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

! **************************************************************************************************
!> \par History
!>      CJM APRIL-30-2009: only uses fist_env
!>      Teodoro Laino [tlaino] - 05.2009 : Generalization to different Ewald
!>                                         methods (initial framework)
!> \author CJM
! **************************************************************************************************

MODULE fist_pol_scf
   USE atomic_kind_types,               ONLY: atomic_kind_type,&
                                              get_atomic_kind
   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 distribution_1d_types,           ONLY: distribution_1d_type
   USE ewald_environment_types,         ONLY: ewald_env_get,&
                                              ewald_environment_type
   USE ewald_pw_types,                  ONLY: ewald_pw_type
   USE ewalds_multipole,                ONLY: ewald_multipole_evaluate
   USE fist_energy_types,               ONLY: fist_energy_type
   USE fist_nonbond_env_types,          ONLY: fist_nonbond_env_type
   USE input_constants,                 ONLY: do_fist_pol_cg,&
                                              do_fist_pol_sc
   USE input_section_types,             ONLY: section_vals_type
   USE kinds,                           ONLY: dp
   USE message_passing,                 ONLY: mp_sum
   USE multipole_types,                 ONLY: multipole_type
   USE particle_types,                  ONLY: particle_type
   USE pw_poisson_types,                ONLY: do_ewald_ewald,&
                                              do_ewald_pme,&
                                              do_ewald_spme
#include "./base/base_uses.f90"

   IMPLICIT NONE
   PRIVATE
   LOGICAL, PRIVATE                     :: debug_this_module = .FALSE.
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'fist_pol_scf'

   PUBLIC :: fist_pol_evaluate

CONTAINS

! **************************************************************************************************
!> \brief Main driver for evaluating energy/forces in a polarizable forcefield
!> \param atomic_kind_set ...
!> \param multipoles ...
!> \param ewald_env ...
!> \param ewald_pw ...
!> \param fist_nonbond_env ...
!> \param cell ...
!> \param particle_set ...
!> \param local_particles ...
!> \param thermo ...
!> \param vg_coulomb ...
!> \param pot_nonbond ...
!> \param f_nonbond ...
!> \param fg_coulomb ...
!> \param use_virial ...
!> \param pv_g ...
!> \param pv_nonbond ...
!> \param mm_section ...
!> \param do_ipol ...
!> \author Toon.Verstraelen@gmail.com (2010-03-01)
! **************************************************************************************************
   SUBROUTINE fist_pol_evaluate(atomic_kind_set, multipoles, ewald_env, &
                                ewald_pw, fist_nonbond_env, cell, particle_set, local_particles, &
                                thermo, vg_coulomb, pot_nonbond, f_nonbond, fg_coulomb, use_virial, &
                                pv_g, pv_nonbond, mm_section, do_ipol)

      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(multipole_type), POINTER                      :: multipoles
      TYPE(ewald_environment_type), POINTER              :: ewald_env
      TYPE(ewald_pw_type), POINTER                       :: ewald_pw
      TYPE(fist_nonbond_env_type), POINTER               :: fist_nonbond_env
      TYPE(cell_type), POINTER                           :: cell
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(distribution_1d_type), POINTER                :: local_particles
      TYPE(fist_energy_type), POINTER                    :: thermo
      REAL(KIND=dp)                                      :: vg_coulomb, pot_nonbond
      REAL(KIND=dp), DIMENSION(:, :)                     :: f_nonbond, fg_coulomb
      LOGICAL, INTENT(IN)                                :: use_virial
      REAL(KIND=dp), DIMENSION(3, 3)                     :: pv_g, pv_nonbond
      TYPE(section_vals_type), POINTER                   :: mm_section
      INTEGER                                            :: do_ipol

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

      SELECT CASE (do_ipol)
      CASE (do_fist_pol_sc)
         CALL fist_pol_evaluate_sc(atomic_kind_set, multipoles, ewald_env, &
                                   ewald_pw, fist_nonbond_env, cell, particle_set, local_particles, &
                                   thermo, vg_coulomb, pot_nonbond, f_nonbond, fg_coulomb, use_virial, &
                                   pv_g, pv_nonbond, mm_section)
      CASE (do_fist_pol_cg)
         CALL fist_pol_evaluate_cg(atomic_kind_set, multipoles, ewald_env, &
                                   ewald_pw, fist_nonbond_env, cell, particle_set, local_particles, &
                                   thermo, vg_coulomb, pot_nonbond, f_nonbond, fg_coulomb, use_virial, &
                                   pv_g, pv_nonbond, mm_section)
      END SELECT

