++) {
      parentNodeAndIdFine[p - pStartF][0] = -1;
      parentNodeAndIdFine[p - pStartF][1] = -1;
      parentNodeAndIdFine[p - pStartF][2] = -1;
    }
    ierr = PetscSFBcastBegin(coarseToFineEmbedded,threeInt,parentNodeAndIdCoarse,parentNodeAndIdFine);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(coarseToFineEmbedded,threeInt,parentNodeAndIdCoarse,parentNodeAndIdFine);CHKERRQ(ierr);
    for (p = pStartF, nleavesToParents = 0; p < pEndF; p++) {
      PetscInt dof;

      ierr = PetscSectionGetDof(leafIndicesSec,p,&dof);CHKERRQ(ierr);
      if (dof) {
        PetscInt off;

        ierr = PetscSectionGetOffset(leafIndicesSec,p,&off);CHKERRQ(ierr);
        if (gatheredIndices) {
          leafInds[off] = PetscMax(childIds[p-pStartF],parentNodeAndIdFine[p-pStartF][2]);
        } else if (gatheredValues) {
          leafVals[off] = (PetscScalar) PetscMax(childIds[p-pStartF],parentNodeAndIdFine[p-pStartF][2]);
        }
      }
      if (parentNodeAndIdFine[p-pStartF][0] >= 0) {
        nleavesToParents++;
      }
    }
    ierr = PetscMalloc1(nleavesToParents,&ilocalToParents);CHKERRQ(ierr);
    ierr = PetscMalloc1(nleavesToParents,&iremoteToParents);CHKERRQ(ierr);
    for (p = pStartF, nleavesToParents = 0; p < pEndF; p++) {
      if (parentNodeAndIdFine[p-pStartF][0] >= 0) {
        ilocalToParents[nleavesToParents] = p - pStartF;
        iremoteToParents[nleavesToParents].rank  = parentNodeAndIdFine[p-pStartF][0];
        iremoteToParents[nleavesToParents].index = parentNodeAndIdFine[p-pStartF][1];
        nleavesToParents++;
      }
    }
    ierr = PetscSFCreate(PetscObjectComm((PetscObject)coarse),&sfToParents);CHKERRQ(ierr);
    ierr = PetscSFSetGraph(sfToParents,pEndC-pStartC,nleavesToParents,ilocalToParents,PETSC_OWN_POINTER,iremoteToParents,PETSC_OWN_POINTER);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);

    coarseToFineEmbedded = sfToParents;

    ierr = PetscFree2(parentNodeAndIdCoarse,parentNodeAndIdFine);CHKERRQ(ierr);
    ierr = MPI_Type_free(&threeInt);CHKERRQ(ierr);
  }

  { /* winnow out coarse points that don't have dofs */
    PetscInt dof, cdof, numPointsWithDofs, offset, *pointsWithDofs;
    PetscSF  sfDofsOnly;

    for (p = pStartC, numPointsWithDofs = 0; p < pEndC; p++) {
      ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
      if ((dof - cdof) > 0) {
        numPointsWithDofs++;
      }
    }
    ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
    for (p = pStartC, offset = 0; p < pEndC; p++) {
      ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
      if ((dof - cdof) > 0) {
        pointsWithDofs[offset++] = p - pStartC;
      }
    }
    ierr = PetscSFCreateEmbeddedSF(coarseToFineEmbedded, numPointsWithDofs, pointsWithDofs, &sfDofsOnly);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
    ierr = PetscFree(pointsWithDofs);CHKERRQ(ierr);
    coarseToFineEmbedded = sfDofsOnly;
  }

  /* communicate back to the coarse mesh which coarse points have children (that may require injection) */
  ierr = PetscSFComputeDegreeBegin(coarseToFineEmbedded,&rootDegrees);CHKERRQ(ierr);
  ierr = PetscSFComputeDegreeEnd(coarseToFineEmbedded,&rootDegrees);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&multiRootSec);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(multiRootSec,pStartC,pEndC);CHKERRQ(ierr);
  for (p = pStartC; p < pEndC; p++) {
    ierr = PetscSectionSetDof(multiRootSec,p,rootDegrees[p-pStartC]);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(multiRootSec);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(multiRootSec,&numMulti);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootIndicesSec);CHKERRQ(ierr);
  { /* distribute the leaf section */
    PetscSF multi, multiInv, indicesSF;
    PetscInt *remoteOffsets, numRootIndices;

