utils.h

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// Copyright (C) 2013-2020 Johan Hake, Jan Blechta and Garth N. Wells
//
// This file is part of DOLFINx (https://www.fenicsproject.org)
//
// SPDX-License-Identifier:    LGPL-3.0-or-later
 
#pragma once
 
#include "Constant.h"
#include "CoordinateElement.h"
#include "DofMap.h"
#include "ElementDofLayout.h"
#include "Expression.h"
#include "Form.h"
#include "Function.h"
#include <dolfinx/la/SparsityPattern.h>
#include <dolfinx/mesh/cell_types.h>
#include <functional>
#include <memory>
#include <set>
#include <stdexcept>
#include <string>
#include <ufcx.h>
#include <utility>
#include <vector>
#include <xtensor/xadapt.hpp>
#include <xtensor/xtensor.hpp>
#include <xtl/xspan.hpp>
 
 
namespace basix
{
class FiniteElement;
}
 
namespace dolfinx::common
{
class IndexMap;
}
 
namespace dolfinx::mesh
{
class Mesh;
class Topology;
} // namespace dolfinx::mesh
 
namespace dolfinx::fem
{
class FunctionSpace;
 
template <typename T>
std::vector<std::vector<std::array<std::shared_ptr<const FunctionSpace>, 2>>>
extract_function_spaces(const std::vector<std::vector<const Form<T>*>>& a)
{
  std::vector<std::vector<std::array<std::shared_ptr<const FunctionSpace>, 2>>>
      spaces(a.size(),
             std::vector<std::array<std::shared_ptr<const FunctionSpace>, 2>>(
                 a[0].size()));
  for (std::size_t i = 0; i < a.size(); ++i)
  {
    for (std::size_t j = 0; j < a[i].size(); ++j)
    {
      if (const Form<T>* form = a[i][j]; form)
        spaces[i][j] = {form->function_spaces()[0], form->function_spaces()[1]};
    }
  }
  return spaces;
}
 
la::SparsityPattern create_sparsity_pattern(
    const mesh::Topology& topology,
    const std::array<std::reference_wrapper<const DofMap>, 2>& dofmaps,
    const std::set<IntegralType>& integrals);
 
template <typename T>
la::SparsityPattern create_sparsity_pattern(const Form<T>& a)
{
  if (a.rank() != 2)
  {
    throw std::runtime_error(
        "Cannot create sparsity pattern. Form is not a bilinear form");
  }
 
  // Get dof maps and mesh
  std::array<std::reference_wrapper<const DofMap>, 2> dofmaps{
      *a.function_spaces().at(0)->dofmap(),
      *a.function_spaces().at(1)->dofmap()};
  std::shared_ptr mesh = a.mesh();
  assert(mesh);
 
  const std::set<IntegralType> types = a.integral_types();
  if (types.find(IntegralType::interior_facet) != types.end()
      or types.find(IntegralType::exterior_facet) != types.end())
  {
    // FIXME: cleanup these calls? Some of the happen internally again.
    const int tdim = mesh->topology().dim();
    mesh->topology_mutable().create_entities(tdim - 1);
    mesh->topology_mutable().create_connectivity(tdim - 1, tdim);
  }
 
  return create_sparsity_pattern(mesh->topology(), dofmaps, types);
}
 
ElementDofLayout create_element_dof_layout(const ufcx_dofmap& dofmap,
                                           const mesh::CellType cell_type,
                                           const std::vector<int>& parent_map
                                           = {});
 
DofMap
create_dofmap(MPI_Comm comm, const ElementDofLayout& layout,
              mesh::Topology& topology,
              const std::function<std::vector<int>(
                  const graph::AdjacencyList<std::int32_t>&)>& reorder_fn,
              const FiniteElement& element);
 
std::vector<std::string> get_coefficient_names(const ufcx_form& ufcx_form);
 
std::vector<std::string> get_constant_names(const ufcx_form& ufcx_form);
 
