propagation.F90

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!! Copyright (C) 2002-2006 M. Marques, A. Castro, A. Rubio, G. Bertsch
!!
!! This program is free software; you can redistribute it and/or modify
!! it under the terms of the GNU General Public License as published by
!! the Free Software Foundation; either version 2, or (at your option)
!! any later version.
!!
!! This program is distributed in the hope that it will be useful,
!! but WITHOUT ANY WARRANTY; without even the implied warranty of
!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!! GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License
!! along with this program; if not, write to the Free Software
!! Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
!! 02110-1301, USA.
!!
 
#include "global.h"
 
module propagation_oct_m
  use absorbing_boundaries_oct_m
  use batch_oct_m
  use batch_ops_oct_m
  use controlfunction_oct_m
  use debug_oct_m
  use density_oct_m
  use derivatives_oct_m
  use electrons_oct_m
  use electron_space_oct_m
  use energy_calc_oct_m
  use epot_oct_m
  use excited_states_oct_m
  use ext_partner_list_oct_m
  use forces_oct_m
  use gauge_field_oct_m
  use global_oct_m
  use grid_oct_m
  use hamiltonian_elec_oct_m
  use interaction_partner_oct_m
  use ion_dynamics_oct_m
  use ions_oct_m
  use, intrinsic :: iso_fortran_env
  use kpoints_oct_m
  use ks_potential_oct_m
  use lasers_oct_m
  use lalg_basic_oct_m
  use loct_oct_m
  use mesh_oct_m
  use mesh_function_oct_m
  use messages_oct_m
  use mpi_oct_m
  use multicomm_oct_m
  use namespace_oct_m
  use oct_exchange_oct_m
  use opt_control_state_oct_m
  use parser_oct_m
  use perturbation_ionic_oct_m
  use potential_interpolation_oct_m
  use propagator_elec_oct_m
  use propagator_base_oct_m
  use profiling_oct_m
  use restart_oct_m
  use space_oct_m
  use states_elec_oct_m
  use states_elec_dim_oct_m
  use states_elec_restart_oct_m
  use target_oct_m
  use target_low_oct_m
  use td_oct_m
  use td_write_oct_m
  use v_ks_oct_m
 
  implicit none
 
  private
 
  public ::               &
    propagation_mod_init, &
    propagate_forward,    &
    propagate_backward,   &
    fwd_step,             &
    bwd_step,             &
    bwd_step_2,           &
    oct_prop_t,           &
    oct_prop_init,        &
    oct_prop_check,       &
    oct_prop_end
 
 
  type oct_prop_t
    private
    integer :: number_checkpoints
    integer, allocatable :: iter(:)
    integer :: niter
    character(len=100) :: dirname
    type(restart_t) :: restart_load
    type(restart_t) :: restart_dump
  end type oct_prop_t
 
 
  integer :: niter_
  integer :: number_checkpoints_
  real(real64)   :: eta_
  real(real64)   :: delta_
  logical :: zbr98_
  logical :: gradients_
 
contains
 
  subroutine propagation_mod_init(niter, eta, delta, number_checkpoints, zbr98, gradients)
    integer, intent(in) :: niter
    real(real64),   intent(in) :: eta
    real(real64),   intent(in) :: delta
    integer, intent(in) :: number_checkpoints
    logical, intent(in) :: zbr98
    logical, intent(in) :: gradients
 
    assert(.not. (zbr98 .and. gradients))
 
    push_sub(propagation_mod_init)
 
    niter_              = niter
    eta_                = eta
    delta_              = delta
    number_checkpoints_ = number_checkpoints
    zbr98_              = zbr98
    gradients_          = gradients
 
    pop_sub(propagation_mod_init)
  end subroutine propagation_mod_init
  ! ---------------------------------------------------------
 
 
  subroutine propagate_forward(sys, td, par, tg, qcpsi, prop, write_iter)
    type(electrons_t),          intent(inout)  :: sys
    type(td_t),                 intent(inout)  :: td
    type(controlfunction_t),    intent(in)     :: par
    type(target_t),             intent(inout)  :: tg
    type(opt_control_state_t),  intent(inout)  :: qcpsi
    type(oct_prop_t), optional, intent(inout)  :: prop
    logical, optional,          intent(in)     :: write_iter
 
    integer :: ii, istep, ierr
    logical :: write_iter_ = .false.
    type(td_write_t)           :: write_handler
    real(real64), allocatable :: x_initial(:,:)
    logical :: vel_target_ = .false.
    type(states_elec_t), pointer :: psi
 
    real(real64) :: init_time, final_time
 
    push_sub(propagate_forward)
 
    message(1) = "Info: Forward propagation."
    call messages_info(1, namespace=sys%namespace)
 
    call controlfunction_to_h(par, sys%ext_partners)
 
    write_iter_ = .false.
    if (present(write_iter)) write_iter_ = write_iter
 
    psi => opt_control_point_qs(qcpsi)
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi%pack()
    call opt_control_get_classical(sys%ions, qcpsi)
 
    if (write_iter_) then
      call td_write_init(write_handler, sys%namespace, sys%space, sys%outp, sys%gr, sys%st, sys%hm, &
        sys%ions, sys%ext_partners, sys%ks, td%ions_dyn%ions_move(), &
        list_has_gauge_field(sys%ext_partners), sys%hm%kick, td%iter, td%max_iter, &
        td%dt, sys%mc)
      call td_write_data(write_handler)
    end if
 
    call hamiltonian_elec_not_adjoint(sys%hm)
 