   END SUBROUTINE fist_pol_evaluate

! **************************************************************************************************
!> \brief Self-consistent solver for a polarizable force-field
!> \param atomic_kind_set ...
!> \param multipoles ...
!> \param ewald_env ...
!> \param ewald_pw ...
!> \param fist_nonbond_env ...
!> \param cell ...
!> \param particle_set ...
!> \param local_particles ...
!> \param thermo ...
!> \param vg_coulomb ...
!> \param pot_nonbond ...
!> \param f_nonbond ...
!> \param fg_coulomb ...
!> \param use_virial ...
!> \param pv_g ...
!> \param pv_nonbond ...
!> \param mm_section ...
!> \author Toon.Verstraelen@gmail.com (2010-03-01)
!> \note
!>    Method: Given an initial guess of the induced dipoles, the electrostatic
!>    field is computed at each dipole. Then new induced dipoles are computed
!>    following p = alpha x E. This is repeated until a convergence criterion is
!>    met. The convergence is measured as the RSMD of the derivatives of the
!>    electrostatic energy (including dipole self-energy) towards the components
!>    of the dipoles.
! **************************************************************************************************
   SUBROUTINE fist_pol_evaluate_sc(atomic_kind_set, multipoles, ewald_env, ewald_pw, &
                                   fist_nonbond_env, cell, particle_set, local_particles, thermo, vg_coulomb, &
                                   pot_nonbond, f_nonbond, fg_coulomb, use_virial, pv_g, pv_nonbond, mm_section)

      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(multipole_type), POINTER                      :: multipoles
      TYPE(ewald_environment_type), POINTER              :: ewald_env
      TYPE(ewald_pw_type), POINTER                       :: ewald_pw
      TYPE(fist_nonbond_env_type), POINTER               :: fist_nonbond_env
      TYPE(cell_type), POINTER                           :: cell
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(distribution_1d_type), POINTER                :: local_particles
      TYPE(fist_energy_type), POINTER                    :: thermo
      REAL(KIND=dp)                                      :: vg_coulomb, pot_nonbond
      REAL(KIND=dp), DIMENSION(:, :)                     :: f_nonbond, fg_coulomb
      LOGICAL, INTENT(IN)                                :: use_virial
      REAL(KIND=dp), DIMENSION(3, 3)                     :: pv_g, pv_nonbond
      TYPE(section_vals_type), POINTER                   :: mm_section

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

      INTEGER                                            :: ewald_type, handle, i, iatom, ii, ikind, &
                                                            iter, iw, iw2, j, max_ipol_iter, &
                                                            natom_of_kind, natoms, nkind, ntot
      INTEGER, DIMENSION(:), POINTER                     :: atom_list
      LOGICAL                                            :: iwarn
      REAL(KIND=dp)                                      :: apol, cpol, eps_pol, pot_nonbond_local, &
                                                            rmsd, tmp_trace
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: efield1, efield2
      TYPE(atomic_kind_type), POINTER                    :: atomic_kind
      TYPE(cp_logger_type), POINTER                      :: logger

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

      iw = cp_print_key_unit_nr(logger, mm_section, "PRINT%ITER_INFO", &
                                extension=".mmLog")
      iw2 = cp_print_key_unit_nr(logger, mm_section, "PRINT%EWALD_INFO", &
                                 extension=".mmLog")

      CALL ewald_env_get(ewald_env, max_ipol_iter=max_ipol_iter, eps_pol=eps_pol, &
                         ewald_type=ewald_type)

      natoms = SIZE(particle_set)
      ALLOCATE (efield1(3, natoms))
      ALLOCATE (efield2(9, natoms))

      nkind = SIZE(atomic_kind_set)
      IF (iw > 0) WRITE (iw, FMT='(/,T5,"POL_SCF|","Method: self-consistent")')
      IF (iw > 0) WRITE (iw, FMT='(T5,"POL_SCF|","  Iteration",7X,"Conv.",T49,"Electrostatic & Induction Energy")')
      pol_scf: DO iter = 1, max_ipol_iter
         ! Evaluate the electrostatic with Ewald schemes
         CALL eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, cell, &
                             particle_set, local_particles, vg_coulomb, pot_nonbond_local, thermo, &
                             multipoles, do_correction_bonded=.TRUE., do_forces=.FALSE., &
                             do_stress=.FALSE., do_efield=.TRUE., iw2=iw2, do_debug=.FALSE., &
                             atomic_kind_set=atomic_kind_set, mm_section=mm_section, &
                             efield1=efield1, efield2=efield2)
         CALL mp_sum(pot_nonbond_local, logger%para_env%group)

