dipolar_direct_sum.cpp

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/*
 * Copyright (C) 2010-2022 The ESPResSo project
 * Copyright (C) 2002,2003,2004,2005,2006,2007,2008,2009,2010
 *   Max-Planck-Institute for Polymer Research, Theory Group
 *
 * This file is part of ESPResSo.
 *
 * ESPResSo is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * ESPResSo is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */
 
#include <config/config.hpp>
 
#ifdef ESPRESSO_DIPOLES
 
#include "magnetostatics/dipolar_direct_sum.hpp"
 
#include "BoxGeometry.hpp"
#include "cells.hpp"
#include "communication.hpp"
#include "errorhandling.hpp"
#include "system/System.hpp"
 
#include <utils/cartesian_product.hpp>
#include <utils/math/sqr.hpp>
#include <utils/mpi/iall_gatherv.hpp>
 
#include <boost/mpi/collectives.hpp>
#include <boost/mpi/communicator.hpp>
 
#include <mpi.h>
 
#include <algorithm>
#include <cassert>
#include <cmath>
#include <iterator>
#include <ranges>
#include <stdexcept>
#include <tuple>
#include <utility>
#include <vector>
 
/**
 * @brief Pair force of two interacting dipoles.
 *
 * @param d Distance vector.
 * @param m1 Dipole moment of one particle.
 * @param m2 Dipole moment of the other particle.
 *
 * @return Resulting force.
 */
static auto pair_force(Utils::Vector3d const &d, Utils::Vector3d const &m1,
                       Utils::Vector3d const &m2) {
  auto const pe2 = m1 * d;
  auto const pe3 = m2 * d;
 
  auto const r2 = d.norm2();
  auto const r = std::sqrt(r2);
  auto const r5 = r2 * r2 * r;
  auto const r7 = r5 * r2;
 
  auto const a = 3.0 * (m1 * m2) / r5;
  auto const b = -15.0 * pe2 * pe3 / r7;
 
  auto const f = (a + b) * d + 3.0 * (pe3 * m1 + pe2 * m2) / r5;
  auto const r3 = r2 * r;
  auto const t =
      -vector_product(m1, m2) / r3 + 3.0 * pe3 * vector_product(m1, d) / r5;
 
  return ParticleForce{f, t};
}
 
/**
 * @brief Pair potential for two interacting dipoles.
 *
 * @param d Distance vector.
 * @param m1 Dipole moment of one particle.
 * @param m2 Dipole moment of the other particle.
 *
 * @return Interaction energy.
 */
static auto pair_potential(Utils::Vector3d const &d, Utils::Vector3d const &m1,
                           Utils::Vector3d const &m2) {
  auto const r2 = d * d;
  auto const r = sqrt(r2);
  auto const r3 = r2 * r;
  auto const r5 = r3 * r2;
 
  auto const pe1 = m1 * m2;
  auto const pe2 = m1 * d;
  auto const pe3 = m2 * d;
 
  return pe1 / r3 - 3.0 * pe2 * pe3 / r5;
}
 
#ifdef ESPRESSO_DIPOLE_FIELD_TRACKING
/**
 * @brief Dipole field contribution from a particle with dipole moment @c m1
 * at a distance @c d.
 *
 * @param d Distance vector.
 * @param m1 Dipole moment of one particle.
 *
 * @return Utils::Vector3d containing dipole field components.
 */
static auto dipole_field(Utils::Vector3d const &d, Utils::Vector3d const &m1) {
  auto const r2 = d * d;
  auto const r = sqrt(r2);
  auto const r3 = r2 * r;
  auto const r5 = r3 * r2;
  auto const pe2 = m1 * d;
 
  return 3.0 * pe2 * d / r5 - m1 / r3;
}
#endif
 
/**
 * @brief Call kernel for every 3d index in a sphere around the origin.
 *
 * This calls a callable for all index-triples
 * that are within ball around the origin with
 * radius |ncut|.
 *
 * @tparam F Callable
 * @param ncut Limits in the three directions,
 *             all non-zero elements have to be
 *             the same number.
 * @param f will be called for each index triple
 *        within the limits of @p ncut.
 */
template <typename F> void for_each_image(Utils::Vector3i const &ncut, F f) {
  auto const ncut2 = ncut.norm2();
 
