MueLu_AggregationExportFactory_def.hpp

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/*
 * MueLu_AggregationExportFactory_def.hpp
 *
 *  Created on: Feb 10, 2012
 *      Author: wiesner
 */
 
#ifndef MUELU_AGGREGATIONEXPORTFACTORY_DEF_HPP_
#define MUELU_AGGREGATIONEXPORTFACTORY_DEF_HPP_
 
#include <Xpetra_Matrix.hpp>
#include <Xpetra_CrsMatrixWrap.hpp>
#include <Xpetra_ImportFactory.hpp>
#include <Xpetra_MultiVectorFactory.hpp>
#include "MueLu_AggregationExportFactory_decl.hpp"
#include "MueLu_Level.hpp"
#include "MueLu_Aggregates.hpp"
#include "MueLu_Graph.hpp"
#include "MueLu_AmalgamationFactory.hpp"
#include "MueLu_AmalgamationInfo.hpp"
#include "MueLu_Monitor.hpp"
#include "MueLu_Utilities.hpp"
#include <vector>
#include <list>
#include <algorithm>
#include <string>
#include <stdexcept>
#include <cstdio>
#include <cmath>
//For alpha hulls (is optional feature requiring a third-party library)
#ifdef HAVE_MUELU_CGAL //Include all headers needed for both 2D and 3D fixed-alpha alpha shapes
#include "CGAL/Exact_predicates_inexact_constructions_kernel.h"
#include "CGAL/Delaunay_triangulation_2.h"
#include "CGAL/Delaunay_triangulation_3.h"
#include "CGAL/Alpha_shape_2.h"
#include "CGAL/Fixed_alpha_shape_3.h"
#include "CGAL/algorithm.h"
#endif
 
namespace MueLu {
 
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  RCP<const ParameterList> AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::GetValidParameterList() const {
    RCP<ParameterList> validParamList = rcp(new ParameterList());
 
    std::string output_msg = "Output filename template (%TIMESTEP is replaced by \'Output file: time step\' variable,"
        "%ITER is replaced by \'Output file: iter\' variable, %LEVELID is replaced level id, %PROCID is replaced by processor id)";
    std::string output_def = "aggs_level%LEVELID_proc%PROCID.out";
 
    validParamList->set< RCP<const FactoryBase> >("A", Teuchos::null, "Factory for A.");
    validParamList->set< RCP<const FactoryBase> >("Coordinates", Teuchos::null, "Factory for Coordinates.");
    validParamList->set< RCP<const FactoryBase> >("Graph", Teuchos::null, "Factory for Graph.");
    validParamList->set< RCP<const FactoryBase> >("Aggregates", Teuchos::null, "Factory for Aggregates.");
    validParamList->set< RCP<const FactoryBase> >("UnAmalgamationInfo", Teuchos::null, "Factory for UnAmalgamationInfo.");
    validParamList->set< RCP<const FactoryBase> >("DofsPerNode", Teuchos::null, "Factory for DofsPerNode.");
    // CMS/BMK: Old style factory-only options.  Deprecate me.
    validParamList->set< std::string >           ("Output filename",           output_def, output_msg);
    validParamList->set< int >                   ("Output file: time step",             0, "time step variable for output file name");
    validParamList->set< int >                   ("Output file: iter",                  0, "nonlinear iteration variable for output file name");
 
    // New-style master list options (here are same defaults as in masterList.xml)
    validParamList->set< std::string >           ("aggregation: output filename",                    "",                    "filename for VTK-style visualization output");
    validParamList->set< int >                   ("aggregation: output file: time step",             0,                     "time step variable for output file name");// Remove me?
    validParamList->set< int >                   ("aggregation: output file: iter",                  0,                     "nonlinear iteration variable for output file name");//Remove me?
    validParamList->set<std::string>             ("aggregation: output file: agg style",             "Point Cloud",         "style of aggregate visualization for VTK output");
    validParamList->set<bool>                    ("aggregation: output file: fine graph edges",      false,                 "Whether to draw all fine node connections along with the aggregates.");
    validParamList->set<bool>                    ("aggregation: output file: coarse graph edges",    false,                 "Whether to draw all coarse node connections along with the aggregates.");
    validParamList->set<bool>                    ("aggregation: output file: build colormap",        false,                 "Whether to output a random colormap for ParaView in a separate XML file.");
    return validParamList;
  }
 
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::DeclareInput(Level &fineLevel, Level &coarseLevel) const {
    Input(fineLevel, "Aggregates");         //< factory which created aggregates
    Input(fineLevel, "DofsPerNode");        //< CoalesceAndDropFactory (needed for DofsPerNode variable)
    Input(fineLevel, "UnAmalgamationInfo"); //< AmalgamationFactory (needed for UnAmalgamationInfo variable)
 
    const ParameterList & pL = GetParameterList();
    //Only pull in coordinates if the user explicitly requests direct VTK output, so as not to break uses of old code
    if(pL.isParameter("aggregation: output filename") && pL.get<std::string>("aggregation: output filename").length())
    {
      Input(fineLevel, "Coordinates");
      Input(fineLevel, "A");
      Input(fineLevel, "Graph");
      if(pL.get<bool>("aggregation: output file: coarse graph edges"))
      {
        Input(coarseLevel, "Coordinates");
        Input(coarseLevel, "A");
        Input(coarseLevel, "Graph");
      }
    }
  }
 
