fe_series.h

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// ---------------------------------------------------------------------
//
// Copyright (C) 2016 - 2020 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.md at
// the top level directory of deal.II.
//
// ---------------------------------------------------------------------
 
#ifndef dealii_fe_series_h
#define dealii_fe_series_h
 
 
 
#include <deal.II/base/config.h>
 
#include <deal.II/base/exceptions.h>
#include <deal.II/base/subscriptor.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_common.h>
 
#include <memory>
#include <string>
#include <vector>
 
 
DEAL_II_NAMESPACE_OPEN
 
 
 
 
namespace FESeries
{
  template <int dim, int spacedim = dim>
  class Fourier : public Subscriptor
  {
  public:
    using CoefficientType = typename std::complex<double>;
 
    Fourier(const std::vector<unsigned int> &      n_coefficients_per_direction,
            const hp::FECollection<dim, spacedim> &fe_collection,
            const hp::QCollection<dim> &           q_collection);
 
    DEAL_II_DEPRECATED
    Fourier(const unsigned int                     n_coefficients_per_direction,
            const hp::FECollection<dim, spacedim> &fe_collection,
            const hp::QCollection<dim> &           q_collection);
 
    template <typename Number>
    void
    calculate(const ::Vector<Number> &local_dof_values,
              const unsigned int            cell_active_fe_index,
              Table<dim, CoefficientType> & fourier_coefficients);
 
    unsigned int
    get_n_coefficients_per_direction(const unsigned int index) const;
 
    void
    precalculate_all_transformation_matrices();
 
    template <class Archive>
    void
    save_transformation_matrices(Archive &ar, const unsigned int version);
 
    template <class Archive>
    void
    load_transformation_matrices(Archive &ar, const unsigned int version);
 
    bool
    operator==(const Fourier<dim, spacedim> &fourier) const;
 
  private:
    const std::vector<unsigned int> n_coefficients_per_direction;
 
    SmartPointer<const hp::FECollection<dim, spacedim>> fe_collection;
 
    const hp::QCollection<dim> q_collection;
 
    Table<dim, Tensor<1, dim>> k_vectors;
 
    std::vector<FullMatrix<CoefficientType>> fourier_transform_matrices;
 
    std::vector<CoefficientType> unrolled_coefficients;
  };
 
 
 
  template <int dim, int spacedim = dim>
  class Legendre : public Subscriptor
  {
  public:
    using CoefficientType = double;
 
    Legendre(const std::vector<unsigned int> &n_coefficients_per_direction,
             const hp::FECollection<dim, spacedim> &fe_collection,
             const hp::QCollection<dim> &           q_collection);
 
    DEAL_II_DEPRECATED
    Legendre(const unsigned int n_coefficients_per_direction,
             const hp::FECollection<dim, spacedim> &fe_collection,
             const hp::QCollection<dim> &           q_collection);
 
    template <typename Number>
    void
    calculate(const ::Vector<Number> &local_dof_values,
              const unsigned int            cell_active_fe_index,
              Table<dim, CoefficientType> & legendre_coefficients);
 
    unsigned int
    get_n_coefficients_per_direction(const unsigned int index) const;
 
    void
    precalculate_all_transformation_matrices();
 
    template <class Archive>
    void
    save_transformation_matrices(Archive &ar, const unsigned int version);
 
    template <class Archive>
    void
    load_transformation_matrices(Archive &ar, const unsigned int version);
 
    bool
    operator==(const Legendre<dim, spacedim> &legendre) const;
 
  private:
    const std::vector<unsigned int> n_coefficients_per_direction;
 
    SmartPointer<const hp::FECollection<dim, spacedim>> fe_collection;
 
    const hp::QCollection<dim> q_collection;
 
    std::vector<FullMatrix<CoefficientType>> legendre_transform_matrices;
 
    std::vector<CoefficientType> unrolled_coefficients;
  };
 
 
 
  template <int dim, typename CoefficientType>
  std::pair<std::vector<unsigned int>, std::vector<double>>
  process_coefficients(const Table<dim, CoefficientType> &coefficients,
                       const std::function<std::pair<bool, unsigned int>(
                         const TableIndices<dim> &)> &    predicate,
                       const VectorTools::NormType        norm_type,
                       const double smallest_abs_coefficient = 1e-10);
 
  std::pair<double, double>
  linear_regression(const std::vector<double> &x, const std::vector<double> &y);
 
