DiscreteFunction.hpp

#pragma once

#include <vector>

#include <dune/common/std/optional.hh>
#include <dune/functions/common/defaultderivativetraits.hh>
#include <dune/functions/functionspacebases/defaultnodetorangemap.hh>
#include <dune/functions/functionspacebases/flatvectorview.hh>
#include <dune/functions/gridfunctions/gridviewentityset.hh>
#include <dune/typetree/childextraction.hh>

#include <amdis/common/Tags.hpp>
#include <amdis/typetree/FiniteElementType.hpp>
#include <amdis/typetree/RangeType.hpp>
#include <amdis/typetree/TreePath.hpp>

namespace AMDiS
{
  /// \class DiscreteFunction
  /// \brief A view on a subspace of a \ref DOFVector
  /**
  * \ingroup GridFunctions
  *
  * \tparam Coeff     Const or mutable coefficient type of the DOFVector
  * \tparam GB        Thy type of the global basis
  * \tparam TreePath  A realization of \ref Dune::TypeTree::HybridTreePath
  *
  * **Requirements:**
  * - GB models \ref Dune::Functions::Concept::GlobalBasis
  **/
  template <class Coeff, class GB, class TreePath = Dune::TypeTree::HybridTreePath<>>
  class DiscreteFunction;

#if DUNE_HAVE_CXX_CLASS_TEMPLATE_ARGUMENT_DEDUCTION
  template <class Coeff, class GB, class TreePath = RootTreePath>
  DiscreteFunction(Coeff&, GB const&, TreePath = {})
    -> DiscreteFunction<Coeff, GB, TreePath_t<TreePath>>;
#endif

  /// A Generator for a mutable \ref DiscreteFunction
  template <class Coeff, class GB, class Path = RootTreePath,
    class = void_t<decltype(std::declval<GB>().localView())> >
  auto makeDiscreteFunction(Coeff& coefficients, GB const& basis, Path const& path = {})
  {
    return DiscreteFunction<Coeff, GB, TreePath_t<Path>>{coefficients, basis, path};
  }


  /// A mutable view on the subspace of a DOFVector, \relates DiscreteFunction
  template <class Coeff, class GB, class TreePath>
  class DiscreteFunction
      : public DiscreteFunction<Coeff const,GB,TreePath>
  {
    using Self = DiscreteFunction<Coeff,GB,TreePath>;
    using Super = DiscreteFunction<Coeff const,GB,TreePath>;

    using Coefficients = Coeff;
    using GlobalBasis = GB;
    using ValueType = typename Coeff::value_type;

  public:
    /// Constructor. Stores a pointer to the mutable `dofvector`.
    template <class Path = TreePath>
    DiscreteFunction(Coefficients& dofVector, GlobalBasis const& basis, Path const& path = {})
      : Super(dofVector, basis, path)
      , mutableCoeff_(&dofVector)
    {}

  public:
    /// \brief Interpolation of GridFunction to DOFVector, assuming that there is no
    /// reference to this DOFVector in the expression.
    /**
     * **Example:**
     * ```
     * auto v = makeDiscreteFunction(prob.solutionVector(),0);
     * v.interpolate_noalias([](auto const& x) { return x[0]; });
     * ```
     **/
    template <class Expr, class Tag = tag::average>
    void interpolate_noalias(Expr&& expr, Tag strategy = {});

    /// \brief Interpolation of GridFunction to DOFVector
    /**
     * **Example:**
     * ```
     * auto v = makeDiscreteFunction(prob.solutionVector(),0);
     * v.interpolate(v + [](auto const& x) { return x[0]; });
     * ```
     * Allows to have a reference to the DOFVector in the expression, e.g. as
     * \ref DiscreteFunction or \ref gradientAtQP() of a DiscreteFunction.
     **/
    template <class Expr, class Tag = tag::average>
    void interpolate(Expr&& expr, Tag strategy = {});

    /// \brief Interpolation of GridFunction to DOFVector, alias to \ref interpolate()
    template <class Expr>
    Self& operator<<(Expr&& expr)
    {
      interpolate(FWD(expr));
      return *this;
    }

