tmc_tree_search.F

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!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright 2000-2026 CP2K developers group <https://cp2k.org>                                   !
!                                                                                                  !
!   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
!--------------------------------------------------------------------------------------------------!
 
! **************************************************************************************************
!> \brief tree nodes search etc.
!> \par History
!>      11.2012 created [Mandes Schoenherr]
!> \author Mandes
! **************************************************************************************************
 
MODULE tmc_tree_search
   USE cp_log_handling,                 ONLY: cp_to_string
   USE kinds,                           ONLY: dp
   USE tmc_stati,                       ONLY: tmc_status_wait_for_new_task
   USE tmc_tree_references,             ONLY: add_to_references,&
                                              search_and_remove_reference_in_list
   USE tmc_tree_types,                  ONLY: &
        elem_array_type, global_tree_type, status_accepted, status_accepted_result, &
        status_calc_approx_ener, status_calculate_md, status_calculate_nmc_steps, &
        status_calculate_energy, status_calculated, status_cancel_ener, status_cancel_nmc, &
        status_canceled_ener, status_canceled_nmc, status_created, status_deleted, &
        status_deleted_result, status_rejected, status_rejected_result, tree_type
   USE tmc_types,                       ONLY: tmc_env_type
#include "../base/base_uses.f90"
 
   IMPLICIT NONE
 
   PRIVATE
 
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'tmc_tree_search'
 
   PUBLIC :: most_prob_end
   PUBLIC :: search_next_energy_calc
   PUBLIC :: search_canceling_elements
   PUBLIC :: search_parent_element, get_subtree_elements_to_check
   PUBLIC :: search_next_gt_element_to_check
   PUBLIC :: search_end_of_clean_g_tree, search_end_of_clean_tree
   PUBLIC :: count_prepared_nodes_in_trees, count_nodes_in_trees
CONTAINS
 
   !============================================================================
   ! search tree node
   !============================================================================
! **************************************************************************************************
!> \brief search most probable end in global tree to create a new tree node
!>         using the acceptance probabilities for each move type
!>          of each temperature
!>        routine distinguishes the search for most probable node
!>         for energy and most probable node with open end
!>         for new configuration
!>        In case of searching open end:
!>         routine stops in branch with canceled NMC,
!>         using this a one possibility
!> \param global_tree_elem starting point for search
!> \param prob return value, the probability of reaching the tree node
!> \param n_acc drection of branch the next tree node should extend
!> \param search_energy_node ...
!> \parma search_energy_node flag if configuration for calculating exact
!>        energy should be searched
!> \author Mandes 12.2012
! **************************************************************************************************
   RECURSIVE SUBROUTINE most_prob_end(global_tree_elem, prob, n_acc, &
                                      search_energy_node)
      TYPE(global_tree_type), POINTER                    :: global_tree_elem
      REAL(kind=dp), INTENT(OUT)                         :: prob
      LOGICAL, INTENT(INOUT)                             :: n_acc
      LOGICAL, OPTIONAL                                  :: search_energy_node
 
      CHARACTER(LEN=*), PARAMETER                        :: routinen = 'most_prob_end'
 
      INTEGER                                            :: handle
      LOGICAL                                            :: check_accepted, check_rejected, keep_on, &
                                                            tmp_acc, tmp_nacc
      REAL(kind=dp)                                      :: prob_n_acc, prob_n_nacc
      TYPE(global_tree_type), POINTER                    :: ptr_acc, ptr_nacc
      TYPE(tree_type), POINTER                           :: st_elem
 
      NULLIFY (st_elem, ptr_acc, ptr_nacc)
 
      prob_n_acc = -100000
      prob_n_nacc = -100000
      check_accepted = .false.
      check_rejected = .false.
      keep_on = .true.
 
