Expression.h

// Copyright (C) 2020-2021 Jack S. Hale and Michal Habera.
//
// This file is part of DOLFINx (https://www.fenicsproject.org)
//
// SPDX-License-Identifier:    LGPL-3.0-or-later
 
#pragma once
 
#include "Constant.h"
#include "Function.h"
#include <algorithm>
#include <array>
#include <concepts>
#include <dolfinx/common/types.h>
#include <dolfinx/mesh/Mesh.h>
#include <functional>
#include <span>
#include <utility>
#include <vector>
 
namespace dolfinx::fem
{
template <dolfinx::scalar T>
class Constant;
 
template <dolfinx::scalar T,
          std::floating_point U = dolfinx::scalar_value_type_t<T>>
class Expression
{
public:
  using scalar_type = T;
 
  using geometry_type = U;
 
  Expression(
      const std::vector<std::shared_ptr<
          const Function<scalar_type, geometry_type>>>& coefficients,
      const std::vector<std::shared_ptr<const Constant<scalar_type>>>&
          constants,
      std::span<const geometry_type> X, std::array<std::size_t, 2> Xshape,
      std::function<void(scalar_type*, const scalar_type*, const scalar_type*,
                         const geometry_type*, const int*, const uint8_t*)>
          fn,
      const std::vector<int>& value_shape,
      std::shared_ptr<const FunctionSpace<geometry_type>>
          argument_function_space
      = nullptr)
      : _coefficients(coefficients), _constants(constants),
        _x_ref(std::vector<geometry_type>(X.begin(), X.end()), Xshape), _fn(fn),
        _value_shape(value_shape),
        _argument_function_space(argument_function_space)
  {
    for (auto& c : _coefficients)
    {
      assert(c);
      if (c->function_space()->mesh()
          != _coefficients.front()->function_space()->mesh())
      {
        throw std::runtime_error("Coefficients not all defined on same mesh.");
      }
    }
  }
 
  Expression(Expression&& e) = default;
 
  virtual ~Expression() = default;
 
  std::shared_ptr<const FunctionSpace<geometry_type>>
  argument_function_space() const
  {
    return _argument_function_space;
  };
 
  const std::vector<
      std::shared_ptr<const Function<scalar_type, geometry_type>>>&
  coefficients() const
  {
    return _coefficients;
  }
 
  const std::vector<std::shared_ptr<const Constant<scalar_type>>>&
  constants() const
  {
    return _constants;
  }
 
  std::vector<int> coefficient_offsets() const
  {
    std::vector<int> n{0};
    for (auto& c : _coefficients)
    {
      if (!c)
        throw std::runtime_error("Not all form coefficients have been set.");
      n.push_back(n.back() + c->function_space()->element()->space_dimension());
    }
    return n;
  }
 
  void eval(const mesh::Mesh<geometry_type>& mesh,
            std::span<const std::int32_t> entities,
            std::span<scalar_type> values,
            std::array<std::size_t, 2> vshape) const
  {
    std::size_t estride;
    if (mesh.topology()->dim() == _x_ref.second[1])
    {
      estride = 1;
    }
    else if (mesh.topology()->dim() == _x_ref.second[1] + 1)
    {
      estride = 2;
    }
    else
    {
      throw std::runtime_error("Invalid dimension of evaluation points.");
    }
    // Prepare coefficients and constants
    const auto [coeffs, cstride] = pack_coefficients(*this, entities, estride);
    const std::vector<scalar_type> constant_data = pack_constants(*this);
    auto fn = this->get_tabulate_expression();
 
    // Prepare cell geometry
    auto x_dofmap = mesh.geometry().dofmap();
 
    // Get geometry data
    auto& cmap = mesh.geometry().cmap();
 
    const std::size_t num_dofs_g = cmap.dim();
    auto x_g = mesh.geometry().x();
 
