test_03.cpp

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// Questions? Contact Pavel Bochev  (pbboche@sandia.gov)
//                    Denis Ridzal  (dridzal@sandia.gov), or
//                    Kara Peterson (kjpeter@sandia.gov)
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#include "Intrepid_CellTools.hpp"
#include "Intrepid_FieldContainer.hpp"
#include "Intrepid_DefaultCubatureFactory.hpp"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_GlobalMPISession.hpp"
#include "Teuchos_ScalarTraits.hpp"

using namespace std;
using namespace Intrepid;


void testSubcellParametrizations(int&                               errorFlag,
                                 const shards::CellTopology&        parentCell,
                                 const FieldContainer<double>&      subcParamVert_A,
                                 const FieldContainer<double>&      subcParamVert_B,
                                 const int                          subcDim,
                                 const Teuchos::RCP<std::ostream>&  outStream);
  

//IKT, 10/8/15: The following is a helper function that takes in a shards::CellTopology
//and returns a pointer to the Intrepid::Basis associated with this topology. 
Teuchos::RCP<Intrepid::Basis<double, Intrepid::FieldContainer<double> > >
getIntrepidBasis(const shards::CellTopology &cellTopo)
{
  Teuchos::RCP< Basis< double, FieldContainer<double> > > HGRAD_Basis;
  // Choose the H(grad) basis depending on the cell topology. \todo define maps for shells and beams
  switch( cellTopo.getKey() ){
      
    // Standard Base topologies (number of cellWorkset = number of vertices)
    case shards::Line<2>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_LINE_C1_FEM<double, FieldContainer<double> >() );
    break;
        
    case shards::Triangle<3>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TRI_C1_FEM<double, FieldContainer<double> >() );
    break;
        
    case shards::Quadrilateral<4>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_QUAD_C1_FEM<double, FieldContainer<double> >() );
    break;
        
    case shards::Tetrahedron<4>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_C1_FEM<double, FieldContainer<double> >() );
    break;
        
    case shards::Hexahedron<8>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_C1_FEM<double, FieldContainer<double> >() );
    break;
        
    case shards::Wedge<6>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_C1_FEM<double, FieldContainer<double> >() );
    break;

    case shards::Pyramid<5>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_PYR_C1_FEM<double, FieldContainer<double> >() );
    break;
        
    // Standard Extended topologies
    case shards::Triangle<6>::key:    
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TRI_C2_FEM<double, FieldContainer<double> >() );
    break;

    case shards::Quadrilateral<9>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_QUAD_C2_FEM<double, FieldContainer<double> >() );
    break;
        
    case shards::Tetrahedron<10>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_C2_FEM<double, FieldContainer<double> >() );
    break;

    case shards::Tetrahedron<11>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_TET_COMP12_FEM<double, FieldContainer<double> >() );
    break;

    case shards::Hexahedron<20>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_I2_FEM<double, FieldContainer<double> >() );
    break;
        
    case shards::Hexahedron<27>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_HEX_C2_FEM<double, FieldContainer<double> >() );
    break;

    case shards::Wedge<15>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_I2_FEM<double, FieldContainer<double> >() );
    break;
        
    case shards::Wedge<18>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_WEDGE_C2_FEM<double, FieldContainer<double> >() );
    break;

    case shards::Pyramid<13>::key:
    HGRAD_Basis = Teuchos::rcp( new Basis_HGRAD_PYR_I2_FEM<double, FieldContainer<double> >() );
    break;
       
    // These extended topologies are not used for mapping purposes
    case shards::Quadrilateral<8>::key:
    TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument, 
                            ">>> ERROR (getIntrepidBasis): Cell topology not supported. ");
    break;
        
    // Base and Extended Line, Beam and Shell topologies  
    case shards::Line<3>::key:
    case shards::Beam<2>::key:
    case shards::Beam<3>::key:
    case shards::ShellLine<2>::key:
    case shards::ShellLine<3>::key:
    case shards::ShellTriangle<3>::key:
    case shards::ShellTriangle<6>::key:
    case shards::ShellQuadrilateral<4>::key:
    case shards::ShellQuadrilateral<8>::key:
    case shards::ShellQuadrilateral<9>::key:
        TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument, 
                            ">>> ERROR (getIntrepidBasis): Cell topology not supported. ");
    break;
    default:
        TEUCHOS_TEST_FOR_EXCEPTION( (true), std::invalid_argument, 
                            ">>> ERROR (getIntrepidBasis): Cell topology not supported.");        
    }// switch  
  return HGRAD_Basis;  
}

int main(int argc, char *argv[]) {
 
  Teuchos::GlobalMPISession mpiSession(&argc, &argv);

  typedef CellTools<double>       CellTools;
  typedef shards::CellTopology    CellTopology;
  