    ! setup the Hamiltonian
    call density_calc(psi, sys%gr, psi%rho)
    call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners, time = m_zero)
    call sys%hm%ks_pot%run_zero_iter(td%tr%vks_old)
    if (td%ions_dyn%ions_move()) then
      call hamiltonian_elec_epot_generate(sys%hm, sys%namespace,  sys%space, sys%gr, sys%ions, &
        sys%ext_partners, psi, time = m_zero)
      call forces_calculate(sys%gr, sys%namespace, sys%ions, sys%hm, sys%ext_partners, psi, sys%ks, t = m_zero, dt = td%dt)
    end if
 
 
    if (target_type(tg) == oct_tg_hhgnew) then
      call target_init_propagation(tg)
    end if
 
    if (target_type(tg) == oct_tg_velocity .or. target_type(tg) == oct_tg_hhgnew) then
      safe_allocate_source_a(x_initial, sys%ions%pos)
      vel_target_ = .true.
      sys%ions%vel = m_zero
      sys%ions%tot_force = m_zero
    end if
 
    if (.not. target_move_ions(tg)) call epot_precalc_local_potential(sys%hm%ep, sys%namespace, sys%gr, sys%ions)
 
    call target_tdcalc(tg, sys%namespace, sys%space, sys%hm, sys%gr, sys%ions, sys%ext_partners, psi, 0, td%max_iter)
 
    if (present(prop)) then
      call oct_prop_dump_states(prop, sys%space, 0, psi, sys%gr, sys%kpoints, ierr)
      if (ierr /= 0) then
        message(1) = "Unable to write OCT states restart."
        call messages_warning(1, namespace=sys%namespace)
      end if
    end if
 
    init_time = loct_clock()
    if (mpi_grp_is_root(mpi_world)) call loct_progress_bar(-1, td%max_iter)
 
    ii = 1
    do istep = 1, td%max_iter
      ! time-iterate wavefunctions
 
      call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, psi, td%tr, istep*td%dt, td%dt, istep, &
        td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
 
      if (present(prop)) then
        call oct_prop_dump_states(prop, sys%space, istep, psi, sys%gr, sys%kpoints, ierr)
        if (ierr /= 0) then
          message(1) = "Unable to write OCT states restart."
          call messages_warning(1, namespace=sys%namespace)
        end if
      end if
 
      ! update
      call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners, time = istep*td%dt)
      call energy_calc_total(sys%namespace, sys%space, sys%hm, sys%gr, psi, sys%ext_partners)
 
      if (sys%hm%abs_boundaries%abtype == mask_absorbing) call zvmask(sys%gr, sys%hm, psi)
 
      ! if td_target
      call target_tdcalc(tg, sys%namespace, sys%space, sys%hm, sys%gr, sys%ions, sys%ext_partners, psi, istep, td%max_iter)
 
      ! only write in final run
      if (write_iter_) then
        call td_write_iter(write_handler, sys%namespace, sys%space, sys%outp, sys%gr, psi, sys%hm,  sys%ions, &
          sys%ext_partners, sys%hm%kick, sys%ks, td%dt, istep, sys%mc, sys%td%recalculate_gs)
        ii = ii + 1
        if (any(ii == sys%outp%output_interval + 1) .or. istep == td%max_iter) then ! output
          if (istep == td%max_iter) sys%outp%output_interval = ii - 1
          ii = istep
          call td_write_data(write_handler)
        end if
      end if
 
      if ((mod(istep, 100) == 0) .and. mpi_grp_is_root(mpi_world)) call loct_progress_bar(istep, td%max_iter)
    end do
    if (mpi_grp_is_root(mpi_world)) write(stdout, '(1x)')
 
    final_time = loct_clock()
    write(message(1),'(a,f12.2,a)') 'Propagation time: ', final_time - init_time, ' seconds.'
    call messages_info(1, namespace=sys%namespace)
 
    if (vel_target_) then
      sys%ions%pos = x_initial
      safe_deallocate_a(x_initial)
    end if
 
    call opt_control_set_classical(sys%ions, qcpsi)
 
    if (write_iter_) call td_write_end(write_handler)
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi%unpack()
    nullify(psi)
    pop_sub(propagate_forward)
  end subroutine propagate_forward
  ! ---------------------------------------------------------
 
 
  subroutine propagate_backward(sys, td, qcpsi, prop)
    type(electrons_t),         intent(inout) :: sys
    type(td_t),                intent(inout) :: td
    type(opt_control_state_t), intent(inout) :: qcpsi
    type(oct_prop_t),          intent(inout) :: prop
 
    integer :: istep, ierr
    type(states_elec_t), pointer :: psi
 
    push_sub(propagate_backward)
 
    message(1) = "Info: Backward propagation."
    call messages_info(1, namespace=sys%namespace)
 
    psi => opt_control_point_qs(qcpsi)
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi%pack()
 
    call hamiltonian_elec_adjoint(sys%hm)
 
    ! setup the Hamiltonian
    call density_calc(psi, sys%gr, psi%rho)
    call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners)
    call sys%hm%ks_pot%run_zero_iter(td%tr%vks_old)
 
    call oct_prop_dump_states(prop, sys%space, td%max_iter, psi, sys%gr, sys%kpoints, ierr)
    if (ierr /= 0) then
      message(1) = "Unable to write OCT states restart."
      call messages_warning(1, namespace=sys%namespace)
    end if
 
    if (mpi_grp_is_root(mpi_world)) call loct_progress_bar(-1, td%max_iter)
 
    do istep = td%max_iter, 1, -1
      call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, psi, td%tr, &
        (istep - 1)*td%dt, -td%dt, istep-1, td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
 
      call oct_prop_dump_states(prop, sys%space, istep - 1, psi, sys%gr, sys%kpoints, ierr)
      if (ierr /= 0) then
        message(1) = "Unable to write OCT states restart."
        call messages_warning(1, namespace=sys%namespace)
      end if
 
      call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners)
      if (mod(istep, 100) == 0 .and. mpi_grp_is_root(mpi_world)) call loct_progress_bar(td%max_iter - istep + 1, td%max_iter)
    end do
 
