MueLu_IntrepidPCoarsenFactory_def.hpp

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#ifndef MUELU_IPCFACTORY_DEF_HPP
#define MUELU_IPCFACTORY_DEF_HPP

#include <Xpetra_Matrix.hpp>
#include <Xpetra_IO.hpp>
#include <sstream>
#include <algorithm>

#include "MueLu_IntrepidPCoarsenFactory_decl.hpp"

#include "MueLu_FactoryManagerBase.hpp"
#include "MueLu_Level.hpp"
#include "MueLu_MasterList.hpp"
#include "MueLu_Monitor.hpp"
#include "MueLu_PerfUtils.hpp"
#include "MueLu_SingleLevelFactoryBase.hpp"
#include "MueLu_Utilities.hpp"

#include "Teuchos_ScalarTraits.hpp"

// Intrepid Headers

//Intrepid_HGRAD_HEX_C1_FEM.hpp
//Intrepid_HGRAD_HEX_C2_FEM.hpp
//Intrepid_HGRAD_HEX_Cn_FEM.hpp
//Intrepid_HGRAD_HEX_I2_FEM.hpp
#include "Intrepid2_HGRAD_LINE_C1_FEM.hpp"
#include "Intrepid2_HGRAD_LINE_Cn_FEM.hpp"
//Intrepid_HGRAD_LINE_Cn_FEM_JACOBI.hpp
//Intrepid_HGRAD_POLY_C1_FEM.hpp
//Intrepid_HGRAD_PYR_C1_FEM.hpp
//Intrepid_HGRAD_PYR_I2_FEM.hpp
#include "Intrepid2_HGRAD_QUAD_C1_FEM.hpp"
//#include Intrepid_HGRAD_QUAD_C2_FEM.hpp
#include "Intrepid2_HGRAD_QUAD_Cn_FEM.hpp"
//Intrepid_HGRAD_TET_C1_FEM.hpp
//Intrepid_HGRAD_TET_C2_FEM.hpp
//Intrepid_HGRAD_TET_Cn_FEM.hpp
//Intrepid_HGRAD_TET_Cn_FEM_ORTH.hpp
//Intrepid_HGRAD_TET_COMP12_FEM.hpp
//Intrepid_HGRAD_TRI_C1_FEM.hpp
//Intrepid_HGRAD_TRI_C2_FEM.hpp
//Intrepid_HGRAD_TRI_Cn_FEM.hpp
//Intrepid_HGRAD_TRI_Cn_FEM_ORTH.hpp
//Intrepid_HGRAD_WEDGE_C1_FEM.hpp
//Intrepid_HGRAD_WEDGE_C2_FEM.hpp
//Intrepid_HGRAD_WEDGE_I2_FEM.hpp

// Helper Macro to avoid "unrequested" warnings
#define MUELU_LEVEL_SET_IF_REQUESTED_OR_KEPT(level,ename,entry) \
  {if (level.IsRequested(ename,this) || level.GetKeepFlag(ename,this) != 0) this->Set(level,ename,entry);}



namespace MueLu {


/*********************************************************************************************************/
namespace MueLuIntrepid {
inline std::string tolower(const std::string & str) {
  std::string data(str);
  std::transform(data.begin(), data.end(), data.begin(), [](unsigned char c) { return std::tolower(c); });
  return data;
}


/*********************************************************************************************************/
  template<class Basis, class LOFieldContainer, class LocalOrdinal, class GlobalOrdinal, class Node>
  void FindGeometricSeedOrdinals(Teuchos::RCP<Basis> basis, const LOFieldContainer &elementToNodeMap,
                                 std::vector<std::vector<LocalOrdinal> > &seeds,
                                 const Xpetra::Map<LocalOrdinal,GlobalOrdinal,Node> &rowMap,
                                 const Xpetra::Map<LocalOrdinal,GlobalOrdinal,Node> &columnMap)
  {

    // For each subcell represented by the elements in elementToNodeMap, we want to identify a globally
    // unique degree of freedom.  Because the other "seed" interfaces in MueLu expect a local ordinal, we
    // store local ordinals in the resulting seeds container.

    // The approach is as follows.  For each element, we iterate through the subcells of the domain topology.
    // We determine which, if any, of these has the lowest global ID owned that is locally owned.  We then insert
    // the local ID corresponding to this in a vector<set<int>> container whose outer index is the spatial dimension
    // of the subcell.  The set lets us conveniently enforce uniqueness of the stored LIDs.

    shards::CellTopology cellTopo = basis->getBaseCellTopology();
    int spaceDim = cellTopo.getDimension();
    seeds.clear();
    seeds.resize(spaceDim + 1);
    typedef GlobalOrdinal GO;
    typedef LocalOrdinal LO;

    LocalOrdinal  lo_invalid = Teuchos::OrdinalTraits<LO>::invalid();
    GlobalOrdinal go_invalid = Teuchos::OrdinalTraits<GO>::invalid();


    std::vector<std::set<LocalOrdinal>> seedSets(spaceDim+1);

    int numCells = elementToNodeMap.extent(0);
    for (int cellOrdinal=0; cellOrdinal<numCells; cellOrdinal++)
    {
      for (int d=0; d<=spaceDim; d++)
      {
        int subcellCount = cellTopo.getSubcellCount(d);
        for (int subcord=0; subcord<subcellCount; subcord++)
        {
          int dofCount = basis->getDofCount(d,subcord);
          if (dofCount == 0) continue;
          // otherwise, we want to insert the LID corresponding to the least globalID that is locally owned
          GO leastGlobalDofOrdinal = go_invalid;
          LO LID_leastGlobalDofOrdinal = lo_invalid;
          for (int basisOrdinalOrdinal=0; basisOrdinalOrdinal<dofCount; basisOrdinalOrdinal++)
          {
            int basisOrdinal = basis->getDofOrdinal(d,subcord,basisOrdinalOrdinal);
            int colLID = elementToNodeMap(cellOrdinal,basisOrdinal);
            if (colLID != Teuchos::OrdinalTraits<LO>::invalid())
            {
              GlobalOrdinal colGID = columnMap.getGlobalElement(colLID);
              LocalOrdinal rowLID = rowMap.getLocalElement(colGID);
              if (rowLID != lo_invalid)
              {
                if ((leastGlobalDofOrdinal == go_invalid) || (colGID < leastGlobalDofOrdinal))
                {
                  // replace with rowLID
                  leastGlobalDofOrdinal = colGID;
                  LID_leastGlobalDofOrdinal = rowLID;
                }
              }
            }
          }
          if (leastGlobalDofOrdinal != go_invalid)
          {
            seedSets[d].insert(LID_leastGlobalDofOrdinal);
          }
        }
      }
    }
    for (int d=0; d<=spaceDim;d++)
    {
      seeds[d] = std::vector<LocalOrdinal>(seedSets[d].begin(),seedSets[d].end());
    }
  }