  // This little trick lets us print to std::cout only if a (dummy) command-line argument is provided.
  int iprint     = argc - 1;
  
  Teuchos::RCP<std::ostream> outStream;
  Teuchos::oblackholestream bhs; // outputs nothing
  
  if (iprint > 0)
    outStream = Teuchos::rcp(&std::cout, false);
  else
    outStream = Teuchos::rcp(&bhs, false);
  
  // Save the format state of the original std::cout.
  Teuchos::oblackholestream oldFormatState;
  oldFormatState.copyfmt(std::cout);
  
  *outStream \
    << "===============================================================================\n" \
    << "|                                                                             |\n" \
    << "|                              Unit Test CellTools                            |\n" \
    << "|                                                                             |\n" \
    << "|     1) Edge parametrizations                                                |\n" \
    << "|     2) Face parametrizations                                                |\n" \
    << "|     3) Edge tangents                                                        |\n" \
    << "|     4) Face tangents and normals                                            |\n" \
    << "|                                                                             |\n" \
    << "|  Questions? Contact  Pavel Bochev (pbboche@sandia.gov)                      |\n" \
    << "|                      Denis Ridzal (dridzal@sandia.gov), or                  |\n" \
    << "|                      Kara Peterson (kjpeter@sandia.gov)                     |\n" \
    << "|                                                                             |\n" \
    << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
    << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
    << "|                                                                             |\n" \
    << "===============================================================================\n";
  
  int errorFlag  = 0;

    
  // Vertices of the parametrization domain for 1-subcells: standard 1-cube [-1,1]
  FieldContainer<double> cube_1(2, 1);
  cube_1(0,0) = -1.0; 
  cube_1(1,0) = 1.0;

  
  // Vertices of the parametrization domain for triangular faces: the standard 2-simplex
  FieldContainer<double> simplex_2(3, 2);
  simplex_2(0, 0) = 0.0;   simplex_2(0, 1) = 0.0;
  simplex_2(1, 0) = 1.0;   simplex_2(1, 1) = 0.0;
  simplex_2(2, 0) = 0.0;   simplex_2(2, 1) = 1.0;
  
  
  // Vertices of the parametrization domain for quadrilateral faces: the standard 2-cube
  FieldContainer<double> cube_2(4, 2);
  cube_2(0, 0) =  -1.0;    cube_2(0, 1) =  -1.0;
  cube_2(1, 0) =   1.0;    cube_2(1, 1) =  -1.0;
  cube_2(2, 0) =   1.0;    cube_2(2, 1) =   1.0;
  cube_2(3, 0) =  -1.0;    cube_2(3, 1) =   1.0;

  
  // Pull all available topologies from Shards
  std::vector<shards::CellTopology> allTopologies;
  shards::getTopologies(allTopologies);
  
  
  // Set to 1 for edge and 2 for face tests
  int subcDim;

  try{
    
    *outStream \
    << "\n"
    << "===============================================================================\n"\
    << "| Test 1: edge parametrizations:                                              |\n"\
    << "===============================================================================\n\n";
    
    subcDim      = 1;
        
    // Loop over the cell topologies
    for(int topoOrd = 0; topoOrd < (int)allTopologies.size(); topoOrd++){
            
      // Test only 2D and 3D topologies that have reference cells, e.g., exclude Line, Pentagon, etc.
      if(allTopologies[topoOrd].getDimension() > 1 && CellTools::hasReferenceCell(allTopologies[topoOrd]) ){
        *outStream << " Testing edge parametrization for " <<  allTopologies[topoOrd].getName() <<"\n";
        testSubcellParametrizations(errorFlag,
                                    allTopologies[topoOrd],
                                    cube_1,
                                    cube_1,
                                    subcDim,
                                    outStream);
      }
    }

