fe_series.h

// ---------------------------------------------------------------------
//
// Copyright (C) 2016 - 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_fe_series_H
#define dealii_fe_series_H



#include <deal.II/base/config.h>
#include <deal.II/base/subscriptor.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/base/table.h>
#include <deal.II/base/table_indices.h>
#include <deal.II/base/tensor.h>
#include <deal.II/hp/fe_collection.h>
#include <deal.II/hp/q_collection.h>
#include <deal.II/lac/full_matrix.h>
#include <deal.II/lac/vector.h>
#include <deal.II/numerics/vector_tools.h>

#include <vector>
#include <string>
#include <memory>


DEAL_II_NAMESPACE_OPEN




namespace FESeries
{
  template <int dim>
  class Fourier : public Subscriptor
  {
  public:
    Fourier(const unsigned int size_in_each_direction,
            const hp::FECollection<dim> &fe_collection,
            const hp::QCollection<dim> &q_collection);

    void calculate(const ::Vector<double>     &local_dof_values,
                   const unsigned int                cell_active_fe_index,
                   Table<dim,std::complex<double> > &fourier_coefficients);

  private:
    SmartPointer<const hp::FECollection<dim> > fe_collection;

    SmartPointer<const hp::QCollection<dim> >  q_collection;

    void ensure_existence(const unsigned int fe_index);

    Table<dim, Tensor<1,dim> > k_vectors;

    std::vector<FullMatrix<std::complex<double> > > fourier_transform_matrices;

    std::vector<std::complex<double> > unrolled_coefficients;

  };

  template <int dim>
  class Legendre : public Subscriptor
  {
  public:
    Legendre(const unsigned int size_in_each_direction,
             const hp::FECollection<dim> &fe_collection,
             const hp::QCollection<dim> &q_collection);

    void calculate(const ::Vector<double> &local_dof_values,
                   const unsigned int            cell_active_fe_index,
                   Table<dim,double>            &legendre_coefficients);

  private:
    const unsigned int N;

    SmartPointer<const hp::FECollection<dim> > fe_collection;

    SmartPointer<const hp::QCollection<dim> > q_collection;

    void ensure_existence(const unsigned int fe_index);

    std::vector<FullMatrix<double> > legendre_transform_matrices;

    std::vector<double> unrolled_coefficients;

  };


  template <int dim, typename T>
  std::pair<std::vector<unsigned int>,std::vector<double> >
  process_coefficients(const Table<dim,T> &coefficients,
                       const std::function<std::pair<bool,unsigned int>(const TableIndices<dim> &)> &predicate,
                       const VectorTools::NormType norm);



  std::pair<double,double> linear_regression(const std::vector<double> &x,
                                             const std::vector<double> &y);

}

#ifndef DOXYGEN

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

namespace
{
  template <int dim,typename T>
  void fill_map_index(const Table<dim,T> &coefficients,
                      const TableIndices<dim> &ind,
                      const std::function<std::pair<bool,unsigned int>(const TableIndices<dim> &)> &predicate,
                      std::map<unsigned int, std::vector<T> > &pred_to_values)
  {
    const std::pair<bool,unsigned int> pred_pair = predicate(ind);
    // don't add a value if predicate is false
    if (pred_pair.first == false)
      return;

    const unsigned int &pred_value = pred_pair.second;
    const T &coeff_value = coefficients(ind);
    // If pred_value is not in the pred_to_values map, the element will be created.
    // Otherwise a reference to the existing element is returned.
    pred_to_values[pred_value].push_back(coeff_value);
  }

  template <typename T>
  void fill_map(const Table<1,T> &coefficients,
                const std::function<std::pair<bool,unsigned int>(const TableIndices<1> &)> &predicate,
                std::map<unsigned int, std::vector<T> > &pred_to_values)
  {
    for (unsigned int i = 0; i < coefficients.size(0); i++)
      {
        const TableIndices<1> ind(i);
        fill_map_index(coefficients,ind,predicate,pred_to_values);
      }

  }

  template <typename T>
  void fill_map(const Table<2,T> &coefficients,
                const std::function<std::pair<bool,unsigned int>(const TableIndices<2> &)> &predicate,
                std::map<unsigned int, std::vector<T> > &pred_to_values)
  {
    for (unsigned int i = 0; i < coefficients.size(0); i++)
      for (unsigned int j = 0; j < coefficients.size(1); j++)
        {
          const TableIndices<2> ind(i,j);
          fill_map_index(coefficients,ind,predicate,pred_to_values);
        }

  }

  template <typename T>
  void fill_map(const Table<3,T> &coefficients,
                const std::function<std::pair<bool,unsigned int>(const TableIndices<3> &)> &predicate,
                std::map<unsigned int, std::vector<T> > &pred_to_values)
  {
    for (unsigned int i = 0; i < coefficients.size(0); i++)
      for (unsigned int j = 0; j < coefficients.size(1); j++)
        for (unsigned int k = 0; k < coefficients.size(2); k++)
          {
            const TableIndices<3> ind(i,j,k);
            fill_map_index(coefficients,ind,predicate,pred_to_values);
          }
  }


  template <typename T>
  double complex_mean_value(const T &value)
  {
    return value;
  }

  template <typename T>
  double complex_mean_value(const std::complex<T> &value)
  {
    AssertThrow(false, ExcMessage("FESeries::process_coefficients() can not be used with"
                                  "complex-valued coefficients and VectorTools::mean norm."));
    return std::abs(value);
  }

}


template <int dim, typename T>
std::pair<std::vector<unsigned int>,std::vector<double> >
FESeries::process_coefficients(const Table<dim,T> &coefficients,
                               const std::function<std::pair<bool,unsigned int>(const TableIndices<dim> &)> &predicate,
                               const VectorTools::NormType norm)
{
  std::vector<unsigned int> predicate_values;
  std::vector<double> norm_values;

  // first, parse all table elements into a map of predicate values and coefficients.
  // We could have stored (predicate values ->TableIndicies) map, but its
  // processing would have been much harder later on.
  std::map<unsigned int, std::vector<T> > pred_to_values;
  fill_map(coefficients,predicate,pred_to_values);

  // now go through the map and populate the @p norm_values based on @p norm:
  for (typename std::map<unsigned int, std::vector<T> >::const_iterator it = pred_to_values.begin();
       it != pred_to_values.end(); ++it)
    {
      predicate_values.push_back(it->first);
      Vector<T> values(it->second.begin(),
                       it->second.end());

      switch (norm)
        {
        case VectorTools::L2_norm:
        {
          norm_values.push_back(values.l2_norm());
          break;
        }
        case VectorTools::L1_norm:
        {
          norm_values.push_back(values.l1_norm());
          break;
        }
        case VectorTools::Linfty_norm:
        {
          norm_values.push_back(values.linfty_norm());
          break;
        }
        case VectorTools::mean:
        {
          norm_values.push_back(complex_mean_value(values.mean_value()));
          break;
        }
        default:
          AssertThrow(false, ExcNotImplemented());
          break;
        }
    }

  return std::make_pair(predicate_values,norm_values);
}


#endif // DOXYGEN

DEAL_II_NAMESPACE_CLOSE

#endif // dealii_fe_series_H