point_value_history.cc

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// ---------------------------------------------------------------------
//
// Copyright (C) 2009 - 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.
//
// ---------------------------------------------------------------------
 
 
#include <deal.II/lac/block_vector.h>
#include <deal.II/lac/la_parallel_block_vector.h>
#include <deal.II/lac/la_parallel_vector.h>
#include <deal.II/lac/la_vector.h>
#include <deal.II/lac/petsc_block_vector.h>
#include <deal.II/lac/petsc_vector.h>
#include <deal.II/lac/trilinos_parallel_block_vector.h>
#include <deal.II/lac/trilinos_vector.h>
#include <deal.II/lac/vector.h>
#include <deal.II/lac/vector_element_access.h>
 
#include <deal.II/numerics/point_value_history.h>
#include <deal.II/numerics/vector_tools_point_value.h>
 
#include <algorithm>
 
 
DEAL_II_NAMESPACE_OPEN
 
 
namespace internal
{
  namespace PointValueHistoryImplementation
  {
    template <int dim>
    PointGeometryData<dim>::PointGeometryData(
      const Point<dim> &                          new_requested_location,
      const std::vector<Point<dim>> &             new_locations,
      const std::vector<types::global_dof_index> &new_sol_indices)
    {
      requested_location      = new_requested_location;
      support_point_locations = new_locations;
      solution_indices        = new_sol_indices;
    }
  } // namespace PointValueHistoryImplementation
} // namespace internal
 
 
 
template <int dim>
PointValueHistory<dim>::PointValueHistory(
  const unsigned int n_independent_variables)
  : n_indep(n_independent_variables)
{
  closed                = false;
  cleared               = false;
  triangulation_changed = false;
  have_dof_handler      = false;
 
  // make a vector for keys
  dataset_key = std::vector<double>(); // initialize the std::vector
 
  // make a vector of independent values
  independent_values =
    std::vector<std::vector<double>>(n_indep, std::vector<double>(0));
  indep_names = std::vector<std::string>();
}
 
 
 
template <int dim>
PointValueHistory<dim>::PointValueHistory(
  const DoFHandler<dim> &dof_handler,
  const unsigned int     n_independent_variables)
  : dof_handler(&dof_handler)
  , n_indep(n_independent_variables)
{
  closed                = false;
  cleared               = false;
  triangulation_changed = false;
  have_dof_handler      = true;
 
  // make a vector to store keys
  dataset_key = std::vector<double>(); // initialize the std::vector
 
  // make a vector for the independent values
  independent_values =
    std::vector<std::vector<double>>(n_indep, std::vector<double>(0));
  indep_names = std::vector<std::string>();
 
  tria_listener = dof_handler.get_triangulation().signals.any_change.connect(
    [this]() { this->tria_change_listener(); });
}
 
 
 
template <int dim>
PointValueHistory<dim>::PointValueHistory(
  const PointValueHistory &point_value_history)
{
  dataset_key         = point_value_history.dataset_key;
  independent_values  = point_value_history.independent_values;
  indep_names         = point_value_history.indep_names;
  data_store          = point_value_history.data_store;
  component_mask      = point_value_history.component_mask;
  component_names_map = point_value_history.component_names_map;
  point_geometry_data = point_value_history.point_geometry_data;
 
  closed  = point_value_history.closed;
  cleared = point_value_history.cleared;
 
  dof_handler = point_value_history.dof_handler;
 
  triangulation_changed = point_value_history.triangulation_changed;
  have_dof_handler      = point_value_history.have_dof_handler;
  n_indep               = point_value_history.n_indep;
 
  // What to do with tria_listener?
  // Presume subscribe new instance?
  if (have_dof_handler)
    {
      tria_listener =
        dof_handler->get_triangulation().signals.any_change.connect(
          [this]() { this->tria_change_listener(); });
    }
}
 
 
 
template <int dim>
PointValueHistory<dim> &
PointValueHistory<dim>::operator=(const PointValueHistory &point_value_history)
{
  dataset_key         = point_value_history.dataset_key;
  independent_values  = point_value_history.independent_values;
  indep_names         = point_value_history.indep_names;
  data_store          = point_value_history.data_store;
  component_mask      = point_value_history.component_mask;
  component_names_map = point_value_history.component_names_map;
  point_geometry_data = point_value_history.point_geometry_data;
 
  closed  = point_value_history.closed;
  cleared = point_value_history.cleared;
 
  dof_handler = point_value_history.dof_handler;
 
  triangulation_changed = point_value_history.triangulation_changed;
  have_dof_handler      = point_value_history.have_dof_handler;
  n_indep               = point_value_history.n_indep;
 
  // What to do with tria_listener?
  // Presume subscribe new instance?
  if (have_dof_handler)
    {
      tria_listener =
        dof_handler->get_triangulation().signals.any_change.connect(
          [this]() { this->tria_change_listener(); });
    }
 
  return *this;
}
 
 
 
template <int dim>
PointValueHistory<dim>::~PointValueHistory()
{
  if (have_dof_handler)
    {
      tria_listener.disconnect();
    }
}
 
 
 
template <int dim>
void
PointValueHistory<dim>::add_point(const Point<dim> &location)
{
  // can't be closed to add additional points
  // or vectors
  AssertThrow(!closed, ExcInvalidState());
  AssertThrow(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
  AssertThrow(!triangulation_changed, ExcDoFHandlerChanged());
 
  // Implementation assumes that support
  // points locations are dofs locations
  AssertThrow(dof_handler->get_fe().has_support_points(), ExcNotImplemented());
 