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi%unpack()
    nullify(psi)
    pop_sub(propagate_backward)
  end subroutine propagate_backward
  ! ---------------------------------------------------------
 
 
  subroutine fwd_step(sys, td, tg, par, par_chi, qcpsi, prop_chi, prop_psi)
    type(electrons_t),         intent(inout) :: sys
    type(td_t),                intent(inout) :: td
    type(target_t),            intent(inout) :: tg
    type(controlfunction_t),   intent(inout) :: par
    type(controlfunction_t),   intent(in)    :: par_chi
    type(opt_control_state_t), intent(inout) :: qcpsi
    type(oct_prop_t),          intent(inout) :: prop_chi
    type(oct_prop_t),          intent(inout) :: prop_psi
 
    integer :: i, ierr
    logical :: aux_fwd_propagation
    type(states_elec_t) :: psi2
    type(opt_control_state_t) :: qcchi
    type(controlfunction_t) :: par_prev
    type(propagator_base_t) :: tr_chi, tr_psi2
    type(states_elec_t), pointer :: psi, chi
 
    push_sub(fwd_step)
 
    message(1) = "Info: Forward propagation."
    call messages_info(1, namespace=sys%namespace)
 
    call controlfunction_to_realtime(par)
 
    call opt_control_state_null(qcchi)
    call opt_control_state_copy(qcchi, qcpsi)
 
    psi => opt_control_point_qs(qcpsi)
    chi => opt_control_point_qs(qcchi)
    call propagator_elec_copy(tr_chi, td%tr)
    ! The propagation of chi should not be self-consistent, because the Kohn-Sham
    ! potential used is the one created by psi. Note, however, that it is likely that
    ! the first two iterations are done self-consistently nonetheless.
    call propagator_elec_remove_scf_prop(tr_chi)
 
    aux_fwd_propagation = (target_mode(tg) == oct_targetmode_td .or. &
      (sys%hm%theory_level /= independent_particles .and. &
      .not. sys%ks%frozen_hxc))
    if (aux_fwd_propagation) then
      call states_elec_copy(psi2, psi)
      call controlfunction_copy(par_prev, par)
      if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi2%pack()
    end if
 
    ! setup forward propagation
    call density_calc(psi, sys%gr, psi%rho)
    call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners)
    call sys%hm%ks_pot%run_zero_iter(td%tr%vks_old)
    call sys%hm%ks_pot%run_zero_iter(tr_chi%vks_old)
    if (aux_fwd_propagation) then
      call propagator_elec_copy(tr_psi2, td%tr)
      call sys%hm%ks_pot%run_zero_iter(tr_psi2%vks_old)
    end if
 
    call oct_prop_dump_states(prop_psi, sys%space, 0, psi, sys%gr, sys%kpoints, ierr)
    if (ierr /= 0) then
      message(1) = "Unable to write OCT states restart."
      call messages_warning(1, namespace=sys%namespace)
    end if
    call oct_prop_load_states(prop_chi, sys%namespace, sys%space, chi, sys%gr, sys%kpoints, 0, ierr)
    if (ierr /= 0) then
      message(1) = "Unable to read OCT states restart."
      call messages_fatal(1, namespace=sys%namespace)
    end if
 
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi%pack()
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call chi%pack()
 
    do i = 1, td%max_iter
      call update_field(i, par, sys%space, sys%gr, sys%hm, sys%ext_partners, sys%ions, qcpsi, qcchi, par_chi, dir = 'f')
      call update_hamiltonian_elec_chi(i, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, sys%ext_partners, &
        td, tg, par_chi, sys%ions, psi2)
      call sys%hm%update(sys%gr, sys%namespace, sys%space, sys%ext_partners, time = (i - 1)*td%dt)
      call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, chi, tr_chi, i*td%dt, td%dt, i, &
        td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
      if (aux_fwd_propagation) then
        call update_hamiltonian_elec_psi(i, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, sys%ext_partners, &
          td, tg, par_prev, psi2, sys%ions)
        call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, psi2, tr_psi2, i*td%dt, td%dt, i, &
          td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
      end if
      call update_hamiltonian_elec_psi(i, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, &
        sys%ext_partners, td, tg, par, psi, sys%ions)
      call sys%hm%update(sys%gr, sys%namespace, sys%space, sys%ext_partners, time = (i - 1)*td%dt)
      call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, psi, td%tr, i*td%dt, td%dt, i, &
        td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
      call target_tdcalc(tg, sys%namespace, sys%space, sys%hm, sys%gr, sys%ions, sys%ext_partners, psi, i, td%max_iter)
 
      call oct_prop_dump_states(prop_psi, sys%space, i, psi, sys%gr, sys%kpoints, ierr)
      if (ierr /= 0) then
        message(1) = "Unable to write OCT states restart."
        call messages_warning(1, namespace=sys%namespace)
      end if
      call oct_prop_check(prop_chi, sys%namespace, sys%space, chi, sys%gr, sys%kpoints, i)
    end do
    call update_field(td%max_iter+1, par, sys%space, sys%gr, sys%hm, sys%ext_partners, sys%ions, qcpsi, qcchi, par_chi, dir = 'f')
 
    call density_calc(psi, sys%gr, psi%rho)
    call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners)
 
    if (target_mode(tg) == oct_targetmode_td .or. &
      (sys%hm%theory_level /= independent_particles .and. (.not. sys%ks%frozen_hxc))) then
      call states_elec_end(psi2)
      call controlfunction_end(par_prev)
    end if
 
    call controlfunction_to_basis(par)
    if (aux_fwd_propagation) call propagator_elec_end(tr_psi2)
    call states_elec_end(chi)
    call propagator_elec_end(tr_chi)
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi%unpack()
    nullify(psi)
    nullify(chi)
    pop_sub(fwd_step)
  end subroutine fwd_step
  ! ---------------------------------------------------------
 
 
  subroutine bwd_step(sys, td, tg, par, par_chi, qcchi, prop_chi, prop_psi)
    type(electrons_t),         intent(inout) :: sys
    type(td_t),                intent(inout) :: td
    type(target_t),            intent(inout) :: tg
    type(controlfunction_t),   intent(in)    :: par
    type(controlfunction_t),   intent(inout) :: par_chi
    type(opt_control_state_t), intent(inout) :: qcchi
    type(oct_prop_t),          intent(inout) :: prop_chi
    type(oct_prop_t),          intent(inout) :: prop_psi
 
