http://trilinos.sandia.gov/packages/docs/r10.0/packages/intrepid/test/Discretization/Basis/HDIV_TRI_I1_FEM/test_01.cpp

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// ************************************************************************
//
//                           Intrepid Package
//                 Copyright (2007) Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// This library is free software; you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 2.1 of the
// License, or (at your option) any later version.
//
// This library is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA
// Questions? Contact Pavel Bochev  (pbboche@sandia.gov), 
//                    Denis Ridzal  (dridzal@sandia.gov),
//                    Kara Peterson (kjpeter@sandia.gov).
//
// ************************************************************************
// @HEADER

#include "Intrepid_FieldContainer.hpp"
#include "Intrepid_HDIV_TRI_I1_FEM.hpp"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_GlobalMPISession.hpp"

using namespace std;
using namespace Intrepid;

#define INTREPID_TEST_COMMAND( S , throwCounter, nException )                                                              \
{                                                                                                                          \
  ++nException;                                                                                                            \
  try {                                                                                                                    \
    S ;                                                                                                                    \
  }                                                                                                                        \
  catch (std::logic_error err) {                                                                                           \
      ++throwCounter;                                                                                                      \
      *outStream << "Expected Error " << nException << " -------------------------------------------------------------\n"; \
      *outStream << err.what() << '\n';                                                                                    \
      *outStream << "-------------------------------------------------------------------------------" << "\n\n";           \
  };                                                                                                                       \
}

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_TRI_I1_FEM)                           |\n" \
    << "|                                                                             |\n" \
    << "|     1) Conversion of Dof tags into Dof ordinals and back                    |\n" \
    << "|     3) Exception tests on input arguments and invalid operators             |\n" \
    << "|     2) Basis values for VALUE and DIV operators                             |\n" \
    << "|                                                                             |\n" \
    << "|  Questions? Contact  Pavel Bochev  (pbboche@sandia.gov),                    |\n" \
    << "|                      Denis Ridzal  (dridzal@sandia.gov),                    |\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"\
    << "| TEST 1: Basis creation, exception testing                                   |\n"\
    << "===============================================================================\n";
  
  // Define basis and error flag
  Basis_HDIV_TRI_I1_FEM<double, FieldContainer<double> > triBasis;
  int errorFlag = 0;

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

  // Define array containing the 3 vertices of the reference TRI and its 3 edge midpoints.
  FieldContainer<double> triNodes(6, 2);
  triNodes(0,0) =  0.0;  triNodes(0,1) =  0.0;  
  triNodes(1,0) =  1.0;  triNodes(1,1) =  0.0;  
  triNodes(2,0) =  0.0;  triNodes(2,1) =  1.0;  
  // edge midpoints
  triNodes(3,0) =  0.5;  triNodes(3,1) =  0.0;  
  triNodes(4,0) =  0.5;  triNodes(4,1) =  0.5;  
  triNodes(5,0) =  0.0;  triNodes(5,1) =  0.5;  


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

  try{
    // 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(triBasis.getCardinality(), triNodes.dimension(0), triBasis.getBaseCellTopology().getDimension() );
    INTREPID_TEST_COMMAND( triBasis.getValues(vals, triNodes, OPERATOR_GRAD), throwCounter, nException );

    // exception #2: CURL cannot be applied to HDIV functions
    INTREPID_TEST_COMMAND( triBasis.getValues(vals, triNodes, 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( triBasis.getDofOrdinal(3,0,0), throwCounter, nException );
    // exception #4
    INTREPID_TEST_COMMAND( triBasis.getDofOrdinal(1,1,1), throwCounter, nException );
    // exception #5
    INTREPID_TEST_COMMAND( triBasis.getDofOrdinal(0,2,1), throwCounter, nException );
    // exception #6
    INTREPID_TEST_COMMAND( triBasis.getDofTag(3), throwCounter, nException );
    // exception #7
    INTREPID_TEST_COMMAND( triBasis.getDofTag(-1), throwCounter, nException );

#ifdef HAVE_INTREPID_DEBUG
    // Exceptions 8-15 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( triBasis.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, triBasis.getBaseCellTopology().getDimension() + 1);
    INTREPID_TEST_COMMAND( triBasis.getValues(vals, badPoints2, OPERATOR_VALUE), throwCounter, nException );
    
    // exception #10 output values must be of rank-3 for OPERATOR_VALUE
    FieldContainer<double> badVals1(4, 3);
    INTREPID_TEST_COMMAND( triBasis.getValues(badVals1, triNodes, OPERATOR_VALUE), throwCounter, nException );
 
    // exception #11 output values must be of rank-2 for OPERATOR_DIV
    FieldContainer<double> badVals2(4, 3, 1);
    INTREPID_TEST_COMMAND( triBasis.getValues(badVals2, triNodes, OPERATOR_VALUE), throwCounter, nException );

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

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

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

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

    // exception #16: incorrect 2nd dimension of output array (must equal the space dimension)
    FieldContainer<double> badVals7(triBasis.getCardinality(), triNodes.dimension(0), triBasis.getBaseCellTopology().getDimension() + 1);
    INTREPID_TEST_COMMAND( triBasis.getValues(badVals7, triNodes, 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 = triBasis.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  = triBasis.getDofOrdinal(allTags[i][0], allTags[i][1], allTags[i][2]);
      
      std::vector<int> myTag = triBasis.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 < triBasis.getCardinality(); bfOrd++) {
      std::vector<int> myTag  = triBasis.getDofTag(bfOrd);
      int myBfOrd = triBasis.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: Correct basis values in (F,P,D) format: each group of two rows gives basis function
  // values at vertices followed by midpoints. This is the same array format as the output from getValues.
  double basisValues[] = {
    // basis function 0 at 3 vertices followed by 3 midpoints
    0.0,-1.0,                  1.0,-1.0,                               0.0, 0.0,  
    0.5,-1.0,                  0.5,-0.5,                               0.0,-0.5,
    // basis function 1 at 3 vertices followed by 3 midpoints
    0.0, 0.0,                  1.0, 0.0,                0.0, 1.0,
    0.5, 0.0,                  0.5, 0.5,                0.0, 0.5,
    // basis function 2 at 3 vertices followed by 3 midpoints
    -1.0, 0.0,                 0.0, 0.0,                              -1.0, 1.0,
    -0.5, 0.0,                -0.5, 0.5,                              -1.0, 0.5
  };
  
  // DIV: each row gives the 3 correct values of the divergence of the 3 basis functions
  double basisDivs[] = {   
    // 3 vertices
    2.0,  2.0,   2.0,
    2.0,  2.0,   2.0,
    2.0,  2.0,   2.0,
    // 3 edge centers
    2.0,  2.0,   2.0,
    2.0,  2.0,   2.0,
    2.0,  2.0,   2.0,
  };
  
  try{
        
    // Dimensions for the output arrays:
    int numFields = triBasis.getCardinality();
    int numPoints = triNodes.dimension(0);
    int spaceDim  = triBasis.getBaseCellTopology().getDimension();
    
    // Generic array for values and divs 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);
    triBasis.getValues(vals, triNodes, OPERATOR_VALUE);
    for (int i = 0; i < numFields; i++) {
      for (int j = 0; j < numPoints; j++) {
        for (int k = 0; k < spaceDim; k++) {
          // basisValues are in (F,P,D) format and the multiindex is (i,j,k), here's the offset:
           int l = k + j * spaceDim + i * spaceDim * numPoints;
                    
           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 << " address =  "<< l <<"\n";
             *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);
    triBasis.getValues(vals, triNodes, 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 (Field,Point,Dim) 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;
}

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