impls/network/network.c

#include <petsc/private/dmnetworkimpl.h>  /*I  "petscdmnetwork.h"  I*/
#include <petscdmplex.h>
#include <petscsf.h>

/*@
  DMNetworkGetPlex - Gets the Plex DM associated with this network DM

  Not collective

  Input Parameters:
+ netdm - the dm object
- plexmdm - the plex dm object

  Level: Advanced

.seealso: DMNetworkCreate()
@*/
PetscErrorCode DMNetworkGetPlex(DM netdm, DM *plexdm)
{
  DM_Network     *network = (DM_Network*) netdm->data;

  PetscFunctionBegin;
  *plexdm = network->plex;
  PetscFunctionReturn(0);
}

/*@
  DMNetworkSetSizes - Sets the local and global vertices and edges.

  Collective on DM

  Input Parameters:
+ dm - the dm object
. nV - number of local vertices
. nE - number of local edges
. NV - number of global vertices (or PETSC_DETERMINE)
- NE - number of global edges (or PETSC_DETERMINE)

   Notes
   If one processor calls this with NV (NE) of PETSC_DECIDE then all processors must, otherwise the prgram will hang.

   You cannot change the sizes once they have been set

   Level: intermediate

.seealso: DMNetworkCreate()
@*/
PetscErrorCode DMNetworkSetSizes(DM dm, PetscInt nV, PetscInt nE, PetscInt NV, PetscInt NE)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*) dm->data;
  PetscInt       a[2],b[2];

  PetscFunctionBegin;
  PetscValidHeaderSpecific(dm,DM_CLASSID,1);
  if (NV > 0) PetscValidLogicalCollectiveInt(dm,NV,4);
  if (NE > 0) PetscValidLogicalCollectiveInt(dm,NE,5);
  if (NV > 0 && nV > NV) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Local vertex size %D cannot be larger than global vertex size %D",nV,NV);
  if (NE > 0 && nE > NE) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Local edge size %D cannot be larger than global edge size %D",nE,NE);
  if ((network->nNodes >= 0 || network->NNodes >= 0) && (network->nNodes != nV || network->NNodes != NV)) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot change/reset vertex sizes to %D local %D global after previously setting them to %D local %D global",nV,NV,network->nNodes,network->NNodes);
  if ((network->nEdges >= 0 || network->NEdges >= 0) && (network->nEdges != nE || network->NEdges != NE)) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot change/reset edge sizes to %D local %D global after previously setting them to %D local %D global",nE,NE,network->nEdges,network->NEdges);
  if (NE < 0 || NV < 0) {
    a[0] = nV; a[1] = nE;
    ierr = MPIU_Allreduce(a,b,2,MPIU_INT,MPI_SUM,PetscObjectComm((PetscObject)dm));CHKERRQ(ierr);
    NV = b[0]; NE = b[1];
  }
  network->nNodes = nV;
  network->NNodes = NV;
  network->nEdges = nE;
  network->NEdges = NE;
  PetscFunctionReturn(0);
}

/*@
  DMNetworkSetEdgeList - Sets the list of local edges (vertex connectivity) for the network

  Logically collective on DM

  Input Parameters:
. edges - list of edges

  Notes:
  There is no copy involved in this operation, only the pointer is referenced. The edgelist should
  not be destroyed before the call to DMNetworkLayoutSetUp

  Level: intermediate

.seealso: DMNetworkCreate, DMNetworkSetSizes
@*/
PetscErrorCode DMNetworkSetEdgeList(DM dm, int edgelist[])
{
  DM_Network *network = (DM_Network*) dm->data;

  PetscFunctionBegin;
  network->edges = edgelist;
  PetscFunctionReturn(0);
}

/*@
  DMNetworkLayoutSetUp - Sets up the bare layout (graph) for the network

  Collective on DM

  Input Parameters
. DM - the dmnetwork object

  Notes:
  This routine should be called after the network sizes and edgelists have been provided. It creates
  the bare layout of the network and sets up the network to begin insertion of components.

  All the components should be registered before calling this routine.

  Level: intermediate

.seealso: DMNetworkSetSizes, DMNetworkSetEdgeList
@*/
PetscErrorCode DMNetworkLayoutSetUp(DM dm)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*) dm->data;
  PetscInt       dim = 1; /* One dimensional network */
  PetscInt       numCorners=2;
  PetscInt       spacedim=2;
  double         *vertexcoords=NULL;
  PetscInt       i;
  PetscInt       ndata;

  PetscFunctionBegin;
  if (network->nNodes) {
    ierr = PetscCalloc1(numCorners*network->nNodes,&vertexcoords);CHKERRQ(ierr);
  }
  ierr = DMPlexCreateFromCellList(PetscObjectComm((PetscObject)dm),dim,network->nEdges,network->nNodes,numCorners,PETSC_FALSE,network->edges,spacedim,vertexcoords,&network->plex);CHKERRQ(ierr);
  if (network->nNodes) {
    ierr = PetscFree(vertexcoords);CHKERRQ(ierr);
  }
  ierr = DMPlexGetChart(network->plex,&network->pStart,&network->pEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(network->plex,0,&network->eStart,&network->eEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(network->plex,1,&network->vStart,&network->vEnd);CHKERRQ(ierr);

  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&network->DataSection);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)dm),&network->DofSection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(network->DataSection,network->pStart,network->pEnd);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(network->DofSection,network->pStart,network->pEnd);CHKERRQ(ierr);


  network->dataheadersize = sizeof(struct _p_DMNetworkComponentHeader)/sizeof(DMNetworkComponentGenericDataType);
  ierr = PetscCalloc1(network->pEnd-network->pStart,&network->header);CHKERRQ(ierr);
  for (i = network->pStart; i < network->pEnd; i++) {
    if (i < network->vStart) {
      network->header[i].id = i;
    } else {
      network->header[i].id = i - network->vStart;
    }
    network->header[i].ndata = 0;
    ndata = network->header[i].ndata;
    ierr = PetscSectionAddDof(network->DataSection,i,network->dataheadersize);CHKERRQ(ierr);
    network->header[i].offset[ndata] = 0;
  }
  ierr = PetscMalloc1(network->pEnd-network->pStart,&network->cvalue);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  DMNetworkRegisterComponent - Registers the network component

  Logically collective on DM

  Input Parameters
+ dm   - the network object
. name - the component name
- size - the storage size in bytes for this component data

   Output Parameters
.   key - an integer key that defines the component

   Notes
   This routine should be called by all processors before calling DMNetworkLayoutSetup().

   Level: intermediate

.seealso: DMNetworkLayoutSetUp, DMNetworkCreate
@*/
PetscErrorCode DMNetworkRegisterComponent(DM dm,const char *name,PetscInt size,PetscInt *key)
{
  PetscErrorCode        ierr;
  DM_Network            *network = (DM_Network*) dm->data;
  DMNetworkComponent    *component=&network->component[network->ncomponent];
  PetscBool             flg=PETSC_FALSE;
  PetscInt              i;

  PetscFunctionBegin;

  for (i=0; i < network->ncomponent; i++) {
    ierr = PetscStrcmp(component->name,name,&flg);CHKERRQ(ierr);
    if (flg) {
      *key = i;
      PetscFunctionReturn(0);
    }
  }

  ierr = PetscStrcpy(component->name,name);CHKERRQ(ierr);
  component->size = size/sizeof(DMNetworkComponentGenericDataType);
  *key = network->ncomponent;
  network->ncomponent++;
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetVertexRange - Get the bounds [start, end) for the vertices.

  Not Collective

  Input Parameters:
+ dm - The DMNetwork object

  Output Paramters:
+ vStart - The first vertex point
- vEnd   - One beyond the last vertex point

  Level: intermediate

.seealso: DMNetworkGetEdgeRange
@*/
PetscErrorCode DMNetworkGetVertexRange(DM dm,PetscInt *vStart,PetscInt *vEnd)
{
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  if (vStart) *vStart = network->vStart;
  if (vEnd) *vEnd = network->vEnd;
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetEdgeRange - Get the bounds [start, end) for the edges.