/*********************************************************************************************************/
// Syntax [HGRAD|HCURL|HDIV][_| ][HEX|LINE|POLY|PYR|QUAD|TET|TRI|WEDGE][_| ][C|I][1|2|n]
// Inputs:
//  name - name of the intrepid basis to generate
// Outputs:
//  degree - order of resulting discretization
//  return value - Intrepid2 basis correspionding to the name
template<class Scalar,class KokkosExecutionSpace>
Teuchos::RCP< Intrepid2::Basis<KokkosExecutionSpace,Scalar,Scalar> > BasisFactory(const std::string & name, int & degree)
{
    using std::string;
    using Teuchos::rcp;
    string myerror("IntrepidBasisFactory: cannot parse string name '"+name+"'");

    // Syntax [HGRAD|HCURL|HDIV][_| ][HEX|LINE|POLY|PYR|QUAD|TET|TRI|WEDGE][_| ][C|I][1|2|n]

    // Get the derivative type
    size_t pos1 = name.find_first_of(" _");
    if(pos1==0) throw std::runtime_error(myerror);
    string deriv = tolower(name.substr(0,pos1));
    if(deriv!="hgrad" && deriv!="hcurl" && deriv!="hdiv") throw std::runtime_error(myerror);

    // Get the element type
    pos1++;
    size_t pos2 = name.find_first_of(" _",pos1);
    if(pos2==0) throw std::runtime_error(myerror);
    string el = tolower(name.substr(pos1,pos2-pos1));
    if(el!="hex" && el!="line" && el!="poly" && el!="pyr" && el!="quad" && el!="tet" && el!="tri" && el!="wedge") throw std::runtime_error(myerror);

    // Get the polynomial type
    pos2++;
    string poly = tolower(name.substr(pos2,1));
    if(poly!="c" && poly!="i") throw std::runtime_error(myerror);

    // Get the degree
    pos2++;
    degree=std::stoi(name.substr(pos2,1));
    if(degree<=0) throw std::runtime_error(myerror);

    // FIXME LATER: Allow for alternative point types for Kirby elements
    if(deriv=="hgrad" && el=="quad" && poly=="c"){
      if(degree==1) return rcp(new Intrepid2::Basis_HGRAD_QUAD_C1_FEM<KokkosExecutionSpace,Scalar,Scalar>());
      else          return rcp(new Intrepid2::Basis_HGRAD_QUAD_Cn_FEM<KokkosExecutionSpace,Scalar,Scalar>(degree,Intrepid2::POINTTYPE_EQUISPACED));
    }
    else if(deriv=="hgrad" && el=="line" && poly=="c"){
      if(degree==1) return rcp(new Intrepid2::Basis_HGRAD_LINE_C1_FEM<KokkosExecutionSpace,Scalar,Scalar>());
      else          return rcp(new Intrepid2::Basis_HGRAD_LINE_Cn_FEM<KokkosExecutionSpace,Scalar,Scalar>(degree,Intrepid2::POINTTYPE_EQUISPACED));
    }

    // Error out
    throw std::runtime_error(myerror);
    TEUCHOS_UNREACHABLE_RETURN(Teuchos::null);
}

/*********************************************************************************************************/
// Gets the "lo" nodes nested into a "hi" basis.  Only works on quads and lines for a lo basis of p=1
// Inputs:
//  hi_basis - Higher order Basis
// Outputs:
//  lo_node_in_hi   - std::vector<size_t> of size lo dofs in the reference element, which describes the coindcident hi dots
//  hi_DofCoords    - FC<Scalar> of size (#hi dofs, dim) with the coordinate locations of the hi dofs on the reference element
template<class Scalar,class KokkosDeviceType>
void IntrepidGetP1NodeInHi(const Teuchos::RCP<Intrepid2::Basis<typename KokkosDeviceType::execution_space,Scalar,Scalar> >&hi_basis,
                           std::vector<size_t> & lo_node_in_hi,
                           Kokkos::DynRankView<Scalar,KokkosDeviceType> & hi_DofCoords) {

  typedef typename KokkosDeviceType::execution_space KokkosExecutionSpace;
  // Figure out which unknowns in hi_basis correspond to nodes on lo_basis. This varies by element type.
  size_t degree         = hi_basis->getDegree();
  lo_node_in_hi.resize(0);

  if(!rcp_dynamic_cast<Intrepid2::Basis_HGRAD_QUAD_Cn_FEM<KokkosExecutionSpace,Scalar,Scalar> >(hi_basis).is_null()) {
    // HGRAD QUAD Cn: Numbering as per the Kirby convention (straight across, bottom to top)
    lo_node_in_hi.insert(lo_node_in_hi.end(),{0,degree, (degree+1)*(degree+1)-1, degree*(degree+1)});
  }
  else if(!rcp_dynamic_cast<Intrepid2::Basis_HGRAD_LINE_Cn_FEM<KokkosExecutionSpace,Scalar,Scalar> >(hi_basis).is_null()) {
    // HGRAD LINE Cn: Numbering as per the Kirby convention (straight across)
    lo_node_in_hi.insert(lo_node_in_hi.end(),{0,degree});
  }
  else
    throw std::runtime_error("IntrepidPCoarsenFactory: Unknown element type");

