// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:

#ifndef DUNE_LOCALFUNCTIONS_COMMON_LOCALTOGLOBALADAPTORS_HH
#define DUNE_LOCALFUNCTIONS_COMMON_LOCALTOGLOBALADAPTORS_HH

#include <cstddef>
#include <vector>

#include <dune/common/fmatrix.hh>
#include <dune/common/fvector.hh>
#include <dune/common/typetraits.hh>

#include <dune/geometry/type.hh>

namespace Dune {

  //! Traits class for local-to-global basis adaptors
  /**
   * \tparam LocalBasisTraits Traits class of the LocalBasis to be adapted.
   * \tparam dimDomainGlobal_ Dimension of the global coordinates,
   *                          i.e. Geometry::coorddimension, if the global
   *                          coordinates are determined by a Geometry.
   *
   * \implements BasisInterface::Traits
   */
  template<class LocalBasisTraits, std::size_t dimDomainGlobal_>
  struct LocalToGlobalBasisAdaptorTraits {
    typedef typename LocalBasisTraits::DomainFieldType DomainField;
    static const std::size_t dimDomainLocal = LocalBasisTraits::dimDomain;
    static const std::size_t dimDomainGlobal = dimDomainGlobal_;
    typedef typename LocalBasisTraits::DomainType DomainLocal;
    typedef FieldVector<DomainField, dimDomainGlobal> DomainGlobal;

    typedef typename LocalBasisTraits::RangeFieldType RangeField;
    static const std::size_t dimRange = LocalBasisTraits::dimRange;
    typedef typename LocalBasisTraits::RangeType Range;

    typedef FieldMatrix<RangeField, dimRange, dimDomainGlobal> Jacobian;

    static const std::size_t diffOrder = LocalBasisTraits::diffOrder;
  };

  //! Convert a simple scalar local basis into a global basis
  /**
   * The local basis must be scalar, i.e. LocalBasis::Traits::dimRange must be
   * 1.  It's values are not transformed.
   *
   * For scalar function \f$f\f$, the gradient is equivalent to the transposed
   * Jacobian \f$\nabla f|_x = J_f^T(x)\f$.  The Jacobian is thus transformed
   * using
   * \f[
   *   \nabla f|_{\mu(\hat x)} =
   *       \hat J_\mu^{-T}(\hat x) \cdot \hat\nabla\hat f|_{\hat x}
   * \f]
   * Here the hat \f$\hat{\phantom x}\f$ denotes local quantities and
   * \f$\mu\f$ denotes the local-to-global map of the geometry.
   *
   * \tparam LocalBasis Type of the local basis to adapt.
   * \tparam Geometry   Type of the local-to-global transformation.
   *
   * \implements BasisInterface
   */
  template<class LocalBasis, class Geometry>
  class ScalarLocalToGlobalBasisAdaptor {
    static_assert(LocalBasis::Traits::dimRange == 1,
                  "ScalarLocalToGlobalBasisAdaptor can only wrap a "
                  "scalar local basis.");
    static_assert((is_same<typename LocalBasis::Traits::DomainFieldType,
                           typename Geometry::ctype>::value),
                   "ScalarLocalToGlobalBasisAdaptor: LocalBasis must use "
                   "the same ctype as Geometry");
    static_assert
      ( static_cast<std::size_t>(LocalBasis::Traits::dimDomain) ==
      static_cast<std::size_t>(Geometry::mydimension),
      "ScalarLocalToGlobalBasisAdaptor: LocalBasis domain dimension must "
      "match local dimension of Geometry");

    const LocalBasis& localBasis;
    Geometry geometry;

  public:
    typedef LocalToGlobalBasisAdaptorTraits<typename LocalBasis::Traits,
        Geometry::coorddimension> Traits;

    //! construct a ScalarLocalToGlobalBasisAdaptor
    /**
     * \param localBasis_ The local basis object to adapt.
     * \param geometry_   The geometry object to use for adaption.
     *
     * \note This class stores the references passed here.  Any use of this
     *       class after these references have become invalid results in
     *       undefined behaviour.  The exception is that the destructor of
     *       this class may still be called.
     */
    ScalarLocalToGlobalBasisAdaptor(const LocalBasis& localBasis_,
                                    const Geometry& geometry_) :
      localBasis(localBasis_), geometry(geometry_)
    { }

    std::size_t size() const { return localBasis.size(); }
    //! return maximum polynomial order of the base function
    /**
     * This is to determine the required quadrature order.  For an affine
     * geometry this is the same order as for the local basis.  For other
     * geometries this returns the order of the local basis plus the global
     * dimension minus 1.  The assumtion for non-affine geometries is that
     * they are still multi-linear.
     */
    std::size_t order() const {
      if(geometry.affine())
        // affine linear
        return localBasis.order();
      else
        // assume at most order dim
        return localBasis.order() + Traits::dimDomainGlobal - 1;
    }

    void evaluateFunction(const typename Traits::DomainLocal& in,
                          std::vector<typename Traits::Range>& out) const
    {
      localBasis.evaluateFunction(in, out);
    }

    void evaluateJacobian(const typename Traits::DomainLocal& in,
                          std::vector<typename Traits::Jacobian>& out) const
    {
      std::vector<typename LocalBasis::Traits::JacobianType>
      localJacobian(size());
      localBasis.evaluateJacobian(in, localJacobian);

      const typename Geometry::JacobianInverseTransposed &geoJacobian =
        geometry.jacobianInverseTransposed(in);

      out.resize(size());
      for(std::size_t i = 0; i < size(); ++i)
        geoJacobian.mv(localJacobian[i][0], out[i][0]);
    }
  };