      cpassert(ASSOCIATED(global_tree_elem))
      st_elem => global_tree_elem%conf(global_tree_elem%mv_conf)%elem
      cpassert(ASSOCIATED(st_elem))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      !-- follow trajectory until end
      !-- evaluate following elements using status, and probabilites
      SELECT CASE (global_tree_elem%stat)
      CASE (status_accepted, status_accepted_result)
         check_accepted = .true.
      CASE (status_rejected, status_rejected_result)
         check_rejected = .true.
      CASE DEFAULT
         !-- set directions of searching
         SELECT CASE (st_elem%stat)
         CASE (status_created, status_canceled_ener)
            ! just for searching next element to calculate energy for (found)
            IF (PRESENT(search_energy_node)) THEN
               prob = 0.0_dp ! = log(1)
               n_acc = .false. ! not needed, but maybe for initialisation
               keep_on = .false.
            ELSE
               check_accepted = .true.
               check_rejected = .true.
            END IF
         CASE (status_canceled_nmc)
            ! just for search new element to create (found)
            ! canceled elements can be reactivated
            ! the parent element is returned,
            !  the create_new_pt_tree_node check for existing of this node
            IF (.NOT. PRESENT(search_energy_node)) THEN
               prob = 0.0_dp
               n_acc = ASSOCIATED(global_tree_elem%parent%acc, global_tree_elem)
               global_tree_elem => global_tree_elem%parent
               keep_on = .false.
            END IF
         CASE (status_calculated, status_calculate_energy, &
               status_accepted_result, status_accepted, &
               status_rejected, status_rejected_result)
            ! status accepted and rejection needed for swapped
            !  configurations in parallel tempering
            check_accepted = .true.
            check_rejected = .true.
         CASE (status_calculate_md, status_calculate_nmc_steps, &
               status_calc_approx_ener)
            ! just for searching next element to create
            IF (.NOT. PRESENT(search_energy_node)) THEN
               check_rejected = .true.
            END IF
         CASE (status_cancel_nmc, status_cancel_ener)
         CASE DEFAULT
            CALL cp_abort(__location__, &
                          "unknown sub tree element status "// &
                          cp_to_string(st_elem%stat))
         END SELECT
      END SELECT
 
      IF (keep_on) THEN
         !-- recursive search, remembering lowest element (tree end),
         !     and multiply probabilities to go there
         !-- search in ACCEPTED branch
         IF (check_accepted) THEN
            ! test if probable accepted child exist and is not rejected
            IF (ASSOCIATED(global_tree_elem%acc)) THEN
               ptr_acc => global_tree_elem%acc
               IF (PRESENT(search_energy_node)) THEN
                  CALL most_prob_end(global_tree_elem=ptr_acc, prob=prob_n_acc, &
                                     n_acc=tmp_acc, &
                                     search_energy_node=search_energy_node)
               ELSE
                  CALL most_prob_end(global_tree_elem=ptr_acc, prob=prob_n_acc, &
                                     n_acc=tmp_acc)
               END IF
               !-- do probability multiplication
               !    (in logscale because of really small probabilities)
               prob_n_acc = prob_n_acc + log(global_tree_elem%prob_acc)
            ELSE
               ! prob of going in acc or rej direction is
               !   calculated in parent element
               prob_n_acc = log(global_tree_elem%prob_acc)
               IF (PRESENT(search_energy_node)) prob_n_acc = -100000
               ptr_acc => global_tree_elem
               tmp_acc = .true.
            END IF
         END IF
 
