Geometry.h

// Copyright (C) 2006-2022 Anders Logg 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 "Topology.h"
#include <basix/mdspan.hpp>
#include <concepts>
#include <cstdint>
#include <dolfinx/common/IndexMap.h>
#include <dolfinx/common/MPI.h>
#include <dolfinx/common/sort.h>
#include <dolfinx/fem/CoordinateElement.h>
#include <dolfinx/fem/ElementDofLayout.h>
#include <dolfinx/fem/dofmapbuilder.h>
#include <dolfinx/graph/AdjacencyList.h>
#include <dolfinx/graph/partition.h>
#include <functional>
#include <memory>
#include <span>
#include <utility>
#include <vector>
 
namespace dolfinx::mesh
{
 
template <std::floating_point T>
class Geometry
{
public:
  using value_type = T;
 
  template <typename U, typename V, typename W>
    requires std::is_convertible_v<std::remove_cvref_t<U>,
                                   std::vector<std::int32_t>>
                 and std::is_convertible_v<std::remove_cvref_t<V>,
                                           std::vector<T>>
                 and std::is_convertible_v<std::remove_cvref_t<W>,
                                           std::vector<std::int64_t>>
  Geometry(
      std::shared_ptr<const common::IndexMap> index_map, U&& dofmap,
      const fem::CoordinateElement<
          typename std::remove_reference_t<typename V::value_type>>& element,
      V&& x, int dim, W&& input_global_indices)
      : _dim(dim), _dofmaps({dofmap}), _index_map(index_map), _cmaps({element}),
        _x(std::forward<V>(x)),
        _input_global_indices(std::forward<W>(input_global_indices))
  {
    assert(_x.size() % 3 == 0);
    if (_x.size() / 3 != _input_global_indices.size())
      throw std::runtime_error("Geometry size mis-match");
  }
 
  template <typename V, typename W>
    requires std::is_convertible_v<std::remove_cvref_t<V>, std::vector<T>>
                 and std::is_convertible_v<std::remove_cvref_t<W>,
                                           std::vector<std::int64_t>>
  Geometry(
      std::shared_ptr<const common::IndexMap> index_map,
      const std::vector<std::vector<std::int32_t>>& dofmaps,
      const std::vector<fem::CoordinateElement<
          typename std::remove_reference_t<typename V::value_type>>>& elements,
      V&& x, int dim, W&& input_global_indices)
      : _dim(dim), _dofmaps(dofmaps), _index_map(index_map), _cmaps(elements),
        _x(std::forward<V>(x)),
        _input_global_indices(std::forward<W>(input_global_indices))
  {
    assert(_x.size() % 3 == 0);
    if (_x.size() / 3 != _input_global_indices.size())
      throw std::runtime_error("Geometry size mis-match");
  }
 
  Geometry(const Geometry&) = default;
 
  Geometry(Geometry&&) = default;
 
  ~Geometry() = default;
 
  Geometry& operator=(const Geometry&) = delete;
 
  Geometry& operator=(Geometry&&) = default;
 
  int dim() const { return _dim; }
 
  MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan<
      const std::int32_t,
      MDSPAN_IMPL_STANDARD_NAMESPACE::dextents<std::size_t, 2>>
  dofmap() const
  {
    if (_dofmaps.size() != 1)
      throw std::runtime_error("Multiple dofmaps");
 
    int ndofs = _cmaps.front().dim();
    return MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan<
        const std::int32_t,
        MDSPAN_IMPL_STANDARD_NAMESPACE::dextents<std::size_t, 2>>(
        _dofmaps.front().data(), _dofmaps.front().size() / ndofs, ndofs);
  }
 
  MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan<
      const std::int32_t,
      MDSPAN_IMPL_STANDARD_NAMESPACE::dextents<std::size_t, 2>>
  dofmap(std::int32_t i) const
  {
    if (i < 0 or i >= (int)_dofmaps.size())
    {
      throw std::out_of_range("Cannot get dofmap:" + std::to_string(i)
                              + " out of range");
    }
    int ndofs = _cmaps[i].dim();
 
    return MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan<
        const std::int32_t,
        MDSPAN_IMPL_STANDARD_NAMESPACE::dextents<std::size_t, 2>>(
        _dofmaps[i].data(), _dofmaps[i].size() / ndofs, ndofs);
  }
 
  std::shared_ptr<const common::IndexMap> index_map() const
  {
    return _index_map;
  }
 
  std::span<const value_type> x() const { return _x; }
 
  std::span<value_type> x() { return _x; }
 
  const fem::CoordinateElement<value_type>& cmap() const
  {
    if (_cmaps.size() != 1)
      throw std::runtime_error("Multiple cmaps.");
    return _cmaps.front();
  }
 
  const fem::CoordinateElement<value_type>& cmap(std::int32_t i) const
  {
    if (i < 0 or i >= (int)_cmaps.size())
    {
      throw std::out_of_range("Cannot get cmap:" + std::to_string(i)
                              + " out of range");
    }
    return _cmaps[i];
  }
 
  const std::vector<std::int64_t>& input_global_indices() const
  {
    return _input_global_indices;
  }
 
private:
  // Geometric dimension
  int _dim;
 