    integer :: i, ierr
    type(propagator_base_t) :: tr_chi
    type(opt_control_state_t) :: qcpsi
    type(states_elec_t), pointer :: chi, psi
 
    push_sub(bwd_step)
 
    message(1) = "Info: Backward propagation."
    call messages_info(1, namespace=sys%namespace)
 
    call controlfunction_to_realtime(par_chi)
 
    chi => opt_control_point_qs(qcchi)
    psi => opt_control_point_qs(qcpsi)
 
    call propagator_elec_copy(tr_chi, td%tr)
    ! The propagation of chi should not be self-consistent, because the Kohn-Sham
    ! potential used is the one created by psi. Note, however, that it is likely that
    ! the first two iterations are done self-consistently nonetheless.
    call propagator_elec_remove_scf_prop(tr_chi)
 
    call states_elec_copy(psi, chi)
    call oct_prop_load_states(prop_psi, sys%namespace, sys%space, psi, sys%gr, sys%kpoints, td%max_iter, ierr)
    if (ierr /= 0) then
      message(1) = "Unable to read OCT states restart."
      call messages_fatal(1, namespace=sys%namespace)
    end if
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi%pack()
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call chi%pack()
 
    call density_calc(psi, sys%gr, psi%rho)
    call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners)
    call sys%hm%update(sys%gr, sys%namespace, sys%space, sys%ext_partners)
    call sys%hm%ks_pot%run_zero_iter(td%tr%vks_old)
    call sys%hm%ks_pot%run_zero_iter(tr_chi%vks_old)
 
    td%dt = -td%dt
    call oct_prop_dump_states(prop_chi, sys%space, td%max_iter, chi, sys%gr, sys%kpoints, ierr)
    if (ierr /= 0) then
      message(1) = "Unable to write OCT states restart."
      call messages_warning(1, namespace=sys%namespace)
    end if
 
    do i = td%max_iter, 1, -1
      call oct_prop_check(prop_psi, sys%namespace, sys%space, psi, sys%gr, sys%kpoints, i)
      call update_field(i, par_chi, sys%space, sys%gr, sys%hm, sys%ext_partners, sys%ions, qcpsi, qcchi, par, dir = 'b')
      call update_hamiltonian_elec_chi(i-1, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, sys%ext_partners, &
        td, tg, par_chi, sys%ions, psi)
      call sys%hm%update(sys%gr, sys%namespace, sys%space, sys%ext_partners, time = abs(i*td%dt))
      call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, chi, tr_chi, abs((i-1)*td%dt), td%dt, &
        i-1, td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
      call oct_prop_dump_states(prop_chi, sys%space, i-1, chi, sys%gr, sys%kpoints, ierr)
      if (ierr /= 0) then
        message(1) = "Unable to write OCT states restart."
        call messages_warning(1, namespace=sys%namespace)
      end if
      call update_hamiltonian_elec_psi(i-1, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, sys%ext_partners, &
        td, tg, par, psi, sys%ions)
      call sys%hm%update(sys%gr, sys%namespace, sys%space, sys%ext_partners, time = abs(i*td%dt))
      call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, psi, td%tr, abs((i-1)*td%dt), td%dt, &
        i-1, td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
    end do
    td%dt = -td%dt
    call update_field(0, par_chi, sys%space, sys%gr, sys%hm, sys%ext_partners, sys%ions, qcpsi, qcchi, par, dir = 'b')
 
    call density_calc(psi, sys%gr, psi%rho)
    call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners)
    call sys%hm%update(sys%gr, sys%namespace, sys%space, sys%ext_partners)
 
    call controlfunction_to_basis(par_chi)
    call states_elec_end(psi)
    call propagator_elec_end(tr_chi)
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call chi%unpack()
    nullify(chi)
    nullify(psi)
    pop_sub(bwd_step)
  end subroutine bwd_step
  ! ---------------------------------------------------------
 
 
  subroutine bwd_step_2(sys, td, tg, par, par_chi, qcchi, prop_chi, prop_psi)
    type(electrons_t),                 intent(inout) :: sys
    type(td_t),                        intent(inout) :: td
    type(target_t),                    intent(inout) :: tg
    type(controlfunction_t),           intent(in)    :: par
    type(controlfunction_t),           intent(inout) :: par_chi
    type(opt_control_state_t),         intent(inout) :: qcchi
    type(oct_prop_t),                  intent(inout) :: prop_chi
    type(oct_prop_t),                  intent(inout) :: prop_psi
 
    integer :: i, ierr, ik, ib
    logical :: freeze
    type(propagator_base_t) :: tr_chi
    type(opt_control_state_t) :: qcpsi
    type(states_elec_t) :: st_ref
    type(states_elec_t), pointer :: chi, psi
    real(real64), pointer :: q(:, :), p(:, :)
    real(real64), allocatable :: qtildehalf(:, :), qinitial(:, :)
    real(real64), allocatable :: vhxc(:, :)
    real(real64), allocatable :: fold(:, :), fnew(:, :)
    type(ion_state_t) :: ions_state_initial, ions_state_final
 
    real(real64) :: init_time, final_time
 
    push_sub(bwd_step_2)
 
    chi => opt_control_point_qs(qcchi)
    q => opt_control_point_q(qcchi)
    p => opt_control_point_p(qcchi)
    safe_allocate(qtildehalf(1:sys%ions%natoms, 1:sys%ions%space%dim))
    safe_allocate(qinitial(1:sys%ions%space%dim, 1:sys%ions%natoms))
 
    call propagator_elec_copy(tr_chi, td%tr)
    ! The propagation of chi should not be self-consistent, because the Kohn-Sham
    ! potential used is the one created by psi. Note, however, that it is likely that
    ! the first two iterations are done self-consistently nonetheless.
    call propagator_elec_remove_scf_prop(tr_chi)
 