  // Get coordinates of the hi_basis dof's
  Kokkos::resize(hi_DofCoords,hi_basis->getCardinality(),hi_basis->getBaseCellTopology().getDimension());
  hi_basis->getDofCoords(hi_DofCoords);
}


/*********************************************************************************************************/
// Given a list of candidates picks a definitive list of "representative" higher order nodes for each lo order node via the "smallest GID" rule
// Input:
//  representative_node_candidates - std::vector<std::vector<size_t> > of lists of "representative candidate" hi dofs for each lo dof
//  hi_elemToNode   - FC<LO> containing the high order element-to-node map
//  hi_columnMap    - Column map of the higher order matrix
// Output:
//  lo_elemToHiRepresentativeNode - FC<LO> of size (# elements, # lo dofs per element) listing the hi unknown chosen as the single representative for each lo unknown for counting purposes
template<class LocalOrdinal, class GlobalOrdinal, class Node, class LOFieldContainer>
void GenerateLoNodeInHiViaGIDs(const std::vector<std::vector<size_t> > & candidates,const LOFieldContainer & hi_elemToNode,
                               RCP<const Xpetra::Map<LocalOrdinal,GlobalOrdinal,Node> > & hi_columnMap,
                               LOFieldContainer & lo_elemToHiRepresentativeNode) {
  typedef GlobalOrdinal GO;

  // Given: A set of "candidate" hi-DOFs to serve as the "representative" DOF for each lo-DOF on the reference element.
  // Algorithm:  For each element, we choose the lowest GID of the candidates for each DOF to generate the lo_elemToHiRepresentativeNode map

   size_t numElem     = hi_elemToNode.extent(0);
   size_t lo_nperel   = candidates.size();
   Kokkos::resize(lo_elemToHiRepresentativeNode,numElem, lo_nperel);


   for(size_t i=0; i<numElem; i++)
     for(size_t j=0; j<lo_nperel; j++) {
       if(candidates[j].size() == 1)
         lo_elemToHiRepresentativeNode(i,j) =  hi_elemToNode(i,candidates[j][0]);
       else {
         // First we get the GIDs for each candidate
         std::vector<GO> GID(candidates[j].size());
         for(size_t k=0; k<(size_t)candidates[j].size(); k++)
           GID[k] = hi_columnMap->getGlobalElement(hi_elemToNode(i,candidates[j][k]));

         // Find the one with smallest GID
         size_t which = std::distance(GID.begin(),std::min_element(GID.begin(),GID.end()));

         // Record this
         lo_elemToHiRepresentativeNode(i,j) =  hi_elemToNode(i,candidates[j][which]);
       }
     }
}

/*********************************************************************************************************/
// Inputs:
//  hi_elemToNode   - FC<LO> containing the high order element-to-node map
//  hi_nodeIsOwned  - std::vector<bool> of size hi's column map, which described hi node ownership
//  lo_elemToHiRepresentativeNode - FC<LO> of size (# elements, # lo dofs per element) listing the hi unknown chosen as the single representative for each lo unknown for counting purposes
// Outputs:
//  lo_elemToNode   - FC<LO> containing the low order element-to-node map.
//  lo_nodeIsOwned  - std::vector<bool> of size lo's (future) column map, which described lo node ownership
//  hi_to_lo_map    - std::vector<LO> of size equal to hi's column map, which contains the lo id each hi idea maps to (or invalid if it doesn't)
//  lo_numOwnedNodes- Number of lo owned nodes
template <class LocalOrdinal, class LOFieldContainer>
void BuildLoElemToNodeViaRepresentatives(const LOFieldContainer & hi_elemToNode,
                                         const std::vector<bool> & hi_nodeIsOwned,
                                         const LOFieldContainer & lo_elemToHiRepresentativeNode,
                                         LOFieldContainer & lo_elemToNode,
                                         std::vector<bool> & lo_nodeIsOwned,
                                         std::vector<LocalOrdinal> & hi_to_lo_map,
                                         int & lo_numOwnedNodes) {
  typedef LocalOrdinal LO;
  using Teuchos::RCP;
  //  printf("CMS:BuildLoElemToNodeViaRepresentatives: hi_elemToNode.rank() = %d hi_elemToNode.size() = %d\n",hi_elemToNode.rank(), hi_elemToNode.size());
  size_t numElem     = hi_elemToNode.extent(0);
  size_t hi_numNodes = hi_nodeIsOwned.size();
  size_t lo_nperel = lo_elemToHiRepresentativeNode.extent(1);
  Kokkos::resize(lo_elemToNode,numElem, lo_nperel);

  // Start by flagginc the representative nodes
  std::vector<bool> is_low_order(hi_numNodes,false);
  for(size_t i=0; i<numElem; i++)
    for(size_t j=0; j<lo_nperel; j++) {
      LO id = lo_elemToHiRepresentativeNode(i,j);
      is_low_order[id] = true; // This can overwrite and that is OK.
    }

  // Count the number of lo owned nodes, generating a local index for lo nodes
  lo_numOwnedNodes=0;
  size_t lo_numNodes=0;
  hi_to_lo_map.resize(hi_numNodes,Teuchos::OrdinalTraits<LO>::invalid());

  for(size_t i=0; i<hi_numNodes; i++)
    if(is_low_order[i]) {
      hi_to_lo_map[i] = lo_numNodes;
      lo_numNodes++;
      if(hi_nodeIsOwned[i]) lo_numOwnedNodes++;
    }

  // Flag the owned lo nodes
  lo_nodeIsOwned.resize(lo_numNodes,false);
  for(size_t i=0; i<hi_numNodes; i++) {
    if(is_low_order[i] && hi_nodeIsOwned[i])
      lo_nodeIsOwned[hi_to_lo_map[i]]=true;
  }

  // Translate lo_elemToNode to a lo local index
  for(size_t i=0; i<numElem; i++)
    for(size_t j=0; j<lo_nperel; j++)
      lo_elemToNode(i,j) = hi_to_lo_map[lo_elemToHiRepresentativeNode(i,j)];


