qs_fb_distribution_methods.F

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!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright 2000-2024 CP2K developers group <https://cp2k.org>                                   !
!                                                                                                  !
!   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
!--------------------------------------------------------------------------------------------------!
 
MODULE qs_fb_distribution_methods
 
   USE cell_types,                      ONLY: cell_type
   USE cp_log_handling,                 ONLY: cp_get_default_logger,&
                                              cp_logger_type
   USE cp_output_handling,              ONLY: cp_print_key_finished_output,&
                                              cp_print_key_unit_nr
   USE dbcsr_api,                       ONLY: dbcsr_distribution_get,&
                                              dbcsr_distribution_type,&
                                              dbcsr_get_info,&
                                              dbcsr_nblkcols_total,&
                                              dbcsr_p_type,&
                                              dbcsr_type
   USE input_section_types,             ONLY: section_vals_type
   USE kinds,                           ONLY: dp
   USE message_passing,                 ONLY: mp_para_env_type
   USE particle_types,                  ONLY: particle_type
   USE qs_environment_types,            ONLY: get_qs_env,&
                                              qs_environment_type
   USE qs_fb_atomic_halo_types,         ONLY: &
        fb_atomic_halo_build_halo_atoms, fb_atomic_halo_cost, fb_atomic_halo_create, &
        fb_atomic_halo_init, fb_atomic_halo_nullify, fb_atomic_halo_obj, fb_atomic_halo_release, &
        fb_atomic_halo_set, fb_build_pair_radii
   USE qs_fb_env_types,                 ONLY: fb_env_get,&
                                              fb_env_obj,&
                                              fb_env_set
   USE qs_kind_types,                   ONLY: qs_kind_type
   USE util,                            ONLY: sort
#include "./base/base_uses.f90"
 
   IMPLICIT NONE
 
   PRIVATE
 
   PUBLIC :: fb_distribution_build
 
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'qs_fb_distribution_methods'
 
! **************************************************************************************************
!> \brief derived type containing cost data used for process distribution
!> \param id               : global atomic index
!> \param cost             : computational cost for the atomic matrix associated
!>                           to this atom
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   TYPE fb_distribution_element
      INTEGER :: id
      REAL(KIND=dp) :: cost
   END TYPE fb_distribution_element
 
! **************************************************************************************************
!> \brief derived type containing the list of atoms currently allocated to a
!>        processor
!> \param list             : list of atoms and their associated costs
!> \param cost             : total cost of the list
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   TYPE fb_distribution_list
      TYPE(fb_distribution_element), DIMENSION(:), POINTER :: list => null()
      INTEGER :: nelements
      REAL(KIND=dp) :: cost
   END TYPE fb_distribution_list
 
! **************************************************************************************************
!> \brief In filter matrix algorithm, each atomic matrix contributes to a
!>        column in the filter matrix, which is stored in DBCSR format.
!>        When distributing the atoms (and hence the atomic matrics) to the
!>        processors, we want the processors to have atoms that would be
!>        correspond to the block columns in the DBCSR format local to them.
!>        This derived type stores this information. For each atom, it
!>        corresponds to a DBCSR block column, and the list of processors
!>        in the 2D processor grid responsible for this column will be the
!>        preferred processors for this atom.
!> \param list             : list of preferred processors for an atom
!>                           note that here the processors are indexed from
!>                           1, i.e. = MPI_RANK+1
!> \param nprocs           : number of processors in the list
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   TYPE fb_preferred_procs_list
      INTEGER, DIMENSION(:), POINTER :: list => null()
      INTEGER :: nprocs
   END TYPE fb_preferred_procs_list
 
! Parameters related to automatic resizing of the hash_table:
! Resize by EXPAND_FACTOR if total no. slots / no. of filled slots < ENLARGE_RATIO
   INTEGER, PARAMETER, PRIVATE :: ENLARGE_RATIO = 1
   INTEGER, PARAMETER, PRIVATE :: REDUCE_RATIO = 3
   INTEGER, PARAMETER, PRIVATE :: EXPAND_FACTOR = 2
   INTEGER, PARAMETER, PRIVATE :: SHRINK_FACTOR = 2
 
