Function.h

// Copyright (C) 2003-2020 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 "FunctionSpace.h"
#include "interpolate.h"
#include <dolfinx/common/IndexMap.h>
#include <dolfinx/common/UniqueIdGenerator.h>
#include <dolfinx/common/array2d.h>
#include <dolfinx/fem/DofMap.h>
#include <dolfinx/fem/FiniteElement.h>
#include <dolfinx/la/PETScVector.h>
#include <dolfinx/la/Vector.h>
#include <dolfinx/mesh/Geometry.h>
#include <dolfinx/mesh/Mesh.h>
#include <dolfinx/mesh/Topology.h>
#include <functional>
#include <memory>
#include <numeric>
#include <petscvec.h>
#include <string>
#include <utility>
#include <variant>
#include <vector>
#include <xtensor/xadapt.hpp>
#include <xtensor/xtensor.hpp>
#include <xtl/xspan.hpp>
 
namespace dolfinx::fem
{
 
class FunctionSpace;
 
 
template <typename T>
class Function
{
public:
  explicit Function(std::shared_ptr<const FunctionSpace> V)
      : _id(common::UniqueIdGenerator::id()), _function_space(V),
        _x(std::make_shared<la::Vector<T>>(V->dofmap()->index_map,
                                           V->dofmap()->index_map_bs()))
  {
    if (!V->component().empty())
    {
      throw std::runtime_error("Cannot create Function from subspace. Consider "
                               "collapsing the function space");
    }
  }
 
  Function(std::shared_ptr<const FunctionSpace> V,
           std::shared_ptr<la::Vector<T>> x)
      : _id(common::UniqueIdGenerator::id()), _function_space(V), _x(x)
  {
    // We do not check for a subspace since this constructor is used for
    // creating subfunctions
 
    // Assertion uses '<=' to deal with sub-functions
    assert(V->dofmap());
    assert(V->dofmap()->index_map->size_global() * V->dofmap()->index_map_bs()
           <= _x->bs() * _x->map()->size_global());
  }
 
  // Copy constructor
  Function(const Function& v) = delete;
 
  Function(Function&& v)
      : name(std::move(v.name)), _id(std::move(v._id)),
        _function_space(std::move(v._function_space)), _x(std::move(v._x)),
        _petsc_vector(std::exchange(v._petsc_vector, nullptr))
  {
  }
 
  virtual ~Function()
  {
    if (_petsc_vector)
      VecDestroy(&_petsc_vector);
  }
 
  Function& operator=(Function&& v) noexcept
  {
    name = std::move(v.name);
    _id = std::move(v._id);
    _function_space = std::move(v._function_space);
    _x = std::move(v._x);
    std::swap(_petsc_vector, v._petsc_vector);
 
    return *this;
  }
 
  // Assignment
  Function& operator=(const Function& v) = delete;
 
  Function sub(int i) const
  {
    auto sub_space = _function_space->sub({i});
    assert(sub_space);
    return Function(sub_space, _x);
  }
 
  Function collapse() const
  {
    // Create new collapsed FunctionSpace
    const auto [function_space_new, collapsed_map]
        = _function_space->collapse();
 
    // Create new vector
    assert(function_space_new);
    auto vector_new = std::make_shared<la::Vector<T>>(
        function_space_new->dofmap()->index_map,
        function_space_new->dofmap()->index_map_bs());
 
    // Copy values into new vector
    const std::vector<T>& x_old = _x->array();
    std::vector<T>& x_new = vector_new->mutable_array();
    for (std::size_t i = 0; i < collapsed_map.size(); ++i)
    {
      assert((int)i < x_new.size());
      assert(collapsed_map[i] < x_old.size());
      x_new[i] = x_old[collapsed_map[i]];
    }
 
    return Function(function_space_new, vector_new);
  }
 
  std::shared_ptr<const FunctionSpace> function_space() const
  {
    return _function_space;
  }
 
  Vec vector() const
  {
    // Check that this is not a sub function
    assert(_function_space->dofmap());
    assert(_function_space->dofmap()->index_map);
    if (_x->bs() * _x->map()->size_global()
        != _function_space->dofmap()->index_map->size_global()
               * _function_space->dofmap()->index_map_bs())
    {
      throw std::runtime_error(
          "Cannot access a non-const vector from a subfunction");
    }
 
