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 std::vector<fem::CoordinateElement<
               typename
 
               std::remove_reference_t<typename V::value_type>>>& elements,
           V&& x, int dim, W&& input_global_indices)
      : _dim(dim), _dofmap(std::forward<U>(dofmap)), _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
  {
    int ndofs = _cmaps[0].dim();
    return MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan<
        const std::int32_t,
        MDSPAN_IMPL_STANDARD_NAMESPACE::dextents<std::size_t, 2>>(
        _dofmap.data(), _dofmap.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 std::vector<fem::CoordinateElement<value_type>>& cmaps() const
  {
    return _cmaps;
  }
 
  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
  std::vector<std::int32_t> _dofmap;
 
  // 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>
mesh::Geometry<typename std::remove_reference_t<typename U::value_type>>
create_geometry(
    MPI_Comm comm, const Topology& topology,
    const std::vector<fem::CoordinateElement<
        std::remove_reference_t<typename U::value_type>>>& elements,
    const graph::AdjacencyList<std::int64_t>& cell_nodes, const U& x, int dim,
    std::function<std::vector<int>(const graph::AdjacencyList<std::int32_t>&)>
        reorder_fn
    = nullptr)
{
  // TODO: make sure required entities are initialised, or extend
  // fem::build_dofmap_data
 
  std::vector<fem::ElementDofLayout> dof_layouts;
  for (auto e : elements)
    dof_layouts.push_back(e.create_dof_layout());
 
  //  Build 'geometry' dofmap on the topology
  auto [_dof_index_map, bs, dofmap]
      = fem::build_dofmap_data(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[0].needs_dof_permutations())
  {
    if (elements.size() > 1)
      throw std::runtime_error("Unsupported for Mixed Topology");
    const int D = topology.dim();
    const int num_cells = topology.connectivity(D, 0)->num_nodes();
    const std::vector<std::uint32_t>& cell_info
        = topology.get_cell_permutation_info();
 
    int dim = elements[0].dim();
    for (std::int32_t cell = 0; cell < num_cells; ++cell)
    {
      std::span<std::int32_t> dofs(dofmap.data() + cell * dim, dim);
      elements[0].unpermute_dofs(dofs, cell_info[cell]);
    }
  }
 
  auto remap_data
      = [](auto comm, auto& cell_nodes, auto& x, int dim, auto& dofmap)
  {
    // Build list of unique (global) node indices from adjacency list
    // (geometry nodes)
    std::vector<std::int64_t> indices = cell_nodes.array();
    dolfinx::radix_sort(std::span(indices));
    indices.erase(std::unique(indices.begin(), indices.end()), indices.end());
 
    //  Distribute  node coordinates by global index from other ranks.
    //  Order of coords matches order of the indices in 'indices'.
    std::vector coords = dolfinx::MPI::distribute_data(comm, indices, x, dim);
 
    // Compute local-to-global map from local indices in dofmap to the
    // corresponding global indices in cell_nodes
    std::vector l2g
        = graph::build::compute_local_to_global(cell_nodes.array(), dofmap);
 
    // 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
    std::vector l2l = graph::build::compute_local_to_local(l2g, indices);
 
    // Allocate space for input global indices and copy data
    std::vector<std::int64_t> igi(indices.size());
    std::transform(l2l.cbegin(), l2l.cend(), igi.begin(),
                   [&indices](auto index) { return indices[index]; });
 
    return std::tuple(std::move(coords), std::move(l2l), std::move(igi));
  };
 
  auto [coords, l2l, igi] = remap_data(comm, cell_nodes, x, dim, dofmap);
 
  // Build coordinate dof array, copying coordinates to correct
  // position
  assert(coords.size() % dim == 0);
  const std::size_t shape0 = coords.size() / dim;
  const std::size_t shape1 = dim;
  std::vector<typename std::remove_reference_t<typename U::value_type>> xg(
      3 * shape0, 0);
  for (std::size_t i = 0; i < shape0; ++i)
  {
    std::copy_n(std::next(coords.cbegin(), shape1 * l2l[i]), shape1,
                std::next(xg.begin(), 3 * i));
  }
 
  return Geometry<typename std::remove_reference_t<typename U::value_type>>(
      dof_index_map, std::move(dofmap), elements, std::move(xg), dim,
      std::move(igi));
}
 
template <std::floating_point T>
std::pair<mesh::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)
{
  if (geometry.cmaps().size() > 1)
    throw std::runtime_error("Mixed topology not supported");
 
  // Get the geometry dofs in the sub-geometry based on the entities in
  // sub-geometry
  const fem::ElementDofLayout layout = geometry.cmaps()[0].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::MDSPAN_IMPL_PROPOSED_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);
  auto subx_to_x_dofmap
      = common::compute_owned_indices(sub_x_dofs, *x_index_map);
  std::shared_ptr<common::IndexMap> sub_x_dof_index_map;
  {
    std::pair<common::IndexMap, std::vector<int32_t>> map_data
        = x_index_map->create_submap(subx_to_x_dofmap);
    sub_x_dof_index_map
        = std::make_shared<common::IndexMap>(std::move(map_data.first));
 
    // Create a map from the dofs in the sub-geometry to the geometry
    subx_to_x_dofmap.reserve(sub_x_dof_index_map->size_local()
                             + sub_x_dof_index_map->num_ghosts());
    std::transform(map_data.second.begin(), map_data.second.end(),
                   std::back_inserter(subx_to_x_dofmap),
                   [offset = x_index_map->size_local()](auto x_dof_index)
                   { return offset + x_dof_index; });
  }
 
  // 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.cmaps()[0].cell_shape(), dim, 0);
  fem::CoordinateElement<T> sub_coord_ele(sub_coord_cell,
                                          geometry.cmaps()[0].degree(),
                                          geometry.cmaps()[0].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<T>(sub_x_dof_index_map, std::move(sub_x_dofmap),
                      {sub_coord_ele}, std::move(sub_x), geometry.dim(),
                      std::move(sub_igi)),
          std::move(subx_to_x_dofmap)};
}
 
} // namespace dolfinx::mesh