  Not Collective

  Input Parameters:
+ dm - The DMNetwork object

  Output Paramters:
+ eStart - The first edge point
- eEnd   - One beyond the last edge point

  Level: intermediate

.seealso: DMNetworkGetVertexRange
@*/
PetscErrorCode DMNetworkGetEdgeRange(DM dm,PetscInt *eStart,PetscInt *eEnd)
{
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  if (eStart) *eStart = network->eStart;
  if (eEnd) *eEnd = network->eEnd;
  PetscFunctionReturn(0);
}


/*@
  DMNetworkGetEdgeVertexID - Get the user numbering for the edge or vertex.

  Not Collective

  Input Parameters:
+ dm - DMNetwork object
- p  - vertex/edge point

  Output Paramters:
. id - user numbering

  Level: intermediate

.seealso: DMNetworkGetEdgeRange, DMNetworkGetVertexRange
@*/
PetscErrorCode DMNetworkGetEdgeVertexID(DM dm,PetscInt p,PetscInt *id)
{
  PetscErrorCode    ierr;
  DM_Network        *network = (DM_Network*)dm->data;
  PetscInt          offsetp;
  DMNetworkComponentHeader header;

  PetscFunctionBegin;
  ierr = PetscSectionGetOffset(network->DataSection,p,&offsetp);CHKERRQ(ierr);
  header = (DMNetworkComponentHeader)(network->componentdataarray+offsetp);
  *id    = header->id;
  PetscFunctionReturn(0);
}

/*@
  DMNetworkAddComponent - Adds a network component at the given point (vertex/edge)

  Not Collective

  Input Parameters:
+ dm           - The DMNetwork object
. p            - vertex/edge point
. componentkey - component key returned while registering the component
- compvalue    - pointer to the data structure for the component

  Level: intermediate

.seealso: DMNetworkGetVertexRange, DMNetworkGetEdgeRange, DMNetworkRegisterComponent
@*/
PetscErrorCode DMNetworkAddComponent(DM dm, PetscInt p,PetscInt componentkey,void* compvalue)
{
  DM_Network               *network = (DM_Network*)dm->data;
  DMNetworkComponent       *component = &network->component[componentkey];
  DMNetworkComponentHeader header = &network->header[p];
  DMNetworkComponentValue  cvalue = &network->cvalue[p];
  PetscErrorCode           ierr;

  PetscFunctionBegin;
  if (header->ndata == MAX_DATA_AT_POINT) SETERRQ1(PetscObjectComm((PetscObject)dm),PETSC_ERR_ARG_OUTOFRANGE,"Number of components at a point exceeds the max %D",MAX_DATA_AT_POINT);

  header->size[header->ndata] = component->size;
  ierr = PetscSectionAddDof(network->DataSection,p,component->size);CHKERRQ(ierr);
  header->key[header->ndata] = componentkey;
  if (header->ndata != 0) header->offset[header->ndata] = header->offset[header->ndata-1] + header->size[header->ndata-1];

  cvalue->data[header->ndata] = (void*)compvalue;
  header->ndata++;
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetNumComponents - Get the number of components at a vertex/edge

  Not Collective

  Input Parameters:
+ dm - The DMNetwork object
. p  - vertex/edge point

  Output Parameters:
. numcomponents - Number of components at the vertex/edge

  Level: intermediate

.seealso: DMNetworkRegisterComponent, DMNetworkAddComponent
@*/
PetscErrorCode DMNetworkGetNumComponents(DM dm,PetscInt p,PetscInt *numcomponents)
{
  PetscErrorCode ierr;
  PetscInt       offset;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = PetscSectionGetOffset(network->DataSection,p,&offset);CHKERRQ(ierr);
  *numcomponents = ((DMNetworkComponentHeader)(network->componentdataarray+offset))->ndata;
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetComponentTypeOffset - Gets the type along with the offset for indexing the
                                    component value from the component data array

  Not Collective

  Input Parameters:
+ dm      - The DMNetwork object
. p       - vertex/edge point
- compnum - component number

  Output Parameters:
+ compkey - the key obtained when registering the component
- offset  - offset into the component data array associated with the vertex/edge point

  Notes:
  Typical usage:

  DMNetworkGetComponentDataArray(dm, &arr);
  DMNetworkGetVertex/EdgeRange(dm,&Start,&End);
  Loop over vertices or edges
    DMNetworkGetNumComponents(dm,v,&numcomps);
    Loop over numcomps
      DMNetworkGetComponentTypeOffset(dm,v,compnum,&key,&offset);
      compdata = (UserCompDataType)(arr+offset);

  Level: intermediate

.seealso: DMNetworkGetNumComponents, DMNetworkGetComponentDataArray,
@*/
PetscErrorCode DMNetworkGetComponentTypeOffset(DM dm,PetscInt p, PetscInt compnum, PetscInt *compkey, PetscInt *offset)
{
  PetscErrorCode           ierr;
  PetscInt                 offsetp;
  DMNetworkComponentHeader header;
  DM_Network               *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = PetscSectionGetOffset(network->DataSection,p,&offsetp);CHKERRQ(ierr);
  header = (DMNetworkComponentHeader)(network->componentdataarray+offsetp);
  if (compkey) *compkey = header->key[compnum];
  if (offset) *offset  = offsetp+network->dataheadersize+header->offset[compnum];
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetVariableOffset - Get the offset for accessing the variable associated with the given vertex/edge from the local vector.

  Not Collective

  Input Parameters:
+ dm     - The DMNetwork object
- p      - the edge/vertex point

  Output Parameters:
. offset - the offset

  Level: intermediate

.seealso: DMNetworkGetVariableGlobalOffset, DMGetLocalVector
@*/
PetscErrorCode DMNetworkGetVariableOffset(DM dm,PetscInt p,PetscInt *offset)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = PetscSectionGetOffset(network->plex->defaultSection,p,offset);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetVariableGlobalOffset - Get the global offset for the variable associated with the given vertex/edge from the global vector.

  Not Collective

  Input Parameters:
+ dm      - The DMNetwork object
- p       - the edge/vertex point

  Output Parameters:
. offsetg - the offset

  Level: intermediate

.seealso: DMNetworkGetVariableOffset, DMGetLocalVector
@*/
PetscErrorCode DMNetworkGetVariableGlobalOffset(DM dm,PetscInt p,PetscInt *offsetg)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = PetscSectionGetOffset(network->plex->defaultGlobalSection,p,offsetg);CHKERRQ(ierr);
  if (*offsetg < 0) *offsetg = -(*offsetg + 1); /* Convert to actual global offset for ghost node */
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetEdgeOffset - Get the offset for accessing the variable associated with the given edge from the local subvector.

  Not Collective

  Input Parameters:
+ dm     - The DMNetwork object
- p      - the edge point

  Output Parameters:
. offset - the offset

  Level: intermediate

.seealso: DMNetworkGetVariableGlobalOffset, DMGetLocalVector
@*/
PetscErrorCode DMNetworkGetEdgeOffset(DM dm,PetscInt p,PetscInt *offset)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;

  ierr = PetscSectionGetOffset(network->edge.DofSection,p,offset);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetVertexOffset - Get the offset for accessing the variable associated with the given vertex from the local subvector.

  Not Collective

  Input Parameters:
+ dm     - The DMNetwork object
- p      - the vertex point

  Output Parameters:
. offset - the offset

  Level: intermediate

.seealso: DMNetworkGetVariableGlobalOffset, DMGetLocalVector
@*/
PetscErrorCode DMNetworkGetVertexOffset(DM dm,PetscInt p,PetscInt *offset)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;

  p -= network->vStart;

  ierr = PetscSectionGetOffset(network->vertex.DofSection,p,offset);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/*@
  DMNetworkAddNumVariables - Add number of variables associated with a given point.

  Not Collective

  Input Parameters:
+ dm   - The DMNetworkObject
. p    - the vertex/edge point
- nvar - number of additional variables

  Level: intermediate

.seealso: DMNetworkSetNumVariables
@*/
PetscErrorCode DMNetworkAddNumVariables(DM dm,PetscInt p,PetscInt nvar)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = PetscSectionAddDof(network->DofSection,p,nvar);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMNetworkGetNumVariables - Gets number of variables for a vertex/edge point.