template <typename T>
Form<T> create_form(
    const ufcx_form& ufcx_form,
    const std::vector<std::shared_ptr<const FunctionSpace>>& spaces,
    const std::vector<std::shared_ptr<const Function<T>>>& coefficients,
    const std::vector<std::shared_ptr<const Constant<T>>>& constants,
    const std::map<IntegralType, const mesh::MeshTags<int>*>& subdomains,
    const std::shared_ptr<const mesh::Mesh>& mesh = nullptr)
{
  if (ufcx_form.rank != (int)spaces.size())
    throw std::runtime_error("Wrong number of argument spaces for Form.");
  if (ufcx_form.num_coefficients != (int)coefficients.size())
  {
    throw std::runtime_error(
        "Mismatch between number of expected and provided Form coefficients.");
  }
  if (ufcx_form.num_constants != (int)constants.size())
  {
    throw std::runtime_error(
        "Mismatch between number of expected and provided Form constants.");
  }
 
  // Check argument function spaces
#ifndef NDEBUG
  for (std::size_t i = 0; i < spaces.size(); ++i)
  {
    assert(spaces[i]->element());
    ufcx_finite_element* ufcx_element = ufcx_form.finite_elements[i];
    assert(ufcx_element);
    if (std::string(ufcx_element->signature)
        != spaces[i]->element()->signature())
    {
      throw std::runtime_error(
          "Cannot create form. Wrong type of function space for argument.");
    }
  }
#endif
 
  // Get list of integral IDs, and load tabulate tensor into memory for
  // each
  using kern = std::function<void(T*, const T*, const T*, const double*,
                                  const int*, const std::uint8_t*)>;
  std::map<IntegralType, std::pair<std::vector<std::pair<int, kern>>,
                                   const mesh::MeshTags<int>*>>
      integral_data;
 
  bool needs_facet_permutations = false;
 
  // Attach cell kernels
  std::vector<int> cell_integral_ids(ufcx_form.integral_ids(cell),
                                     ufcx_form.integral_ids(cell)
                                         + ufcx_form.num_integrals(cell));
  for (int i = 0; i < ufcx_form.num_integrals(cell); ++i)
  {
    ufcx_integral* integral = ufcx_form.integrals(cell)[i];
    assert(integral);
 
    kern k = nullptr;
    if constexpr (std::is_same<T, float>::value)
      k = integral->tabulate_tensor_float32;
    else if constexpr (std::is_same<T, std::complex<float>>::value)
    {
      k = reinterpret_cast<void (*)(T*, const T*, const T*, const double*,
                                    const int*, const unsigned char*)>(
          integral->tabulate_tensor_complex64);
    }
    else if constexpr (std::is_same<T, double>::value)
      k = integral->tabulate_tensor_float64;
    else if constexpr (std::is_same<T, std::complex<double>>::value)
    {
      k = reinterpret_cast<void (*)(T*, const T*, const T*, const double*,
                                    const int*, const unsigned char*)>(
          integral->tabulate_tensor_complex128);
    }
    assert(k);
 
    integral_data[IntegralType::cell].first.emplace_back(cell_integral_ids[i],
                                                         k);
    if (integral->needs_facet_permutations)
      needs_facet_permutations = true;
  }
 
  // Attach cell subdomain data
  if (auto it = subdomains.find(IntegralType::cell);
      it != subdomains.end() and !cell_integral_ids.empty())
  {
    integral_data[IntegralType::cell].second = it->second;
  }
 
  // FIXME: Can facets be handled better?
 
  // Create facets, if required
  if (ufcx_form.num_integrals(exterior_facet) > 0
      or ufcx_form.num_integrals(interior_facet) > 0)
  {
    if (!spaces.empty())
    {
      auto mesh = spaces[0]->mesh();
      const int tdim = mesh->topology().dim();
      spaces[0]->mesh()->topology_mutable().create_entities(tdim - 1);
    }
  }
 
