polynomial_space.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2002 - 2017 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_polynomial_space_h
#define dealii_polynomial_space_h


#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/tensor.h>
#include <deal.II/base/point.h>
#include <deal.II/base/polynomial.h>
#include <deal.II/base/smartpointer.h>

#include <vector>

DEAL_II_NAMESPACE_OPEN

template <int dim>
class PolynomialSpace
{
public:
  static const unsigned int dimension = dim;

  template <class Pol>
  PolynomialSpace (const std::vector<Pol> &pols);

  template <class StreamType>
  void output_indices(StreamType &out) const;

  void set_numbering(const std::vector<unsigned int> &renumber);

  void compute (const Point<dim>            &unit_point,
                std::vector<double>         &values,
                std::vector<Tensor<1,dim> > &grads,
                std::vector<Tensor<2,dim> > &grad_grads,
                std::vector<Tensor<3,dim> > &third_derivatives,
                std::vector<Tensor<4,dim> > &fourth_derivatives) const;

  double compute_value (const unsigned int i,
                        const Point<dim> &p) const;

  template <int order>
  Tensor<order,dim> compute_derivative (const unsigned int i,
                                        const Point<dim> &p) const;

  Tensor<1,dim> compute_grad (const unsigned int i,
                              const Point<dim> &p) const;

  Tensor<2,dim> compute_grad_grad (const unsigned int i,
                                   const Point<dim> &p) const;

  unsigned int n () const;

  unsigned int degree () const;

  static unsigned int compute_n_pols (const unsigned int n);

protected:

  void compute_index (const unsigned int n,
                      unsigned int      (&index)[dim>0?dim:1]) const;

private:
  const std::vector<Polynomials::Polynomial<double> > polynomials;

  const unsigned int n_pols;

  std::vector<unsigned int> index_map;

  std::vector<unsigned int> index_map_inverse;
};


/* -------------- declaration of explicit specializations --- */

template <>
void PolynomialSpace<1>::compute_index(const unsigned int n,
                                       unsigned int      (&index)[1]) const;
template <>
void PolynomialSpace<2>::compute_index(const unsigned int n,
                                       unsigned int      (&index)[2]) const;
template <>
void PolynomialSpace<3>::compute_index(const unsigned int n,
                                       unsigned int      (&index)[3]) const;



/* -------------- inline and template functions ------------- */

template <int dim>
template <class Pol>
PolynomialSpace<dim>::PolynomialSpace (const std::vector<Pol> &pols)
  :
  polynomials (pols.begin(), pols.end()),
  n_pols (compute_n_pols(polynomials.size())),
  index_map(n_pols),
  index_map_inverse(n_pols)
{
  // per default set this index map
  // to identity. This map can be
  // changed by the user through the
  // set_numbering function
  for (unsigned int i=0; i<n_pols; ++i)
    {
      index_map[i]=i;
      index_map_inverse[i]=i;
    }
}


template <int dim>
inline
unsigned int
PolynomialSpace<dim>::n() const
{
  return n_pols;
}



template <int dim>
inline
unsigned int
PolynomialSpace<dim>::degree() const
{
  return polynomials.size();
}


template <int dim>
template <class StreamType>
void
PolynomialSpace<dim>::output_indices(StreamType &out) const
{
  unsigned int ix[dim];
  for (unsigned int i=0; i<n_pols; ++i)
    {
      compute_index(i,ix);
      out << i << "\t";
      for (unsigned int d=0; d<dim; ++d)
        out << ix[d] << " ";
      out << std::endl;
    }
}

template <int dim>
template <int order>
Tensor<order,dim>
PolynomialSpace<dim>::compute_derivative (const unsigned int i,
                                          const Point<dim> &p) const
{
  unsigned int indices[dim];
  compute_index (i, indices);

  double v [dim][order+1];
  {
    std::vector<double> tmp (order+1);
    for (unsigned int d=0; d<dim; ++d)
      {
        polynomials[indices[d]].value (p(d), tmp);
        for (unsigned int j=0; j<order+1; ++j)
          v[d][j] = tmp[j];
      }
  }

  Tensor<order,dim> derivative;
  switch (order)
    {
    case 1:
    {
      Tensor<1,dim> &derivative_1 = *reinterpret_cast<Tensor<1,dim>*>(&derivative);
      for (unsigned int d=0; d<dim; ++d)
        {
          derivative_1[d] = 1.;
          for (unsigned int x=0; x<dim; ++x)
            {
              unsigned int x_order=0;
              if (d==x) ++x_order;

              derivative_1[d] *= v[x][x_order];
            }
        }

      return derivative;
    }
    case 2:
    {
      Tensor<2,dim> &derivative_2 = *reinterpret_cast<Tensor<2,dim>*>(&derivative);
      for (unsigned int d1=0; d1<dim; ++d1)
        for (unsigned int d2=0; d2<dim; ++d2)
          {
            derivative_2[d1][d2] = 1.;
            for (unsigned int x=0; x<dim; ++x)
              {
                unsigned int x_order=0;
                if (d1==x) ++x_order;
                if (d2==x) ++x_order;

                derivative_2[d1][d2] *= v[x][x_order];
              }
          }

      return derivative;
    }
    case 3:
    {
      Tensor<3,dim> &derivative_3 = *reinterpret_cast<Tensor<3,dim>*>(&derivative);
      for (unsigned int d1=0; d1<dim; ++d1)
        for (unsigned int d2=0; d2<dim; ++d2)
          for (unsigned int d3=0; d3<dim; ++d3)
            {
              derivative_3[d1][d2][d3] = 1.;
              for (unsigned int x=0; x<dim; ++x)
                {
                  unsigned int x_order=0;
                  if (d1==x) ++x_order;
                  if (d2==x) ++x_order;
                  if (d3==x) ++x_order;

                  derivative_3[d1][d2][d3] *= v[x][x_order];
                }
            }

      return derivative;
    }
    case 4:
    {
      Tensor<4,dim> &derivative_4 = *reinterpret_cast<Tensor<4,dim>*>(&derivative);
      for (unsigned int d1=0; d1<dim; ++d1)
        for (unsigned int d2=0; d2<dim; ++d2)
          for (unsigned int d3=0; d3<dim; ++d3)
            for (unsigned int d4=0; d4<dim; ++d4)
              {
                derivative_4[d1][d2][d3][d4] = 1.;
                for (unsigned int x=0; x<dim; ++x)
                  {
                    unsigned int x_order=0;
                    if (d1==x) ++x_order;
                    if (d2==x) ++x_order;
                    if (d3==x) ++x_order;
                    if (d4==x) ++x_order;

                    derivative_4[d1][d2][d3][d4] *= v[x][x_order];
                  }
              }

      return derivative;
    }
    default:
    {
      Assert (false, ExcNotImplemented());
      return derivative;
    }
    }

}


DEAL_II_NAMESPACE_CLOSE

#endif