  Not Collective

  Input Parameters:
+ dm   - The DMNetworkObject
- p    - the vertex/edge point

  Output Parameters:
. nvar - number of variables

  Level: intermediate

.seealso: DMNetworkAddNumVariables, DMNetworkSddNumVariables
@*/
PetscErrorCode DMNetworkGetNumVariables(DM dm,PetscInt p,PetscInt *nvar)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = PetscSectionGetDof(network->DofSection,p,nvar);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMNetworkSetNumVariables - Sets number of variables for a vertex/edge point.

  Not Collective

  Input Parameters:
+ dm   - The DMNetworkObject
. p    - the vertex/edge point
- nvar - number of variables

  Level: intermediate

.seealso: DMNetworkAddNumVariables
@*/
PetscErrorCode DMNetworkSetNumVariables(DM dm,PetscInt p,PetscInt nvar)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = PetscSectionSetDof(network->DofSection,p,nvar);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* Sets up the array that holds the data for all components and its associated section. This
   function is called during DMSetUp() */
PetscErrorCode DMNetworkComponentSetUp(DM dm)
{
  PetscErrorCode              ierr;
  DM_Network     *network = (DM_Network*)dm->data;
  PetscInt                    arr_size;
  PetscInt                    p,offset,offsetp;
  DMNetworkComponentHeader header;
  DMNetworkComponentValue  cvalue;
  DMNetworkComponentGenericDataType      *componentdataarray;
  PetscInt ncomp, i;

  PetscFunctionBegin;
  ierr = PetscSectionSetUp(network->DataSection);CHKERRQ(ierr);
  ierr = PetscSectionGetStorageSize(network->DataSection,&arr_size);CHKERRQ(ierr);
  ierr = PetscMalloc1(arr_size,&network->componentdataarray);CHKERRQ(ierr);
  componentdataarray = network->componentdataarray;
  for (p = network->pStart; p < network->pEnd; p++) {
    ierr = PetscSectionGetOffset(network->DataSection,p,&offsetp);CHKERRQ(ierr);
    /* Copy header */
    header = &network->header[p];
    ierr = PetscMemcpy(componentdataarray+offsetp,header,network->dataheadersize*sizeof(DMNetworkComponentGenericDataType));CHKERRQ(ierr);
    /* Copy data */
    cvalue = &network->cvalue[p];
    ncomp = header->ndata;
    for (i = 0; i < ncomp; i++) {
      offset = offsetp + network->dataheadersize + header->offset[i];
      ierr = PetscMemcpy(componentdataarray+offset,cvalue->data[i],header->size[i]*sizeof(DMNetworkComponentGenericDataType));CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

/* Sets up the section for dofs. This routine is called during DMSetUp() */
PetscErrorCode DMNetworkVariablesSetUp(DM dm)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = PetscSectionSetUp(network->DofSection);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  DMNetworkGetComponentDataArray - Returns the component data array

  Not Collective

  Input Parameters:
. dm - The DMNetwork Object

  Output Parameters:
. componentdataarray - array that holds data for all components

  Level: intermediate

.seealso: DMNetworkGetComponentTypeOffset, DMNetworkGetNumComponents
@*/
PetscErrorCode DMNetworkGetComponentDataArray(DM dm,DMNetworkComponentGenericDataType **componentdataarray)
{
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  *componentdataarray = network->componentdataarray;
  PetscFunctionReturn(0);
}

/* Get a subsection from a range of points */
PetscErrorCode DMNetworkGetSubSection_private(PetscSection master, PetscInt pstart, PetscInt pend,PetscSection *subsection)
{
  PetscErrorCode ierr;
  PetscInt       i, nvar;

  PetscFunctionBegin;
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)master), subsection);CHKERRQ(ierr);
  ierr = PetscSectionSetChart(*subsection, 0, pend - pstart);CHKERRQ(ierr);
  for (i = pstart; i < pend; i++) {
    ierr = PetscSectionGetDof(master,i,&nvar);CHKERRQ(ierr);
    ierr = PetscSectionSetDof(*subsection, i - pstart, nvar);CHKERRQ(ierr);
  }

  ierr = PetscSectionSetUp(*subsection);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* Create a submap of points with a GlobalToLocal structure */
PetscErrorCode DMNetworkSetSubMap_private(PetscInt pstart, PetscInt pend, ISLocalToGlobalMapping *map)
{
  PetscErrorCode ierr;
  PetscInt       i, *subpoints;

  PetscFunctionBegin;
  /* Create index sets to map from "points" to "subpoints" */
  ierr = PetscMalloc1(pend - pstart, &subpoints);CHKERRQ(ierr);
  for (i = pstart; i < pend; i++) {
    subpoints[i - pstart] = i;
  }
  ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_WORLD,1,pend-pstart,subpoints,PETSC_COPY_VALUES,map);CHKERRQ(ierr);
  ierr = PetscFree(subpoints);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMNetworkAssembleGraphStructures - Assembles vertex and edge data structures. Must be called after DMNetworkDistribute.

  Collective

  Input Parameters:
. dm   - The DMNetworkObject

  Note: the routine will create alternative orderings for the vertices and edges. Assume global network points are:

  points = [0 1 2 3 4 5 6]

  where edges = [0, 3] and vertices = [4, 6]. The new orderings will be specific to the subset (i.e vertices = [0, 2]).

  With this new ordering a local PetscSection, global PetscSection and PetscSF will be created specific to the subset.

  Level: intermediate

@*/
PetscErrorCode DMNetworkAssembleGraphStructures(DM dm)
{
  PetscErrorCode ierr;
  MPI_Comm       comm;
  PetscMPIInt    rank, size;
  DM_Network     *network = (DM_Network*)dm->data;

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

  /* Create maps for vertices and edges */
  ierr = DMNetworkSetSubMap_private(network->vStart,network->vEnd,&network->vertex.mapping);CHKERRQ(ierr);
  ierr = DMNetworkSetSubMap_private(network->eStart,network->eEnd,&network->edge.mapping);CHKERRQ(ierr);

  /* Create local sub-sections */
  ierr = DMNetworkGetSubSection_private(network->DofSection,network->vStart,network->vEnd,&network->vertex.DofSection);CHKERRQ(ierr);
  ierr = DMNetworkGetSubSection_private(network->DofSection,network->eStart,network->eEnd,&network->edge.DofSection);CHKERRQ(ierr);

  if (size > 1) {
    ierr = PetscSFGetSubSF(network->plex->sf, network->vertex.mapping, &network->vertex.sf);CHKERRQ(ierr);
    ierr = PetscSectionCreateGlobalSection(network->vertex.DofSection, network->vertex.sf, PETSC_FALSE, PETSC_FALSE, &network->vertex.GlobalDofSection);CHKERRQ(ierr);
  ierr = PetscSFGetSubSF(network->plex->sf, network->edge.mapping, &network->edge.sf);CHKERRQ(ierr);
  ierr = PetscSectionCreateGlobalSection(network->edge.DofSection, network->edge.sf, PETSC_FALSE, PETSC_FALSE, &network->edge.GlobalDofSection);CHKERRQ(ierr);
  } else {
  /* create structures for vertex */
  ierr = PetscSectionClone(network->vertex.DofSection,&network->vertex.GlobalDofSection);CHKERRQ(ierr);
  /* create structures for edge */
  ierr = PetscSectionClone(network->edge.DofSection,&network->edge.GlobalDofSection);CHKERRQ(ierr);
  }


  /* Add viewers */
  ierr = PetscObjectSetName((PetscObject)network->edge.GlobalDofSection,"Global edge dof section");CHKERRQ(ierr);
  ierr = PetscObjectSetName((PetscObject)network->vertex.GlobalDofSection,"Global vertex dof section");CHKERRQ(ierr);
  ierr = PetscSectionViewFromOptions(network->edge.GlobalDofSection, NULL, "-edge_global_section_view");CHKERRQ(ierr);
  ierr = PetscSectionViewFromOptions(network->vertex.GlobalDofSection, NULL, "-vertex_global_section_view");CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

/*@
  DMNetworkDistribute - Distributes the network and moves associated component data.