         !-- search in REJECTED branch
         IF (check_rejected) THEN
            ! test if probabliy rejected child exist
            IF (ASSOCIATED(global_tree_elem%nacc)) THEN
               ptr_nacc => global_tree_elem%nacc
               IF (PRESENT(search_energy_node)) THEN
                  CALL most_prob_end(global_tree_elem=ptr_nacc, prob=prob_n_nacc, &
                                     n_acc=tmp_nacc, &
                                     search_energy_node=search_energy_node)
               ELSE
                  CALL most_prob_end(global_tree_elem=ptr_nacc, prob=prob_n_nacc, &
                                     n_acc=tmp_nacc)
               END IF
               !-- do probability multiplication
               !     (in logscale because of really small probabilities)
               prob_n_nacc = prob_n_nacc + log(1 - global_tree_elem%prob_acc)
            ELSE
               ! prob of going in acc or rej direction is
               !   calculated in parent element
               prob_n_nacc = log(1 - global_tree_elem%prob_acc)
               IF (PRESENT(search_energy_node)) prob_n_nacc = -100000
               ptr_nacc => global_tree_elem
               tmp_nacc = .false.
            END IF
         END IF
         ! test which direction is more likely
         !   and set result pointer and probability,
         ! remembering the direction
         IF (prob_n_acc >= prob_n_nacc) THEN
            prob = prob_n_acc
            global_tree_elem => ptr_acc
            n_acc = tmp_acc
         ELSE
            prob = prob_n_nacc
            global_tree_elem => ptr_nacc
            n_acc = tmp_nacc
         END IF
      END IF
      ! end the timing
      CALL timestop(handle)
   END SUBROUTINE most_prob_end
 
! **************************************************************************************************
!> \brief gt_head head of the global tree
!> \param gt_head ...
!> \param new_gt_elem return value the energy should be calculated for
!> \param stat routine status return value
!> \param react_count reactivation counter
!> \author Mandes 12.2012
! **************************************************************************************************
   SUBROUTINE search_next_energy_calc(gt_head, new_gt_elem, stat, react_count)
      TYPE(global_tree_type), POINTER                    :: gt_head, new_gt_elem
      INTEGER                                            :: stat, react_count
 
      CHARACTER(LEN=*), PARAMETER :: routinen = 'search_next_energy_calc'
      REAL(kind=dp), PARAMETER                           :: eps_exp_prob = 1.0e-10_dp
 
      INTEGER                                            :: handle
      LOGICAL                                            :: flag
      REAL(kind=dp)                                      :: prob
 
      prob = 0.0_dp
      flag = .false.
      cpassert(ASSOCIATED(gt_head))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      new_gt_elem => gt_head
 
      CALL most_prob_end(global_tree_elem=new_gt_elem, prob=prob, n_acc=flag, &
                         search_energy_node=.true.)
 
      stat = status_created
      ! set status for master
      !   (if TMC_STATUS_WAIT_FOR_NEW_TASK, no calculation necessary)
      IF (.NOT. ASSOCIATED(new_gt_elem) .OR. (exp(prob) < eps_exp_prob)) THEN
         stat = tmc_status_wait_for_new_task
      ELSE
         ! reactivate canceled elements
         IF (new_gt_elem%conf(new_gt_elem%mv_conf)%elem%stat == &
             status_canceled_ener) THEN
            CALL add_to_references(gt_elem=new_gt_elem)
            react_count = react_count + 1
            new_gt_elem%conf(new_gt_elem%mv_conf)%elem%stat = status_created
         END IF
         ! if elem status is not status_created
         IF (new_gt_elem%conf(new_gt_elem%mv_conf)%elem%stat /= status_created) THEN
            stat = tmc_status_wait_for_new_task
         END IF
      END IF
      ! end the timing
      CALL timestop(handle)
   END SUBROUTINE search_next_energy_calc
 
! **************************************************************************************************
!> \brief searching the parent element (last accepted configuration before)
!> \param current actual tree element
!> \return parent tree element (last accepted one)
!> \author Mandes 12.2012
!> \note routine searches last (assumed) accepted element in subtree
! **************************************************************************************************
   RECURSIVE FUNCTION search_parent_element(current) RESULT(parent)
      TYPE(tree_type), POINTER                           :: current, parent
 
      CHARACTER(LEN=*), PARAMETER :: routinen = 'search_parent_element'
 
      INTEGER                                            :: handle
 
      cpassert(ASSOCIATED(current))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      IF (ASSOCIATED(current%parent)) THEN
         ! the result value if the child (we came from) is in acc direction
         parent => current%parent
         IF (ASSOCIATED(parent%nacc, current)) THEN
            parent => search_parent_element(parent)
         END IF
      ELSE
         ! if parent not exist, we are at the head of the tree
         parent => current
      END IF
      ! end the timing
      CALL timestop(handle)
      cpassert(ASSOCIATED(parent))
   END FUNCTION search_parent_element
 