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::Build(Level &fineLevel, Level &coarseLevel) const {
    using namespace std;
    //Decide which build function to follow, based on input params
    const ParameterList& pL = GetParameterList();
    FactoryMonitor m(*this, "AggregationExportFactory", coarseLevel);
    Teuchos::RCP<Aggregates> aggregates      = Get< Teuchos::RCP<Aggregates> >(fineLevel,"Aggregates");
    Teuchos::RCP<const Teuchos::Comm<int> > comm = aggregates->GetMap()->getComm();
    int numProcs = comm->getSize();
    int myRank   = comm->getRank();
    string masterFilename = pL.get<std::string>("aggregation: output filename"); //filename parameter from master list
    string pvtuFilename = ""; //only root processor will set this
    string localFilename = pL.get<std::string>("Output filename");
    string filenameToWrite;
    bool useVTK = false;
    doCoarseGraphEdges_ = pL.get<bool>("aggregation: output file: coarse graph edges");
    doFineGraphEdges_ = pL.get<bool>("aggregation: output file: fine graph edges");
    if(masterFilename.length())
    {
      useVTK = true;
      filenameToWrite = masterFilename;
      if(filenameToWrite.rfind(".vtu") == string::npos) //Must have the file extension in the name
        filenameToWrite.append(".vtu");
      if(numProcs > 1 && filenameToWrite.rfind("%PROCID") == string::npos) //filename can't be identical between processsors in parallel problem
        filenameToWrite.insert(filenameToWrite.rfind(".vtu"), "-proc%PROCID");
    }
    else
      filenameToWrite = localFilename;
    LocalOrdinal DofsPerNode                 = Get< LocalOrdinal >            (fineLevel,"DofsPerNode");
    Teuchos::RCP<AmalgamationInfo> amalgInfo = Get< RCP<AmalgamationInfo> >   (fineLevel,"UnAmalgamationInfo");
    Teuchos::RCP<Matrix> Amat = Get<RCP<Matrix> >(fineLevel, "A");
    Teuchos::RCP<Matrix> Ac;
    if(doCoarseGraphEdges_)
      Ac = Get<RCP<Matrix> >(coarseLevel, "A");
    Teuchos::RCP<Xpetra::MultiVector<typename Teuchos::ScalarTraits<Scalar>::coordinateType, LocalOrdinal, GlobalOrdinal, Node> > coords = Teuchos::null;
    Teuchos::RCP<Xpetra::MultiVector<typename Teuchos::ScalarTraits<Scalar>::coordinateType, LocalOrdinal, GlobalOrdinal, Node> > coordsCoarse = Teuchos::null;
    Teuchos::RCP<GraphBase> fineGraph = Teuchos::null;
    Teuchos::RCP<GraphBase> coarseGraph = Teuchos::null;
    if(doFineGraphEdges_)
      fineGraph = Get<RCP<GraphBase> >(fineLevel, "Graph");
    if(doCoarseGraphEdges_)
      coarseGraph = Get<RCP<GraphBase> >(coarseLevel, "Graph");
    if(useVTK) //otherwise leave null, will not be accessed by non-vtk code
    {
      coords = Get<RCP<Xpetra::MultiVector<typename Teuchos::ScalarTraits<Scalar>::coordinateType, LocalOrdinal, GlobalOrdinal, Node> > >(fineLevel, "Coordinates");
      if(doCoarseGraphEdges_)
        coordsCoarse = Get<RCP<Xpetra::MultiVector<typename Teuchos::ScalarTraits<Scalar>::coordinateType, LocalOrdinal, GlobalOrdinal, Node> > >(coarseLevel, "Coordinates");
      dims_ = coords->getNumVectors();  //2D or 3D?
      if(numProcs > 1)
      {
        if (aggregates->AggregatesCrossProcessors())
        { // Do we want to use the map from aggregates here instead of the map from A? Using the map from A seems to be problematic with multiple dofs per node
          RCP<Import> coordImporter = Xpetra::ImportFactory<LocalOrdinal, GlobalOrdinal, Node>::Build(coords->getMap(), Amat->getColMap());
          RCP<Xpetra::MultiVector<typename Teuchos::ScalarTraits<Scalar>::coordinateType, LocalOrdinal, GlobalOrdinal, Node> > ghostedCoords = Xpetra::MultiVectorFactory<typename Teuchos::ScalarTraits<Scalar>::coordinateType, LocalOrdinal, GlobalOrdinal, Node>::Build(Amat->getColMap(), dims_);
          ghostedCoords->doImport(*coords, *coordImporter, Xpetra::INSERT);
          coords = ghostedCoords;
        }
        if(doCoarseGraphEdges_)
        {
          RCP<Import> coordImporter = Xpetra::ImportFactory<LocalOrdinal, GlobalOrdinal, Node>::Build(coordsCoarse->getMap(), Ac->getColMap());
          RCP<Xpetra::MultiVector<typename Teuchos::ScalarTraits<Scalar>::coordinateType, LocalOrdinal, GlobalOrdinal, Node> > ghostedCoords = Xpetra::MultiVectorFactory<typename Teuchos::ScalarTraits<Scalar>::coordinateType, LocalOrdinal, GlobalOrdinal, Node>::Build(Ac->getColMap(), dims_);
          ghostedCoords->doImport(*coordsCoarse, *coordImporter, Xpetra::INSERT);
          coordsCoarse = ghostedCoords;
        }
      }
    }
    GetOStream(Runtime0) << "AggregationExportFactory: DofsPerNode: " << DofsPerNode << std::endl;
    Teuchos::RCP<LocalOrdinalMultiVector> vertex2AggId_vector = aggregates->GetVertex2AggId();
    Teuchos::RCP<LocalOrdinalVector>      procWinner_vector   = aggregates->GetProcWinner();
    Teuchos::ArrayRCP<LocalOrdinal>       vertex2AggId        = aggregates->GetVertex2AggId()->getDataNonConst(0);
    Teuchos::ArrayRCP<LocalOrdinal>       procWinner          = aggregates->GetProcWinner()->getDataNonConst(0);
 
    vertex2AggId_ = vertex2AggId;
 