  // Map per cell for extracting coordinate data for each cmap
  std::vector<std::vector<std::int32_t>> _dofmaps;
 
  // IndexMap for geometry 'dofmap'
  std::shared_ptr<const common::IndexMap> _index_map;
 
  // The coordinate elements
  std::vector<fem::CoordinateElement<value_type>> _cmaps;
 
  // Coordinates for all points stored as a contiguous array (row-major,
  // column size = 3)
  std::vector<value_type> _x;
 
  // Global indices as provided on Geometry creation
  std::vector<std::int64_t> _input_global_indices;
};
 
template <typename U, typename V, typename W>
Geometry(std::shared_ptr<const common::IndexMap>, U,
         const std::vector<fem::CoordinateElement<
             typename std::remove_reference_t<typename V::value_type>>>&,
         V, int,
         W) -> Geometry<typename std::remove_cvref_t<typename V::value_type>>;
 
template <typename U>
Geometry<typename std::remove_reference_t<typename U::value_type>>
create_geometry(
    const Topology& topology,
    const std::vector<fem::CoordinateElement<
        std::remove_reference_t<typename U::value_type>>>& elements,
    std::span<const std::int64_t> nodes, std::span<const std::int64_t> xdofs,
    const U& x, int dim,
    std::function<std::vector<int>(const graph::AdjacencyList<std::int32_t>&)>
        reorder_fn
    = nullptr)
{
  LOG(INFO) << "Create Geometry (multiple)";
 
  assert(std::is_sorted(nodes.begin(), nodes.end()));
  using T = typename std::remove_reference_t<typename U::value_type>;
 
  // Check elements match cell types in topology
  const int tdim = topology.dim();
  const std::size_t num_cell_types = topology.entity_types(tdim).size();
  if (elements.size() != num_cell_types)
    throw std::runtime_error("Mismatch between topology and geometry.");
 
  std::vector<fem::ElementDofLayout> dof_layouts;
  for (const auto& el : elements)
    dof_layouts.push_back(el.create_dof_layout());
 
  LOG(INFO) << "Got " << dof_layouts.size() << " dof layouts";
 
  //  Build 'geometry' dofmap on the topology
  auto [_dof_index_map, bs, dofmaps]
      = fem::build_dofmap_data(topology.index_map(topology.dim())->comm(),
                               topology, dof_layouts, reorder_fn);
  auto dof_index_map
      = std::make_shared<common::IndexMap>(std::move(_dof_index_map));
 
  // If the mesh has higher order geometry, permute the dofmap
  if (elements.front().needs_dof_permutations())
  {
    const std::int32_t num_cells
        = topology.connectivity(topology.dim(), 0)->num_nodes();
    const std::vector<std::uint32_t>& cell_info
        = topology.get_cell_permutation_info();
    int d = elements.front().dim();
    for (std::int32_t cell = 0; cell < num_cells; ++cell)
    {
      std::span dofs(dofmaps.front().data() + cell * d, d);
      elements.front().permute_inv(dofs, cell_info[cell]);
    }
  }
 
  LOG(INFO) << "Calling compute_local_to_global";
  // Compute local-to-global map from local indices in dofmap to the
  // corresponding global indices in cells, and pass to function to
  // compute local (dof) to local (position in coords) map from (i)
  // local-to-global for dofs and (ii) local-to-global for entries in
  // coords
 
  LOG(INFO) << "xdofs.size = " << xdofs.size();
  std::vector<std::int32_t> all_dofmaps;
  std::stringstream s;
  for (auto q : dofmaps)
  {
    s << q.size() << " ";
    all_dofmaps.insert(all_dofmaps.end(), q.begin(), q.end());
  }
  LOG(INFO) << "dofmap sizes = " << s.str();
  LOG(INFO) << "all_dofmaps.size = " << all_dofmaps.size();
  LOG(INFO) << "nodes.size = " << nodes.size();
 
  const std::vector<std::int32_t> l2l = graph::build::compute_local_to_local(
      graph::build::compute_local_to_global(xdofs, all_dofmaps), nodes);
 
