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

! **************************************************************************************************
!> \brief Contains types used for a Dimer Method calculations
!> \par History
!>     -Luca Bellucci 11.2017 - CNR-NANO, Pisa
!>      add K-DIMER from doi:10.1063/1.4898664
!> \author Luca Bellucci and Teodoro Laino - created [tlaino] - 01.2008
! **************************************************************************************************
MODULE dimer_methods
   USE bibliography,                    ONLY: Henkelman2014,&
                                              cite_reference
   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 cp_subsys_types,                 ONLY: cp_subsys_get,&
                                              cp_subsys_type
   USE dimer_types,                     ONLY: dimer_env_type,&
                                              dimer_fixed_atom_control
   USE dimer_utils,                     ONLY: get_theta
   USE force_env_methods,               ONLY: force_env_calc_energy_force
   USE force_env_types,                 ONLY: force_env_get
   USE geo_opt,                         ONLY: cp_rot_opt
   USE gopt_f_types,                    ONLY: gopt_f_type
   USE input_constants,                 ONLY: do_first_rotation_step,&
                                              do_second_rotation_step,&
                                              do_third_rotation_step
   USE input_section_types,             ONLY: section_vals_get_subs_vals,&
                                              section_vals_type
   USE kinds,                           ONLY: dp
   USE motion_utils,                    ONLY: rot_ana,&
                                              thrs_motion
   USE particle_list_types,             ONLY: particle_list_type
#include "../base/base_uses.f90"

   IMPLICIT NONE
   PRIVATE

   LOGICAL, PRIVATE, PARAMETER :: debug_this_module = .FALSE.
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'dimer_methods'

   PUBLIC :: cp_eval_at_ts

CONTAINS

! **************************************************************************************************
!> \brief Computes the dimer energy/gradients (including the rotation of the dimer)
!> \param gopt_env ...
!> \param x ...
!> \param f ...
!> \param gradient ...
!> \param calc_force ...
!> \date  01.2008
!> \par History
!>      none
!> \author Luca Bellucci and Teodoro Laino - created [tlaino]
! **************************************************************************************************
   RECURSIVE SUBROUTINE cp_eval_at_ts(gopt_env, x, f, gradient, calc_force)
      TYPE(gopt_f_type), POINTER                         :: gopt_env
      REAL(KIND=dp), DIMENSION(:), POINTER               :: x
      REAL(KIND=dp), INTENT(OUT)                         :: f
      REAL(KIND=dp), DIMENSION(:), POINTER               :: gradient
      LOGICAL, INTENT(IN)                                :: calc_force

      CHARACTER(len=*), PARAMETER :: routineN = 'cp_eval_at_ts', routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, iw
      LOGICAL                                            :: eval_analytical
      REAL(KIND=dp)                                      :: angle1, angle2, f1, gm1, gm2, norm, swf
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dimer_env_type), POINTER                      :: dimer_env
      TYPE(section_vals_type), POINTER                   :: print_section

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

      CPASSERT(ASSOCIATED(gopt_env))
      dimer_env => gopt_env%dimer_env
      CPASSERT(ASSOCIATED(dimer_env))
      iw = cp_print_key_unit_nr(logger, gopt_env%geo_section, "PRINT%PROGRAM_RUN_INFO", extension=".log")
      ! Possibly rotate Dimer or just compute Gradients of point 0 for Translation
      IF (gopt_env%dimer_rotation) THEN
         IF (debug_this_module .AND. (iw > 0)) THEN
            WRITE (iw, '(A)') "NVEC:"
            WRITE (iw, '(3F15.9)') dimer_env%nvec
         END IF
         SELECT CASE (dimer_env%rot%rotation_step)
         CASE (do_first_rotation_step, do_third_rotation_step)
            eval_analytical = .TRUE.
            IF ((dimer_env%rot%rotation_step == do_third_rotation_step) .AND. (dimer_env%rot%interpolate_gradient)) THEN
               eval_analytical = .FALSE.
            END IF
            IF (eval_analytical) THEN
               ! Compute energy, gradients and rotation vector for R1
               CALL cp_eval_at_ts_low(gopt_env, x, 1, dimer_env, calc_force, f1, dimer_env%rot%g1)
            ELSE
               angle1 = dimer_env%rot%angle1
               angle2 = dimer_env%rot%angle2
               dimer_env%rot%g1 = SIN(angle1-angle2)/SIN(angle1)*dimer_env%rot%g1+ &
                                  SIN(angle2)/SIN(angle1)*dimer_env%rot%g1p+ &
                                  (1.0_dp-COS(angle2)-SIN(angle2)*TAN(angle1/2.0_dp))*dimer_env%rot%g0
            END IF

