Esempio n. 1
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 (Basis_HDIV_QUAD_I1_FEM)                           |\n" \
            << "|                                                                             |\n" \
            << "|     1) Conversion of Dof tags into Dof ordinals and back                    |\n" \
            << "|     2) Basis values for VALUE and DIV operators                             |\n" \
            << "|                                                                             |\n" \
            << "|  Questions? Contact  Pavel Bochev  ([email protected]),                    |\n" \
            << "|                      Denis Ridzal  ([email protected]),                    |\n" \
            << "|                      Kara Peterson ([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: Basis creation, exception testing                                   |\n"\
            << "===============================================================================\n";

    // Define basis and error flag
    Basis_HDIV_QUAD_I1_FEM<double, FieldContainer<double> > quadBasis;
    int errorFlag = 0;

    // Initialize throw counter for exception testing
    int nException     = 0;
    int throwCounter   = 0;

    // Array with the 4 vertices of the reference Quadrilateral, its center and 4 more points
    FieldContainer<double> quadNodes(9, 2);
    quadNodes(0,0) = -1.0;
    quadNodes(0,1) = -1.0;
    quadNodes(1,0) =  1.0;
    quadNodes(1,1) = -1.0;
    quadNodes(2,0) =  1.0;
    quadNodes(2,1) =  1.0;
    quadNodes(3,0) = -1.0;
    quadNodes(3,1) =  1.0;

    quadNodes(4,0) =  0.0;
    quadNodes(4,1) =  0.0;
    quadNodes(5,0) =  0.0;
    quadNodes(5,1) = -0.5;
    quadNodes(6,0) =  0.0;
    quadNodes(6,1) =  0.5;
    quadNodes(7,0) = -0.5;
    quadNodes(7,1) =  0.0;
    quadNodes(8,0) =  0.5;
    quadNodes(8,1) =  0.0;

    // Generic array for the output values; needs to be properly resized depending on the operator type
    FieldContainer<double> vals;

    try {

        int spaceDim  = quadBasis.getBaseCellTopology().getDimension();

        // exception #1: GRAD cannot be applied to HDIV functions
        // resize vals to rank-3 container with dimensions (num. basis functions, num. points, arbitrary)
        vals.resize(quadBasis.getCardinality(), quadNodes.dimension(0), spaceDim );
        INTREPID_TEST_COMMAND( quadBasis.getValues(vals, quadNodes, OPERATOR_GRAD), throwCounter, nException );

        // exception #2: CURL cannot be applied to HDIV functions
        INTREPID_TEST_COMMAND( quadBasis.getValues(vals, quadNodes, OPERATOR_CURL), throwCounter, nException );

        // Exceptions 3-7: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
        // getDofTag() to access invalid array elements thereby causing bounds check exception
        // exception #3
        INTREPID_TEST_COMMAND( quadBasis.getDofOrdinal(3,0,0), throwCounter, nException );
        // exception #4
        INTREPID_TEST_COMMAND( quadBasis.getDofOrdinal(1,1,1), throwCounter, nException );
        // exception #5
        INTREPID_TEST_COMMAND( quadBasis.getDofOrdinal(0,4,1), throwCounter, nException );
        // exception #6
        INTREPID_TEST_COMMAND( quadBasis.getDofTag(12), throwCounter, nException );
        // exception #7
        INTREPID_TEST_COMMAND( quadBasis.getDofTag(-1), throwCounter, nException );

#ifdef HAVE_INTREPID_DEBUG
        // Exceptions 8- test exception handling with incorrectly dimensioned input/output arrays
        // exception #8: input points array must be of rank-2
        FieldContainer<double> badPoints1(4, 5, 3);
        INTREPID_TEST_COMMAND( quadBasis.getValues(vals, badPoints1, OPERATOR_VALUE), throwCounter, nException );

        // exception #9 dimension 1 in the input point array must equal space dimension of the cell
        FieldContainer<double> badPoints2(4, spaceDim + 1);
        INTREPID_TEST_COMMAND( quadBasis.getValues(vals, badPoints2, OPERATOR_VALUE), throwCounter, nException );

        // exception #10 output values must be of rank-3 for OPERATOR_VALUE
        FieldContainer<double> badVals1(4, 5);
        INTREPID_TEST_COMMAND( quadBasis.getValues(badVals1, quadNodes, OPERATOR_VALUE), throwCounter, nException );