    /// \brief interpolate `(*this) + expr` to DOFVector
    template <class Expr>
    Self& operator+=(Expr&& expr)
    {
      interpolate((*this) + expr);
      return *this;
    }

    /// \brief interpolate `(*this) - expr` to DOFVector
    template <class Expr>
    Self& operator-=(Expr&& expr)
    {
      interpolate((*this) - expr);
      return *this;
    }

    /// Return the mutable DOFVector
    Coefficients& coefficients()
    {
      return *mutableCoeff_;
    }

    /// Return the const DOFVector
    using Super::coefficients;

    template <class Path = RootTreePath>
    auto child(Path const& path = {})
    {
      auto tp = cat(this->treePath_, makeTreePath(path));
      return makeDiscreteFunction(*mutableCoeff_, this->basis(), tp);
    }

    using Super::child;

  protected:
    Coefficients* mutableCoeff_;
  };

  /// A Const DiscreteFunction
  template <class Coeff, class GB, class TreePath>
  class DiscreteFunction<Coeff const,GB,TreePath>
  {
  private:
    using Coefficients = std::remove_const_t<Coeff>;
    using GlobalBasis = GB;
    using ValueType = typename Coefficients::value_type;

    using Tree = typename GlobalBasis::LocalView::Tree;
    using SubTree = typename Dune::TypeTree::ChildForTreePath<Tree, TreePath>;
    using NodeToRangeEntry = Dune::Functions::DefaultNodeToRangeMap<SubTree>;
    using GridView = typename GlobalBasis::GridView;

  public:
    /// Set of entities the DiscreteFunction is defined on
    using EntitySet = Dune::Functions::GridViewEntitySet<GridView, 0>;

    /// Global coordinates of the EntitySet
    using Domain = typename EntitySet::GlobalCoordinate;

    /// Range type of this DiscreteFunction
    using Range = RangeType_t<SubTree,ValueType>;

    /// \brief This GridFunction has no derivative function, it can be created
    /// by \ref DiscreteGridFunction.
    enum { hasDerivative = false };

  public:
    /// A LocalFunction representing the derivative of the DOFVector on a bound element
    template <class Type>
    class DerivativeLocalFunctionBase;

    class GradientLocalFunction;
    class PartialLocalFunction;
    class DivergenceLocalFunction;

    /// A LocalFunction representing the value the DOFVector on a bound element
    class LocalFunction;

  public:
    /// Constructor. Stores a pointer to the dofVector and a copy of the treePath.
    template <class Path = TreePath>
    DiscreteFunction(Coefficients const& coefficients, GlobalBasis const& basis, Path const& path = {})
      : coefficients_(&coefficients)
      , basis_(&basis)
      , treePath_(makeTreePath(path))
      , entitySet_(basis_->gridView())
      , nodeToRangeEntry_(Dune::Functions::makeDefaultNodeToRangeMap(*basis_, treePath_))
    {}

    /// \brief Evaluate DiscreteFunction in global coordinates. NOTE: expensive
    Range operator()(Domain const& x) const;

    /// \brief Create a local function for this view on the DOFVector. \relates LocalFunction
    LocalFunction makeLocalFunction() const
    {
      return LocalFunction{*this};
    }

    /// \brief Return a \ref Dune::Functions::GridViewEntitySet
    EntitySet const& entitySet() const
    {
      return entitySet_;
    }

    /// \brief Return global basis bound to the DOFVector
    GlobalBasis const& basis() const
    {
      return *basis_;
    }

    /// \brief Return treePath associated with this discrete function
    TreePath const& treePath() const
    {
      return treePath_;
    }

    /// \brief Return const coefficient vector
    Coefficients const& coefficients() const
    {
      return *coefficients_;
    }

    template <class Path = RootTreePath>
    auto child(Path const& path = {}) const
    {
      auto tp = cat(this->treePath_, makeTreePath(path));
      return makeDiscreteFunction(*coefficients_, *basis_, tp);
    }

  protected:
    Coefficients const* coefficients_;
    GlobalBasis const* basis_;
    TreePath treePath_;
    EntitySet entitySet_;
    NodeToRangeEntry nodeToRangeEntry_;
  };

} // end namespace AMDiS

#include "DiscreteLocalFunction.inc.hpp"
#include "DiscreteFunction.inc.hpp"