// -*- tab-width: 4; indent-tabs-mode: nil -*-
#ifndef DUNE_P1_LOCALBASIS_HH
#define DUNE_P1_LOCALBASIS_HH

#include <dune/common/fmatrix.hh>

#include <dune/localfunctions/common/localbasis.hh>

namespace Dune
{
  /**@ingroup LocalBasisImplementation
	 \brief Linear Lagrange shape functions on the simplex.

	 Defines the linear shape functions on the simplex.

	 \tparam D Type to represent the field in the domain.
	 \tparam R Type to represent the field in the range.
     \tparam dim The dimension of the simplex

	 \nosubgrouping
  */
    template<class D, class R, int dim>
  class P1LocalBasis 
  {
  public:
	//! \brief export type traits for function signature
    typedef LocalBasisTraits<D,dim,Dune::FieldVector<D,dim>,R,1,Dune::FieldVector<R,1>,
							   Dune::FieldMatrix<R,1,dim>, 2> Traits;

    //! \brief number of shape functions
    unsigned int size () const
    {
      return dim+1;
    }

    //! \brief Evaluate all shape functions
    inline void evaluateFunction (const typename Traits::DomainType& in,
                                  std::vector<typename Traits::RangeType>& out) const
    { 
        out.resize(size());
        out[0] = 1.0;
        for (size_t i=0; i<dim; i++) {
            out[0]  -= in[i];
            out[i+1] = in[i];
        }
    }

    //! \brief Evaluate Jacobian of all shape functions
    inline void 
    evaluateJacobian (const typename Traits::DomainType& in,         // position
                      std::vector<typename Traits::JacobianType>& out) const      // return value
    {  
        out.resize(size());

        for (int i=0; i<dim; i++)
            out[0][0][i] = -1;

        for (int i=0; i<dim; i++)
            for (int j=0; j<dim; j++)
                out[i+1][0][j] = (i==j);

    }

    //! \brief Evaluate all shape functions
    template<unsigned int k>
    inline void evaluate (const typename Dune::array<int,k>& directions,
                                  const typename Traits::DomainType& in,
                                  std::vector<typename Traits::RangeType>& out) const
    {
        if (k==0)
            evaluateFunction(in, out);
        else if (k==1)
        {
            out.resize(size());

            out[0] = -1;
            for (int i=0; i<dim; i++)
                out[i+1] = (i==directions[0]);
        }
        else if (k==2)
        {
            out.resize(size());

            for (int i=0; i<dim+1; i++)
                out[i] = 0;
        }
    }

    //! \brief Polynomial order of the shape functions
    unsigned int order () const
    {
      return 1;
    }
  };
}
#endif