    // Create data structures used in evaluation
    std::vector<geometry_type> coord_dofs(3 * num_dofs_g);
 
    int num_argument_dofs = 1;
    std::span<const std::uint32_t> cell_info;
    std::function<void(std::span<scalar_type>, std::span<const std::uint32_t>,
                       std::int32_t, int)>
        post_dof_transform
        = [](std::span<scalar_type>, std::span<const std::uint32_t>,
             std::int32_t, int)
    {
      // Do nothing
    };
 
    if (_argument_function_space)
    {
      num_argument_dofs
          = _argument_function_space->dofmap()->element_dof_layout().num_dofs();
      auto element = _argument_function_space->element();
 
      assert(element);
      if (element->needs_dof_transformations())
      {
        mesh.topology_mutable()->create_entity_permutations();
        cell_info = std::span(mesh.topology()->get_cell_permutation_info());
        post_dof_transform
            = element->template dof_transformation_right_fn<scalar_type>(
                doftransform::transpose);
      }
    }
 
    // Create get entity index function
    std::function<const std::int32_t*(std::span<const std::int32_t>,
                                      std::size_t)>
        get_entity_index
        = []([[maybe_unused]] std::span<const std::int32_t> entities,
             [[maybe_unused]] std::size_t idx) { return nullptr; };
    if (estride == 2)
    {
      get_entity_index
          = [](std::span<const std::int32_t> entities, std::size_t idx)
      { return entities.data() + 2 * idx + 1; };
    }
 
    // Iterate over cells and 'assemble' into values
    const int size0 = _x_ref.second[0] * value_size();
    std::vector<scalar_type> values_local(size0 * num_argument_dofs, 0);
    for (std::size_t e = 0; e < entities.size() / estride; ++e)
    {
      const std::int32_t entity = entities[e * estride];
      auto x_dofs = MDSPAN_IMPL_STANDARD_NAMESPACE::submdspan(
          x_dofmap, entity, MDSPAN_IMPL_STANDARD_NAMESPACE::full_extent);
      for (std::size_t i = 0; i < x_dofs.size(); ++i)
      {
        std::copy_n(std::next(x_g.begin(), 3 * x_dofs[i]), 3,
                    std::next(coord_dofs.begin(), 3 * i));
      }
 
      const scalar_type* coeff_cell = coeffs.data() + e * cstride;
      const int* entity_index = get_entity_index(entities, e);
 
      std::fill(values_local.begin(), values_local.end(), 0);
      _fn(values_local.data(), coeff_cell, constant_data.data(),
          coord_dofs.data(), entity_index, nullptr);
 
      post_dof_transform(values_local, cell_info, e, size0);
      for (std::size_t j = 0; j < values_local.size(); ++j)
        values[e * vshape[1] + j] = values_local[j];
    }
  }
 
  const std::function<void(scalar_type*, const scalar_type*, const scalar_type*,
                           const geometry_type*, const int*, const uint8_t*)>&
  get_tabulate_expression() const
  {
    return _fn;
  }
 
  int value_size() const
  {
    return std::reduce(_value_shape.begin(), _value_shape.end(), 1,
                       std::multiplies{});
  }
 
  const std::vector<int>& value_shape() const { return _value_shape; }
 
  std::pair<std::vector<geometry_type>, std::array<std::size_t, 2>> X() const
  {
    return _x_ref;
  }
 
private:
  // Function space for Argument
  std::shared_ptr<const FunctionSpace<geometry_type>> _argument_function_space;
 
  // Coefficients associated with the Expression
  std::vector<std::shared_ptr<const Function<scalar_type, geometry_type>>>
      _coefficients;
 
  // Constants associated with the Expression
  std::vector<std::shared_ptr<const Constant<scalar_type>>> _constants;
 
  // Function to evaluate the Expression
  std::function<void(scalar_type*, const scalar_type*, const scalar_type*,
                     const geometry_type*, const int*, const uint8_t*)>
      _fn;
 
  // Shape of the evaluated expression
  std::vector<int> _value_shape;
 
  // Evaluation points on reference cell. Synonymous with X in public
  // interface.
  std::pair<std::vector<geometry_type>, std::array<std::size_t, 2>> _x_ref;
};
} // namespace dolfinx::fem