         ! compute the new dipoles, qudrupoles, and check for convergence
         ntot = 0
         rmsd = 0.0_dp
         thermo%e_induction = 0.0_dp
         DO ikind = 1, nkind
            atomic_kind => atomic_kind_set(ikind)
            CALL get_atomic_kind(atomic_kind, apol=apol, cpol=cpol, natom=natom_of_kind, atom_list=atom_list)
            ! ignore atoms with dipole and quadrupole polarizability zero
            IF (apol == 0 .AND. cpol == 0) CYCLE
            ! increment counter correctly
            IF (apol /= 0) ntot = ntot+natom_of_kind
            IF (cpol /= 0) ntot = ntot+natom_of_kind

            DO iatom = 1, natom_of_kind
               ii = atom_list(iatom)
               IF (apol /= 0) THEN
                  DO i = 1, 3
                     ! the rmsd of the derivatives of the energy towards the
                     ! components of the atomic dipole moments
                     rmsd = rmsd+(multipoles%dipoles(i, ii)/apol-efield1(i, ii))**2
                  END DO
               END IF
               IF (cpol /= 0) THEN
                  rmsd = rmsd+(multipoles%quadrupoles(1, 1, ii)/cpol-efield2(1, ii))**2
                  rmsd = rmsd+(multipoles%quadrupoles(2, 1, ii)/cpol-efield2(2, ii))**2
                  rmsd = rmsd+(multipoles%quadrupoles(3, 1, ii)/cpol-efield2(3, ii))**2
                  rmsd = rmsd+(multipoles%quadrupoles(1, 2, ii)/cpol-efield2(4, ii))**2
                  rmsd = rmsd+(multipoles%quadrupoles(2, 2, ii)/cpol-efield2(5, ii))**2
                  rmsd = rmsd+(multipoles%quadrupoles(3, 2, ii)/cpol-efield2(6, ii))**2
                  rmsd = rmsd+(multipoles%quadrupoles(1, 3, ii)/cpol-efield2(7, ii))**2
                  rmsd = rmsd+(multipoles%quadrupoles(2, 3, ii)/cpol-efield2(8, ii))**2
                  rmsd = rmsd+(multipoles%quadrupoles(3, 3, ii)/cpol-efield2(9, ii))**2
               END IF
! compute dipole
               multipoles%dipoles(:, ii) = apol*efield1(:, ii)
! compute quadrupole
               IF (cpol /= 0) THEN
                  multipoles%quadrupoles(1, 1, ii) = cpol*efield2(1, ii)
                  multipoles%quadrupoles(2, 1, ii) = cpol*efield2(2, ii)
                  multipoles%quadrupoles(3, 1, ii) = cpol*efield2(3, ii)
                  multipoles%quadrupoles(1, 2, ii) = cpol*efield2(4, ii)
                  multipoles%quadrupoles(2, 2, ii) = cpol*efield2(5, ii)
                  multipoles%quadrupoles(3, 2, ii) = cpol*efield2(6, ii)
                  multipoles%quadrupoles(1, 3, ii) = cpol*efield2(7, ii)
                  multipoles%quadrupoles(2, 3, ii) = cpol*efield2(8, ii)
                  multipoles%quadrupoles(3, 3, ii) = cpol*efield2(9, ii)
               END IF
               ! Compute the new induction term while we are here
               IF (apol /= 0) THEN
                  thermo%e_induction = thermo%e_induction+ &
                                       DOT_PRODUCT(multipoles%dipoles(:, ii), &
                                                   multipoles%dipoles(:, ii))/apol/2.0_dp
               END IF
               IF (cpol /= 0) THEN
                  tmp_trace = 0._dp
                  DO i = 1, 3
                     DO j = 1, 3
                        tmp_trace = tmp_trace+ &
                                    multipoles%quadrupoles(i, j, ii)*multipoles%quadrupoles(i, j, ii)
                     END DO
                  END DO
                  thermo%e_induction = thermo%e_induction+tmp_trace/cpol/6.0_dp
               END IF
            END DO
         END DO
         rmsd = SQRT(rmsd/REAL(ntot, KIND=dp))
         IF (iw > 0) THEN
            ! print the energy that is minimized (this is electrostatic + induction)
            WRITE (iw, FMT='(T5,"POL_SCF|",5X,I5,5X,E12.6,T61,F20.10)') iter, &
               rmsd, vg_coulomb+pot_nonbond_local+thermo%e_induction
         END IF
         IF (rmsd <= eps_pol) THEN
            IF (iw > 0) WRITE (iw, FMT='(T5,"POL_SCF|",1X,"Self-consistent Polarization achieved.")')
            EXIT pol_scf
         END IF

         iwarn = ((rmsd > eps_pol) .AND. (iter == max_ipol_iter))
         IF (iwarn .AND. iw > 0) WRITE (iw, FMT='(T5,"POL_SCF|",1X,"Self-consistent Polarization not converged!")')
         IF (iwarn) &
            CPWARN("Self-consistent Polarization not converged! ")
      END DO pol_scf