  Collective

  Input Parameter:
+ DM - the DMNetwork object
- overlap - The overlap of partitions, 0 is the default

  Notes:
  Distributes the network with <overlap>-overlapping partitioning of the edges.

  Level: intermediate

.seealso: DMNetworkCreate
@*/
PetscErrorCode DMNetworkDistribute(DM *dm,PetscInt overlap)
{
  MPI_Comm       comm;
  PetscErrorCode ierr;
  PetscMPIInt    size;
  DM_Network     *oldDMnetwork = (DM_Network*)((*dm)->data);
  DM_Network     *newDMnetwork;
  PetscSF        pointsf;
  DM             newDM;
  PetscPartitioner part;

  PetscFunctionBegin;

  ierr = PetscObjectGetComm((PetscObject)*dm,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &size);CHKERRQ(ierr);
  if (size == 1) PetscFunctionReturn(0);

  ierr = DMNetworkCreate(PetscObjectComm((PetscObject)*dm),&newDM);CHKERRQ(ierr);
  newDMnetwork = (DM_Network*)newDM->data;
  newDMnetwork->dataheadersize = sizeof(struct _p_DMNetworkComponentHeader)/sizeof(DMNetworkComponentGenericDataType);

  /* Enable runtime options for petscpartitioner */
  ierr = DMPlexGetPartitioner(oldDMnetwork->plex,&part);CHKERRQ(ierr);
  ierr = PetscPartitionerSetFromOptions(part);CHKERRQ(ierr);

  /* Distribute plex dm and dof section */
  ierr = DMPlexDistribute(oldDMnetwork->plex,overlap,&pointsf,&newDMnetwork->plex);CHKERRQ(ierr);

  /* Distribute dof section */
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)*dm),&newDMnetwork->DofSection);CHKERRQ(ierr);
  ierr = PetscSFDistributeSection(pointsf,oldDMnetwork->DofSection,NULL,newDMnetwork->DofSection);CHKERRQ(ierr);
  ierr = PetscSectionCreate(PetscObjectComm((PetscObject)*dm),&newDMnetwork->DataSection);CHKERRQ(ierr);

  /* Distribute data and associated section */
  ierr = DMPlexDistributeData(newDMnetwork->plex,pointsf,oldDMnetwork->DataSection,MPIU_INT,(void*)oldDMnetwork->componentdataarray,newDMnetwork->DataSection,(void**)&newDMnetwork->componentdataarray);CHKERRQ(ierr);

  ierr = PetscSectionGetChart(newDMnetwork->DataSection,&newDMnetwork->pStart,&newDMnetwork->pEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(newDMnetwork->plex,0, &newDMnetwork->eStart,&newDMnetwork->eEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(newDMnetwork->plex,1,&newDMnetwork->vStart,&newDMnetwork->vEnd);CHKERRQ(ierr);
  newDMnetwork->nEdges = newDMnetwork->eEnd - newDMnetwork->eStart;
  newDMnetwork->nNodes = newDMnetwork->vEnd - newDMnetwork->vStart;
  newDMnetwork->NNodes = oldDMnetwork->NNodes;
  newDMnetwork->NEdges = oldDMnetwork->NEdges;

  /* Set Dof section as the default section for dm */
  ierr = DMSetDefaultSection(newDMnetwork->plex,newDMnetwork->DofSection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(newDMnetwork->plex,&newDMnetwork->GlobalDofSection);CHKERRQ(ierr);

  /* Destroy point SF */
  ierr = PetscSFDestroy(&pointsf);CHKERRQ(ierr);

  ierr = DMDestroy(dm);CHKERRQ(ierr);
  *dm  = newDM;
  PetscFunctionReturn(0);
}

/*@C
  PetscSFGetSubSF - Returns an SF for a specific subset of points. Leaves are re-numbered to reflect the new ordering.

  Input Parameters:
+ masterSF - the original SF structure
- map      - a ISLocalToGlobal mapping that contains the subset of points

  Output Parameters:
. subSF    - a subset of the masterSF for the desired subset.
*/

PetscErrorCode PetscSFGetSubSF(PetscSF mastersf, ISLocalToGlobalMapping map, PetscSF *subSF) {

  PetscErrorCode        ierr;
  PetscInt              nroots, nleaves, *ilocal_sub;
  PetscInt              i, *ilocal_map, nroots_sub, nleaves_sub = 0;
  PetscInt              *local_points, *remote_points;
  PetscSFNode           *iremote_sub;
  const PetscInt        *ilocal;
  const PetscSFNode     *iremote;

  PetscFunctionBegin;
  ierr = PetscSFGetGraph(mastersf,&nroots,&nleaves,&ilocal,&iremote);CHKERRQ(ierr);

  /* Look for leaves that pertain to the subset of points. Get the local ordering */
  ierr = PetscMalloc1(nleaves,&ilocal_map);CHKERRQ(ierr);
  ierr = ISGlobalToLocalMappingApply(map,IS_GTOLM_MASK,nleaves,ilocal,NULL,ilocal_map);CHKERRQ(ierr);
  for (i = 0; i < nleaves; i++) {
    if (ilocal_map[i] != -1) nleaves_sub += 1;
  }
  /* Re-number ilocal with subset numbering. Need information from roots */
  ierr = PetscMalloc2(nroots,&local_points,nroots,&remote_points);CHKERRQ(ierr);
  for (i = 0; i < nroots; i++) local_points[i] = i;
  ierr = ISGlobalToLocalMappingApply(map,IS_GTOLM_MASK,nroots,local_points,NULL,local_points);CHKERRQ(ierr);
  ierr = PetscSFBcastBegin(mastersf, MPIU_INT, local_points, remote_points);CHKERRQ(ierr);
  ierr = PetscSFBcastEnd(mastersf, MPIU_INT, local_points, remote_points);CHKERRQ(ierr);
  /* Fill up graph using local (that is, local to the subset) numbering. */
  ierr = PetscMalloc1(nleaves_sub,&ilocal_sub);CHKERRQ(ierr);
  ierr = PetscMalloc1(nleaves_sub,&iremote_sub);CHKERRQ(ierr);
  nleaves_sub = 0;
  for (i = 0; i < nleaves; i++) {
    if (ilocal_map[i] != -1) {
      ilocal_sub[nleaves_sub] = ilocal_map[i];
      iremote_sub[nleaves_sub].rank = iremote[i].rank;
      iremote_sub[nleaves_sub].index = remote_points[ilocal[i]];
      nleaves_sub += 1;
    }
  }
  ierr = PetscFree2(local_points,remote_points);CHKERRQ(ierr);
  ierr = ISLocalToGlobalMappingGetSize(map,&nroots_sub);CHKERRQ(ierr);

  /* Create new subSF */
  ierr = PetscSFCreate(PETSC_COMM_WORLD,subSF);CHKERRQ(ierr);
  ierr = PetscSFSetFromOptions(*subSF);CHKERRQ(ierr);
  ierr = PetscSFSetGraph(*subSF,nroots_sub,nleaves_sub,ilocal_sub,PETSC_OWN_POINTER,iremote_sub,PETSC_COPY_VALUES);CHKERRQ(ierr);
  ierr = PetscFree(ilocal_map);CHKERRQ(ierr);
  ierr = PetscFree(iremote_sub);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}

/*@C
  DMNetworkGetSupportingEdges - Return the supporting edges for this vertex point

  Not Collective

  Input Parameters:
+ dm - The DMNetwork object
- p  - the vertex point

  Output Paramters:
+ nedges - number of edges connected to this vertex point
- edges  - List of edge points

  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: DMNetworkCreate, DMNetworkGetConnectedNodes
@*/
PetscErrorCode DMNetworkGetSupportingEdges(DM dm,PetscInt vertex,PetscInt *nedges,const PetscInt *edges[])
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = DMPlexGetSupportSize(network->plex,vertex,nedges);CHKERRQ(ierr);
  ierr = DMPlexGetSupport(network->plex,vertex,edges);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@C
  DMNetworkGetConnectedNodes - Return the connected vertices for this edge point