    
    *outStream \
      << "\n"
      << "===============================================================================\n"\
      << "| Test 2: face parametrizations:                                              |\n"\
      << "===============================================================================\n\n";
    
    subcDim      = 2;
    
    // Loop over the cell topologies
    for(int topoOrd = 0; topoOrd < (int)allTopologies.size(); topoOrd++){
      
      // Test only 3D topologies that have reference cells
      if(allTopologies[topoOrd].getDimension() > 2 && CellTools::hasReferenceCell(allTopologies[topoOrd]) ){
        *outStream << " Testing face parametrization for cell topology " <<  allTopologies[topoOrd].getName() <<"\n";
        testSubcellParametrizations(errorFlag,
                                    allTopologies[topoOrd],
                                    simplex_2,
                                    cube_2,
                                    subcDim,
                                    outStream);
      }
    }
    
    
    /***********************************************************************************************
      *
      * Common for test 3 and 4: edge tangents and face normals for standard cells with base topo
      *
      **********************************************************************************************/
    
    // Allocate storage and extract all standard cells with base topologies
    std::vector<shards::CellTopology> standardBaseTopologies;    
    shards::getTopologies(standardBaseTopologies, 4, shards::STANDARD_CELL, shards::BASE_TOPOLOGY);

    // Define topologies for the edge and face parametrization domains. (faces are Tri or Quad)
    CellTopology paramEdge    (shards::getCellTopologyData<shards::Line<2> >() );
    CellTopology paramTriFace (shards::getCellTopologyData<shards::Triangle<3> >() );
    CellTopology paramQuadFace(shards::getCellTopologyData<shards::Quadrilateral<4> >() );
    
    // Define CubatureFactory:
    DefaultCubatureFactory<double>  cubFactory;   
    
    *outStream \
      << "\n"
      << "===============================================================================\n"\
      << "| Test 3: edge tangents/normals for stand. cells with base topologies:        |\n"\
      << "===============================================================================\n\n";
    // This test loops over standard cells with base topologies, creates a set of nodes and tests tangents/normals 
    std::vector<shards::CellTopology>::iterator cti;
    
    // Define cubature on the edge parametrization domain:
    Teuchos::RCP<Cubature<double> > edgeCubature = cubFactory.create(paramEdge, 6); 
    int cubDim       = edgeCubature -> getDimension();
    int numCubPoints = edgeCubature -> getNumPoints();

    // Allocate storage for cubature points and weights on edge parameter domain and fill with points:
    FieldContainer<double> paramEdgePoints(numCubPoints, cubDim);
    FieldContainer<double> paramEdgeWeights(numCubPoints);
    edgeCubature -> getCubature(paramEdgePoints, paramEdgeWeights);
    
    // Loop over admissible topologies 
    for(cti = standardBaseTopologies.begin(); cti !=standardBaseTopologies.end(); ++cti){
      
      // Exclude 0D (node), 1D (Line) and Pyramid<5> cells
      if( ( (*cti).getDimension() >= 2) && ( (*cti).getKey() != shards::Pyramid<5>::key) ){ 
    
        int cellDim = (*cti).getDimension();
        int vCount  = (*cti).getVertexCount();
        FieldContainer<double> refCellVertices(vCount, cellDim);
        CellTools::getReferenceSubcellVertices(refCellVertices, cellDim, 0, (*cti) );
        
        *outStream << " Testing edge tangents";
          if(cellDim == 2) { *outStream << " and normals"; }          
        *outStream <<" for cell topology " <<  (*cti).getName() <<"\n";
        
        
        // Array for physical cell vertices ( must have rank 3 for setJacobians)
        FieldContainer<double> physCellVertices(1, vCount, cellDim);

        // Randomize reference cell vertices by moving them up to +/- (1/8) units along their
        // coordinate axis. Guaranteed to be non-degenerate for standard cells with base topology 
        for(int v = 0; v < vCount; v++){
          for(int d = 0; d < cellDim; d++){
            double delta = Teuchos::ScalarTraits<double>::random()/8.0;
            physCellVertices(0, v, d) = refCellVertices(v, d) + delta;
          } //for d
        }// for v     
        