  // Check for the [E|T]petra column map ordering property, namely LIDs for owned nodes should all appear first.
  // Since we're injecting from the higher-order mesh, it should be true, but we should add an error check & throw in case.
  bool map_ordering_test_passed=true;
  for(size_t i=0; i<lo_numNodes-1; i++)
    if(!lo_nodeIsOwned[i] && lo_nodeIsOwned[i+1])
      map_ordering_test_passed=false;

  if(!map_ordering_test_passed)
    throw std::runtime_error("MueLu::MueLuIntrepid::BuildLoElemToNodeViaRepresentatives failed map ordering test");

}


/*********************************************************************************************************/
// Inputs:
//  hi_elemToNode   - FC<LO> containing the high order element-to-node map
//  hi_nodeIsOwned  - std::vector<bool> of size hi's column map, which described hi node ownership
//  lo_node_in_hi   - std::vector<size_t> of size lo dofs in the reference element, which describes the coindcident hi dots
//  hi_isDirichlet  - ArrayView<int> of size of hi's column map, which has a 1 if the unknown is Dirichlet and a 0 if it isn't.
// Outputs:
//  lo_elemToNode   - FC<LO> containing the low order element-to-node map.
//  lo_nodeIsOwned  - std::vector<bool> of size lo's (future) column map, which described lo node ownership
//  hi_to_lo_map    - std::vector<LO> of size equal to hi's column map, which contains the lo id each hi idea maps to (or invalid if it doesn't)
//  lo_numOwnedNodes- Number of lo owned nodes
template <class LocalOrdinal, class LOFieldContainer>
void BuildLoElemToNode(const LOFieldContainer & hi_elemToNode,
                       const std::vector<bool> & hi_nodeIsOwned,
                       const std::vector<size_t> & lo_node_in_hi,
                       const Teuchos::ArrayRCP<const int> & hi_isDirichlet,
                       LOFieldContainer & lo_elemToNode,
                       std::vector<bool> & lo_nodeIsOwned,
                       std::vector<LocalOrdinal> & hi_to_lo_map,
                       int & lo_numOwnedNodes) {
  typedef LocalOrdinal LO;
  using Teuchos::RCP;
  LocalOrdinal LOINVALID = Teuchos::OrdinalTraits<LocalOrdinal>::invalid();
  //  printf("CMS:BuildLoElemToNode: hi_elemToNode.rank() = %d hi_elemToNode.size() = %d\n",hi_elemToNode.rank(), hi_elemToNode.size());

  size_t numElem     = hi_elemToNode.extent(0);
  size_t hi_numNodes = hi_nodeIsOwned.size();

  size_t lo_nperel = lo_node_in_hi.size();
  Kokkos::resize(lo_elemToNode,numElem, lo_nperel);

  // Build lo_elemToNode (in the hi local index ordering) and flag owned ones
  std::vector<bool> is_low_order(hi_numNodes,false);
  for(size_t i=0; i<numElem; i++)
    for(size_t j=0; j<lo_nperel; j++) {
      LO lid = hi_elemToNode(i,lo_node_in_hi[j]);

      // Remove Dirichlet
      if(hi_isDirichlet[lid])
        lo_elemToNode(i,j) = LOINVALID;
      else {
        lo_elemToNode(i,j)  = lid;
        is_low_order[hi_elemToNode(i,lo_node_in_hi[j])] = true; // This can overwrite and that is OK.
      }
    }

  // Count the number of lo owned nodes, generating a local index for lo nodes
  lo_numOwnedNodes=0;
  size_t lo_numNodes=0;
  hi_to_lo_map.resize(hi_numNodes,Teuchos::OrdinalTraits<LO>::invalid());

  for(size_t i=0; i<hi_numNodes; i++)
    if(is_low_order[i]) {
      hi_to_lo_map[i] = lo_numNodes;
      lo_numNodes++;
      if(hi_nodeIsOwned[i]) lo_numOwnedNodes++;
    }

  // Flag the owned lo nodes
  lo_nodeIsOwned.resize(lo_numNodes,false);
  for(size_t i=0; i<hi_numNodes; i++) {
    if(is_low_order[i] && hi_nodeIsOwned[i])
      lo_nodeIsOwned[hi_to_lo_map[i]]=true;
  }

  // Translate lo_elemToNode to a lo local index
  for(size_t i=0; i<numElem; i++)
    for(size_t j=0; j<lo_nperel; j++) {
      if(lo_elemToNode(i,j) != LOINVALID)
        lo_elemToNode(i,j) = hi_to_lo_map[lo_elemToNode(i,j)];
    }

  // Check for the [E|T]petra column map ordering property, namely LIDs for owned nodes should all appear first.
  // Since we're injecting from the higher-order mesh, it should be true, but we should add an error check & throw in case.
  bool map_ordering_test_passed=true;
  for(size_t i=0; i<lo_numNodes-1; i++)
    if(!lo_nodeIsOwned[i] && lo_nodeIsOwned[i+1])
      map_ordering_test_passed=false;

  if(!map_ordering_test_passed)
    throw std::runtime_error("MueLu::MueLuIntrepid::BuildLoElemToNode failed map ordering test");

}

/*********************************************************************************************************/
// Generates the lo_columnMap
// Input:
//  hi_importer        - Importer from the hi matrix
//  hi_to_lo_map       - std::vector<LO> of size equal to hi's column map, which contains the lo id each hi idea maps to (or invalid if it doesn't)
//  lo_DomainMap       - Domain map for the lo matrix
//  lo_columnMapLength - Number of local columns in the lo column map
// Output:
//  lo_columnMap       - Column map of the lower order matrix
  template <class LocalOrdinal, class GlobalOrdinal, class Node>
  void GenerateColMapFromImport(const Xpetra::Import<LocalOrdinal,GlobalOrdinal, Node> & hi_importer,const std::vector<LocalOrdinal> &hi_to_lo_map,const Xpetra::Map<LocalOrdinal,GlobalOrdinal,Node> & lo_domainMap, const size_t & lo_columnMapLength, RCP<const Xpetra::Map<LocalOrdinal,GlobalOrdinal,Node> > & lo_columnMap) {
  typedef LocalOrdinal LO;
  typedef GlobalOrdinal GO;
  typedef Node NO;
  typedef Xpetra::Map<LO,GO,NO> Map;
  typedef Xpetra::Vector<GO,LO,GO,NO> GOVector;