    // prepare for calculating global aggregate ids
    std::vector<GlobalOrdinal> numAggsGlobal (numProcs, 0);
    std::vector<GlobalOrdinal> numAggsLocal  (numProcs, 0);
    std::vector<GlobalOrdinal> minGlobalAggId(numProcs, 0);
 
    numAggsLocal[myRank] = aggregates->GetNumAggregates();
    Teuchos::reduceAll(*comm, Teuchos::REDUCE_SUM, numProcs, &numAggsLocal[0], &numAggsGlobal[0]);
    for (int i = 1; i < Teuchos::as<int>(numAggsGlobal.size()); ++i)
    {
      numAggsGlobal [i] += numAggsGlobal[i-1];
      minGlobalAggId[i]  = numAggsGlobal[i-1];
    }
    if(numProcs == 0)
      aggsOffset_ = 0;
    else
      aggsOffset_ = minGlobalAggId[myRank];
    ArrayRCP<LO>            aggStart;
    ArrayRCP<GlobalOrdinal> aggToRowMap;
    amalgInfo->UnamalgamateAggregates(*aggregates, aggStart, aggToRowMap);
    int timeStep = pL.get< int > ("Output file: time step");
    int iter = pL.get< int > ("Output file: iter");
    filenameToWrite = this->replaceAll(filenameToWrite, "%LEVELID",  toString(fineLevel.GetLevelID()));
    filenameToWrite = this->replaceAll(filenameToWrite, "%TIMESTEP", toString(timeStep));
    filenameToWrite = this->replaceAll(filenameToWrite, "%ITER",     toString(iter));
    //Proc id MUST be included in vtu filenames to distinguish them (if multiple procs)
    //In all other cases (else), including processor # in filename is optional
    string masterStem = "";
    if(useVTK)
    {
      masterStem = filenameToWrite.substr(0, filenameToWrite.rfind(".vtu"));
      masterStem = this->replaceAll(masterStem, "%PROCID", "");
    }
    pvtuFilename = masterStem + "-master.pvtu";
    string baseFname = filenameToWrite;  //get a version of the filename string with the %PROCID token, but without substituting myRank (needed for pvtu output)
    filenameToWrite = this->replaceAll(filenameToWrite, "%PROCID", toString(myRank));
    GetOStream(Runtime0) << "AggregationExportFactory: outputfile \"" << filenameToWrite << "\"" << std::endl;
    ofstream fout(filenameToWrite.c_str());
    GO numAggs = aggregates->GetNumAggregates();
    if(!useVTK)
    {
      GO indexBase = aggregates->GetMap()->getIndexBase(); // extract indexBase from overlapping map within aggregates structure. The indexBase is constant throughout the whole simulation (either 0 = C++ or 1 = Fortran)
      GO offset    = amalgInfo->GlobalOffset();            // extract offset for global dof ids
      vector<GlobalOrdinal> nodeIds;
      for (int i = 0; i < numAggs; ++i) {
        fout << "Agg " << minGlobalAggId[myRank] + i << " Proc " << myRank << ":";
 
        // TODO: Use k+=DofsPerNode instead of ++k and get rid of std::unique call afterwards
        for (int k = aggStart[i]; k < aggStart[i+1]; ++k) {
          nodeIds.push_back((aggToRowMap[k] - offset - indexBase) / DofsPerNode + indexBase);
        }
 
        // remove duplicate entries from nodeids
        std::sort(nodeIds.begin(), nodeIds.end());
        typename std::vector<GlobalOrdinal>::iterator endLocation = std::unique(nodeIds.begin(), nodeIds.end());
        nodeIds.erase(endLocation, nodeIds.end());
 