  // While in general quadrature points seems
  // to refer to Gauss quadrature points, in
  // this case the quadrature points are
  // forced to be the support points of the
  // FE.
  Quadrature<dim> support_point_quadrature(
    dof_handler->get_fe().get_unit_support_points());
  FEValues<dim> fe_values(dof_handler->get_fe(),
                          support_point_quadrature,
                          update_quadrature_points);
  unsigned int  n_support_points =
    dof_handler->get_fe().get_unit_support_points().size();
  unsigned int n_components = dof_handler->get_fe(0).n_components();
 
  // set up a loop over all the cells in the
  // DoFHandler
  typename DoFHandler<dim>::active_cell_iterator cell =
    dof_handler->begin_active();
  typename DoFHandler<dim>::active_cell_iterator endc = dof_handler->end();
 
  // default values to be replaced as closer
  // points are found however they need to be
  // consistent in case they are actually
  // chosen
  typename DoFHandler<dim>::active_cell_iterator current_cell = cell;
  std::vector<unsigned int>                      current_fe_index(n_components,
                                             0); // need one index per component
  fe_values.reinit(cell);
  std::vector<Point<dim>> current_points(n_components, Point<dim>());
  for (unsigned int support_point = 0; support_point < n_support_points;
       support_point++)
    {
      // setup valid data in the empty
      // vectors
      unsigned int component =
        dof_handler->get_fe().system_to_component_index(support_point).first;
      current_points[component]   = fe_values.quadrature_point(support_point);
      current_fe_index[component] = support_point;
    }
 
  // check each cell to find a suitable
  // support points
  // GridTools::find_active_cell_around_point
  // is an alternative. That method is not
  // used here mostly because of the history
  // of the class. The algorithm used in
  // add_points below may be slightly more
  // efficient than find_active_cell_around_point
  // because it operates on a set of points.
 
  for (; cell != endc; cell++)
    {
      fe_values.reinit(cell);
 
      for (unsigned int support_point = 0; support_point < n_support_points;
           support_point++)
        {
          unsigned int component = dof_handler->get_fe()
                                     .system_to_component_index(support_point)
                                     .first;
          const Point<dim> &test_point =
            fe_values.quadrature_point(support_point);
 
          if (location.distance(test_point) <
              location.distance(current_points[component]))
            {
              // save the data
              current_points[component]   = test_point;
              current_cell                = cell;
              current_fe_index[component] = support_point;
            }
        }
    }
 
 
  std::vector<types::global_dof_index> local_dof_indices(
    dof_handler->get_fe().n_dofs_per_cell());
  std::vector<types::global_dof_index> new_solution_indices;
  current_cell->get_dof_indices(local_dof_indices);
  // there is an implicit assumption here
  // that all the closest support point to
  // the requested point for all finite
  // element components lie in the same cell.
  // this could possibly be violated if
  // components use different FE orders,
  // requested points are on the edge or
  // vertex of a cell and we are unlucky with
  // floating point rounding. Worst case
  // scenario however is that the point
  // selected isn't the closest possible, it
  // will still lie within one cell distance.
  // calling
  // GridTools::find_active_cell_around_point
  // to obtain a cell to search is an
  // option for these methods, but currently
  // the GridTools function does not cater for
  // a vector of points, and does not seem to
  // be intrinsicly faster than this method.
  for (unsigned int component = 0;
       component < dof_handler->get_fe(0).n_components();
       component++)
    {
      new_solution_indices.push_back(
        local_dof_indices[current_fe_index[component]]);
    }
 
  internal::PointValueHistoryImplementation::PointGeometryData<dim>
    new_point_geometry_data(location, current_points, new_solution_indices);
  point_geometry_data.push_back(new_point_geometry_data);
 
  for (auto &data_entry : data_store)
    {
      // add an extra row to each vector entry
      const ComponentMask &current_mask =
        (component_mask.find(data_entry.first))->second;
      unsigned int n_stored = current_mask.n_selected_components();
      data_entry.second.resize(data_entry.second.size() + n_stored);
    }
}
 
 
 
template <int dim>
void
PointValueHistory<dim>::add_points(const std::vector<Point<dim>> &locations)
{
  // This algorithm adds points in the same
  // order as they appear in the vector
  // locations and users may depend on this
  // so do not change order added!
 
  // can't be closed to add additional points or vectors
  AssertThrow(!closed, ExcInvalidState());
  AssertThrow(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
  AssertThrow(!triangulation_changed, ExcDoFHandlerChanged());
 
 
  // Implementation assumes that support
  // points locations are dofs locations
  AssertThrow(dof_handler->get_fe().has_support_points(), ExcNotImplemented());
 
  // While in general quadrature points seems
  // to refer to Gauss quadrature points, in
  // this case the quadrature points are
  // forced to be the support points of the
  // FE.
  Quadrature<dim> support_point_quadrature(
    dof_handler->get_fe().get_unit_support_points());
  FEValues<dim> fe_values(dof_handler->get_fe(),
                          support_point_quadrature,
                          update_quadrature_points);
  unsigned int  n_support_points =
    dof_handler->get_fe().get_unit_support_points().size();
  unsigned int n_components = dof_handler->get_fe(0).n_components();
 
  // set up a loop over all the cells in the
  // DoFHandler
  typename DoFHandler<dim>::active_cell_iterator cell =
    dof_handler->begin_active();
  typename DoFHandler<dim>::active_cell_iterator endc = dof_handler->end();
 
  // default values to be replaced as closer
  // points are found however they need to be
  // consistent in case they are actually
  // chosen vector <vector>s defined where
  // previously single vectors were used
 