    ierr = PetscSFGetMultiSF(coarseToFineEmbedded,&multi);CHKERRQ(ierr);
    ierr = PetscSFCreateInverseSF(multi,&multiInv);CHKERRQ(ierr);
    ierr = PetscSFDistributeSection(multiInv,leafIndicesSec,&remoteOffsets,rootIndicesSec);CHKERRQ(ierr);
    ierr = PetscSFCreateSectionSF(multiInv,leafIndicesSec,remoteOffsets,rootIndicesSec,&indicesSF);CHKERRQ(ierr);
    ierr = PetscFree(remoteOffsets);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&multiInv);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(rootIndicesSec,&numRootIndices);CHKERRQ(ierr);
    if (gatheredIndices) {
      ierr = PetscMalloc1(numRootIndices,&rootInds);CHKERRQ(ierr);
      ierr = PetscSFBcastBegin(indicesSF,MPIU_INT,leafInds,rootInds);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(indicesSF,MPIU_INT,leafInds,rootInds);CHKERRQ(ierr);
    }
    if (gatheredValues) {
      ierr = PetscMalloc1(numRootIndices,&rootVals);CHKERRQ(ierr);
      ierr = PetscSFBcastBegin(indicesSF,MPIU_SCALAR,leafVals,rootVals);CHKERRQ(ierr);
      ierr = PetscSFBcastEnd(indicesSF,MPIU_SCALAR,leafVals,rootVals);CHKERRQ(ierr);
    }
    ierr = PetscSFDestroy(&indicesSF);CHKERRQ(ierr);
  }
  ierr = PetscSectionDestroy(&leafIndicesSec);CHKERRQ(ierr);
  ierr = PetscFree(leafInds);CHKERRQ(ierr);
  ierr = PetscFree(leafVals);CHKERRQ(ierr);
  ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
  *rootMultiSec = multiRootSec;
  *multiLeafSec = rootIndicesSec;
  if (gatheredIndices) *gatheredIndices = rootInds;
  if (gatheredValues)  *gatheredValues  = rootVals;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexComputeInjectorTree"
PetscErrorCode DMPlexComputeInjectorTree(DM coarse, DM fine, PetscSF coarseToFine, PetscInt *childIds, Mat mat)
{
  DM             refTree;
  PetscSection   multiRootSec, rootIndicesSec;
  PetscSection   globalCoarse, globalFine;
  PetscSection   localCoarse, localFine;
  PetscSection   cSecRef;
  PetscInt       *rootIndices, *parentIndices, pRefStart, pRefEnd;
  Mat            injRef;
  PetscInt       numFields, maxDof;
  PetscInt       pStartC, pEndC, pStartF, pEndF, p;
  PetscInt       *offsets, *offsetsCopy, *rowOffsets;
  PetscLayout    rowMap, colMap;
  PetscInt       rowStart, rowEnd, colStart, colEnd, *nnzD, *nnzO;
  PetscScalar    ***childrenMats=NULL ; /* gcc -O gives 'may be used uninitialized' warning'. Initializing to suppress this warning */
  PetscErrorCode ierr;

  PetscFunctionBegin;

  /* get the templates for the fine-to-coarse injection from the reference tree */
  ierr = DMPlexGetReferenceTree(coarse,&refTree);CHKERRQ(ierr);
  ierr = DMGetDefaultConstraints(refTree,&cSecRef,NULL);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(cSecRef,&pRefStart,&pRefEnd);CHKERRQ(ierr);
  ierr = DMPlexReferenceTreeGetInjector(refTree,&injRef);CHKERRQ(ierr);

  ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(localFine,&numFields);CHKERRQ(ierr);
  ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(localCoarse,&maxDof);CHKERRQ(ierr);
  {
    PetscInt maxFields = PetscMax(1,numFields) + 1;
    ierr = PetscMalloc3(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&rowOffsets);CHKERRQ(ierr);
  }

  ierr = DMPlexTransferInjectorTree(coarse,fine,coarseToFine,childIds,NULL,numFields,offsets,&multiRootSec,&rootIndicesSec,&rootIndices,NULL);CHKERRQ(ierr);

  ierr = PetscMalloc1(maxDof,&parentIndices);CHKERRQ(ierr);

  /* count indices */
  ierr = MatGetLayouts(mat,&rowMap,&colMap);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(rowMap);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(colMap);CHKERRQ(ierr);
  ierr = PetscLayoutGetRange(rowMap,&rowStart,&rowEnd);CHKERRQ(ierr);
  ierr = PetscLayoutGetRange(colMap,&colStart,&colEnd);CHKERRQ(ierr);
  ierr = PetscCalloc2(rowEnd-rowStart,&nnzD,rowEnd-rowStart,&nnzO);CHKERRQ(ierr);
  for (p = pStartC; p < pEndC; p++) {
    PetscInt numLeaves, leafStart, leafEnd, l, dof, cdof, gOff;

    ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
    ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
    if ((dof - cdof) <= 0) continue;
    ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);

    rowOffsets[0] = 0;
    offsetsCopy[0] = 0;
    if (numFields) {
      PetscInt f;

      for (f = 0; f < numFields; f++) {
        PetscInt fDof;
        ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
        rowOffsets[f + 1] = offsetsCopy[f + 1] = fDof + rowOffsets[f];
      }
      DMPlexGetIndicesPointFields_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
    }
    else {
      DMPlexGetIndicesPoint_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
      rowOffsets[1] = offsetsCopy[0];
    }

    ierr = PetscSectionGetDof(multiRootSec,p,&numLeaves);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(multiRootSec,p,&leafStart);CHKERRQ(ierr);
    leafEnd = leafStart + numLeaves;
    for (l = leafStart; l < leafEnd; l++) {
      PetscInt numIndices, childId, offset;
      const PetscInt *childIndices;

      ierr = PetscSectionGetDof(rootIndicesSec,l,&numIndices);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(rootIndicesSec,l,&offset);CHKERRQ(ierr);
      childId = rootIndices[offset++];
      childIndices = &rootIndices[offset];
      numIndices--;

      if (childId == -1) { /* equivalent points: scatter */
        PetscInt i;

        for (i = 0; i < numIndices; i++) {
          PetscInt colIndex = childIndices[i];
          PetscInt rowIndex = parentIndices[i];
          if (rowIndex < 0) continue;
          if (colIndex < 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unconstrained fine and constrained coarse");
          if (colIndex >= colStart && colIndex < colEnd) {
            nnzD[rowIndex - rowStart] = 1;
          }
          else {
            nnzO[rowIndex - rowStart] = 1;
          }
        }
      }
      else {
        PetscInt parentId, f, lim;

        ierr = DMPlexGetTreeParent(refTree,childId,&parentId,NULL);CHKERRQ(ierr);

        lim = PetscMax(1,numFields);
        offsets[0] = 0;
        if (numFields) {
          PetscInt f;

          for (f = 0; f < numFields; f++) {
            PetscInt fDof;
            ierr = PetscSectionGetFieldDof(cSecRef,childId,f,&fDof);CHKERRQ(ierr);

            offsets[f + 1] = fDof + offsets[f];
          }
        }
        else {
          PetscInt cDof;