        // Allocate storage for cub. points on a ref. edge; Jacobians, phys. edge tangents/normals
        FieldContainer<double> refEdgePoints(numCubPoints, cellDim);        
        FieldContainer<double> edgePointsJacobians(1, numCubPoints, cellDim, cellDim);
        FieldContainer<double> edgePointTangents(1, numCubPoints, cellDim);
        FieldContainer<double> edgePointNormals(1, numCubPoints, cellDim);        

        // Loop over edges:
        for(int edgeOrd = 0; edgeOrd < (int)(*cti).getEdgeCount(); edgeOrd++){
          /* 
           * Compute tangents on the specified physical edge using CellTools:
           *    1. Map points from edge parametrization domain to ref. edge with specified ordinal
           *    2. Compute parent cell Jacobians at ref. edge points
           *    3. Compute physical edge tangents
           */
          CellTools::mapToReferenceSubcell(refEdgePoints, paramEdgePoints, 1, edgeOrd, (*cti) );
          CellTools::setJacobian(edgePointsJacobians, refEdgePoints, physCellVertices, getIntrepidBasis(*cti) );
          CellTools::getPhysicalEdgeTangents(edgePointTangents, edgePointsJacobians, edgeOrd, (*cti)); 
          /*
           * Compute tangents directly using parametrization of phys. edge and compare with CellTools tangents.
           *    1. Get edge vertices
           *    2. For affine edges tangent coordinates are given by F'(t) = (V1-V0)/2
           *       (for now we only test affine edges, but later we will test edges for cells 
           *        with extended topologies.)
           */
          int v0ord = (*cti).getNodeMap(1, edgeOrd, 0);
          int v1ord = (*cti).getNodeMap(1, edgeOrd, 1);
          
          for(int pt = 0; pt < numCubPoints; pt++){

            // Temp storage for directly computed edge tangents
            FieldContainer<double> edgeBenchmarkTangents(3);
            
            for(int d = 0; d < cellDim; d++){
              edgeBenchmarkTangents(d) = (physCellVertices(0, v1ord, d) - physCellVertices(0, v0ord, d))/2.0;
              
              // Compare with d-component of edge tangent by CellTools
              if( abs(edgeBenchmarkTangents(d) - edgePointTangents(0, pt, d)) > INTREPID_THRESHOLD ){
                errorFlag++;
                *outStream
                  << std::setw(70) << "^^^^----FAILURE!" << "\n"
                  << " Edge tangent computation by CellTools failed for: \n"
                  << "       Cell Topology = " << (*cti).getName() << "\n"
                  << "        Edge ordinal = " << edgeOrd << "\n"
                  << "   Edge point number = " << pt << "\n"
                  << "  Tangent coordinate = " << d << "\n"
                  << "     CellTools value = " <<  edgePointTangents(0, pt, d) << "\n"
                  << "     Benchmark value = " <<  edgeBenchmarkTangents(d) << "\n\n";
              }
            } // for d
            
            // Test side normals for 2D cells only: edge normal has coordinates (t1, -t0)
            if(cellDim == 2) {
              CellTools::getPhysicalSideNormals(edgePointNormals, edgePointsJacobians, edgeOrd, (*cti));
              if( abs(edgeBenchmarkTangents(1) - edgePointNormals(0, pt, 0)) > INTREPID_THRESHOLD ){
                errorFlag++;
                *outStream
                  << std::setw(70) << "^^^^----FAILURE!" << "\n"
                  << " Edge Normal computation by CellTools failed for: \n"
                  << "       Cell Topology = " << (*cti).getName() << "\n"
                  << "        Edge ordinal = " << edgeOrd << "\n"
                  << "   Edge point number = " << pt << "\n"
                  << "   Normal coordinate = " << 0 << "\n"
                  << "     CellTools value = " <<  edgePointNormals(0, pt, 0) << "\n"
                  << "     Benchmark value = " <<  edgeBenchmarkTangents(1) << "\n\n";
              }
              if( abs(edgeBenchmarkTangents(0) + edgePointNormals(0, pt, 1)) > INTREPID_THRESHOLD ){
                errorFlag++;
                *outStream
                  << std::setw(70) << "^^^^----FAILURE!" << "\n"
                  << " Edge Normal computation by CellTools failed for: \n"
                  << "       Cell Topology = " << (*cti).getName() << "\n"
                  << "        Edge ordinal = " << edgeOrd << "\n"
                  << "   Edge point number = " << pt << "\n"
                  << "   Normal coordinate = " << 1  << "\n"
                  << "     CellTools value = " <<  edgePointNormals(0, pt, 1) << "\n"
                  << "     Benchmark value = " << -edgeBenchmarkTangents(0) << "\n\n";
              }
            } // edge normals            
          } // for pt
        }// for edgeOrd
      }// if admissible cell
    }// for cti
    