! **************************************************************************************************
!> \brief search the next global element in the Markov Chain to check
!> \param ptr start point for search, should be on the known Markov Chain
!> \param found flag if routine was successful
!> \author Mandes 12.2012
! **************************************************************************************************
   RECURSIVE SUBROUTINE search_next_gt_element_to_check(ptr, found)
      TYPE(global_tree_type), POINTER                    :: ptr
      LOGICAL                                            :: found
 
      CHARACTER(LEN=*), PARAMETER :: routinen = 'search_next_gt_element_to_check'
 
      INTEGER                                            :: handle
 
      found = .false.
 
      cpassert(ASSOCIATED(ptr))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      ! -- global tree status is not updated after receiving calculations
      !    (not intrinsically), hence try to check elements with could be ready
      SELECT CASE (ptr%stat)
      CASE (status_accepted_result)
         IF (ASSOCIATED(ptr%acc)) THEN
            ptr => ptr%acc
            CALL search_next_gt_element_to_check(ptr, found)
         END IF
      CASE (status_rejected_result)
         IF (ASSOCIATED(ptr%nacc)) THEN
            ptr => ptr%nacc
            CALL search_next_gt_element_to_check(ptr, found)
         END IF
      CASE (status_calculate_energy, status_created, &
            status_calculate_md, status_calculated, status_calculate_nmc_steps, &
            status_calc_approx_ener, status_accepted, status_rejected)
         found = .true.
      CASE (status_cancel_nmc, status_cancel_ener, status_canceled_nmc, &
            status_canceled_ener)
         ! nothing to do
      CASE DEFAULT
         CALL cp_abort(__location__, &
                       "unexpected status "//cp_to_string(ptr%stat)// &
                       "of global tree elem "//cp_to_string(ptr%nr))
      END SELECT
      ! end the timing
      CALL timestop(handle)
 
      cpassert(ASSOCIATED(ptr))
   END SUBROUTINE search_next_gt_element_to_check
 
! **************************************************************************************************
!> \brief get the changed element of the actual global tree element and its
!>        related last accepted parent
!> \param gt_act_elem actual global tree element
!> \param elem1 two subtree elements which should be compared
!> \param elem2 two subtree elements which should be compared
!> \author Mandes 12.2012
! **************************************************************************************************
   SUBROUTINE get_subtree_elements_to_check(gt_act_elem, elem1, elem2)
      TYPE(global_tree_type), POINTER                    :: gt_act_elem
      TYPE(tree_type), INTENT(OUT), POINTER              :: elem1, elem2
 
      CHARACTER(LEN=*), PARAMETER :: routinen = 'get_subtree_elements_to_check'
 
      INTEGER                                            :: handle
 
      cpassert(ASSOCIATED(gt_act_elem))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      IF (gt_act_elem%swaped) THEN
         !------------------------------------------------------------
         !-- take the last accepted configurations for check of both configurations, because
         !-- in case of swapping, the last accepted elements have to be compared
         IF (gt_act_elem%conf_n_acc(gt_act_elem%conf(gt_act_elem%mv_conf)%elem%sub_tree_nr)) THEN
            elem1 => gt_act_elem%conf(gt_act_elem%mv_conf)%elem
         ELSE
            elem1 => search_parent_element(gt_act_elem%conf(gt_act_elem%mv_conf)%elem)
         END IF
         ! second element
         IF (gt_act_elem%conf_n_acc(gt_act_elem%conf(gt_act_elem%mv_conf + 1)%elem%sub_tree_nr)) THEN
            elem2 => gt_act_elem%conf(gt_act_elem%mv_conf + 1)%elem
         ELSE
            elem2 => search_parent_element(gt_act_elem%conf(gt_act_elem%mv_conf + 1)%elem)
         END IF
      ELSE
         elem1 => gt_act_elem%conf(gt_act_elem%mv_conf)%elem
         elem2 => search_parent_element(elem1)
      END IF
 