  // need to store one value per point per component
  std::vector<typename DoFHandler<dim>::active_cell_iterator> current_cell(
    locations.size(), cell);
 
  fe_values.reinit(cell);
  std::vector<Point<dim>>   temp_points(n_components, Point<dim>());
  std::vector<unsigned int> temp_fe_index(n_components, 0);
  for (unsigned int support_point = 0; support_point < n_support_points;
       support_point++)
    {
      // setup valid data in the empty
      // vectors
      unsigned int component =
        dof_handler->get_fe().system_to_component_index(support_point).first;
      temp_points[component]   = fe_values.quadrature_point(support_point);
      temp_fe_index[component] = support_point;
    }
  std::vector<std::vector<Point<dim>>> current_points(
    locations.size(), temp_points); // give a valid start point
  std::vector<std::vector<unsigned int>> current_fe_index(locations.size(),
                                                          temp_fe_index);
 
  // check each cell to find suitable support
  // points
  // GridTools::find_active_cell_around_point
  // is an alternative. That method is not
  // used here mostly because of the history
  // of the class. The algorithm used here
  // may be slightly more
  // efficient than find_active_cell_around_point
  // because it operates on a set of points.
  for (; cell != endc; cell++)
    {
      fe_values.reinit(cell);
      for (unsigned int support_point = 0; support_point < n_support_points;
           support_point++)
        {
          unsigned int component = dof_handler->get_fe()
                                     .system_to_component_index(support_point)
                                     .first;
          const Point<dim> &test_point =
            fe_values.quadrature_point(support_point);
 
          for (unsigned int point = 0; point < locations.size(); point++)
            {
              if (locations[point].distance(test_point) <
                  locations[point].distance(current_points[point][component]))
                {
                  // save the data
                  current_points[point][component]   = test_point;
                  current_cell[point]                = cell;
                  current_fe_index[point][component] = support_point;
                }
            }
        }
    }
 
  std::vector<types::global_dof_index> local_dof_indices(
    dof_handler->get_fe().n_dofs_per_cell());
  for (unsigned int point = 0; point < locations.size(); point++)
    {
      current_cell[point]->get_dof_indices(local_dof_indices);
      std::vector<types::global_dof_index> new_solution_indices;
 
      for (unsigned int component = 0;
           component < dof_handler->get_fe(0).n_components();
           component++)
        {
          new_solution_indices.push_back(
            local_dof_indices[current_fe_index[point][component]]);
        }
 
      internal::PointValueHistoryImplementation::PointGeometryData<dim>
        new_point_geometry_data(locations[point],
                                current_points[point],
                                new_solution_indices);
 
      point_geometry_data.push_back(new_point_geometry_data);
 
      for (auto &data_entry : data_store)
        {
          // add an extra row to each vector entry
          const ComponentMask current_mask =
            (component_mask.find(data_entry.first))->second;
          unsigned int n_stored = current_mask.n_selected_components();
          data_entry.second.resize(data_entry.second.size() + n_stored);
        }
    }
}
 
 
 
template <int dim>
void
PointValueHistory<dim>::add_field_name(const std::string &  vector_name,
                                       const ComponentMask &mask)
{
  // can't be closed to add additional points
  // or vectors
  AssertThrow(!closed, ExcInvalidState());
  AssertThrow(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
  AssertThrow(!triangulation_changed, ExcDoFHandlerChanged());
 
  // insert a component mask that is always of the right size
  if (mask.represents_the_all_selected_mask() == false)
    component_mask.insert(std::make_pair(vector_name, mask));
  else
    component_mask.insert(
      std::make_pair(vector_name,
                     ComponentMask(std::vector<bool>(
                       dof_handler->get_fe(0).n_components(), true))));
 
  // insert an empty vector of strings
  // to ensure each field has an entry
  // in the map
  std::pair<std::string, std::vector<std::string>> empty_names(
    vector_name, std::vector<std::string>());
  component_names_map.insert(empty_names);
 
  // make and add a new vector
  // point_geometry_data.size() long
  std::pair<std::string, std::vector<std::vector<double>>> pair_data;
  pair_data.first = vector_name;
  const unsigned int n_stored =
    (mask.represents_the_all_selected_mask() == false ?
       mask.n_selected_components() :
       dof_handler->get_fe(0).n_components());
 
  int n_datastreams =
    point_geometry_data.size() * n_stored; // each point has n_stored sub parts
  std::vector<std::vector<double>> vector_size(n_datastreams,
                                               std::vector<double>(0));
  pair_data.second = vector_size;
  data_store.insert(pair_data);
}
 
 
template <int dim>
void
PointValueHistory<dim>::add_field_name(const std::string &vector_name,
                                       const unsigned int n_components)
{
  std::vector<bool> temp_mask(n_components, true);
  add_field_name(vector_name, temp_mask);
}
 
 
template <int dim>
void
PointValueHistory<dim>::add_component_names(
  const std::string &             vector_name,
  const std::vector<std::string> &component_names)
{
  typename std::map<std::string, std::vector<std::string>>::iterator names =
    component_names_map.find(vector_name);
  Assert(names != component_names_map.end(),
         ExcMessage("vector_name not in class"));
 
  typename std::map<std::string, ComponentMask>::iterator mask =
    component_mask.find(vector_name);
  Assert(mask != component_mask.end(), ExcMessage("vector_name not in class"));
  unsigned int n_stored = mask->second.n_selected_components();
  (void)n_stored;
  Assert(component_names.size() == n_stored,
         ExcDimensionMismatch(component_names.size(), n_stored));
 
  names->second = component_names;
}
 
 
template <int dim>
void
PointValueHistory<dim>::add_independent_names(
  const std::vector<std::string> &independent_names)
{
  Assert(independent_names.size() == n_indep,
         ExcDimensionMismatch(independent_names.size(), n_indep));
 
  indep_names = independent_names;
}
 
 
template <int dim>
void
PointValueHistory<dim>::close()
{
  closed = true;
}
 
 
 
template <int dim>
void
PointValueHistory<dim>::clear()
{
  cleared          = true;
  dof_handler      = nullptr;
  have_dof_handler = false;
}
 
// Need to test that the internal data has a full and complete dataset for
// each key. That is that the data has not got 'out of sync'. Testing that
// dataset_key is within 1 of independent_values is cheap and is done in all
// three methods. Evaluate_field will check that its vector_name is within 1
// of dataset_key. However this leaves the possibility that the user has
// neglected to call evaluate_field on one vector_name consistently. To catch
// this case start_new_dataset will call bool deap_check () which will test
// all vector_names and return a bool. This can be called from an Assert
// statement.
 