            ! Determine the theta vector (i.e. the search direction for line minimization)
            gradient = -2.0_dp*(dimer_env%rot%g1-dimer_env%rot%g0)
            IF (debug_this_module .AND. (iw > 0)) THEN
               WRITE (iw, '(A)') "G1 vector:"
               WRITE (iw, '(3F15.9)') dimer_env%rot%g1
               WRITE (iw, '(A)') "-2*(G1-G0) vector:"
               WRITE (iw, '(3F15.9)') gradient
            END IF
            CALL get_theta(gradient, dimer_env, norm)
            f = norm
            dimer_env%cg_rot%norm_theta_old = dimer_env%cg_rot%norm_theta
            dimer_env%cg_rot%norm_theta = norm

            IF (debug_this_module .AND. (iw > 0)) THEN
               WRITE (iw, '(A,F20.10)') "Rotational Force step (1,3): module:", norm
               WRITE (iw, '(3F15.9)') gradient
            END IF

            ! Compute curvature and derivative of the curvature w.r.t. the rotational angle
            dimer_env%rot%curvature = DOT_PRODUCT(dimer_env%rot%g1-dimer_env%rot%g0, dimer_env%nvec)/dimer_env%dr
            dimer_env%rot%dCdp = 2.0_dp*DOT_PRODUCT(dimer_env%rot%g1-dimer_env%rot%g0, gradient)/dimer_env%dr

            dimer_env%rot%rotation_step = do_second_rotation_step
            gradient = -gradient
         CASE (do_second_rotation_step)
            ! Compute energy, gradients and rotation vector for R1
            CALL cp_eval_at_ts_low(gopt_env, x, 1, dimer_env, calc_force, f1, dimer_env%rot%g1p)
            dimer_env%rot%curvature = DOT_PRODUCT(dimer_env%rot%g1p-dimer_env%rot%g0, dimer_env%nvec)/dimer_env%dr
            dimer_env%rot%rotation_step = do_third_rotation_step

            ! Determine the theta vector (i.e. the search direction for line minimization)
            ! This is never used for getting a new theta but is consistent in order to
            ! give back the right value of f
            gradient = -2.0_dp*(dimer_env%rot%g1p-dimer_env%rot%g0)
            CALL get_theta(gradient, dimer_env, norm)
            f = norm

            IF (debug_this_module .AND. (iw > 0)) THEN
               WRITE (iw, '(A)') "Rotational Force step (1,3):"
               WRITE (iw, '(3F15.9)') gradient
            END IF
         END SELECT
      ELSE
         ! Compute energy, gradients and rotation vector for R0
         CALL cp_eval_at_ts_low(gopt_env, x, 0, dimer_env, calc_force, f, dimer_env%rot%g0)

         ! The dimer is rotated only when we are out of the translation line search
         IF (.NOT. gopt_env%do_line_search) THEN
            IF (debug_this_module .AND. (iw > 0)) THEN
               WRITE (iw, '(A)') "Entering the rotation module"
               WRITE (iw, '(A)') "G0 vector:"
               WRITE (iw, '(3F15.9)') dimer_env%rot%g0
            END IF
            CALL cp_rot_opt(gopt_env%gopt_dimer_env, x, gopt_env%gopt_dimer_param, &
                            gopt_env%gopt_dimer_env%geo_section)
            dimer_env%rot%rotation_step = do_first_rotation_step
         END IF

         print_section => section_vals_get_subs_vals(gopt_env%gopt_dimer_env%geo_section, "PRINT")