   INTERFACE fb_distribution_remove
      MODULE PROCEDURE fb_distribution_remove_ind, &
         fb_distribution_remove_el
   END INTERFACE fb_distribution_remove
 
   INTERFACE fb_distribution_move
      MODULE PROCEDURE fb_distribution_move_ind, &
         fb_distribution_move_el
   END INTERFACE fb_distribution_move
 
CONTAINS
 
! **************************************************************************************************
!> \brief Build local atoms associated to filter matrix algorithm for each
!>        MPI process, trying to balance the load for calculating the
!>        filter matrix
!> \param fb_env : the filter matrix environment
!> \param qs_env : quickstep environment
!> \param scf_section : SCF input section
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_build(fb_env, qs_env, scf_section)
      TYPE(fb_env_obj), INTENT(INOUT)                    :: fb_env
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(section_vals_type), POINTER                   :: scf_section
 
      CHARACTER(len=*), PARAMETER :: routinen = 'fb_distribution_build'
 
      INTEGER :: handle, i_common_set, iatom, ii, ipe, lb, lowest_cost_ind, my_pe, n_common_sets, &
         natoms, nhalo_atoms, nkinds, nprocs, owner_id_in_halo, pref_pe, ub
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: common_set_ids, local_atoms_all, &
                                                            local_atoms_sizes, local_atoms_starts, &
                                                            pe, pos_in_preferred_list
      INTEGER, DIMENSION(:), POINTER                     :: halo_atoms, local_atoms
      LOGICAL                                            :: acceptable_move, move_happened
      REAL(kind=dp)                                      :: average_cost
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:)           :: cost_per_atom, cost_per_proc
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :)        :: pair_radii
      REAL(kind=dp), DIMENSION(:), POINTER               :: rcut
      TYPE(cell_type), POINTER                           :: cell
      TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: mat_ks
      TYPE(fb_atomic_halo_obj)                           :: atomic_halo
      TYPE(fb_distribution_element)                      :: element
      TYPE(fb_distribution_list), ALLOCATABLE, &
         DIMENSION(:)                                    :: dist
      TYPE(fb_preferred_procs_list), ALLOCATABLE, &
         DIMENSION(:)                                    :: preferred_procs_set
      TYPE(mp_para_env_type), POINTER                    :: para_env
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
 
      CALL timeset(routinen, handle)
 
      NULLIFY (mat_ks, rcut, cell, para_env, particle_set, qs_kind_set, &
               halo_atoms, local_atoms)
      CALL fb_atomic_halo_nullify(atomic_halo)
 
      ! obtain relevant data from fb_env, qs_env
      CALL fb_env_get(fb_env=fb_env, &
                      rcut=rcut)
      CALL get_qs_env(qs_env=qs_env, &
                      natom=natoms, &
                      particle_set=particle_set, &
                      qs_kind_set=qs_kind_set, &
                      nkind=nkinds, &
                      cell=cell, &
                      para_env=para_env, &
                      matrix_ks=mat_ks)
      nprocs = para_env%num_pe
      my_pe = para_env%mepos + 1 ! counting from 1
 
      ! for each global atom, build atomic halo and get the associated cost
      ALLOCATE (pair_radii(nkinds, nkinds))
      CALL fb_build_pair_radii(rcut, nkinds, pair_radii)
      CALL fb_atomic_halo_create(atomic_halo)
      ALLOCATE (cost_per_atom(natoms))
      DO iatom = 1, natoms
         CALL fb_atomic_halo_init(atomic_halo)
         CALL fb_atomic_halo_build_halo_atoms(iatom, &
                                              particle_set, &
                                              cell, &
                                              pair_radii, &
                                              halo_atoms, &
                                              nhalo_atoms, &
                                              owner_id_in_halo)
         CALL fb_atomic_halo_set(atomic_halo=atomic_halo, &
                                 owner_atom=iatom, &
                                 natoms=nhalo_atoms, &
                                 halo_atoms=halo_atoms)
         NULLIFY (halo_atoms)
         cost_per_atom(iatom) = fb_atomic_halo_cost(atomic_halo, particle_set, qs_kind_set)
      END DO
      DEALLOCATE (pair_radii)
      CALL fb_atomic_halo_release(atomic_halo)
 