 
 
template <int dim>
template <typename VectorType>
void
PointValueHistory<dim>::evaluate_field(const std::string &vector_name,
                                       const VectorType & solution)
{
  // must be closed to add data to internal
  // members.
  Assert(closed, ExcInvalidState());
  Assert(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
  AssertThrow(!triangulation_changed, ExcDoFHandlerChanged());
 
  if (n_indep != 0) // hopefully this will get optimized, can't test
                    // independent_values[0] unless n_indep > 0
    {
      Assert(std::abs(static_cast<int>(dataset_key.size()) -
                      static_cast<int>(independent_values[0].size())) < 2,
             ExcDataLostSync());
    }
  // Look up the field name and get an
  // iterator for the map. Doing this
  // up front means that it only needs
  // to be done once and also allows us
  // to check vector_name is in the map.
  typename std::map<std::string, std::vector<std::vector<double>>>::iterator
    data_store_field = data_store.find(vector_name);
  Assert(data_store_field != data_store.end(),
         ExcMessage("vector_name not in class"));
  // Repeat for component_mask
  typename std::map<std::string, ComponentMask>::iterator mask =
    component_mask.find(vector_name);
  Assert(mask != component_mask.end(), ExcMessage("vector_name not in class"));
 
  unsigned int n_stored =
    mask->second.n_selected_components(dof_handler->get_fe(0).n_components());
 
  typename std::vector<
    internal::PointValueHistoryImplementation::PointGeometryData<dim>>::iterator
    point = point_geometry_data.begin();
  for (unsigned int data_store_index = 0; point != point_geometry_data.end();
       ++point, ++data_store_index)
    {
      // Look up the components to add
      // in the component_mask, and
      // access the data associated with
      // those components
 
      for (unsigned int store_index = 0, comp = 0;
           comp < dof_handler->get_fe(0).n_components();
           comp++)
        {
          if (mask->second[comp])
            {
              unsigned int solution_index = point->solution_indices[comp];
              data_store_field
                ->second[data_store_index * n_stored + store_index]
                .push_back(
                  internal::ElementAccess<VectorType>::get(solution,
                                                           solution_index));
              store_index++;
            }
        }
    }
}
 
 
 
template <int dim>
template <typename VectorType>
void
PointValueHistory<dim>::evaluate_field(
  const std::vector<std::string> &vector_names,
  const VectorType &              solution,
  const DataPostprocessor<dim> &  data_postprocessor,
  const Quadrature<dim> &         quadrature)
{
  // must be closed to add data to internal
  // members.
  Assert(closed, ExcInvalidState());
  Assert(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
  if (n_indep != 0) // hopefully this will get optimized, can't test
                    // independent_values[0] unless n_indep > 0
    {
      Assert(std::abs(static_cast<int>(dataset_key.size()) -
                      static_cast<int>(independent_values[0].size())) < 2,
             ExcDataLostSync());
    }
 
  // Make an FEValues object
  const UpdateFlags update_flags =
    data_postprocessor.get_needed_update_flags() | update_quadrature_points;
  Assert(
    !(update_flags & update_normal_vectors),
    ExcMessage(
      "The update of normal vectors may not be requested for evaluation of "
      "data on cells via DataPostprocessor."));
  FEValues<dim> fe_values(dof_handler->get_fe(), quadrature, update_flags);
  unsigned int  n_components        = dof_handler->get_fe(0).n_components();
  unsigned int  n_quadrature_points = quadrature.size();
 
  unsigned int n_output_variables = data_postprocessor.get_names().size();
 
  // declare some temp objects for evaluating the solution at quadrature
  // points. we will either need the scalar or vector version in the code
  // below
  std::vector<typename VectorType::value_type> scalar_solution_values(
    n_quadrature_points);
  std::vector<Tensor<1, dim, typename VectorType::value_type>>
    scalar_solution_gradients(n_quadrature_points);
  std::vector<Tensor<2, dim, typename VectorType::value_type>>
    scalar_solution_hessians(n_quadrature_points);
 
  std::vector<Vector<typename VectorType::value_type>> vector_solution_values(
    n_quadrature_points, Vector<typename VectorType::value_type>(n_components));
 
  std::vector<std::vector<Tensor<1, dim, typename VectorType::value_type>>>
    vector_solution_gradients(
      n_quadrature_points,
      std::vector<Tensor<1, dim, typename VectorType::value_type>>(
        n_components, Tensor<1, dim, typename VectorType::value_type>()));
 
  std::vector<std::vector<Tensor<2, dim, typename VectorType::value_type>>>
    vector_solution_hessians(
      n_quadrature_points,
      std::vector<Tensor<2, dim, typename VectorType::value_type>>(
        n_components, Tensor<2, dim, typename VectorType::value_type>()));
 
  // Loop over points and find correct cell
  typename std::vector<
    internal::PointValueHistoryImplementation::PointGeometryData<dim>>::iterator
    point = point_geometry_data.begin();
  for (unsigned int data_store_index = 0; point != point_geometry_data.end();
       ++point, ++data_store_index)
    {
      // we now have a point to query, need to know what cell it is in
      const Point<dim> requested_location = point->requested_location;
      const typename DoFHandler<dim>::active_cell_iterator cell =
        GridTools::find_active_cell_around_point(StaticMappingQ1<dim>::mapping,
                                                 *dof_handler,
                                                 requested_location)
          .first;
 
 
      fe_values.reinit(cell);
      std::vector<Vector<double>> computed_quantities(
        1, Vector<double>(n_output_variables)); // just one point needed
 