    call opt_control_state_null(qcpsi)
    call opt_control_state_copy(qcpsi, qcchi)
    psi => opt_control_point_qs(qcpsi)
    call oct_prop_load_states(prop_psi, sys%namespace, sys%space, psi, sys%gr, sys%kpoints, td%max_iter, ierr)
    if (ierr /= 0) then
      message(1) = "Unable to read OCT states restart."
      call messages_fatal(1, namespace=sys%namespace)
    end if
 
    safe_allocate(vhxc(1:sys%gr%np, 1:sys%hm%d%nspin))
 
    call density_calc(psi, sys%gr, psi%rho)
    call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners)
    call sys%hm%update(sys%gr, sys%namespace, sys%space, sys%ext_partners)
    call sys%hm%ks_pot%run_zero_iter(td%tr%vks_old)
    call sys%hm%ks_pot%run_zero_iter(tr_chi%vks_old)
    td%dt = -td%dt
    call oct_prop_dump_states(prop_chi, sys%space, td%max_iter, chi, sys%gr, sys%kpoints, ierr)
    if (ierr /= 0) then
      message(1) = "Unable to write OCT states restart."
      call messages_warning(1, namespace=sys%namespace)
    end if
 
    call states_elec_copy(st_ref, psi)
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call psi%pack()
    if (sys%st%pack_states .and. sys%hm%apply_packed()) call st_ref%pack()
 
    if (td%ions_dyn%ions_move()) then
      call forces_calculate(sys%gr, sys%namespace, sys%ions, sys%hm, sys%ext_partners, &
        psi, sys%ks, t = td%max_iter*abs(td%dt), dt = td%dt)
    end if
 
    message(1) = "Info: Backward propagation."
    call messages_info(1, namespace=sys%namespace)
    if (mpi_grp_is_root(mpi_world)) call loct_progress_bar(-1, td%max_iter)
 
    init_time = loct_clock()
 
    do i = td%max_iter, 1, -1
 
      call oct_prop_check(prop_psi, sys%namespace, sys%space, psi, sys%gr, sys%kpoints, i)
      call update_field(i, par_chi, sys%space, sys%gr, sys%hm, sys%ext_partners, sys%ions, qcpsi, qcchi, par, dir = 'b')
 
      select case (td%tr%method)
 
      case (prop_explicit_runge_kutta4)
 
        call update_hamiltonian_elec_psi(i-1, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, sys%ext_partners, &
          td, tg, par, psi, sys%ions)
        call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, psi, td%tr, abs((i-1)*td%dt), td%dt, &
          i-1, td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler, qcchi = qcchi)
 
      case default
 
        if (td%ions_dyn%ions_move()) then
          qtildehalf = q
 
          call ion_dynamics_save_state(td%ions_dyn, sys%ions, ions_state_initial)
          call ion_dynamics_propagate(td%ions_dyn, sys%ions, abs((i-1)*td%dt), m_half * td%dt, sys%namespace)
          qinitial = sys%ions%pos
          call ion_dynamics_restore_state(td%ions_dyn, sys%ions, ions_state_initial)
 
          safe_allocate(fold(1:sys%ions%natoms, 1:sys%ions%space%dim))
          safe_allocate(fnew(1:sys%ions%natoms, 1:sys%ions%space%dim))
          call forces_costate_calculate(sys%gr, sys%namespace, sys%ions, sys%hm, psi, chi, fold, q)
 
          call ion_dynamics_verlet_step1(sys%ions, qtildehalf, p, fold, m_half * td%dt)
          call ion_dynamics_verlet_step1(sys%ions, q, p, fold, td%dt)
        end if
 
        if (td%ions_dyn%cell_relax()) then
          call messages_not_implemented("OCT with cell dynamics")
        end if
 
        ! Here propagate psi one full step, and then simply interpolate to get the state
        ! at half the time interval. Perhaps one could gain some accuracy by performing two
        ! successive propagations of half time step.
        call update_hamiltonian_elec_psi(i-1, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, sys%ext_partners, &
          td, tg, par, psi, sys%ions)
 
        do ik = psi%d%kpt%start, psi%d%kpt%end
          do ib = psi%group%block_start, psi%group%block_end
            call psi%group%psib(ib, ik)%copy_data_to(sys%gr%np, st_ref%group%psib(ib, ik))
          end do
        end do
 
        vhxc(:, :) = sys%hm%ks_pot%vhxc(:, :)
        call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, psi, td%tr, abs((i-1)*td%dt), td%dt, &
          i-1, td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
 
        if (td%ions_dyn%ions_move()) then
          call ion_dynamics_save_state(td%ions_dyn, sys%ions, ions_state_final)
          sys%ions%pos = qinitial
          call hamiltonian_elec_epot_generate(sys%hm, sys%namespace, sys%space, sys%gr, sys%ions, &
            sys%ext_partners, psi, time = abs((i-1)*td%dt))
        end if
 
        do ik = psi%d%kpt%start, psi%d%kpt%end
          do ib = psi%group%block_start, psi%group%block_end
            call batch_scal(sys%gr%np, cmplx(m_half, m_zero, real64) , &
              st_ref%group%psib(ib, ik))
            call batch_axpy(sys%gr%np, cmplx(m_half, m_zero, real64) , &
              psi%group%psib(ib, ik), st_ref%group%psib(ib, ik))
          end do
        end do
 
        sys%hm%ks_pot%vhxc(:, :) = m_half * (sys%hm%ks_pot%vhxc(:, :) + vhxc(:, :))
        call update_hamiltonian_elec_chi(i-1, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, sys%ext_partners, &
          td, tg, par, sys%ions, st_ref, qtildehalf)
        freeze = ion_dynamics_freeze(td%ions_dyn)
        call propagator_elec_dt(sys%ks, sys%namespace, sys%space, sys%hm, sys%gr, chi, tr_chi, abs((i-1)*td%dt), td%dt, &
          i-1, td%ions_dyn, sys%ions, sys%ext_partners, sys%mc, sys%outp, td%write_handler)
        if (freeze) call ion_dynamics_unfreeze(td%ions_dyn)
 