        // print out nodeids
        for(typename std::vector<GlobalOrdinal>::iterator printIt = nodeIds.begin(); printIt != nodeIds.end(); printIt++)
          fout << " " << *printIt;
        nodeIds.clear();
        fout << std::endl;
      }
    }
    else
    {
      using namespace std;
      //Make sure we have coordinates
      TEUCHOS_TEST_FOR_EXCEPTION(coords.is_null(), Exceptions::RuntimeError,"AggExportFactory could not get coordinates, but they are required for VTK output.");
      numAggs_ = numAggs;
      numNodes_ = coords->getLocalLength();
      //get access to the coord data
      xCoords_ = Teuchos::arcp_reinterpret_cast<const typename Teuchos::ScalarTraits<Scalar>::coordinateType>(coords->getData(0));
      yCoords_ = Teuchos::arcp_reinterpret_cast<const typename Teuchos::ScalarTraits<Scalar>::coordinateType>(coords->getData(1));
      zCoords_ = Teuchos::null;
      if(doCoarseGraphEdges_)
      {
        cx_ = Teuchos::arcp_reinterpret_cast<const typename Teuchos::ScalarTraits<Scalar>::coordinateType>(coordsCoarse->getData(0));
        cy_ = Teuchos::arcp_reinterpret_cast<const typename Teuchos::ScalarTraits<Scalar>::coordinateType>(coordsCoarse->getData(1));
        cz_ = Teuchos::null;
      }
      if(dims_ == 3)
      {
        zCoords_ = Teuchos::arcp_reinterpret_cast<const typename Teuchos::ScalarTraits<Scalar>::coordinateType>(coords->getData(2));
        if(doCoarseGraphEdges_)
          cz_ = Teuchos::arcp_reinterpret_cast<const typename Teuchos::ScalarTraits<Scalar>::coordinateType>(coordsCoarse->getData(2));
      }
      //Get the sizes of the aggregates to speed up grabbing node IDs
      aggSizes_ = aggregates->ComputeAggregateSizes();
      myRank_ = myRank;
      string aggStyle = "Point Cloud";
      try
      {
        aggStyle = pL.get<string>("aggregation: output file: agg style"); //Let "Point Cloud" be the default style
      }
      catch(std::exception& e) {}
      vector<int> vertices;
      vector<int> geomSizes;
      string indent = "";
      nodeMap_ = Amat->getMap();
      for(LocalOrdinal i = 0; i < numNodes_; i++)
      {
        isRoot_.push_back(aggregates->IsRoot(i));
      }
      //If problem is serial and not outputting fine nor coarse graph edges, don't make pvtu file
      //Otherwise create it
      if(myRank == 0 && (numProcs != 1 || doCoarseGraphEdges_ || doFineGraphEdges_))
      {
        ofstream pvtu(pvtuFilename.c_str());
        writePVTU_(pvtu, baseFname, numProcs);
        pvtu.close();
      }
      if(aggStyle == "Point Cloud")
        this->doPointCloud(vertices, geomSizes, numAggs_, numNodes_);
      else if(aggStyle == "Jacks")
        this->doJacks(vertices, geomSizes, numAggs_, numNodes_, isRoot_, vertex2AggId_);
      else if(aggStyle == "Jacks++") //Not actually implemented
        doJacksPlus_(vertices, geomSizes);
      else if(aggStyle == "Convex Hulls")
        doConvexHulls(vertices, geomSizes);
      else if(aggStyle == "Alpha Hulls")
      {
        #ifdef HAVE_MUELU_CGAL
        doAlphaHulls_(vertices, geomSizes);
        #else
        GetOStream(Warnings0) << "   Trilinos was not configured with CGAL so Alpha Hulls not available.\n   Using Convex Hulls instead." << std::endl;
        doConvexHulls(vertices, geomSizes);
        #endif
      }
      else
      {
        GetOStream(Warnings0) << "   Unrecognized agg style.\n   Possible values are Point Cloud, Jacks, Jacks++, Convex Hulls and Alpha Hulls.\n   Defaulting to Point Cloud." << std::endl;
        aggStyle = "Point Cloud";
        this->doPointCloud(vertices, geomSizes, numAggs_, numNodes_);
      }
      writeFile_(fout, aggStyle, vertices, geomSizes);
      if(doCoarseGraphEdges_)
      {
        string fname = filenameToWrite;
        string cEdgeFile = fname.insert(fname.rfind(".vtu"), "-coarsegraph");
        std::ofstream edgeStream(cEdgeFile.c_str());
        doGraphEdges_(edgeStream, Ac, coarseGraph, false, DofsPerNode);
      }
      if(doFineGraphEdges_)
      {
        string fname = filenameToWrite;
        string fEdgeFile = fname.insert(fname.rfind(".vtu"), "-finegraph");
        std::ofstream edgeStream(fEdgeFile.c_str());
        doGraphEdges_(edgeStream, Amat, fineGraph, true, DofsPerNode);
      }
      if(myRank == 0 && pL.get<bool>("aggregation: output file: build colormap"))
      {
        buildColormap_();
      }
    }
    fout.close();
  }
 
  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::doJacksPlus_(std::vector<int>& /* vertices */, std::vector<int>& /* geomSizes */) const
  {
    //TODO
  }
 
  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::doConvexHulls(std::vector<int>& vertices, std::vector<int>& geomSizes) const
  {
    if(dims_ == 2)
      this->doConvexHulls2D(vertices, geomSizes, numAggs_, numNodes_, isRoot_, vertex2AggId_, xCoords_, yCoords_);
    else
      this->doConvexHulls3D(vertices, geomSizes, numAggs_, numNodes_, isRoot_, vertex2AggId_, xCoords_, yCoords_, zCoords_);
  }
 
#ifdef HAVE_MUELU_CGAL
  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::doAlphaHulls_(std::vector<int>& vertices, std::vector<int>& geomSizes) const
  {
    using namespace std;
    if(dims_ == 2)
      doAlphaHulls2D_(vertices, geomSizes);
    else if(dims_ == 3)
      doAlphaHulls3D_(vertices, geomSizes);
  }
 