      ! Now evaluate after convergence to obtain forces and converged energies
      CALL eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, cell, &
                          particle_set, local_particles, vg_coulomb, pot_nonbond_local, thermo, &
                          multipoles, do_correction_bonded=.TRUE., do_forces=.TRUE., &
                          do_stress=use_virial, do_efield=.FALSE., iw2=iw2, do_debug=.FALSE., &
                          atomic_kind_set=atomic_kind_set, mm_section=mm_section, &
                          forces_local=fg_coulomb, forces_glob=f_nonbond, &
                          pv_local=pv_g, pv_glob=pv_nonbond)
      pot_nonbond = pot_nonbond+pot_nonbond_local
      CALL mp_sum(pot_nonbond_local, logger%para_env%group)

      IF (iw > 0) THEN
         ! print the energy that is minimized (this is electrostatic + induction)
         WRITE (iw, FMT='(T5,"POL_SCF|",5X,"Final",T61,F20.10,/)') &
            vg_coulomb+pot_nonbond_local+thermo%e_induction
      END IF

      ! Deallocate working arrays
      DEALLOCATE (efield1)
      DEALLOCATE (efield2)
      CALL cp_print_key_finished_output(iw2, logger, mm_section, &
                                        "PRINT%EWALD_INFO")
      CALL cp_print_key_finished_output(iw, logger, mm_section, &
                                        "PRINT%ITER_INFO")

      CALL timestop(handle)
   END SUBROUTINE fist_pol_evaluate_sc

! **************************************************************************************************
!> \brief Conjugate-gradient solver for a polarizable force-field
!> \param atomic_kind_set ...
!> \param multipoles ...
!> \param ewald_env ...
!> \param ewald_pw ...
!> \param fist_nonbond_env ...
!> \param cell ...
!> \param particle_set ...
!> \param local_particles ...
!> \param thermo ...
!> \param vg_coulomb ...
!> \param pot_nonbond ...
!> \param f_nonbond ...
!> \param fg_coulomb ...
!> \param use_virial ...
!> \param pv_g ...
!> \param pv_nonbond ...
!> \param mm_section ...
!> \author Toon.Verstraelen@gmail.com (2010-03-01)
!> \note
!>     Method: The dipoles are found by minimizing the sum of the electrostatic
!>     and the induction energy directly using a conjugate gradient method. This
!>     routine assumes that the energy is a quadratic function of the dipoles.
!>     Finding the minimum is then done by solving a linear system. This will
!>     not work for polarizable force fields that include hyperpolarizability.
!>
!>     The implementation of the conjugate gradient solver for linear systems
!>     is described in chapter 2.7 Sparse Linear Systems, under the section
!>     "Conjugate Gradient Method for a Sparse System". Although the inducible
!>     dipoles are the solution of a dense linear system, the same algorithm is
!>     still recommended for this situation. One does not have access to the
!>     entire hardness kernel to compute the solution with conventional linear
!>     algebra routines, but one only has a function that computes the dot
!>     product of the hardness kernel and a vector. (This is the routine that
!>     computes the electrostatic field at the atoms for a given vector of
!>     inducible dipoles.) Given such function, the conjugate gradient method
!>     is an efficient way to compute the solution of a linear system, and it
!>     scales well towards many degrees of freedom in terms of efficiency and
!>     memory usage.
! **************************************************************************************************
   SUBROUTINE fist_pol_evaluate_cg(atomic_kind_set, multipoles, ewald_env, ewald_pw, &
                                   fist_nonbond_env, cell, particle_set, local_particles, thermo, vg_coulomb, &
                                   pot_nonbond, f_nonbond, fg_coulomb, use_virial, pv_g, pv_nonbond, mm_section)

      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(multipole_type), POINTER                      :: multipoles
      TYPE(ewald_environment_type), POINTER              :: ewald_env
      TYPE(ewald_pw_type), POINTER                       :: ewald_pw
      TYPE(fist_nonbond_env_type), POINTER               :: fist_nonbond_env
      TYPE(cell_type), POINTER                           :: cell
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(distribution_1d_type), POINTER                :: local_particles
      TYPE(fist_energy_type), POINTER                    :: thermo
      REAL(KIND=dp)                                      :: vg_coulomb, pot_nonbond
      REAL(KIND=dp), DIMENSION(:, :)                     :: f_nonbond, fg_coulomb
      LOGICAL, INTENT(IN)                                :: use_virial
      REAL(KIND=dp), DIMENSION(3, 3)                     :: pv_g, pv_nonbond
      TYPE(section_vals_type), POINTER                   :: mm_section