        if (td%ions_dyn%ions_move()) then
          call ion_dynamics_restore_state(td%ions_dyn, sys%ions, ions_state_final)
          call hamiltonian_elec_epot_generate(sys%hm, sys%namespace, sys%space, sys%gr, sys%ions, &
            sys%ext_partners, psi, time = abs((i-1)*td%dt))
          call forces_calculate(sys%gr, sys%namespace, sys%ions, sys%hm, sys%ext_partners, &
            psi, sys%ks, t = abs((i-1)*td%dt), dt = td%dt)
          call forces_costate_calculate(sys%gr, sys%namespace, sys%ions, sys%hm, psi, chi, fnew, q)
          call ion_dynamics_verlet_step2(sys%ions, p, fold, fnew, td%dt)
          safe_deallocate_a(fold)
          safe_deallocate_a(fnew)
        end if
 
        sys%hm%ks_pot%vhxc(:, :) = vhxc(:, :)
 
      end select
 
      call oct_prop_dump_states(prop_chi, sys%space, i-1, chi, sys%gr, sys%kpoints, ierr)
      if (ierr /= 0) then
        message(1) = "Unable to write OCT states restart."
        call messages_warning(1, namespace=sys%namespace)
      end if
 
      if ((mod(i, 100) == 0).and. mpi_grp_is_root(mpi_world)) call loct_progress_bar(td%max_iter-i, td%max_iter)
    end do
    if (mpi_grp_is_root(mpi_world)) then
      call loct_progress_bar(td%max_iter, td%max_iter)
      write(stdout, '(1x)')
    end if
 
    final_time = loct_clock()
    write(message(1),'(a,f12.2,a)') 'Propagation time: ', final_time - init_time, ' seconds.'
    call messages_info(1, namespace=sys%namespace)
 
    call states_elec_end(st_ref)
 
    td%dt = -td%dt
    call update_hamiltonian_elec_psi(0, sys%namespace, sys%space, sys%gr, sys%ks, sys%hm, sys%ext_partners, &
      td, tg, par, psi, sys%ions)
    call update_field(0, par_chi, sys%space, sys%gr, sys%hm, sys%ext_partners, sys%ions, qcpsi, qcchi, par, dir = 'b')
 
    call density_calc(psi, sys%gr, psi%rho)
    call v_ks_calc(sys%ks, sys%namespace, sys%space, sys%hm, psi, sys%ions, sys%ext_partners)
    call sys%hm%update(sys%gr, sys%namespace, sys%space, sys%ext_partners)
 
    call propagator_elec_end(tr_chi)
 
    safe_deallocate_a(vhxc)
    call states_elec_end(psi)
 
    nullify(chi)
    nullify(psi)
    nullify(q)
    nullify(p)
    safe_deallocate_a(qtildehalf)
    safe_deallocate_a(qinitial)
    pop_sub(bwd_step_2)
  end subroutine bwd_step_2
  ! ----------------------------------------------------------
 
 
  ! ----------------------------------------------------------
  !
  ! ----------------------------------------------------------
  subroutine update_hamiltonian_elec_chi(iter, namespace, space, gr, ks, hm, ext_partners, td, tg, par_chi, ions, st, qtildehalf)
    integer,                  intent(in)    :: iter
    type(namespace_t),        intent(in)    :: namespace
    class(space_t),           intent(in)    :: space
    type(grid_t),             intent(inout) :: gr
    type(v_ks_t),             intent(inout) :: ks
    type(hamiltonian_elec_t), intent(inout) :: hm
    type(partner_list_t),     intent(in)    :: ext_partners
    type(td_t),               intent(inout) :: td
    type(target_t),           intent(inout) :: tg
    type(controlfunction_t),  intent(in)    :: par_chi
    type(ions_t),             intent(in)    :: ions
    type(states_elec_t),      intent(inout) :: st
    real(real64),   optional, intent(in)    :: qtildehalf(:, :)
 
    type(states_elec_t) :: inh
    type(perturbation_ionic_t), pointer :: pert
    integer :: j, iatom, idim
    complex(real64), allocatable :: dvpsi(:, :, :), zpsi(:, :), inhzpsi(:, :)
    integer :: ist, ik, ib
 
    push_sub(update_hamiltonian_elec_chi)
 
    assert(.not. st%parallel_in_states)
    assert(.not. st%d%kpt%parallel)
 
    if (target_mode(tg) == oct_targetmode_td) then
      call states_elec_copy(inh, st)
      call target_inh(st, gr, hm%kpoints, tg, abs(td%dt)*iter, inh, iter)
      call hamiltonian_elec_set_inh(hm, inh)
      call states_elec_end(inh)
    end if
 
    if (td%ions_dyn%ions_move()) then
      call states_elec_copy(inh, st)
      safe_allocate(dvpsi(1:gr%np_part, 1:st%d%dim, 1:space%dim))
      do ik = inh%d%kpt%start, inh%d%kpt%end
        do ib = inh%group%block_start, inh%group%block_end
          call batch_set_zero(inh%group%psib(ib, ik))
        end do
      end do
      safe_allocate(zpsi(1:gr%np_part, 1:st%d%dim))
      safe_allocate(inhzpsi(1:gr%np_part, 1:st%d%dim))
      do ist = 1, st%nst
        do ik = 1, st%nik
 
          call states_elec_get_state(st, gr, ist, ik, zpsi)
          call states_elec_get_state(inh, gr, ist, ik, inhzpsi)
 
          pert => perturbation_ionic_t(namespace, ions)
          do iatom = 1, ions%natoms
            call pert%setup_atom(iatom)
            do idim = 1, space%dim
              call pert%setup_dir(idim)
              call pert%zapply(namespace, space, gr, hm, ik, zpsi(:, :), dvpsi(:, :, idim))
 