    
    
    *outStream \
      << "\n"
      << "===============================================================================\n"\
      << "| Test 4: face/side normals for stand. 3D cells with base topologies:         |                                                      |\n"\
      << "===============================================================================\n\n";
    // This test loops over standard 3D cells with base topologies, creates a set of nodes and tests normals 

    // Define cubature on the edge parametrization domain:
    Teuchos::RCP<Cubature<double> > triFaceCubature  = cubFactory.create(paramTriFace, 6); 
    Teuchos::RCP<Cubature<double> > quadFaceCubature = cubFactory.create(paramQuadFace, 6); 
    
    int faceCubDim           = triFaceCubature -> getDimension();
    int numTriFaceCubPoints  = triFaceCubature -> getNumPoints();
    int numQuadFaceCubPoints = quadFaceCubature -> getNumPoints();    
        
    // Allocate storage for cubature points and weights on face parameter domain and fill with points:
    FieldContainer<double> paramTriFacePoints(numTriFaceCubPoints, faceCubDim);
    FieldContainer<double> paramTriFaceWeights(numTriFaceCubPoints);
    FieldContainer<double> paramQuadFacePoints(numQuadFaceCubPoints, faceCubDim);
    FieldContainer<double> paramQuadFaceWeights(numQuadFaceCubPoints);
    
    triFaceCubature -> getCubature(paramTriFacePoints, paramTriFaceWeights);
    quadFaceCubature -> getCubature(paramQuadFacePoints, paramQuadFaceWeights);
    
    // Loop over admissible topologies 
    for(cti = standardBaseTopologies.begin(); cti !=standardBaseTopologies.end(); ++cti){
      
      // Exclude 2D and Pyramid<5> cells
      if( ( (*cti).getDimension() == 3) && ( (*cti).getKey() != shards::Pyramid<5>::key) ){ 
        
        int cellDim = (*cti).getDimension();
        int vCount  = (*cti).getVertexCount();
        FieldContainer<double> refCellVertices(vCount, cellDim);
        CellTools::getReferenceSubcellVertices(refCellVertices, cellDim, 0, (*cti) );
        
        *outStream << " Testing face/side normals for cell topology " <<  (*cti).getName() <<"\n";
        
        // Array for physical cell vertices ( must have rank 3 for setJacobians)
        FieldContainer<double> physCellVertices(1, vCount, cellDim);
        
        // Randomize reference cell vertices by moving them up to +/- (1/8) units along their
        // coordinate axis. Guaranteed to be non-degenerate for standard cells with base topology 
        for(int v = 0; v < vCount; v++){
          for(int d = 0; d < cellDim; d++){
            double delta = Teuchos::ScalarTraits<double>::random()/8.0;
            physCellVertices(0, v, d) = refCellVertices(v, d) + delta;
          } //for d
        }// for v     
        
        // Allocate storage for cub. points on a ref. face; Jacobians, phys. face normals and 
        // benchmark normals.
        FieldContainer<double> refTriFacePoints(numTriFaceCubPoints, cellDim);        
        FieldContainer<double> refQuadFacePoints(numQuadFaceCubPoints, cellDim);        
        FieldContainer<double> triFacePointsJacobians(1, numTriFaceCubPoints, cellDim, cellDim);
        FieldContainer<double> quadFacePointsJacobians(1, numQuadFaceCubPoints, cellDim, cellDim);
        FieldContainer<double> triFacePointNormals(1, numTriFaceCubPoints, cellDim);
        FieldContainer<double> triSidePointNormals(1, numTriFaceCubPoints, cellDim);
        FieldContainer<double> quadFacePointNormals(1, numQuadFaceCubPoints, cellDim);
        FieldContainer<double> quadSidePointNormals(1, numQuadFaceCubPoints, cellDim);
        
        
        // Loop over faces:
        for(int faceOrd = 0; faceOrd < (int)(*cti).getSideCount(); faceOrd++){
          
