!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright (C) 2000 - 2018  CP2K developers group                                               !
!--------------------------------------------------------------------------------------------------!

! **************************************************************************************************
!> \brief Generate the atomic neighbor lists for FIST.
!> \par History
!>      - build and update merged (11.02.2005,MK)
!>      - bug fix for PERIODIC NONE (24.02.06,MK)
!>      - Major rewriting (light memory neighbor lists): teo and joost (05.2006)
!>      - Completely new algorithm for the neighbor lists
!>        (faster and memory lighter) (Teo 08.2006)
!> \author MK (19.11.2002,24.07.2003)
!>      Teodoro Laino (08.2006) - MAJOR REWRITING
! **************************************************************************************************
MODULE fist_neighbor_lists

   USE atomic_kind_types,               ONLY: atomic_kind_type,&
                                              get_atomic_kind,&
                                              get_atomic_kind_set
   USE cell_types,                      ONLY: cell_type,&
                                              get_cell,&
                                              pbc,&
                                              plane_distance,&
                                              scaled_to_real
   USE cp_log_handling,                 ONLY: cp_get_default_logger,&
                                              cp_logger_get_default_unit_nr,&
                                              cp_logger_type
   USE cp_output_handling,              ONLY: cp_p_file,&
                                              cp_print_key_finished_output,&
                                              cp_print_key_should_output,&
                                              cp_print_key_unit_nr
   USE cp_para_types,                   ONLY: cp_para_env_type
   USE cp_units,                        ONLY: cp_unit_from_cp2k
   USE distribution_1d_types,           ONLY: distribution_1d_type
   USE exclusion_types,                 ONLY: exclusion_type
   USE fist_neighbor_list_types,        ONLY: fist_neighbor_add,&
                                              fist_neighbor_deallocate,&
                                              fist_neighbor_init,&
                                              fist_neighbor_type,&
                                              neighbor_kind_pairs_type
   USE input_section_types,             ONLY: section_vals_type,&
                                              section_vals_val_get
   USE kinds,                           ONLY: default_string_length,&
                                              dp
   USE mathlib,                         ONLY: matvec_3x3
   USE memory_utilities,                ONLY: reallocate
   USE particle_types,                  ONLY: particle_type
   USE qmmm_ff_fist,                    ONLY: qmmm_ff_precond_only_qm
   USE string_utilities,                ONLY: compress
   USE subcell_types,                   ONLY: allocate_subcell,&
                                              deallocate_subcell,&
                                              give_ijk_subcell,&
                                              reorder_atoms_subcell,&
                                              subcell_type
   USE util,                            ONLY: sort
#include "./base/base_uses.f90"

   IMPLICIT NONE

   PRIVATE

   ! Global parameters (in this module)
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'fist_neighbor_lists'

   TYPE local_atoms_type
      INTEGER, DIMENSION(:), POINTER                   :: list, &
                                                          list_local_a_index
   END TYPE local_atoms_type

   ! Public subroutines
   PUBLIC :: build_fist_neighbor_lists

CONTAINS

! **************************************************************************************************
!> \brief ...
!> \param atomic_kind_set ...
!> \param particle_set ...
!> \param local_particles ...
!> \param cell ...
!> \param r_max ...
!> \param r_minsq ...
!> \param ei_scale14 ...
!> \param vdw_scale14 ...
!> \param nonbonded ...
!> \param para_env ...
!> \param build_from_scratch ...
!> \param geo_check ...
!> \param mm_section ...
!> \param full_nl ...
!> \param exclusions ...
!> \par History
!>      08.2006 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
   SUBROUTINE build_fist_neighbor_lists(atomic_kind_set, particle_set, &
                                        local_particles, cell, r_max, r_minsq, ei_scale14, vdw_scale14, &
                                        nonbonded, para_env, build_from_scratch, geo_check, mm_section, &
                                        full_nl, exclusions)

      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(distribution_1d_type), OPTIONAL, POINTER      :: local_particles
      TYPE(cell_type), POINTER                           :: cell
      REAL(dp), DIMENSION(:, :), INTENT(IN)              :: r_max, r_minsq
      REAL(KIND=DP), INTENT(IN)                          :: ei_scale14, vdw_scale14
      TYPE(fist_neighbor_type), POINTER                  :: nonbonded
      TYPE(cp_para_env_type), POINTER                    :: para_env
      LOGICAL, INTENT(IN)                                :: build_from_scratch, geo_check
      TYPE(section_vals_type), POINTER                   :: mm_section
      LOGICAL, DIMENSION(:, :), OPTIONAL, POINTER        :: full_nl
      TYPE(exclusion_type), DIMENSION(:), OPTIONAL       :: exclusions

      CHARACTER(LEN=*), PARAMETER :: routineN = 'build_fist_neighbor_lists', &
         routineP = moduleN//':'//routineN

      CHARACTER(LEN=default_string_length)               :: kind_name, print_key_path, unit_str
      INTEGER                                            :: atom_a, handle, iatom_local, ikind, iw, &
                                                            maxatom, natom_local_a, nkind, &
                                                            output_unit
      LOGICAL                                            :: present_local_particles, &
                                                            print_subcell_grid
      LOGICAL, DIMENSION(:), POINTER                     :: skip_kind
      LOGICAL, DIMENSION(:, :), POINTER                  :: my_full_nl
      TYPE(atomic_kind_type), POINTER                    :: atomic_kind
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(local_atoms_type), ALLOCATABLE, DIMENSION(:)  :: atom

      CALL timeset(routineN, handle)
      NULLIFY (logger)
      logger => cp_get_default_logger()

      print_subcell_grid = .FALSE.
      output_unit = cp_print_key_unit_nr(logger, mm_section, "PRINT%SUBCELL", &
                                         extension=".Log")
      IF (output_unit > 0) print_subcell_grid = .TRUE.