      // find the closest quadrature point
      std::vector<Point<dim>> quadrature_points =
        fe_values.get_quadrature_points();
      double       distance       = cell->diameter();
      unsigned int selected_point = 0;
      for (unsigned int q_point = 0; q_point < n_quadrature_points; q_point++)
        {
          if (requested_location.distance(quadrature_points[q_point]) <
              distance)
            {
              selected_point = q_point;
              distance =
                requested_location.distance(quadrature_points[q_point]);
            }
        }
 
 
      // The case of a scalar FE
      if (n_components == 1)
        {
          // Extract data for the DataPostprocessor object
          DataPostprocessorInputs::Scalar<dim> postprocessor_input;
 
          // for each quantity that is requested (values, gradients, hessians),
          // first get them at all quadrature points, then restrict to the
          // one value on the quadrature point closest to the evaluation
          // point in question
          //
          // we need temporary objects because the underlying scalar
          // type of the solution vector may be different from 'double',
          // but the DataPostprocessorInputs only allow for 'double'
          // data types
          if (update_flags & update_values)
            {
              fe_values.get_function_values(solution, scalar_solution_values);
              postprocessor_input.solution_values =
                std::vector<double>(1, scalar_solution_values[selected_point]);
            }
          if (update_flags & update_gradients)
            {
              fe_values.get_function_gradients(solution,
                                               scalar_solution_gradients);
              postprocessor_input.solution_gradients =
                std::vector<Tensor<1, dim>>(
                  1, scalar_solution_gradients[selected_point]);
            }
          if (update_flags & update_hessians)
            {
              fe_values.get_function_hessians(solution,
                                              scalar_solution_hessians);
              postprocessor_input.solution_hessians =
                std::vector<Tensor<2, dim>>(
                  1, scalar_solution_hessians[selected_point]);
            }
 
          // then also set the single evaluation point
          postprocessor_input.evaluation_points =
            std::vector<Point<dim>>(1, quadrature_points[selected_point]);
 
          // and finally do the postprocessing
          data_postprocessor.evaluate_scalar_field(postprocessor_input,
                                                   computed_quantities);
        }
      else // The case of a vector FE
        {
          // exact same idea as above
          DataPostprocessorInputs::Vector<dim> postprocessor_input;
 
          if (update_flags & update_values)
            {
              fe_values.get_function_values(solution, vector_solution_values);
              postprocessor_input.solution_values.resize(
                1, Vector<double>(n_components));
              std::copy(vector_solution_values[selected_point].begin(),
                        vector_solution_values[selected_point].end(),
                        postprocessor_input.solution_values[0].begin());
            }
          if (update_flags & update_gradients)
            {
              fe_values.get_function_gradients(solution,
                                               vector_solution_gradients);
              postprocessor_input.solution_gradients.resize(
                1, std::vector<Tensor<1, dim>>(n_components));
              std::copy(vector_solution_gradients[selected_point].begin(),
                        vector_solution_gradients[selected_point].end(),
                        postprocessor_input.solution_gradients[0].begin());
            }
          if (update_flags & update_hessians)
            {
              fe_values.get_function_hessians(solution,
                                              vector_solution_hessians);
              postprocessor_input.solution_hessians.resize(
                1, std::vector<Tensor<2, dim>>(n_components));
              std::copy(vector_solution_hessians[selected_point].begin(),
                        vector_solution_hessians[selected_point].end(),
                        postprocessor_input.solution_hessians[0].begin());
            }
 
          postprocessor_input.evaluation_points =
            std::vector<Point<dim>>(1, quadrature_points[selected_point]);
 
          data_postprocessor.evaluate_vector_field(postprocessor_input,
                                                   computed_quantities);
        }
 
 
      // we now have the data and need to save it
      // loop over data names
      typename std::vector<std::string>::const_iterator name =
        vector_names.begin();
      for (; name != vector_names.end(); ++name)
        {
          typename std::map<std::string,
                            std::vector<std::vector<double>>>::iterator
            data_store_field = data_store.find(*name);
          Assert(data_store_field != data_store.end(),
                 ExcMessage("vector_name not in class"));
          // Repeat for component_mask
          typename std::map<std::string, ComponentMask>::iterator mask =
            component_mask.find(*name);
          Assert(mask != component_mask.end(),
                 ExcMessage("vector_name not in class"));
 
          unsigned int n_stored =
            mask->second.n_selected_components(n_output_variables);
 
          // Push back computed quantities according
          // to the component_mask.
          for (unsigned int store_index = 0, comp = 0;
               comp < n_output_variables;
               comp++)
            {
              if (mask->second[comp])
                {
                  data_store_field
                    ->second[data_store_index * n_stored + store_index]
                    .push_back(computed_quantities[0](comp));
                  store_index++;
                }
            }
        }
    } // end of loop over points
}
 
 
 
template <int dim>
template <typename VectorType>
void
PointValueHistory<dim>::evaluate_field(
  const std::string &           vector_name,
  const VectorType &            solution,
  const DataPostprocessor<dim> &data_postprocessor,
  const Quadrature<dim> &       quadrature)
{
  std::vector<std::string> vector_names;
  vector_names.push_back(vector_name);
  evaluate_field(vector_names, solution, data_postprocessor, quadrature);
}
 