} // namespace FESeries
 
#ifndef DOXYGEN
 
// -------------------  inline and template functions ----------------
 
namespace internal
{
  namespace FESeriesImplementation
  {
    template <int dim, typename CoefficientType>
    void
    fill_map_index(
      const Table<dim, CoefficientType> &coefficients,
      const TableIndices<dim> &          ind,
      const std::function<
        std::pair<bool, unsigned int>(const TableIndices<dim> &)> &predicate,
      std::map<unsigned int, std::vector<CoefficientType>> &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 CoefficientType &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 CoefficientType>
    void
    fill_map(
      const Table<1, CoefficientType> &coefficients,
      const std::function<
        std::pair<bool, unsigned int>(const TableIndices<1> &)> &predicate,
      std::map<unsigned int, std::vector<CoefficientType>> &     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 CoefficientType>
    void
    fill_map(
      const Table<2, CoefficientType> &coefficients,
      const std::function<
        std::pair<bool, unsigned int>(const TableIndices<2> &)> &predicate,
      std::map<unsigned int, std::vector<CoefficientType>> &     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 CoefficientType>
    void
    fill_map(
      const Table<3, CoefficientType> &coefficients,
      const std::function<
        std::pair<bool, unsigned int>(const TableIndices<3> &)> &predicate,
      std::map<unsigned int, std::vector<CoefficientType>> &     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 Number>
    double
    complex_mean_value(const Number &value)
    {
      return value;
    }
 
 
 
    template <typename Number>
    double
    complex_mean_value(const std::complex<Number> &value)
    {
      AssertThrow(false,
                  ExcMessage(
                    "FESeries::process_coefficients() can not be used with "
                    "complex-valued coefficients and VectorTools::mean norm."));
      return std::abs(value);
    }
  } // namespace FESeriesImplementation
} // namespace internal
 
 
 
template <int dim, typename CoefficientType>
std::pair<std::vector<unsigned int>, std::vector<double>>
FESeries::process_coefficients(
  const Table<dim, CoefficientType> &coefficients,
  const std::function<std::pair<bool, unsigned int>(const TableIndices<dim> &)>
    &                         predicate,
  const VectorTools::NormType norm_type,
  const double                smallest_abs_coefficient)
{
  Assert(smallest_abs_coefficient >= 0.,
         ExcMessage("smallest_abs_coefficient should be non-negative."));
 
  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<CoefficientType>> pred_to_values;
  internal::FESeriesImplementation::fill_map(coefficients,
                                             predicate,
                                             pred_to_values);
 
  // now go through the map and populate the @p norm_values based on @p norm:
  for (const auto &pred_to_value : pred_to_values)
    {
      Vector<CoefficientType> values(pred_to_value.second.cbegin(),
                                     pred_to_value.second.cend());
 
      double norm_value = 0;
      switch (norm_type)
        {
          case VectorTools::L2_norm:
            {
              norm_value = values.l2_norm();
              break;
            }
          case VectorTools::L1_norm:
            {
              norm_value = values.l1_norm();
              break;
            }
          case VectorTools::Linfty_norm:
            {
              norm_value = values.linfty_norm();
              break;
            }
          case VectorTools::mean:
            {
              norm_value = internal::FESeriesImplementation::complex_mean_value(
                values.mean_value());
              break;
            }
          default:
            AssertThrow(false, ExcNotImplemented());
            break;
        }
 
      // will use all non-zero coefficients
      if (std::abs(norm_value) > smallest_abs_coefficient)
        {
          predicate_values.push_back(pred_to_value.first);
          norm_values.push_back(norm_value);
        }
    }
 
  return std::make_pair(predicate_values, norm_values);
}
 
 
 
template <int dim, int spacedim>
template <class Archive>
inline void
FESeries::Fourier<dim, spacedim>::save_transformation_matrices(
  Archive &ar,
  const unsigned int /*version*/)
{
  // Store information about those resources which have been used to generate
  // the transformation matrices.
  // mode vector
  ar &n_coefficients_per_direction;
 