  //! Convert a local interpolation into a global interpolation
  /**
   * \tparam LocalInterpolation Type of the local interpolation to adapt.
   * \tparam Traits_            Traits of the corresposnding basis class.
   *
   * \implements InterpolationInterface
   */
  template<class LocalInterpolation, class Traits_>
  class LocalToGlobalInterpolationAdaptor {
    const LocalInterpolation& localInterpolation;

  public:
    typedef Traits_ Traits;

    //! construct a LocalToGlobalInterpolationAdaptor
    /**
     * \param localInterpolation_ The local interpolation object to adapt.
     *
     * \note This class stores the reference to the local interpolation object
     *       passed here.  Any use of this class after the reference have
     *       become invalid results in undefined behaviour.  The exception is
     *       that the destructor of this class may still be called.
     */
    LocalToGlobalInterpolationAdaptor
      ( const LocalInterpolation& localInterpolation_) :
      localInterpolation(localInterpolation_)
    { }

    template<class Function, class Coeff>
    void interpolate(const Function& function, std::vector<Coeff>& out) const
    { localInterpolation.interpolate(function, out); }
  };

  //! \brief Convert a simple scalar local finite element into a global finite
  //!        element
  /**
   * The local finite elememt must be scalar,
   * i.e. LocalBasis::Traits::dimRange must be 1.  It's values are not
   * transformed, but the Jacobian is (see ScalarLocalToGlobalBasisAdaptor).
   *
   * \tparam LocalFiniteElement Type of the local finite element to adapt.
   * \tparam Geometry           Type of the local-to-global transformation.
   *
   * \implements FiniteElementInterface
   */
  template<class LocalFiniteElement, class Geometry>
  struct ScalarLocalToGlobalFiniteElementAdaptor {
    /**
     * \implements FiniteElementInterface::Traits
     */
    struct Traits {
      typedef ScalarLocalToGlobalBasisAdaptor<typename LocalFiniteElement::
          Traits::LocalBasisType, Geometry> Basis;
      typedef LocalToGlobalInterpolationAdaptor<typename LocalFiniteElement::
          Traits::LocalInterpolationType, typename Basis::Traits>
      Interpolation;
      typedef typename LocalFiniteElement::Traits::LocalCoefficientsType
      Coefficients;
    };

  private:
    const LocalFiniteElement &localFE;
    typename Traits::Basis basis_;
    typename Traits::Interpolation interpolation_;

  public:
    //! construct a ScalarLocalToGlobalFiniteElementAdaptor
    /**
     * \param localFE_  The local finite element object to adapt.
     * \param geometry  The geometry object to use for adaption.
     *
     * \note This class stores the references passed here.  Any use of this
     *       class after these references have become invalid results in
     *       undefined behaviour.  The exception is that the destructor of
     *       this class may still be called.
     */
    ScalarLocalToGlobalFiniteElementAdaptor
      ( const LocalFiniteElement& localFE_, const Geometry &geometry) :
      localFE(localFE_),
      basis_(localFE.localBasis(), geometry),
      interpolation_(localFE.localInterpolation())
    { }

    const typename Traits::Basis& basis() const { return basis_; }
    const typename Traits::Interpolation& interpolation() const
    { return interpolation_; }
    const typename Traits::Coefficients& coefficients() const
    { return localFE.localCoefficients(); }
    GeometryType type() const { return localFE.type(); }
  };

  //! Factory for ScalarLocalToGlobalFiniteElementAdaptor objects
  /**
   * Constructs ScalarLocalToGlobalFiniteElementAdaptor objects given a local
   * finite element object and a geometry.  This class is restricted to one
   * base variant of the local finite element.
   *
   * \tparam LocalFiniteElement Type of the local finite element to adapt.
   * \tparam Geometry           Type of the local-to-global transformation.
   *
   * \implements FiniteElementFactoryInterface
   */
  template<class LocalFiniteElement, class Geometry>
  class ScalarLocalToGlobalFiniteElementAdaptorFactory {
    const LocalFiniteElement& localFE;

  public:
    typedef ScalarLocalToGlobalFiniteElementAdaptor<LocalFiniteElement,
        Geometry> FiniteElement;

    //! construct a ScalarLocalToGlobalFiniteElementAdaptorFactory
    /**
     * \param localFE_ The local finite element object to adapt.
     *
     * \note This class stores the reference to the local finite element
     *       object passed here.  Any use of this class after this reference
     *       has become invalid results in undefined behaviour.  The exception
     *       is that the destructor of this class may still be called.
     */
    ScalarLocalToGlobalFiniteElementAdaptorFactory
      (const LocalFiniteElement &localFE_) : localFE(localFE_) {}

    //! construct ScalarLocalToGlobalFiniteElementAdaptor
    /**
     * \param geometry The geometry object to use for adaption.
     *
     * \note The returned object stores the reference to the geometry passed
     *       here as well as references to internal data of this factory.  Any
     *       use of the returned value after the geometry reference or the
     *       factory object was become invalid results in undefined behaviour.
     *       The exception is that the destructor of the returned value may
     *       still be called.
     */
    const FiniteElement make(const Geometry& geometry) {
      return FiniteElement(localFE, geometry);
    }
  };

} // namespace Dune

#endif // DUNE_LOCALFUNCTIONS_COMMON_LOCALTOGLOBALADAPTORS_HH
