localprojectedfefunctiontest.cc

#include <config.h>

#include <fenv.h>
#include <iostream>
#include <iomanip>

#include <dune/common/fvector.hh>

#include <dune/geometry/quadraturerules.hh>
#include <dune/geometry/type.hh>
#include <dune/geometry/referenceelements.hh>

#include <dune/localfunctions/lagrange/lagrangelfecache.hh>

#include <dune/gfe/spaces/productmanifold.hh>
#include <dune/gfe/spaces/realtuple.hh>
#include <dune/gfe/spaces/rotation.hh>
#include <dune/gfe/spaces/unitvector.hh>

#include <dune/gfe/localprojectedfefunction.hh>
#include "multiindex.hh"
#include "valuefactory.hh"

const double eps = 1e-6;

using namespace Dune;

/** \brief Computes the diameter of a set */
template <class TargetSpace>
double diameter(const std::vector<TargetSpace>& v)
{
  double d = 0;
  for (size_t i=0; i<v.size(); i++)
    for (size_t j=0; j<v.size(); j++)
      d = std::max(d, TargetSpace::distance(v[i],v[j]));
  return d;
}

template <int dim, class ctype, class LocalFunction>
auto
evaluateDerivativeFD(const LocalFunction& f, const Dune::FieldVector<ctype, dim>& local)
-> decltype(f.evaluateDerivative(local))
{
  double eps = 1e-8;
  static const int embeddedDim = LocalFunction::TargetSpace::embeddedDim;
  Dune::FieldMatrix<ctype, embeddedDim, dim> result;

  for (int i=0; i<dim; i++) {

    Dune::FieldVector<ctype, dim> forward  = local;
    Dune::FieldVector<ctype, dim> backward = local;

    forward[i]  += eps;
    backward[i] -= eps;

    auto fdDer = f.evaluate(forward).globalCoordinates() - f.evaluate(backward).globalCoordinates();
    fdDer /= 2*eps;

    for (int j=0; j<embeddedDim; j++)
      result[j][i] = fdDer[j];

  }

  return result;
}


template <int domainDim, int dim>
void testDerivativeTangentiality(const RealTuple<double,dim>& x,
                                 const FieldMatrix<double,dim,domainDim>& derivative)
{
  // By construction, derivatives of RealTuples are always tangent
}

// the columns of the derivative must be tangential to the manifold
template <int domainDim, int vectorDim>
void testDerivativeTangentiality(const UnitVector<double,vectorDim>& x,
                                 const FieldMatrix<double,vectorDim,domainDim>& derivative)
{
  for (int i=0; i<domainDim; i++) {

    // The i-th column is a tangent vector if its scalar product with the global coordinates
    // of x vanishes.
    double sp = 0;
    for (int j=0; j<vectorDim; j++)
      sp += x.globalCoordinates()[j] * derivative[j][i];

    if (std::fabs(sp) > 1e-8)
      DUNE_THROW(Dune::Exception, "Derivative is not tangential: Column: " << i << ",  product: " << sp);

  }

}

// the columns of the derivative must be tangential to the manifold
template <int domainDim, int vectorDim>
void testDerivativeTangentiality(const Rotation<double,vectorDim-1>& x,
                                 const FieldMatrix<double,vectorDim,domainDim>& derivative)
{}

// the columns of the derivative must be tangential to the manifold
template <int domainDim, int vectorDim,typename ... TargetSpaces>
void testDerivativeTangentiality(const Dune::GFE::ProductManifold<TargetSpaces...>& x,
                                 const FieldMatrix<double,vectorDim,domainDim>& derivative)
{
  size_t posHelper=0;
  using namespace Dune::Hybrid;
  forEach(integralRange(Dune::Hybrid::size(x)), [&](auto&& i) {
    using Manifold = std::remove_reference_t<decltype(x[i])>;
    testDerivativeTangentiality(x[i],Dune::GFE::blockAt<Manifold::embeddedDim,domainDim>( derivative,posHelper,0));
    posHelper +=Manifold::embeddedDim;
  });
}