  // finite element collection
  unsigned int size = fe_collection->size();
  ar &         size;
  for (unsigned int i = 0; i < size; ++i)
    ar &(*fe_collection)[i].get_name();
 
  // quadrature collection
  size = q_collection.size();
  ar &size;
  for (unsigned int i = 0; i < size; ++i)
    ar &q_collection[i];
 
  // Store the actual transform matrices.
  ar &fourier_transform_matrices;
}
 
 
 
template <int dim, int spacedim>
template <class Archive>
inline void
FESeries::Fourier<dim, spacedim>::load_transformation_matrices(
  Archive &ar,
  const unsigned int /*version*/)
{
  // Check whether the currently registered resources are compatible with
  // the transformation matrices to load.
  // mode vector
  std::vector<unsigned int> compare_coefficients;
  ar &                      compare_coefficients;
  Assert(compare_coefficients == n_coefficients_per_direction,
         ExcMessage("A different number of coefficients vector has been used "
                    "to generate the transformation matrices you are about "
                    "to load!"));
 
  // finite element collection
  unsigned int size;
  ar &         size;
  AssertDimension(size, fe_collection->size());
  std::string name;
  for (unsigned int i = 0; i < size; ++i)
    {
      ar &name;
      Assert(name.compare((*fe_collection)[i].get_name()) == 0,
             ExcMessage("A different FECollection has been used to generate "
                        "the transformation matrices you are about to load!"));
    }
 
  // quadrature collection
  ar &size;
  AssertDimension(size, q_collection.size());
  Quadrature<dim> quadrature;
  for (unsigned int i = 0; i < size; ++i)
    {
      ar &quadrature;
      Assert(quadrature == q_collection[i],
             ExcMessage("A different QCollection has been used to generate "
                        "the transformation matrices you are about to load!"));
    }
 
  // Restore the transform matrices since all prerequisites are fulfilled.
  ar &fourier_transform_matrices;
}
 
 
 
template <int dim, int spacedim>
template <class Archive>
inline void
FESeries::Legendre<dim, spacedim>::save_transformation_matrices(
  Archive &ar,
  const unsigned int /*version*/)
{
  // Store information about those resources which have been used to generate
  // the transformation matrices.
  // mode vector
  ar &n_coefficients_per_direction;
 
  // finite element collection
  unsigned int size = fe_collection->size();
  ar &         size;
  for (unsigned int i = 0; i < size; ++i)
    ar &(*fe_collection)[i].get_name();
 
  // quadrature collection
  size = q_collection.size();
  ar &size;
  for (unsigned int i = 0; i < size; ++i)
    ar &q_collection[i];
 
  // Store the actual transform matrices.
  ar &legendre_transform_matrices;
}
 
 
 
template <int dim, int spacedim>
template <class Archive>
inline void
FESeries::Legendre<dim, spacedim>::load_transformation_matrices(
  Archive &ar,
  const unsigned int /*version*/)
{
  // Check whether the currently registered resources are compatible with
  // the transformation matrices to load.
  // mode vector
  std::vector<unsigned int> compare_coefficients;
  ar &                      compare_coefficients;
  Assert(compare_coefficients == n_coefficients_per_direction,
         ExcMessage("A different number of coefficients vector has been used "
                    "to generate the transformation matrices you are about "
                    "to load!"));
 
  // finite element collection
  unsigned int size;
  ar &         size;
  AssertDimension(size, fe_collection->size());
  std::string name;
  for (unsigned int i = 0; i < size; ++i)
    {
      ar &name;
      Assert(name.compare((*fe_collection)[i].get_name()) == 0,
             ExcMessage("A different FECollection has been used to generate "
                        "the transformation matrices you are about to load!"));
    }
 
  // quadrature collection
  ar &size;
  AssertDimension(size, q_collection.size());
  Quadrature<dim> quadrature;
  for (unsigned int i = 0; i < size; ++i)
    {
      ar &quadrature;
      Assert(quadrature == q_collection[i],
             ExcMessage("A different QCollection has been used to generate "
                        "the transformation matrices you are about to load!"));
    }
 
  // Restore the transform matrices since all prerequisites are fulfilled.
  ar &legendre_transform_matrices;
}
 
 
#endif // DOXYGEN
 
DEAL_II_NAMESPACE_CLOSE
 
#endif // dealii_fe_series_h