        // exception #11 output values must be of rank-2 for OPERATOR_DIV
        FieldContainer<double> badVals2(4, 5, spaceDim);
        INTREPID_TEST_COMMAND( quadBasis.getValues(badVals2, quadNodes, OPERATOR_DIV), throwCounter, nException );

        // exception #12 incorrect 0th dimension of output array (must equal number of basis functions)
        FieldContainer<double> badVals3(quadBasis.getCardinality() + 1, quadNodes.dimension(0), spaceDim);
        INTREPID_TEST_COMMAND( quadBasis.getValues(badVals3, quadNodes, OPERATOR_VALUE), throwCounter, nException );

        // exception #13 incorrect 0th dimension of output array (must equal number of basis functions)
        FieldContainer<double> badVals4(quadBasis.getCardinality() + 1, quadNodes.dimension(0));
        INTREPID_TEST_COMMAND( quadBasis.getValues(badVals4, quadNodes, OPERATOR_DIV), throwCounter, nException );

        // exception #14 incorrect 1st dimension of output array (must equal number of points)
        FieldContainer<double> badVals5(quadBasis.getCardinality(), quadNodes.dimension(0) + 1, spaceDim);
        INTREPID_TEST_COMMAND( quadBasis.getValues(badVals5, quadNodes, OPERATOR_VALUE), throwCounter, nException );

        // exception #15 incorrect 1st dimension of output array (must equal number of points)
        FieldContainer<double> badVals6(quadBasis.getCardinality(), quadNodes.dimension(0) + 1);
        INTREPID_TEST_COMMAND( quadBasis.getValues(badVals6, quadNodes, OPERATOR_DIV), throwCounter, nException );

        // exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
        FieldContainer<double> badVals7(quadBasis.getCardinality(), quadNodes.dimension(0), spaceDim + 1);
        INTREPID_TEST_COMMAND( quadBasis.getValues(badVals7, quadNodes, OPERATOR_VALUE), throwCounter, nException );
#endif

    }
    catch (std::logic_error err) {
        *outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
        *outStream << err.what() << '\n';
        *outStream << "-------------------------------------------------------------------------------" << "\n\n";
        errorFlag = -1000;
    };

    // Check if number of thrown exceptions matches the one we expect
    if (throwCounter != nException) {
        errorFlag++;
        *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
    }

    *outStream \
            << "\n"
            << "===============================================================================\n"\
            << "| TEST 2: correctness of tag to enum and enum to tag lookups                  |\n"\
            << "===============================================================================\n";

    try {
        std::vector<std::vector<int> > allTags = quadBasis.getAllDofTags();

        // Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
        for (unsigned i = 0; i < allTags.size(); i++) {
            int bfOrd  = quadBasis.getDofOrdinal(allTags[i][0], allTags[i][1], allTags[i][2]);

            std::vector<int> myTag = quadBasis.getDofTag(bfOrd);
            if( !( (myTag[0] == allTags[i][0]) &&
                    (myTag[1] == allTags[i][1]) &&
                    (myTag[2] == allTags[i][2]) &&
                    (myTag[3] == allTags[i][3]) ) ) {
                errorFlag++;
                *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
                *outStream << " getDofOrdinal( {"
                           << allTags[i][0] << ", "
                           << allTags[i][1] << ", "
                           << allTags[i][2] << ", "
                           << allTags[i][3] << "}) = " << bfOrd <<" but \n";
                *outStream << " getDofTag(" << bfOrd << ") = { "
                           << myTag[0] << ", "
                           << myTag[1] << ", "
                           << myTag[2] << ", "
                           << myTag[3] << "}\n";
            }
        }

        // Now do the same but loop over basis functions
        for( int bfOrd = 0; bfOrd < quadBasis.getCardinality(); bfOrd++) {
            std::vector<int> myTag  = quadBasis.getDofTag(bfOrd);
            int myBfOrd = quadBasis.getDofOrdinal(myTag[0], myTag[1], myTag[2]);
            if( bfOrd != myBfOrd) {
                errorFlag++;
                *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
                *outStream << " getDofTag(" << bfOrd << ") = { "
                           << myTag[0] << ", "
                           << myTag[1] << ", "
                           << myTag[2] << ", "
                           << myTag[3] << "} but getDofOrdinal({"
                           << myTag[0] << ", "
                           << myTag[1] << ", "
                           << myTag[2] << ", "
                           << myTag[3] << "} ) = " << myBfOrd << "\n";
            }
        }
    }
    catch (std::logic_error err) {
        *outStream << err.what() << "\n\n";
        errorFlag = -1000;
    };