  GO go_invalid = Teuchos::OrdinalTraits<GO>::invalid();
  LO lo_invalid = Teuchos::OrdinalTraits<LO>::invalid();

  RCP<const Map> hi_domainMap = hi_importer.getSourceMap();
  RCP<const Map> hi_columnMap = hi_importer.getTargetMap();
  // Figure out the GIDs of my non-owned P1 nodes
  // HOW: We can build a GOVector(domainMap) and fill the values with either invalid() or the P1 domainMap.GID() for that guy.
  // Then we can use A's importer to get a GOVector(colMap) with that information.

  // NOTE: This assumes rowMap==colMap and [E|T]petra ordering of all the locals first in the colMap
  RCP<GOVector> dvec = Xpetra::VectorFactory<GO, LO, GO, NO>::Build(hi_domainMap);
  ArrayRCP<GO> dvec_data = dvec->getDataNonConst(0);
  for(size_t i=0; i<hi_domainMap->getNodeNumElements(); i++) {
    if(hi_to_lo_map[i]!=lo_invalid) dvec_data[i] = lo_domainMap.getGlobalElement(hi_to_lo_map[i]);
    else dvec_data[i] = go_invalid;
  }


  RCP<GOVector> cvec = Xpetra::VectorFactory<GO, LO, GO, NO>::Build(hi_columnMap,true);
  cvec->doImport(*dvec,hi_importer,Xpetra::ADD);

  // Generate the lo_columnMap
  // HOW: We can use the local hi_to_lo_map from the GID's in cvec to generate the non-contiguous colmap ids.
  Array<GO> lo_col_data(lo_columnMapLength);
  ArrayRCP<GO> cvec_data = cvec->getDataNonConst(0);
  for(size_t i=0,idx=0; i<hi_columnMap->getNodeNumElements(); i++) {
    if(hi_to_lo_map[i]!=lo_invalid) {
      lo_col_data[idx] = cvec_data[i];
      idx++;
    }
  }

  lo_columnMap = Xpetra::MapFactory<LO,GO,NO>::Build(lo_domainMap.lib(),Teuchos::OrdinalTraits<Xpetra::global_size_t>::invalid(),lo_col_data(),lo_domainMap.getIndexBase(),lo_domainMap.getComm());
}

/*********************************************************************************************************/
// Generates a list of "representative candidate" hi dofs for each lo dof on the reference element.  This is to be used in global numbering.
// Input:
//  basis                  - The low order basis
//  ReferenceNodeLocations - FC<Scalar> of size (#hidofs, dim) Locations of higher order nodes on the reference element
//  threshold              - tolerance for equivalance testing
// Output:
//  representative_node_candidates - std::vector<std::vector<size_t> > of lists of "representative candidate" hi dofs for each lo dof
template<class Basis, class SCFieldContainer>
void GenerateRepresentativeBasisNodes(const Basis & basis, const SCFieldContainer & ReferenceNodeLocations, const double threshold,std::vector<std::vector<size_t> > & representative_node_candidates) {
 typedef SCFieldContainer FC;
 typedef typename FC::data_type SC;

 // Evaluate the linear basis functions at the Pn nodes
 size_t numFieldsHi = ReferenceNodeLocations.extent(0);
 // size_t dim         = ReferenceNodeLocations.extent(1);
 size_t numFieldsLo = basis.getCardinality();
 
 FC LoValues("LoValues",numFieldsLo,numFieldsHi);

 basis.getValues(LoValues, ReferenceNodeLocations , Intrepid2::OPERATOR_VALUE);


#if 0
  printf("** LoValues[%d,%d] **\n",(int)numFieldsLo,(int)numFieldsHi);
  for(size_t i=0; i<numFieldsLo; i++) {
    for(size_t j=0; j<numFieldsHi; j++)
      printf("%6.4e ",LoValues(i,j));
    printf("\n");
  }
  printf("**************\n");fflush(stdout);
#endif

  representative_node_candidates.resize(numFieldsLo);
  for(size_t i=0; i<numFieldsLo; i++) {
    // 1st pass: find the max value
    typename Teuchos::ScalarTraits<SC>::magnitudeType vmax = Teuchos::ScalarTraits<typename Teuchos::ScalarTraits<SC>::magnitudeType>::zero();
    for(size_t j=0; j<numFieldsHi; j++)
      vmax = std::max(vmax,Teuchos::ScalarTraits<SC>::magnitude(LoValues(i,j)));

    // 2nd pass: Find all values w/i threshhold of target
    for(size_t j=0; j<numFieldsHi; j++) {
      if(Teuchos::ScalarTraits<SC>::magnitude(vmax - LoValues(i,j)) < threshold*vmax)
        representative_node_candidates[i].push_back(j);
    }
  }

  // Sanity check
  for(size_t i=0; i<numFieldsLo; i++)
    if(!representative_node_candidates[i].size())
      throw std::runtime_error("ERROR: GenerateRepresentativeBasisNodes: No candidates found!");


