petsc.h

// Copyright (C) 2018-2021 Garth N. Wells
//
// This file is part of DOLFINx (https://www.fenicsproject.org)
//
// SPDX-License-Identifier:    LGPL-3.0-or-later
 
#pragma once
 
#ifdef HAS_PETSC
 
#include "Form.h"
#include "assembler.h"
#include "utils.h"
#include <concepts>
#include <dolfinx/la/petsc.h>
#include <functional>
#include <map>
#include <memory>
#include <optional>
#include <petscmat.h>
#include <petscvec.h>
#include <span>
#include <utility>
#include <vector>
 
namespace dolfinx::common
{
class IndexMap;
}
 
namespace dolfinx::fem
{
template <dolfinx::scalar T, std::floating_point U>
class DirichletBC;

namespace petsc
{
template <std::floating_point T>
Mat create_matrix(const Form<PetscScalar, T>& a,
                  std::optional<std::string> type = std::nullopt)
{
  la::SparsityPattern pattern = fem::create_sparsity_pattern(a);
  pattern.finalize();
  return la::petsc::create_matrix(a.mesh()->comm(), pattern, type);
}

template <std::floating_point T>
Mat create_matrix_block(
    const std::vector<std::vector<const Form<PetscScalar, T>*>>& a,
    std::optional<std::string> type = std::nullopt)
{
  // Extract and check row/column ranges
  std::array<std::vector<std::shared_ptr<const FunctionSpace<T>>>, 2> V
      = fem::common_function_spaces(extract_function_spaces(a));
  std::array<std::vector<int>, 2> bs_dofs;
  for (std::size_t i = 0; i < 2; ++i)
  {
    for (auto& _V : V[i])
      bs_dofs[i].push_back(_V->dofmap()->bs());
  }
 
  // Build sparsity pattern for each block
  std::shared_ptr<const mesh::Mesh<T>> mesh;
  std::vector<std::vector<std::unique_ptr<la::SparsityPattern>>> patterns(
      V[0].size());
  for (std::size_t row = 0; row < V[0].size(); ++row)
  {
    for (std::size_t col = 0; col < V[1].size(); ++col)
    {
      if (const Form<PetscScalar, T>* form = a[row][col]; form)
      {
        patterns[row].push_back(std::make_unique<la::SparsityPattern>(
            create_sparsity_pattern(*form)));
        if (!mesh)
          mesh = form->mesh();
      }
      else
        patterns[row].push_back(nullptr);
    }
  }
 
  if (!mesh)
    throw std::runtime_error("Could not find a Mesh.");
 
  // Compute offsets for the fields
  std::array<std::vector<std::pair<
                 std::reference_wrapper<const common::IndexMap>, int>>,
             2>
      maps;
  for (std::size_t d = 0; d < 2; ++d)
  {
    for (auto& space : V[d])
    {
      maps[d].emplace_back(*space->dofmap()->index_map,
                           space->dofmap()->index_map_bs());
    }
  }
 
  // Create merged sparsity pattern
  std::vector<std::vector<const la::SparsityPattern*>> p(V[0].size());
  for (std::size_t row = 0; row < V[0].size(); ++row)
    for (std::size_t col = 0; col < V[1].size(); ++col)
      p[row].push_back(patterns[row][col].get());
 
  la::SparsityPattern pattern(mesh->comm(), p, maps, bs_dofs);
  pattern.finalize();
 
  // FIXME: Add option to pass customised local-to-global map to PETSc
  // Mat constructor
 
  // Initialise matrix
  Mat A = la::petsc::create_matrix(mesh->comm(), pattern, type);
 
  // Create row and column local-to-global maps (field0, field1, field2,
  // etc), i.e. ghosts of field0 appear before owned indices of field1
  std::array<std::vector<PetscInt>, 2> _maps;
  for (int d = 0; d < 2; ++d)
  {
    // TODO: Index map concatenation has already been computed inside
    // the SparsityPattern constructor, but we also need it here to
    // build the PETSc local-to-global map. Compute outside and pass
    // into SparsityPattern constructor.
    // TODO: avoid concatenating the same maps twice in case that V[0]
    // == V[1].
 
    const std::vector<
        std::pair<std::reference_wrapper<const common::IndexMap>, int>>& map
        = maps[d];
    std::vector<PetscInt>& _map = _maps[d];
 
    // Concatenate the block index map in the row and column directions
    const auto [rank_offset, local_offset, ghosts, _]
        = common::stack_index_maps(map);
    for (std::size_t f = 0; f < map.size(); ++f)
    {
      auto offset = local_offset[f];
      const common::IndexMap& imap = map[f].first.get();
      int bs = map[f].second;
      for (std::int32_t i = 0; i < bs * imap.size_local(); ++i)
        _map.push_back(i + rank_offset + offset);
      for (std::int32_t i = 0; i < bs * imap.num_ghosts(); ++i)
        _map.push_back(ghosts[f][i]);
    }
  }
 