          ierr = PetscSectionGetDof(cSecRef,childId,&cDof);CHKERRQ(ierr);
          offsets[1] = cDof;
        }
        for (f = 0; f < lim; f++) {
          PetscInt parentStart = rowOffsets[f], parentEnd = rowOffsets[f + 1];
          PetscInt childStart = offsets[f], childEnd = offsets[f + 1];
          PetscInt i, numD = 0, numO = 0;

          for (i = childStart; i < childEnd; i++) {
            PetscInt colIndex = childIndices[i];

            if (colIndex < 0) continue;
            if (colIndex >= colStart && colIndex < colEnd) {
              numD++;
            }
            else {
              numO++;
            }
          }
          for (i = parentStart; i < parentEnd; i++) {
            PetscInt rowIndex = parentIndices[i];

            if (rowIndex < 0) continue;
            nnzD[rowIndex - rowStart] += numD;
            nnzO[rowIndex - rowStart] += numO;
          }
        }
      }
    }
  }
  /* preallocate */
  ierr = MatXAIJSetPreallocation(mat,1,nnzD,nnzO,NULL,NULL);CHKERRQ(ierr);
  ierr = PetscFree2(nnzD,nnzO);CHKERRQ(ierr);
  /* insert values */
  ierr = DMPlexReferenceTreeGetChildrenMatrices_Injection(refTree,injRef,&childrenMats);CHKERRQ(ierr);
  for (p = pStartC; p < pEndC; p++) {
    PetscInt numLeaves, leafStart, leafEnd, l, dof, cdof, gOff;

    ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
    ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
    if ((dof - cdof) <= 0) continue;
    ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);

    rowOffsets[0] = 0;
    offsetsCopy[0] = 0;
    if (numFields) {
      PetscInt f;

      for (f = 0; f < numFields; f++) {
        PetscInt fDof;
        ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
        rowOffsets[f + 1] = offsetsCopy[f + 1] = fDof + rowOffsets[f];
      }
      DMPlexGetIndicesPointFields_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
    }
    else {
      DMPlexGetIndicesPoint_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
      rowOffsets[1] = offsetsCopy[0];
    }

    ierr = PetscSectionGetDof(multiRootSec,p,&numLeaves);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(multiRootSec,p,&leafStart);CHKERRQ(ierr);
    leafEnd = leafStart + numLeaves;
    for (l = leafStart; l < leafEnd; l++) {
      PetscInt numIndices, childId, offset;
      const PetscInt *childIndices;

      ierr = PetscSectionGetDof(rootIndicesSec,l,&numIndices);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(rootIndicesSec,l,&offset);CHKERRQ(ierr);
      childId = rootIndices[offset++];
      childIndices = &rootIndices[offset];
      numIndices--;

      if (childId == -1) { /* equivalent points: scatter */
        PetscInt i;

        for (i = 0; i < numIndices; i++) {
          ierr = MatSetValue(mat,parentIndices[i],childIndices[i],1.,INSERT_VALUES);CHKERRQ(ierr);
        }
      }
      else {
        PetscInt parentId, f, lim;

        ierr = DMPlexGetTreeParent(refTree,childId,&parentId,NULL);CHKERRQ(ierr);

        lim = PetscMax(1,numFields);
        offsets[0] = 0;
        if (numFields) {
          PetscInt f;

          for (f = 0; f < numFields; f++) {
            PetscInt fDof;
            ierr = PetscSectionGetFieldDof(cSecRef,childId,f,&fDof);CHKERRQ(ierr);

            offsets[f + 1] = fDof + offsets[f];
          }
        }
        else {
          PetscInt cDof;

          ierr = PetscSectionGetDof(cSecRef,childId,&cDof);CHKERRQ(ierr);
          offsets[1] = cDof;
        }
        for (f = 0; f < lim; f++) {
          PetscScalar    *childMat   = &childrenMats[childId - pRefStart][f][0];
          PetscInt       *rowIndices = &parentIndices[rowOffsets[f]];
          const PetscInt *colIndices = &childIndices[offsets[f]];

          ierr = MatSetValues(mat,rowOffsets[f+1]-rowOffsets[f],rowIndices,offsets[f+1]-offsets[f],colIndices,childMat,INSERT_VALUES);CHKERRQ(ierr);
        }
      }
    }
  }
  ierr = PetscSectionDestroy(&multiRootSec);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&rootIndicesSec);CHKERRQ(ierr);
  ierr = PetscFree(parentIndices);CHKERRQ(ierr);
  ierr = DMPlexReferenceTreeRestoreChildrenMatrices_Injection(refTree,injRef,&childrenMats);CHKERRQ(ierr);
  ierr = PetscFree(rootIndices);CHKERRQ(ierr);
  ierr = PetscFree3(offsets,offsetsCopy,rowOffsets);CHKERRQ(ierr);

  ierr = MatAssemblyBegin(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(mat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexTransferVecTree_Interpolate"
static PetscErrorCode DMPlexTransferVecTree_Interpolate(DM coarse, Vec vecCoarseLocal, DM fine, Vec vecFine, PetscSF coarseToFine, PetscInt *cids, Vec grad, Vec cellGeom)
{
  PetscDS           ds;
  PetscSF           coarseToFineEmbedded;
  PetscSection      globalCoarse, globalFine;
  PetscSection      localCoarse, localFine;
  PetscSection      aSec, cSec;
  PetscSection      rootValuesSec;
  PetscSection      leafValuesSec;
  PetscScalar       *rootValues, *leafValues;
  IS                aIS;
  const PetscInt    *anchors;
  Mat               cMat;
  PetscInt          numFields;
  PetscInt          pStartC, pEndC, pStartF, pEndF, p, cellStart, cellEnd, cellEndInterior;
  PetscInt          aStart, aEnd, cStart, cEnd;
  PetscInt          *maxChildIds;
  PetscInt          *offsets, *newOffsets, *offsetsCopy, *newOffsetsCopy, *rowOffsets, *numD, *numO;
  PetscFV           fv = NULL;
  PetscInt          dim, numFVcomps = -1, fvField = -1;
  DM                cellDM = NULL, gradDM = NULL;
  const PetscScalar *cellGeomArray = NULL;
  const PetscScalar *gradArray = NULL;
  PetscErrorCode    ierr;