}



}//end MueLu::MueLuIntrepid namespace


/*********************************************************************************************************/
/*********************************************************************************************************/
/*********************************************************************************************************/
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void IntrepidPCoarsenFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::GenerateLinearCoarsening_pn_kirby_to_p1(const LOFieldContainer & hi_elemToNode,
                                                                                                                 const std::vector<bool> & hi_nodeIsOwned,
                                                                                                                 const SCFieldContainer & hi_DofCoords,
                                                                                                                 const std::vector<size_t> &lo_node_in_hi,
                                                                                                                 const Basis &lo_basis,
                                                                                                                 const std::vector<LocalOrdinal> & hi_to_lo_map,
                                                                                                                 const Teuchos::RCP<const Map> & lo_colMap,
                                                                                                                 const Teuchos::RCP<const Map> & lo_domainMap,
                                                                                                                 const Teuchos::RCP<const Map> & hi_map,
                                                                                                                 Teuchos::RCP<Matrix>& P) const{
  typedef SCFieldContainer FC;
  // Evaluate the linear basis functions at the Pn nodes
  size_t numFieldsHi = hi_elemToNode.extent(1);
  size_t numFieldsLo = lo_basis.getCardinality();
  LocalOrdinal LOINVALID = Teuchos::OrdinalTraits<LocalOrdinal>::invalid();
  FC LoValues_at_HiDofs("LoValues_at_HiDofs",numFieldsLo,numFieldsHi);
  lo_basis.getValues(LoValues_at_HiDofs, hi_DofCoords, Intrepid2::OPERATOR_VALUE);

  typedef typename Teuchos::ScalarTraits<SC>::halfPrecision SClo;
  typedef typename Teuchos::ScalarTraits<SClo>::magnitudeType MT;
  MT effective_zero = Teuchos::ScalarTraits<MT>::eps();

  // Allocate P
  P = rcp(new CrsMatrixWrap(hi_map,lo_colMap,0)); //FIXLATER: Need faster fill
  RCP<CrsMatrix> Pcrs   = rcp_dynamic_cast<CrsMatrixWrap>(P)->getCrsMatrix();

  // Slow-ish fill
  size_t Nelem=hi_elemToNode.extent(0);
  std::vector<bool> touched(hi_map->getNodeNumElements(),false);
  Teuchos::Array<GO> col_gid(1);
  Teuchos::Array<SC> val(1);
  for(size_t i=0; i<Nelem; i++) {
    for(size_t j=0; j<numFieldsHi; j++) {
      LO row_lid = hi_elemToNode(i,j);
      GO row_gid = hi_map->getGlobalElement(row_lid);
      if(hi_nodeIsOwned[row_lid] && !touched[row_lid]) {
        for(size_t k=0; k<numFieldsLo; k++) {
          // Get the local id in P1's column map
          LO col_lid = hi_to_lo_map[hi_elemToNode(i,lo_node_in_hi[k])];
          if(col_lid==LOINVALID) continue;

          col_gid[0] = {lo_colMap->getGlobalElement(col_lid)};
          val[0]     = LoValues_at_HiDofs(k,j);

          // Skip near-zeros
          if(Teuchos::ScalarTraits<SC>::magnitude(val[0]) >= effective_zero)
            P->insertGlobalValues(row_gid,col_gid(),val());
        }
        touched[row_lid]=true;
      }
    }
  }
  P->fillComplete(lo_domainMap,hi_map);
}

/*********************************************************************************************************/
template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
void IntrepidPCoarsenFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::GenerateLinearCoarsening_pn_kirby_to_pm(const LOFieldContainer & hi_elemToNode,
                                                                                                                 const std::vector<bool> & hi_nodeIsOwned,
                                                                                                                 const SCFieldContainer & hi_DofCoords,
                                                                                                                 const LOFieldContainer & lo_elemToHiRepresentativeNode,
                                                                                                                 const Basis &lo_basis,
                                                                                                                 const std::vector<LocalOrdinal> & hi_to_lo_map,
                                                                                                                 const Teuchos::RCP<const Map> & lo_colMap,
                                                                                                                 const Teuchos::RCP<const Map> & lo_domainMap,
                                                                                                                 const Teuchos::RCP<const Map> & hi_map,
                                                                                                                 Teuchos::RCP<Matrix>& P) const{
  typedef SCFieldContainer FC;
  // Evaluate the linear basis functions at the Pn nodes
  size_t numFieldsHi = hi_elemToNode.extent(1);
  size_t numFieldsLo = lo_basis.getCardinality();
  FC LoValues_at_HiDofs("LoValues_at_HiDofs",numFieldsLo,numFieldsHi);
  lo_basis.getValues(LoValues_at_HiDofs, hi_DofCoords, Intrepid2::OPERATOR_VALUE);

  typedef typename Teuchos::ScalarTraits<SC>::halfPrecision SClo;
  typedef typename Teuchos::ScalarTraits<SClo>::magnitudeType MT;
  MT effective_zero = Teuchos::ScalarTraits<MT>::eps();

  // Allocate P
  P = rcp(new CrsMatrixWrap(hi_map,lo_colMap,0)); //FIXLATER: Need faster fill
  RCP<CrsMatrix> Pcrs   = rcp_dynamic_cast<CrsMatrixWrap>(P)->getCrsMatrix();

  // Slow-ish fill
  size_t Nelem=hi_elemToNode.extent(0);
  std::vector<bool> touched(hi_map->getNodeNumElements(),false);
  Teuchos::Array<GO> col_gid(1);
  Teuchos::Array<SC> val(1);
  for(size_t i=0; i<Nelem; i++) {
    for(size_t j=0; j<numFieldsHi; j++) {
      LO row_lid = hi_elemToNode(i,j);
      GO row_gid = hi_map->getGlobalElement(row_lid);
      if(hi_nodeIsOwned[row_lid] && !touched[row_lid]) {
        for(size_t k=0; k<numFieldsLo; k++) {
          // Get the local id in P1's column map
          LO col_lid = hi_to_lo_map[lo_elemToHiRepresentativeNode(i,k)];
          col_gid[0] = {lo_colMap->getGlobalElement(col_lid)};
          val[0]     = LoValues_at_HiDofs(k,j);

          // Skip near-zeros
          if(Teuchos::ScalarTraits<SC>::magnitude(val[0]) >= effective_zero)
            P->insertGlobalValues(row_gid,col_gid(),val());
        }
        touched[row_lid]=true;
      }
    }
  }
  P->fillComplete(lo_domainMap,hi_map);
}

/*********************************************************************************************************/
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  RCP<const ParameterList> IntrepidPCoarsenFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::GetValidParameterList() const {
    RCP<ParameterList> validParamList = rcp(new ParameterList());