      CALL get_atomic_kind_set(atomic_kind_set=atomic_kind_set, &
                               maxatom=maxatom)

      present_local_particles = PRESENT(local_particles)

      ! if exclusions matters local particles are present. Seems like only the exclusions
      ! for the local particles are needed, which would imply a huge memory savings for fist
      IF (PRESENT(exclusions)) THEN
         CPASSERT(present_local_particles)
      ENDIF

      ! Allocate work storage
      nkind = SIZE(atomic_kind_set)
      ALLOCATE (atom(nkind))
      ALLOCATE (skip_kind(nkind))
      ! full_nl
      IF (PRESENT(full_nl)) THEN
         my_full_nl => full_nl
      ELSE
         ALLOCATE (my_full_nl(nkind, nkind))
         my_full_nl = .FALSE.
      END IF
      ! Initialize the local data structures
      DO ikind = 1, nkind
         atomic_kind => atomic_kind_set(ikind)
         NULLIFY (atom(ikind)%list)
         NULLIFY (atom(ikind)%list_local_a_index)

         CALL get_atomic_kind(atomic_kind=atomic_kind, &
                              atom_list=atom(ikind)%list, name=kind_name)
         skip_kind(ikind) = qmmm_ff_precond_only_qm(kind_name)
         IF (present_local_particles) THEN
            natom_local_a = local_particles%n_el(ikind)
         ELSE
            natom_local_a = SIZE(atom(ikind)%list)
         END IF
         IF (natom_local_a > 0) THEN
            ALLOCATE (atom(ikind)%list_local_a_index(natom_local_a))
            ! Build index vector for mapping
            DO iatom_local = 1, natom_local_a
               IF (present_local_particles) THEN
                  atom_a = local_particles%list(ikind)%array(iatom_local)
               ELSE
                  atom_a = atom(ikind)%list(iatom_local)
               END IF
               atom(ikind)%list_local_a_index(iatom_local) = atom_a
            END DO

         END IF
      END DO

      IF (build_from_scratch) THEN
         IF (ASSOCIATED(nonbonded)) THEN
            CALL fist_neighbor_deallocate(nonbonded)
         END IF
      END IF

      ! Build the nonbonded neighbor lists
      CALL build_neighbor_lists(nonbonded, particle_set, atom, cell, &
                                print_subcell_grid, output_unit, r_max, r_minsq, &
                                ei_scale14, vdw_scale14, geo_check, "NONBONDED", skip_kind, &
                                my_full_nl, exclusions)

      ! Sort the list according kinds for each cell
      CALL sort_neighbor_lists(nonbonded, nkind)

      print_key_path = "PRINT%NEIGHBOR_LISTS"

      IF (BTEST(cp_print_key_should_output(logger%iter_info, mm_section, print_key_path), &
                cp_p_file)) THEN
         iw = cp_print_key_unit_nr(logger=logger, &
                                   basis_section=mm_section, &
                                   print_key_path=print_key_path, &
                                   extension=".out", &
                                   middle_name="nonbonded_nl", &
                                   local=.TRUE., &
                                   log_filename=.FALSE., &
                                   file_position="REWIND")
         CALL section_vals_val_get(mm_section, TRIM(print_key_path)//"%UNIT", c_val=unit_str)
         CALL write_neighbor_lists(nonbonded, particle_set, cell, para_env, iw, &
                                   "NONBONDED NEIGHBOR LISTS", unit_str)
         CALL cp_print_key_finished_output(unit_nr=iw, &
                                           logger=logger, &
                                           basis_section=mm_section, &
                                           print_key_path=print_key_path, &
                                           local=.TRUE.)
      END IF

      ! Release work storage
      DO ikind = 1, nkind
         NULLIFY (atom(ikind)%list)
         IF (ASSOCIATED(atom(ikind)%list_local_a_index)) THEN
            DEALLOCATE (atom(ikind)%list_local_a_index)
         END IF
      END DO
      IF (PRESENT(full_nl)) THEN
         NULLIFY (my_full_nl)
      ELSE
         DEALLOCATE (my_full_nl)
      END IF
      DEALLOCATE (atom)

      DEALLOCATE (skip_kind)

      CALL cp_print_key_finished_output(unit_nr=output_unit, &
                                        logger=logger, &
                                        basis_section=mm_section, &
                                        print_key_path="PRINT%SUBCELL")
      CALL timestop(handle)