    // Check that data type is the same as the PETSc build
    if constexpr (std::is_same<T, PetscScalar>::value)
    {
      if (!_petsc_vector)
      {
        _petsc_vector = la::create_ghosted_vector(
            *_function_space->dofmap()->index_map,
            _function_space->dofmap()->index_map_bs(), _x->mutable_array());
      }
      return _petsc_vector;
    }
    else
    {
      throw std::runtime_error(
          "Cannot return PETSc vector wrapper. Type mismatch");
    }
  }
 
  std::shared_ptr<const la::Vector<T>> x() const { return _x; }
 
  std::shared_ptr<la::Vector<T>> x() { return _x; }
 
  void interpolate(const Function<T>& v) { fem::interpolate(*this, v); }
 
  void interpolate(
      const std::function<xt::xarray<T>(const xt::xtensor<double, 2>&)>& f)
  {
    assert(_function_space);
    assert(_function_space->element());
    assert(_function_space->mesh());
    const int tdim = _function_space->mesh()->topology().dim();
    auto cell_map = _function_space->mesh()->topology().index_map(tdim);
    assert(cell_map);
    const int num_cells = cell_map->size_local() + cell_map->num_ghosts();
    std::vector<std::int32_t> cells(num_cells, 0);
    std::iota(cells.begin(), cells.end(), 0);
    // FIXME: Remove interpolation coords as it should be done internally in
    // fem::interpolate
    const xt::xtensor<double, 2> x = fem::interpolation_coords(
        *_function_space->element(), *_function_space->mesh(), cells);
    fem::interpolate(*this, f, x, cells);
  }
 
  void eval(const xt::xtensor<double, 2>& x,
            const xtl::span<const std::int32_t>& cells,
            xt::xtensor<T, 2>& u) const
  {
    // TODO: This could be easily made more efficient by exploiting points
    // being ordered by the cell to which they belong.
 
    if (x.shape(0) != cells.size())
    {
      throw std::runtime_error(
          "Number of points and number of cells must be equal.");
    }
    if (x.shape(0) != u.shape(0))
    {
      throw std::runtime_error(
          "Length of array for Function values must be the "
          "same as the number of points.");
    }
 
    // Get mesh
    assert(_function_space);
    std::shared_ptr<const mesh::Mesh> mesh = _function_space->mesh();
    assert(mesh);
    const std::size_t gdim = mesh->geometry().dim();
    const std::size_t tdim = mesh->topology().dim();
    auto map = mesh->topology().index_map(tdim);
 
    // Get geometry data
    const graph::AdjacencyList<std::int32_t>& x_dofmap
        = mesh->geometry().dofmap();
    // FIXME: Add proper interface for num coordinate dofs
    const std::size_t num_dofs_g = x_dofmap.num_links(0);
    const xt::xtensor<double, 2>& x_g = mesh->geometry().x();
 
    // Get coordinate map
    const fem::CoordinateElement& cmap = mesh->geometry().cmap();
 
    // Get element
    assert(_function_space->element());
    std::shared_ptr<const fem::FiniteElement> element
        = _function_space->element();
    assert(element);
    const int bs_element = element->block_size();
    const std::size_t reference_value_size
        = element->reference_value_size() / bs_element;
    const std::size_t value_size = element->value_size() / bs_element;
    const std::size_t space_dimension = element->space_dimension() / bs_element;
 
    // If the space has sub elements, concatenate the evaluations on the sub
    // elements
    const int num_sub_elements = element->num_sub_elements();
    if (num_sub_elements > 1 and num_sub_elements != bs_element)
    {
      throw std::runtime_error("Function::eval is not supported for mixed "
                               "elements. Extract subspaces.");
    }
 
    // Prepare geometry data structures
    xt::xtensor<double, 2> X({1, tdim});
    xt::xtensor<double, 3> J
        = xt::zeros<double>({static_cast<std::size_t>(1), gdim, tdim});
    xt::xtensor<double, 3> K
        = xt::zeros<double>({static_cast<std::size_t>(1), tdim, gdim});
    xt::xtensor<double, 1> detJ = xt::zeros<double>({1});
 
    // Prepare basis function data structures
    xt::xtensor<double, 4> basis_derivatives_reference_values(
        {1, 1, space_dimension, reference_value_size});
    auto basis_reference_values = xt::view(basis_derivatives_reference_values,
                                           0, xt::all(), xt::all(), xt::all());
    xt::xtensor<double, 3> basis_values(
        {static_cast<std::size_t>(1), space_dimension, value_size});
 
    // Create work vector for expansion coefficients
    std::vector<T> coefficients(space_dimension * bs_element);
 
    // Get dofmap
    std::shared_ptr<const fem::DofMap> dofmap = _function_space->dofmap();
    assert(dofmap);
    const int bs_dof = dofmap->bs();
 
    xtl::span<const std::uint32_t> cell_info;
    if (element->needs_dof_transformations())
    {
      mesh->topology_mutable().create_entity_permutations();
      cell_info = xtl::span(mesh->topology().get_cell_permutation_info());
    }
 
    xt::xtensor<double, 2> coordinate_dofs
        = xt::zeros<double>({num_dofs_g, gdim});
    xt::xtensor<double, 2> xp
        = xt::zeros<double>({static_cast<std::size_t>(1), gdim});
 