/** \brief Test whether interpolation is invariant under permutation of the simplex vertices
 * \todo Implement this for all dimensions
 */
template <int domainDim, class TargetSpace>
void testPermutationInvariance(const std::vector<TargetSpace>& corners)
{
  // works only for 2d domains
  if (domainDim!=2)
    return;

  LagrangeLocalFiniteElementCache<double,double,domainDim,1> feCache;
  typedef typename LagrangeLocalFiniteElementCache<double,double,domainDim,1>::FiniteElementType LocalFiniteElement;

  GeometryType simplex = GeometryTypes::simplex(domainDim);

  //
  std::vector<TargetSpace> cornersRotated1(domainDim+1);
  std::vector<TargetSpace> cornersRotated2(domainDim+1);

  cornersRotated1[0] = cornersRotated2[2] = corners[1];
  cornersRotated1[1] = cornersRotated2[0] = corners[2];
  cornersRotated1[2] = cornersRotated2[1] = corners[0];

  GFE::LocalProjectedFEFunction<2,double,LocalFiniteElement,TargetSpace> f0(feCache.get(simplex), corners);
  GFE::LocalProjectedFEFunction<2,double,LocalFiniteElement,TargetSpace> f1(feCache.get(simplex), cornersRotated1);
  GFE::LocalProjectedFEFunction<2,double,LocalFiniteElement,TargetSpace> f2(feCache.get(simplex), cornersRotated2);

  // A quadrature rule as a set of test points
  int quadOrder = 3;

  const Dune::QuadratureRule<double, domainDim>& quad
    = Dune::QuadratureRules<double, domainDim>::rule(simplex, quadOrder);

  for (size_t pt=0; pt<quad.size(); pt++) {

    const Dune::FieldVector<double,domainDim>& quadPos = quad[pt].position();

    Dune::FieldVector<double,domainDim> l0 = quadPos;
    Dune::FieldVector<double,domainDim> l1, l2;

    l1[0] = quadPos[1];
    l1[1] = 1-quadPos[0]-quadPos[1];

    l2[0] = 1-quadPos[0]-quadPos[1];
    l2[1] = quadPos[0];

    // evaluate the three functions
    TargetSpace v0 = f0.evaluate(l0);
    TargetSpace v1 = f1.evaluate(l1);
    TargetSpace v2 = f2.evaluate(l2);

    // Check that they are all equal
    assert(TargetSpace::distance(v0,v1) < eps);
    assert(TargetSpace::distance(v0,v2) < eps);

  }

}

template <int domainDim, class TargetSpace, bool conforming=true>
void testDerivative(const GFE::LocalProjectedFEFunction<domainDim,double,typename LagrangeLocalFiniteElementCache<double,double,domainDim,1>::FiniteElementType, TargetSpace, conforming>& f)
{
  static const int embeddedDim = TargetSpace::EmbeddedTangentVector::dimension;

  // A quadrature rule as a set of test points
  int quadOrder = 3;

  const auto& quad = Dune::QuadratureRules<double, domainDim>::rule(f.type(), quadOrder);

  for (size_t pt=0; pt<quad.size(); pt++) {

    const Dune::FieldVector<double,domainDim>& quadPos = quad[pt].position();

    // evaluate actual derivative
    Dune::FieldMatrix<double, embeddedDim, domainDim> derivative = f.evaluateDerivative(quadPos);

    // evaluate fd approximation of derivative
    Dune::FieldMatrix<double, embeddedDim, domainDim> fdDerivative = evaluateDerivativeFD(f,quadPos);

    Dune::FieldMatrix<double, embeddedDim, domainDim> diff = derivative;
    diff -= fdDerivative;

    if ( diff.infinity_norm() > 100*eps ) {
      std::cout << className<TargetSpace>() << ": Analytical gradient does not match fd approximation." << std::endl;
      std::cout << "Analytical: " << derivative << std::endl;
      std::cout << "FD        : " << fdDerivative << std::endl;
      assert(false);
    }

    if(conforming)
      testDerivativeTangentiality(f.evaluate(quadPos), derivative);