          // This test presently includes only Triangle<3> and Quadrilateral<4> faces. Once we support
          // cells with extended topologies we will add their faces as well.
          switch( (*cti).getCellTopologyData(2, faceOrd) -> key ) {
        
            case shards::Triangle<3>::key: 
              {
                // Compute face normals using CellTools
                CellTools::mapToReferenceSubcell(refTriFacePoints, paramTriFacePoints, 2, faceOrd, (*cti) );
                CellTools::setJacobian(triFacePointsJacobians, refTriFacePoints, physCellVertices, getIntrepidBasis(*cti) );
                CellTools::getPhysicalFaceNormals(triFacePointNormals, triFacePointsJacobians, faceOrd, (*cti));               
                CellTools::getPhysicalSideNormals(triSidePointNormals, triFacePointsJacobians, faceOrd, (*cti));               
                /* 
                 * Compute face normals using direct linear parametrization of the face: the map from
                 * standard 2-simplex to physical Triangle<3> face in 3D is 
                 * F(x,y) = V0 + (V1-V0)x + (V2-V0)*y 
                 * Face normal is vector product Tx X Ty where Tx = (V1-V0); Ty = (V2-V0)
                 */
                int v0ord = (*cti).getNodeMap(2, faceOrd, 0);
                int v1ord = (*cti).getNodeMap(2, faceOrd, 1);
                int v2ord = (*cti).getNodeMap(2, faceOrd, 2);
                
                // Loop over face points: redundant for affine faces, but CellTools gives one vector 
                // per point so need to check all points anyways.
                for(int pt = 0; pt < numTriFaceCubPoints; pt++){
                  FieldContainer<double> tanX(3), tanY(3), faceNormal(3);
                  for(int d = 0; d < cellDim; d++){
                    tanX(d) = (physCellVertices(0, v1ord, d) - physCellVertices(0, v0ord, d));
                    tanY(d) = (physCellVertices(0, v2ord, d) - physCellVertices(0, v0ord, d));
                  }// for d
                  
                  RealSpaceTools<double>::vecprod(faceNormal, tanX, tanY); 
                  
                  // Compare direct normal with d-component of the face/side normal by CellTools
                  for(int d = 0; d < cellDim; d++){
                    
                    // face normal method
                    if( abs(faceNormal(d) - triFacePointNormals(0, pt, d)) > INTREPID_THRESHOLD ){
                      errorFlag++;
                      *outStream
                        << std::setw(70) << "^^^^----FAILURE!" << "\n"
                        << " Face normal computation by CellTools failed for: \n"
                        << "       Cell Topology = " << (*cti).getName() << "\n"
                        << "       Face Topology = " << (*cti).getCellTopologyData(2, faceOrd) -> name << "\n"
                        << "        Face ordinal = " << faceOrd << "\n"
                        << "   Face point number = " << pt << "\n"
                        << "   Normal coordinate = " << d  << "\n"
                        << "     CellTools value = " <<  triFacePointNormals(0, pt, d)
                        << "     Benchmark value = " <<  faceNormal(d) << "\n\n";
                    }
                    //side normal method
                    if( abs(faceNormal(d) - triSidePointNormals(0, pt, d)) > INTREPID_THRESHOLD ){
                      errorFlag++;
                      *outStream
                        << std::setw(70) << "^^^^----FAILURE!" << "\n"
                        << " Side normal computation by CellTools failed for: \n"
                        << "       Cell Topology = " << (*cti).getName() << "\n"
                        << "       Side Topology = " << (*cti).getCellTopologyData(2, faceOrd) -> name << "\n"
                        << "        Side ordinal = " << faceOrd << "\n"
                        << "   Side point number = " << pt << "\n"
                        << "   Normal coordinate = " << d  << "\n"
                        << "     CellTools value = " <<  triSidePointNormals(0, pt, d)
                        << "     Benchmark value = " <<  faceNormal(d) << "\n\n";
                    }
                  } // for d
                } // for pt
              }
              break;
              