   END SUBROUTINE build_fist_neighbor_lists

! **************************************************************************************************
!> \brief ...
!> \param nonbonded ...
!> \param particle_set ...
!> \param atom ...
!> \param cell ...
!> \param print_subcell_grid ...
!> \param output_unit ...
!> \param r_max ...
!> \param r_minsq ...
!> \param ei_scale14 ...
!> \param vdw_scale14 ...
!> \param geo_check ...
!> \param name ...
!> \param skip_kind ...
!> \param full_nl ...
!> \param exclusions ...
!> \par History
!>      08.2006 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
   SUBROUTINE build_neighbor_lists(nonbonded, particle_set, atom, cell, &
                                   print_subcell_grid, output_unit, r_max, r_minsq, &
                                   ei_scale14, vdw_scale14, geo_check, name, skip_kind, full_nl, exclusions)

      TYPE(fist_neighbor_type), POINTER                  :: nonbonded
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(local_atoms_type), DIMENSION(:), INTENT(IN)   :: atom
      TYPE(cell_type), POINTER                           :: cell
      LOGICAL, INTENT(IN)                                :: print_subcell_grid
      INTEGER, INTENT(IN)                                :: output_unit
      REAL(dp), DIMENSION(:, :), INTENT(IN)              :: r_max, r_minsq
      REAL(KIND=dp), INTENT(IN)                          :: ei_scale14, vdw_scale14
      LOGICAL, INTENT(IN)                                :: geo_check
      CHARACTER(LEN=*), INTENT(IN)                       :: name
      LOGICAL, DIMENSION(:), POINTER                     :: skip_kind
      LOGICAL, DIMENSION(:, :), POINTER                  :: full_nl
      TYPE(exclusion_type), DIMENSION(:), OPTIONAL       :: exclusions

      CHARACTER(LEN=*), PARAMETER :: routineN = 'build_neighbor_lists', &
         routineP = moduleN//':'//routineN

      INTEGER :: a_i, a_j, a_k, atom_a, atom_b, b_i, b_j, b_k, b_pi, b_pj, b_pk, bg_i, bg_j, bg_k, &
         handle, i, i1, iatom_local, icell, icellmap, id_kind, ii, ii_start, ij, ij_start, ik, &
         ik_start, ikind, imap, imax_cell, invcellmap, iw, ix, j, j1, jatom_local, jcell, jkind, &
         jx, k, kcell, kx, natom_local_a, ncellmax, nkind, nkind00, tmpdim, xdim, ydim, zdim
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: kind_of, work
      INTEGER, ALLOCATABLE, DIMENSION(:, :, :)           :: cellmap
      INTEGER, DIMENSION(3)                              :: isubcell, ncell, nsubcell, periodic
      LOGICAL                                            :: any_full, atom_order, check_spline, &
                                                            is_full, subcell000
      LOGICAL, ALLOCATABLE, DIMENSION(:, :, :)           :: sphcub
      REAL(dp)                                           :: rab2, rab2_max, rab2_min, rab_max
      REAL(dp), DIMENSION(3)                             :: abc, cell_v, cv_b, rab, rb, sab_max
      REAL(KIND=dp)                                      :: ic(3), icx(3), radius, vv
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: coord
      TYPE(neighbor_kind_pairs_type), POINTER            :: inv_neighbor_kind_pair, &
                                                            neighbor_kind_pair
      TYPE(subcell_type), DIMENSION(:, :, :), POINTER    :: subcell_a, subcell_b

      CALL timeset(routineN, handle)
      nkind = SIZE(atom)
      nsubcell = 1
      isubcell = 0
      ncell = 0
      any_full = ANY(full_nl)
      CALL get_cell(cell=cell, &
                    abc=abc, &
                    periodic=periodic)
      ! Determines the number of subcells
      DO ikind = 1, nkind
         DO jkind = ikind, nkind
            ! Calculate the square of the maximum interaction distance
            rab_max = r_max(ikind, jkind)
            IF (skip_kind(ikind) .AND. skip_kind(jkind)) CYCLE
            nsubcell(1) = MAX(nsubcell(1), CEILING(plane_distance(1, 0, 0, cell)/rab_max))
            nsubcell(2) = MAX(nsubcell(2), CEILING(plane_distance(0, 1, 0, cell)/rab_max))
            nsubcell(3) = MAX(nsubcell(3), CEILING(plane_distance(0, 0, 1, cell)/rab_max))
         END DO
      END DO
      ! Determines the number of periodic images and the number of interacting subcells
      DO ikind = 1, nkind
         DO jkind = ikind, nkind
            IF (skip_kind(ikind) .AND. skip_kind(jkind)) CYCLE
            ! Calculate the square of the maximum interaction distance
            rab_max = r_max(ikind, jkind)
            sab_max(1) = rab_max/plane_distance(1, 0, 0, cell)
            sab_max(2) = rab_max/plane_distance(0, 1, 0, cell)
            sab_max(3) = rab_max/plane_distance(0, 0, 1, cell)
            ncell = MAX(ncell(:), CEILING(sab_max(:)*periodic(:)))
            isubcell = MAX(isubcell(:), CEILING(sab_max(:)*REAL(nsubcell(:), KIND=dp)))
         END DO
      END DO
      CALL fist_neighbor_init(nonbonded, ncell)
      ! Print headline
      IF (print_subcell_grid) THEN
         WRITE (UNIT=output_unit, FMT="(/,/,T2,A,/)") &
            "SUBCELL GRID  INFO FOR THE "//TRIM(name)//" NEIGHBOR LISTS"
         WRITE (UNIT=output_unit, FMT="(T4,A,10X,3I10)") " NUMBER OF SUBCELLS             ::", nsubcell
         WRITE (UNIT=output_unit, FMT="(T4,A,10X,3I10)") " NUMBER OF PERIODIC      IMAGES ::", ncell
         WRITE (UNIT=output_unit, FMT="(T4,A,10X,3I10)") " NUMBER OF INTERACTING SUBCELLS ::", isubcell
      END IF
      ! Allocate subcells
      CALL allocate_subcell(subcell_a, nsubcell, cell=cell)
      CALL allocate_subcell(subcell_b, nsubcell, cell=cell)
      ! Let's map the sequence of the periodic images
      ncellmax = MAXVAL(ncell)
      ALLOCATE (cellmap(-ncellmax:ncellmax, -ncellmax:ncellmax, -ncellmax:ncellmax))
      cellmap = -1
      imap = 0
      nkind00 = nkind*(nkind+1)/2
      DO imax_cell = 0, ncellmax
         DO kcell = -imax_cell, imax_cell
            DO jcell = -imax_cell, imax_cell
               DO icell = -imax_cell, imax_cell
                  IF (cellmap(icell, jcell, kcell) == -1) THEN
                     imap = imap+1
                     cellmap(icell, jcell, kcell) = imap
                     CPASSERT(imap <= nonbonded%nlists)
                     neighbor_kind_pair => nonbonded%neighbor_kind_pairs(imap)