         ! Correcting gradients for Translation K-DIMER or STANDARD
         IF (dimer_env%kdimer) THEN
            CALL cite_reference(Henkelman2014)
            ! K-DIMER
            IF (iw > 0) THEN
               WRITE (iw, '(T2,A)') "DIMER| Correcting gradients for Translation with K-DIMER method"
            END IF
            swf = 1.0_dp+EXP(dimer_env%beta*dimer_env%rot%curvature)
            gm2 = 1.0_dp-(1.0_dp/swf)
            gm1 = (2.0_dp/swf)-1.0_dp
            gradient = gm2*(dimer_env%rot%g0-2.0_dp*DOT_PRODUCT(dimer_env%rot%g0, dimer_env%nvec)*dimer_env%nvec) &
                       -gm1*(DOT_PRODUCT(dimer_env%rot%g0, dimer_env%nvec)*dimer_env%nvec)
            CALL remove_rot_transl_component(gopt_env, gradient, print_section)
            IF (debug_this_module .AND. (iw > 0)) WRITE (iw, *) "K-DIMER", dimer_env%beta, dimer_env%rot%curvature, &
               dimer_env%rot%dCdp, gm1, gm2, swf
         ELSE
            IF (iw > 0) THEN
               WRITE (iw, '(T2,A)') "DIMER| Correcting gradients for Translation with standard method"
            END IF
            IF (dimer_env%rot%curvature > 0) THEN
               gradient = -DOT_PRODUCT(dimer_env%rot%g0, dimer_env%nvec)*dimer_env%nvec
               CALL remove_rot_transl_component(gopt_env, gradient, print_section)
            ELSE
               gradient = dimer_env%rot%g0-2.0_dp*DOT_PRODUCT(dimer_env%rot%g0, dimer_env%nvec)*dimer_env%nvec
               CALL remove_rot_transl_component(gopt_env, gradient, print_section)
            END IF
         END IF
         IF (debug_this_module .AND. (iw > 0)) THEN
            WRITE (iw, *) "final gradient:", gradient
            WRITE (iw, '(A,F20.10)') "norm gradient:", SQRT(DOT_PRODUCT(gradient, gradient))
         END IF
         IF (.NOT. gopt_env%do_line_search) THEN
            f = SQRT(DOT_PRODUCT(gradient, gradient))
         ELSE
            f = -DOT_PRODUCT(gradient, dimer_env%tsl%tls_vec)
         END IF
      END IF
      CALL cp_print_key_finished_output(iw, logger, gopt_env%geo_section, "PRINT%PROGRAM_RUN_INFO")
      CALL timestop(handle)
   END SUBROUTINE cp_eval_at_ts

! **************************************************************************************************
!> \brief This function removes translational forces after project of the gradient
!> \param gopt_env ...
!> \param gradient ...
!> \param print_section ...
!> \par History
!>      2016/03/02 [LTong] added fixed atom constraint for gradient
!> \author Luca Bellucci and Teodoro Laino - created [tlaino] - 01.2008
! **************************************************************************************************
   SUBROUTINE remove_rot_transl_component(gopt_env, gradient, print_section)
      TYPE(gopt_f_type), POINTER                         :: gopt_env
      REAL(KIND=dp), DIMENSION(:)                        :: gradient
      TYPE(section_vals_type), POINTER                   :: print_section

      CHARACTER(len=*), PARAMETER :: routineN = 'remove_rot_transl_component', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: dof, handle, i, j, natoms
      REAL(KIND=dp)                                      :: norm, norm_gradient_old
      REAL(KIND=dp), DIMENSION(:, :), POINTER            :: D, mat
      TYPE(cp_subsys_type), POINTER                      :: subsys
      TYPE(particle_list_type), POINTER                  :: particles

