function.h

// ---------------------------------------------------------------------
//
// Copyright (C) 1998 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------

#ifndef dealii__function_h
#define dealii__function_h


#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/function_time.h>
#include <deal.II/base/subscriptor.h>
#include <deal.II/base/tensor.h>
#include <deal.II/base/symmetric_tensor.h>
#include <deal.II/base/point.h>
#include <deal.II/base/std_cxx11/function.h>

#include <vector>

DEAL_II_NAMESPACE_OPEN


template <typename number> class Vector;
template <int rank, int dim, typename Number> class TensorFunction;

template <int dim, typename Number=double>
class Function : public FunctionTime<Number>,
  public Subscriptor
{
public:
  static const unsigned int dimension = dim;

  const unsigned int n_components;

  Function (const unsigned int n_components = 1,
            const Number       initial_time = 0.0);

  virtual ~Function () = 0;

  Function &operator= (const Function &f);

  virtual Number value (const Point<dim>   &p,
                        const unsigned int  component = 0) const;

  virtual void vector_value (const Point<dim>   &p,
                             Vector<Number>     &values) const;

  virtual void value_list (const std::vector<Point<dim> > &points,
                           std::vector<Number>            &values,
                           const unsigned int              component = 0) const;

  virtual void vector_value_list (const std::vector<Point<dim> > &points,
                                  std::vector<Vector<Number> >   &values) const;

  virtual void vector_values (const std::vector<Point<dim> > &points,
                              std::vector<std::vector<Number> > &values) const;

  virtual Tensor<1,dim, Number> gradient (const Point<dim>   &p,
                                          const unsigned int  component = 0) const;

  virtual void vector_gradient (const Point<dim>            &p,
                                std::vector<Tensor<1,dim, Number> > &gradients) const;

  virtual void gradient_list (const std::vector<Point<dim> > &points,
                              std::vector<Tensor<1,dim, Number> >    &gradients,
                              const unsigned int              component = 0) const;

  virtual void vector_gradients (const std::vector<Point<dim> >            &points,
                                 std::vector<std::vector<Tensor<1,dim, Number> > > &gradients) const;

  virtual void vector_gradient_list (const std::vector<Point<dim> >            &points,
                                     std::vector<std::vector<Tensor<1,dim, Number> > > &gradients) const;

  virtual Number laplacian (const Point<dim>   &p,
                            const unsigned int  component = 0) const;

  virtual void vector_laplacian (const Point<dim>   &p,
                                 Vector<Number>     &values) const;

  virtual void laplacian_list (const std::vector<Point<dim> > &points,
                               std::vector<Number>            &values,
                               const unsigned int              component = 0) const;

  virtual void vector_laplacian_list (const std::vector<Point<dim> > &points,
                                      std::vector<Vector<Number> >   &values) const;

  virtual SymmetricTensor<2,dim,Number> hessian (const Point<dim>   &p,
                                                 const unsigned int          component = 0) const;

  virtual void vector_hessian (const Point<dim>                           &p,
                               std::vector<SymmetricTensor<2,dim,Number> > &values) const;

  virtual void hessian_list (const std::vector<Point<dim> >              &points,
                             std::vector<SymmetricTensor<2,dim,Number> > &values,
                             const unsigned int                          component = 0) const;

  virtual void vector_hessian_list (const std::vector<Point<dim> >                            &points,
                                    std::vector<std::vector<SymmetricTensor<2,dim,Number> > > &values) const;


  std::size_t memory_consumption () const;
};



template <int dim, typename Number=double>
class ZeroFunction : public Function<dim, Number>
{
public:
  ZeroFunction (const unsigned int n_components = 1);

  virtual ~ZeroFunction ();

  virtual Number value (const Point<dim>   &p,
                        const unsigned int  component) const;

  virtual void vector_value (const Point<dim> &p,
                             Vector<Number>   &return_value) const;

  virtual void value_list (const std::vector<Point<dim> > &points,
                           std::vector<Number>            &values,
                           const unsigned int              component = 0) const;

  virtual void vector_value_list (const std::vector<Point<dim> > &points,
                                  std::vector<Vector<Number> >   &values) const;

  virtual Tensor<1,dim, Number> gradient (const Point<dim> &p,
                                          const unsigned int component = 0) const;

