http://trilinos.sandia.gov/packages/docs/r10.0/packages/intrepid/test/Discretization/Basis/OrthogonalBases/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
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// Lesser General Public License for more details.
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// You should have received a copy of the GNU Lesser General Public
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// Questions? Contact Pavel Bochev (pbboche@sandia.gov) or
//                    Denis Ridzal (dridzal@sandia.gov) or
//                    Robert Kirby (robert.c.kirby@ttu.edu)
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#include "Intrepid_FieldContainer.hpp"
#include "Teuchos_oblackholestream.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_GlobalMPISession.hpp"
#include "Intrepid_OrthogonalBases.hpp"
#include <Intrepid_CubatureDirectTriDefault.hpp>
#include <iostream>
using namespace Intrepid;

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 OrthogonalBases                         |\n" \
    << "|                                                                             |\n" \
    << "|     1) Tests orthogonality of triangular orthogonal basis (Dubiner)         |\n" \
    << "|                                                                             |\n" \
    << "|  Questions? Contact  Pavel Bochev (pbboche@sandia.gov) or                   |\n" \
    << "|                      Denis Ridzal (dridzal@sandia.gov) or                   |\n" \
    << "|                      Robert Kirby (robert.c.kirby@ttu.edu)                  |\n" \
    << "|                                                                             |\n" \
    << "|  Intrepid's website: http://trilinos.sandia.gov/packages/intrepid           |\n" \
    << "|  Trilinos website:   http://trilinos.sandia.gov                             |\n" \
    << "|                                                                             |\n" \
    << "===============================================================================\n";
  
  int errorFlag  = 0;
  
  // First, get a reference quadrature rule

  CubatureDirectTriDefault<double,FieldContainer<double> > myCub(20);
  FieldContainer<double> cubPts( myCub.getNumPoints() , 2 );
  FieldContainer<double> cubWts( myCub.getNumPoints() );

  myCub.getCubature( cubPts , cubWts );
  
  // Tabulate the basis functions at the cubature points
  const int deg = 10;
  const int polydim = (deg+1)*(deg+2)/2;
  FieldContainer<double> basisAtCubPts( polydim , myCub.getNumPoints() );
  OrthogonalBases::tabulateTriangle<double,FieldContainer<double>,FieldContainer<double> >( cubPts , deg , basisAtCubPts );

  // Now let's compute the mass matrix
  for (int i=0;i<polydim;i++) {
    for (int j=0;j<polydim;j++) {
      double cur = 0;
      for (int k=0;k<myCub.getNumPoints();k++) {
        cur += cubWts(k) * basisAtCubPts( i , k ) * basisAtCubPts( j , k );
      }
      if (i != j && fabs( cur ) > INTREPID_TOL) {
        errorFlag++;
      }
      else if (i == j && fabs( cur ) < INTREPID_TOL ) {
        errorFlag++;
      }

    }
  }

  
  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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