      ! build the preferred_procs_set according to DBCSR mat H
      ALLOCATE (preferred_procs_set(natoms))
      ALLOCATE (common_set_ids(natoms))
      CALL fb_build_preferred_procs(mat_ks(1)%matrix, &
                                    natoms, &
                                    preferred_procs_set, &
                                    common_set_ids, &
                                    n_common_sets)
 
      ! for each atomic halo, construct distribution_element, and assign
      ! the element to a processors using preferred_procs_set in a
      ! round-robin manner
      ALLOCATE (dist(nprocs))
      DO ipe = 1, nprocs
         CALL fb_distribution_init(dist=dist(ipe))
      END DO
      ALLOCATE (pos_in_preferred_list(n_common_sets))
      pos_in_preferred_list(:) = 0
      DO iatom = 1, natoms
         element%id = iatom
         element%cost = cost_per_atom(iatom)
         i_common_set = common_set_ids(iatom)
         pos_in_preferred_list(i_common_set) = &
            mod(pos_in_preferred_list(i_common_set), &
                preferred_procs_set(iatom)%nprocs) + 1
         ipe = preferred_procs_set(iatom)%list(pos_in_preferred_list(i_common_set))
         CALL fb_distribution_add(dist(ipe), element)
      END DO
 
      DEALLOCATE (pos_in_preferred_list)
      DEALLOCATE (common_set_ids)
      DEALLOCATE (cost_per_atom)
 
      ! sort processors according to the overall cost of their assigned
      ! corresponding distribution
      ALLOCATE (cost_per_proc(nprocs))
      DO ipe = 1, nprocs
         cost_per_proc(ipe) = dist(ipe)%cost
      END DO
      ALLOCATE (pe(nprocs))
      CALL sort(cost_per_proc, nprocs, pe)
      ! now that cost_per_proc is sorted, ipe's no longer give mpi
      ! ranks, the correct one to use should be pe(ipe)
 
      ! work out the ideal average cost per proc if work load is evenly
      ! distributed
      average_cost = sum(cost_per_proc)/real(nprocs, dp)
 
      DEALLOCATE (cost_per_proc)
 
      ! loop over the processors, starting with the highest cost, move
      ! atoms one by one:
      !   1. FIRST to the next processor in the preferred list that has
      !      cost below average. IF no such proc is found, THEN
      !   2. to the next procesor in the overall list that has cost
      !      below average.
      ! repeat until the cost on this processor is less than or equal
      ! to the average cost
      lowest_cost_ind = 1
      DO ipe = nprocs, 1, -1
         redistribute: DO WHILE (dist(pe(ipe))%cost .GT. average_cost)
            iatom = dist(pe(ipe))%list(lowest_cost_ind)%id
            move_happened = .false.
            ! first try to move to a preferred process
            preferred: DO ii = 1, preferred_procs_set(iatom)%nprocs
               pref_pe = preferred_procs_set(iatom)%list(ii)
               acceptable_move = &
                  fb_distribution_acceptable_move(dist(pe(ipe)), &
                                                  dist(pe(ipe))%list(lowest_cost_ind), &
                                                  dist(pref_pe), &
                                                  average_cost)
               IF ((pref_pe .NE. pe(ipe)) .AND. acceptable_move) THEN
                  CALL fb_distribution_move(dist(pe(ipe)), &
                                            lowest_cost_ind, &
                                            dist(pref_pe))
                  move_happened = .true.
                  EXIT preferred
               END IF
            END DO preferred
            ! if no preferred process is available, move to a proc in
            ! the sorted list that has cost less than average.  remember
            ! that some of the proc may have already taken redistributed
            ! atoms, and thus may become unavailable (full)
            IF (.NOT. move_happened) THEN
               ! searching from the proc with the least initial cost
               next_in_line: DO ii = 1, nprocs
                  acceptable_move = &
                     fb_distribution_acceptable_move(dist(pe(ipe)), &
                                                     dist(pe(ipe))%list(lowest_cost_ind), &
                                                     dist(pe(ii)), &
                                                     average_cost)
                  IF ((pe(ii) .NE. pe(ipe)) .AND. acceptable_move) THEN
                     CALL fb_distribution_move(dist(pe(ipe)), &
                                               lowest_cost_ind, &
                                               dist(pe(ii)))
                     move_happened = .true.
                     EXIT next_in_line
                  END IF
               END DO next_in_line
            END IF
            ! if the atom cannot be moved, then this means it is too
            ! costly for all other processes to accept. When this
            ! happens we must stop the redistribution process for this
            ! processor---as all other of its atoms will be even more
            ! costly
            IF (.NOT. move_happened) THEN
               EXIT redistribute
            END IF
         END DO redistribute ! while
      END DO ! ipe
 