    *outStream \
            << "\n"
            << "===============================================================================\n"\
            << "| TEST 3: correctness of basis function values                                |\n"\
            << "===============================================================================\n";

    outStream -> precision(20);

    // VALUE: Each row pair gives the 6x3 correct basis set values at an evaluation point: (P,F,D) layout
    double basisValues[] = {
        0, -0.500000, 0, 0, 0, 0, -0.500000, 0, 0, -0.500000, 0.500000, 0, 0, \
        0, 0, 0, 0, 0, 0.500000, 0, 0, 0.500000, 0, 0, 0, 0, 0, 0, 0, \
        0.500000, -0.500000, 0, 0, -0.250000, 0.250000, 0, 0, 0.250000, \
        -0.250000, 0, 0, -0.375000, 0.250000, 0, 0, 0.125000, -0.250000, 0, \
        0, -0.125000, 0.250000, 0, 0, 0.375000, -0.250000, 0, 0, -0.250000, \
        0.125000, 0, 0, 0.250000, -0.375000, 0, 0, -0.250000, 0.375000, 0, 0, \
        0.250000, -0.125000, 0
    };

    // DIV: each row gives the 6 correct values of the divergence of the 6 basis functions: (P,F) layout
    double basisDivs[] = {
        0.25, 0.25, 0.25, 0.25,
        0.25, 0.25, 0.25, 0.25,
        0.25, 0.25, 0.25, 0.25,
        0.25, 0.25, 0.25, 0.25,
        0.25, 0.25, 0.25, 0.25,
        0.25, 0.25, 0.25, 0.25,
        0.25, 0.25, 0.25, 0.25,
        0.25, 0.25, 0.25, 0.25,
        0.25, 0.25, 0.25, 0.25,
    };

    try {

        // Dimensions for the output arrays:
        int numPoints = quadNodes.dimension(0);
        int numFields = quadBasis.getCardinality();
        int spaceDim  = quadBasis.getBaseCellTopology().getDimension();

        // Generic array for values and curls that will be properly sized before each call
        FieldContainer<double> vals;

        // Check VALUE of basis functions: resize vals to rank-3 container:
        vals.resize(numFields, numPoints, spaceDim);
        quadBasis.getValues(vals, quadNodes, OPERATOR_VALUE);
        for (int i = 0; i < numFields; i++) {
            for (int j = 0; j < numPoints; j++) {
                for (int k = 0; k < spaceDim; k++) {

                    // compute offset for (P,F,D) data layout: indices are P->j, F->i, D->k
                    int l = k + i * spaceDim + j * spaceDim * numFields;
                    if (std::abs(vals(i,j,k) - basisValues[l]) > INTREPID_TOL) {
                        errorFlag++;
                        *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";

                        // Output the multi-index of the value where the error is:
                        *outStream << " At multi-index { ";
                        *outStream << i << " ";
                        *outStream << j << " ";
                        *outStream << k << " ";
                        *outStream << "}  computed value: " << vals(i,j,k)
                                   << " but reference value: " << basisValues[l] << "\n";
                    }
                }
            }
        }

        // Check DIV of basis function: resize vals to rank-2 container
        vals.resize(numFields, numPoints);
        quadBasis.getValues(vals, quadNodes, OPERATOR_DIV);
        for (int i = 0; i < numFields; i++) {
            for (int j = 0; j < numPoints; j++) {
                int l =  i + j * numFields;
                if (std::abs(vals(i,j) - basisDivs[l]) > INTREPID_TOL) {
                    errorFlag++;
                    *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";

                    // Output the multi-index of the value where the error is:
                    *outStream << " At multi-index { ";
                    *outStream << i << " ";
                    *outStream << j << " ";
                    *outStream << "}  computed divergence component: " << vals(i,j)
                               << " but reference divergence component: " << basisDivs[l] << "\n";
                }
            }
        }

    }

    // Catch unexpected errors
    catch (std::logic_error err) {
        *outStream << err.what() << "\n\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;
}
Esempio n. 2
0
    int HDIV_QUAD_I1_FEM_Test01(const bool verbose) {