                     neighbor_kind_pair%cell_vector(1) = icell
                     neighbor_kind_pair%cell_vector(2) = jcell
                     neighbor_kind_pair%cell_vector(3) = kcell
                  ENDIF
               ENDDO
            ENDDO
         ENDDO
      ENDDO
      ! Mapping the spherical interaction between subcells
      ALLOCATE (sphcub(-isubcell(1):isubcell(1), &
                       -isubcell(2):isubcell(2), &
                       -isubcell(3):isubcell(3)))
      sphcub = .FALSE.
      IF (ALL(isubcell /= 0)) THEN
         radius = REAL(isubcell(1), KIND=dp)**2+REAL(isubcell(2), KIND=dp)**2+ &
                  REAL(isubcell(3), KIND=dp)**2
         loop1: DO k = -isubcell(3), isubcell(3)
            loop2: DO j = -isubcell(2), isubcell(2)
               loop3: DO i = -isubcell(1), isubcell(1)
                  ic = REAL((/i, j, k/), KIND=dp)
                  ! subcell cube vertex
                  DO kx = -1, 1
                     icx(3) = ic(3)+SIGN(0.5_dp, REAL(kx, KIND=dp))
                     DO jx = -1, 1
                        icx(2) = ic(2)+SIGN(0.5_dp, REAL(jx, KIND=dp))
                        DO ix = -1, 1
                           icx(1) = ic(1)+SIGN(0.5_dp, REAL(ix, KIND=dp))
                           vv = icx(1)*icx(1)+icx(2)*icx(2)+icx(3)*icx(3)
                           vv = vv/radius
                           IF (vv <= 1.0_dp) THEN
                              sphcub(i, j, k) = .TRUE.
                              CYCLE loop3
                           END IF
                        END DO
                     END DO
                  END DO
               END DO loop3
            END DO loop2
         END DO loop1
      END IF
      ! Mapping locally all atoms in the zeroth cell
      ALLOCATE (coord(3, SIZE(particle_set)))
      DO atom_a = 1, SIZE(particle_set)
         coord(:, atom_a) = pbc(particle_set(atom_a)%r, cell)
      END DO
      ! Associate particles to subcells (local particles)
      DO ikind = 1, nkind
         IF (.NOT. ASSOCIATED(atom(ikind)%list_local_a_index)) CYCLE
         natom_local_a = SIZE(atom(ikind)%list_local_a_index)
         DO iatom_local = 1, natom_local_a
            atom_a = atom(ikind)%list_local_a_index(iatom_local)
            CALL give_ijk_subcell(coord(:, atom_a), i, j, k, cell, nsubcell)
            subcell_a(i, j, k)%natom = subcell_a(i, j, k)%natom+1
         END DO
      END DO
      DO k = 1, nsubcell(3)
         DO j = 1, nsubcell(2)
            DO i = 1, nsubcell(1)
               ALLOCATE (subcell_a(i, j, k)%atom_list(subcell_a(i, j, k)%natom))
               subcell_a(i, j, k)%natom = 0
            END DO
         END DO
      END DO
      DO ikind = 1, nkind
         IF (.NOT. ASSOCIATED(atom(ikind)%list_local_a_index)) CYCLE
         natom_local_a = SIZE(atom(ikind)%list_local_a_index)
         DO iatom_local = 1, natom_local_a
            atom_a = atom(ikind)%list_local_a_index(iatom_local)
            CALL give_ijk_subcell(coord(:, atom_a), i, j, k, cell, nsubcell)
            subcell_a(i, j, k)%natom = subcell_a(i, j, k)%natom+1
            subcell_a(i, j, k)%atom_list(subcell_a(i, j, k)%natom) = atom_a
         END DO
      END DO
      ! Associate particles to subcells (distributed particles)
      DO atom_b = 1, SIZE(particle_set)
         CALL give_ijk_subcell(coord(:, atom_b), i, j, k, cell, nsubcell)
         subcell_b(i, j, k)%natom = subcell_b(i, j, k)%natom+1
      END DO
      DO k = 1, nsubcell(3)
         DO j = 1, nsubcell(2)
            DO i = 1, nsubcell(1)
               ALLOCATE (subcell_b(i, j, k)%atom_list(subcell_b(i, j, k)%natom))
               subcell_b(i, j, k)%natom = 0
            END DO
         END DO
      END DO
      DO atom_b = 1, SIZE(particle_set)
         CALL give_ijk_subcell(coord(:, atom_b), i, j, k, cell, nsubcell)
         subcell_b(i, j, k)%natom = subcell_b(i, j, k)%natom+1
         subcell_b(i, j, k)%atom_list(subcell_b(i, j, k)%natom) = atom_b
      END DO
      ! Reorder atoms associated to subcells
      tmpdim = MAXVAL(subcell_a(:, :, :)%natom)
      tmpdim = MAX(tmpdim, MAXVAL(subcell_b(:, :, :)%natom))