      ! end the timing
      CALL timestop(handle)
 
      cpassert(ASSOCIATED(gt_act_elem))
      cpassert(ASSOCIATED(elem1))
      cpassert(ASSOCIATED(elem2))
   END SUBROUTINE get_subtree_elements_to_check
 
! **************************************************************************************************
!> \brief searches last element on trajectory,
!>        until where the sides of the tree are deleted (of global tree)
!>        also found the last accepted element before
!> \param last_acc returns last accepted element in cleaned tree part
!> \param tree_ptr end point of search
!> \author Mandes 12.2012
! **************************************************************************************************
   RECURSIVE SUBROUTINE search_end_of_clean_g_tree(last_acc, tree_ptr)
      TYPE(global_tree_type), POINTER                    :: last_acc, tree_ptr
 
      CHARACTER(LEN=*), PARAMETER :: routinen = 'search_end_of_clean_g_tree'
 
      INTEGER                                            :: handle
 
      cpassert(ASSOCIATED(last_acc))
      cpassert(ASSOCIATED(tree_ptr))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      SELECT CASE (tree_ptr%stat)
      CASE (status_accepted_result)
         IF (ASSOCIATED(tree_ptr%acc) .AND. .NOT. ASSOCIATED(tree_ptr%nacc)) THEN
            last_acc => tree_ptr
            tree_ptr => tree_ptr%acc
            CALL search_end_of_clean_g_tree(last_acc, tree_ptr)
         END IF
      CASE (status_rejected_result)
         IF (ASSOCIATED(tree_ptr%nacc) .AND. .NOT. ASSOCIATED(tree_ptr%acc)) THEN
            tree_ptr => tree_ptr%nacc
            CALL search_end_of_clean_g_tree(last_acc, tree_ptr)
         END IF
      CASE (status_calculated, status_calculate_energy, status_created, status_accepted, status_rejected, &
            status_calculate_md, status_calculate_nmc_steps, status_calc_approx_ener, &
            status_canceled_ener, status_canceled_nmc, &
            status_cancel_nmc, status_cancel_ener)
         ! nothing to do
      CASE DEFAULT
         CALL cp_abort(__location__, &
                       "the global tree element "//cp_to_string(tree_ptr%nr)// &
                       " stat "//cp_to_string(tree_ptr%stat)//" is UNknown")
      END SELECT
      ! end the timing
      CALL timestop(handle)
      cpassert(ASSOCIATED(last_acc))
      cpassert(ASSOCIATED(tree_ptr))
   END SUBROUTINE search_end_of_clean_g_tree
 
! **************************************************************************************************
!> \brief searches last element on trajectory,
!>        until where the sides of the tree are deleted (in sub tree)
!>        also found the last accepted element before.
!>        searches the last element which at least have ONE (not calculated)
!>        node in the tree branch
!> \param tree_ptr  ...
!> \param last_acc ...
!> \author Mandes 12.2012
! **************************************************************************************************
   RECURSIVE SUBROUTINE search_end_of_clean_tree(tree_ptr, last_acc)
      TYPE(tree_type), POINTER                           :: tree_ptr
      TYPE(tree_type), INTENT(IN), POINTER               :: last_acc
 
      CHARACTER(LEN=*), PARAMETER :: routinen = 'search_end_of_clean_tree'
 
      INTEGER                                            :: handle
 
      cpassert(ASSOCIATED(tree_ptr))
      cpassert(ASSOCIATED(last_acc))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      IF (.NOT. ASSOCIATED(last_acc, tree_ptr)) THEN
         IF (ASSOCIATED(tree_ptr%acc) .AND. .NOT. ASSOCIATED(tree_ptr%nacc)) THEN
            tree_ptr => tree_ptr%acc
            CALL search_end_of_clean_tree(tree_ptr, last_acc)
         ELSE IF (ASSOCIATED(tree_ptr%nacc) .AND. .NOT. ASSOCIATED(tree_ptr%acc)) THEN
            tree_ptr => tree_ptr%nacc
            CALL search_end_of_clean_tree(tree_ptr, last_acc)
         END IF
      END IF
      ! end the timing
      CALL timestop(handle)
      cpassert(ASSOCIATED(tree_ptr))
      cpassert(ASSOCIATED(last_acc))
   END SUBROUTINE search_end_of_clean_tree
 
