dualq1localbasis.hh

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// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
#ifndef DUNE_DUAL_Q1_LOCALBASIS_HH
#define DUNE_DUAL_Q1_LOCALBASIS_HH
 
#include <array>
#include <numeric>
 
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
 
#include <dune/localfunctions/common/localbasis.hh>
 
namespace Dune
{
  template<class D, class R, int dim>
  class DualQ1LocalBasis
  {
  public:
    typedef LocalBasisTraits<D,dim,Dune::FieldVector<D,dim>,R,1,Dune::FieldVector<R,1>,
        Dune::FieldMatrix<R,1,dim> > Traits;
 
    void setCoefficients(const std::array<Dune::FieldVector<R, (1<<dim)> ,(1<<dim)>& coefficients)
    {
      coefficients_ = coefficients;
    }
 
    unsigned int size () const
    {
      return 1<<dim;
    }
 
    inline void evaluateFunction (const typename Traits::DomainType& in,
                                  std::vector<typename Traits::RangeType>& out) const
    {
      // compute q1 values
      std::vector<typename Traits::RangeType> q1Values(size());
 
      for (size_t i=0; i<size(); i++) {
 
        q1Values[i] = 1;
 
        for (int j=0; j<dim; j++)
          // if j-th bit of i is set multiply with in[j], else with 1-in[j]
          q1Values[i] *= (i & (1<<j)) ? in[j] :  1-in[j];
 
      }
 
      // compute the dual values by using that they are linear combinations of q1 functions
      out.resize(size());
      for (size_t i=0; i<size(); i++)
        out[i] = 0;
 
      for (size_t i=0; i<size(); i++)
        for (size_t j=0; j<size(); j++)
          out[i] += coefficients_[i][j]*q1Values[j];
 
 
    }
 
    inline void
    evaluateJacobian (const typename Traits::DomainType& in,             // position
                      std::vector<typename Traits::JacobianType>& out) const // return value
    {
      // compute q1 jacobians
      std::vector<typename Traits::JacobianType> q1Jacs(size());
 
      // Loop over all shape functions
      for (size_t i=0; i<size(); i++) {
 
        // Loop over all coordinate directions
        for (int j=0; j<dim; j++) {
 
          // Initialize: the overall expression is a product
          // if j-th bit of i is set to -1, else 1
          q1Jacs[i][0][j] = (i & (1<<j)) ? 1 : -1;
 
          for (int k=0; k<dim; k++) {
 
            if (j!=k)
              // if k-th bit of i is set multiply with in[j], else with 1-in[j]
              q1Jacs[i][0][j] *= (i & (1<<k)) ? in[k] :  1-in[k];
 
          }
 
        }
 
      }
 
      // compute the dual jacobians by using that they are linear combinations of q1 functions
      out.resize(size());
      for (size_t i=0; i<size(); i++)
        out[i] = 0;
 
      for (size_t i=0; i<size(); i++)
        for (size_t j=0; j<size(); j++)
          out[i].axpy(coefficients_[i][j],q1Jacs[j]);
 
    }
 
    void partial (const std::array<unsigned int, dim>& order,
                  const typename Traits::DomainType& in,         // position
                  std::vector<typename Traits::RangeType>& out) const      // return value
    {
      auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
      if (totalOrder == 0) {
        evaluateFunction(in, out);
      } else {
        DUNE_THROW(NotImplemented, "Desired derivative order is not implemented");
      }
    }
 
    unsigned int order () const
    {
      return 1;
    }
 
  private:
    std::array<Dune::FieldVector<R, (1<<dim)> ,(1<<dim)> coefficients_;
  };
}
#endif