#define SET_VALID_ENTRY(name) validParamList->setEntry(name, MasterList::getEntry(name))
    SET_VALID_ENTRY("pcoarsen: hi basis");
    SET_VALID_ENTRY("pcoarsen: lo basis");
#undef  SET_VALID_ENTRY

    validParamList->set< RCP<const FactoryBase> >("A",              Teuchos::null, "Generating factory of the matrix A used during the prolongator smoothing process");

    validParamList->set< RCP<const FactoryBase> >("Nullspace",      Teuchos::null, "Generating factory of the nullspace");
    validParamList->set< RCP<const FactoryBase> >("pcoarsen: element to node map",          Teuchos::null, "Generating factory of the element to node map");
    return validParamList;
  }

/*********************************************************************************************************/
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void IntrepidPCoarsenFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::DeclareInput(Level &fineLevel, Level &/* coarseLevel */) const {
    Input(fineLevel, "A");
    Input(fineLevel, "pcoarsen: element to node map");
    Input(fineLevel, "Nullspace");
  }

/*********************************************************************************************************/
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void IntrepidPCoarsenFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Build(Level& fineLevel, Level &coarseLevel) const {
    return BuildP(fineLevel, coarseLevel);
  }

/*********************************************************************************************************/
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void IntrepidPCoarsenFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::BuildP(Level &fineLevel, Level &coarseLevel) const {
    FactoryMonitor m(*this, "P Coarsening", coarseLevel);
    std::string levelIDs = toString(coarseLevel.GetLevelID());
    const std::string prefix = "MueLu::IntrepidPCoarsenFactory(" + levelIDs + "): ";

    // NOTE: This is hardwired to double on purpose.  See the note below.
    typedef Kokkos::DynRankView<LocalOrdinal,typename Node::device_type> FCi;
    typedef Kokkos::DynRankView<double,typename Node::device_type> FC;

    // Level Get
    RCP<Matrix> A     = Get< RCP<Matrix> >(fineLevel, "A");
    RCP<MultiVector> fineNullspace = Get< RCP<MultiVector> >(fineLevel, "Nullspace");
    Xpetra::CrsMatrixWrap<Scalar,LocalOrdinal,GlobalOrdinal,Node>& Acrs = dynamic_cast<Xpetra::CrsMatrixWrap<Scalar,LocalOrdinal,GlobalOrdinal,Node>&>(*A);


    if (restrictionMode_) {
      SubFactoryMonitor m2(*this, "Transpose A", coarseLevel);
      A = Utilities::Transpose(*A, true); // build transpose of A explicitly
    }

    // Find the Dirichlet rows in A
    std::vector<LocalOrdinal> A_dirichletRows;
    Utilities::FindDirichletRows(A,A_dirichletRows);

    // Build final prolongator
    RCP<Matrix> finalP;

    // Reuse pattern if available
    RCP<ParameterList> APparams = rcp(new ParameterList);
    if (coarseLevel.IsAvailable("AP reuse data", this)) {
      GetOStream(static_cast<MsgType>(Runtime0 | Test)) << "Reusing previous AP data" << std::endl;

      APparams = coarseLevel.Get< RCP<ParameterList> >("AP reuse data", this);

      if (APparams->isParameter("graph"))
        finalP = APparams->get< RCP<Matrix> >("graph");
    }
    const ParameterList& pL = GetParameterList();

    /*******************/
    // FIXME LATER: Allow these to be manually specified instead of Intrepid
    // Get the Intrepid bases
    // NOTE: To make sure Stokhos works we only instantiate these guys with double.  There's a lot
    // of stuff in the guts of Intrepid2 that doesn't play well with Stokhos as of yet.
    int lo_degree, hi_degree;
    RCP<Basis> hi_basis = MueLuIntrepid::BasisFactory<double,typename Node::device_type::execution_space>(pL.get<std::string>("pcoarsen: hi basis"),hi_degree);
    RCP<Basis> lo_basis = MueLuIntrepid::BasisFactory<double,typename Node::device_type::execution_space>(pL.get<std::string>("pcoarsen: lo basis"),lo_degree);

    // Useful Output
    GetOStream(Statistics1) << "P-Coarsening from basis "<<pL.get<std::string>("pcoarsen: hi basis")<<" to "<<pL.get<std::string>("pcoarsen: lo basis") <<std::endl;

    /*******************/
    // Get the higher-order element-to-node map
    const Teuchos::RCP<FCi> Pn_elemToNode = Get<Teuchos::RCP<FCi> >(fineLevel,"pcoarsen: element to node map");

    // Calculate node ownership (the quick and dirty way)
    // NOTE: This exploits two things:
    //  1) domainMap == rowMap
    //  2) Standard [e|t]petra ordering (namely the local unknowns are always numbered first).
    // This routine does not work in general.
    RCP<const Map> rowMap = A->getRowMap();
    RCP<const Map> colMap = Acrs.getColMap();
    RCP<const Map> domainMap = A->getDomainMap();
    int NumProc = rowMap->getComm()->getSize();
    assert(rowMap->isSameAs(*domainMap));
    std::vector<bool> Pn_nodeIsOwned(colMap->getNodeNumElements(),false);
    LO num_owned_rows = 0;
    for(size_t i=0; i<rowMap->getNodeNumElements(); i++) {
      if(rowMap->getGlobalElement(i) == colMap->getGlobalElement(i)) {
        Pn_nodeIsOwned[i] = true;
        num_owned_rows++;
      }
    }

    // Used in all cases
    FC hi_DofCoords;
    Teuchos::RCP<FCi> P1_elemToNode = rcp(new FCi());

    std::vector<bool> P1_nodeIsOwned;
    int P1_numOwnedNodes;
    std::vector<LO> hi_to_lo_map;

    // Degree-1 variables
    std::vector<size_t> lo_node_in_hi;

    // Degree-n variables
    FCi lo_elemToHiRepresentativeNode;