              call lalg_axpy(gr%np, st%d%dim, -st%occ(ist, ik)*qtildehalf(iatom, idim), &
                dvpsi(:, :, idim), inhzpsi(:,  :))
            end do
          end do
          safe_deallocate_p(pert)
          call states_elec_set_state(inh, gr, ist, ik, inhzpsi)
        end do
      end do
 
      safe_deallocate_a(zpsi)
      safe_deallocate_a(inhzpsi)
      safe_deallocate_a(dvpsi)
      call hamiltonian_elec_set_inh(hm, inh)
      call states_elec_end(inh)
    end if
 
    if (hm%theory_level /= independent_particles .and. (.not. ks%frozen_hxc)) then
      call density_calc(st, gr, st%rho)
      call oct_exchange_set(hm%oct_exchange, st, gr)
    end if
 
    call hamiltonian_elec_adjoint(hm)
 
    do j = iter - 2, iter + 2
      if (j >= 0 .and. j <= td%max_iter) then
        call controlfunction_to_h_val(par_chi, ext_partners, j+1)
      end if
    end do
 
    pop_sub(update_hamiltonian_elec_chi)
  end subroutine update_hamiltonian_elec_chi
  ! ---------------------------------------------------------
 
 
  ! ----------------------------------------------------------
  !
  ! ----------------------------------------------------------
  subroutine update_hamiltonian_elec_psi(iter, namespace, space, gr, ks, hm, ext_partners, td, tg, par, st, ions)
    integer,                  intent(in)    :: iter
    type(namespace_t),        intent(in)    :: namespace
    type(electron_space_t),   intent(in)    :: space
    type(grid_t),             intent(inout) :: gr
    type(v_ks_t),             intent(inout) :: ks
    type(hamiltonian_elec_t), intent(inout) :: hm
    type(partner_list_t),     intent(in)    :: ext_partners
    type(td_t),               intent(inout) :: td
    type(target_t),           intent(inout) :: tg
    type(controlfunction_t),  intent(in)    :: par
    type(states_elec_t),      intent(inout) :: st
    type(ions_t),             intent(in)    :: ions
 
    integer :: j
 
    push_sub(update_hamiltonian_elec_psi)
 
    if (target_mode(tg) == oct_targetmode_td) then
      call hamiltonian_elec_remove_inh(hm)
    end if
 
    if (td%ions_dyn%ions_move()) then
      call hamiltonian_elec_remove_inh(hm)
    end if
 
    if (hm%theory_level /= independent_particles .and. (.not. ks%frozen_hxc)) then
      call oct_exchange_remove(hm%oct_exchange)
    end if
 
    call hamiltonian_elec_not_adjoint(hm)
 
    do j = iter - 2, iter + 2
      if (j >= 0 .and. j <= td%max_iter) then
        call controlfunction_to_h_val(par, ext_partners, j+1)
      end if
    end do
    if (hm%theory_level /= independent_particles .and. (.not. ks%frozen_hxc)) then
      call density_calc(st, gr, st%rho)
      call v_ks_calc(ks, namespace, space, hm, st, ions, ext_partners)
      call hm%update(gr, namespace, space, ext_partners)
    end if
 
    pop_sub(update_hamiltonian_elec_psi)
  end subroutine update_hamiltonian_elec_psi
  ! ---------------------------------------------------------
 
 
  ! ---------------------------------------------------------
  subroutine calculate_g(space, gr, hm, lasers, psi, chi, dl, dq)
    class(space_t),                 intent(in)    :: space
    type(grid_t),                   intent(inout) :: gr
    type(hamiltonian_elec_t),       intent(in)    :: hm
    type(lasers_t),                 intent(in)    :: lasers
    type(states_elec_t),            intent(inout) :: psi
    type(states_elec_t),            intent(inout) :: chi
    complex(real64),                intent(inout) :: dl(:), dq(:)
 
    complex(real64), allocatable :: zpsi(:, :), zoppsi(:, :)
    integer :: no_parameters, j, ik, p
 
    push_sub(calculate_g)
 
    no_parameters = lasers%no_lasers
 
    safe_allocate(zpsi(1:gr%np_part, 1:chi%d%dim))
    safe_allocate(zoppsi(1:gr%np_part, 1:chi%d%dim))
 
    do j = 1, no_parameters
 
      dl(j) = m_z0
      do ik = 1, psi%nik
        do p = 1, psi%nst
 
          call states_elec_get_state(psi, gr, p, ik, zpsi)
 
          zoppsi = m_z0
          if (allocated(hm%ep%a_static)) then
            call vlaser_operator_linear(lasers%lasers(j), gr%der, hm%d, zpsi, &
              zoppsi, ik, hm%ep%gyromagnetic_ratio, hm%ep%a_static)
          else
            call vlaser_operator_linear(lasers%lasers(j), gr%der, hm%d, zpsi, &
              zoppsi, ik, hm%ep%gyromagnetic_ratio)
          end if
 
          call states_elec_get_state(chi, gr, p, ik, zpsi)
          dl(j) = dl(j) + zmf_dotp(gr, psi%d%dim, zpsi, zoppsi)
        end do
      end do
 
      ! The quadratic part should only be computed if necessary.
      if (laser_kind(lasers%lasers(j)) == e_field_magnetic) then
 
        dq(j) = m_z0
        do ik = 1, psi%nik
          do p = 1, psi%nst
            zoppsi = m_z0
 
            call states_elec_get_state(psi, gr, p, ik, zpsi)
            call vlaser_operator_quadratic(lasers%lasers(j), gr, space, zpsi, zoppsi)
 
            call states_elec_get_state(chi, gr, p, ik, zpsi)
            dq(j) = dq(j) + zmf_dotp(gr, psi%d%dim, zpsi, zoppsi)
 
          end do
        end do
 
      else
        dq(j) = m_z0
      end if
    end do
 
    safe_deallocate_a(zpsi)
    safe_deallocate_a(zoppsi)
 
    pop_sub(calculate_g)
  end subroutine calculate_g
  ! ---------------------------------------------------------
 
