#include <deal.II/grid/tria.h>
#include <deal.II/dofs/dof_handler.h>
#include <deal.II/grid/grid_generator.h>
#include <deal.II/grid/tria_accessor.h>
#include <deal.II/grid/tria_iterator.h>
#include <deal.II/dofs/dof_accessor.h>
#include <deal.II/fe/fe_q.h>
#include <deal.II/dofs/dof_tools.h>
#include <deal.II/fe/fe_values.h>
#include <deal.II/base/quadrature_lib.h>
#include <deal.II/base/function.h>
#include <deal.II/numerics/vector_tools.h>
#include <deal.II/numerics/matrix_tools.h>
#include <deal.II/lac/vector.h>
#include <deal.II/lac/full_matrix.h>
#include <deal.II/lac/sparse_matrix.h>
#include <deal.II/lac/dynamic_sparsity_pattern.h>
#include <deal.II/lac/solver_cg.h>
#include <deal.II/lac/precondition.h>
#include <deal.II/numerics/data_out.h>
#include <fstream>
#include <iostream>

using namespace dealii;

class Step3
{
public:
  Step3 ();

  void run ();

private:
  void make_grid ( );
  void setup_system ();
  void assemble_system ();
  void solve ();
  void output_results () const;

  Triangulation<2>     triangulation;
  FE_Q<2>              fe;
  DoFHandler<2>        dof_handler;

  SparsityPattern      sparsity_pattern;
  SparseMatrix<double> system_matrix;

  Vector<double>       solution;
  Vector<double>       system_rhs;
};

Step3::Step3 ()
  :
  fe (1),
  dof_handler (triangulation)
{}

void Step3::make_grid ( )
{
  GridGenerator::hyper_cube ( triangulation, -1, 1 );
//
//  CHANGE: Only refine once to start with.
//
  triangulation.refine_global ( 1 );
//
//  End change.
//
  std::cout << "Number of active cells: "
            << triangulation.n_active_cells()
            << std::endl;
}
void Step3::setup_system ()
{
  dof_handler.distribute_dofs (fe);
  std::cout << "Number of degrees of freedom: "
            << dof_handler.n_dofs()
            << std::endl;

  DynamicSparsityPattern dsp(dof_handler.n_dofs());
  DoFTools::make_sparsity_pattern (dof_handler, dsp);
  sparsity_pattern.copy_from(dsp);

  system_matrix.reinit (sparsity_pattern);

  solution.reinit (dof_handler.n_dofs());
  system_rhs.reinit (dof_handler.n_dofs());
}

void Step3::assemble_system ()
{
  QGauss<2>  quadrature_formula(2);

  FEValues<2> fe_values (fe, quadrature_formula,
                         update_values | update_gradients | update_JxW_values);

  const unsigned int   dofs_per_cell = fe.dofs_per_cell;
  const unsigned int   n_q_points    = quadrature_formula.size();

  FullMatrix<double>   cell_matrix (dofs_per_cell, dofs_per_cell);
  Vector<double>       cell_rhs (dofs_per_cell);

  std::vector<types::global_dof_index> local_dof_indices (dofs_per_cell);

  DoFHandler<2>::active_cell_iterator
  cell = dof_handler.begin_active(),
  endc = dof_handler.end();
  for (; cell!=endc; ++cell)
    {
      fe_values.reinit (cell);

      cell_matrix = 0;
      cell_rhs = 0;

      for (unsigned int q_index=0; q_index<n_q_points; ++q_index)
        {
          for (unsigned int i=0; i<dofs_per_cell; ++i)
            for (unsigned int j=0; j<dofs_per_cell; ++j)
              cell_matrix(i,j) += (fe_values.shape_grad (i, q_index) *
                                   fe_values.shape_grad (j, q_index) *
                                   fe_values.JxW (q_index));

          for (unsigned int i=0; i<dofs_per_cell; ++i)
            cell_rhs(i) += (fe_values.shape_value (i, q_index) *
                            1 *
                            fe_values.JxW (q_index));
        }
      cell->get_dof_indices (local_dof_indices);

      for (unsigned int i=0; i<dofs_per_cell; ++i)
        for (unsigned int j=0; j<dofs_per_cell; ++j)
          system_matrix.add (local_dof_indices[i],
                             local_dof_indices[j],
                             cell_matrix(i,j));

      for (unsigned int i=0; i<dofs_per_cell; ++i)
        system_rhs(local_dof_indices[i]) += cell_rhs(i);
    }

  std::map<types::global_dof_index,double> boundary_values;
  VectorTools::interpolate_boundary_values (dof_handler,
                                            0,
                                            ZeroFunction<2>(),
                                            boundary_values);

  MatrixTools::apply_boundary_values (boundary_values,
                                      system_matrix,
                                      solution,
                                      system_rhs);
}

void Step3::solve ()
{
  SolverControl           solver_control (1000, 1e-12);
  SolverCG<>              solver (solver_control);
  solver.solve (system_matrix, solution, system_rhs,
                PreconditionIdentity());
}
void Step3::output_results () const
{
  DataOut<2> data_out;

  data_out.attach_dof_handler (dof_handler);
  data_out.add_data_vector (solution, "solution");

  data_out.build_patches ();
//
//  CHANGE TO PRINT SOLUTION AT (1/3,1/3).
//
  std::cout << "Solution at (1/3,1/3): "
            << VectorTools::point_value (dof_handler, solution, Point<2>(1./3, 1./3))
            << std::endl;
//
//  CHANGE TO PRINT SOLUTION AVERAGE.
//
  std::cout << "Mean value: "
            << VectorTools::compute_mean_value ( dof_handler, QGauss<2>(3), solution, 0 )
            << std::endl;
//
//  WE DON'T WANT ANY GRAPHICS OUTPUT.
//
//std::ofstream output_gpl ( "solution.gpl" );
//data_out.write_gnuplot ( output_gpl );
//std::ofstream output_vtk ( "solution.vtk" );
//data_out.write_vtk ( output_vtk );
//
//  END THESE CHANGES
//
}

void Step3::run ()
{
//
//  CHANGE TO DO 9 REFINEMENT STEPS, ONE AT A TIME.
//
  int refinements;

  for ( refinements = 1; refinements <= 9; refinements++ )
  {
    if ( refinements == 1 )
    {
      make_grid ( );
    }
    else
    {
      triangulation.refine_global ( 1 );
    }
  
    setup_system ();
    assemble_system ();
    solve ();
    output_results ();
  }
//
//  END THESE CHANGES.
//
}

int main ()
{
  deallog.depth_console (2);

  Step3 laplace_problem;
  laplace_problem.run ();

  return 0;
}