            case shards::Quadrilateral<4>::key:
              {
                // Compute face normals using CellTools
                CellTools::mapToReferenceSubcell(refQuadFacePoints, paramQuadFacePoints, 2, faceOrd, (*cti) );
                CellTools::setJacobian(quadFacePointsJacobians, refQuadFacePoints, physCellVertices, getIntrepidBasis(*cti) );
                CellTools::getPhysicalFaceNormals(quadFacePointNormals, quadFacePointsJacobians, faceOrd, (*cti));               
                CellTools::getPhysicalSideNormals(quadSidePointNormals, quadFacePointsJacobians, faceOrd, (*cti)); 
                /*
                 * Compute face normals using direct bilinear parametrization of the face: the map from
                 * [-1,1]^2 to physical Quadrilateral<4> face in 3D is 
                 * F(x,y) = ((V0+V1+V2+V3) + (-V0+V1+V2-V3)*X + (-V0-V1+V2+V3)*Y + (V0-V1+V2-V3)*X*Y)/4 
                 * Face normal is vector product Tx X Ty where
                 *          Tx = ((-V0+V1+V2-V3) + (V0-V1+V2-V3)*Y)/4
                 *          Ty = ((-V0-V1+V2+V3) + (V0-V1+V2-V3)*X)/4
                 */
                int v0ord = (*cti).getNodeMap(2, faceOrd, 0);
                int v1ord = (*cti).getNodeMap(2, faceOrd, 1);
                int v2ord = (*cti).getNodeMap(2, faceOrd, 2);
                int v3ord = (*cti).getNodeMap(2, faceOrd, 3);
                
                // Loop over face points (redundant for affine faces, but needed for later when we handle non-affine ones)
                for(int pt = 0; pt < numTriFaceCubPoints; pt++){
                  FieldContainer<double> tanX(3), tanY(3), faceNormal(3);
                  for(int d = 0; d < cellDim; d++){
                    tanX(d) = (physCellVertices(0, v0ord, d)*(-1.0 + paramQuadFacePoints(pt,1) )  +
                               physCellVertices(0, v1ord, d)*( 1.0 - paramQuadFacePoints(pt,1) ) + 
                               physCellVertices(0, v2ord, d)*( 1.0 + paramQuadFacePoints(pt,1) ) + 
                               physCellVertices(0, v3ord, d)*(-1.0 - paramQuadFacePoints(pt,1) ) )/4.0;
                    
                    tanY(d) = (physCellVertices(0, v0ord, d)*(-1.0 + paramQuadFacePoints(pt,0) ) +
                               physCellVertices(0, v1ord, d)*(-1.0 - paramQuadFacePoints(pt,0) ) + 
                               physCellVertices(0, v2ord, d)*( 1.0 + paramQuadFacePoints(pt,0) ) + 
                               physCellVertices(0, v3ord, d)*( 1.0 - paramQuadFacePoints(pt,0) ) )/4.0;
                  }// for d
                  
                  RealSpaceTools<double>::vecprod(faceNormal, tanX, tanY); 
                  // Compare direct normal with d-component of the face/side normal by CellTools
                  for(int d = 0; d < cellDim; d++){
                    
                    // face normal method
                    if( abs(faceNormal(d) - quadFacePointNormals(0, pt, d)) > INTREPID_THRESHOLD ){
                      errorFlag++;
                      *outStream
                        << std::setw(70) << "^^^^----FAILURE!" << "\n"
                        << " Face normal computation by CellTools failed for: \n"
                        << "       Cell Topology = " << (*cti).getName() << "\n"
                        << "       Face Topology = " << (*cti).getCellTopologyData(2, faceOrd) -> name << "\n"
                        << "        Face ordinal = " << faceOrd << "\n"
                        << "   Face point number = " << pt << "\n"
                        << "   Normal coordinate = " << d  << "\n"
                        << "     CellTools value = " <<  quadFacePointNormals(0, pt, d)
                        << "     Benchmark value = " <<  faceNormal(d) << "\n\n";
                    }
                    //side normal method
                    if( abs(faceNormal(d) - quadSidePointNormals(0, pt, d)) > INTREPID_THRESHOLD ){
                      errorFlag++;
                      *outStream
                        << std::setw(70) << "^^^^----FAILURE!" << "\n"
                        << " Side normal computation by CellTools failed for: \n"
                        << "       Cell Topology = " << (*cti).getName() << "\n"
                        << "       Side Topology = " << (*cti).getCellTopologyData(2, faceOrd) -> name << "\n"
                        << "        Side ordinal = " << faceOrd << "\n"
                        << "   Side point number = " << pt << "\n"
                        << "   Normal coordinate = " << d  << "\n"
                        << "     CellTools value = " <<  quadSidePointNormals(0, pt, d)
                        << "     Benchmark value = " <<  faceNormal(d) << "\n\n";
                    }
                  } // for d
                }// for pt
              }// case Quad
              break;
            default:
              errorFlag++;
              *outStream << " Face normals test failure: face topology not supported \n\n";
          } // switch 
        }// for faceOrd
      }// if admissible
      }// for cti
  }// try
  