 
 
template <int dim>
template <typename VectorType>
void
PointValueHistory<dim>::evaluate_field_at_requested_location(
  const std::string &vector_name,
  const VectorType & solution)
{
  using number = typename VectorType::value_type;
  // must be closed to add data to internal
  // members.
  Assert(closed, ExcInvalidState());
  Assert(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
 
  if (n_indep != 0) // hopefully this will get optimized, can't test
                    // independent_values[0] unless n_indep > 0
    {
      Assert(std::abs(static_cast<int>(dataset_key.size()) -
                      static_cast<int>(independent_values[0].size())) < 2,
             ExcDataLostSync());
    }
  // Look up the field name and get an
  // iterator for the map. Doing this
  // up front means that it only needs
  // to be done once and also allows us
  // to check vector_name is in the map.
  typename std::map<std::string, std::vector<std::vector<double>>>::iterator
    data_store_field = data_store.find(vector_name);
  Assert(data_store_field != data_store.end(),
         ExcMessage("vector_name not in class"));
  // Repeat for component_mask
  typename std::map<std::string, ComponentMask>::iterator mask =
    component_mask.find(vector_name);
  Assert(mask != component_mask.end(), ExcMessage("vector_name not in class"));
 
  unsigned int n_stored =
    mask->second.n_selected_components(dof_handler->get_fe(0).n_components());
 
  typename std::vector<
    internal::PointValueHistoryImplementation::PointGeometryData<dim>>::iterator
                 point = point_geometry_data.begin();
  Vector<number> value(dof_handler->get_fe(0).n_components());
  for (unsigned int data_store_index = 0; point != point_geometry_data.end();
       ++point, ++data_store_index)
    {
      // Make a Vector <double> for the value
      // at the point. It will have as many
      // components as there are in the fe.
      VectorTools::point_value(*dof_handler,
                               solution,
                               point->requested_location,
                               value);
 
      // Look up the component_mask and add
      // in components according to that mask
      for (unsigned int store_index = 0, comp = 0; comp < mask->second.size();
           comp++)
        {
          if (mask->second[comp])
            {
              data_store_field
                ->second[data_store_index * n_stored + store_index]
                .push_back(value(comp));
              store_index++;
            }
        }
    }
}
 
 
template <int dim>
void
PointValueHistory<dim>::start_new_dataset(double key)
{
  // must be closed to add data to internal
  // members.
  Assert(closed, ExcInvalidState());
  Assert(!cleared, ExcInvalidState());
  Assert(deep_check(false), ExcDataLostSync());
 
  dataset_key.push_back(key);
}
 
 
 
template <int dim>
void
PointValueHistory<dim>::push_back_independent(
  const std::vector<double> &indep_values)
{
  // must be closed to add data to internal
  // members.
  Assert(closed, ExcInvalidState());
  Assert(!cleared, ExcInvalidState());
  Assert(indep_values.size() == n_indep,
         ExcDimensionMismatch(indep_values.size(), n_indep));
  Assert(n_indep != 0, ExcNoIndependent());
  Assert(std::abs(static_cast<int>(dataset_key.size()) -
                  static_cast<int>(independent_values[0].size())) < 2,
         ExcDataLostSync());
 
  for (unsigned int component = 0; component < n_indep; component++)
    independent_values[component].push_back(indep_values[component]);
}
 
 
 
template <int dim>
void
PointValueHistory<dim>::write_gnuplot(
  const std::string &            base_name,
  const std::vector<Point<dim>> &postprocessor_locations)
{
  AssertThrow(closed, ExcInvalidState());
  AssertThrow(!cleared, ExcInvalidState());
  AssertThrow(deep_check(true), ExcDataLostSync());
 
  // write inputs to a file
  if (n_indep != 0)
    {
      std::string   filename = base_name + "_indep.gpl";
      std::ofstream to_gnuplot(filename.c_str());
 
      to_gnuplot << "# Data independent of mesh location\n";
 
      // write column headings
      to_gnuplot << "# <Key> ";
 
      if (indep_names.size() > 0)
        {
          for (const auto &indep_name : indep_names)
            {
              to_gnuplot << "<" << indep_name << "> ";
            }
          to_gnuplot << "\n";
        }
      else
        {
          for (unsigned int component = 0; component < n_indep; component++)
            {
              to_gnuplot << "<Indep_" << component << "> ";
            }
          to_gnuplot << "\n";
        }
      // write general data stored
      for (unsigned int key = 0; key < dataset_key.size(); key++)
        {
          to_gnuplot << dataset_key[key];
 
          for (unsigned int component = 0; component < n_indep; component++)
            {
              to_gnuplot << " " << independent_values[component][key];
            }
          to_gnuplot << "\n";
        }
 
      to_gnuplot.close();
    }
 
 
 
  // write points to a file
  if (have_dof_handler)
    {
      AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
      AssertThrow(postprocessor_locations.size() == 0 ||
                    postprocessor_locations.size() ==
                      point_geometry_data.size(),
                  ExcDimensionMismatch(postprocessor_locations.size(),
                                       point_geometry_data.size()));
      // We previously required the
      // number of dofs to remain the
      // same to provide some sort of
      // test on the relevance of the
      // support point indices stored.
      // We now relax that to allow
      // adaptive refinement strategies
      // to make use of the
      // evaluate_field_requested_locations
      // method. Note that the support point
      // information is not meaningful if
      // the number of dofs has changed.
      // AssertThrow (!triangulation_changed, ExcDoFHandlerChanged ());
 
      typename std::vector<internal::PointValueHistoryImplementation::
                             PointGeometryData<dim>>::iterator point =
        point_geometry_data.begin();
      for (unsigned int data_store_index = 0;
           point != point_geometry_data.end();
           ++point, ++data_store_index)
        {
          // for each point, open a file to
          // be written to
          std::string filename = base_name + "_" +
                                 Utilities::int_to_string(data_store_index, 2) +
                                 ".gpl"; // store by order pushed back
          // due to
          // Utilities::int_to_string(data_store_index,
          // 2) call, can handle up to 100
          // points
          std::ofstream to_gnuplot(filename.c_str());
 