! **************************************************************************************************
!> \brief searches in all branches down below the entered global tree element
!>        for elements to cancel, if prob is present start searching at the
!>        related tree child node
!> \param pt_elem_in start search point
!> \param prob the acceptance probability of the tree element to define
!>        the direction to start with
!> \param tmc_env TMC environment
!> \author Mandes 12.2012
! **************************************************************************************************
   RECURSIVE SUBROUTINE search_canceling_elements(pt_elem_in, prob, tmc_env)
      TYPE(global_tree_type), INTENT(IN), POINTER        :: pt_elem_in
      REAL(kind=dp), OPTIONAL                            :: prob
      TYPE(tmc_env_type), POINTER                        :: tmc_env
 
      CHARACTER(LEN=*), PARAMETER :: routinen = 'search_canceling_elements'
      REAL(kind=dp), PARAMETER                           :: eps_prob = 1.0e-10_dp
 
      INTEGER                                            :: handle
      LOGICAL                                            :: ready
      TYPE(global_tree_type), POINTER                    :: act_pt_ptr, pt_elem
 
      NULLIFY (pt_elem, act_pt_ptr)
      cpassert(ASSOCIATED(pt_elem_in))
      cpassert(ASSOCIATED(tmc_env))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      ready = .true.
      ! if prob present select the related branch
      IF (PRESENT(prob)) THEN
         IF (prob < eps_prob .AND. ASSOCIATED(pt_elem_in%acc)) THEN
            pt_elem => pt_elem_in%acc
         ELSE IF (prob > (1.0_dp - eps_prob) .AND. ASSOCIATED(pt_elem_in%nacc)) THEN
            pt_elem => pt_elem_in%nacc
         ELSE
            ready = .false.
         END IF
      ELSE
         pt_elem => pt_elem_in
      END IF
 
      IF (ready) THEN
         IF (ASSOCIATED(pt_elem%conf(pt_elem%mv_conf)%elem)) THEN
            SELECT CASE (pt_elem%conf(pt_elem%mv_conf)%elem%stat)
            CASE (status_accepted_result, status_accepted, status_rejected_result, &
                  status_rejected, status_created, status_cancel_nmc, &
                  status_cancel_ener, status_canceled_nmc, status_canceled_ener, &
                  status_calculated, status_deleted, status_deleted_result, &
                  status_calc_approx_ener) ! no canceling
            CASE (status_calculate_nmc_steps, status_calculate_md, &
                  status_calculate_energy)
               CALL search_and_remove_reference_in_list(gt_ptr=pt_elem, &
                                                        elem=pt_elem%conf(pt_elem%mv_conf)%elem, tmc_env=tmc_env)
 
            CASE DEFAULT
               CALL cp_abort(__location__, &
                             "unknown status of subtree element"// &
                             cp_to_string(pt_elem%conf(pt_elem%mv_conf)%elem%stat))
            END SELECT
         END IF
         !-- go until the ends ot he tree, to search for elements to cancel
         !-- check if child nodes exist
         IF (ASSOCIATED(pt_elem%acc)) THEN
            act_pt_ptr => pt_elem%acc
            CALL search_canceling_elements(pt_elem_in=act_pt_ptr, tmc_env=tmc_env)
         END IF
         IF (ASSOCIATED(pt_elem%nacc)) THEN
            act_pt_ptr => pt_elem%nacc
            CALL search_canceling_elements(pt_elem_in=act_pt_ptr, tmc_env=tmc_env)
         END IF
      END IF
      ! end the timing
      CALL timestop(handle)
      cpassert(ASSOCIATED(pt_elem_in))
   END SUBROUTINE search_canceling_elements
 