  virtual void vector_gradient (const Point<dim>            &p,
                                std::vector<Tensor<1,dim, Number> > &gradients) const;

  virtual void gradient_list (const std::vector<Point<dim> > &points,
                              std::vector<Tensor<1,dim, Number> >    &gradients,
                              const unsigned int              component = 0) const;

  virtual void vector_gradient_list (const std::vector<Point<dim> >            &points,
                                     std::vector<std::vector<Tensor<1,dim, Number> > > &gradients) const;
};



template <int dim, typename Number=double>
class ConstantFunction : public ZeroFunction<dim, Number>
{
public:
  ConstantFunction (const Number       value,
                    const unsigned int n_components = 1);

  ConstantFunction (const std::vector<Number> &values);

  ConstantFunction (const Vector<Number> &values);

  ConstantFunction (const Number *begin_ptr, const unsigned int n_components);

  virtual ~ConstantFunction ();

  virtual Number value (const Point<dim>   &p,
                        const unsigned int  component) const;

  virtual void vector_value (const Point<dim> &p,
                             Vector<Number>   &return_value) const;

  virtual void value_list (const std::vector<Point<dim> > &points,
                           std::vector<Number>            &return_values,
                           const unsigned int              component = 0) const;

  virtual void vector_value_list (const std::vector<Point<dim> > &points,
                                  std::vector<Vector<Number> >   &return_values) const;

  std::size_t memory_consumption () const;

protected:
  std::vector<Number> function_value_vector;
};


template <int dim, typename Number=double>
class ComponentSelectFunction : public ConstantFunction<dim, Number>
{
public:
  ComponentSelectFunction (const unsigned int selected,
                           const Number       value,
                           const unsigned int n_components);

  ComponentSelectFunction (const unsigned int selected,
                           const unsigned int n_components);

  ComponentSelectFunction (const std::pair<unsigned int, unsigned int> &selected,
                           const unsigned int n_components);


  virtual void substitute_function_value_with (const ConstantFunction<dim, Number> &f);

  virtual void vector_value (const Point<dim> &p,
                             Vector<Number>   &return_value) const;

  virtual void vector_value_list (const std::vector<Point<dim> > &points,
                                  std::vector<Vector<Number> >   &values) const;

  std::size_t memory_consumption () const;

protected:
  const std::pair<unsigned int,unsigned int> selected_components;
};



template <int dim, typename Number=double>
class ScalarFunctionFromFunctionObject : public Function<dim, Number>
{
public:
  ScalarFunctionFromFunctionObject (const std_cxx11::function<Number (const Point<dim> &)> &function_object);

  virtual Number value (const Point<dim>   &p,
                        const unsigned int  component = 0) const;

private:
  const std_cxx11::function<Number (const Point<dim> &)> function_object;
};



template <int dim, typename Number=double>
class VectorFunctionFromScalarFunctionObject : public Function<dim, Number>
{
public:
  VectorFunctionFromScalarFunctionObject (const std_cxx11::function<Number (const Point<dim> &)> &function_object,
                                          const unsigned int selected_component,
                                          const unsigned int n_components);

  virtual Number value (const Point<dim>   &p,
                        const unsigned int  component = 0) const;

  virtual void vector_value (const Point<dim>   &p,
                             Vector<Number>     &values) const;

private:
  const std_cxx11::function<Number (const Point<dim> &)> function_object;

  const unsigned int selected_component;
};


template <int dim, typename Number=double>
class VectorFunctionFromTensorFunction : public Function<dim, Number>
{
public:
  VectorFunctionFromTensorFunction (const TensorFunction<1,dim, Number> &tensor_function,
                                    const unsigned int selected_component=0,
                                    const unsigned int n_components=dim);

  virtual ~VectorFunctionFromTensorFunction();

  virtual Number value (const Point<dim> &p,
                        const unsigned int component = 0) const;

  virtual void vector_value (const Point<dim> &p,
                             Vector<Number>   &values) const;

  virtual void vector_value_list (const std::vector<Point<dim> > &points,
                                  std::vector<Vector<Number> >   &value_list) const;

private:
  const TensorFunction<1,dim,Number> &tensor_function;

  const unsigned int selected_component;
};


DEAL_II_NAMESPACE_CLOSE

#endif