Vector.h

// Copyright (C) 2020 Garth N. Wells
//
// This file is part of DOLFINx (https://www.fenicsproject.org)
//
// SPDX-License-Identifier:    LGPL-3.0-or-later
 
#pragma once
 
#include "utils.h"
#include <complex>
#include <dolfinx/common/IndexMap.h>
#include <dolfinx/common/Scatterer.h>
#include <limits>
#include <memory>
#include <numeric>
#include <span>
#include <vector>
 
namespace dolfinx::la
{
 
 
template <typename T, class Allocator = std::allocator<T>>
class Vector
{
public:
  using value_type = T;
 
  using allocator_type = Allocator;
 
  Vector(const std::shared_ptr<const common::IndexMap>& map, int bs,
         const Allocator& alloc = Allocator())
      : _map(map), _scatterer(std::make_shared<common::Scatterer>(*_map, bs)),
        _bs(bs), _buffer_local(_scatterer->local_buffer_size(), alloc),
        _buffer_remote(_scatterer->remote_buffer_size(), alloc),
        _x(bs * (map->size_local() + map->num_ghosts()), alloc)
  {
  }
 
  Vector(const Vector& x)
      : _map(x._map), _scatterer(x._scatterer), _bs(x._bs),
        _request(MPI_REQUEST_NULL), _buffer_local(x._buffer_local),
        _buffer_remote(x._buffer_remote), _x(x._x)
  {
  }
 
  Vector(Vector&& x)
      : _map(std::move(x._map)), _scatterer(std::move(x._scatterer)),
        _bs(std::move(x._bs)),
        _request(std::exchange(x._request, MPI_REQUEST_NULL)),
        _buffer_local(std::move(x._buffer_local)),
        _buffer_remote(std::move(x._buffer_remote)), _x(std::move(x._x))
  {
  }
 
  // Assignment operator (disabled)
  Vector& operator=(const Vector& x) = delete;
 
  Vector& operator=(Vector&& x) = default;
 
  void set(T v) { std::fill(_x.begin(), _x.end(), v); }
 
  void scatter_fwd_begin()
  {
    const std::int32_t local_size = _bs * _map->size_local();
    std::span<const T> x_local(_x.data(), local_size);
 
    auto pack = [](const auto& in, const auto& idx, auto& out)
    {
      for (std::size_t i = 0; i < idx.size(); ++i)
        out[i] = in[idx[i]];
    };
    pack(x_local, _scatterer->local_indices(), _buffer_local);
 
    _scatterer->scatter_fwd_begin(std::span<const T>(_buffer_local),
                                  std::span<T>(_buffer_remote), _request);
  }
 
  void scatter_fwd_end()
  {
    const std::int32_t local_size = _bs * _map->size_local();
    const std::int32_t num_ghosts = _bs * _map->num_ghosts();
    std::span<T> x_remote(_x.data() + local_size, num_ghosts);
    _scatterer->scatter_fwd_end(_request);
 
    auto unpack = [](const auto& in, const auto& idx, auto& out, auto op)
    {
      for (std::size_t i = 0; i < idx.size(); ++i)
        out[idx[i]] = op(out[idx[i]], in[i]);
    };
 
    unpack(_buffer_remote, _scatterer->remote_indices(), x_remote,
           [](auto /*a*/, auto b) { return b; });
  }
 
  void scatter_fwd()
  {
    this->scatter_fwd_begin();
    this->scatter_fwd_end();
  }
 
  void scatter_rev_begin()
  {
    const std::int32_t local_size = _bs * _map->size_local();
    const std::int32_t num_ghosts = _bs * _map->num_ghosts();
    std::span<T> x_remote(_x.data() + local_size, num_ghosts);
 
    auto pack = [](const auto& in, const auto& idx, auto& out)
    {
      for (std::size_t i = 0; i < idx.size(); ++i)
        out[i] = in[idx[i]];
    };
    pack(x_remote, _scatterer->remote_indices(), _buffer_remote);
 
    _scatterer->scatter_rev_begin(std::span<const T>(_buffer_remote),
                                  std::span<T>(_buffer_local), _request);
  }
 
  template <class BinaryOperation>
  void scatter_rev_end(BinaryOperation op)
  {
    const std::int32_t local_size = _bs * _map->size_local();
    std::span<T> x_local(_x.data(), local_size);
    _scatterer->scatter_rev_end(_request);
 
    auto unpack = [](const auto& in, const auto& idx, auto& out, auto op)
    {
      for (std::size_t i = 0; i < idx.size(); ++i)
        out[idx[i]] = op(out[idx[i]], in[i]);
    };
    unpack(_buffer_local, _scatterer->local_indices(), x_local, op);
  }
 
  template <class BinaryOperation>
  void scatter_rev(BinaryOperation op)
  {
    this->scatter_rev_begin();
    this->scatter_rev_end(op);
  }
 
  std::shared_ptr<const common::IndexMap> map() const { return _map; }
 
  constexpr int bs() const { return _bs; }
 
  std::span<const T> array() const { return std::span<const T>(_x); }
 
  std::span<T> mutable_array() { return std::span(_x); }
 
  constexpr allocator_type allocator() const { return _x.get_allocator(); }
 
private:
  // Map describing the data layout
  std::shared_ptr<const common::IndexMap> _map;
 