  // Attach exterior facet kernels
  std::vector<int> exterior_facet_integral_ids(
      ufcx_form.integral_ids(exterior_facet),
      ufcx_form.integral_ids(exterior_facet)
          + ufcx_form.num_integrals(exterior_facet));
  for (int i = 0; i < ufcx_form.num_integrals(exterior_facet); ++i)
  {
    ufcx_integral* integral = ufcx_form.integrals(exterior_facet)[i];
    assert(integral);
 
    kern k = nullptr;
    if constexpr (std::is_same<T, float>::value)
      k = integral->tabulate_tensor_float32;
    else if constexpr (std::is_same<T, std::complex<float>>::value)
    {
      k = reinterpret_cast<void (*)(T*, const T*, const T*, const double*,
                                    const int*, const unsigned char*)>(
          integral->tabulate_tensor_complex64);
    }
    else if constexpr (std::is_same<T, double>::value)
      k = integral->tabulate_tensor_float64;
    else if constexpr (std::is_same<T, std::complex<double>>::value)
    {
      k = reinterpret_cast<void (*)(T*, const T*, const T*, const double*,
                                    const int*, const unsigned char*)>(
          integral->tabulate_tensor_complex128);
    }
    assert(k);
 
    integral_data[IntegralType::exterior_facet].first.emplace_back(
        exterior_facet_integral_ids[i], k);
    if (integral->needs_facet_permutations)
      needs_facet_permutations = true;
  }
 
  // Attach exterior facet subdomain data
  if (auto it = subdomains.find(IntegralType::exterior_facet);
      it != subdomains.end() and !exterior_facet_integral_ids.empty())
  {
    integral_data[IntegralType::exterior_facet].second = it->second;
  }
 
  // Attach interior facet kernels
  std::vector<int> interior_facet_integral_ids(
      ufcx_form.integral_ids(interior_facet),
      ufcx_form.integral_ids(interior_facet)
          + ufcx_form.num_integrals(interior_facet));
  for (int i = 0; i < ufcx_form.num_integrals(interior_facet); ++i)
  {
    ufcx_integral* integral = ufcx_form.integrals(interior_facet)[i];
    assert(integral);
 
    kern k = nullptr;
    if constexpr (std::is_same<T, float>::value)
      k = integral->tabulate_tensor_float32;
    else if constexpr (std::is_same<T, std::complex<float>>::value)
    {
      k = reinterpret_cast<void (*)(T*, const T*, const T*, const double*,
                                    const int*, const unsigned char*)>(
          integral->tabulate_tensor_complex64);
    }
    else if constexpr (std::is_same<T, double>::value)
      k = integral->tabulate_tensor_float64;
    else if constexpr (std::is_same<T, std::complex<double>>::value)
    {
      k = reinterpret_cast<void (*)(T*, const T*, const T*, const double*,
                                    const int*, const unsigned char*)>(
          integral->tabulate_tensor_complex128);
    }
    assert(k);
 
    integral_data[IntegralType::interior_facet].first.emplace_back(
        interior_facet_integral_ids[i], k);
    if (integral->needs_facet_permutations)
      needs_facet_permutations = true;
  }
 
  // Attach interior facet subdomain data
  if (auto it = subdomains.find(IntegralType::interior_facet);
      it != subdomains.end() and !interior_facet_integral_ids.empty())
  {
    integral_data[IntegralType::interior_facet].second = it->second;
  }
 
  return Form<T>(spaces, integral_data, coefficients, constants,
                 needs_facet_permutations, mesh);
}
 
template <typename T>
Form<T> create_form(
    const ufcx_form& ufcx_form,
    const std::vector<std::shared_ptr<const FunctionSpace>>& spaces,
    const std::map<std::string, std::shared_ptr<const Function<T>>>&
        coefficients,
    const std::map<std::string, std::shared_ptr<const Constant<T>>>& constants,
    const std::map<IntegralType, const mesh::MeshTags<int>*>& subdomains,
    const std::shared_ptr<const mesh::Mesh>& mesh = nullptr)
{
  // Place coefficients in appropriate order
  std::vector<std::shared_ptr<const Function<T>>> coeff_map;
  for (const std::string& name : get_coefficient_names(ufcx_form))
  {
    if (auto it = coefficients.find(name); it != coefficients.end())
      coeff_map.push_back(it->second);
    else
    {
      throw std::runtime_error("Form coefficient \"" + name
                               + "\" not provided.");
    }
  }
 