  // Allocate space for input global indices and copy data
  std::vector<std::int64_t> igi(nodes.size());
  std::transform(l2l.cbegin(), l2l.cend(), igi.begin(),
                 [&nodes](auto index) { return nodes[index]; });
 
  // Build coordinate dof array, copying coordinates to correct position
  assert(x.size() % dim == 0);
  const std::size_t shape0 = x.size() / dim;
  const std::size_t shape1 = dim;
  std::vector<T> xg(3 * shape0, 0);
  for (std::size_t i = 0; i < shape0; ++i)
  {
    std::copy_n(std::next(x.begin(), shape1 * l2l[i]), shape1,
                std::next(xg.begin(), 3 * i));
  }
 
  LOG(INFO) << "Creating geometry with " << dofmaps.size() << " dofmaps";
 
  return Geometry(dof_index_map, std::move(dofmaps), elements, std::move(xg),
                  dim, std::move(igi));
}
 
template <typename U>
Geometry<typename std::remove_reference_t<typename U::value_type>>
create_geometry(
    const Topology& topology,
    const fem::CoordinateElement<
        std::remove_reference_t<typename U::value_type>>& element,
    std::span<const std::int64_t> nodes, std::span<const std::int64_t> xdofs,
    const U& x, int dim,
    std::function<std::vector<int>(const graph::AdjacencyList<std::int32_t>&)>
        reorder_fn
    = nullptr)
{
  assert(std::is_sorted(nodes.begin(), nodes.end()));
  using T = typename std::remove_reference_t<typename U::value_type>;
 
  fem::ElementDofLayout dof_layout = element.create_dof_layout();
 
  //  Build 'geometry' dofmap on the topology
  auto [_dof_index_map, bs, dofmaps]
      = fem::build_dofmap_data(topology.index_map(topology.dim())->comm(),
                               topology, {dof_layout}, reorder_fn);
  auto dof_index_map
      = std::make_shared<common::IndexMap>(std::move(_dof_index_map));
 
  // If the mesh has higher order geometry, permute the dofmap
  if (element.needs_dof_permutations())
  {
    const std::int32_t num_cells
        = topology.connectivity(topology.dim(), 0)->num_nodes();
    const std::vector<std::uint32_t>& cell_info
        = topology.get_cell_permutation_info();
    int d = element.dim();
    for (std::int32_t cell = 0; cell < num_cells; ++cell)
    {
      std::span dofs(dofmaps.front().data() + cell * d, d);
      element.permute_inv(dofs, cell_info[cell]);
    }
  }
 
  // Compute local-to-global map from local indices in dofmap to the
  // corresponding global indices in cells, and pass to function to
  // compute local (dof) to local (position in coords) map from (i)
  // local-to-global for dofs and (ii) local-to-global for entries in
  // coords
  const std::vector<std::int32_t> l2l = graph::build::compute_local_to_local(
      graph::build::compute_local_to_global(xdofs, dofmaps.front()), nodes);
 
  // Allocate space for input global indices and copy data
  std::vector<std::int64_t> igi(nodes.size());
  std::transform(l2l.cbegin(), l2l.cend(), igi.begin(),
                 [&nodes](auto index) { return nodes[index]; });
 
  // Build coordinate dof array, copying coordinates to correct position
  assert(x.size() % dim == 0);
  const std::size_t shape0 = x.size() / dim;
  const std::size_t shape1 = dim;
  std::vector<T> xg(3 * shape0, 0);
  for (std::size_t i = 0; i < shape0; ++i)
  {
    std::copy_n(std::next(x.cbegin(), shape1 * l2l[i]), shape1,
                std::next(xg.begin(), 3 * i));
  }
 
  return Geometry(dof_index_map, std::move(dofmaps.front()), {element},
                  std::move(xg), dim, std::move(igi));
}
 
template <std::floating_point T>
std::pair<Geometry<T>, std::vector<int32_t>>
create_subgeometry(const Topology& topology, const Geometry<T>& geometry,
                   int dim, std::span<const std::int32_t> subentity_to_entity)
{
  // Get the geometry dofs in the sub-geometry based on the entities in
  // sub-geometry
  const fem::ElementDofLayout layout = geometry.cmap().create_dof_layout();
  // NOTE: Unclear what this return for prisms
  const std::size_t num_entity_dofs = layout.num_entity_closure_dofs(dim);
 
  std::vector<std::int32_t> x_indices;
  x_indices.reserve(num_entity_dofs * subentity_to_entity.size());
  {
    auto xdofs = geometry.dofmap();
    const int tdim = topology.dim();
 