      Teuchos::RCP<std::ostream> outStream;
      Teuchos::oblackholestream bhs; // outputs nothing

      if (verbose)
        outStream = Teuchos::rcp(&std::cout, false);
      else
        outStream = Teuchos::rcp(&bhs,       false);

      Teuchos::oblackholestream oldFormatState;
      oldFormatState.copyfmt(std::cout);

      typedef typename
        Kokkos::Impl::is_space<DeviceSpaceType>::host_mirror_space::execution_space HostSpaceType ;

      *outStream << "DeviceSpace::  "; DeviceSpaceType::print_configuration(*outStream, false);
      *outStream << "HostSpace::    ";   HostSpaceType::print_configuration(*outStream, false);

      *outStream
        << "===============================================================================\n"
        << "|                                                                             |\n"
        << "|                 Unit Test (Basis_HDIV_QUAD_I1_FEM)                          |\n"
        << "|                                                                             |\n"
        << "|     1) Conversion of Dof tags into Dof ordinals and back                    |\n"
        << "|     2) Basis values for VALUE and DIV operators                             |\n"
        << "|                                                                             |\n"
        << "|  Questions? Contact  Pavel Bochev  ([email protected]),                    |\n"
        << "|                      Denis Ridzal  ([email protected]),                    |\n"
        << "|                      Kara Peterson ([email protected]),                    |\n"
        << "|                      Kyungjoo Kim  ([email protected]).                     |\n"
        << "|                                                                             |\n"
        << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n"
        << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n"
        << "|                                                                             |\n"
        << "===============================================================================\n";

      typedef Kokkos::DynRankView<ValueType,DeviceSpaceType> DynRankView;
      typedef Kokkos::DynRankView<ValueType,HostSpaceType> DynRankViewHost;
#define ConstructWithLabel(obj, ...) obj(#obj, __VA_ARGS__)
      const ValueType tol = tolerence<ValueType>();
      int errorFlag = 0;

      typedef ValueType outputValueType;
      typedef ValueType pointValueType;
      Basis_HDIV_QUAD_I1_FEM<DeviceSpaceType,outputValueType,pointValueType> quadBasis;

      *outStream
        << "\n"
        << "===============================================================================\n"
        << "| TEST 1: Basis creation, exceptions tests                                    |\n"
        << "===============================================================================\n";

      try{
        ordinal_type nthrow = 0, ncatch = 0;
#ifdef HAVE_INTREPID2_DEBUG

        // Array with the 4 vertices of the reference Quadrilateral, its center and 4 more points
        DynRankView ConstructWithLabel(quadNodes, 9, 2);

        const auto numFields = quadBasis.getCardinality();
        const auto numPoints = quadNodes.dimension(0);
        const auto spaceDim = quadBasis.getBaseCellTopology().getDimension();
        DynRankView ConstructWithLabel(vals, numFields, numPoints, spaceDim );

        {
          // exception #1: GRAD cannot be applied to HDIV functions
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(vals, quadNodes, OPERATOR_GRAD) );
          
          // exception #2: CURL cannot be applied to HDIV functions
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(vals, quadNodes, OPERATOR_CURL) );
        }
        {
          // Exceptions 3-7: all bf tags/bf Ids below are wrong and should cause getDofOrdinal() and
          // getDofTag() to access invalid array elements thereby causing bounds check exception
          // exception #3
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getDofOrdinal(3,0,0) );
          // exception #4
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getDofOrdinal(1,1,1) );
          // exception #5
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getDofOrdinal(0,4,1) );
          // exception #6
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getDofTag(12) );
          // exception #7
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getDofTag(-1) );
        }
    