      DEALLOCATE (pe)
      DO ii = 1, SIZE(preferred_procs_set)
         CALL fb_preferred_procs_list_release(preferred_procs_set(ii))
      END DO
      DEALLOCATE (preferred_procs_set)
 
      ! generate local atoms from dist
      ALLOCATE (local_atoms_all(natoms))
      ALLOCATE (local_atoms_starts(nprocs))
      ALLOCATE (local_atoms_sizes(nprocs))
      CALL fb_distribution_to_local_atoms(dist, &
                                          local_atoms_all, &
                                          local_atoms_starts, &
                                          local_atoms_sizes)
      ALLOCATE (local_atoms(local_atoms_sizes(my_pe)))
      lb = local_atoms_starts(my_pe)
      ub = local_atoms_starts(my_pe) + local_atoms_sizes(my_pe) - 1
      local_atoms(1:local_atoms_sizes(my_pe)) = local_atoms_all(lb:ub)
      CALL fb_env_set(fb_env=fb_env, &
                      local_atoms=local_atoms, &
                      nlocal_atoms=local_atoms_sizes(my_pe))
 
      ! write out info
      CALL fb_distribution_write_info(dist, scf_section)
 
      DEALLOCATE (local_atoms_all)
      DEALLOCATE (local_atoms_starts)
      DEALLOCATE (local_atoms_sizes)
      DO ipe = 1, SIZE(dist)
         CALL fb_distribution_release(dist(ipe))
      END DO
      DEALLOCATE (dist)
 
      CALL timestop(handle)
 
   END SUBROUTINE fb_distribution_build
 
! **************************************************************************************************
!> \brief Checks if moving an element from one distribution to another is
!>        allowed in mind of load balancing.
!> \param dist_from : the source distribution
!> \param element   : the element in source distribution considered for the
!>                    move
!> \param dist_to   : the destination distribution
!> \param threshold ...
!> \return : TRUE or FALSE
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   PURE FUNCTION fb_distribution_acceptable_move(dist_from, &
                                                 element, &
                                                 dist_to, &
                                                 threshold) &
      result(acceptable)
      TYPE(fb_distribution_list), INTENT(IN)             :: dist_from
      TYPE(fb_distribution_element), INTENT(IN)          :: element
      TYPE(fb_distribution_list), INTENT(IN)             :: dist_to
      REAL(kind=dp), INTENT(IN)                          :: threshold
      LOGICAL                                            :: acceptable
 
      acceptable = (dist_to%cost + element%cost .LT. dist_from%cost) .AND. &
                   (dist_to%cost .LT. threshold)
   END FUNCTION fb_distribution_acceptable_move
 
! **************************************************************************************************
!> \brief Write out information on the load distribution on processors
!> \param dist_set    : set of distributions for the processors
!> \param scf_section : SCF input section
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_write_info(dist_set, scf_section)
      TYPE(fb_distribution_list), DIMENSION(:), &
         INTENT(IN)                                      :: dist_set
      TYPE(section_vals_type), POINTER                   :: scf_section
 
