//---------------------------------------------------------------------------//
// Get the parameteric center of an entity.
void MoabEntityLocalMap::parametricCenter(
    const Entity& entity,
    Teuchos::Array<double>& center ) const
{
    moab::EntityType moab_type = d_moab_mesh->get_moab()->type_from_handle(
	MoabHelpers::extractEntity(entity) );

    switch( moab_type )
    {
	case moab::MBTRI:
	    center.assign( 2, 1.0 / 3.0 );
	    break;
	case moab::MBQUAD:
	    center.assign( 2, 0.0 );
	    break;
	case moab::MBTET:
	    center.assign( 3, 1.0 / 6.0 );
	    break;
	case moab::MBHEX:
	    center.assign( 3, 0.0 );
	    break;
	default:
	    center.resize( 0 );
	    break;
    }
}
//---------------------------------------------------------------------------//
// Given an entity, get the ids of its support locations
void LibmeshNodalShapeFunction::entitySupportIds( 
    const DataTransferKit::Entity& entity,
    Teuchos::Array<DataTransferKit::SupportId>& support_ids ) const
{
    // Node case.
    if ( 0 == entity.topologicalDimension() )
    {
	DTK_CHECK( extractGeom<libMesh::Node>(entity)->valid_id() );
	support_ids.assign( 1, extractGeom<libMesh::Node>(entity)->id() );
    }

    // Element case.
    else
    {
	Teuchos::Ptr<libMesh::Elem> elem = extractGeom<libMesh::Elem>(entity);
	int num_nodes = elem->n_nodes();
	support_ids.resize( num_nodes );
	for ( int n = 0; n < num_nodes; ++n )
	{
	    DTK_CHECK( elem->get_node(n)->valid_id() );
	    support_ids[n] = elem->get_node(n)->id();
	}
    }
}
示例#3
0
int main(int argc, char *argv[]) {

  Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
  // 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 (CubatureDirect,CubatureTensor,DefaultCubatureFactory)       |\n" \
  << "|                                                                             |\n" \
  << "|     1) Computing integrals of monomials on reference cells in 3D            |\n" \
  << "|                         - using Level 2 BLAS -                              |\n" \
  << "|                                                                             |\n" \
  << "|  Questions? Contact  Pavel Bochev ([email protected]) or                   |\n" \
  << "|                      Denis Ridzal ([email protected]).                     |\n" \
  << "|                                                                             |\n" \
  << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
  << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
  << "|                                                                             |\n" \
  << "===============================================================================\n"\
  << "| TEST 1: integrals of monomials in 3D (Level 2 BLAS version)                 |\n"\
  << "===============================================================================\n";

  // internal variables:
  int                                      errorFlag = 0;
  int                                      polyCt = 0;
  int                                      offset = 0;
  Teuchos::Array< Teuchos::Array<double> > testInt;
  Teuchos::Array< Teuchos::Array<double> > analyticInt;
  Teuchos::Array<double>                   tmparray(1);
  double                                   reltol = 1.0e+04 * INTREPID_TOL;
  int                                      maxDeg[4];
  int                                      maxOffset[4];
  int                                      numPoly[4];
  int                                      numAnalytic[4];
  // max polynomial degree tested, per cell type:
  maxDeg[0]                              = INTREPID2_CUBATURE_TET_DEFAULT_MAX;
  maxDeg[1]                              = 20; // can be as large as INTREPID2_CUBATURE_LINE_GAUSS_MAX, but runtime is excessive
  maxDeg[2]                              = std::min(INTREPID2_CUBATURE_LINE_GAUSS_MAX, INTREPID2_CUBATURE_TRI_DEFAULT_MAX);
  maxDeg[3]                              = std::min(INTREPID2_CUBATURE_LINE_GAUSS_MAX, INTREPID2_CUBATURE_LINE_GAUSSJACOBI20_MAX);
  // max polynomial degree recorded in analytic comparison files, per cell type:
  maxOffset[0]                           = INTREPID2_CUBATURE_TET_DEFAULT_MAX;
  maxOffset[1]                           = INTREPID2_CUBATURE_LINE_GAUSS_MAX;
  maxOffset[2]                           = std::min(INTREPID2_CUBATURE_LINE_GAUSS_MAX, INTREPID2_CUBATURE_TRI_DEFAULT_MAX);
  maxOffset[3]                           = std::min(INTREPID2_CUBATURE_LINE_GAUSS_MAX, INTREPID2_CUBATURE_LINE_GAUSSJACOBI20_MAX);
  for (int i=0; i<4; i++) {
    numPoly[i] = (maxDeg[i]+1)*(maxDeg[i]+2)*(maxDeg[i]+3)/6;
  }
  for (int i=0; i<4; i++) {
    numAnalytic[i] = (maxOffset[i]+1)*(maxOffset[i]+2)*(maxOffset[i]+3)/6;
  }