        // Exceptions 8- test exception handling with incorrectly dimensioned input/output arrays
        {
          // exception #8: input points array must be of rank-2
          DynRankView ConstructWithLabel(badPoints1, 4, 5, 3);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(vals, badPoints1, OPERATOR_VALUE) );
        }
        {
          // exception #9 dimension 1 in the input point array must equal space dimension of the cell
          DynRankView ConstructWithLabel(badPoints2, 4, spaceDim + 1);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(vals, badPoints2, OPERATOR_VALUE) );
        }
        {
          // exception #10 output values must be of rank-3 for OPERATOR_VALUE
          DynRankView ConstructWithLabel(badVals1, 4, 5);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(badVals1, quadNodes, OPERATOR_VALUE) );
        }
        {
          // exception #11 output values must be of rank-2 for OPERATOR_DIV
          DynRankView ConstructWithLabel(badVals2, 4, 5, spaceDim);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(badVals2, quadNodes, OPERATOR_DIV) );
        }
        {
          // exception #12 incorrect 0th dimension of output array (must equal number of basis functions)
          DynRankView ConstructWithLabel(badVals3, quadBasis.getCardinality() + 1, quadNodes.dimension(0), spaceDim);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(badVals3, quadNodes, OPERATOR_VALUE) );
        }
        {
          // exception #13 incorrect 0th dimension of output array (must equal number of basis functions)
          DynRankView ConstructWithLabel(badVals4, quadBasis.getCardinality() + 1, quadNodes.dimension(0));
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(badVals4, quadNodes, OPERATOR_DIV) );
        }
        {
          // exception #14 incorrect 1st dimension of output array (must equal number of points)
          DynRankView ConstructWithLabel(badVals5, quadBasis.getCardinality(), quadNodes.dimension(0) + 1, spaceDim);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(badVals5, quadNodes, OPERATOR_VALUE) );
        }
        {
          // exception #15 incorrect 1st dimension of output array (must equal number of points)
          DynRankView ConstructWithLabel(badVals6, quadBasis.getCardinality(), quadNodes.dimension(0) + 1);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(badVals6, quadNodes, OPERATOR_DIV) );
        }
        {
          // exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
          DynRankView ConstructWithLabel(badVals7, quadBasis.getCardinality(), quadNodes.dimension(0), spaceDim + 1);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getValues(badVals7, quadNodes, OPERATOR_VALUE) );
        }
#endif
        // Check if number of thrown exceptions matches the one we expect
        if (nthrow != ncatch) {
          errorFlag++;
          *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
          *outStream << "# of catch ("<< ncatch << ") is different from # of throw (" << nthrow << ")\n";
        }
      } catch (std::logic_error err) {
        *outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
        *outStream << err.what() << '\n';
        *outStream << "-------------------------------------------------------------------------------" << "\n\n";
        errorFlag = -1000;
      };

      *outStream
        << "\n"
        << "===============================================================================\n"
        << "| TEST 2: correctness of tag to enum and enum to tag lookups                  |\n"
        << "===============================================================================\n";
  
      try {
    
        const auto numFields = quadBasis.getCardinality();
        const auto allTags = quadBasis.getAllDofTags();

        // Loop over all tags, lookup the associated dof enumeration and then lookup the tag again
        const auto dofTagSize = allTags.dimension(0);
        for (size_type i=0;i<dofTagSize;++i) {
          const auto bfOrd = quadBasis.getDofOrdinal(allTags(i,0), allTags(i,1), allTags(i,2));
    
          const auto myTag = quadBasis.getDofTag(bfOrd);
          if( !( (myTag(0) == allTags(i,0)) &&
                 (myTag(1) == allTags(i,1)) &&
                 (myTag(2) == allTags(i,2)) &&
                 (myTag(3) == allTags(i,3)) ) ) {
            errorFlag++;
            *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
            *outStream << " getDofOrdinal( {"
                       << allTags(i,0) << ", "
                       << allTags(i,1) << ", "
                       << allTags(i,2) << ", "
                       << allTags(i,3) << "}) = " << bfOrd <<" but \n";
            *outStream << " getDofTag(" << bfOrd << ") = { "
                       << myTag(0) << ", "
                       << myTag(1) << ", "
                       << myTag(2) << ", "
                       << myTag(3) << "}\n";
          }
        }

        // Now do the same but loop over basis functions
        for(auto bfOrd=0;bfOrd<numFields;++bfOrd) {
          const auto myTag  = quadBasis.getDofTag(bfOrd);
          const auto myBfOrd = quadBasis.getDofOrdinal(myTag(0), myTag(1), myTag(2));
          if( bfOrd != myBfOrd) {
            errorFlag++;
            *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
            *outStream << " getDofTag(" << bfOrd << ") = { "
                       << myTag(0) << ", "
                       << myTag(1) << ", "
                       << myTag(2) << ", "
                       << myTag(3) << "} but getDofOrdinal({"
                       << myTag(0) << ", "
                       << myTag(1) << ", "
                       << myTag(2) << ", "
                       << myTag(3) << "} ) = " << myBfOrd << "\n";
          }
        }
      } catch (std::logic_error err){
        *outStream << "UNEXPECTED ERROR !!! ----------------------------------------------------------\n";
        *outStream << err.what() << '\n';
        *outStream << "-------------------------------------------------------------------------------" << "\n\n";
        errorFlag = -1000;
      };