  // Scatter for managing MPI communication
  std::shared_ptr<const common::Scatterer> _scatterer;
 
  // Block size
  int _bs;
 
  // MPI request handle
  MPI_Request _request = MPI_REQUEST_NULL;
 
  // Buffers for ghost scatters
  std::vector<T, Allocator> _buffer_local, _buffer_remote;
 
  // Vector data
  std::vector<T, Allocator> _x;
};
 
template <typename T, class Allocator>
T inner_product(const Vector<T, Allocator>& a, const Vector<T, Allocator>& b)
{
  const std::int32_t local_size = a.bs() * a.map()->size_local();
  if (local_size != b.bs() * b.map()->size_local())
    throw std::runtime_error("Incompatible vector sizes");
  std::span<const T> x_a = a.array().subspan(0, local_size);
  std::span<const T> x_b = b.array().subspan(0, local_size);
 
  const T local = std::transform_reduce(
      x_a.begin(), x_a.end(), x_b.begin(), static_cast<T>(0), std::plus{},
      [](T a, T b) -> T
      {
        if constexpr (std::is_same<T, std::complex<double>>::value
                      or std::is_same<T, std::complex<float>>::value)
        {
          return std::conj(a) * b;
        }
        else
          return a * b;
      });
 
  T result;
  MPI_Allreduce(&local, &result, 1, dolfinx::MPI::mpi_type<T>(), MPI_SUM,
                a.map()->comm());
  return result;
}
 
template <typename T, class Allocator>
auto squared_norm(const Vector<T, Allocator>& a)
{
  T result = inner_product(a, a);
  return std::real(result);
}
 
template <typename T, class Allocator>
auto norm(const Vector<T, Allocator>& a, Norm type = Norm::l2)
{
  switch (type)
  {
  case Norm::l2:
    return std::sqrt(squared_norm(a));
  case Norm::linf:
  {
    const std::int32_t size_local = a.bs() * a.map()->size_local();
    std::span<const T> x_a = a.array().subspan(0, size_local);
    auto max_pos = std::max_element(x_a.begin(), x_a.end(),
                                    [](T a, T b)
                                    { return std::norm(a) < std::norm(b); });
    auto local_linf = std::abs(*max_pos);
    decltype(local_linf) linf = 0;
    MPI_Allreduce(&local_linf, &linf, 1, MPI::mpi_type<decltype(linf)>(),
                  MPI_MAX, a.map()->comm());
    return linf;
  }
  default:
    throw std::runtime_error("Norm type not supported");
  }
}
 
template <typename T, typename U>
void orthonormalize(const std::span<Vector<T, U>>& basis, double tol = 1.0e-10)
{
  // Loop over each vector in basis
  for (std::size_t i = 0; i < basis.size(); ++i)
  {
    // Orthogonalize vector i with respect to previously orthonormalized
    // vectors
    for (std::size_t j = 0; j < i; ++j)
    {
      // basis_i <- basis_i - dot_ij  basis_j
      T dot_ij = inner_product(basis[i], basis[j]);
      std::transform(basis[j].array().begin(), basis[j].array().end(),
                     basis[i].array().begin(), basis[i].mutable_array().begin(),
                     [dot_ij](auto xj, auto xi) { return xi - dot_ij * xj; });
    }
 
    // Normalise basis function
    double norm = la::norm(basis[i], la::Norm::l2);
    if (norm < tol)
    {
      throw std::runtime_error(
          "Linear dependency detected. Cannot orthogonalize.");
    }
    std::transform(basis[i].array().begin(), basis[i].array().end(),
                   basis[i].mutable_array().begin(),
                   [norm](auto x) { return x / norm; });
  }
}
 
template <typename T, typename U>
bool is_orthonormal(const std::span<const Vector<T, U>>& basis,
                    double tol = 1.0e-10)
{
  for (std::size_t i = 0; i < basis.size(); i++)
  {
    for (std::size_t j = i; j < basis.size(); j++)
    {
      const double delta_ij = (i == j) ? 1.0 : 0.0;
      T dot_ij = inner_product(basis[i], basis[j]);
      if (std::abs(delta_ij - dot_ij) > tol)
        return false;
    }
  }
 
  return true;
}
 
} // namespace dolfinx::la