          // put helpful info about the
          // support point into the file as
          // comments
          to_gnuplot << "# Requested location: " << point->requested_location
                     << "\n";
          to_gnuplot << "# DoF_index : Support location (for each component)\n";
          for (unsigned int component = 0;
               component < dof_handler->get_fe(0).n_components();
               component++)
            {
              to_gnuplot << "# " << point->solution_indices[component] << " : "
                         << point->support_point_locations[component] << "\n";
            }
          if (triangulation_changed)
            to_gnuplot
              << "# (Original components and locations, may be invalidated by mesh change.)\n";
 
          if (postprocessor_locations.size() != 0)
            {
              to_gnuplot << "# Postprocessor location: "
                         << postprocessor_locations[data_store_index];
              if (triangulation_changed)
                to_gnuplot << " (may be approximate)\n";
            }
          to_gnuplot << "#\n";
 
 
          // write column headings
          to_gnuplot << "# <Key> ";
 
          if (indep_names.size() > 0)
            {
              for (const auto &indep_name : indep_names)
                {
                  to_gnuplot << "<" << indep_name << "> ";
                }
            }
          else
            {
              for (unsigned int component = 0; component < n_indep; component++)
                {
                  to_gnuplot << "<Indep_" << component << "> ";
                }
            }
 
          for (const auto &data_entry : data_store)
            {
              typename std::map<std::string, ComponentMask>::iterator mask =
                component_mask.find(data_entry.first);
              unsigned int n_stored = mask->second.n_selected_components();
              std::vector<std::string> names =
                (component_names_map.find(data_entry.first))->second;
 
              if (names.size() > 0)
                {
                  AssertThrow(names.size() == n_stored,
                              ExcDimensionMismatch(names.size(), n_stored));
                  for (const auto &name : names)
                    {
                      to_gnuplot << "<" << name << "> ";
                    }
                }
              else
                {
                  for (unsigned int component = 0; component < n_stored;
                       component++)
                    {
                      to_gnuplot << "<" << data_entry.first << "_" << component
                                 << "> ";
                    }
                }
            }
          to_gnuplot << "\n";
 
          // write data stored for the point
          for (unsigned int key = 0; key < dataset_key.size(); key++)
            {
              to_gnuplot << dataset_key[key];
 
              for (unsigned int component = 0; component < n_indep; component++)
                {
                  to_gnuplot << " " << independent_values[component][key];
                }
 
              for (const auto &data_entry : data_store)
                {
                  typename std::map<std::string, ComponentMask>::iterator mask =
                    component_mask.find(data_entry.first);
                  unsigned int n_stored = mask->second.n_selected_components();
 
                  for (unsigned int component = 0; component < n_stored;
                       component++)
                    {
                      to_gnuplot
                        << " "
                        << (data_entry.second)[data_store_index * n_stored +
                                               component][key];
                    }
                }
              to_gnuplot << "\n";
            }
 
          to_gnuplot.close();
        }
    }
}
 
 
 
template <int dim>
Vector<double>
PointValueHistory<dim>::mark_support_locations()
{
  // a method to put a one at each point on
  // the grid where a location is defined
  AssertThrow(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
  AssertThrow(!triangulation_changed, ExcDoFHandlerChanged());
 
  Vector<double> dof_vector(dof_handler->n_dofs());
 
  typename std::vector<
    internal::PointValueHistoryImplementation::PointGeometryData<dim>>::iterator
    point = point_geometry_data.begin();
  for (; point != point_geometry_data.end(); ++point)
    {
      for (unsigned int component = 0;
           component < dof_handler->get_fe(0).n_components();
           component++)
        {
          dof_vector(point->solution_indices[component]) = 1;
        }
    }
  return dof_vector;
}
 
 
template <int dim>
void
PointValueHistory<dim>::get_support_locations(
  std::vector<std::vector<Point<dim>>> &locations)
{
  AssertThrow(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
  AssertThrow(!triangulation_changed, ExcDoFHandlerChanged());
 
  std::vector<std::vector<Point<dim>>> actual_points;
  typename std::vector<
    internal::PointValueHistoryImplementation::PointGeometryData<dim>>::iterator
    point = point_geometry_data.begin();
 
  for (; point != point_geometry_data.end(); ++point)
    {
      actual_points.push_back(point->support_point_locations);
    }
  locations = actual_points;
}
 
 
 
template <int dim>
void
PointValueHistory<dim>::get_postprocessor_locations(
  const Quadrature<dim> &  quadrature,
  std::vector<Point<dim>> &locations)
{
  Assert(!cleared, ExcInvalidState());
  AssertThrow(have_dof_handler, ExcDoFHandlerRequired());
 
  locations = std::vector<Point<dim>>();
 
  FEValues<dim>           fe_values(dof_handler->get_fe(),
                          quadrature,
                          update_quadrature_points);
  unsigned int            n_quadrature_points = quadrature.size();
  std::vector<Point<dim>> evaluation_points;
 