  /* This runs over the index "cube"
   * [-ncut[0], ncut[0]] x ... x [-ncut[2], ncut[2]]
   * (inclusive on both sides), and calls f with
   * all the elements as argument. Counting range
   * is a range that just enumerates a range.
   */
  Utils::cartesian_product(
      [&](int nx, int ny, int nz) {
        if (nx * nx + ny * ny + nz * nz <= ncut2) {
          f(nx, ny, nz);
        }
      },
      std::views::iota(-ncut[0], ncut[0] + 1),
      std::views::iota(-ncut[1], ncut[1] + 1),
      std::views::iota(-ncut[2], ncut[2] + 1));
}
 
/**
 * @brief Position and dipole moment of one particle.
 */
struct PosMom {
  Utils::Vector3d pos;
  Utils::Vector3d m;
 
  template <class Archive> void serialize(Archive &ar, long int) {
    ar & pos & m;
  }
};
 
/**
 * @brief Sum over all pairs with periodic images.
 *
 * This implements the "primed" pair sum, the sum over all
 * pairs between one particles and all other particles,
 * including @p ncut periodic replicas in each direction.
 * Primed means that in the primary replica the self-interaction
 * is excluded, but not with the other periodic replicas. E.g.
 * a particle does not interact with its self, but does with
 * its periodically shifted versions.
 *
 * @param begin Iterator pointing to begin of particle range
 * @param end Iterator pointing past the end of particle range
 * @param it Pointer to particle that is considered
 * @param with_replicas If periodic replicas are to be considered
 *        at all. If false, distances are calculated as Euclidean
 *        distances, and not using minimum image convention.
 * @param ncut Number of replicas in each direction.
 * @param box_geo Box geometry.
 * @param init Initial value of the sum.
 * @param f Binary operation mapping distance and moment of the
 *          interaction partner to the value to be summed up for this pair.
 *
 * @return The total sum.
 */
template <class InputIterator, class T, class F>
T image_sum(InputIterator begin, InputIterator end, InputIterator it,
            bool with_replicas, Utils::Vector3i const &ncut,
            BoxGeometry const &box_geo, T init, F f) {
 
  auto const &box_l = box_geo.length();
  for (auto jt = begin; jt != end; ++jt) {
    auto const exclude_primary = (it == jt);
    auto const primary_distance = (with_replicas)
                                      ? (it->pos - jt->pos)
                                      : box_geo.get_mi_vector(it->pos, jt->pos);
 
    for_each_image(ncut, [&](int nx, int ny, int nz) {
      if (!(exclude_primary && nx == 0 && ny == 0 && nz == 0)) {
        auto const rn =
            primary_distance +
            Utils::Vector3d{nx * box_l[0], ny * box_l[1], nz * box_l[2]};
        init += f(rn, jt->m);
      }
    });
  }
 
  return init;
}
 
static auto gather_particle_data(BoxGeometry const &box_geo,
                                 ParticleRange const &particles) {
  auto const &comm = ::comm_cart;
  std::vector<Particle *> local_particles;
  std::vector<PosMom> local_posmom;
  std::vector<PosMom> all_posmom;
  std::vector<boost::mpi::request> reqs;
 
  local_particles.reserve(particles.size());
  local_posmom.reserve(particles.size());
 
  for (auto &p : particles) {
    if (p.dipm() != 0.0) {
      local_particles.emplace_back(&p);
      local_posmom.emplace_back(
          PosMom{box_geo.folded_position(p.pos()), p.calc_dip()});
    }
  }
 
  auto const local_size = static_cast<int>(local_posmom.size());
  std::vector<int> all_sizes;
  boost::mpi::all_gather(comm, local_size, all_sizes);
 
  auto const offset =
      std::accumulate(all_sizes.begin(), all_sizes.begin() + comm.rank(), 0);
  auto const total_size =
      std::accumulate(all_sizes.begin() + comm.rank(), all_sizes.end(), offset);
 
  if (comm.size() > 1) {
    all_posmom.resize(total_size);
    reqs = Utils::Mpi::iall_gatherv(comm, local_posmom.data(), local_size,
                                    all_posmom.data(), all_sizes.data());
  } else {
    std::swap(all_posmom, local_posmom);
  }
 
  return std::make_tuple(std::move(local_particles), std::move(all_posmom),
                         std::move(reqs), offset);
}
 
static auto get_n_cut(BoxGeometry const &box_geo, int n_replicas) {
  return n_replicas * Utils::Vector3i{static_cast<int>(box_geo.periodic(0)),
                                      static_cast<int>(box_geo.periodic(1)),
                                      static_cast<int>(box_geo.periodic(2))};
}
 