  // Place constants in appropriate order
  std::vector<std::shared_ptr<const Constant<T>>> const_map;
  for (const std::string& name : get_constant_names(ufcx_form))
  {
    if (auto it = constants.find(name); it != constants.end())
      const_map.push_back(it->second);
    else
      throw std::runtime_error("Form constant \"" + name + "\" not provided.");
  }
 
  return create_form(ufcx_form, spaces, coeff_map, const_map, subdomains, mesh);
}
 
template <typename T>
Form<T> create_form(
    ufcx_form* (*fptr)(),
    const std::vector<std::shared_ptr<const FunctionSpace>>& spaces,
    const std::map<std::string, std::shared_ptr<const Function<T>>>&
        coefficients,
    const std::map<std::string, std::shared_ptr<const Constant<T>>>& constants,
    const std::map<IntegralType, const mesh::MeshTags<int>*>& subdomains,
    const std::shared_ptr<const mesh::Mesh>& mesh = nullptr)
{
  ufcx_form* form = fptr();
  Form<T> L = create_form<T>(*form, spaces, coefficients, constants, subdomains,
                             mesh);
  std::free(form);
  return L;
}
 
FunctionSpace
create_functionspace(const std::shared_ptr<mesh::Mesh>& mesh,
                     const basix::FiniteElement& e, int bs,
                     const std::function<std::vector<int>(
                         const graph::AdjacencyList<std::int32_t>&)>& reorder_fn
                     = nullptr);
 
FunctionSpace create_functionspace(
    ufcx_function_space* (*fptr)(const char*), const std::string& function_name,
    const std::shared_ptr<mesh::Mesh>& mesh,
    const std::function<
        std::vector<int>(const graph::AdjacencyList<std::int32_t>&)>& reorder_fn
    = nullptr);
 
namespace impl
{
template <typename T>
xtl::span<const std::uint32_t> get_cell_orientation_info(
    const std::vector<std::shared_ptr<const Function<T>>>& coefficients)
{
  bool needs_dof_transformations = false;
  for (auto coeff : coefficients)
  {
    std::shared_ptr<const FiniteElement> element
        = coeff->function_space()->element();
    if (element->needs_dof_transformations())
    {
      needs_dof_transformations = true;
      break;
    }
  }
 
  xtl::span<const std::uint32_t> cell_info;
  if (needs_dof_transformations)
  {
    auto mesh = coefficients.front()->function_space()->mesh();
    mesh->topology_mutable().create_entity_permutations();
    cell_info = xtl::span(mesh->topology().get_cell_permutation_info());
  }
 
  return cell_info;
}
 
// Pack a single coefficient for a single cell
template <typename T, int _bs, typename Functor>
static inline void pack(const xtl::span<T>& coeffs, std::int32_t cell, int bs,
                        const xtl::span<const T>& v,
                        const xtl::span<const std::uint32_t>& cell_info,
                        const DofMap& dofmap, Functor transform)
{
  auto dofs = dofmap.cell_dofs(cell);
  for (std::size_t i = 0; i < dofs.size(); ++i)
  {
    if constexpr (_bs < 0)
    {
      const int pos_c = bs * i;
      const int pos_v = bs * dofs[i];
      for (int k = 0; k < bs; ++k)
        coeffs[pos_c + k] = v[pos_v + k];
    }
    else
    {
      const int pos_c = _bs * i;
      const int pos_v = _bs * dofs[i];
      for (int k = 0; k < _bs; ++k)
        coeffs[pos_c + k] = v[pos_v + k];
    }
  }
 
  transform(coeffs, cell_info, cell, 1);
}
 
template <typename T, typename E, typename Functor>
void pack_coefficient_entity(const xtl::span<T>& c, int cstride,
                             const Function<T>& u,
                             const xtl::span<const std::uint32_t>& cell_info,
                             const E& entities, Functor fetch_cells,
                             std::int32_t offset)
{
  // Read data from coefficient "u"
  const xtl::span<const T>& v = u.x()->array();
  const DofMap& dofmap = *u.function_space()->dofmap();
  std::shared_ptr<const FiniteElement> element = u.function_space()->element();
  int space_dim = element->space_dimension();
  const auto transformation
      = element->get_dof_transformation_function<T>(false, true);
 
