// @sect3{Functions.cc}
// In this file we keep right hand side function, Dirichlet boundary
// conditions and solution to our Poisson equation problem.  Since
// these classes and functions have been discussed extensively in
// the deal.ii tutorials we won't discuss them any further.
#include <deal.II/base/function.h>
#include <deal.II/base/tensor_function.h>
#include <deal.II/lac/vector.h>
#include <cmath>

using namespace dealii;

template <int dim>
class RightHandSide : public Function<dim>
{
public:
  RightHandSide() : Function<dim>(1)
  {}

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

template <int dim>
class DirichletBoundaryValues : public Function<dim>
{
public:
  DirichletBoundaryValues() : Function<dim>(1)
  {}

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

template<int dim>
class TrueSolution : public Function<dim>
{
public:
  TrueSolution() : Function<dim>(dim+1)
  {}

  virtual void vector_value(const Point<dim> &p,
                            Vector<double> &valuess) const;
};

template <int dim>
double
RightHandSide<dim>::
value(const Point<dim> &p,
      const unsigned int ) const
{
  const double x = p[0];
  const double y = p[1];
  return 4*M_PI*M_PI*(cos(2*M_PI*y) - sin(2*M_PI*x));

}

template <int dim>
double
DirichletBoundaryValues<dim>::
value(const Point<dim> &p,
      const unsigned int ) const
{
  const double x = p[0];
  const double y = p[1];
  return cos(2*M_PI*y) -sin(2*M_PI*x) - x;
}


template <int dim>
void
TrueSolution<dim>::
vector_value(const Point<dim> &p,
             Vector<double> &values) const
{
  Assert(values.size() == dim+1,
         ExcDimensionMismatch(values.size(), dim+1) );

  double x = p[0];
  double y = p[1];

  values(0) = 1 + 2*M_PI*cos(2*M_PI*x);
  values(1) = 2*M_PI*sin(2*M_PI*y);

  values(2) = cos(2*M_PI*y) - sin(2*M_PI*x) - x;
}