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

      INTEGER                                            :: ewald_type, handle, i, iatom, ii, ikind, &
                                                            iter, iw, iw2, max_ipol_iter, &
                                                            natom_of_kind, natoms, nkind, ntot
      INTEGER, DIMENSION(:), POINTER                     :: atom_list
      LOGICAL                                            :: iwarn
      REAL(KIND=dp)                                      :: alpha, apol, beta, denom, eps_pol, &
                                                            pot_nonbond_local, rmsd
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: conjugate, conjugate_applied, efield1, &
                                                            efield1_ext, residual, tmp_dipoles
      TYPE(atomic_kind_type), POINTER                    :: atomic_kind
      TYPE(cp_logger_type), POINTER                      :: logger

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

      iw = cp_print_key_unit_nr(logger, mm_section, "PRINT%ITER_INFO", &
                                extension=".mmLog")
      iw2 = cp_print_key_unit_nr(logger, mm_section, "PRINT%EWALD_INFO", &
                                 extension=".mmLog")

      CALL ewald_env_get(ewald_env, max_ipol_iter=max_ipol_iter, eps_pol=eps_pol, &
                         ewald_type=ewald_type)

      ! allocate work arrays
      natoms = SIZE(particle_set)
      ALLOCATE (efield1(3, natoms))
      ALLOCATE (tmp_dipoles(3, natoms))
      ALLOCATE (residual(3, natoms))
      ALLOCATE (conjugate(3, natoms))
      ALLOCATE (conjugate_applied(3, natoms))
      ALLOCATE (efield1_ext(3, natoms))

      ! Compute the 'external' electrostatic field (all inducible dipoles
      ! equal to zero). this is required for the conjugate gradient solver.
      ! We assume that all dipoles are inducible dipoles.
      tmp_dipoles(:, :) = multipoles%dipoles ! backup of dipoles
      multipoles%dipoles = 0.0_dp
      CALL eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, cell, &
                          particle_set, local_particles, vg_coulomb, pot_nonbond_local, thermo, &
                          multipoles, do_correction_bonded=.TRUE., do_forces=.FALSE., &
                          do_stress=.FALSE., do_efield=.TRUE., iw2=iw2, do_debug=.FALSE., &
                          atomic_kind_set=atomic_kind_set, mm_section=mm_section, &
                          efield1=efield1_ext)
      multipoles%dipoles = tmp_dipoles ! restore backup

      ! Compute the electric field with the initial guess of the dipoles.
      CALL eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, cell, &
                          particle_set, local_particles, vg_coulomb, pot_nonbond_local, thermo, &
                          multipoles, do_correction_bonded=.TRUE., do_forces=.FALSE., &
                          do_stress=.FALSE., do_efield=.TRUE., iw2=iw2, do_debug=.FALSE., &
                          atomic_kind_set=atomic_kind_set, mm_section=mm_section, &
                          efield1=efield1)

      ! Compute the first residual explicitly.
      nkind = SIZE(atomic_kind_set)
      ntot = 0
      residual = 0.0_dp
      DO ikind = 1, nkind
         atomic_kind => atomic_kind_set(ikind)
         CALL get_atomic_kind(atomic_kind, apol=apol, natom=natom_of_kind, atom_list=atom_list)
         ! ignore atoms with polarizability zero
         IF (apol == 0) CYCLE
         ntot = ntot+natom_of_kind
         DO iatom = 1, natom_of_kind
            ii = atom_list(iatom)
            DO i = 1, 3
               ! residual = b - A x
               residual(i, ii) = efield1(i, ii)-multipoles%dipoles(i, ii)/apol
            END DO
         END DO
      END DO
      ! The first conjugate residual is equal to the residual.
      conjugate(:, :) = residual