      INTEGER                                            :: ii, max_natoms, min_natoms, natoms, &
                                                            nprocs, unit_nr
      REAL(kind=dp)                                      :: ave_cost, ave_natoms, max_cost, &
                                                            min_cost, total_cost
      TYPE(cp_logger_type), POINTER                      :: logger
 
      nprocs = SIZE(dist_set)
      natoms = 0
      total_cost = 0.0_dp
      DO ii = 1, nprocs
         natoms = natoms + dist_set(ii)%nelements
         total_cost = total_cost + dist_set(ii)%cost
      END DO
      ave_natoms = real(natoms, dp)/real(nprocs, dp)
      ave_cost = total_cost/real(nprocs, dp)
      max_natoms = 0
      max_cost = 0._dp
      DO ii = 1, nprocs
         max_natoms = max(max_natoms, dist_set(ii)%nelements)
         max_cost = max(max_cost, dist_set(ii)%cost)
      END DO
      min_natoms = natoms
      min_cost = total_cost
      DO ii = 1, nprocs
         min_natoms = min(min_natoms, dist_set(ii)%nelements)
         min_cost = min(min_cost, dist_set(ii)%cost)
      END DO
 
      logger => cp_get_default_logger()
      unit_nr = cp_print_key_unit_nr(logger, scf_section, &
                                     "PRINT%FILTER_MATRIX", &
                                     extension="")
 
      IF (unit_nr > 0) THEN
         WRITE (unit=unit_nr, fmt="(/,A,I6,A)") &
            " FILTER_MAT_DIAG| Load distribution across ", nprocs, " processors:"
         WRITE (unit=unit_nr, &
                fmt="(A,T40,A,T55,A,T70,A,T85,A)") &
            " FILTER_MAT_DIAG| ", "Total", "Average", "Max", "Min"
         WRITE (unit=unit_nr, &
                fmt="(A,T40,I12,T55,F12.1,T70,I12,T85,I10)") &
            " FILTER_MAT_DIAG|   Atomic Matrices", &
            natoms, ave_natoms, max_natoms, min_natoms
         WRITE (unit=unit_nr, &
                fmt="(A,T40,D12.7,T55,D12.7,T70,D12.7,T85,D12.7)") &
            " FILTER_MAT_DIAG|   Cost*", &
            total_cost, ave_cost, max_cost, min_cost
         WRITE (unit=unit_nr, fmt="(A)") &
            " FILTER_MAT_DIAG| (* cost is calculated as sum of cube of atomic matrix sizes)"
      END IF
      CALL cp_print_key_finished_output(unit_nr, logger, scf_section, &
                                        "PRINT%FILTER_MATRIX")
   END SUBROUTINE fb_distribution_write_info
 
! **************************************************************************************************
!> \brief Build the preferred list of processors for atoms
!> \param dbcsr_mat   : the reference DBCSR matrix, from which the local block
!>                      cols and the processor maps are obtained
!> \param natoms      : total number of atoms globally
!> \param preferred_procs_set : set of preferred procs list for each atom
!> \param common_set_ids : atoms (block cols) local to the same processor grid
!>                         col will have the same preferred list. This list
!>                         maps each atom to their corresponding group
!> \param n_common_sets  : number of unique preferred lists (groups)
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_build_preferred_procs(dbcsr_mat, &
                                       natoms, &
                                       preferred_procs_set, &
                                       common_set_ids, &
                                       n_common_sets)
      TYPE(dbcsr_type), POINTER                          :: dbcsr_mat
      INTEGER, INTENT(IN)                                :: natoms
      TYPE(fb_preferred_procs_list), DIMENSION(:), &
         INTENT(INOUT)                                   :: preferred_procs_set
      INTEGER, DIMENSION(:), INTENT(OUT)                 :: common_set_ids
      INTEGER, INTENT(OUT)                               :: n_common_sets
 