    // Get Dirichlet unknown information
    RCP<Xpetra::Vector<int,LocalOrdinal,GlobalOrdinal,Node> > hi_isDirichletRow, hi_isDirichletCol;
    Utilities::FindDirichletRowsAndPropagateToCols(A,hi_isDirichletRow, hi_isDirichletCol);

#if 0
    printf("[%d] isDirichletRow = ",A->getRowMap()->getComm()->getRank());
    for(size_t i=0;i<hi_isDirichletRow->getMap()->getNodeNumElements(); i++)
      printf("%d ",hi_isDirichletRow->getData(0)[i]);
    printf("\n");
    printf("[%d] isDirichletCol = ",A->getRowMap()->getComm()->getRank());
    for(size_t i=0;i<hi_isDirichletCol->getMap()->getNodeNumElements(); i++)
      printf("%d ",hi_isDirichletCol->getData(0)[i]);
    printf("\n");
    fflush(stdout);
#endif

    /*******************/
    if(lo_degree == 1) {
      // Get reference coordinates and the lo-to-hi injection list for the reference element
      MueLuIntrepid::IntrepidGetP1NodeInHi(hi_basis,lo_node_in_hi,hi_DofCoords);

      // Generate lower-order element-to-node map
      MueLuIntrepid::BuildLoElemToNode(*Pn_elemToNode,Pn_nodeIsOwned,lo_node_in_hi,hi_isDirichletCol->getData(0),*P1_elemToNode,P1_nodeIsOwned,hi_to_lo_map,P1_numOwnedNodes);
      assert(hi_to_lo_map.size() == colMap->getNodeNumElements());
   }
    else {
        // Get lo-order candidates
        double threshold = 1e-10;
        std::vector<std::vector<size_t> > candidates;
        Kokkos::resize(hi_DofCoords,hi_basis->getCardinality(),hi_basis->getBaseCellTopology().getDimension());
        hi_basis->getDofCoords(hi_DofCoords);

        MueLu::MueLuIntrepid::GenerateRepresentativeBasisNodes<Basis,FC>(*lo_basis,hi_DofCoords,threshold,candidates);

        // Generate the representative nodes
        MueLu::MueLuIntrepid::GenerateLoNodeInHiViaGIDs(candidates,*Pn_elemToNode,colMap,lo_elemToHiRepresentativeNode);
        MueLu::MueLuIntrepid::BuildLoElemToNodeViaRepresentatives(*Pn_elemToNode,Pn_nodeIsOwned,lo_elemToHiRepresentativeNode,*P1_elemToNode,P1_nodeIsOwned,hi_to_lo_map,P1_numOwnedNodes);
    }
    MUELU_LEVEL_SET_IF_REQUESTED_OR_KEPT(coarseLevel,"pcoarsen: element to node map",P1_elemToNode);

    /*******************/
    // Generate the P1_domainMap
    // HOW: Since we know how many each proc has, we can use the non-uniform contiguous map constructor to do the work for us
    RCP<const Map> P1_domainMap = MapFactory::Build(rowMap->lib(),Teuchos::OrdinalTraits<Xpetra::global_size_t>::invalid(),P1_numOwnedNodes,rowMap->getIndexBase(),rowMap->getComm());
    MUELU_LEVEL_SET_IF_REQUESTED_OR_KEPT(coarseLevel,"CoarseMap",P1_domainMap);

    // Generate the P1_columnMap
    RCP<const Map> P1_colMap;
    if(NumProc==1) P1_colMap = P1_domainMap;
    else MueLuIntrepid::GenerateColMapFromImport<LO,GO,NO>(*Acrs.getCrsGraph()->getImporter(),hi_to_lo_map,*P1_domainMap,P1_nodeIsOwned.size(),P1_colMap);

    /*******************/
    // Generate the coarsening
    if(lo_degree == 1)
      GenerateLinearCoarsening_pn_kirby_to_p1(*Pn_elemToNode,Pn_nodeIsOwned,hi_DofCoords,lo_node_in_hi,*lo_basis,hi_to_lo_map,P1_colMap,P1_domainMap,A->getRowMap(),finalP);
    else
      GenerateLinearCoarsening_pn_kirby_to_pm(*Pn_elemToNode,Pn_nodeIsOwned,hi_DofCoords,lo_elemToHiRepresentativeNode,*lo_basis,hi_to_lo_map,P1_colMap,P1_domainMap,A->getRowMap(),finalP);

    /*******************/
    // Zero out the Dirichlet rows in P
    Utilities::ZeroDirichletRows(finalP,A_dirichletRows);

    /*******************/
    // Build the nullspace
    RCP<MultiVector> coarseNullspace = MultiVectorFactory::Build(P1_domainMap, fineNullspace->getNumVectors());
    finalP->apply(*fineNullspace,*coarseNullspace,Teuchos::TRANS);
    Set(coarseLevel, "Nullspace", coarseNullspace);

    // Level Set
    if (!restrictionMode_) {
      // The factory is in prolongation mode
      Set(coarseLevel, "P",             finalP);

      APparams->set("graph", finalP);
      MUELU_LEVEL_SET_IF_REQUESTED_OR_KEPT(coarseLevel,"AP reuse data",APparams);

      if (IsPrint(Statistics1)) {
        RCP<ParameterList> params = rcp(new ParameterList());
        params->set("printLoadBalancingInfo", true);
        params->set("printCommInfo",          true);
        GetOStream(Statistics1) << PerfUtils::PrintMatrixInfo(*finalP, "P", params);
      }
    } else {
      // The factory is in restriction mode
      RCP<Matrix> R;
      {
        SubFactoryMonitor m2(*this, "Transpose P", coarseLevel);
        R = Utilities::Transpose(*finalP, true);
      }

      Set(coarseLevel, "R", R);

      if (IsPrint(Statistics2)) {
        RCP<ParameterList> params = rcp(new ParameterList());
        params->set("printLoadBalancingInfo", true);
        params->set("printCommInfo",          true);
        GetOStream(Statistics2) << PerfUtils::PrintMatrixInfo(*R, "R", params);
      }
    }

  } //Build()

} //namespace MueLu

#endif // MUELU_IPCFACTORY_DEF_HPP