  PetscFunctionBegin;
  ierr = VecSetOption(vecFine,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);CHKERRQ(ierr);
  ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(coarse,0,&cellStart,&cellEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(coarse,&cellEndInterior,NULL,NULL,NULL);CHKERRQ(ierr);
  cellEnd = (cellEndInterior < 0) ? cellEnd : cellEndInterior;
  ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
  ierr = DMGetCoordinateDim(coarse,&dim);CHKERRQ(ierr);
  { /* winnow fine points that don't have global dofs out of the sf */
    PetscInt       nleaves, l;
    const PetscInt *leaves;
    PetscInt       dof, cdof, numPointsWithDofs, offset, *pointsWithDofs;

    ierr = PetscSFGetGraph(coarseToFine,NULL,&nleaves,&leaves,NULL);CHKERRQ(ierr);

    for (l = 0, numPointsWithDofs = 0; l < nleaves; l++) {
      PetscInt p = leaves ? leaves[l] : l;

      ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
      if ((dof - cdof) > 0) {
        numPointsWithDofs++;
      }
    }
    ierr = PetscMalloc1(numPointsWithDofs,&pointsWithDofs);CHKERRQ(ierr);
    for (l = 0, offset = 0; l < nleaves; l++) {
      PetscInt p = leaves ? leaves[l] : l;

      ierr = PetscSectionGetDof(globalFine,p,&dof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&cdof);CHKERRQ(ierr);
      if ((dof - cdof) > 0) {
        pointsWithDofs[offset++] = l;
      }
    }
    ierr = PetscSFCreateEmbeddedLeafSF(coarseToFine, numPointsWithDofs, pointsWithDofs, &coarseToFineEmbedded);CHKERRQ(ierr);
    ierr = PetscFree(pointsWithDofs);CHKERRQ(ierr);
  }
  /* communicate back to the coarse mesh which coarse points have children (that may require interpolation) */
  ierr = PetscMalloc1(pEndC-pStartC,&maxChildIds);CHKERRQ(ierr);
  for (p = pStartC; p < pEndC; p++) {
    maxChildIds[p - pStartC] = -2;
  }
  ierr = PetscSFReduceBegin(coarseToFineEmbedded,MPIU_INT,cids,maxChildIds,MPIU_MAX);CHKERRQ(ierr);
  ierr = PetscSFReduceEnd(coarseToFineEmbedded,MPIU_INT,cids,maxChildIds,MPIU_MAX);CHKERRQ(ierr);

  ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);

  ierr = DMPlexGetAnchors(coarse,&aSec,&aIS);CHKERRQ(ierr);
  ierr = ISGetIndices(aIS,&anchors);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(aSec,&aStart,&aEnd);CHKERRQ(ierr);

  ierr = DMGetDefaultConstraints(coarse,&cSec,&cMat);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(cSec,&cStart,&cEnd);CHKERRQ(ierr);

  /* create sections that will send to children the indices and matrices they will need to construct the interpolator */
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)coarse),&rootValuesSec);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(rootValuesSec,pStartC,pEndC);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(localCoarse,&numFields);CHKERRQ(ierr);
  {
    PetscInt maxFields = PetscMax(1,numFields) + 1;
    ierr = PetscMalloc7(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&newOffsets,maxFields,&newOffsetsCopy,maxFields,&rowOffsets,maxFields,&numD,maxFields,&numO);CHKERRQ(ierr);
  }
  if (grad) {
    PetscInt i;

    ierr = VecGetDM(cellGeom,&cellDM);CHKERRQ(ierr);
    ierr = VecGetArrayRead(cellGeom,&cellGeomArray);CHKERRQ(ierr);
    ierr = VecGetDM(grad,&gradDM);CHKERRQ(ierr);
    ierr = VecGetArrayRead(grad,&gradArray);CHKERRQ(ierr);
    for (i = 0; i < PetscMax(1,numFields); i++) {
      PetscObject  obj;
      PetscClassId id;

      ierr = DMGetField(coarse, i, &obj);CHKERRQ(ierr);
      ierr = PetscObjectGetClassId(obj,&id);CHKERRQ(ierr);
      if (id == PETSCFV_CLASSID) {
        fv      = (PetscFV) obj;
        ierr    = PetscFVGetNumComponents(fv,&numFVcomps);CHKERRQ(ierr);
        fvField = i;
        break;
      }
    }
  }

  for (p = pStartC; p < pEndC; p++) { /* count the sizes of the indices and matrices */
    PetscInt dof;
    PetscInt maxChildId     = maxChildIds[p - pStartC];
    PetscInt numValues      = 0;

    ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
    if (dof < 0) {
      dof = -(dof + 1);
    }
    offsets[0]    = 0;
    newOffsets[0] = 0;
    if (maxChildId >= 0) { /* this point has children (with dofs) that will need to be interpolated from the closure of p */
      PetscInt *closure = NULL, closureSize, cl;

      ierr = DMPlexGetTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
      for (cl = 0; cl < closureSize; cl++) { /* get the closure */
        PetscInt c = closure[2 * cl], clDof;

        ierr = PetscSectionGetDof(localCoarse,c,&clDof);CHKERRQ(ierr);
        numValues += clDof;
      }
      ierr = DMPlexRestoreTransitiveClosure(coarse,p,PETSC_TRUE,&closureSize,&closure);CHKERRQ(ierr);
    }
    else if (maxChildId == -1) {
      ierr = PetscSectionGetDof(localCoarse,p,&numValues);CHKERRQ(ierr);
    }
    /* we will pack the column indices with the field offsets */
    if (maxChildId >= 0 && grad && p >= cellStart && p < cellEnd) {
      /* also send the centroid, and the gradient */
      numValues += dim * (1 + numFVcomps);
    }
    ierr = PetscSectionSetDof(rootValuesSec,p,numValues);CHKERRQ(ierr);
  }
  ierr = PetscSectionSetUp(rootValuesSec);CHKERRQ(ierr);
  {
    PetscInt          numRootValues;
    const PetscScalar *coarseArray;

    ierr = PetscSectionGetStorageSize(rootValuesSec,&numRootValues);CHKERRQ(ierr);
    ierr = PetscMalloc1(numRootValues,&rootValues);CHKERRQ(ierr);
    ierr = VecGetArrayRead(vecCoarseLocal,&coarseArray);CHKERRQ(ierr);
    for (p = pStartC; p < pEndC; p++) {
      PetscInt    numValues;
      PetscInt    pValOff;
      PetscScalar *pVal;
      PetscInt    maxChildId = maxChildIds[p - pStartC];

      ierr = PetscSectionGetDof(rootValuesSec,p,&numValues);CHKERRQ(ierr);
      if (!numValues) {
        continue;
      }
      ierr = PetscSectionGetOffset(rootValuesSec,p,&pValOff);CHKERRQ(ierr);
      pVal = &(rootValues[pValOff]);
      if (maxChildId >= 0) { /* build an identity matrix, apply matrix constraints on the right */
        PetscInt closureSize = numValues;
        ierr = DMPlexVecGetClosure(coarse,NULL,vecCoarseLocal,p,&closureSize,&pVal);CHKERRQ(ierr);
        if (grad && p >= cellStart && p < cellEnd) {
          PetscFVCellGeom *cg;
          PetscScalar     *gradVals = NULL;
          PetscInt        i;

          pVal += (numValues - dim * (1 + numFVcomps));

          ierr = DMPlexPointLocalRead(cellDM,p,cellGeomArray,(void *) &cg);CHKERRQ(ierr);
          for (i = 0; i < dim; i++) pVal[i] = cg->centroid[i];
          pVal += dim;
          ierr = DMPlexPointGlobalRead(gradDM,p,gradArray,(void *) &gradVals);CHKERRQ(ierr);
          for (i = 0; i < dim * numFVcomps; i++) pVal[i] = gradVals[i];
        }
      }
      else if (maxChildId == -1) {
        PetscInt lDof, lOff, i;

        ierr = PetscSectionGetDof(localCoarse,p,&lDof);CHKERRQ(ierr);
        ierr = PetscSectionGetOffset(localCoarse,p,&lOff);CHKERRQ(ierr);
        for (i = 0; i < lDof; i++) pVal[i] = coarseArray[lOff + i];
      }
    }
    ierr = VecRestoreArrayRead(vecCoarseLocal,&coarseArray);CHKERRQ(ierr);
    ierr = PetscFree(maxChildIds);CHKERRQ(ierr);
  }
  {
    PetscSF  valuesSF;
    PetscInt *remoteOffsetsValues, numLeafValues;

    ierr = PetscSectionCreate(PetscObjectComm((PetscObject)fine),&leafValuesSec);CHKERRQ(ierr);
    ierr = PetscSFDistributeSection(coarseToFineEmbedded,rootValuesSec,&remoteOffsetsValues,leafValuesSec);CHKERRQ(ierr);
    ierr = PetscSFCreateSectionSF(coarseToFineEmbedded,rootValuesSec,remoteOffsetsValues,leafValuesSec,&valuesSF);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&coarseToFineEmbedded);CHKERRQ(ierr);
    ierr = PetscFree(remoteOffsetsValues);CHKERRQ(ierr);
    ierr = PetscSectionGetStorageSize(leafValuesSec,&numLeafValues);CHKERRQ(ierr);
    ierr = PetscMalloc1(numLeafValues,&leafValues);CHKERRQ(ierr);
    ierr = PetscSFBcastBegin(valuesSF,MPIU_SCALAR,rootValues,leafValues);CHKERRQ(ierr);
    ierr = PetscSFBcastEnd(valuesSF,MPIU_SCALAR,rootValues,leafValues);CHKERRQ(ierr);
    ierr = PetscSFDestroy(&valuesSF);CHKERRQ(ierr);
    ierr = PetscFree(rootValues);CHKERRQ(ierr);
    ierr = PetscSectionDestroy(&rootValuesSec);CHKERRQ(ierr);
  }
  ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
  {
    PetscInt    maxDof;
    PetscInt    *rowIndices;
    DM           refTree;
    PetscInt     **refPointFieldN;
    PetscScalar  ***refPointFieldMats;
    PetscSection refConSec, refAnSec;
    PetscInt     pRefStart,pRefEnd,leafStart,leafEnd;
    PetscScalar  *pointWork;