      INTEGER                                            :: icol, nprows, pcol, prow
      INTEGER, DIMENSION(:), POINTER                     :: col_dist
      INTEGER, DIMENSION(:, :), POINTER                  :: pgrid
      LOGICAL                                            :: check_ok
      TYPE(dbcsr_distribution_type)                      :: dbcsr_dist
 
      check_ok = natoms .LE. dbcsr_nblkcols_total(dbcsr_mat)
      cpassert(check_ok)
      check_ok = SIZE(preferred_procs_set) .GE. natoms
      cpassert(check_ok)
      check_ok = SIZE(common_set_ids) .GE. natoms
      cpassert(check_ok)
 
      CALL dbcsr_get_info(dbcsr_mat, distribution=dbcsr_dist, proc_col_dist=col_dist)
      CALL dbcsr_distribution_get(dbcsr_dist, pgrid=pgrid, nprows=nprows, npcols=n_common_sets)
 
      DO icol = 1, natoms
         IF (ASSOCIATED(preferred_procs_set(icol)%list)) THEN
            DEALLOCATE (preferred_procs_set(icol)%list)
         END IF
         ALLOCATE (preferred_procs_set(icol)%list(nprows))
         pcol = col_dist(icol)
         ! dbcsr prow and pcol counts from 0
         DO prow = 0, nprows - 1
            ! here, we count processes from 1, so +1 from mpirank
            preferred_procs_set(icol)%list(prow + 1) = pgrid(prow, pcol) + 1
         END DO
         preferred_procs_set(icol)%nprocs = nprows
      END DO
 
      common_set_ids(:) = 0
      common_set_ids(1:natoms) = col_dist(1:natoms) + 1
 
   END SUBROUTINE fb_build_preferred_procs
 
! **************************************************************************************************
!> \brief Release a preferred_procs_list
!> \param preferred_procs_list  : the preferred procs list in question
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_preferred_procs_list_release(preferred_procs_list)
      TYPE(fb_preferred_procs_list), INTENT(INOUT)       :: preferred_procs_list
 
      IF (ASSOCIATED(preferred_procs_list%list)) THEN
         DEALLOCATE (preferred_procs_list%list)
      END IF
   END SUBROUTINE fb_preferred_procs_list_release
 
! **************************************************************************************************
!> \brief Convert distribution data to 1D array containing information of
!>        which atoms are distributed to which processor
!> \param dist_set    : set of distributions for the processors
!> \param local_atoms : continuous array of atoms arranged in order
!>                      corresponding their allocated processors
!> \param local_atoms_starts : starting position in local_atoms array for
!>                             each processor
!> \param local_atoms_sizes  : number of atoms local to each processor
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_to_local_atoms(dist_set, &
                                             local_atoms, &
                                             local_atoms_starts, &
                                             local_atoms_sizes)
      TYPE(fb_distribution_list), DIMENSION(:), &
         INTENT(IN)                                      :: dist_set
      INTEGER, DIMENSION(:), INTENT(OUT)                 :: local_atoms, local_atoms_starts, &
                                                            local_atoms_sizes
 
      INTEGER                                            :: iatom, ipe, n_procs, pos
      LOGICAL                                            :: check_ok
 
      n_procs = SIZE(dist_set)
 
      check_ok = SIZE(local_atoms_starts) .GE. n_procs
      cpassert(check_ok)
      check_ok = SIZE(local_atoms_sizes) .GE. n_procs
      cpassert(check_ok)
 
      local_atoms(:) = 0
      local_atoms_starts(:) = 0
      local_atoms_sizes(:) = 0
 
      pos = 1
      DO ipe = 1, n_procs
         local_atoms_starts(ipe) = pos
         DO iatom = 1, dist_set(ipe)%nelements
            local_atoms(pos) = dist_set(ipe)%list(iatom)%id
            pos = pos + 1
            local_atoms_sizes(ipe) = local_atoms_sizes(ipe) + 1
         END DO
      END DO
   END SUBROUTINE fb_distribution_to_local_atoms
 