      IF (iw > 0) WRITE (iw, FMT='(/,T5,"POL_SCF|","Method: conjugate-gradient")')
      IF (iw > 0) WRITE (iw, FMT='(T5,"POL_SCF|","  Iteration",7X,"Conv.",T49,"Electrostatic & Induction Energy")')
      pol_scf: DO iter = 1, max_ipol_iter
         IF (debug_this_module) THEN
            ! In principle the residual must not be computed explicitly any more. It
            ! is obtained in an indirect way below. When the DEBUG flag is set, the
            ! explicit residual is computed and compared with the implicitly derived
            ! residual as a double check.
            CALL eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, cell, &
                                particle_set, local_particles, vg_coulomb, pot_nonbond_local, thermo, &
                                multipoles, do_correction_bonded=.TRUE., do_forces=.FALSE., &
                                do_stress=.FALSE., do_efield=.TRUE., iw2=iw2, do_debug=.FALSE., &
                                atomic_kind_set=atomic_kind_set, mm_section=mm_section, &
                                efield1=efield1)
            ! inapropriate use of denom to check the error on the residual
            denom = 0.0_dp
         END IF
         rmsd = 0.0_dp
         ! Compute the rmsd of the residual.
         DO ikind = 1, nkind
            atomic_kind => atomic_kind_set(ikind)
            CALL get_atomic_kind(atomic_kind, apol=apol, natom=natom_of_kind, atom_list=atom_list)
            ! ignore atoms with polarizability zero
            IF (apol == 0) CYCLE
            DO iatom = 1, natom_of_kind
               ii = atom_list(iatom)
               DO i = 1, 3
                  ! residual = b - A x
                  rmsd = rmsd+residual(i, ii)**2
                  IF (debug_this_module) THEN
                     denom = denom+(residual(i, ii)-(efield1(i, ii)- &
                                                     multipoles%dipoles(i, ii)/apol))**2
                  END IF
               END DO
            END DO
         END DO
         rmsd = SQRT(rmsd/ntot)
         IF (iw > 0) THEN
            WRITE (iw, FMT='(T5,"POL_SCF|",5X,I5,5X,E12.6,T67,"(not computed)")') iter, rmsd
            IF (debug_this_module) THEN
               denom = SQRT(denom/ntot)
               WRITE (iw, FMT='(T5,"POL_SCF|",5X,"Error on implicit residual:",5X,E12.6)') denom
            END IF
         END IF

         ! Apply the hardness kernel to the conjugate residual.
         ! We assume that all non-zero dipoles are inducible dipoles.
         tmp_dipoles(:, :) = multipoles%dipoles ! backup of dipoles
         multipoles%dipoles = conjugate
         CALL eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, cell, &
                             particle_set, local_particles, vg_coulomb, pot_nonbond_local, thermo, &
                             multipoles, do_correction_bonded=.TRUE., do_forces=.FALSE., &
                             do_stress=.FALSE., do_efield=.TRUE., iw2=iw2, do_debug=.FALSE., &
                             atomic_kind_set=atomic_kind_set, mm_section=mm_section, &
                             efield1=conjugate_applied)
         multipoles%dipoles = tmp_dipoles ! restore backup
         conjugate_applied(:, :) = efield1_ext-conjugate_applied

         ! Finish conjugate_applied and compute alpha from the conjugate gradient algorithm.
         alpha = 0.0_dp
         denom = 0.0_dp
         DO ikind = 1, nkind
            atomic_kind => atomic_kind_set(ikind)
            CALL get_atomic_kind(atomic_kind, apol=apol, natom=natom_of_kind, atom_list=atom_list)
            ! ignore atoms with polarizability zero
            IF (apol == 0) CYCLE
            DO iatom = 1, natom_of_kind
               ii = atom_list(iatom)
               DO i = 1, 3
                  conjugate_applied(i, ii) = conjugate_applied(i, ii)+conjugate(i, ii)/apol
               END DO
               alpha = alpha+DOT_PRODUCT(residual(:, ii), residual(:, ii))
               denom = denom+DOT_PRODUCT(conjugate(:, ii), conjugate_applied(:, ii))
            END DO
         END DO
         alpha = alpha/denom

         ! Compute the new residual and beta from the conjugate gradient method.
         beta = 0.0_dp
         denom = 0.0_dp
         DO ikind = 1, nkind
            atomic_kind => atomic_kind_set(ikind)
            CALL get_atomic_kind(atomic_kind, apol=apol, natom=natom_of_kind, atom_list=atom_list)
            IF (apol == 0) CYCLE
            DO iatom = 1, natom_of_kind
               ii = atom_list(iatom)
               denom = denom+DOT_PRODUCT(residual(:, ii), residual(:, ii))
               DO i = 1, 3
                  residual(i, ii) = residual(i, ii)-alpha*conjugate_applied(i, ii)
               END DO
               beta = beta+DOT_PRODUCT(residual(:, ii), residual(:, ii))
            END DO
         END DO
         beta = beta/denom