  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::doAlphaHulls2D_(std::vector<int>& vertices, std::vector<int>& geomSizes) const
  {
    //const double ALPHA_VAL = 2; //Make configurable?
    using namespace std;
    //CGAL setup
    typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
    typedef K::FT FT;
    typedef K::Point_2 Point;
    typedef K::Segment_2 Segment;
    typedef CGAL::Alpha_shape_vertex_base_2<K> Vb;
    typedef CGAL::Alpha_shape_face_base_2<K> Fb;
    typedef CGAL::Triangulation_data_structure_2<Vb,Fb> Tds;
    typedef CGAL::Delaunay_triangulation_2<K,Tds> Triangulation_2;
    typedef CGAL::Alpha_shape_2<Triangulation_2> Alpha_shape_2;
    typedef Alpha_shape_2::Alpha_shape_edges_iterator Alpha_shape_edges_iterator;
#if 0 // taw: does not compile with CGAL 4.8
    for(int i = 0; i < numAggs_; i++)
    {
      //Populate a list of Point_2 for this aggregate
      list<Point> aggPoints;
      vector<int> aggNodes;
      for(int j = 0; j < numNodes_; j++)
      {
        if(vertex2AggId_[j] == i)
        {
          Point p(xCoords_[j], yCoords_[j]);
          aggPoints.push_back(p);
          aggNodes.push_back(j);
        }
      }
      Alpha_shape_2 hull(aggPoints.begin(), aggPoints.end(), FT(ALPHA_VAL), Alpha_shape_2::GENERAL);
      vector<Segment> segments;
      CGAL::alpha_edges(hull, back_inserter(segments));
      vertices.reserve(vertices.size() + 2 * segments.size());
      geomSizes.reserve(geomSizes.size() + segments.size());
      for(size_t j = 0; j < segments.size(); j++)
      {
        for(size_t k = 0; k < aggNodes.size(); k++)
        {
          if(fabs(segments[j][0].x == xCoords_[aggNodes[k]]) < 1e-12 && fabs(segments[j][0].y == yCoords_[aggNodes[k]]) < 1e-12)
          {
            vertices.push_back(aggNodes[k]);
            break;
          }
        }
        for(size_t k = 0; k < aggNodes.size(); k++)
        {
          if(fabs(segments[j][1].x  == xCoords_[aggNodes[k]]) < 1e-12 && fabs(segments[j][1].y == yCoords_[aggNodes[k]]) < 1e-12)
          {
            vertices.push_back(aggNodes[k]);
            break;
          }
        }
        geomSizes.push_back(2); //all cells are line segments
      }
    }
#endif // if 0
  }
 
  template<class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::doAlphaHulls3D_(std::vector<int>& vertices, std::vector<int>& geomSizes) const
  {
    typedef CGAL::Exact_predicates_inexact_constructions_kernel Gt;
#if 0 // does not compile with CGAL 4-8
    typedef CGAL::Alpha_shape_cell_base_3<Gt> Fb;
    typedef CGAL::Triangulation_data_structure_3<Vb,Fb> Tds;
    typedef CGAL::Delaunay_triangulation_3<Gt,Tds> Triangulation_3;
    typedef Gt::Point_3 Point;
    typedef Alpha_shape_3::Alpha_iterator Alpha_iterator;
    typedef Alpha_shape_3::Cell_handle Cell_handle;
    typedef Alpha_shape_3::Vertex_handle Vertex_handle;
    typedef Alpha_shape_3::Facet Facet;
    typedef Alpha_shape_3::Edge Edge;
    typedef Gt::Weighted_point Weighted_point;
    typedef Gt::Bare_point Bare_point;
    const double ALPHA_VAL = 2; //Make configurable?
    using namespace std;
 
    for(int i = 0; i < numAggs_; i++)
    {
      list<Point> aggPoints;
      vector<int> aggNodes;
      for(int j = 0; j < numNodes_; j++)
      {
        if(vertex2AggId[j] == i)
        {
          Point p(xCoords_[j], yCoords_[j], zCoords_[j]);
          aggPoints.push_back(p);
          aggNodes.push_back(j);
        }
      }
      Fixed_alpha_shape_3 hull(aggPoints.begin(), aggPoints.end(), FT(ALPHA_VAL));
      list<Cell_handle> cells;
      list<Facet> facets;
      list<Edge> edges;
      hull.get_alpha_shape_cells(back_inserter(cells));
      hull.get_alpha_shape_facets(back_inserter(facets));
      hull.get_alpha_shape_edges(back_inserter(edges));
      for(size_t j = 0; j < cells.size(); j++)
      {
        Point tetPoints[4];
        tetPoints[0] = cells[j]->vertex(0);
        tetPoints[1] = cells[j]->vertex(1);
        tetPoints[2] = cells[j]->vertex(2);
        tetPoints[3] = cells[j]->vertex(3);
        for(int k = 0; k < 4; k++)
        {
          for(size_t l = 0; l < aggNodes.size(); l++)
          {
            if(fabs(tetPoints[k].x - xCoords_[aggNodes[l]]) < 1e-12 &&
               fabs(tetPoints[k].y - yCoords_[aggNodes[l]]) < 1e-12 &&
               fabs(tetPoints[k].z - zCoords_[aggNodes[l]]) < 1e-12)
            {
              vertices.push_back(aggNodes[l]);
              break;
            }
          }
        }
        geomSizes.push_back(-10); //tetrahedron
      }
      for(size_t j = 0; j < facets.size(); j++)
      {
        int indices[3];
        indices[0] = (facets[i].second + 1) % 4;
        indices[1] = (facets[i].second + 2) % 4;
        indices[2] = (facets[i].second + 3) % 4;
        if(facets[i].second % 2 == 0)
          swap(indices[0], indices[1]);
        Point facetPts[3];
        facetPts[0] = facets[i].first->vertex(indices[0])->point();
        facetPts[1] = facets[i].first->vertex(indices[1])->point();
        facetPts[2] = facets[i].first->vertex(indices[2])->point();
        //add triangles in terms of node indices
        for(size_t l = 0; l < aggNodes.size(); l++)
        {
          if(fabs(facetPts[k].x - xCoords_[aggNodes[l]]) < 1e-12 &&
             fabs(facetPts[k].y - yCoords_[aggNodes[l]]) < 1e-12 &&
             fabs(facetPts[k].z - zCoords_[aggNodes[l]]) < 1e-12)
          {
            vertices.push_back(aggNodes[l]);
            break;
          }
        }
        geomSizes.push_back(3);
      }
      for(size_t j = 0; j < edges.size(); j++)
      {
 