  // get names of files with analytic values
  std::string basedir = "./data";
  std::stringstream namestream[4];
  std::string filename[4];
  namestream[0] << basedir << "/TET_integrals" << ".dat";
  namestream[0] >> filename[0];
  namestream[1] << basedir << "/HEX_integrals" << ".dat";
  namestream[1] >> filename[1];
  namestream[2] << basedir << "/TRIPRISM_integrals" << ".dat";
  namestream[2] >> filename[2];
  namestream[3] << basedir << "/PYR_integrals" << ".dat";
  namestream[3] >> filename[3];

  // reference cells tested
  shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Tetrahedron<> >(),
                                     shards::getCellTopologyData< shards::Hexahedron<> >(),
                                     shards::getCellTopologyData< shards::Wedge<> >(),
                                     shards::getCellTopologyData< shards::Pyramid<> >() };
  // format of data files with analytic values
  TypeOfExactData dataFormat[] = {INTREPID2_UTILS_SCALAR, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION, INTREPID_UTILS_FRACTION};

  // compute and compare integrals
  try {
    for (int cellCt=0; cellCt < 4; cellCt++) {
      testInt.assign(numPoly[cellCt], tmparray);
      analyticInt.assign(numAnalytic[cellCt], tmparray);

      *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseCellTopologyData()->name << ":\n";
      std::ifstream filecompare(&filename[cellCt][0]);
      // compute integrals
      for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
        int numMonomials = (cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6; 
        testInt[cubDeg].resize(numMonomials);
        computeIntegral(testInt[cubDeg], cellType[cellCt], cubDeg);
      }
      // get analytic values
      if (filecompare.is_open()) {
        getAnalytic(analyticInt, filecompare, dataFormat[cellCt]);
        // close file
        filecompare.close();
      }
      // perform comparison
      for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
        polyCt = 0;
        offset = 0;
        int oldErrorFlag = errorFlag;
        for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
          for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
            for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
              double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
              double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
              if (absdiff > abstol) {
                *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
                           << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg
                           << " * z^" << std::setw(2) << zDeg << ":" << "   "
                           << std::scientific << std::setprecision(16)
                           << testInt[cubDeg][polyCt] << "   " << analyticInt[polyCt+offset][0] << "   "
                           << std::setprecision(4) << absdiff << "   " << "<?" << "   " << abstol << "\n";
                errorFlag++;
                *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n";
              }
              polyCt++;
            }
            offset = offset + maxOffset[cellCt] - cubDeg;
          }
          offset = offset + (maxOffset[cellCt] - cubDeg)*(maxOffset[cellCt] - cubDeg + 1)/2;
        }
        *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg;
        if (errorFlag == oldErrorFlag)
         *outStream << " passed.\n";
        else
         *outStream << " failed.\n";
      }
      *outStream << "\n";
    }  // end for cellCt
  }
  catch (std::logic_error err) {
    *outStream << err.what() << "\n";
    errorFlag = -1;
  };


  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);
Kokkos::finalize();
  return errorFlag;
}
示例#4
0
int main(int argc, char *argv[]) {

