tensor_product_polynomials.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2000 - 2018 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_tensor_product_polynomials_h
#define dealii_tensor_product_polynomials_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/utilities.h>

#include <vector>

DEAL_II_NAMESPACE_OPEN

template <int dim, typename PolynomialType=Polynomials::Polynomial<double> >
class TensorProductPolynomials
{
public:
  static const unsigned int dimension = dim;

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

  void output_indices(std::ostream &out) const;

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

  const std::vector<unsigned int> &get_numbering() const;

  const std::vector<unsigned int> &get_numbering_inverse() const;

  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;


protected:
  std::vector<PolynomialType> polynomials;

  unsigned int n_tensor_pols;

  std::vector<unsigned int> index_map;

  std::vector<unsigned int> index_map_inverse;

  // fix to avoid compiler warnings about zero length arrays
  void compute_index (const unsigned int i,
                      unsigned int       (&indices)[(dim>0?dim:1)]) const;
};



template <int dim>
class AnisotropicPolynomials
{
public:
  AnisotropicPolynomials (const std::vector<std::vector<Polynomials::Polynomial<double> > > &base_polynomials);

  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;

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

  const unsigned int n_tensor_pols;

  void compute_index (const unsigned int i,
                      unsigned int       (&indices)[dim]) const;

  static
  unsigned int
  get_n_tensor_pols (const std::vector<std::vector<Polynomials::Polynomial<double> > > &pols);
};

#ifndef DOXYGEN


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


template <int dim, typename PolynomialType>
template <class Pol>
inline
TensorProductPolynomials<dim,PolynomialType>::
TensorProductPolynomials(const std::vector<Pol> &pols)
  :
  polynomials (pols.begin(), pols.end()),
  n_tensor_pols(Utilities::fixed_power<dim>(pols.size())),
  index_map(n_tensor_pols),
  index_map_inverse(n_tensor_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_tensor_pols; ++i)
    {
      index_map[i]=i;
      index_map_inverse[i]=i;
    }
}



template <int dim, typename PolynomialType>
inline
unsigned int
TensorProductPolynomials<dim,PolynomialType>::n() const
{
  if (dim == 0)
    return numbers::invalid_unsigned_int;
  else
    return n_tensor_pols;
}



template <int dim, typename PolynomialType>
inline
const std::vector<unsigned int> &
TensorProductPolynomials<dim,PolynomialType>::get_numbering() const
{
  return index_map;
}


template <int dim, typename PolynomialType>
inline
const std::vector<unsigned int> &
TensorProductPolynomials<dim,PolynomialType>::get_numbering_inverse() const
{
  return index_map_inverse;
}

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

  double v [dim][5];
  {
    std::vector<double> tmp (5);
    for (unsigned int d=0; d<dim; ++d)
      {
        polynomials[indices[d]].value (p(d), tmp);
        v[d][0] = tmp[0];
        v[d][1] = tmp[1];
        v[d][2] = tmp[2];
        v[d][3] = tmp[3];
        v[d][4] = tmp[4];
      }
  }

  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;
    }
    }
}

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

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

  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;
    }
    }
}



#endif // DOXYGEN
DEAL_II_NAMESPACE_CLOSE

#endif