      *outStream \
        << "\n"
        << "===============================================================================\n"\
        << "| TEST 3: correctness of basis function values                                |\n"\
        << "===============================================================================\n";

      outStream -> precision(20);
  
      try{

        // VALUE: Each row pair gives the 6x3 correct basis set values at an evaluation point: (P,F,D) layout
        double basisValues[] = {
          0, -0.500000, 0, 0, 0, 0, -0.500000, 0, 0, -0.500000, 0.500000, 0, 0, \
          0, 0, 0, 0, 0, 0.500000, 0, 0, 0.500000, 0, 0, 0, 0, 0, 0, 0, \
          0.500000, -0.500000, 0, 0, -0.250000, 0.250000, 0, 0, 0.250000, \
          -0.250000, 0, 0, -0.375000, 0.250000, 0, 0, 0.125000, -0.250000, 0, \
          0, -0.125000, 0.250000, 0, 0, 0.375000, -0.250000, 0, 0, -0.250000, \
          0.125000, 0, 0, 0.250000, -0.375000, 0, 0, -0.250000, 0.375000, 0, 0, \
          0.250000, -0.125000, 0  };

        // DIV: each row gives the 6 correct values of the divergence of the 6 basis functions: (P,F) layout
        double basisDivs[] = {
            0.25, 0.25, 0.25, 0.25,
            0.25, 0.25, 0.25, 0.25,
            0.25, 0.25, 0.25, 0.25,
            0.25, 0.25, 0.25, 0.25,
            0.25, 0.25, 0.25, 0.25,
            0.25, 0.25, 0.25, 0.25,
            0.25, 0.25, 0.25, 0.25,
            0.25, 0.25, 0.25, 0.25,
            0.25, 0.25, 0.25, 0.25,
        };
  
        DynRankViewHost ConstructWithLabel(quadNodesHost, 9, 2);

        quadNodesHost(0,0) = -1.0;  quadNodesHost(0,1) = -1.0;
        quadNodesHost(1,0) =  1.0;  quadNodesHost(1,1) = -1.0;
        quadNodesHost(2,0) =  1.0;  quadNodesHost(2,1) =  1.0;
        quadNodesHost(3,0) = -1.0;  quadNodesHost(3,1) =  1.0;

        quadNodesHost(4,0) =  0.0;  quadNodesHost(4,1) =  0.0;
        quadNodesHost(5,0) =  0.0;  quadNodesHost(5,1) = -0.5;
        quadNodesHost(6,0) =  0.0;  quadNodesHost(6,1) =  0.5;
        quadNodesHost(7,0) = -0.5;  quadNodesHost(7,1) =  0.0;
        quadNodesHost(8,0) =  0.5;  quadNodesHost(8,1) =  0.0;

        const auto quadNodes = Kokkos::create_mirror_view(typename DeviceSpaceType::memory_space(), quadNodesHost);
        Kokkos::deep_copy(quadNodes, quadNodesHost);

        // Dimensions for the output arrays:
        const auto numPoints = quadNodes.dimension(0);
        const auto numFields = quadBasis.getCardinality();
        const auto spaceDim  = quadBasis.getBaseCellTopology().getDimension();

        { 
        DynRankView ConstructWithLabel(vals, numFields, numPoints, spaceDim);
        quadBasis.getValues(vals, quadNodes, OPERATOR_VALUE);
        const auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
        Kokkos::deep_copy(vals_host, vals);
        for (auto i=0;i<numFields;++i) 
          for (auto j=0;j<numPoints;++j) 
            for (auto k=0;k<spaceDim;++k) {
              
              // compute offset for (P,F,D) data layout: indices are P->j, F->i, D->k
              int l = k + i * spaceDim + j * spaceDim * numFields;
              if (std::abs(vals_host(i,j,k) - basisValues[l]) > tol) {
                errorFlag++;
                *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
                