  Teuchos::GlobalMPISession mpiSession(&argc, &argv);
Kokkos::initialize();
  // 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 (CubatureGenSparse)                          |\n" \
  << "|                                                                             |\n" \
  << "|     1) Computing integrals of monomials on reference cells in 3D            |\n" \
  << "|                         - using Level 2 BLAS -                              |\n" \
  << "|                                                                             |\n" \
  << "|  Questions? Contact  Pavel Bochev ([email protected]),                     |\n" \
  << "|                      Denis Ridzal ([email protected]) or                   |\n" \
  << "|                      Matthew Keegan ([email protected]).                   |\n" \
  << "|                                                                             |\n" \
  << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
  << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
  << "|                                                                             |\n" \
  << "===============================================================================\n"\
  << "| TEST 1: integrals of monomials in 3D (Level 2 BLAS version) using           |\n"\
  << "|           Generalized Sparse Grid Construction                              |\n"\
  << "===============================================================================\n";

  // internal variables:
  int                                      errorFlag = 0;
  int                                      polyCt = 0;
  int                                      offset = 0;
  Teuchos::Array< Teuchos::Array<double> > testInt;
  Teuchos::Array< Teuchos::Array<double> > analyticInt;
  Teuchos::Array<double>                   tmparray(1);
  double                                   reltol = 1.0e+04 * INTREPID_TOL;
  int maxDeg                             = 20; // can be as large as INTREPID2_CUBATURE_SPARSE3D_GAUSS_MAX, but runtime is excessive
  int maxOffset                          = INTREPID2_CUBATURE_LINE_GAUSS_MAX;
  int numPoly                            = (maxDeg+1)*(maxDeg+2)*(maxDeg+3)/6;
  int numAnalytic                        = (maxOffset+1)*(maxOffset+2)*(maxOffset+3)/6;
  testInt.assign(numPoly, tmparray);
  analyticInt.assign(numAnalytic, tmparray);

  // get names of files with analytic values
  std::string basedir = "./data";
  std::stringstream namestream;
  std::string filename;
  namestream << basedir << "/HEX_integrals" << ".dat";
  namestream >> filename;

  // format of data files with analytic values
  TypeOfExactData dataFormat = INTREPID_UTILS_FRACTION;

  // compute and compare integrals
  try {
      *outStream << "\nIntegrals of monomials:\n";
      std::ifstream filecompare(&filename[0]);
      // compute integrals
      for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
        int numMonomials = (cubDeg+1)*(cubDeg+2)*(cubDeg+3)/6; 
        testInt[cubDeg].resize(numMonomials);
        computeIntegral(testInt[cubDeg], cubDeg);
      }
      // get analytic values
      if (filecompare.is_open()) {
        getAnalytic(analyticInt, filecompare, dataFormat);
        // close file
        filecompare.close();
      }
      // perform comparison
      for (int cubDeg=0; cubDeg <= maxDeg; cubDeg++) {
        polyCt = 0;
        offset = 0;
        int oldErrorFlag = errorFlag;
        for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
          for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
            for (int zDeg=0; zDeg <= cubDeg-xDeg-yDeg; zDeg++) {
              double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
              double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
              if (absdiff > abstol) {
                *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
                           << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg
                           << " * z^" << std::setw(2) << zDeg << ":" << "   "
                           << std::scientific << std::setprecision(16)
                           << testInt[cubDeg][polyCt] << "   " << analyticInt[polyCt+offset][0] << "   "
                           << std::setprecision(4) << absdiff << "   " << "<?" << "   " << abstol << "\n";
                errorFlag++;
                *outStream << std::right << std::setw(118) << "^^^^---FAILURE!\n";
              }
              polyCt++;
            }
            offset = offset + maxOffset - cubDeg;
          }
          offset = offset + (maxOffset - cubDeg)*(maxOffset - cubDeg + 1)/2;
        }
        *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg;
        if (errorFlag == oldErrorFlag)
         *outStream << " passed.\n";
        else
         *outStream << " failed.\n";
      }
      *outStream << "\n";
  }
  catch (std::logic_error err) {
    *outStream << err.what() << "\n";
    errorFlag = -1;
  };


  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);
Kokkos::finalize();
  return errorFlag;
}
示例#5
0
int main(int argc, char *argv[]) {
  
  Teuchos::GlobalMPISession mpiSession(&argc, &argv);