  const int bs = dofmap.bs();
  switch (bs)
  {
  case 1:
    for (std::size_t e = 0; e < entities.size(); ++e)
    {
      std::int32_t cell = fetch_cells(entities[e]);
      auto cell_coeff = c.subspan(e * cstride + offset, space_dim);
      pack<T, 1>(cell_coeff, cell, bs, v, cell_info, dofmap, transformation);
    }
    break;
  case 2:
    for (std::size_t e = 0; e < entities.size(); ++e)
    {
      std::int32_t cell = fetch_cells(entities[e]);
      auto cell_coeff = c.subspan(e * cstride + offset, space_dim);
      pack<T, 2>(cell_coeff, cell, bs, v, cell_info, dofmap, transformation);
    }
    break;
  case 3:
    for (std::size_t e = 0; e < entities.size(); ++e)
    {
      std::int32_t cell = fetch_cells(entities[e]);
      auto cell_coeff = c.subspan(e * cstride + offset, space_dim);
      pack<T, 3>(cell_coeff, cell, bs, v, cell_info, dofmap, transformation);
    }
    break;
  default:
    for (std::size_t e = 0; e < entities.size(); ++e)
    {
      std::int32_t cell = fetch_cells(entities[e]);
      auto cell_coeff = c.subspan(e * cstride + offset, space_dim);
      pack<T, -1>(cell_coeff, cell, bs, v, cell_info, dofmap, transformation);
    }
    break;
  }
}
 
} // namespace impl
 
template <typename T>
std::pair<std::vector<T>, int>
allocate_coefficient_storage(const Form<T>& form, IntegralType integral_type,
                             int id)
{
  // Get form coefficient offsets and dofmaps
  const std::vector<std::shared_ptr<const Function<T>>>& coefficients
      = form.coefficients();
  const std::vector<int> offsets = form.coefficient_offsets();
 
  std::size_t num_entities = 0;
  int cstride = 0;
  if (!coefficients.empty())
  {
    cstride = offsets.back();
    switch (integral_type)
    {
    case IntegralType::cell:
      num_entities = form.cell_domains(id).size();
      break;
    case IntegralType::exterior_facet:
      num_entities = form.exterior_facet_domains(id).size();
      break;
    case IntegralType::interior_facet:
      num_entities = form.interior_facet_domains(id).size() * 2;
      break;
    default:
      throw std::runtime_error(
          "Could not allocate coefficient data. Integral type not supported.");
    }
  }
 
  return {std::vector<T>(num_entities * cstride), cstride};
}
 
template <typename T>
std::map<std::pair<IntegralType, int>, std::pair<std::vector<T>, int>>
allocate_coefficient_storage(const Form<T>& form)
{
  std::map<std::pair<IntegralType, int>, std::pair<std::vector<T>, int>> coeffs;
  for (auto integral_type : form.integral_types())
  {
    for (int id : form.integral_ids(integral_type))
    {
      coeffs.emplace_hint(
          coeffs.end(), std::pair(integral_type, id),
          allocate_coefficient_storage(form, integral_type, id));
    }
  }
 
  return coeffs;
}
 
template <typename T>
void pack_coefficients(const Form<T>& form, IntegralType integral_type, int id,
                       const xtl::span<T>& c, int cstride)
{
  // Get form coefficient offsets and dofmaps
  const std::vector<std::shared_ptr<const Function<T>>>& coefficients
      = form.coefficients();
  const std::vector<int> offsets = form.coefficient_offsets();
 
  if (!coefficients.empty())
  {
    xtl::span<const std::uint32_t> cell_info
        = impl::get_cell_orientation_info(coefficients);
 
    switch (integral_type)
    {
    case IntegralType::cell:
    {
      auto fetch_cell = [](auto entity) { return entity; };
      const std::vector<std::int32_t>& cells = form.cell_domains(id);
      // Iterate over coefficients
      for (std::size_t coeff = 0; coeff < coefficients.size(); ++coeff)
      {
        impl::pack_coefficient_entity(c, cstride, *coefficients[coeff],
                                      cell_info, cells, fetch_cell,
                                      offsets[coeff]);
      }
      break;
    }
    case IntegralType::exterior_facet:
    {
      const std::vector<std::pair<std::int32_t, int>>& facets
          = form.exterior_facet_domains(id);
 