! **************************************************************************************************
!> \brief Initialise a distribution
!> \param dist        : the distribution in question
!> \param nmax        : [OPTIONAL] size of the list array to be allocated
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_init(dist, nmax)
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist
      INTEGER, INTENT(IN), OPTIONAL                      :: nmax
 
      INTEGER                                            :: ii, my_nmax
 
      my_nmax = 0
      IF (PRESENT(nmax)) my_nmax = nmax
      IF (ASSOCIATED(dist%list)) THEN
         DEALLOCATE (dist%list)
      END IF
      NULLIFY (dist%list)
      IF (my_nmax .GT. 0) THEN
         ALLOCATE (dist%list(my_nmax))
         DO ii = 1, SIZE(dist%list)
            dist%list(ii)%id = 0
            dist%list(ii)%cost = 0.0_dp
         END DO
      END IF
      dist%nelements = 0
      dist%cost = 0.0_dp
   END SUBROUTINE fb_distribution_init
 
! **************************************************************************************************
!> \brief Resize the list array in a distribution
!> \param dist        : The distribution in question
!> \param nmax        : new size of the list array
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_resize(dist, nmax)
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist
      INTEGER, INTENT(IN)                                :: nmax
 
      INTEGER                                            :: ii, my_nmax
      TYPE(fb_distribution_element), DIMENSION(:), &
         POINTER                                         :: new_list
 
      IF (.NOT. ASSOCIATED(dist%list)) THEN
         my_nmax = max(nmax, 1)
         ALLOCATE (dist%list(my_nmax))
      ELSE
         my_nmax = max(nmax, dist%nelements)
         ALLOCATE (new_list(my_nmax))
         DO ii = 1, SIZE(new_list)
            new_list(ii)%id = 0
            new_list(ii)%cost = 0.0_dp
         END DO
         DO ii = 1, dist%nelements
            new_list(ii) = dist%list(ii)
         END DO
         DEALLOCATE (dist%list)
         dist%list => new_list
      END IF
   END SUBROUTINE fb_distribution_resize
 
! **************************************************************************************************
!> \brief Add an atom (element) to a distribution
!> \param dist        : the distribution in question
!> \param element     : the element to be added
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_add(dist, element)
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist
      TYPE(fb_distribution_element), INTENT(IN)          :: element
 
      INTEGER                                            :: ii, new_nelements, pos
 
      new_nelements = dist%nelements + 1
 
      ! resize list if necessary
      IF (.NOT. ASSOCIATED(dist%list)) THEN
         CALL fb_distribution_resize(dist, new_nelements)
      ELSE IF (new_nelements*enlarge_ratio .GT. SIZE(dist%list)) THEN
         CALL fb_distribution_resize(dist, SIZE(dist%list)*expand_factor)
      END IF
      ! assuming the list of elements is always sorted with respect to cost
      ! slot the new element into the appropriate spot
      IF (new_nelements == 1) THEN
         dist%list(1) = element
      ELSE
         pos = fb_distribution_find_slot(dist, element)
         DO ii = dist%nelements, pos, -1
            dist%list(ii + 1) = dist%list(ii)
         END DO
         dist%list(pos) = element
      END IF
      dist%nelements = new_nelements
      dist%cost = dist%cost + element%cost
   END SUBROUTINE fb_distribution_add
 
! **************************************************************************************************
!> \brief Find the correct slot in the list array to add a new element, so that
!>        the list will always be ordered with respect to cost
!> \param dist        : the distribution in question
!> \param element     : element to be added
!> \return : the correct position to add the new element
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   PURE FUNCTION fb_distribution_find_slot(dist, element) RESULT(pos)
      TYPE(fb_distribution_list), INTENT(IN)             :: dist
      TYPE(fb_distribution_element), INTENT(IN)          :: element
      INTEGER                                            :: pos
 