                // Output the multi-index of the value where the error is:
                *outStream << " At multi-index { ";
                *outStream << i << " ";*outStream << j << " ";*outStream << k << " ";
                *outStream << "}  computed value: " << vals_host(i,j,k)
                           << " but reference value: " << basisValues[l] << "\n";
              }
            }
        }

        {
        // Check DIV of basis function: resize vals to rank-2 container
        DynRankView ConstructWithLabel(vals, numFields, numPoints);
        quadBasis.getValues(vals, quadNodes, OPERATOR_DIV);
        const auto vals_host = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), vals);
        Kokkos::deep_copy(vals_host, vals);
        for (int i = 0; i < numFields; i++) {
          for (int j = 0; j < numPoints; j++) {
              int l =  i + j * numFields;
               if (std::abs(vals_host(i,j) - basisDivs[l]) > tol) {
                 errorFlag++;
                 *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
    
                 // Output the multi-index of the value where the error is:
                 *outStream << " At multi-index { ";
                 *outStream << i << " ";*outStream << j << " ";
                 *outStream << "}  computed divergence component: " << vals_host(i,j)
                   << " but reference divergence component: " << basisDivs[l] << "\n";
             }
          }
        }
        }

      // Catch unexpected errors
      } catch (std::logic_error err) {
        *outStream << err.what() << "\n\n";
        errorFlag = -1000;
      };

      *outStream \
        << "\n"
        << "===============================================================================\n"\
        << "| TEST 4: correctness of DoF locations                                        |\n"\
        << "===============================================================================\n";

      try{
        const auto numFields = quadBasis.getCardinality();
        const auto spaceDim  = quadBasis.getBaseCellTopology().getDimension();

        // Check exceptions.
        ordinal_type nthrow = 0, ncatch = 0;
#ifdef HAVE_INTREPID2_DEBUG
        {
          DynRankView ConstructWithLabel(badVals,1,2,3);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getDofCoords(badVals) );
        }
        {
          DynRankView ConstructWithLabel(badVals, 3,2);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getDofCoords(badVals) );
        }
        {
          DynRankView ConstructWithLabel(badVals, 4,3);
          INTREPID2_TEST_ERROR_EXPECTED( quadBasis.getDofCoords(badVals) );
        }
#endif
         // Check if number of thrown exceptions matches the one we expect
         if (nthrow != ncatch) {
           errorFlag++;
           *outStream << std::setw(70) << "^^^^----FAILURE!" << "\n";
         }
         
        // Check mathematical correctness
        DynRankViewHost ConstructWithLabel(normals, numFields,spaceDim); // normals at each point basis point
        normals(0,0)  =  0.0; normals(0,1)  = -2.0;
        normals(1,0)  =  2.0; normals(1,1)  =  0.0;
        normals(2,0)  =  0.0; normals(2,1)  =  2.0;
        normals(3,0)  = -2.0; normals(3,1)  =  0.0;

        DynRankView ConstructWithLabel(cvals_dev, numFields,spaceDim);
        DynRankView ConstructWithLabel(bvals_dev, numFields, numFields, spaceDim); // last dimension is spatial dim

        quadBasis.getDofCoords(cvals_dev);
        quadBasis.getValues(bvals_dev, cvals_dev, OPERATOR_VALUE);

        const auto bvals = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), bvals_dev);
        Kokkos::deep_copy(bvals, bvals_dev);
        const auto cvals = Kokkos::create_mirror_view(typename HostSpaceType::memory_space(), cvals_dev);
        Kokkos::deep_copy(cvals, cvals_dev);

        ValueType expected_normal;
        for (size_type i=0;i<numFields;++i) {
          for (size_type j=0;j<numFields;++j) {

            ValueType normal = 0.0;
            for (size_type d=0;d<spaceDim;++d)
               normal += bvals(i,j,d)*normals(j,d);

            expected_normal = (i == j);
            if (std::abs(normal - expected_normal) > tol) {
              errorFlag++;
              std::stringstream ss;
              ss << "\nNormal component of basis function " << i << " at (" << cvals(j,0) << ", " << cvals(j,1)<< ") is " << normal << " but should be " << expected_normal << "\n";
              *outStream << ss.str();
            }
          }
        }
      } catch (std::logic_error err) { 
        *outStream << err.what() << "\n\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;
    }