    // Fetch connectivities required to get entity dofs
    const std::vector<std::vector<std::vector<int>>>& closure_dofs
        = layout.entity_closure_dofs_all();
    auto e_to_c = topology.connectivity(dim, tdim);
    assert(e_to_c);
    auto c_to_e = topology.connectivity(tdim, dim);
    assert(c_to_e);
    for (std::size_t i = 0; i < subentity_to_entity.size(); ++i)
    {
      const std::int32_t idx = subentity_to_entity[i];
      assert(!e_to_c->links(idx).empty());
      // Always pick the last cell to be consistent with the e_to_v connectivity
      const std::int32_t cell = e_to_c->links(idx).back();
      auto cell_entities = c_to_e->links(cell);
      auto it = std::find(cell_entities.begin(), cell_entities.end(), idx);
      assert(it != cell_entities.end());
      std::size_t local_entity = std::distance(cell_entities.begin(), it);
 
      auto xc = MDSPAN_IMPL_STANDARD_NAMESPACE::submdspan(
          xdofs, cell, MDSPAN_IMPL_STANDARD_NAMESPACE::full_extent);
      for (std::int32_t entity_dof : closure_dofs[dim][local_entity])
        x_indices.push_back(xc[entity_dof]);
    }
  }
 
  std::vector<std::int32_t> sub_x_dofs = x_indices;
  std::sort(sub_x_dofs.begin(), sub_x_dofs.end());
  sub_x_dofs.erase(std::unique(sub_x_dofs.begin(), sub_x_dofs.end()),
                   sub_x_dofs.end());
 
  // Get the sub-geometry dofs owned by this process
  auto x_index_map = geometry.index_map();
  assert(x_index_map);
 
  std::shared_ptr<common::IndexMap> sub_x_dof_index_map;
  std::vector<std::int32_t> subx_to_x_dofmap;
  {
    auto [map, new_to_old] = common::create_sub_index_map(
        *x_index_map, sub_x_dofs, common::IndexMapOrder::any, true);
    sub_x_dof_index_map = std::make_shared<common::IndexMap>(std::move(map));
    subx_to_x_dofmap = std::move(new_to_old);
  }
 
  // Create sub-geometry coordinates
  std::span<const T> x = geometry.x();
  std::int32_t sub_num_x_dofs = subx_to_x_dofmap.size();
  std::vector<T> sub_x(3 * sub_num_x_dofs);
  for (int i = 0; i < sub_num_x_dofs; ++i)
  {
    std::copy_n(std::next(x.begin(), 3 * subx_to_x_dofmap[i]), 3,
                std::next(sub_x.begin(), 3 * i));
  }
 
  // Create geometry to sub-geometry  map
  std::vector<std::int32_t> x_to_subx_dof_map(
      x_index_map->size_local() + x_index_map->num_ghosts(), -1);
  for (std::size_t i = 0; i < subx_to_x_dofmap.size(); ++i)
    x_to_subx_dof_map[subx_to_x_dofmap[i]] = i;
 
  // Create sub-geometry dofmap
  std::vector<std::int32_t> sub_x_dofmap;
  sub_x_dofmap.reserve(x_indices.size());
  std::transform(x_indices.cbegin(), x_indices.cend(),
                 std::back_inserter(sub_x_dofmap),
                 [&x_to_subx_dof_map](auto x_dof)
                 {
                   assert(x_to_subx_dof_map[x_dof] != -1);
                   return x_to_subx_dof_map[x_dof];
                 });
 
  // Create sub-geometry coordinate element
  CellType sub_coord_cell
      = cell_entity_type(geometry.cmap().cell_shape(), dim, 0);
  fem::CoordinateElement<T> sub_cmap(sub_coord_cell, geometry.cmap().degree(),
                                     geometry.cmap().variant());
 
  // Sub-geometry input_global_indices
  // TODO: Check this
  const std::vector<std::int64_t>& igi = geometry.input_global_indices();
  std::vector<std::int64_t> sub_igi;
  sub_igi.reserve(subx_to_x_dofmap.size());
  std::transform(subx_to_x_dofmap.begin(), subx_to_x_dofmap.end(),
                 std::back_inserter(sub_igi),
                 [&igi](std::int32_t sub_x_dof) { return igi[sub_x_dof]; });
 
  // Create geometry
  return {Geometry(sub_x_dof_index_map, std::move(sub_x_dofmap), {sub_cmap},
                   std::move(sub_x), geometry.dim(), std::move(sub_igi)),
          std::move(subx_to_x_dofmap)};
}
 
} // namespace dolfinx::mesh