/**
 * @brief Calculate and add the interaction forces/torques to the particles.
 *
 * This employs a parallel N-square loop over all particle pairs.
 * The computation the partitioned into several steps so that the
 * communication latency can be hidden behind some local computation:
 *
 * 1. The local particle positions and momenta are packed into
 *    one array.
 * 2. The asynchronous distribution of the local arrays to all
 *    ranks is started.
 * 3. The interaction for the local pairs is started, here every
 *    pair is visited only once, and the force is added to both particles.
 * 4. Wait for the data from the other nodes.
 * 5. Calculate the interaction with the rest of the particles. Here
 *    every pair is visited twice (not necessarily on the same rank)
 *    so that no reduction of the forces is needed.
 *
 * Logically this is equivalent to the potential calculation
 * in @ref DipolarDirectSum::long_range_energy, which calculates
 * a naive N-square sum, but has better performance and scaling.
 */
void DipolarDirectSum::add_long_range_forces() const {
  auto const &system = get_system();
  auto const &box_geo = *system.box_geo;
  auto const &box_l = box_geo.length();
  auto const particles = system.cell_structure->local_particles();
  auto [local_particles, all_posmom, reqs, offset] =
      gather_particle_data(box_geo, particles);
 
  /* Number of image boxes considered */
  auto const ncut = get_n_cut(box_geo, n_replicas);
  auto const with_replicas = (ncut.norm2() > 0);
 
  /* Range of particles we calculate the ia for on this node */
  auto const local_posmom_begin = all_posmom.begin() + offset;
  auto const local_posmom_end =
      local_posmom_begin + static_cast<long>(local_particles.size());
 
  /* Output iterator for the force */
  auto p = local_particles.begin();
 
  /* IA with local particles */
  for (auto it = local_posmom_begin; it != local_posmom_end; ++it, ++p) {
    /* IA with own images */
    auto fi = image_sum(
        it, std::next(it), it, with_replicas, ncut, box_geo, ParticleForce{},
        [it](Utils::Vector3d const &rn, Utils::Vector3d const &mj) {
          return pair_force(rn, it->m, mj);
        });
 
    /* IA with other local particles */
    auto q = std::next(p);
    for (auto jt = std::next(it); jt != local_posmom_end; ++jt, ++q) {
      auto const d = (with_replicas) ? (it->pos - jt->pos)
                                     : box_geo.get_mi_vector(it->pos, jt->pos);
 
      ParticleForce fij{};
      ParticleForce fji{};
      for_each_image(ncut, [&](int nx, int ny, int nz) {
        auto const rn =
            d + Utils::Vector3d{nx * box_l[0], ny * box_l[1], nz * box_l[2]};
        auto const pf = pair_force(rn, it->m, jt->m);
        fij += pf;
        fji.f -= pf.f;
        /* Conservation of angular momentum mandates that
         * 0 = t_i + r_ij x F_ij + t_j */
        fji.torque += vector_product(pf.f, rn) - pf.torque;
      });
 
      fi += fij;
      (*q)->force() += prefactor * fji.f;
      (*q)->torque() += prefactor * fji.torque;
    }
 
    (*p)->force() += prefactor * fi.f;
    (*p)->torque() += prefactor * fi.torque;
  }
 
  /* Wait for the rest of the data to arrive */
  boost::mpi::wait_all(reqs.begin(), reqs.end());
 
  /* Output iterator for the force */
  p = local_particles.begin();
 
