// -*- tab-width: 4; indent-tabs-mode: nil -*-
#ifndef DUNE_Q1_LOCALBASIS_HH
#define DUNE_Q1_LOCALBASIS_HH

#include <dune/common/fmatrix.hh>

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

namespace Dune 
{
  /**@ingroup LocalBasisImplementation
	 \brief Lagrange shape functions of order 1 on the reference cube.

	 Also known as \f$Q^1\f$.

	 \tparam D Type to represent the field in the domain.
	 \tparam R Type to represent the field in the range.
     \tparam dim Dimension of the cube

	 \nosubgrouping
  */
    template<class D, class R, int dim>
  class Q1LocalBasis
  {
  public:
	typedef LocalBasisTraits<D,dim,Dune::FieldVector<D,dim>,R,1,Dune::FieldVector<R,1>,
							   Dune::FieldMatrix<R,1,dim> > Traits;

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

    //! \brief Evaluate all shape functions
    inline void evaluateFunction (const typename Traits::DomainType& in,
                                  std::vector<typename Traits::RangeType>& out) const
    { 
        out.resize(size());

        for (size_t i=0; i<size(); i++) {

            out[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]
                out[i] *= (i & (1<<j)) ? in[j] :  1-in[j];

        }

    }

    //! \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());

        // 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
                out[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]
                        out[i][0][j] *= (i & (1<<k)) ? in[k] :  1-in[k];

                }

            }

        }

    }

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