  }
}


template <class TargetSpace, int domainDim>
void test(const GeometryType& element)
{
  std::cout << " --- Testing " << className<TargetSpace>() << ", domain dimension: " << element.dim() << " ---" << std::endl;

  std::vector<TargetSpace> testPoints;
  ValueFactory<TargetSpace>::get(testPoints);

  int nTestPoints = testPoints.size();
  size_t nVertices = Dune::ReferenceElements<double,domainDim>::general(element).size(domainDim);

  // Set up elements of the target space
  std::vector<TargetSpace> corners(nVertices);

  MultiIndex index(nVertices, nTestPoints);
  int numIndices = index.cycle();

  for (int i=0; i<numIndices; i++, ++index) {

    for (size_t j=0; j<nVertices; j++)
      corners[j] = testPoints[index[j]];

    if (diameter(corners) > 0.5*M_PI)
      continue;

    // Make local gfe function to be tested
    LagrangeLocalFiniteElementCache<double,double,domainDim,1> feCache;
    typedef typename LagrangeLocalFiniteElementCache<double,double,domainDim,1>::FiniteElementType LocalFiniteElement;

    GFE::LocalProjectedFEFunction<domainDim,double,LocalFiniteElement,TargetSpace> f(feCache.get(element),corners);
    GFE::LocalProjectedFEFunction<domainDim, double, LocalFiniteElement, TargetSpace,false> f_nonconforming(feCache.get(element), corners);

    //testPermutationInvariance(corners);
    testDerivative<domainDim>(f);
    testDerivative<domainDim>(f_nonconforming);
  }

}


int main()
{
  // choke on NaN -- don't enable this by default, as there are
  // a few harmless NaN in the loopsolver
  //feenableexcept(FE_INVALID);

  std::cout << std::setw(15) << std::setprecision(12);

  ////////////////////////////////////////////////////////////////
  //  Test functions on 1d elements
  ////////////////////////////////////////////////////////////////

  test<RealTuple<double,1>,1>(GeometryTypes::line);
  test<UnitVector<double,2>,1>(GeometryTypes::line);
  test<UnitVector<double,3>,1>(GeometryTypes::line);
  test<Rotation<double,3>,1>(GeometryTypes::line);
  typedef Dune::GFE::ProductManifold<RealTuple<double,1>,Rotation<double,3>,UnitVector<double,2> > CrazyManifold;
  test<CrazyManifold, 1>(GeometryTypes::line);

  ////////////////////////////////////////////////////////////////
  //  Test functions on 2d simplex elements
  ////////////////////////////////////////////////////////////////

  test<RealTuple<double,1>,2>(GeometryTypes::triangle);
  test<UnitVector<double,2>,2>(GeometryTypes::triangle);
  test<RealTuple<double,3>,2>(GeometryTypes::triangle);
  test<UnitVector<double,3>,2>(GeometryTypes::triangle);
  test<Rotation<double,3>,2>(GeometryTypes::triangle);
  typedef Dune::GFE::ProductManifold<RealTuple<double,1>,Rotation<double,3>,UnitVector<double,2> > CrazyManifold;
  test<CrazyManifold, 2>(GeometryTypes::triangle);

  ////////////////////////////////////////////////////////////////
  //  Test functions on 2d quadrilateral elements
  ////////////////////////////////////////////////////////////////

  test<RealTuple<double,1>,2>(GeometryTypes::quadrilateral);
  test<UnitVector<double,2>,2>(GeometryTypes::quadrilateral);
  test<UnitVector<double,3>,2>(GeometryTypes::quadrilateral);
  test<Rotation<double,3>,2>(GeometryTypes::quadrilateral);
  typedef Dune::GFE::ProductManifold<RealTuple<double,1>,Rotation<double,3>,UnitVector<double,2> > CrazyManifold;
  test<CrazyManifold, 2>(GeometryTypes::quadrilateral);

}