      ALLOCATE (work(3*tmpdim))
      ALLOCATE (kind_of(SIZE(particle_set)))
      DO i = 1, SIZE(particle_set)
         kind_of(i) = particle_set(i)%atomic_kind%kind_number
      END DO
      DO k = 1, nsubcell(3)
         DO j = 1, nsubcell(2)
            DO i = 1, nsubcell(1)
               CALL reorder_atoms_subcell(subcell_a(i, j, k)%atom_list, kind_of, work)
               CALL reorder_atoms_subcell(subcell_b(i, j, k)%atom_list, kind_of, work)
            END DO
         END DO
      END DO
      DEALLOCATE (work, kind_of)
      zdim = nsubcell(3)
      ydim = nsubcell(2)
      xdim = nsubcell(1)
      is_full = .FALSE.
      ! We can skip until ik>=0.. this prescreens the order of the subcells
      ik_start = -isubcell(3)
      IF (.NOT. any_full) ik_start = 0
      ! Loop over first subcell
      loop_a_k: DO a_k = 1, nsubcell(3)
      loop_a_j: DO a_j = 1, nsubcell(2)
      loop_a_i: DO a_i = 1, nsubcell(1)
         IF (subcell_a(a_i, a_j, a_k)%natom == 0) CYCLE
         ! Loop over second subcell
         loop_b_k: DO ik = ik_start, isubcell(3)
            bg_k = a_k+ik
            b_k = MOD(bg_k, zdim)
            b_pk = bg_k/zdim
            IF (b_k <= 0) THEN
               b_k = zdim+b_k
               b_pk = b_pk-1
            END IF
            IF ((periodic(3) == 0) .AND. (ABS(b_pk) > 0)) CYCLE
            ! Setup the starting point.. this prescreens the order of the subcells
            ij_start = -isubcell(2)
            IF ((ik == 0) .AND. (ik_start == 0)) ij_start = 0
            loop_b_j: DO ij = ij_start, isubcell(2)
               bg_j = a_j+ij
               b_j = MOD(bg_j, ydim)
               b_pj = bg_j/ydim
               IF (b_j <= 0) THEN
                  b_j = ydim+b_j
                  b_pj = b_pj-1
               END IF
               IF ((periodic(2) == 0) .AND. (ABS(b_pj) > 0)) CYCLE
               ! Setup the starting point.. this prescreens the order of the subcells
               ii_start = -isubcell(1)
               IF ((ij == 0) .AND. (ij_start == 0)) ii_start = 0
               loop_b_i: DO ii = ii_start, isubcell(1)
                  ! Ellipsoidal screening of subcells
                  IF (.NOT. sphcub(ii, ij, ik)) CYCLE
                  bg_i = a_i+ii
                  b_i = MOD(bg_i, xdim)
                  b_pi = bg_i/xdim
                  IF (b_i <= 0) THEN
                     b_i = xdim+b_i
                     b_pi = b_pi-1
                  END IF
                  IF ((periodic(1) == 0) .AND. (ABS(b_pi) > 0)) CYCLE
                  IF (subcell_b(b_i, b_j, b_k)%natom == 0) CYCLE
                  ! Find the proper neighbor kind pair
                  icellmap = cellmap(b_pi, b_pj, b_pk)
                  neighbor_kind_pair => nonbonded%neighbor_kind_pairs(icellmap)
                  ! Find the replica vector
                  cell_v = 0.0_dp
                  IF ((b_pi /= 0) .OR. (b_pj /= 0) .OR. (b_pk /= 0)) THEN
                     cv_b(1) = b_pi; cv_b(2) = b_pj; cv_b(3) = b_pk
                     CALL scaled_to_real(cell_v, cv_b, cell)
                  END IF
                  subcell000 = (a_k == bg_k) .AND. (a_j == bg_j) .AND. (a_i == bg_i)
                  ! Loop over particles inside subcell_a and subcell_b
                  DO jatom_local = 1, subcell_b(b_i, b_j, b_k)%natom
                     atom_b = subcell_b(b_i, b_j, b_k)%atom_list(jatom_local)
                     jkind = particle_set(atom_b)%atomic_kind%kind_number
                     rb(1) = coord(1, atom_b)+cell_v(1)
                     rb(2) = coord(2, atom_b)+cell_v(2)
                     rb(3) = coord(3, atom_b)+cell_v(3)
                     DO iatom_local = 1, subcell_a(a_i, a_j, a_k)%natom
                        atom_a = subcell_a(a_i, a_j, a_k)%atom_list(iatom_local)
                        ikind = particle_set(atom_a)%atomic_kind%kind_number
                        ! Screen interaction to avoid double counting
                        atom_order = (atom_a <= atom_b)
                        ! Special case for kind combination requiring the full NL
                        IF (any_full) THEN