         ! Compute the new dipoles, the new conjugate residual, and the induction
         ! energy.
         thermo%e_induction = 0.0_dp
         DO ikind = 1, nkind
            atomic_kind => atomic_kind_set(ikind)
            CALL get_atomic_kind(atomic_kind, apol=apol, natom=natom_of_kind, atom_list=atom_list)
            ! ignore atoms with polarizability zero
            IF (apol == 0) CYCLE
            DO iatom = 1, natom_of_kind
               ii = atom_list(iatom)
               DO i = 1, 3
                  multipoles%dipoles(i, ii) = multipoles%dipoles(i, ii)+alpha*conjugate(i, ii)
                  conjugate(i, ii) = residual(i, ii)+beta*conjugate(i, ii)
                  thermo%e_induction = thermo%e_induction+multipoles%dipoles(i, ii)**2/apol/2.0_dp
               END DO
            END DO
         END DO

         ! Quit if rmsd is low enough.
         IF (rmsd <= eps_pol) THEN
            IF (iw > 0) WRITE (iw, FMT='(T5,"POL_SCF|",1X,"Self-consistent Polarization achieved.")')
            EXIT pol_scf
         END IF

         ! Print warning when not converged.
         iwarn = ((rmsd > eps_pol) .AND. (iter == max_ipol_iter))
         IF (iwarn .AND. iw > 0) WRITE (iw, FMT='(T5,"POL_SCF|",1X,"Self-consistent Polarization not converged!")')
         IF (iwarn) &
            CPWARN("Self-consistent Polarization not converged! ")
      END DO pol_scf

      IF (debug_this_module) THEN
         ! Now evaluate after convergence to obtain forces and converged energies
         CALL eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, cell, &
                             particle_set, local_particles, vg_coulomb, pot_nonbond_local, thermo, &
                             multipoles, do_correction_bonded=.TRUE., do_forces=.TRUE., &
                             do_stress=use_virial, do_efield=.TRUE., iw2=iw2, do_debug=.FALSE., &
                             atomic_kind_set=atomic_kind_set, mm_section=mm_section, &
                             forces_local=fg_coulomb, forces_glob=f_nonbond, &
                             pv_local=pv_g, pv_glob=pv_nonbond, efield1=efield1)

         ! Do a final check on the convergence: compute the residual explicitely
         rmsd = 0.0_dp
         DO ikind = 1, nkind
            atomic_kind => atomic_kind_set(ikind)
            CALL get_atomic_kind(atomic_kind, apol=apol, natom=natom_of_kind, atom_list=atom_list)
            ! ignore atoms with polarizability zero
            IF (apol == 0) CYCLE
            DO iatom = 1, natom_of_kind
               ii = atom_list(iatom)
               DO i = 1, 3
                  ! residual = b - A x
                  rmsd = rmsd+(efield1(i, ii)-multipoles%dipoles(i, ii)/apol)**2
               END DO
            END DO
         END DO
         rmsd = SQRT(rmsd/ntot)
         IF (iw > 0) WRITE (iw, FMT='(T5,"POL_SCF|",1X,"Final RMSD of residual:",5X,E12.6)') rmsd
         ! Stop program when congergence is not reached after all
         IF (rmsd > eps_pol) THEN
            CPWARN("Error in the conjugate gradient method for self-consistent polarization! ")
         END IF
      ELSE
         ! Now evaluate after convergence to obtain forces and converged energies
         CALL eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, cell, &
                             particle_set, local_particles, vg_coulomb, pot_nonbond_local, thermo, &
                             multipoles, do_correction_bonded=.TRUE., do_forces=.TRUE., &
                             do_stress=use_virial, do_efield=.FALSE., iw2=iw2, do_debug=.FALSE., &
                             atomic_kind_set=atomic_kind_set, mm_section=mm_section, &
                             forces_local=fg_coulomb, forces_glob=f_nonbond, &
                             pv_local=pv_g, pv_glob=pv_nonbond)
      ENDIF
      pot_nonbond = pot_nonbond+pot_nonbond_local
      CALL mp_sum(pot_nonbond_local, logger%para_env%group)

      IF (iw > 0) THEN
         WRITE (iw, FMT='(T5,"POL_SCF|",5X,"Final",T61,F20.10,/)') &
            vg_coulomb+pot_nonbond_local+thermo%e_induction
      END IF

      ! Deallocate working arrays
      DEALLOCATE (efield1)
      DEALLOCATE (tmp_dipoles)
      DEALLOCATE (residual)
      DEALLOCATE (conjugate)
      DEALLOCATE (conjugate_applied)
      DEALLOCATE (efield1_ext)
      CALL cp_print_key_finished_output(iw2, logger, mm_section, &
                                        "PRINT%EWALD_INFO")
      CALL cp_print_key_finished_output(iw, logger, mm_section, &
                                        "PRINT%ITER_INFO")

