Vector.h

// Copyright (C) 2020-2025 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 <algorithm>
#include <cmath>
#include <complex>
#include <dolfinx/common/IndexMap.h>
#include <dolfinx/common/Scatterer.h>
#include <dolfinx/common/types.h>
#include <limits>
#include <memory>
#include <numeric>
#include <span>
#include <type_traits>
#include <vector>
 
namespace dolfinx::la
{
template <class F, class Container, class ScatterContainer>
concept VectorPackKernel = requires(F f, ScatterContainer idx, Container x) {
  f(idx.cbegin(), idx.cend(), x.cbegin(), x.begin());
};

template <class GetPtr, class U, class T>
concept GetPtrConcept = requires(GetPtr f, U x) {
  { f(x) } -> std::same_as<T*>;
} and requires(GetPtr f, const U x) {
  { f(x) } -> std::same_as<const T*>;
};

template <typename T, typename Container = std::vector<T>,
          typename ScatterContainer = std::vector<std::int32_t>>
class Vector
{
  static_assert(std::is_same_v<typename Container::value_type, T>);
 
private:
  auto get_pack()
  {
    return [](typename ScatterContainer::const_iterator idx_first,
              typename ScatterContainer::const_iterator idx_last,
              const auto in_first, auto out_first)
    {
      // out[i] = in[idx[i]]
      std::transform(idx_first, idx_last, out_first,
                     [in_first](auto p) { return *std::next(in_first, p); });
    };
  }

  auto get_unpack()
  {
    return [](typename ScatterContainer::const_iterator idx_first,
              typename ScatterContainer::const_iterator idx_last,
              const auto in_first, auto out_first)
    {
      // out[idx[i]] = in[i]
      for (typename ScatterContainer::const_iterator idx = idx_first;
           idx != idx_last; ++idx)
      {
        std::size_t d = std::distance(idx_first, idx);
        *std::next(out_first, *idx) = *std::next(in_first, d);
      }
    };
  }

  template <typename BinaryOp>
  auto get_unpack_op(BinaryOp op)
  {
    return [op](typename ScatterContainer::const_iterator idx_first,
                typename ScatterContainer::const_iterator idx_last,
                const auto in_first, auto out_first)
    {
      // out[idx[i]] = op(out[idx[i]], in[i])
      for (typename ScatterContainer::const_iterator idx = idx_first;
           idx != idx_last; ++idx)
      {
        std::size_t d = std::distance(idx_first, idx);
        auto& out = *std::next(out_first, *idx);
        out = op(out, *std::next(in_first, d));
      }
    };
  }
 
public:
  using container_type = Container;

  using value_type = container_type::value_type;
 
  static_assert(std::is_same_v<value_type, typename container_type::value_type>,
                "Scalar type and container value type must be the same.");

  Vector(std::shared_ptr<const common::IndexMap> map, int bs)
      : _map(map), _bs(bs), _x(bs * (map->size_local() + map->num_ghosts())),
        _scatterer(
            std::make_shared<common::Scatterer<ScatterContainer>>(*_map, bs)),
        _buffer_local(_scatterer->local_indices().size()),
        _buffer_remote(_scatterer->remote_indices().size())
  {
  }

  Vector(const Vector& x) = default;

  Vector(Vector&& x) = default;
 
  // Assignment operator (disabled)
  Vector& operator=(const Vector& x) = delete;

  Vector& operator=(Vector&& x) = default;

  [[deprecated("Use std::ranges::fill(u.array(), v) instead.")]] void
  set(value_type v)
  {
    std::ranges::fill(_x, v);
  }

  template <typename U, typename GetPtr>
    requires VectorPackKernel<U, container_type, ScatterContainer>
             and GetPtrConcept<GetPtr, Container, T>
  void scatter_fwd_begin(U pack, GetPtr get_ptr)
  {
    pack(_scatterer->local_indices().begin(), _scatterer->local_indices().end(),
         _x.begin(), _buffer_local.begin());
    _scatterer->scatter_fwd_begin(get_ptr(_buffer_local),
                                  get_ptr(_buffer_remote), _request);
  }

  void scatter_fwd_begin()
    requires requires(Container c) {
      { c.data() } -> std::same_as<T*>;
    }
  {
    scatter_fwd_begin(get_pack(), [](auto&& x) { return x.data(); });
  }

  template <typename U>
    requires VectorPackKernel<U, container_type, ScatterContainer>
  void scatter_fwd_end(U unpack)
  {
    _scatterer->scatter_end(_request);
    unpack(_scatterer->remote_indices().begin(),
           _scatterer->remote_indices().end(), _buffer_remote.begin(),
           std::next(_x.begin(), _bs * _map->size_local()));
  }

  void scatter_fwd_end()
    requires requires(Container c) {
      { c.data() } -> std::same_as<T*>;
    }
  {
    this->scatter_fwd_end(get_unpack());
  }

  void scatter_fwd()
    requires requires(Container c) {
      { c.data() } -> std::same_as<T*>;
    }
  {
    this->scatter_fwd_begin(get_pack(), [](auto&& x) { return x.data(); });
    this->scatter_fwd_end(get_unpack());
  }

  template <typename U, typename GetPtr>
    requires VectorPackKernel<U, container_type, ScatterContainer>
             and GetPtrConcept<GetPtr, Container, T>
  void scatter_rev_begin(U pack, GetPtr get_ptr)
  {
    std::int32_t local_size = _bs * _map->size_local();
    pack(_scatterer->remote_indices().begin(),
         _scatterer->remote_indices().end(), std::next(_x.begin(), local_size),
         _buffer_remote.begin());
    _scatterer->scatter_rev_begin(get_ptr(_buffer_remote),
                                  get_ptr(_buffer_local), _request);
  }