    // Loop over points
    std::fill(u.data(), u.data() + u.size(), 0.0);
    const std::vector<T>& _v = _x->mutable_array();
 
    const std::function<void(const xtl::span<double>&,
                             const xtl::span<const std::uint32_t>&,
                             std::int32_t, int)>
        apply_dof_transformation
        = element->get_dof_transformation_function<double>();
 
    for (std::size_t p = 0; p < cells.size(); ++p)
    {
      const int cell_index = cells[p];
 
      // Skip negative cell indices
      if (cell_index < 0)
        continue;
 
      // Get cell geometry (coordinate dofs)
      auto x_dofs = x_dofmap.links(cell_index);
      for (std::size_t i = 0; i < num_dofs_g; ++i)
        for (std::size_t j = 0; j < gdim; ++j)
          coordinate_dofs(i, j) = x_g(x_dofs[i], j);
 
      for (std::size_t j = 0; j < gdim; ++j)
        xp(0, j) = x(p, j);
 
      // Compute reference coordinates X, and J, detJ and K
      cmap.pull_back(X, J, detJ, K, xp, coordinate_dofs);
 
      // Compute basis on reference element
      element->tabulate(basis_derivatives_reference_values, X, 0);
 
      // Permute the reference values to account for the cell's orientation
      apply_dof_transformation(xtl::span(basis_reference_values.data(),
                                         basis_reference_values.size()),
                               cell_info, cell_index, reference_value_size);
 
      // Push basis forward to physical element
      element->transform_reference_basis(basis_values, basis_reference_values,
                                         J, detJ, K);
 
      // Get degrees of freedom for current cell
      xtl::span<const std::int32_t> dofs = dofmap->cell_dofs(cell_index);
      for (std::size_t i = 0; i < dofs.size(); ++i)
        for (int k = 0; k < bs_dof; ++k)
          coefficients[bs_dof * i + k] = _v[bs_dof * dofs[i] + k];
 
      // Compute expansion
      auto u_row = xt::row(u, p);
      for (int k = 0; k < bs_element; ++k)
      {
        for (std::size_t i = 0; i < space_dimension; ++i)
        {
          for (std::size_t j = 0; j < value_size; ++j)
          {
            u_row[j * bs_element + k]
                += coefficients[bs_element * i + k] * basis_values(0, i, j);
          }
        }
      }
    }
  }
 
  xt::xtensor<T, 2> compute_point_values() const
  {
    assert(_function_space);
    std::shared_ptr<const mesh::Mesh> mesh = _function_space->mesh();
    assert(mesh);
    const int tdim = mesh->topology().dim();
 
    // Compute in tensor (one for scalar function, . . .)
    const std::size_t value_size_loc = _function_space->element()->value_size();
 
    // Resize Array for holding point values
    xt::xtensor<T, 2> point_values(
        {mesh->geometry().x().shape(0), value_size_loc});
 
    // Prepare cell geometry
    const graph::AdjacencyList<std::int32_t>& x_dofmap
        = mesh->geometry().dofmap();
 
    // FIXME: Add proper interface for num coordinate dofs
    const int num_dofs_g = x_dofmap.num_links(0);
    const xt::xtensor<double, 2>& x_g = mesh->geometry().x();
 
    // Interpolate point values on each cell (using last computed value if
    // not continuous, e.g. discontinuous Galerkin methods)
    auto map = mesh->topology().index_map(tdim);
    assert(map);
    const std::int32_t num_cells = map->size_local() + map->num_ghosts();
 
    std::vector<std::int32_t> cells(x_g.shape(0));
    for (std::int32_t c = 0; c < num_cells; ++c)
    {
      // Get coordinates for all points in cell
      xtl::span<const std::int32_t> dofs = x_dofmap.links(c);
      for (int i = 0; i < num_dofs_g; ++i)
        cells[dofs[i]] = c;
    }
 
    eval(x_g, cells, point_values);
 
    return point_values;
  }
 
  std::string name = "u";
 
  std::size_t id() const { return _id; }
 
private:
  // ID
  std::size_t _id;
 
  // The function space
  std::shared_ptr<const FunctionSpace> _function_space;
 
  // The vector of expansion coefficients (local)
  std::shared_ptr<la::Vector<T>> _x;
 
  // PETSc wrapper of the expansion coefficients
  mutable Vec _petsc_vector = nullptr;
};
} // namespace dolfinx::fem