    ierr = PetscSectionGetMaxDof(globalFine,&maxDof);CHKERRQ(ierr);
    ierr = DMGetWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
    ierr = DMGetWorkArray(fine,maxDof,PETSC_SCALAR,&pointWork);CHKERRQ(ierr);
    ierr = DMPlexGetReferenceTree(fine,&refTree);CHKERRQ(ierr);
    ierr = DMGetDS(fine,&ds);CHKERRQ(ierr);
    ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
    ierr = DMPlexReferenceTreeGetChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
    ierr = DMGetDefaultConstraints(refTree,&refConSec,NULL);CHKERRQ(ierr);
    ierr = DMPlexGetAnchors(refTree,&refAnSec,NULL);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(refConSec,&pRefStart,&pRefEnd);CHKERRQ(ierr);
    ierr = PetscSectionGetChart(leafValuesSec,&leafStart,&leafEnd);CHKERRQ(ierr);
    ierr = DMPlexGetHeightStratum(fine,0,&cellStart,&cellEnd);CHKERRQ(ierr);
    ierr = DMPlexGetHybridBounds(fine,&cellEndInterior,NULL,NULL,NULL);CHKERRQ(ierr);
    cellEnd = (cellEndInterior < 0) ? cellEnd : cellEndInterior;
    for (p = leafStart; p < leafEnd; p++) {
      PetscInt          gDof, gcDof, gOff, lDof;
      PetscInt          numValues, pValOff;
      PetscInt          childId;
      const PetscScalar *pVal;
      const PetscScalar *fvGradData = NULL;

      ierr = PetscSectionGetDof(globalFine,p,&gDof);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(localFine,p,&lDof);CHKERRQ(ierr);
      ierr = PetscSectionGetConstraintDof(globalFine,p,&gcDof);CHKERRQ(ierr);
      if ((gDof - gcDof) <= 0) {
        continue;
      }
      ierr = PetscSectionGetOffset(globalFine,p,&gOff);CHKERRQ(ierr);
      ierr = PetscSectionGetDof(leafValuesSec,p,&numValues);CHKERRQ(ierr);
      if (!numValues) continue;
      ierr = PetscSectionGetOffset(leafValuesSec,p,&pValOff);CHKERRQ(ierr);
      pVal = &leafValues[pValOff];
      offsets[0]        = 0;
      offsetsCopy[0]    = 0;
      newOffsets[0]     = 0;
      newOffsetsCopy[0] = 0;
      childId           = cids[p - pStartF];
      if (numFields) {
        PetscInt f;
        for (f = 0; f < numFields; f++) {
          PetscInt rowDof;

          ierr = PetscSectionGetFieldDof(localFine,p,f,&rowDof);CHKERRQ(ierr);
          offsets[f + 1]        = offsets[f] + rowDof;
          offsetsCopy[f + 1]    = offsets[f + 1];
          /* TODO: closure indices */
          newOffsets[f + 1]     = newOffsets[f] + ((childId == -1) ? rowDof : refPointFieldN[childId - pRefStart][f]);
        }
        ierr = DMPlexGetIndicesPointFields_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
      }
      else {
        offsets[0]    = 0;
        offsets[1]    = lDof;
        newOffsets[0] = 0;
        newOffsets[1] = (childId == -1) ? lDof : refPointFieldN[childId - pRefStart][0];
        ierr = DMPlexGetIndicesPoint_Internal(localFine,p,gOff,offsetsCopy,PETSC_FALSE,0,rowIndices);CHKERRQ(ierr);
      }
      if (childId == -1) { /* no child interpolation: one nnz per */
        ierr = VecSetValues(vecFine,numValues,rowIndices,pVal,INSERT_VALUES);CHKERRQ(ierr);
      } else {
        PetscInt f;

        if (grad && p >= cellStart && p < cellEnd) {
          numValues -= (dim * (1 + numFVcomps));
          fvGradData = &pVal[numValues];
        }
        for (f = 0; f < PetscMax(1,numFields); f++) {
          const PetscScalar *childMat = refPointFieldMats[childId - pRefStart][f];
          PetscInt numRows = offsets[f+1] - offsets[f];
          PetscInt numCols = newOffsets[f + 1] - newOffsets[f];
          const PetscScalar *cVal = &pVal[newOffsets[f]];
          PetscScalar *rVal = &pointWork[offsets[f]];
          PetscInt i, j;

#if 0
          ierr = PetscInfo6(coarse,"field %D, numFields %D, childId %D, numRows %D, numCols %D, refPointFieldN %D\n",f,numFields,childId,numRows,numCols,refPointFieldN[childId - pRefStart][f]);CHKERRQ(ierr);
#endif
          for (i = 0; i < numRows; i++) {
            PetscScalar val = 0.;
            for (j = 0; j < numCols; j++) {
              val += childMat[i * numCols + j] * cVal[j];
            }
            rVal[i] = val;
          }
          if (f == fvField && p >= cellStart && p < cellEnd) {
            PetscReal   centroid[3];
            PetscScalar diff[3];
            const PetscScalar *parentCentroid = &fvGradData[0];
            const PetscScalar *gradient       = &fvGradData[dim];

            ierr = DMPlexComputeCellGeometryFVM(fine,p,NULL,centroid,NULL);CHKERRQ(ierr);
            for (i = 0; i < dim; i++) {
              diff[i] = centroid[i] - parentCentroid[i];
            }
            for (i = 0; i < numFVcomps; i++) {
              PetscScalar val = 0.;