      // Create lambda function fetching cell index from exterior facet entity
      auto fetch_cell = [](auto& entity) { return entity.first; };
 
      // Iterate over coefficients
      for (std::size_t coeff = 0; coeff < coefficients.size(); ++coeff)
      {
        impl::pack_coefficient_entity(c, cstride, *coefficients[coeff],
                                      cell_info, facets, fetch_cell,
                                      offsets[coeff]);
      }
 
      break;
    }
    case IntegralType::interior_facet:
    {
      const std::vector<std::tuple<std::int32_t, int, std::int32_t, int>>&
          facets
          = form.interior_facet_domains(id);
      // Lambda functions to fetch cell index from interior facet entity
      auto fetch_cell0 = [](auto& entity) { return std::get<0>(entity); };
      auto fetch_cell1 = [](auto& entity) { return std::get<2>(entity); };
 
      // Iterate over coefficients
      for (std::size_t coeff = 0; coeff < coefficients.size(); ++coeff)
      {
        // Pack coefficient ['+']
        impl::pack_coefficient_entity(c, 2 * cstride, *coefficients[coeff],
                                      cell_info, facets, fetch_cell0,
                                      2 * offsets[coeff]);
        // Pack coefficient ['-']
        impl::pack_coefficient_entity(c, 2 * cstride, *coefficients[coeff],
                                      cell_info, facets, fetch_cell1,
                                      offsets[coeff] + offsets[coeff + 1]);
      }
      break;
    }
    default:
      throw std::runtime_error(
          "Could not pack coefficient. Integral type not supported.");
    }
  }
}
 
template <typename T>
fem::Expression<T> create_expression(
    const ufcx_expression& expression,
    const std::vector<std::shared_ptr<const fem::Function<T>>>& coefficients,
    const std::vector<std::shared_ptr<const fem::Constant<T>>>& constants,
    const std::shared_ptr<const mesh::Mesh>& mesh = nullptr,
    const std::shared_ptr<const fem::FunctionSpace>& argument_function_space
    = nullptr)
{
  if (expression.rank > 0 and !argument_function_space)
  {
    throw std::runtime_error(
        "Expression has Argument but no Argument function space was provided.");
  }
 
  const int size = expression.num_points * expression.topological_dimension;
  const xt::xtensor<double, 2> points = xt::adapt(
      expression.points, size, xt::no_ownership(),
      std::vector<std::size_t>(
          {static_cast<std::size_t>(expression.num_points),
           static_cast<std::size_t>(expression.topological_dimension)}));
 
  std::vector<int> value_shape;
  for (int i = 0; i < expression.num_components; ++i)
    value_shape.push_back(expression.value_shape[i]);
 
  std::function<void(T*, const T*, const T*, const double*, const int*,
                     const std::uint8_t*)>
      tabulate_tensor = nullptr;
  if constexpr (std::is_same<T, float>::value)
    tabulate_tensor = expression.tabulate_tensor_float32;
  else if constexpr (std::is_same<T, std::complex<float>>::value)
  {
    tabulate_tensor
        = reinterpret_cast<void (*)(T*, const T*, const T*, const double*,
                                    const int*, const unsigned char*)>(
            expression.tabulate_tensor_complex64);
  }
  else if constexpr (std::is_same<T, double>::value)
    tabulate_tensor = expression.tabulate_tensor_float64;
  else if constexpr (std::is_same<T, std::complex<double>>::value)
  {
    tabulate_tensor
        = reinterpret_cast<void (*)(T*, const T*, const T*, const double*,
                                    const int*, const unsigned char*)>(
            expression.tabulate_tensor_complex128);
  }
  else
  {
    throw std::runtime_error("Type not supported.");
  }
  assert(tabulate_tensor);
 