      }
    }
#endif // if 0
  }
#endif
 
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::doGraphEdges_(std::ofstream& fout, Teuchos::RCP<Matrix>& A, Teuchos::RCP<GraphBase>& G, bool fine, int dofs) const
  {
    using namespace std;
    ArrayView<const Scalar> values;
    ArrayView<const LocalOrdinal> neighbors;
    //Allow two different colors of connections (by setting "aggregates" scalar to CONTRAST_1 or CONTRAST_2)
    vector<pair<int, int> > vert1; //vertices (node indices)
    vector<pair<int, int> > vert2; //size of every cell is assumed to be 2 vertices, since all edges are drawn as lines
    if(A->isGloballyIndexed())
    {
      ArrayView<const GlobalOrdinal> indices;
      for(GlobalOrdinal globRow = 0; globRow < GlobalOrdinal(A->getGlobalNumRows()); globRow++)
      {
        if(dofs == 1)
          A->getGlobalRowView(globRow, indices, values);
        neighbors = G->getNeighborVertices((LocalOrdinal) globRow);
        int gEdge = 0;
        int aEdge = 0;
        while(gEdge != int(neighbors.size()))
        {
          if(dofs == 1)
          {
            if(neighbors[gEdge] == indices[aEdge])
            {
              //graph and matrix both have this edge, wasn't filtered, show as color 1
              vert1.push_back(pair<int, int>(int(globRow), neighbors[gEdge]));
              gEdge++;
              aEdge++;
            }
            else
            {
              //graph contains an edge at gEdge which was filtered from A, show as color 2
              vert2.push_back(pair<int, int>(int(globRow), neighbors[gEdge]));
              gEdge++;
            }
          }
          else //for multiple DOF problems, don't try to detect filtered edges and ignore A
          {
            vert1.push_back(pair<int, int>(int(globRow), neighbors[gEdge]));
            gEdge++;
          }
        }
      }
    }
    else
    {
      ArrayView<const LocalOrdinal> indices;
      for(LocalOrdinal locRow = 0; locRow < LocalOrdinal(A->getLocalNumRows()); locRow++)
      {
        if(dofs == 1)
          A->getLocalRowView(locRow, indices, values);
        neighbors = G->getNeighborVertices(locRow);
        //Add those local indices (columns) to the list of connections (which are pairs of the form (localM, localN))
        int gEdge = 0;
        int aEdge = 0;
        while(gEdge != int(neighbors.size()))
        {
          if(dofs == 1)
          {
            if(neighbors[gEdge] == indices[aEdge])
            {
              vert1.push_back(pair<int, int>(locRow, neighbors[gEdge]));
              gEdge++;
              aEdge++;
            }
            else
            {
              vert2.push_back(pair<int, int>(locRow, neighbors[gEdge]));
              gEdge++;
            }
          }
          else
          {
            vert1.push_back(pair<int, int>(locRow, neighbors[gEdge]));
            gEdge++;
          }
        }
      }
    }
    for(size_t i = 0; i < vert1.size(); i ++)
    {
      if(vert1[i].first > vert1[i].second)
      {
        int temp = vert1[i].first;
        vert1[i].first = vert1[i].second;
        vert1[i].second = temp;
      }
    }
    for(size_t i = 0; i < vert2.size(); i++)
    {
      if(vert2[i].first > vert2[i].second)
      {
        int temp = vert2[i].first;
        vert2[i].first = vert2[i].second;
        vert2[i].second = temp;
      }
    }
    sort(vert1.begin(), vert1.end());
    vector<pair<int, int> >::iterator newEnd = unique(vert1.begin(), vert1.end()); //remove duplicate edges
    vert1.erase(newEnd, vert1.end());
    sort(vert2.begin(), vert2.end());
    newEnd = unique(vert2.begin(), vert2.end());
    vert2.erase(newEnd, vert2.end());
    vector<int> points1;
    points1.reserve(2 * vert1.size());
    for(size_t i = 0; i < vert1.size(); i++)
    {
      points1.push_back(vert1[i].first);
      points1.push_back(vert1[i].second);
    }
    vector<int> points2;
    points2.reserve(2 * vert2.size());
    for(size_t i = 0; i < vert2.size(); i++)
    {
      points2.push_back(vert2[i].first);
      points2.push_back(vert2[i].second);
    }
    vector<int> unique1 = this->makeUnique(points1);
    vector<int> unique2 = this->makeUnique(points2);
    fout << "<VTKFile type=\"UnstructuredGrid\" byte_order=\"LittleEndian\">" << endl;
    fout << "  <UnstructuredGrid>" << endl;
    fout << "    <Piece NumberOfPoints=\"" << unique1.size() + unique2.size() << "\" NumberOfCells=\"" << vert1.size() + vert2.size() << "\">" << endl;
    fout << "      <PointData Scalars=\"Node Aggregate Processor\">" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"Node\" format=\"ascii\">" << endl; //node and aggregate will be set to CONTRAST_1|2, but processor will have its actual value
    string indent = "          ";
    fout << indent;
    for(size_t i = 0; i < unique1.size(); i++)
    {
      fout << CONTRAST_1_ << " ";
      if(i % 25 == 24)
        fout << endl << indent;
    }
    for(size_t i = 0; i < unique2.size(); i++)
    {
      fout << CONTRAST_2_ << " ";
      if((i + 2 * vert1.size()) % 25 == 24)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"Aggregate\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < unique1.size(); i++)
    {
      fout << CONTRAST_1_ << " ";
      if(i % 25 == 24)
        fout << endl << indent;
    }
    for(size_t i = 0; i < unique2.size(); i++)
    {
      fout << CONTRAST_2_ << " ";
      if((i + 2 * vert2.size()) % 25 == 24)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"Processor\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < unique1.size() + unique2.size(); i++)
    {
      fout << myRank_ << " ";
      if(i % 25 == 24)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "      </PointData>" << endl;
    fout << "      <Points>" << endl;
    fout << "        <DataArray type=\"Float64\" NumberOfComponents=\"3\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < unique1.size(); i++)
    {
      if(fine)
      {
        fout << xCoords_[unique1[i]] << " " << yCoords_[unique1[i]] << " ";
        if(dims_ == 3)
          fout << zCoords_[unique1[i]] << " ";
        else
          fout << "0 ";
        if(i % 2)
          fout << endl << indent;
      }
      else
      {
        fout << cx_[unique1[i]] << " " << cy_[unique1[i]] << " ";
        if(dims_ == 3)
          fout << cz_[unique1[i]] << " ";
        else
          fout << "0 ";
        if(i % 2)
          fout << endl << indent;
      }
    }
    for(size_t i = 0; i < unique2.size(); i++)
    {
      if(fine)
      {
        fout << xCoords_[unique2[i]] << " " << yCoords_[unique2[i]] << " ";
        if(dims_ == 3)
          fout << zCoords_[unique2[i]] << " ";
        else
          fout << "0 ";
        if(i % 2)
          fout << endl << indent;
      }
      else
      {
        fout << cx_[unique2[i]] << " " << cy_[unique2[i]] << " ";
        if(dims_ == 3)
          fout << cz_[unique2[i]] << " ";
        else
          fout << "0 ";
        if((i + unique1.size()) % 2)
          fout << endl << indent;
      }
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "      </Points>" << endl;
    fout << "      <Cells>" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"connectivity\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < points1.size(); i++)
    {
      fout << points1[i] << " ";
      if(i % 10 == 9)
        fout << endl << indent;
    }
    for(size_t i = 0; i < points2.size(); i++)
    {
      fout << points2[i] + unique1.size() << " ";
      if((i + points1.size()) % 10 == 9)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>"  << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"offsets\" format=\"ascii\">" << endl;
    fout << indent;
    int offset = 0;
    for(size_t i = 0; i < vert1.size() + vert2.size(); i++)
    {
      offset += 2;
      fout << offset << " ";
      if(i % 10 == 9)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>"  << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"types\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < vert1.size() + vert2.size(); i++)
    {
      fout << "3 ";
      if(i % 25 == 24)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>"  << endl;
    fout << "      </Cells>" << endl;
    fout << "    </Piece>" << endl;
    fout << "  </UnstructuredGrid>" << endl;
    fout << "</VTKFile>" << endl;
  }
 