              for (j = 0; j < dim; j++) {
                val += gradient[dim * i + j] * diff[j];
              }
              rVal[i] += val;
            }
          }
          ierr = VecSetValues(vecFine,numRows,&rowIndices[offsets[f]],rVal,INSERT_VALUES);CHKERRQ(ierr);
        }
      }
    }
    ierr = DMPlexReferenceTreeRestoreChildrenMatrices(refTree,&refPointFieldMats,&refPointFieldN);CHKERRQ(ierr);
    ierr = DMRestoreWorkArray(fine,maxDof,PETSC_INT,&rowIndices);CHKERRQ(ierr);
    ierr = DMRestoreWorkArray(fine,maxDof,PETSC_SCALAR,&pointWork);CHKERRQ(ierr);
  }
  ierr = PetscFree(leafValues);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&leafValuesSec);CHKERRQ(ierr);
  ierr = PetscFree7(offsets,offsetsCopy,newOffsets,newOffsetsCopy,rowOffsets,numD,numO);CHKERRQ(ierr);
  ierr = ISRestoreIndices(aIS,&anchors);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexTransferVecTree_Inject"
static PetscErrorCode DMPlexTransferVecTree_Inject(DM fine, Vec vecFine, DM coarse, Vec vecCoarse, PetscSF coarseToFine, PetscInt *cids)
{
  PetscDS        ds;
  DM             refTree;
  PetscSection   multiRootSec, rootIndicesSec;
  PetscSection   globalCoarse, globalFine;
  PetscSection   localCoarse, localFine;
  PetscSection   cSecRef;
  PetscInt       *parentIndices, pRefStart, pRefEnd;
  PetscScalar    *rootValues, *parentValues;
  Mat            injRef;
  PetscInt       numFields, maxDof;
  PetscInt       pStartC, pEndC, pStartF, pEndF, p;
  PetscInt       *offsets, *offsetsCopy, *rowOffsets;
  PetscLayout    rowMap, colMap;
  PetscInt       rowStart, rowEnd, colStart, colEnd;
  PetscScalar    ***childrenMats=NULL ; /* gcc -O gives 'may be used uninitialized' warning'. Initializing to suppress this warning */
  PetscErrorCode ierr;

  PetscFunctionBegin;

  /* get the templates for the fine-to-coarse injection from the reference tree */
  ierr = VecSetOption(vecFine,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);CHKERRQ(ierr);
  ierr = VecSetOption(vecCoarse,VEC_IGNORE_NEGATIVE_INDICES,PETSC_TRUE);CHKERRQ(ierr);
  ierr = DMPlexGetReferenceTree(coarse,&refTree);CHKERRQ(ierr);
  ierr = DMGetDS(coarse,&ds);CHKERRQ(ierr);
  ierr = DMSetDS(refTree,ds);CHKERRQ(ierr);
  ierr = DMGetDefaultConstraints(refTree,&cSecRef,NULL);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(cSecRef,&pRefStart,&pRefEnd);CHKERRQ(ierr);
  ierr = DMPlexReferenceTreeGetInjector(refTree,&injRef);CHKERRQ(ierr);

  ierr = DMPlexGetChart(fine,&pStartF,&pEndF);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(fine,&localFine);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(fine,&globalFine);CHKERRQ(ierr);
  ierr = PetscSectionGetNumFields(localFine,&numFields);CHKERRQ(ierr);
  ierr = DMPlexGetChart(coarse,&pStartC,&pEndC);CHKERRQ(ierr);
  ierr = DMGetDefaultSection(coarse,&localCoarse);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(coarse,&globalCoarse);CHKERRQ(ierr);
  ierr = PetscSectionGetMaxDof(localCoarse,&maxDof);CHKERRQ(ierr);
  {
    PetscInt maxFields = PetscMax(1,numFields) + 1;
    ierr = PetscMalloc3(maxFields,&offsets,maxFields,&offsetsCopy,maxFields,&rowOffsets);CHKERRQ(ierr);
  }

  ierr = DMPlexTransferInjectorTree(coarse,fine,coarseToFine,cids,vecFine,numFields,offsets,&multiRootSec,&rootIndicesSec,NULL,&rootValues);CHKERRQ(ierr);

  ierr = PetscMalloc2(maxDof,&parentIndices,maxDof,&parentValues);CHKERRQ(ierr);

  /* count indices */
  ierr = VecGetLayout(vecFine,&colMap);CHKERRQ(ierr);
  ierr = VecGetLayout(vecCoarse,&rowMap);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(rowMap);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(colMap);CHKERRQ(ierr);
  ierr = PetscLayoutGetRange(rowMap,&rowStart,&rowEnd);CHKERRQ(ierr);
  ierr = PetscLayoutGetRange(colMap,&colStart,&colEnd);CHKERRQ(ierr);
  /* insert values */
  ierr = DMPlexReferenceTreeGetChildrenMatrices_Injection(refTree,injRef,&childrenMats);CHKERRQ(ierr);
  for (p = pStartC; p < pEndC; p++) {
    PetscInt  numLeaves, leafStart, leafEnd, l, dof, cdof, gOff;
    PetscBool contribute = PETSC_FALSE;

    ierr = PetscSectionGetDof(globalCoarse,p,&dof);CHKERRQ(ierr);
    ierr = PetscSectionGetConstraintDof(globalCoarse,p,&cdof);CHKERRQ(ierr);
    if ((dof - cdof) <= 0) continue;
    ierr = PetscSectionGetDof(localCoarse,p,&dof);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(globalCoarse,p,&gOff);CHKERRQ(ierr);

    rowOffsets[0] = 0;
    offsetsCopy[0] = 0;
    if (numFields) {
      PetscInt f;

      for (f = 0; f < numFields; f++) {
        PetscInt fDof;
        ierr = PetscSectionGetFieldDof(localCoarse,p,f,&fDof);CHKERRQ(ierr);
        rowOffsets[f + 1] = offsetsCopy[f + 1] = fDof + rowOffsets[f];
      }
      DMPlexGetIndicesPointFields_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
    }
    else {
      DMPlexGetIndicesPoint_Internal(localCoarse,p,gOff < 0 ? -(gOff + 1) : gOff,offsetsCopy,PETSC_FALSE,0,parentIndices);CHKERRQ(ierr);
      rowOffsets[1] = offsetsCopy[0];
    }

    ierr = PetscSectionGetDof(multiRootSec,p,&numLeaves);CHKERRQ(ierr);
    ierr = PetscSectionGetOffset(multiRootSec,p,&leafStart);CHKERRQ(ierr);
    leafEnd = leafStart + numLeaves;
    for (l = 0; l < dof; l++) parentValues[l] = 0.;
    for (l = leafStart; l < leafEnd; l++) {
      PetscInt numIndices, childId, offset;
      const PetscScalar *childValues;