                           is_full = full_nl(ikind, jkind)
                           IF (is_full) THEN
                              atom_order = (atom_a == atom_b)
                           ELSE
                              IF (ik < 0) CYCLE
                              IF (ik == 0 .AND. ij < 0) CYCLE
                              IF (ij == 0 .AND. ii < 0) CYCLE
                           END IF
                        END IF
                        IF (subcell000 .AND. atom_order) CYCLE
                        rab(1) = rb(1)-coord(1, atom_a)
                        rab(2) = rb(2)-coord(2, atom_a)
                        rab(3) = rb(3)-coord(3, atom_a)
                        rab2 = rab(1)*rab(1)+rab(2)*rab(2)+rab(3)*rab(3)
                        rab_max = r_max(ikind, jkind)
                        rab2_max = rab_max*rab_max
                        IF (rab2 < rab2_max) THEN
                           ! Diagonal storage
                           j1 = MIN(ikind, jkind)
                           i1 = MAX(ikind, jkind)-j1+1
                           j1 = nkind-j1+1
                           id_kind = nkind00-(j1*(j1+1)/2)+i1
                           ! Store the pair
                           CALL fist_neighbor_add(neighbor_kind_pair, atom_a, atom_b, &
                                                  rab=rab, &
                                                  check_spline=check_spline, id_kind=id_kind, &
                                                  skip=(skip_kind(ikind) .AND. skip_kind(jkind)), &
                                                  cell=cell, ei_scale14=ei_scale14, &
                                                  vdw_scale14=vdw_scale14, exclusions=exclusions)
                           ! This is to handle properly when interaction radius is larger than cell size
                           IF ((atom_a == atom_b) .AND. (ik_start == 0)) THEN
                              invcellmap = cellmap(-b_pi, -b_pj, -b_pk)
                              inv_neighbor_kind_pair => nonbonded%neighbor_kind_pairs(invcellmap)
                              rab = rab-2.0_dp*cell_v
                              CALL fist_neighbor_add(inv_neighbor_kind_pair, atom_a, atom_b, &
                                                     rab=rab, &
                                                     check_spline=check_spline, id_kind=id_kind, &
                                                     skip=(skip_kind(ikind) .AND. skip_kind(jkind)), &
                                                     cell=cell, ei_scale14=ei_scale14, &
                                                     vdw_scale14=vdw_scale14, exclusions=exclusions)
                           END IF
                           ! Check for too close hits
                           IF (check_spline) THEN
                              rab2_min = r_minsq(ikind, jkind)
                              IF (rab2 < rab2_min) THEN
                                 iw = cp_logger_get_default_unit_nr()
                                 WRITE (iw, '(T2,A,2I7,2(A,F15.8),A)') "WARNING| Particles: ", &
                                    atom_a, atom_b, &
                                    " at distance [au]:", SQRT(rab2), " less than: ", &
                                    SQRT(rab2_min), &
                                    "; increase EMAX_SPLINE."
                                 IF (rab2 < rab2_min/(1.06_dp)**2) THEN
                                    IF (geo_check) THEN
                                       CPABORT("GEOMETRY wrong or EMAX_SPLINE too small!")
                                    END IF
                                 END IF
                              END IF
                           END IF
                        END IF
                     END DO
                  END DO
               END DO loop_b_i
            END DO loop_b_j
         END DO loop_b_k
      END DO loop_a_i
      END DO loop_a_j
      END DO loop_a_k
      DEALLOCATE (coord)
      DEALLOCATE (cellmap)
      DEALLOCATE (sphcub)
      CALL deallocate_subcell(subcell_a)
      CALL deallocate_subcell(subcell_b)