  Not Collective

  Input Parameters:
+ dm - The DMNetwork object
- p  - the edge point

  Output Paramters:
. vertices  - vertices connected to this edge

  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: DMNetworkCreate, DMNetworkGetSupportingEdges
@*/
PetscErrorCode DMNetworkGetConnectedNodes(DM dm,PetscInt edge,const PetscInt *vertices[])
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = DMPlexGetCone(network->plex,edge,vertices);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
  DMNetworkIsGhostVertex - Returns TRUE if the vertex is a ghost vertex

  Not Collective

  Input Parameters:
+ dm - The DMNetwork object
. p  - the vertex point

  Output Parameter:
. isghost - TRUE if the vertex is a ghost point

  Level: intermediate

.seealso: DMNetworkCreate, DMNetworkGetConnectedNodes, DMNetworkGetVertexRange
@*/
PetscErrorCode DMNetworkIsGhostVertex(DM dm,PetscInt p,PetscBool *isghost)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*)dm->data;
  PetscInt       offsetg;
  PetscSection   sectiong;

  PetscFunctionBegin;
  *isghost = PETSC_FALSE;
  ierr = DMGetDefaultGlobalSection(network->plex,&sectiong);CHKERRQ(ierr);
  ierr = PetscSectionGetOffset(sectiong,p,&offsetg);CHKERRQ(ierr);
  if (offsetg < 0) *isghost = PETSC_TRUE;
  PetscFunctionReturn(0);
}

PetscErrorCode DMSetUp_Network(DM dm)
{
  PetscErrorCode ierr;
  DM_Network     *network=(DM_Network*)dm->data;

  PetscFunctionBegin;
  ierr = DMNetworkComponentSetUp(dm);CHKERRQ(ierr);
  ierr = DMNetworkVariablesSetUp(dm);CHKERRQ(ierr);

  ierr = DMSetDefaultSection(network->plex,network->DofSection);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(network->plex,&network->GlobalDofSection);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*@
    DMNetworkHasJacobian - Sets global flag for using user's sub Jacobian matrices
                            -- replaced by DMNetworkSetOption(network,userjacobian,PETSC_TURE)?

    Collective

    Input Parameters:
+   dm - The DMNetwork object
.   eflg - turn the option on (PETSC_TRUE) or off (PETSC_FALSE) if user provides Jacobian for edges
-   vflg - turn the option on (PETSC_TRUE) or off (PETSC_FALSE) if user provides Jacobian for vertices

    Level: intermediate

@*/
PetscErrorCode DMNetworkHasJacobian(DM dm,PetscBool eflg,PetscBool vflg)
{
  DM_Network     *network=(DM_Network*)dm->data;

  PetscFunctionBegin;
  network->userEdgeJacobian   = eflg;
  network->userVertexJacobian = vflg;
  PetscFunctionReturn(0);
}

/*@
    DMNetworkEdgeSetMatrix - Sets user-provided Jacobian matrices for this edge to the network

    Not Collective

    Input Parameters:
+   dm - The DMNetwork object
.   p  - the edge point
-   J - array (size = 3) of Jacobian submatrices for this edge point:
        J[0]: this edge
        J[1] and J[2]: connected vertices, obtained by calling DMNetworkGetConnectedNodes()

    Level: intermediate

.seealso: DMNetworkVertexSetMatrix
@*/
PetscErrorCode DMNetworkEdgeSetMatrix(DM dm,PetscInt p,Mat J[])
{
  PetscErrorCode ierr;
  DM_Network     *network=(DM_Network*)dm->data;

  PetscFunctionBegin;
  if (!network->userEdgeJacobian) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_ORDER,"Must call DMNetworkHasJacobian() collectively before calling DMNetworkEdgeSetMatrix");
  if (!network->Je) {
    ierr = PetscCalloc1(3*network->nEdges,&network->Je);CHKERRQ(ierr);
  }
  network->Je[3*p]   = J[0];
  network->Je[3*p+1] = J[1];
  network->Je[3*p+2] = J[2];
  PetscFunctionReturn(0);
}

/*@
    DMNetworkVertexSetMatrix - Sets user-provided Jacobian matrix for this vertex to the network

    Not Collective

    Input Parameters:
+   dm - The DMNetwork object
.   p  - the vertex point
-   J - array of Jacobian (size = 2*(num of supporting edges) + 1) submatrices for this vertex point:
        J[0]:       this vertex
        J[1+2*i]:   i-th supporting edge
        J[1+2*i+1]: i-th connected vertex

    Level: intermediate

.seealso: DMNetworkEdgeSetMatrix
@*/
PetscErrorCode DMNetworkVertexSetMatrix(DM dm,PetscInt p,Mat J[])
{
  PetscErrorCode ierr;
  DM_Network     *network=(DM_Network*)dm->data;
  PetscInt       i,*vptr,nedges,vStart,vEnd;
  const PetscInt *edges;

  PetscFunctionBegin;
  if (!network->userVertexJacobian) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_ORDER,"Must call DMNetworkHasJacobian() collectively before calling DMNetworkVertexSetMatrix");

  ierr = DMNetworkGetVertexRange(dm,&vStart,&vEnd);CHKERRQ(ierr);

  if (!network->Jv) {
    PetscInt nNodes = network->nNodes,nedges_total;
    /* count nvertex_total */
    nedges_total = 0;
    ierr = DMNetworkGetVertexRange(dm,&vStart,&vEnd);CHKERRQ(ierr);
    ierr = PetscMalloc1(nNodes+1,&vptr);CHKERRQ(ierr);

    vptr[0] = 0;
    for (i=0; i<nNodes; i++) {
      ierr = DMNetworkGetSupportingEdges(dm,i+vStart,&nedges,&edges);CHKERRQ(ierr);
      nedges_total += nedges;
      vptr[i+1] = vptr[i] + 2*nedges + 1;
    }

    ierr = PetscCalloc1(2*nedges_total+nNodes,&network->Jv);CHKERRQ(ierr);
    network->Jvptr = vptr;
  }

  vptr = network->Jvptr;
  network->Jv[vptr[p-vStart]] = J[0]; /* Set Jacobian for this vertex */

  /* Set Jacobian for each supporting edge and connected vertex */
  ierr = DMNetworkGetSupportingEdges(dm,p,&nedges,&edges);CHKERRQ(ierr);
  for (i=1; i<=2*nedges; i++) network->Jv[vptr[p-vStart]+i] = J[i];
  PetscFunctionReturn(0);
}

PETSC_STATIC_INLINE PetscErrorCode MatSetPreallocationDenseblock_private(PetscInt nrows,PetscInt *rows,PetscInt ncols,PetscBool ghost,Vec vdnz,Vec vonz)
{
  PetscErrorCode ierr;
  PetscInt       j;
  PetscScalar    val=(PetscScalar)ncols;

  PetscFunctionBegin;
  if (!ghost) {
    for (j=0; j<nrows; j++) {
      ierr = VecSetValues(vdnz,1,&rows[j],&val,ADD_VALUES);CHKERRQ(ierr);
    }
  } else {
    for (j=0; j<nrows; j++) {
      ierr = VecSetValues(vonz,1,&rows[j],&val,ADD_VALUES);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

PETSC_STATIC_INLINE PetscErrorCode MatSetPreallocationUserblock_private(Mat Ju,PetscInt nrows,PetscInt *rows,PetscInt ncols,PetscBool ghost,Vec vdnz,Vec vonz)
{
  PetscErrorCode ierr;
  PetscInt       j,ncols_u;
  PetscScalar    val;

  PetscFunctionBegin;
  if (!ghost) {
    for (j=0; j<nrows; j++) {
      ierr = MatGetRow(Ju,j,&ncols_u,NULL,NULL);CHKERRQ(ierr);
      val = (PetscScalar)ncols_u;
      ierr = VecSetValues(vdnz,1,&rows[j],&val,ADD_VALUES);CHKERRQ(ierr);
      ierr = MatRestoreRow(Ju,j,&ncols_u,NULL,NULL);CHKERRQ(ierr);
    }
  } else {
    for (j=0; j<nrows; j++) {
      ierr = MatGetRow(Ju,j,&ncols_u,NULL,NULL);CHKERRQ(ierr);
      val = (PetscScalar)ncols_u;
      ierr = VecSetValues(vonz,1,&rows[j],&val,ADD_VALUES);CHKERRQ(ierr);
      ierr = MatRestoreRow(Ju,j,&ncols_u,NULL,NULL);CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