  // 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 (CubaturePolylib)                         |\n" \
  << "|                                                                             |\n" \
  << "|     1) Computing integrals of monomials on reference cells in 1D            |\n" \
  << "|                                                                             |\n" \
  << "|  Questions? Contact  Pavel Bochev ([email protected]) or                   |\n" \
  << "|                      Denis Ridzal ([email protected]).                     |\n" \
  << "|                                                                             |\n" \
  << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
  << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
  << "|                                                                             |\n" \
  << "===============================================================================\n"\
  << "| TEST 1: integrals of monomials in 1D                                        |\n"\
  << "===============================================================================\n";

  // internal variables:
  int                                      errorFlag = 0;
  Teuchos::Array< Teuchos::Array<double> > testInt;
  Teuchos::Array< Teuchos::Array<double> > analyticInt;
  Teuchos::Array<double>                   tmparray(1);
  double                                   reltol = 1.0e+03 * INTREPID_TOL;
  testInt.assign(INTREPID_CUBATURE_LINE_MAX+1, tmparray);
  analyticInt.assign(INTREPID_CUBATURE_LINE_MAX+1, tmparray);

  // open file with analytic values
  std::string basedir = "./data";
  std::stringstream namestream;
  std::string filename;
  namestream <<  basedir << "/EDGE_integrals" << ".dat";
  namestream >> filename;
  std::ifstream filecompare(&filename[0]);

  *outStream << "\nIntegrals of monomials on a reference line (edge):\n";

  // compute and compare integrals
  try {
    for (EIntrepidPLPoly poly_type=PL_GAUSS; poly_type <= PL_GAUSS_LOBATTO; poly_type++) {
      // compute integrals
      for (int cubDeg=0; cubDeg <= INTREPID_CUBATURE_LINE_MAX; cubDeg++) {
        testInt[cubDeg].resize(cubDeg+1);
        for (int polyDeg=0; polyDeg <= cubDeg; polyDeg++) {
          testInt[cubDeg][polyDeg] = computeIntegral(cubDeg, polyDeg, poly_type);
        }
      }
      // get analytic values
      if (filecompare.is_open()) {
        getAnalytic(analyticInt, filecompare);
        // close file
        filecompare.close();
      }
      // perform comparison
      for (int cubDeg=0; cubDeg <= INTREPID_CUBATURE_LINE_MAX; cubDeg++) {
        for (int polyDeg=0; polyDeg <= cubDeg; polyDeg++) {
          double abstol = ( analyticInt[polyDeg][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyDeg][0]) );
          double absdiff = std::fabs(analyticInt[polyDeg][0] - testInt[cubDeg][polyDeg]);
          *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
                     << "x^" << std::setw(2) << std::left << polyDeg <<  ":" << "   "
                     << std::scientific << std::setprecision(16) << testInt[cubDeg][polyDeg] << "   " << analyticInt[polyDeg][0] << "   "
                     << std::setprecision(4) << absdiff << "   " << "<?" << "   " << abstol << "\n";
          if (absdiff > abstol) {
            errorFlag++;
            *outStream << std::right << std::setw(104) << "^^^^---FAILURE!\n";
          }
        }
        *outStream << "\n";
      } // end for cubDeg
    } // end for poly_type
  }
  catch (std::logic_error err) {
    *outStream << err.what() << "\n";
    errorFlag = -1;
  };


  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;
}
示例#6
0
int main(int argc, char *argv[]) {

  Teuchos::GlobalMPISession mpiSession(&argc, &argv);

  // 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 (CubatureDirect,CubatureTensor,DefaultCubatureFactory)        |\n" \
  << "|                                                                             |\n" \
  << "|     1) Computing integrals of monomials on reference cells in 2D            |\n" \
  << "|                                                                             |\n" \
  << "|  Questions? Contact  Pavel Bochev ([email protected]) or                   |\n" \
  << "|                      Denis Ridzal ([email protected]).                     |\n" \
  << "|                                                                             |\n" \
  << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
  << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
  << "|                                                                             |\n" \
  << "===============================================================================\n"\
  << "| TEST 1: integrals of monomials in 2D                                        |\n"\
  << "===============================================================================\n";