      CALL timestop(handle)
   END SUBROUTINE build_neighbor_lists

! **************************************************************************************************
!> \brief Write a set of neighbor lists to the output unit.
!> \param nonbonded ...
!> \param particle_set ...
!> \param cell ...
!> \param para_env ...
!> \param output_unit ...
!> \param name ...
!> \param unit_str ...
!> \par History
!>      08.2006 created [tlaino]
!> \author Teodoro Laino
! **************************************************************************************************
   SUBROUTINE write_neighbor_lists(nonbonded, particle_set, cell, para_env, output_unit, &
                                   name, unit_str)

      TYPE(fist_neighbor_type), POINTER                  :: nonbonded
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(cell_type), POINTER                           :: cell
      TYPE(cp_para_env_type), POINTER                    :: para_env
      INTEGER, INTENT(IN)                                :: output_unit
      CHARACTER(LEN=*), INTENT(IN)                       :: name, unit_str

      CHARACTER(LEN=default_string_length)               :: string
      INTEGER                                            :: atom_a, atom_b, iab, ilist, mype, &
                                                            nneighbor
      LOGICAL                                            :: print_headline
      REAL(dp)                                           :: conv, dab
      REAL(dp), DIMENSION(3)                             :: cell_v, ra, rab, rb
      TYPE(neighbor_kind_pairs_type), POINTER            :: neighbor_kind_pair

      mype = para_env%mepos
      ! Print headline
      string = ""
      WRITE (UNIT=string, FMT="(A,I5,A)") &
         TRIM(name)//" IN "//TRIM(unit_str)//" (PROCESS", mype, ")"
      CALL compress(string)
      IF (output_unit > 0) WRITE (UNIT=output_unit, FMT="(/,/,T2,A)") TRIM(string)

      print_headline = .TRUE.
      nneighbor = 0
      conv = cp_unit_from_cp2k(1.0_dp, TRIM(unit_str))
      DO iab = 1, SIZE(nonbonded%neighbor_kind_pairs)
         neighbor_kind_pair => nonbonded%neighbor_kind_pairs(iab)
         CALL matvec_3x3(cell_v, cell%hmat, REAL(neighbor_kind_pair%cell_vector, KIND=dp))
         DO ilist = 1, neighbor_kind_pair%npairs
            nneighbor = nneighbor+1
            IF (output_unit > 0) THEN
               ! Print second part of the headline
               atom_a = neighbor_kind_pair%list(1, ilist)
               atom_b = neighbor_kind_pair%list(2, ilist)
               IF (print_headline) THEN
                  WRITE (UNIT=output_unit, FMT="(T3,2(A6,3(5X,A,5X)),1X,A11,10X,A8,A5,A10,A9)") &
                     "Atom-A", "X", "Y", "Z", "Atom-B", "X", "Y", "Z", "Cell(i,j,k)", &
                     "Distance", "ONFO", "VDW-scale", "EI-scale"
                  print_headline = .FALSE.
               END IF

               ra(:) = pbc(particle_set(atom_a)%r, cell)
               rb(:) = pbc(particle_set(atom_b)%r, cell)
               rab = rb(:)-ra(:)+cell_v
               dab = SQRT(DOT_PRODUCT(rab, rab))
               IF (ilist <= neighbor_kind_pair%nscale) THEN
                  WRITE (UNIT=output_unit, FMT="(T3,2(I6,3(1X,F10.6)),3(1X,I3),10X,F8.4,L4,F11.5,F9.5)") &
                     atom_a, ra(1:3)*conv, &
                     atom_b, rb(1:3)*conv, &
                     neighbor_kind_pair%cell_vector, &
                     dab*conv, &
                     neighbor_kind_pair%is_onfo(ilist), &
                     neighbor_kind_pair%vdw_scale(ilist), &
                     neighbor_kind_pair%ei_scale(ilist)
               ELSE
                  WRITE (UNIT=output_unit, FMT="(T3,2(I6,3(1X,F10.6)),3(1X,I3),10X,F8.4)") &
                     atom_a, ra(1:3)*conv, &
                     atom_b, rb(1:3)*conv, &
                     neighbor_kind_pair%cell_vector, &
                     dab*conv
               END IF
            END IF
         END DO ! ilist
      END DO ! iab

      string = ""
      WRITE (UNIT=string, FMT="(A,I12,A,I12)") &
         "Total number of neighbor interactions for process", mype, ":", &
         nneighbor
      CALL compress(string)
      IF (output_unit > 0) WRITE (UNIT=output_unit, FMT="(/,T2,A)") TRIM(string)

   END SUBROUTINE write_neighbor_lists

! **************************************************************************************************
!> \brief Sort the generated neighbor list according the kind
!> \param nonbonded ...
!> \param nkinds ...
!> \par History
!>      09.2007 created [tlaino] University of Zurich - Reducing memory usage
!>              for the FIST neighbor lists
!> \author Teodoro Laino - University of Zurich
! **************************************************************************************************
   SUBROUTINE sort_neighbor_lists(nonbonded, nkinds)

      TYPE(fist_neighbor_type), POINTER                  :: nonbonded
      INTEGER, INTENT(IN)                                :: nkinds

      CHARACTER(LEN=*), PARAMETER :: routineN = 'sort_neighbor_lists', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, iab, id_kind, ikind, ipair, &
                                                            jkind, max_alloc_size, npairs, nscale, &
                                                            tmp
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: indj
      INTEGER, DIMENSION(:), POINTER                     :: work
      INTEGER, DIMENSION(:, :), POINTER                  :: list_copy
      TYPE(neighbor_kind_pairs_type), POINTER            :: neighbor_kind_pair