      CALL timeset(routineN, handle)
      NULLIFY (mat)
      CALL force_env_get(gopt_env%force_env, subsys=subsys)
      CALL cp_subsys_get(subsys, particles=particles)

      natoms = particles%n_els
      norm_gradient_old = SQRT(DOT_PRODUCT(gradient, gradient))
      IF (norm_gradient_old > 0.0_dp) THEN
         IF (natoms > 1) THEN
            CALL rot_ana(particles%els, mat, dof, print_section, keep_rotations=.FALSE., &
                         mass_weighted=.FALSE., natoms=natoms)

            ! Orthogonalize gradient with respect to the full set of Roto-Trasl vectors
            ALLOCATE (D(3*natoms, dof))
            ! Check First orthogonality in the first element of the basis set
            DO i = 1, dof
               D(:, i) = mat(:, i)
               DO j = i+1, dof
                  norm = DOT_PRODUCT(mat(:, i), mat(:, j))
                  CPASSERT(ABS(norm) < thrs_motion)
               END DO
            END DO
            DO i = 1, dof
               norm = DOT_PRODUCT(gradient, D(:, i))
               gradient = gradient-norm*D(:, i)
            END DO
            DEALLOCATE (D)
            DEALLOCATE (mat)
         END IF
      END IF
      ! apply constraint
      CALL dimer_fixed_atom_control(gradient, subsys)
      CALL timestop(handle)
   END SUBROUTINE remove_rot_transl_component

! **************************************************************************************************
!> \brief ...
!> \param gopt_env ...
!> \param x ...
!> \param dimer_index ...
!> \param dimer_env ...
!> \param calc_force ...
!> \param f ...
!> \param gradient ...
!> \par History
!>      none
!> \author Luca Bellucci and Teodoro Laino - created [tlaino] - 01.2008
! **************************************************************************************************
   SUBROUTINE cp_eval_at_ts_low(gopt_env, x, dimer_index, dimer_env, calc_force, &
                                f, gradient)
      TYPE(gopt_f_type), POINTER                         :: gopt_env
      REAL(KIND=dp), DIMENSION(:), POINTER               :: x
      INTEGER, INTENT(IN)                                :: dimer_index
      TYPE(dimer_env_type), POINTER                      :: dimer_env
      LOGICAL, INTENT(IN)                                :: calc_force
      REAL(KIND=dp), INTENT(OUT), OPTIONAL               :: f
      REAL(KIND=dp), DIMENSION(:), OPTIONAL              :: gradient

      CHARACTER(len=*), PARAMETER :: routineN = 'cp_eval_at_ts_low', &
         routineP = moduleN//':'//routineN

      INTEGER                                            :: handle, idg, idir, ip
      TYPE(cp_subsys_type), POINTER                      :: subsys
      TYPE(particle_list_type), POINTER                  :: particles

      CALL timeset(routineN, handle)
      idg = 0
      CALL force_env_get(gopt_env%force_env, subsys=subsys)
      CALL cp_subsys_get(subsys, particles=particles)
      DO ip = 1, particles%n_els
         DO idir = 1, 3
            idg = idg+1
            particles%els(ip)%r(idir) = x(idg)+REAL(dimer_index, KIND=dp)*dimer_env%nvec(idg)*dimer_env%dr
         END DO
      END DO

      ! Compute energy and forces
      CALL force_env_calc_energy_force(gopt_env%force_env, calc_force=calc_force)

      ! Possibly take the potential energy
      IF (PRESENT(f)) THEN
         CALL force_env_get(gopt_env%force_env, potential_energy=f)
      END IF

      ! Possibly take the gradients
      IF (PRESENT(gradient)) THEN
         idg = 0
         CALL cp_subsys_get(subsys, particles=particles)
         DO ip = 1, particles%n_els
            DO idir = 1, 3
               idg = idg+1
               CPASSERT(SIZE(gradient) >= idg)
               gradient(idg) = -particles%els(ip)%f(idir)
            END DO
         END DO
      END IF
      CALL timestop(handle)
   END SUBROUTINE cp_eval_at_ts_low

END MODULE dimer_methods