PETSC_STATIC_INLINE PetscErrorCode MatSetPreallocationblock_private(Mat Ju,PetscInt nrows,PetscInt *rows,PetscInt ncols,PetscBool ghost,Vec vdnz,Vec vonz)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (Ju) {
    ierr = MatSetPreallocationUserblock_private(Ju,nrows,rows,ncols,ghost,vdnz,vonz);CHKERRQ(ierr);
  } else {
    ierr = MatSetPreallocationDenseblock_private(nrows,rows,ncols,ghost,vdnz,vonz);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

PETSC_STATIC_INLINE PetscErrorCode MatSetDenseblock_private(PetscInt nrows,PetscInt *rows,PetscInt ncols,PetscInt cstart,Mat *J)
{
  PetscErrorCode ierr;
  PetscInt       j,*cols;
  PetscScalar    *zeros;

  PetscFunctionBegin;
  ierr = PetscCalloc2(ncols,&cols,nrows*ncols,&zeros);CHKERRQ(ierr);
  for (j=0; j<ncols; j++) cols[j] = j+ cstart;
  ierr = MatSetValues(*J,nrows,rows,ncols,cols,zeros,INSERT_VALUES);CHKERRQ(ierr);
  ierr = PetscFree2(cols,zeros);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PETSC_STATIC_INLINE PetscErrorCode MatSetUserblock_private(Mat Ju,PetscInt nrows,PetscInt *rows,PetscInt ncols,PetscInt cstart,Mat *J)
{
  PetscErrorCode ierr;
  PetscInt       j,M,N,row,col,ncols_u;
  const PetscInt *cols;
  PetscScalar    zero=0.0;

  PetscFunctionBegin;
  ierr = MatGetSize(Ju,&M,&N);CHKERRQ(ierr);
  if (nrows != M || ncols != N) SETERRQ4(PetscObjectComm((PetscObject)Ju),PETSC_ERR_USER,"%D by %D must equal %D by %D",nrows,ncols,M,N);

  for (row=0; row<nrows; row++) {
    ierr = MatGetRow(Ju,row,&ncols_u,&cols,NULL);CHKERRQ(ierr);
    for (j=0; j<ncols_u; j++) {
      col = cols[j] + cstart;
      ierr = MatSetValues(*J,1,&rows[row],1,&col,&zero,INSERT_VALUES);CHKERRQ(ierr);
    }
    ierr = MatRestoreRow(Ju,row,&ncols_u,&cols,NULL);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

PETSC_STATIC_INLINE PetscErrorCode MatSetblock_private(Mat Ju,PetscInt nrows,PetscInt *rows,PetscInt ncols,PetscInt cstart,Mat *J)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (Ju) {
    ierr = MatSetUserblock_private(Ju,nrows,rows,ncols,cstart,J);CHKERRQ(ierr);
  } else {
    ierr = MatSetDenseblock_private(nrows,rows,ncols,cstart,J);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}


/* Creates a GlobalToLocal mapping with a Local and Global section. This is akin to the routine DMGetLocalToGlobalMapping but without the need of providing a dm.
*/
PetscErrorCode CreateSubGlobalToLocalMapping_private(PetscSection globalsec, PetscSection localsec, ISLocalToGlobalMapping *ltog)
{
  PetscErrorCode ierr;
  PetscInt       i, size, dof;
  PetscInt       *glob2loc;

  PetscFunctionBegin;
  ierr = PetscSectionGetStorageSize(localsec,&size);CHKERRQ(ierr);
  ierr = PetscMalloc1(size,&glob2loc);CHKERRQ(ierr);

  for (i = 0; i < size; i++) {
    ierr = PetscSectionGetOffset(globalsec,i,&dof);CHKERRQ(ierr);
    dof = (dof >= 0) ? dof : -(dof + 1);
    glob2loc[i] = dof;
  }

  ierr = ISLocalToGlobalMappingCreate(PETSC_COMM_WORLD,1,size,glob2loc,PETSC_OWN_POINTER,ltog);CHKERRQ(ierr);
#if 0
  ierr = PetscIntView(size,glob2loc,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
#endif
  PetscFunctionReturn(0);
}

PetscErrorCode DMCreateMatrix_Network(DM dm,Mat *J)
{
  PetscErrorCode ierr;
  PetscMPIInt    rank, size;
  DM_Network     *network = (DM_Network*) dm->data;
  PetscInt       eStart,eEnd,vStart,vEnd,rstart,nrows,*rows,localSize;
  PetscInt       cstart,ncols,j,e,v;
  PetscBool      ghost,ghost_vc,ghost2,isNest;
  Mat            Juser;
  PetscSection   sectionGlobal;
  PetscInt       nedges,*vptr=NULL,vc,*rows_v; /* suppress maybe-uninitialized warning */
  const PetscInt *edges,*cone;
  MPI_Comm       comm;
  MatType        mtype;
  Vec            vd_nz,vo_nz;
  PetscInt       *dnnz,*onnz;
  PetscScalar    *vdnz,*vonz;

  PetscFunctionBegin;
  mtype = dm->mattype;
  ierr = PetscStrcmp(mtype, MATNEST, &isNest);CHKERRQ(ierr);

  if (isNest) {
    /* ierr = DMCreateMatrix_Network_Nest(); */
    PetscInt   eDof, vDof;
    Mat        j11, j12, j21, j22, bA[2][2];
    ISLocalToGlobalMapping eISMap, vISMap;

    ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
    ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
    ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);

    ierr = PetscSectionGetConstrainedStorageSize(network->edge.GlobalDofSection,&eDof);CHKERRQ(ierr);
    ierr = PetscSectionGetConstrainedStorageSize(network->vertex.GlobalDofSection,&vDof);CHKERRQ(ierr);

    ierr = MatCreate(PETSC_COMM_WORLD, &j11);CHKERRQ(ierr);
    ierr = MatSetSizes(j11, eDof, eDof, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = MatSetType(j11, MATMPIAIJ);CHKERRQ(ierr);

    ierr = MatCreate(PETSC_COMM_WORLD, &j12);CHKERRQ(ierr);
    ierr = MatSetSizes(j12, eDof, vDof, PETSC_DETERMINE ,PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = MatSetType(j12, MATMPIAIJ);CHKERRQ(ierr);

    ierr = MatCreate(PETSC_COMM_WORLD, &j21);CHKERRQ(ierr);
    ierr = MatSetSizes(j21, vDof, eDof, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = MatSetType(j21, MATMPIAIJ);CHKERRQ(ierr);

    ierr = MatCreate(PETSC_COMM_WORLD, &j22);CHKERRQ(ierr);
    ierr = MatSetSizes(j22, vDof, vDof, PETSC_DETERMINE, PETSC_DETERMINE);CHKERRQ(ierr);
    ierr = MatSetType(j22, MATMPIAIJ);CHKERRQ(ierr);

    bA[0][0] = j11;
    bA[0][1] = j12;
    bA[1][0] = j21;
    bA[1][1] = j22;

    ierr = CreateSubGlobalToLocalMapping_private(network->edge.GlobalDofSection,network->edge.DofSection,&eISMap);CHKERRQ(ierr);
    ierr = CreateSubGlobalToLocalMapping_private(network->vertex.GlobalDofSection,network->vertex.DofSection,&vISMap);CHKERRQ(ierr);

    ierr = MatSetLocalToGlobalMapping(j11,eISMap,eISMap);CHKERRQ(ierr);
    ierr = MatSetLocalToGlobalMapping(j12,eISMap,vISMap);CHKERRQ(ierr);
    ierr = MatSetLocalToGlobalMapping(j21,vISMap,eISMap);CHKERRQ(ierr);
    ierr = MatSetLocalToGlobalMapping(j22,vISMap,vISMap);CHKERRQ(ierr);

    ierr = MatSetUp(j11);CHKERRQ(ierr);
    ierr = MatSetUp(j12);CHKERRQ(ierr);
    ierr = MatSetUp(j21);CHKERRQ(ierr);
    ierr = MatSetUp(j22);CHKERRQ(ierr);

    ierr = MatCreateNest(PETSC_COMM_WORLD,2,NULL,2,NULL,&bA[0][0],J);CHKERRQ(ierr);
    ierr = MatSetUp(*J);CHKERRQ(ierr);
    ierr = MatNestSetVecType(*J,VECNEST);CHKERRQ(ierr);
    ierr = MatDestroy(&j11);CHKERRQ(ierr);
    ierr = MatDestroy(&j12);CHKERRQ(ierr);
    ierr = MatDestroy(&j21);CHKERRQ(ierr);
    ierr = MatDestroy(&j22);CHKERRQ(ierr);

    ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

    /* Free structures */
    ierr = ISLocalToGlobalMappingDestroy(&eISMap);CHKERRQ(ierr);
    ierr = ISLocalToGlobalMappingDestroy(&vISMap);CHKERRQ(ierr);

    PetscFunctionReturn(0);
  } else if (!network->userEdgeJacobian && !network->userVertexJacobian) {
    /* user does not provide Jacobian blocks */
    ierr = DMCreateMatrix(network->plex,J);CHKERRQ(ierr);
    ierr = MatSetDM(*J,dm);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = MatCreate(PetscObjectComm((PetscObject)dm),J);CHKERRQ(ierr);
  ierr = DMGetDefaultGlobalSection(network->plex,&sectionGlobal);CHKERRQ(ierr);
  ierr = PetscSectionGetConstrainedStorageSize(sectionGlobal,&localSize);CHKERRQ(ierr);
  ierr = MatSetSizes(*J,localSize,localSize,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);

  ierr = MatSetType(*J,MATAIJ);CHKERRQ(ierr);
  ierr = MatSetFromOptions(*J);CHKERRQ(ierr);

  /* (1) Set matrix preallocation */
  /*------------------------------*/
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = VecCreate(comm,&vd_nz);CHKERRQ(ierr);
  ierr = VecSetSizes(vd_nz,localSize,PETSC_DECIDE);CHKERRQ(ierr);
  ierr = VecSetFromOptions(vd_nz);CHKERRQ(ierr);
  ierr = VecSet(vd_nz,0.0);CHKERRQ(ierr);
  ierr = VecDuplicate(vd_nz,&vo_nz);CHKERRQ(ierr);

  /* Set preallocation for edges */
  /*-----------------------------*/
  ierr = DMNetworkGetEdgeRange(dm,&eStart,&eEnd);CHKERRQ(ierr);

  ierr = PetscMalloc1(localSize,&rows);CHKERRQ(ierr);
  for (e=eStart; e<eEnd; e++) {
    /* Get row indices */
    ierr = DMNetworkGetVariableGlobalOffset(dm,e,&rstart);CHKERRQ(ierr);
    ierr = DMNetworkGetNumVariables(dm,e,&nrows);CHKERRQ(ierr);
    if (nrows) {
      if (!network->Je) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"Uer must provide Je");
      for (j=0; j<nrows; j++) rows[j] = j + rstart;

      /* Set preallocation for conntected vertices */
      ierr = DMNetworkGetConnectedNodes(dm,e,&cone);CHKERRQ(ierr);
      for (v=0; v<2; v++) {
        ierr = DMNetworkGetNumVariables(dm,cone[v],&ncols);CHKERRQ(ierr);

        Juser = network->Je[3*e+1+v]; /* Jacobian(e,v) */
        ierr = DMNetworkIsGhostVertex(dm,cone[v],&ghost);CHKERRQ(ierr);
        ierr = MatSetPreallocationblock_private(Juser,nrows,rows,ncols,ghost,vd_nz,vo_nz);CHKERRQ(ierr);
      }

      /* Set preallocation for edge self */
      cstart = rstart;
      Juser = network->Je[3*e]; /* Jacobian(e,e) */
      ierr = MatSetPreallocationblock_private(Juser,nrows,rows,nrows,PETSC_FALSE,vd_nz,vo_nz);CHKERRQ(ierr);
    }
  }

  /* Set preallocation for vertices */
  /*--------------------------------*/
  ierr = DMNetworkGetVertexRange(dm,&vStart,&vEnd);CHKERRQ(ierr);
  if (vEnd - vStart) {
    if (!network->Jv) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"Uer must provide Jv");
    vptr = network->Jvptr;
    if (!vptr) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"Uer must provide vptr");
  }

  for (v=vStart; v<vEnd; v++) {
    /* Get row indices */
    ierr = DMNetworkGetVariableGlobalOffset(dm,v,&rstart);CHKERRQ(ierr);
    ierr = DMNetworkGetNumVariables(dm,v,&nrows);CHKERRQ(ierr);
    if (!nrows) continue;

    ierr = DMNetworkIsGhostVertex(dm,v,&ghost);CHKERRQ(ierr);
    if (ghost) {
      ierr = PetscMalloc1(nrows,&rows_v);CHKERRQ(ierr);
    } else {
      rows_v = rows;
    }

    for (j=0; j<nrows; j++) rows_v[j] = j + rstart;

    /* Get supporting edges and connected vertices */
    ierr = DMNetworkGetSupportingEdges(dm,v,&nedges,&edges);CHKERRQ(ierr);

    for (e=0; e<nedges; e++) {
      /* Supporting edges */
      ierr = DMNetworkGetVariableGlobalOffset(dm,edges[e],&cstart);CHKERRQ(ierr);
      ierr = DMNetworkGetNumVariables(dm,edges[e],&ncols);CHKERRQ(ierr);

      Juser = network->Jv[vptr[v-vStart]+2*e+1]; /* Jacobian(v,e) */
      ierr = MatSetPreallocationblock_private(Juser,nrows,rows_v,ncols,ghost,vd_nz,vo_nz);CHKERRQ(ierr);

      /* Connected vertices */
      ierr = DMNetworkGetConnectedNodes(dm,edges[e],&cone);CHKERRQ(ierr);
      vc = (v == cone[0]) ? cone[1]:cone[0];
      ierr = DMNetworkIsGhostVertex(dm,vc,&ghost_vc);CHKERRQ(ierr);

      ierr = DMNetworkGetNumVariables(dm,vc,&ncols);CHKERRQ(ierr);

      Juser = network->Jv[vptr[v-vStart]+2*e+2]; /* Jacobian(v,vc) */
      if (ghost_vc||ghost) {
        ghost2 = PETSC_TRUE;
      } else {
        ghost2 = PETSC_FALSE;
      }
      ierr = MatSetPreallocationblock_private(Juser,nrows,rows_v,ncols,ghost2,vd_nz,vo_nz);CHKERRQ(ierr);
    }

    /* Set preallocation for vertex self */
    ierr = DMNetworkIsGhostVertex(dm,v,&ghost);CHKERRQ(ierr);
    if (!ghost) {
      ierr = DMNetworkGetVariableGlobalOffset(dm,v,&cstart);CHKERRQ(ierr);
      Juser = network->Jv[vptr[v-vStart]]; /* Jacobian(v,v) */
      ierr = MatSetPreallocationblock_private(Juser,nrows,rows_v,nrows,PETSC_FALSE,vd_nz,vo_nz);CHKERRQ(ierr);
    }
    if (ghost) {
      ierr = PetscFree(rows_v);CHKERRQ(ierr);
    }
  }

  ierr = VecAssemblyBegin(vd_nz);CHKERRQ(ierr);
  ierr = VecAssemblyBegin(vo_nz);CHKERRQ(ierr);

  ierr = PetscMalloc2(localSize,&dnnz,localSize,&onnz);CHKERRQ(ierr);

  ierr = VecAssemblyEnd(vd_nz);CHKERRQ(ierr);
  ierr = VecAssemblyEnd(vo_nz);CHKERRQ(ierr);

  ierr = VecGetArray(vd_nz,&vdnz);CHKERRQ(ierr);
  ierr = VecGetArray(vo_nz,&vonz);CHKERRQ(ierr);
  for (j=0; j<localSize; j++) {
    dnnz[j] = (PetscInt)PetscRealPart(vdnz[j]);
    onnz[j] = (PetscInt)PetscRealPart(vonz[j]);
  }
  ierr = VecRestoreArray(vd_nz,&vdnz);CHKERRQ(ierr);
  ierr = VecRestoreArray(vo_nz,&vonz);CHKERRQ(ierr);
  ierr = VecDestroy(&vd_nz);CHKERRQ(ierr);
  ierr = VecDestroy(&vo_nz);CHKERRQ(ierr);

  ierr = MatSeqAIJSetPreallocation(*J,0,dnnz);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(*J,0,dnnz,0,onnz);CHKERRQ(ierr);
  ierr = MatSetOption(*J,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);

  ierr = PetscFree2(dnnz,onnz);CHKERRQ(ierr);