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::writeFile_(std::ofstream& fout, std::string styleName, std::vector<int>& vertices, std::vector<int>& geomSizes) const
  {
    using namespace std;
    vector<int> uniqueFine = this->makeUnique(vertices);
    string indent = "      ";
    fout << "<!--" << styleName << " Aggregates Visualization-->" << endl;
    fout << "<VTKFile type=\"UnstructuredGrid\" byte_order=\"LittleEndian\">" << endl;
    fout << "  <UnstructuredGrid>" << endl;
    fout << "    <Piece NumberOfPoints=\"" << uniqueFine.size() << "\" NumberOfCells=\"" << geomSizes.size() << "\">" << endl;
    fout << "      <PointData Scalars=\"Node Aggregate Processor\">" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"Node\" format=\"ascii\">" << endl;
    indent = "          ";
    fout << indent;
    bool localIsGlobal = GlobalOrdinal(nodeMap_->getGlobalNumElements()) == GlobalOrdinal(nodeMap_->getLocalNumElements());
    for(size_t i = 0; i < uniqueFine.size(); i++)
    {
      if(localIsGlobal)
      {
        fout << uniqueFine[i] << " "; //if all nodes are on this processor, do not map from local to global
      }
      else
        fout << nodeMap_->getGlobalElement(uniqueFine[i]) << " ";
      if(i % 10 == 9)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"Aggregate\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < uniqueFine.size(); i++)
    {
      if(vertex2AggId_[uniqueFine[i]]==-1)
        fout << vertex2AggId_[uniqueFine[i]] << " ";
      else
        fout << aggsOffset_ + vertex2AggId_[uniqueFine[i]] << " ";
      if(i % 10 == 9)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"Processor\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < uniqueFine.size(); i++)
    {
      fout << myRank_ << " ";
      if(i % 20 == 19)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "      </PointData>" << endl;
    fout << "      <Points>" << endl;
    fout << "        <DataArray type=\"Float64\" NumberOfComponents=\"3\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < uniqueFine.size(); i++)
    {
      fout << xCoords_[uniqueFine[i]] << " " << yCoords_[uniqueFine[i]] << " ";
      if(dims_ == 2)
        fout << "0 ";
      else
        fout << zCoords_[uniqueFine[i]] << " ";
      if(i % 3 == 2)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "      </Points>" << endl;
    fout << "      <Cells>" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"connectivity\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < vertices.size(); i++)
    {
      fout << vertices[i] << " ";
      if(i % 10 == 9)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"offsets\" format=\"ascii\">" << endl;
    fout << indent;
    int accum = 0;
    for(size_t i = 0; i < geomSizes.size(); i++)
    {
      accum += geomSizes[i];
      fout << accum << " ";
      if(i % 10 == 9)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "        <DataArray type=\"Int32\" Name=\"types\" format=\"ascii\">" << endl;
    fout << indent;
    for(size_t i = 0; i < geomSizes.size(); i++)
    {
      switch(geomSizes[i])
      {
        case 1:
          fout << "1 "; //Point
          break;
        case 2:
          fout << "3 "; //Line
          break;
        case 3:
          fout << "5 "; //Triangle
          break;
        default:
          fout << "7 "; //Polygon
      }
      if(i % 30 == 29)
        fout << endl << indent;
    }
    fout << endl;
    fout << "        </DataArray>" << endl;
    fout << "      </Cells>" << endl;
    fout << "    </Piece>" << endl;
    fout << "  </UnstructuredGrid>" << endl;
    fout << "</VTKFile>" << endl;
  }
 