  //============================================================================================//
  // Wrap up test: check if the test broke down unexpectedly due to an exception                //
  //============================================================================================//
  catch (const std::logic_error & err) {
    *outStream << err.what() << "\n";
    errorFlag = -1000;
  };
  
  
  if (errorFlag != 0)
    std::cout << "End Result: TEST FAILED\n";
  else
    std::cout << "End Result: TEST PASSED\n";
  
  // reset format state of std::cout
  std::cout.copyfmt(oldFormatState);
  
  return errorFlag;
}



void testSubcellParametrizations(int&                               errorFlag,
                                 const shards::CellTopology&        parentCell,
                                 const FieldContainer<double>&      subcParamVert_A,
                                 const FieldContainer<double>&      subcParamVert_B,
                                 const int                          subcDim,
                                 const Teuchos::RCP<std::ostream>&  outStream){
  
  // Get cell dimension and subcell count
  int cellDim      = parentCell.getDimension();
  int subcCount    = parentCell.getSubcellCount(subcDim);
  
  
  // Loop over subcells of the specified dimension
  for(int subcOrd = 0; subcOrd < subcCount; subcOrd++){
    int subcVertexCount = parentCell.getVertexCount(subcDim, subcOrd);
    
    
    // Storage for correct reference subcell vertices and for the images of the parametrization domain points
    FieldContainer<double> refSubcellVertices(subcVertexCount, cellDim);
    FieldContainer<double> mappedParamVertices(subcVertexCount, cellDim);
    
    
    // Retrieve correct reference subcell vertices
    CellTools<double>::getReferenceSubcellVertices(refSubcellVertices, subcDim, subcOrd, parentCell);
    
    
    // Map vertices of the parametrization domain to 1 or 2-subcell with ordinal subcOrd
    // For edges parametrization domain is always 1-cube passed as "subcParamVert_A"
    if(subcDim == 1) {
      CellTools<double>::mapToReferenceSubcell(mappedParamVertices,
                                               subcParamVert_A,
                                               subcDim,
                                               subcOrd,
                                               parentCell);
    }
    // For faces need to treat Triangle and Quadrilateral faces separately
    else if(subcDim == 2) {
      
      // domain "subcParamVert_A" is the standard 2-simplex  
      if(subcVertexCount == 3){
        CellTools<double>::mapToReferenceSubcell(mappedParamVertices,
                                                 subcParamVert_A,
                                                 subcDim,
                                                 subcOrd,
                                                 parentCell);
      }
      // Domain "subcParamVert_B" is the standard 2-cube
      else if(subcVertexCount == 4){
        CellTools<double>::mapToReferenceSubcell(mappedParamVertices,
                                                 subcParamVert_B,
                                                 subcDim,
                                                 subcOrd,
                                                 parentCell);
      }
    }
    
    // Compare the images of the parametrization domain vertices with the true vertices.
    for(int subcVertOrd = 0; subcVertOrd < subcVertexCount; subcVertOrd++){
      for(int dim = 0; dim <  cellDim; dim++){
        
        if(mappedParamVertices(subcVertOrd, dim) != refSubcellVertices(subcVertOrd, dim) ) {
          errorFlag++; 
          *outStream 
            << std::setw(70) << "^^^^----FAILURE!" << "\n"
            << " Cell Topology = " << parentCell.getName() << "\n"
            << " Parametrization of subcell " << subcOrd << " which is "
            << parentCell.getName(subcDim,subcOrd) << " failed for vertex " << subcVertOrd << ":\n"
            << " parametrization map fails to map correctly coordinate " << dim << " of that vertex\n\n";
          
        }//if
      }// for dim 
    }// for subcVertOrd      
  }// for subcOrd
  
}