      CALL timestop(handle)
   END SUBROUTINE fist_pol_evaluate_cg

! **************************************************************************************************
!> \brief Main driver for evaluating electrostatic in polarible forcefields
!>        All the dependence on the Ewald method should go here!
!> \param ewald_type ...
!> \param ewald_env ...
!> \param ewald_pw ...
!> \param fist_nonbond_env ...
!> \param cell ...
!> \param particle_set ...
!> \param local_particles ...
!> \param vg_coulomb ...
!> \param pot_nonbond ...
!> \param thermo ...
!> \param multipoles ...
!> \param do_correction_bonded ...
!> \param do_forces ...
!> \param do_stress ...
!> \param do_efield ...
!> \param iw2 ...
!> \param do_debug ...
!> \param atomic_kind_set ...
!> \param mm_section ...
!> \param efield0 ...
!> \param efield1 ...
!> \param efield2 ...
!> \param forces_local ...
!> \param forces_glob ...
!> \param pv_local ...
!> \param pv_glob ...
!> \author Teodoro Laino [tlaino] 05.2009
! **************************************************************************************************
   SUBROUTINE eval_pol_ewald(ewald_type, ewald_env, ewald_pw, fist_nonbond_env, &
                             cell, particle_set, local_particles, vg_coulomb, pot_nonbond, thermo, &
                             multipoles, do_correction_bonded, do_forces, do_stress, do_efield, iw2, &
                             do_debug, atomic_kind_set, mm_section, efield0, efield1, efield2, forces_local, &
                             forces_glob, pv_local, pv_glob)

      INTEGER, INTENT(IN)                                :: ewald_type
      TYPE(ewald_environment_type), POINTER              :: ewald_env
      TYPE(ewald_pw_type), POINTER                       :: ewald_pw
      TYPE(fist_nonbond_env_type), POINTER               :: fist_nonbond_env
      TYPE(cell_type), POINTER                           :: cell
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(distribution_1d_type), POINTER                :: local_particles
      REAL(KIND=dp), INTENT(OUT)                         :: vg_coulomb, pot_nonbond
      TYPE(fist_energy_type), POINTER                    :: thermo
      TYPE(multipole_type), POINTER                      :: multipoles
      LOGICAL, INTENT(IN)                                :: do_correction_bonded, do_forces, &
                                                            do_stress, do_efield
      INTEGER, INTENT(IN)                                :: iw2
      LOGICAL, INTENT(IN)                                :: do_debug
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(section_vals_type), POINTER                   :: mm_section
      REAL(KIND=dp), DIMENSION(:), OPTIONAL              :: efield0
      REAL(KIND=dp), DIMENSION(:, :), OPTIONAL           :: efield1, efield2
      REAL(KIND=dp), DIMENSION(:, :), INTENT(INOUT), &
         OPTIONAL                                        :: forces_local, forces_glob, pv_local, &
                                                            pv_glob

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

      INTEGER                                            :: handle

      CALL timeset(routineN, handle)

      pot_nonbond = 0.0_dp ! Initialization..
      vg_coulomb = 0.0_dp ! Initialization..
      SELECT CASE (ewald_type)
      CASE (do_ewald_ewald)
         CALL ewald_multipole_evaluate(ewald_env, ewald_pw, fist_nonbond_env, cell, &
                                       particle_set, local_particles, vg_coulomb, pot_nonbond, thermo%e_neut, &
                                       thermo%e_self, multipoles%task, do_correction_bonded=do_correction_bonded, &
                                       do_forces=do_forces, do_stress=do_stress, do_efield=do_efield, &
                                       radii=multipoles%radii, charges=multipoles%charges, &
                                       dipoles=multipoles%dipoles, quadrupoles=multipoles%quadrupoles, &
                                       forces_local=forces_local, forces_glob=forces_glob, pv_local=pv_local, &
                                       pv_glob=pv_glob, iw=iw2, do_debug=do_debug, atomic_kind_set=atomic_kind_set, &
                                       mm_section=mm_section, efield0=efield0, efield1=efield1, efield2=efield2)
      CASE (do_ewald_pme)
         CPABORT("Multipole Ewald not yet implemented within a PME scheme!")
      CASE (do_ewald_spme)
         CPABORT("Multipole Ewald not yet implemented within a SPME scheme!")
      END SELECT
      CALL timestop(handle)
   END SUBROUTINE eval_pol_ewald

END MODULE fist_pol_scf