      INTEGER                                            :: lower, middle, n, upper
 
      n = dist%nelements
      IF (element%cost .LT. dist%list(1)%cost) THEN
         pos = 1
         RETURN
      END IF
      IF (element%cost .GE. dist%list(n)%cost) THEN
         pos = n + 1
         RETURN
      END IF
      lower = 1
      upper = n
      DO WHILE ((upper - lower) .GT. 1)
         middle = (lower + upper)/2
         IF (element%cost .LT. dist%list(middle)%cost) THEN
            upper = middle
         ELSE
            lower = middle
         END IF
      END DO
      pos = upper
   END FUNCTION fb_distribution_find_slot
 
! **************************************************************************************************
!> \brief Remove the pos-th element from a distribution
!> \param dist        : the distribution in question
!> \param pos         : index of the element in the list array
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_remove_ind(dist, pos)
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist
      INTEGER, INTENT(IN)                                :: pos
 
      INTEGER                                            :: ii
      LOGICAL                                            :: check_ok
 
      check_ok = pos .GT. 0
      cpassert(check_ok)
      IF (pos .LE. dist%nelements) THEN
         dist%cost = dist%cost - dist%list(pos)%cost
         DO ii = pos, dist%nelements - 1
            dist%list(ii) = dist%list(ii + 1)
         END DO
         dist%list(dist%nelements)%id = 0
         dist%list(dist%nelements)%cost = 0.0_dp
         dist%nelements = dist%nelements - 1
         ! auto resize if required
         IF (dist%nelements*reduce_ratio .LT. SIZE(dist%list)) THEN
            CALL fb_distribution_resize(dist, dist%nelements/shrink_factor)
         END IF
      END IF
   END SUBROUTINE fb_distribution_remove_ind
 
! **************************************************************************************************
!> \brief Remove a given element from a distribution
!> \param dist        : the distribution in question
!> \param element     : the element in question
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_remove_el(dist, element)
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist
      TYPE(fb_distribution_element), INTENT(IN)          :: element
 
      INTEGER                                            :: ii, pos
 
      pos = dist%nelements + 1
      DO ii = 1, dist%nelements
         IF (element%id == dist%list(ii)%id) THEN
            pos = ii
            EXIT
         END IF
      END DO
      CALL fb_distribution_remove_ind(dist, pos)
   END SUBROUTINE fb_distribution_remove_el
 
! **************************************************************************************************
!> \brief Move the pos-th element from a distribution to another
!> \param dist_from   : the source distribution
!> \param pos         : index of the element in the source distribution
!> \param dist_to     : the destination distribution
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_move_ind(dist_from, pos, dist_to)
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist_from
      INTEGER, INTENT(IN)                                :: pos
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist_to
 
      LOGICAL                                            :: check_ok
      TYPE(fb_distribution_element)                      :: element
 
      check_ok = ASSOCIATED(dist_from%list)
      cpassert(check_ok)
      check_ok = pos .LE. dist_from%nelements
      cpassert(check_ok)
      element = dist_from%list(pos)
      CALL fb_distribution_add(dist_to, element)
      CALL fb_distribution_remove(dist_from, pos)
   END SUBROUTINE fb_distribution_move_ind
 
! **************************************************************************************************
!> \brief Move a given element from a distribution to another
!> \param dist_from   : the source distribution
!> \param element     : the element in question
!> \param dist_to     : the destination distribution
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_move_el(dist_from, element, dist_to)
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist_from
      TYPE(fb_distribution_element), INTENT(IN)          :: element
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist_to
 
      LOGICAL                                            :: check_ok
 
      check_ok = ASSOCIATED(dist_from%list)
      cpassert(check_ok)
      CALL fb_distribution_add(dist_to, element)
      CALL fb_distribution_remove(dist_from, element)
   END SUBROUTINE fb_distribution_move_el
 
! **************************************************************************************************
!> \brief Release a distribution
!> \param dist  : the distribution in question
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_distribution_release(dist)
      TYPE(fb_distribution_list), INTENT(INOUT)          :: dist
 
      IF (ASSOCIATED(dist%list)) THEN
         DEALLOCATE (dist%list)
      END IF
   END SUBROUTINE fb_distribution_release
 
END MODULE qs_fb_distribution_methods