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::buildColormap_() const
  {
    using namespace std;
    try
    {
      ofstream color("random-colormap.xml");
      color << "<ColorMap name=\"MueLu-Random\" space=\"RGB\">" << endl;
      //Give -1, -2, -3 distinctive colors (so that the style functions can have constrasted geometry types)
      //Do red, orange, yellow to constrast with cool color spectrum for other types
      color << "  <Point x=\"" << CONTRAST_1_ << "\" o=\"1\" r=\"1\" g=\"0\" b=\"0\"/>" << endl;
      color << "  <Point x=\"" << CONTRAST_2_ << "\" o=\"1\" r=\"1\" g=\"0.6\" b=\"0\"/>" << endl;
      color << "  <Point x=\"" << CONTRAST_3_ << "\" o=\"1\" r=\"1\" g=\"1\" b=\"0\"/>" << endl;
      srand(time(NULL));
      for(int i = 0; i < 5000; i += 4)
      {
        color << "  <Point x=\"" << i << "\" o=\"1\" r=\"" << (rand() % 50) / 256.0 << "\" g=\"" << (rand() % 256) / 256.0 << "\" b=\"" << (rand() % 256) / 256.0 << "\"/>" << endl;
      }
      color << "</ColorMap>" << endl;
      color.close();
    }
    catch(std::exception& e)
    {
      GetOStream(Warnings0) << "   Error while building colormap file: " << e.what() << endl;
    }
  }
 
  template <class Scalar, class LocalOrdinal, class GlobalOrdinal, class Node>
  void AggregationExportFactory<Scalar, LocalOrdinal, GlobalOrdinal, Node>::writePVTU_(std::ofstream& pvtu, std::string baseFname, int numProcs) const
  {
    using namespace std;
    //If using vtk, filenameToWrite now contains final, correct ***.vtu filename (for the current proc)
    //So the root proc will need to use its own filenameToWrite to make a list of the filenames of all other procs to put in
    //pvtu file.
    pvtu << "<VTKFile type=\"PUnstructuredGrid\" byte_order=\"LittleEndian\">" << endl;
    pvtu << "  <PUnstructuredGrid GhostLevel=\"0\">" << endl;
    pvtu << "    <PPointData Scalars=\"Node Aggregate Processor\">" << endl;
    pvtu << "      <PDataArray type=\"Int32\" Name=\"Node\"/>" << endl;
    pvtu << "      <PDataArray type=\"Int32\" Name=\"Aggregate\"/>" << endl;
    pvtu << "      <PDataArray type=\"Int32\" Name=\"Processor\"/>" << endl;
    pvtu << "    </PPointData>" << endl;
    pvtu << "    <PPoints>" << endl;
    pvtu << "      <PDataArray type=\"Float64\" NumberOfComponents=\"3\"/>" << endl;
    pvtu << "    </PPoints>" << endl;
    for(int i = 0; i < numProcs; i++)
    {
      //specify the piece for each proc (the replaceAll expression matches what the filenames will be on other procs)
      pvtu << "    <Piece Source=\"" << this->replaceAll(baseFname, "%PROCID", toString(i)) << "\"/>" << endl;
    }
    //reference files with graph pieces, if applicable
    if(doFineGraphEdges_)
    {
      for(int i = 0; i < numProcs; i++)
      {
        string fn = this->replaceAll(baseFname, "%PROCID", toString(i));
        pvtu << "    <Piece Source=\"" << fn.insert(fn.rfind(".vtu"), "-finegraph") << "\"/>" << endl;
      }
    }
    if(doCoarseGraphEdges_)
    {
      for(int i = 0; i < numProcs; i++)
      {
        string fn = this->replaceAll(baseFname, "%PROCID", toString(i));
        pvtu << "    <Piece Source=\"" << fn.insert(fn.rfind(".vtu"), "-coarsegraph") << "\"/>" << endl;
      }
    }
    pvtu << "  </PUnstructuredGrid>" << endl;
    pvtu << "</VTKFile>" << endl;
    pvtu.close();
  }
} // namespace MueLu
 
#endif /* MUELU_AGGREGATIONEXPORTFACTORY_DEF_HPP_ */