      ierr = PetscSectionGetDof(rootIndicesSec,l,&numIndices);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(rootIndicesSec,l,&offset);CHKERRQ(ierr);
      childId = (PetscInt) PetscRealPart(rootValues[offset++]);
      childValues = &rootValues[offset];
      numIndices--;

      if (childId == -2) { /* skip */
        continue;
      } else if (childId == -1) { /* equivalent points: scatter */
        PetscInt m;

        contribute = PETSC_TRUE;
        for (m = 0; m < numIndices; m++) parentValues[m] = childValues[m];
      } else { /* contributions from children: sum with injectors from reference tree */
        PetscInt parentId, f, lim;

        contribute = PETSC_TRUE;
        ierr = DMPlexGetTreeParent(refTree,childId,&parentId,NULL);CHKERRQ(ierr);

        lim = PetscMax(1,numFields);
        offsets[0] = 0;
        if (numFields) {
          PetscInt f;

          for (f = 0; f < numFields; f++) {
            PetscInt fDof;
            ierr = PetscSectionGetFieldDof(cSecRef,childId,f,&fDof);CHKERRQ(ierr);

            offsets[f + 1] = fDof + offsets[f];
          }
        }
        else {
          PetscInt cDof;

          ierr = PetscSectionGetDof(cSecRef,childId,&cDof);CHKERRQ(ierr);
          offsets[1] = cDof;
        }
        for (f = 0; f < lim; f++) {
          PetscScalar       *childMat   = &childrenMats[childId - pRefStart][f][0];
          PetscInt          n           = offsets[f+1]-offsets[f];
          PetscInt          i, j;
          const PetscScalar *colValues  = &childValues[offsets[f]];

          for (i = rowOffsets[f]; i < rowOffsets[f + 1]; i++) {
            PetscScalar val = 0.;
            for (j = 0; j < n; j++) {
              val += childMat[n * i + j] * colValues[j];
            }
            parentValues[i] += val;
          }
        }
      }
    }
    if (contribute) {ierr = VecSetValues(vecCoarse,dof,parentIndices,parentValues,INSERT_VALUES);CHKERRQ(ierr);}
  }
  ierr = PetscSectionDestroy(&multiRootSec);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&rootIndicesSec);CHKERRQ(ierr);
  ierr = PetscFree2(parentIndices,parentValues);CHKERRQ(ierr);
  ierr = DMPlexReferenceTreeRestoreChildrenMatrices_Injection(refTree,injRef,&childrenMats);CHKERRQ(ierr);
  ierr = PetscFree(rootValues);CHKERRQ(ierr);
  ierr = PetscFree3(offsets,offsetsCopy,rowOffsets);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMPlexTransferVecTree"
PetscErrorCode DMPlexTransferVecTree(DM dmIn, Vec vecIn, DM dmOut, Vec vecOut, PetscSF sfIn, PetscSF sfOut, PetscInt *cidsIn, PetscInt *cidsOut, PetscBool useBCs, PetscReal time)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = VecSet(vecOut,0.0);CHKERRQ(ierr);
  if (sfIn) {
    Vec vecInLocal;
    DM  dmGrad = NULL;
    Vec faceGeom = NULL, cellGeom = NULL, grad = NULL;

    ierr = DMGetLocalVector(dmIn,&vecInLocal);CHKERRQ(ierr);
    ierr = VecSet(vecInLocal,0.0);CHKERRQ(ierr);
    {
      PetscInt  numFields, i;

      ierr = DMGetNumFields(dmIn, &numFields);CHKERRQ(ierr);
      for (i = 0; i < numFields; i++) {
        PetscObject  obj;
        PetscClassId classid;

        ierr = DMGetField(dmIn, i, &obj);CHKERRQ(ierr);
        ierr = PetscObjectGetClassId(obj, &classid);CHKERRQ(ierr);
        if (classid == PETSCFV_CLASSID) {
          ierr = DMPlexGetDataFVM(dmIn,(PetscFV)obj,&cellGeom,&faceGeom,&dmGrad);CHKERRQ(ierr);
          break;
        }
      }
    }
    if (useBCs) {
      ierr = DMPlexInsertBoundaryValues(dmIn,PETSC_TRUE,vecInLocal,time,faceGeom,cellGeom,NULL);CHKERRQ(ierr);
    }
    ierr = DMGlobalToLocalBegin(dmIn,vecIn,INSERT_VALUES,vecInLocal);CHKERRQ(ierr);
    ierr = DMGlobalToLocalEnd(dmIn,vecIn,INSERT_VALUES,vecInLocal);CHKERRQ(ierr);
    if (dmGrad) {
      ierr = DMGetGlobalVector(dmGrad,&grad);CHKERRQ(ierr);
      ierr = DMPlexReconstructGradientsFVM(dmIn,vecInLocal,grad);CHKERRQ(ierr);
    }
    ierr = DMPlexTransferVecTree_Interpolate(dmIn,vecInLocal,dmOut,vecOut,sfIn,cidsIn,grad,cellGeom);CHKERRQ(ierr);
    ierr = DMRestoreLocalVector(dmIn,&vecInLocal);CHKERRQ(ierr);
    if (dmGrad) {
      ierr = DMRestoreGlobalVector(dmGrad,&grad);CHKERRQ(ierr);
    }
  }
  if (sfOut) {
    ierr = DMPlexTransferVecTree_Inject(dmIn,vecIn,dmOut,vecOut,sfOut,cidsOut);CHKERRQ(ierr);
  }
  ierr = VecAssemblyBegin(vecOut);CHKERRQ(ierr);
  ierr = VecAssemblyEnd(vecOut);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}