      NULLIFY (neighbor_kind_pair)
      CALL timeset(routineN, handle)
      ! define a lookup table to get jkind for a given id_kind
      ALLOCATE (indj(nkinds*(nkinds+1)/2))
      id_kind = 0
      DO jkind = 1, nkinds
         DO ikind = jkind, nkinds
            id_kind = id_kind+1
            indj(id_kind) = jkind
         END DO
      END DO
      ! loop over all nlists and sort the pairs within each list.
      DO iab = 1, nonbonded%nlists
         neighbor_kind_pair => nonbonded%neighbor_kind_pairs(iab)
         npairs = neighbor_kind_pair%npairs
         nscale = neighbor_kind_pair%nscale
         IF (npairs /= 0) THEN
            IF (npairs > nscale) THEN
               ! 1) Sort the atom pairs by id_kind. Pairs whose interactions are
               ! scaled (possibly to zero for exclusion) are not touched. They
               ! stay packed in the beginning. Sorting is skipped altogether when
               ! all pairs have scaled interactions.
               ALLOCATE (work(1:npairs-nscale))
               ALLOCATE (list_copy(2, 1:npairs-nscale))
               ! Copy of the pair list is required to perform the permutation below
               ! correctly.
               list_copy = neighbor_kind_pair%list(:, nscale+1:npairs)
               CALL sort(neighbor_kind_pair%id_kind(nscale+1:npairs), npairs-nscale, work)
               ! Reorder atoms using the same permutation that was used to sort
               ! the array id_kind.
               DO ipair = nscale+1, npairs
                  tmp = work(ipair-nscale)
                  neighbor_kind_pair%list(1, ipair) = list_copy(1, tmp)
                  neighbor_kind_pair%list(2, ipair) = list_copy(2, tmp)
               END DO
               DEALLOCATE (work)
               DEALLOCATE (list_copy)
            END IF
            ! 2) determine the intervals (groups) in the pair list that correspond
            !    to a certain id_kind. also store the corresponding ikind and
            !    jkind. Note that this part does not assume ikind to be sorted,
            !    but it only makes sense when contiguous blobs of the same ikind
            !    are present.
            ! Allocate sufficient memory in case all pairs of atom kinds are
            ! present, and also provide storage for the pairs with exclusion
            ! flags, which are unsorted.
            max_alloc_size = nkinds*(nkinds+1)/2+nscale
            IF (ASSOCIATED(neighbor_kind_pair%grp_kind_start)) THEN
               DEALLOCATE (neighbor_kind_pair%grp_kind_start)
            END IF
            ALLOCATE (neighbor_kind_pair%grp_kind_start(max_alloc_size))
            IF (ASSOCIATED(neighbor_kind_pair%grp_kind_end)) THEN
               DEALLOCATE (neighbor_kind_pair%grp_kind_end)
            END IF
            ALLOCATE (neighbor_kind_pair%grp_kind_end(max_alloc_size))
            IF (ASSOCIATED(neighbor_kind_pair%ij_kind)) THEN
               DEALLOCATE (neighbor_kind_pair%ij_kind)
            END IF
            ALLOCATE (neighbor_kind_pair%ij_kind(2, max_alloc_size))
            ! Start the first interval.
            ipair = 1
            neighbor_kind_pair%ngrp_kind = 1
            neighbor_kind_pair%grp_kind_start(neighbor_kind_pair%ngrp_kind) = ipair
            ! Get ikind and jkind corresponding to id_kind.
            id_kind = neighbor_kind_pair%id_kind(ipair)
            jkind = indj(id_kind)
            tmp = nkinds-jkind
            ikind = nkinds+id_kind-nkinds*(nkinds+1)/2+(tmp*(tmp+1)/2)
            neighbor_kind_pair%ij_kind(1, neighbor_kind_pair%ngrp_kind) = ikind
            neighbor_kind_pair%ij_kind(2, neighbor_kind_pair%ngrp_kind) = jkind
            ! Define the remaining intervals.
            DO ipair = 2, npairs
               IF (neighbor_kind_pair%id_kind(ipair) /= neighbor_kind_pair%id_kind(ipair-1)) THEN
                  neighbor_kind_pair%grp_kind_end(neighbor_kind_pair%ngrp_kind) = ipair-1
                  neighbor_kind_pair%ngrp_kind = neighbor_kind_pair%ngrp_kind+1
                  neighbor_kind_pair%grp_kind_start(neighbor_kind_pair%ngrp_kind) = ipair
                  ! Get ikind and jkind corresponding to id_kind.
                  id_kind = neighbor_kind_pair%id_kind(ipair)
                  jkind = indj(id_kind)
                  tmp = nkinds-jkind
                  ikind = nkinds+id_kind-nkinds*(nkinds+1)/2+(tmp*(tmp+1)/2)
                  neighbor_kind_pair%ij_kind(1, neighbor_kind_pair%ngrp_kind) = ikind
                  neighbor_kind_pair%ij_kind(2, neighbor_kind_pair%ngrp_kind) = jkind
               END IF
            END DO
            ! Finish the last interval.
            neighbor_kind_pair%grp_kind_end(neighbor_kind_pair%ngrp_kind) = npairs
            ! Reduce the grp arrays to the actual size because not all pairs of
            ! atom types have to be present in this pair list.
            CALL reallocate(neighbor_kind_pair%grp_kind_start, 1, neighbor_kind_pair%ngrp_kind)
            CALL reallocate(neighbor_kind_pair%grp_kind_end, 1, neighbor_kind_pair%ngrp_kind)
            CALL reallocate(neighbor_kind_pair%ij_kind, 1, 2, 1, neighbor_kind_pair%ngrp_kind)
         END IF
         ! Clean the memory..
         DEALLOCATE (neighbor_kind_pair%id_kind)
      END DO
      DEALLOCATE (indj)
      CALL timestop(handle)
   END SUBROUTINE sort_neighbor_lists

END MODULE fist_neighbor_lists