  // Create PETSc local-to-global map/index sets and attach to matrix
  ISLocalToGlobalMapping petsc_local_to_global0;
  ISLocalToGlobalMappingCreate(MPI_COMM_SELF, 1, _maps[0].size(),
                               _maps[0].data(), PETSC_COPY_VALUES,
                               &petsc_local_to_global0);
  if (V[0] == V[1])
  {
    MatSetLocalToGlobalMapping(A, petsc_local_to_global0,
                               petsc_local_to_global0);
    ISLocalToGlobalMappingDestroy(&petsc_local_to_global0);
  }
  else
  {
 
    ISLocalToGlobalMapping petsc_local_to_global1;
    ISLocalToGlobalMappingCreate(MPI_COMM_SELF, 1, _maps[1].size(),
                                 _maps[1].data(), PETSC_COPY_VALUES,
                                 &petsc_local_to_global1);
    MatSetLocalToGlobalMapping(A, petsc_local_to_global0,
                               petsc_local_to_global1);
    ISLocalToGlobalMappingDestroy(&petsc_local_to_global0);
    ISLocalToGlobalMappingDestroy(&petsc_local_to_global1);
  }
 
  return A;
}

template <std::floating_point T>
Mat create_matrix_nest(
    const std::vector<std::vector<const Form<PetscScalar, T>*>>& a,
    std::optional<std::vector<std::vector<std::optional<std::string>>>> types)
{
  // Extract and check row/column ranges
  auto V = fem::common_function_spaces(extract_function_spaces(a));
 
  // Loop over each form and create matrix
  int rows = a.size();
  int cols = a.front().size();
  std::vector<Mat> mats(rows * cols, nullptr);
  std::shared_ptr<const mesh::Mesh<T>> mesh;
  for (int i = 0; i < rows; ++i)
  {
    for (int j = 0; j < cols; ++j)
    {
      if (const Form<PetscScalar, T>* form = a[i][j]; form)
      {
        if (types)
          mats[i * cols + j] = create_matrix(*form, types->at(i).at(j));
        else
          mats[i * cols + j] = create_matrix(*form, std::nullopt);
        mesh = form->mesh();
      }
    }
  }
 
  if (!mesh)
    throw std::runtime_error("Could not find a Mesh.");
 
  // Initialise block (MatNest) matrix
  Mat A;
  MatCreate(mesh->comm(), &A);
  MatSetType(A, MATNEST);
  MatNestSetSubMats(A, rows, nullptr, cols, nullptr, mats.data());
  MatSetUp(A);
 
  // De-reference Mat objects
  for (std::size_t i = 0; i < mats.size(); ++i)
  {
    if (mats[i])
      MatDestroy(&mats[i]);
  }
 
  return A;
}

Vec create_vector_block(
    const std::vector<
        std::pair<std::reference_wrapper<const common::IndexMap>, int>>& maps);

Vec create_vector_nest(
    const std::vector<
        std::pair<std::reference_wrapper<const common::IndexMap>, int>>& maps);
 
// -- Vectors ----------------------------------------------------------------

template <std::floating_point T>
void assemble_vector(
    Vec b, const Form<PetscScalar, T>& L,
    std::span<const PetscScalar> constants,
    const std::map<std::pair<IntegralType, int>,
                   std::pair<std::span<const PetscScalar>, int>>& coeffs)
{
  Vec b_local;
  VecGhostGetLocalForm(b, &b_local);
  PetscInt n = 0;
  VecGetSize(b_local, &n);
  PetscScalar* array = nullptr;
  VecGetArray(b_local, &array);
  std::span<PetscScalar> _b(array, n);
  fem::assemble_vector(_b, L, constants, coeffs);
  VecRestoreArray(b_local, &array);
  VecGhostRestoreLocalForm(b, &b_local);
}

template <std::floating_point T>
void assemble_vector(Vec b, const Form<PetscScalar, T>& L)
{
  Vec b_local;
  VecGhostGetLocalForm(b, &b_local);
  PetscInt n = 0;
  VecGetSize(b_local, &n);
  PetscScalar* array = nullptr;
  VecGetArray(b_local, &array);
  std::span<PetscScalar> _b(array, n);
  fem::assemble_vector(_b, L);
  VecRestoreArray(b_local, &array);
  VecGhostRestoreLocalForm(b, &b_local);
}
 