  // Loop over points and find correct cell
  typename std::vector<
    internal::PointValueHistoryImplementation::PointGeometryData<dim>>::iterator
    point = point_geometry_data.begin();
  for (unsigned int data_store_index = 0; point != point_geometry_data.end();
       ++point, ++data_store_index)
    {
      // we now have a point to query,
      // need to know what cell it is in
      Point<dim> requested_location = point->requested_location;
      typename DoFHandler<dim>::active_cell_iterator cell =
        GridTools::find_active_cell_around_point(StaticMappingQ1<dim>::mapping,
                                                 *dof_handler,
                                                 requested_location)
          .first;
      fe_values.reinit(cell);
 
      evaluation_points           = fe_values.get_quadrature_points();
      double       distance       = cell->diameter();
      unsigned int selected_point = 0;
 
      for (unsigned int q_point = 0; q_point < n_quadrature_points; q_point++)
        {
          if (requested_location.distance(evaluation_points[q_point]) <
              distance)
            {
              selected_point = q_point;
              distance =
                requested_location.distance(evaluation_points[q_point]);
            }
        }
 
      locations.push_back(evaluation_points[selected_point]);
    }
}
 
 
template <int dim>
void
PointValueHistory<dim>::status(std::ostream &out)
{
  out << "***PointValueHistory status output***\n\n";
  out << "Closed: " << closed << "\n";
  out << "Cleared: " << cleared << "\n";
  out << "Triangulation_changed: " << triangulation_changed << "\n";
  out << "Have_dof_handler: " << have_dof_handler << "\n";
  out << "Geometric Data"
      << "\n";
 
  typename std::vector<
    internal::PointValueHistoryImplementation::PointGeometryData<dim>>::iterator
    point = point_geometry_data.begin();
  if (point == point_geometry_data.end())
    {
      out << "No points stored currently\n";
    }
  else
    {
      if (!cleared)
        {
          for (; point != point_geometry_data.end(); ++point)
            {
              out << "# Requested location: " << point->requested_location
                  << "\n";
              out << "# DoF_index : Support location (for each component)\n";
              for (unsigned int component = 0;
                   component < dof_handler->get_fe(0).n_components();
                   component++)
                {
                  out << point->solution_indices[component] << " : "
                      << point->support_point_locations[component] << "\n";
                }
              out << "\n";
            }
        }
      else
        {
          out << "#Cannot access DoF_indices once cleared\n";
        }
    }
  out << "\n";
 
  if (independent_values.size() != 0)
    {
      out << "Independent value(s): " << independent_values.size() << " : "
          << independent_values[0].size() << "\n";
      if (indep_names.size() > 0)
        {
          out << "Names: ";
          for (const auto &indep_name : indep_names)
            {
              out << "<" << indep_name << "> ";
            }
          out << "\n";
        }
    }
  else
    {
      out << "No independent values stored\n";
    }
 
  if (data_store.begin() != data_store.end())
    {
      out
        << "Mnemonic: data set size (mask size, n true components) : n data sets\n";
    }
  for (const auto &data_entry : data_store)
    {
      // Find field mnemonic
      std::string vector_name = data_entry.first;
      typename std::map<std::string, ComponentMask>::iterator mask =
        component_mask.find(vector_name);
      Assert(mask != component_mask.end(),
             ExcMessage("vector_name not in class"));
      typename std::map<std::string, std::vector<std::string>>::iterator
        component_names = component_names_map.find(vector_name);
      Assert(component_names != component_names_map.end(),
             ExcMessage("vector_name not in class"));
 
      if (data_entry.second.size() != 0)
        {
          out << data_entry.first << ": " << data_entry.second.size() << " (";
          out << mask->second.size() << ", "
              << mask->second.n_selected_components() << ") : ";
          out << (data_entry.second)[0].size() << "\n";
        }
      else
        {
          out << data_entry.first << ": " << data_entry.second.size() << " (";
          out << mask->second.size() << ", "
              << mask->second.n_selected_components() << ") : ";
          out << "No points added"
              << "\n";
        }
      // add names, if available
      if (component_names->second.size() > 0)
        {
          for (const auto &name : component_names->second)
            {
              out << "<" << name << "> ";
            }
          out << "\n";
        }
    }
  out << "\n";
  out << "***end of status output***\n\n";
}
 
 
 
template <int dim>
bool
PointValueHistory<dim>::deep_check(const bool strict)
{
  // test ways that it can fail, if control
  // reaches last statement return true
  if (strict)
    {
      if (n_indep != 0)
        {
          if (dataset_key.size() != independent_values[0].size())
            {
              return false;
            }
        }
      if (have_dof_handler)
        {
          for (const auto &data_entry : data_store)
            {
              Assert(data_entry.second.size() > 0, ExcInternalError());
              if ((data_entry.second)[0].size() != dataset_key.size())
                return false;
              // this loop only tests one
              // member for each name,
              // i.e. checks the user it will
              // not catch internal errors
              // which do not update all
              // fields for a name.
            }
        }
      return true;
    }
  if (n_indep != 0)
    {
      if (std::abs(static_cast<int>(dataset_key.size()) -
                   static_cast<int>(independent_values[0].size())) >= 2)
        {
          return false;
        }
    }
 
  if (have_dof_handler)
    {
      for (const auto &data_entry : data_store)
        {
          Assert(data_entry.second.size() > 0, ExcInternalError());
 
          if (std::abs(static_cast<int>((data_entry.second)[0].size()) -
                       static_cast<int>(dataset_key.size())) >= 2)
            return false;
          // this loop only tests one member
          // for each name, i.e. checks the
          // user it will not catch internal
          // errors which do not update all
          // fields for a name.
        }
    }
  return true;
}
 
 
 
template <int dim>
void
PointValueHistory<dim>::tria_change_listener()
{
  // this function is called by the
  // Triangulation whenever something
  // changes, by virtue of having
  // attached the function to the
  // signal handler in the
  // triangulation object
 
  // we record the fact that the mesh
  // has changed. we need to take
  // this into account next time we
  // evaluate the solution
  triangulation_changed = true;
}
 
 
// explicit instantiations
#include "point_value_history.inst"
 
 
DEAL_II_NAMESPACE_CLOSE