! **************************************************************************************************
!> \brief searches for created configurations in all subtrees
!> \param global_tree_ptr pointer to one global tree element
!> \param counters array returning the counters for each subtree
!> \author Mandes 01.2013
! **************************************************************************************************
   SUBROUTINE count_prepared_nodes_in_trees(global_tree_ptr, counters)
      TYPE(global_tree_type), INTENT(IN), POINTER        :: global_tree_ptr
      INTEGER, DIMENSION(:), POINTER                     :: counters
 
      CHARACTER(len=*), PARAMETER :: routinen = 'count_prepared_nodes_in_trees'
 
      INTEGER                                            :: handle, i
      TYPE(tree_type), POINTER                           :: begin_ptr
 
      NULLIFY (begin_ptr)
 
      cpassert(ASSOCIATED(global_tree_ptr))
      cpassert(ASSOCIATED(counters))
      cpassert(SIZE(counters(1:)) == SIZE(global_tree_ptr%conf(:)))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      counters(:) = 0
      DO i = 1, SIZE(global_tree_ptr%conf(:))
         begin_ptr => global_tree_ptr%conf(i)%elem
         CALL count_prepared_nodes_in_subtree(tree_ptr=begin_ptr, &
                                              counter=counters(i))
      END DO
 
      ! end the timing
      CALL timestop(handle)
   END SUBROUTINE count_prepared_nodes_in_trees
 
! **************************************************************************************************
!> \brief counts the prepared tree nodes in subtrees
!> \param tree_ptr pointer to one subtree element
!> \param counter returning the amount of prepared
!>        (ready for energy calculation) elements ind certain sub tree
!> \author Mandes 01.2013
! **************************************************************************************************
   RECURSIVE SUBROUTINE count_prepared_nodes_in_subtree(tree_ptr, counter)
      TYPE(tree_type), POINTER                           :: tree_ptr
      INTEGER                                            :: counter
 
      TYPE(tree_type), POINTER                           :: tmp_ptr
 
      NULLIFY (tmp_ptr)
 
      cpassert(ASSOCIATED(tree_ptr))
 
      SELECT CASE (tree_ptr%stat)
      CASE (status_accepted, status_accepted_result)
         IF (ASSOCIATED(tree_ptr%acc)) THEN
            tmp_ptr => tree_ptr%acc
            CALL count_prepared_nodes_in_subtree(tmp_ptr, counter)
         END IF
      CASE (status_rejected, status_rejected_result)
         IF (ASSOCIATED(tree_ptr%nacc)) THEN
            tmp_ptr => tree_ptr%nacc
            CALL count_prepared_nodes_in_subtree(tmp_ptr, counter)
         END IF
      CASE (status_created, status_calculate_md, status_calculate_nmc_steps, &
            status_calc_approx_ener, status_calculated, status_calculate_energy)
         IF (tree_ptr%stat == status_created) counter = counter + 1
         IF (ASSOCIATED(tree_ptr%acc)) THEN
            tmp_ptr => tree_ptr%acc
            CALL count_prepared_nodes_in_subtree(tmp_ptr, counter)
         END IF
         IF (ASSOCIATED(tree_ptr%nacc)) THEN
            tmp_ptr => tree_ptr%nacc
            CALL count_prepared_nodes_in_subtree(tmp_ptr, counter)
         END IF
      CASE (status_cancel_nmc, status_cancel_ener, status_canceled_nmc, &
            status_canceled_ener)
         !TODO maybe also count caneled confs for debug output
      CASE DEFAULT
         CALL cp_abort(__location__, &
                       "stat "//cp_to_string(tree_ptr%stat)// &
                       "of elem "//cp_to_string(tree_ptr%nr)// &
                       "unknown.")
      END SELECT
   END SUBROUTINE count_prepared_nodes_in_subtree
 