  void scatter_rev_begin()
    requires requires(Container c) {
      { c.data() } -> std::same_as<T*>;
    }
  {
    scatter_rev_begin(get_pack(), [](auto&& x) { return x.data(); });
  }

  template <typename U>
    requires VectorPackKernel<U, container_type, ScatterContainer>
  void scatter_rev_end(U unpack)
  {
    _scatterer->scatter_end(_request);
    unpack(_scatterer->local_indices().begin(),
           _scatterer->local_indices().end(), _buffer_local.begin(),
           _x.begin());
  }

  template <class BinaryOperation>
    requires requires(Container c) {
      { c.data() } -> std::same_as<T*>;
    }
  void scatter_rev(BinaryOperation op)
  {
    this->scatter_rev_begin();
    this->scatter_rev_end(get_unpack_op(op));
  }

  std::shared_ptr<const common::IndexMap> index_map() const { return _map; }

  constexpr int bs() const { return _bs; }

  container_type& array() { return _x; }

  const container_type& array() const { return _x; }

  [[deprecated("Use array() instead.")]] container_type& mutable_array()
  {
    return _x;
  }
 
private:
  // Map describing the data layout
  std::shared_ptr<const common::IndexMap> _map;
 
  // Block size
  int _bs;
 
  // Vector data
  container_type _x;
 
  // Scatter for managing MPI communication
  std::shared_ptr<const common::Scatterer<ScatterContainer>> _scatterer;
 
  // MPI request handle
  MPI_Request _request = MPI_REQUEST_NULL;
 
  // Buffers for ghost scatters
  container_type _buffer_local, _buffer_remote;
}; // namespace dolfinx::la

template <class V>
auto inner_product(const V& a, const V& b)
{
  using T = typename V::value_type;
  const std::int32_t local_size = a.bs() * a.index_map()->size_local();
  if (local_size != b.bs() * b.index_map()->size_local())
    throw std::runtime_error("Incompatible vector sizes");
 
  const T local = std::transform_reduce(
      a.array().begin(), std::next(a.array().begin(), local_size),
      b.array().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_t<T>, MPI_SUM,
                a.index_map()->comm());
  return result;
}

template <class V>
auto squared_norm(const V& a)
{
  using T = typename V::value_type;
  T result = inner_product(a, a);
  return std::real(result);
}

template <class V>
auto norm(const V& x, Norm type = Norm::l2)
{
  using T = typename V::value_type;
  switch (type)
  {
  case Norm::l1:
  {
    std::int32_t size_local = x.bs() * x.index_map()->size_local();
    using U = typename dolfinx::scalar_value_t<T>;
    U local_l1 = std::accumulate(
        x.array().begin(), std::next(x.array().begin(), size_local), U(0),
        [](auto norm, auto x) { return norm + std::abs(x); });
    U l1(0);
    MPI_Allreduce(&local_l1, &l1, 1, MPI::mpi_t<U>, MPI_SUM,
                  x.index_map()->comm());
    return l1;
  }
  case Norm::l2:
    return std::sqrt(squared_norm(x));
  case Norm::linf:
  {
    std::int32_t size_local = x.bs() * x.index_map()->size_local();
    auto max_pos = std::max_element(
        x.array().begin(), std::next(x.array().begin(), size_local),
        [](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_t<decltype(linf)>, MPI_MAX,
                  x.index_map()->comm());
    return linf;
  }
  default:
    throw std::runtime_error("Norm type not supported");
  }
}

template <class V>
void orthonormalize(std::vector<std::reference_wrapper<V>> basis)
{
  using T = typename V::value_type;
  using U = typename dolfinx::scalar_value_t<T>;
 
  // 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
    V& bi = basis[i].get();
    for (std::size_t j = 0; j < i; ++j)
    {
      const V& bj = basis[j].get();
 
      // basis_i <- basis_i - dot_ij  basis_j
      auto dot_ij = inner_product(bi, bj);
      std::ranges::transform(bj.array(), bi.array(), bi.array().begin(),
                             [dot_ij](auto xj, auto xi)
                             { return xi - dot_ij * xj; });
    }
 
    // Normalise basis function
    auto norm = la::norm(bi, la::Norm::l2);
    if (norm * norm < std::numeric_limits<U>::epsilon())
    {
      throw std::runtime_error(
          "Linear dependency detected. Cannot orthogonalize.");
    }
    std::ranges::transform(bi.array(), bi.array().begin(),
                           [norm](auto x) { return x / norm; });
  }
}

template <class V>
bool is_orthonormal(
    std::vector<std::reference_wrapper<const V>> basis,
    dolfinx::scalar_value_t<typename V::value_type> eps = std::numeric_limits<
        dolfinx::scalar_value_t<typename V::value_type>>::epsilon())
{
  using T = typename V::value_type;
  for (std::size_t i = 0; i < basis.size(); i++)
  {
    for (std::size_t j = i; j < basis.size(); ++j)
    {
      T delta_ij = (i == j) ? T(1) : T(0);
      auto dot_ij = inner_product(basis[i].get(), basis[j].get());
      if (std::norm(delta_ij - dot_ij) > eps)
        return false;
    }
  }
 
  return true;
}
 
} // namespace dolfinx::la