  return fem::Expression(coefficients, constants, points, tabulate_tensor,
                         value_shape, mesh, argument_function_space);
}
 
template <typename T>
fem::Expression<T> create_expression(
    const ufcx_expression& expression,
    const std::map<std::string, std::shared_ptr<const fem::Function<T>>>&
        coefficients,
    const std::map<std::string, std::shared_ptr<const fem::Constant<T>>>&
        constants,
    const std::shared_ptr<const mesh::Mesh>& mesh = nullptr,
    const std::shared_ptr<const fem::FunctionSpace>& argument_function_space
    = nullptr)
{
  // Place coefficients in appropriate order
  std::vector<std::shared_ptr<const fem::Function<T>>> coeff_map;
  std::vector<std::string> coefficient_names;
  for (int i = 0; i < expression.num_coefficients; ++i)
    coefficient_names.push_back(expression.coefficient_names[i]);
 
  for (const std::string& name : coefficient_names)
  {
    if (auto it = coefficients.find(name); it != coefficients.end())
      coeff_map.push_back(it->second);
    else
    {
      throw std::runtime_error("Expression coefficient \"" + name
                               + "\" not provided.");
    }
  }
 
  // Place constants in appropriate order
  std::vector<std::shared_ptr<const fem::Constant<T>>> const_map;
  std::vector<std::string> constant_names;
  for (int i = 0; i < expression.num_constants; ++i)
    constant_names.push_back(expression.constant_names[i]);
 
  for (const std::string& name : constant_names)
  {
    if (auto it = constants.find(name); it != constants.end())
      const_map.push_back(it->second);
    else
    {
      throw std::runtime_error("Expression constant \"" + name
                               + "\" not provided.");
    }
  }
 
  return create_expression(expression, coeff_map, const_map, mesh,
                           argument_function_space);
}
 
template <typename T>
void pack_coefficients(const Form<T>& form,
                       std::map<std::pair<IntegralType, int>,
                                std::pair<std::vector<T>, int>>& coeffs)
{
  for (auto& [key, val] : coeffs)
    pack_coefficients<T>(form, key.first, key.second, val.first, val.second);
}
 
template <typename T>
std::pair<std::vector<T>, int>
pack_coefficients(const Expression<T>& u,
                  const xtl::span<const std::int32_t>& cells)
{
  // Get form coefficient offsets and dofmaps
  const std::vector<std::shared_ptr<const Function<T>>>& coefficients
      = u.coefficients();
  const std::vector<int> offsets = u.coefficient_offsets();
 
  // Copy data into coefficient array
  const int cstride = offsets.back();
  std::vector<T> c(cells.size() * offsets.back());
  if (!coefficients.empty())
  {
    xtl::span<const std::uint32_t> cell_info
        = impl::get_cell_orientation_info(coefficients);
 
    // Iterate over coefficients
    for (std::size_t coeff = 0; coeff < coefficients.size(); ++coeff)
      impl::pack_coefficient_entity(
          xtl::span(c), cstride, *coefficients[coeff], cell_info, cells,
          [](std::int32_t entity) { return entity; }, offsets[coeff]);
  }
  return {std::move(c), cstride};
}
 
template <typename U>
std::vector<typename U::scalar_type> pack_constants(const U& u)
{
  using T = typename U::scalar_type;
  const std::vector<std::shared_ptr<const Constant<T>>>& constants
      = u.constants();
 
  // Calculate size of array needed to store packed constants
  std::int32_t size = std::accumulate(constants.cbegin(), constants.cend(), 0,
                                      [](std::int32_t sum, auto& constant)
                                      { return sum + constant->value.size(); });
 
  // Pack constants
  std::vector<T> constant_values(size);
  std::int32_t offset = 0;
  for (auto& constant : constants)
  {
    const std::vector<T>& value = constant->value;
    std::copy(value.cbegin(), value.cend(),
              std::next(constant_values.begin(), offset));
    offset += value.size();
  }
 
  return constant_values;
}
 
} // namespace dolfinx::fem