! **************************************************************************************************
!> \brief counts the number of existing nodes in global and subtrees
!> \param global_tree_ptr pointer to one global tree element
!> \param end_of_clean_trees points to the last elements of the clean sub trees
!> \param counters array returning the counters for each subtree
!> \param head_elements_nr node number of the existing
!>        global and sub tree heads
!> \author Mandes 01.2013
! **************************************************************************************************
   SUBROUTINE count_nodes_in_trees(global_tree_ptr, end_of_clean_trees, &
                                   counters, head_elements_nr)
      TYPE(global_tree_type), POINTER                    :: global_tree_ptr
      TYPE(elem_array_type), DIMENSION(:), POINTER       :: end_of_clean_trees
      INTEGER, DIMENSION(:), POINTER                     :: counters, head_elements_nr
 
      CHARACTER(len=*), PARAMETER :: routinen = 'count_nodes_in_trees'
 
      INTEGER                                            :: handle, i
      TYPE(global_tree_type), POINTER                    :: begin_gt_ptr
      TYPE(tree_type), POINTER                           :: begin_ptr
 
      NULLIFY (begin_gt_ptr, begin_ptr)
 
      cpassert(ASSOCIATED(global_tree_ptr))
      cpassert(ASSOCIATED(end_of_clean_trees))
      cpassert(ASSOCIATED(counters))
      cpassert(SIZE(counters(1:)) == SIZE(global_tree_ptr%conf(:)))
 
      ! start the timing
      CALL timeset(routinen, handle)
 
      begin_gt_ptr => global_tree_ptr
      counters(:) = 0
      DO
         IF (.NOT. ASSOCIATED(begin_gt_ptr%parent)) EXIT
         begin_gt_ptr => begin_gt_ptr%parent
      END DO
      head_elements_nr(0) = begin_gt_ptr%nr
      CALL count_nodes_in_global_tree(begin_gt_ptr, counters(0))
      DO i = 1, SIZE(end_of_clean_trees(:))
         begin_ptr => end_of_clean_trees(i)%elem
         DO
            IF (.NOT. ASSOCIATED(begin_ptr%parent)) EXIT
            begin_ptr => begin_ptr%parent
         END DO
         head_elements_nr(i) = begin_ptr%nr
         CALL count_nodes_in_tree(begin_ptr, counters(i))
      END DO
 
      ! end the timing
      CALL timestop(handle)
   END SUBROUTINE count_nodes_in_trees
 
! **************************************************************************************************
!> \brief counts existing nodes in global tree
!> \param ptr global tree head
!> \param counter return value with the amount of existing global tree elements
!> \author Mandes 01.2013
! **************************************************************************************************
   RECURSIVE SUBROUTINE count_nodes_in_global_tree(ptr, counter)
      TYPE(global_tree_type), INTENT(IN), POINTER        :: ptr
      INTEGER, INTENT(INOUT)                             :: counter
 
      cpassert(ASSOCIATED(ptr))
 
      counter = counter + 1
 
      IF (ASSOCIATED(ptr%acc)) THEN
         CALL count_nodes_in_global_tree(ptr%acc, counter)
      END IF
      IF (ASSOCIATED(ptr%nacc)) THEN
         CALL count_nodes_in_global_tree(ptr%nacc, counter)
      END IF
   END SUBROUTINE count_nodes_in_global_tree
 
! **************************************************************************************************
!> \brief counts existing nodes in certain sub tree
!> \param ptr subtree tree head
!> \param counter return value with the amount of existing sub tree elements
!> \author Mandes 01.2013
! **************************************************************************************************
   RECURSIVE SUBROUTINE count_nodes_in_tree(ptr, counter)
      TYPE(tree_type), POINTER                           :: ptr
      INTEGER                                            :: counter
 
      cpassert(ASSOCIATED(ptr))
 
      counter = counter + 1
 
      IF (ASSOCIATED(ptr%acc)) THEN
         CALL count_nodes_in_tree(ptr%acc, counter)
      END IF
      IF (ASSOCIATED(ptr%nacc)) THEN
         CALL count_nodes_in_tree(ptr%nacc, counter)
      END IF
   END SUBROUTINE count_nodes_in_tree
END MODULE tmc_tree_search