// FIXME: clarify how x0 is used
// FIXME: if bcs entries are set
 
// FIXME: need to pass an array of Vec for x0?
// FIXME: clarify zeroing of vector

template <std::floating_point T>
void apply_lifting(
    Vec b,
    std::vector<
        std::optional<std::reference_wrapper<const Form<PetscScalar, T>>>>
        a,
    const std::vector<std::span<const PetscScalar>>& constants,
    const std::vector<std::map<std::pair<IntegralType, int>,
                               std::pair<std::span<const PetscScalar>, int>>>&
        coeffs,
    const std::vector<
        std::vector<std::reference_wrapper<const DirichletBC<PetscScalar, T>>>>&
        bcs1,
    const std::vector<Vec>& x0, PetscScalar alpha)
{
  Vec b_local;
  VecGhostGetLocalForm(b, &b_local);
  PetscInt n = 0;
  VecGetSize(b_local, &n);
  PetscScalar* array = nullptr;
  VecGetArray(b_local, &array);
  std::span<PetscScalar> _b(array, n);
 
  if (x0.empty())
    fem::apply_lifting(_b, a, constants, coeffs, bcs1, {}, alpha);
  else
  {
    std::vector<std::span<const PetscScalar>> x0_ref;
    std::vector<Vec> x0_local(a.size());
    std::vector<const PetscScalar*> x0_array(a.size());
    for (std::size_t i = 0; i < a.size(); ++i)
    {
      assert(x0[i]);
      VecGhostGetLocalForm(x0[i], &x0_local[i]);
      PetscInt n = 0;
      VecGetSize(x0_local[i], &n);
      VecGetArrayRead(x0_local[i], &x0_array[i]);
      x0_ref.emplace_back(x0_array[i], n);
    }
 
    std::vector x0_tmp(x0_ref.begin(), x0_ref.end());
    fem::apply_lifting(_b, a, constants, coeffs, bcs1, x0_tmp, alpha);
 
    for (std::size_t i = 0; i < x0_local.size(); ++i)
    {
      VecRestoreArrayRead(x0_local[i], &x0_array[i]);
      VecGhostRestoreLocalForm(x0[i], &x0_local[i]);
    }
  }
 
  VecRestoreArray(b_local, &array);
  VecGhostRestoreLocalForm(b, &b_local);
}
 
// FIXME: clarify how x0 is used
// FIXME: if bcs entries are set
 
// FIXME: need to pass an array of Vec for x0?
// FIXME: clarify zeroing of vector

template <std::floating_point T>
void apply_lifting(
    Vec b,
    const std::vector<
        std::optional<std::reference_wrapper<const Form<PetscScalar, double>>>>&
        a,
    const std::vector<std::vector<
        std::reference_wrapper<const DirichletBC<PetscScalar, double>>>>& bcs1,
    const std::vector<Vec>& x0, PetscScalar alpha)
{
  Vec b_local;
  VecGhostGetLocalForm(b, &b_local);
  PetscInt n = 0;
  VecGetSize(b_local, &n);
  PetscScalar* array = nullptr;
  VecGetArray(b_local, &array);
  std::span<PetscScalar> _b(array, n);
 
  if (x0.empty())
    fem::apply_lifting(_b, a, bcs1, {}, alpha);
  else
  {
    std::vector<std::span<const PetscScalar>> x0_ref;
    std::vector<Vec> x0_local(a.size());
    std::vector<const PetscScalar*> x0_array(a.size());
    for (std::size_t i = 0; i < a.size(); ++i)
    {
      assert(x0[i]);
      VecGhostGetLocalForm(x0[i], &x0_local[i]);
      PetscInt n = 0;
      VecGetSize(x0_local[i], &n);
      VecGetArrayRead(x0_local[i], &x0_array[i]);
      x0_ref.emplace_back(x0_array[i], n);
    }
 
    std::vector x0_tmp(x0_ref.begin(), x0_ref.end());
    fem::apply_lifting(_b, a, bcs1, x0_tmp, alpha);
 
    for (std::size_t i = 0; i < x0_local.size(); ++i)
    {
      VecRestoreArrayRead(x0_local[i], &x0_array[i]);
      VecGhostRestoreLocalForm(x0[i], &x0_local[i]);
    }
  }
 
  VecRestoreArray(b_local, &array);
  VecGhostRestoreLocalForm(b, &b_local);
}
 
// -- Setting bcs ------------------------------------------------------------
 
// FIXME: Move these function elsewhere?
 
// FIXME: clarify x0
// FIXME: clarify what happens with ghosts

template <std::floating_point T>
void set_bc(
    Vec b,
    const std::vector<std::reference_wrapper<const DirichletBC<PetscScalar, T>>>
        bcs,
    const Vec x0, PetscScalar alpha = 1)
{
  PetscInt n = 0;
  VecGetLocalSize(b, &n);
  PetscScalar* array = nullptr;
  VecGetArray(b, &array);
  std::span<PetscScalar> _b(array, n);
  if (x0)
  {
    Vec x0_local;
    VecGhostGetLocalForm(x0, &x0_local);
    PetscInt n = 0;
    VecGetSize(x0_local, &n);
    const PetscScalar* array = nullptr;
    VecGetArrayRead(x0_local, &array);
    std::span<const PetscScalar> _x0(array, n);
    for (auto& bc : bcs)
      bc.set(_b, _x0, alpha);
    VecRestoreArrayRead(x0_local, &array);
    VecGhostRestoreLocalForm(x0, &x0_local);
  }
  else
  {
    for (auto& bc : bcs)
      bc->set(_b, std::nullopt, alpha);
  }
  VecRestoreArray(b, &array);
}
 
} // namespace petsc
} // namespace dolfinx::fem
 
#endif