  /* (2) Set matrix entries for edges */
  /*----------------------------------*/
  for (e=eStart; e<eEnd; e++) {
    /* Get row indices */
    ierr = DMNetworkGetVariableGlobalOffset(dm,e,&rstart);CHKERRQ(ierr);
    ierr = DMNetworkGetNumVariables(dm,e,&nrows);CHKERRQ(ierr);
    if (nrows) {
      if (!network->Je) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL,"Uer must provide Je");

      for (j=0; j<nrows; j++) rows[j] = j + rstart;

      /* Set matrix entries for conntected vertices */
      ierr = DMNetworkGetConnectedNodes(dm,e,&cone);CHKERRQ(ierr);
      for (v=0; v<2; v++) {
        ierr = DMNetworkGetVariableGlobalOffset(dm,cone[v],&cstart);CHKERRQ(ierr);
        ierr = DMNetworkGetNumVariables(dm,cone[v],&ncols);CHKERRQ(ierr);

        Juser = network->Je[3*e+1+v]; /* Jacobian(e,v) */
        ierr = MatSetblock_private(Juser,nrows,rows,ncols,cstart,J);CHKERRQ(ierr);
      }

      /* Set matrix entries for edge self */
      cstart = rstart;
      Juser = network->Je[3*e]; /* Jacobian(e,e) */
      ierr = MatSetblock_private(Juser,nrows,rows,nrows,cstart,J);CHKERRQ(ierr);
    }
  }

  /* Set matrix entries for vertices */
  /*---------------------------------*/
  for (v=vStart; v<vEnd; v++) {
    /* Get row indices */
    ierr = DMNetworkGetVariableGlobalOffset(dm,v,&rstart);CHKERRQ(ierr);
    ierr = DMNetworkGetNumVariables(dm,v,&nrows);CHKERRQ(ierr);
    if (!nrows) continue;

    ierr = DMNetworkIsGhostVertex(dm,v,&ghost);CHKERRQ(ierr);
    if (ghost) {
      ierr = PetscMalloc1(nrows,&rows_v);CHKERRQ(ierr);
    } else {
      rows_v = rows;
    }
    for (j=0; j<nrows; j++) rows_v[j] = j + rstart;

    /* Get supporting edges and connected vertices */
    ierr = DMNetworkGetSupportingEdges(dm,v,&nedges,&edges);CHKERRQ(ierr);

    for (e=0; e<nedges; e++) {
      /* Supporting edges */
      ierr = DMNetworkGetVariableGlobalOffset(dm,edges[e],&cstart);CHKERRQ(ierr);
      ierr = DMNetworkGetNumVariables(dm,edges[e],&ncols);CHKERRQ(ierr);

      Juser = network->Jv[vptr[v-vStart]+2*e+1]; /* Jacobian(v,e) */
      ierr = MatSetblock_private(Juser,nrows,rows_v,ncols,cstart,J);CHKERRQ(ierr);

      /* Connected vertices */
      ierr = DMNetworkGetConnectedNodes(dm,edges[e],&cone);CHKERRQ(ierr);
      vc = (v == cone[0]) ? cone[1]:cone[0];

      ierr = DMNetworkGetVariableGlobalOffset(dm,vc,&cstart);CHKERRQ(ierr);
      ierr = DMNetworkGetNumVariables(dm,vc,&ncols);CHKERRQ(ierr);

      Juser = network->Jv[vptr[v-vStart]+2*e+2]; /* Jacobian(v,vc) */
      ierr = MatSetblock_private(Juser,nrows,rows_v,ncols,cstart,J);CHKERRQ(ierr);
    }

    /* Set matrix entries for vertex self */
    if (!ghost) {
      ierr = DMNetworkGetVariableGlobalOffset(dm,v,&cstart);CHKERRQ(ierr);
      Juser = network->Jv[vptr[v-vStart]]; /* Jacobian(v,v) */
      ierr = MatSetblock_private(Juser,nrows,rows_v,nrows,cstart,J);CHKERRQ(ierr);
    }
    if (ghost) {
      ierr = PetscFree(rows_v);CHKERRQ(ierr);
    }
  }
  ierr = PetscFree(rows);CHKERRQ(ierr);

  ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  ierr = MatSetDM(*J,dm);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode DMDestroy_Network(DM dm)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*) dm->data;

  PetscFunctionBegin;
  if (--network->refct > 0) PetscFunctionReturn(0);
  if (network->Je) {
    ierr = PetscFree(network->Je);CHKERRQ(ierr);
  }
  if (network->Jv) {
    ierr = PetscFree(network->Jvptr);CHKERRQ(ierr);
    ierr = PetscFree(network->Jv);CHKERRQ(ierr);
  }

  ierr = ISLocalToGlobalMappingDestroy(&network->vertex.mapping);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&network->vertex.DofSection);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&network->vertex.GlobalDofSection);CHKERRQ(ierr);
  if (network->vertex.sf) {
    ierr = PetscSFDestroy(&network->vertex.sf);CHKERRQ(ierr);
  }
  /* edge */
  ierr = ISLocalToGlobalMappingDestroy(&network->edge.mapping);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&network->edge.DofSection);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&network->edge.GlobalDofSection);CHKERRQ(ierr);
  if (network->edge.sf) {
    ierr = PetscSFDestroy(&network->edge.sf);CHKERRQ(ierr);
  }
  ierr = DMDestroy(&network->plex);CHKERRQ(ierr);
  network->edges = NULL;
  ierr = PetscSectionDestroy(&network->DataSection);CHKERRQ(ierr);
  ierr = PetscSectionDestroy(&network->DofSection);CHKERRQ(ierr);

  ierr = PetscFree(network->componentdataarray);CHKERRQ(ierr);
  ierr = PetscFree(network->cvalue);CHKERRQ(ierr);
  ierr = PetscFree(network->header);CHKERRQ(ierr);
  ierr = PetscFree(network);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode DMView_Network(DM dm, PetscViewer viewer)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*) dm->data;

  PetscFunctionBegin;
  ierr = DMView(network->plex,viewer);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode DMGlobalToLocalBegin_Network(DM dm, Vec g, InsertMode mode, Vec l)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*) dm->data;

  PetscFunctionBegin;
  ierr = DMGlobalToLocalBegin(network->plex,g,mode,l);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode DMGlobalToLocalEnd_Network(DM dm, Vec g, InsertMode mode, Vec l)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*) dm->data;

  PetscFunctionBegin;
  ierr = DMGlobalToLocalEnd(network->plex,g,mode,l);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode DMLocalToGlobalBegin_Network(DM dm, Vec l, InsertMode mode, Vec g)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*) dm->data;

  PetscFunctionBegin;
  ierr = DMLocalToGlobalBegin(network->plex,l,mode,g);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode DMLocalToGlobalEnd_Network(DM dm, Vec l, InsertMode mode, Vec g)
{
  PetscErrorCode ierr;
  DM_Network     *network = (DM_Network*) dm->data;

  PetscFunctionBegin;
  ierr = DMLocalToGlobalEnd(network->plex,l,mode,g);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}