  /* Interaction with all the other particles */
  for (auto it = local_posmom_begin; it != local_posmom_end; ++it, ++p) {
    // red particles
    auto fi =
        image_sum(all_posmom.begin(), local_posmom_begin, it, with_replicas,
                  ncut, box_geo, ParticleForce{},
                  [it](Utils::Vector3d const &rn, Utils::Vector3d const &mj) {
                    return pair_force(rn, it->m, mj);
                  });
 
    // black particles
    fi += image_sum(local_posmom_end, all_posmom.end(), it, with_replicas, ncut,
                    box_geo, ParticleForce{},
                    [it](Utils::Vector3d const &rn, Utils::Vector3d const &mj) {
                      return pair_force(rn, it->m, mj);
                    });
 
    (*p)->force() += prefactor * fi.f;
    (*p)->torque() += prefactor * fi.torque;
  }
#ifdef ESPRESSO_DIPOLE_FIELD_TRACKING
  DipolarDirectSum::dipole_field_at_part();
#endif
}
 
/**
 * @brief Calculate the interaction potential.
 *
 * This employs a parallel N-square loop over all particle pairs.
 */
double DipolarDirectSum::long_range_energy() const {
  auto const &system = get_system();
  auto const &box_geo = *system.box_geo;
  auto const particles = system.cell_structure->local_particles();
  auto [local_particles, all_posmom, reqs, offset] =
      gather_particle_data(box_geo, particles);
 
  /* Number of image boxes considered */
  auto const ncut = get_n_cut(box_geo, n_replicas);
  auto const with_replicas = (ncut.norm2() > 0);
 
  /* Wait for the rest of the data to arrive */
  boost::mpi::wait_all(reqs.begin(), reqs.end());
 
  /* Range of particles we calculate the ia for on this node */
  auto const local_posmom_begin = all_posmom.begin() + offset;
  auto const local_posmom_end =
      local_posmom_begin + static_cast<long>(local_particles.size());
 
  auto u = 0.;
  for (auto it = local_posmom_begin; it != local_posmom_end; ++it) {
    u = image_sum(it, all_posmom.end(), it, with_replicas, ncut, box_geo, u,
                  [it](Utils::Vector3d const &rn, Utils::Vector3d const &mj) {
                    return pair_potential(rn, it->m, mj);
                  });
  }
 
  return prefactor * u;
}
 
/**
 * @brief Calculate total dipole field of each particle.
 *
 * This employs a parallel N-square loop over all particles.
 * Logically this is equivalent to the potential calculation
 * in @ref DipolarDirectSum::long_range_energy, which calculates
 * a naive N-square sum. The difference is summation range,
 * and the kernel calculates the dipole field rather than the energy.
 */
#ifdef ESPRESSO_DIPOLE_FIELD_TRACKING
void DipolarDirectSum::dipole_field_at_part() const {
  auto const &system = get_system();
  auto const &box_geo = *system.box_geo;
  auto const particles = system.cell_structure->local_particles();
  /* collect particle data */
  auto [local_particles, all_posmom, reqs, offset] =
      gather_particle_data(box_geo, particles);
 
  auto const ncut = get_n_cut(box_geo, n_replicas);
  auto const with_replicas = (ncut.norm2() > 0);
 
  boost::mpi::wait_all(reqs.begin(), reqs.end());
 
  auto const local_posmom_begin = all_posmom.begin() + offset;
  auto const local_posmom_end =
      local_posmom_begin + static_cast<long>(local_particles.size());
 
  Utils::Vector3d u_init = {0., 0., 0.};
  auto p = local_particles.begin();
  for (auto pi = local_posmom_begin; pi != local_posmom_end; ++pi, ++p) {
    auto const u = image_sum(
        all_posmom.begin(), all_posmom.end(), pi, with_replicas, ncut, box_geo,
        u_init, [](Utils::Vector3d const &rn, Utils::Vector3d const &mj) {
          return dipole_field(rn, mj);
        });
    (*p)->dip_fld() = prefactor * u;
  }
}
#endif
 
DipolarDirectSum::DipolarDirectSum(double prefactor, int n_replicas) {
  set_prefactor(prefactor);
  this->n_replicas = n_replicas;
  if (n_replicas < 0) {
    throw std::domain_error("Parameter 'n_replicas' must be >= 0");
  }
}
 
#endif // ESPRESSO_DIPOLES