  // internal variables:
  int                                      errorFlag = 0;
  int                                      polyCt = 0;
  int                                      offset = 0;
  Teuchos::Array< Teuchos::Array<double> > testInt;
  Teuchos::Array< Teuchos::Array<double> > analyticInt;
  Teuchos::Array<double>                   tmparray(1);
  double                                   reltol = 1.0e+03 * INTREPID_TOL;
  int                                      maxDeg[2];
  int                                      numPoly[2];
  maxDeg[0]  = INTREPID_CUBATURE_TRI_DEFAULT_MAX;
  maxDeg[1]  = INTREPID_CUBATURE_LINE_GAUSS_MAX;
  numPoly[0] = (INTREPID_CUBATURE_TRI_DEFAULT_MAX+1)*(INTREPID_CUBATURE_TRI_DEFAULT_MAX+2)/2;
  numPoly[1] = (INTREPID_CUBATURE_LINE_GAUSS_MAX+1)*(INTREPID_CUBATURE_LINE_GAUSS_MAX+2)/2;

  // get names of files with analytic values
  std::string basedir = "./data";
  std::stringstream namestream[2];
  std::string filename[2];
  namestream[0] << basedir << "/TRI_integrals" << ".dat";
  namestream[0] >> filename[0];
  namestream[1] << basedir << "/QUAD_integrals" << ".dat";
  namestream[1] >> filename[1];

  shards::CellTopology cellType[] = {shards::getCellTopologyData< shards::Triangle<> >(),
                                     shards::getCellTopologyData< shards::Quadrilateral<> >()};

  // compute and compare integrals
  try {
    for (int cellCt=0; cellCt < 2; cellCt++) {
      testInt.assign(numPoly[cellCt], tmparray);
      analyticInt.assign(numPoly[cellCt], tmparray);
      *outStream << "\nIntegrals of monomials on a reference " << cellType[cellCt].getBaseCellTopologyData()->name << ":\n";
      std::ifstream filecompare(&filename[cellCt][0]);
      // compute integrals
      for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
        polyCt = 0;
        testInt[cubDeg].resize((cubDeg+1)*(cubDeg+2)/2);
        for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
          for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
            testInt[cubDeg][polyCt] = computeIntegral(cellType[cellCt], cubDeg, xDeg, yDeg);
            polyCt++; 
          }
        }
      }
      // get analytic values
      if (filecompare.is_open()) {
        getAnalytic(analyticInt, filecompare);
        // close file
        filecompare.close();
      }
      // perform comparison
      for (int cubDeg=0; cubDeg <= maxDeg[cellCt]; cubDeg++) {
        polyCt = 0;
        offset = 0;
        for (int xDeg=0; xDeg <= cubDeg; xDeg++) {
          for (int yDeg=0; yDeg <= cubDeg-xDeg; yDeg++) {
            double abstol = ( analyticInt[polyCt+offset][0] == 0.0 ? reltol : std::fabs(reltol*analyticInt[polyCt+offset][0]) );
            double absdiff = std::fabs(analyticInt[polyCt+offset][0] - testInt[cubDeg][polyCt]);
            *outStream << "Cubature order " << std::setw(2) << std::left << cubDeg << " integrating "
                       << "x^" << std::setw(2) << std::left << xDeg << " * y^" << std::setw(2) << yDeg << ":" << "   "
                       << std::scientific << std::setprecision(16) << testInt[cubDeg][polyCt] << "   " << analyticInt[polyCt+offset][0] << "   "
                       << std::setprecision(4) << absdiff << "   " << "<?" << "   " << abstol << "\n";
            if (absdiff > abstol) {
              errorFlag++;
              *outStream << std::right << std::setw(111) << "^^^^---FAILURE!\n";
            }
            polyCt++;
          }
          offset = offset + maxDeg[cellCt] - cubDeg;
        }
        *outStream << "\n";
      }
      *outStream << "\n";
    }  // end for cellCt
  }
  catch (std::logic_error err) {
    *outStream << err.what() << "\n";
    errorFlag = -1;
  };


  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;
}