 
 
 
  subroutine update_field(iter, cp, space, gr, hm, ext_partners, ions, qcpsi, qcchi, cpp, dir)
    class(space_t),            intent(in)    :: space
    integer,                   intent(in)    :: iter
    type(controlfunction_t),   intent(inout) :: cp
    type(grid_t),              intent(inout) :: gr
    type(hamiltonian_elec_t),  intent(in)    :: hm
    type(partner_list_t),      intent(in)    :: ext_partners
    type(ions_t),              intent(in)    :: ions
    type(opt_control_state_t), intent(inout) :: qcpsi
    type(opt_control_state_t), intent(inout) :: qcchi
    type(controlfunction_t),   intent(in)    :: cpp
    character(len=1),          intent(in)    :: dir
 
    complex(real64) :: d1, pol(3)
    complex(real64), allocatable  :: dl(:), dq(:), zpsi(:, :), zchi(:, :)
    real(real64), allocatable :: d(:)
    integer :: j, no_parameters, iatom
    type(states_elec_t), pointer :: psi, chi
    real(real64), pointer :: q(:, :)
    type(lasers_t), pointer :: lasers
 
    push_sub(update_field)
 
    psi => opt_control_point_qs(qcpsi)
    chi => opt_control_point_qs(qcchi)
    q => opt_control_point_q(qcchi)
 
    no_parameters = controlfunction_number(cp)
 
    safe_allocate(dl(1:no_parameters))
    safe_allocate(dq(1:no_parameters))
    safe_allocate( d(1:no_parameters))
 
 
    lasers => list_get_lasers(ext_partners)
    if(associated(lasers)) then
      call calculate_g(space, gr, hm, lasers, psi, chi, dl, dq)
    end if
 
    d1 = m_z1
    if (zbr98_) then
      safe_allocate(zpsi(1:gr%np, 1:psi%d%dim))
      safe_allocate(zchi(1:gr%np, 1:chi%d%dim))
 
      call states_elec_get_state(psi, gr, 1, 1, zpsi)
      call states_elec_get_state(chi, gr, 1, 1, zchi)
 
      d1 = zmf_dotp(gr, psi%d%dim, zpsi, zchi)
      do j = 1, no_parameters
        d(j) = aimag(d1*dl(j)) / controlfunction_alpha(cp, j)
      end do
 
      safe_deallocate_a(zpsi)
      safe_deallocate_a(zchi)
 
    elseif (gradients_) then
      do j = 1, no_parameters
        d(j) = m_two * aimag(dl(j))
      end do
    else
      do j = 1, no_parameters
        d(j) = aimag(dl(j)) / controlfunction_alpha(cp, j)
      end do
    end if
 
    ! This is for the classical target.
    if (dir == 'b' .and. associated(lasers)) then
      pol = laser_polarization(lasers%lasers(1))
      do iatom = 1, ions%natoms
        d(1) = d(1) - ions%charge(iatom) * real(sum(pol(1:ions%space%dim)*q(iatom, 1:ions%space%dim)), real64)
      end do
    end if
 
 
    if (dir == 'f') then
      call controlfunction_update(cp, cpp, dir, iter, delta_, d, dq)
    else
      call controlfunction_update(cp, cpp, dir, iter, eta_, d, dq)
    end if
 
    nullify(q)
    nullify(psi)
    nullify(chi)
    safe_deallocate_a(d)
    safe_deallocate_a(dl)
    safe_deallocate_a(dq)
    pop_sub(update_field)
  end subroutine update_field
  ! ---------------------------------------------------------
 
 
  ! ---------------------------------------------------------
  subroutine oct_prop_init(prop, namespace, dirname, mesh, mc)
    type(oct_prop_t),  intent(inout) :: prop
    type(namespace_t), intent(in)    :: namespace
    character(len=*),  intent(in)    :: dirname
    class(mesh_t),     intent(in)    :: mesh
    type(multicomm_t), intent(in)    :: mc
 
    integer :: j, ierr
 
    push_sub(oct_prop_init)
 
    prop%dirname = dirname
    prop%niter = niter_
    prop%number_checkpoints = number_checkpoints_
 
    ! The OCT_DIR//trim(dirname) will be used to write and read information during the calculation,
    ! so they need to use the same path.
    call restart_init(prop%restart_dump, namespace, restart_oct, restart_type_dump, mc, ierr, mesh=mesh)
    call restart_init(prop%restart_load, namespace, restart_oct, restart_type_load, mc, ierr, mesh=mesh)
 
    safe_allocate(prop%iter(1:prop%number_checkpoints+2))
    prop%iter(1) = 0
    do j = 1, prop%number_checkpoints
      prop%iter(j+1) = nint(real(niter_, real64) /(prop%number_checkpoints+1) * j)
    end do
    prop%iter(prop%number_checkpoints+2) = niter_
 
    pop_sub(oct_prop_init)
  end subroutine oct_prop_init
  ! ---------------------------------------------------------
 
 
  ! ---------------------------------------------------------
  subroutine oct_prop_end(prop)
    type(oct_prop_t), intent(inout) :: prop
 
    push_sub(oct_prop_end)
 
    call restart_end(prop%restart_load)
    call restart_end(prop%restart_dump)
 
    safe_deallocate_a(prop%iter)
    ! This routine should maybe delete the files?
 
    pop_sub(oct_prop_end)
  end subroutine oct_prop_end
  ! ---------------------------------------------------------
 
 
  ! ---------------------------------------------------------
  subroutine oct_prop_check(prop, namespace, space, psi, mesh, kpoints, iter)
    type(oct_prop_t),    intent(inout) :: prop
    type(namespace_t),   intent(in)    :: namespace
    class(space_t),      intent(in)    :: space
    type(states_elec_t), intent(inout) :: psi
    class(mesh_t),       intent(in)    :: mesh
    type(kpoints_t),     intent(in)    :: kpoints
    integer,             intent(in)    :: iter
 
    type(states_elec_t) :: stored_st
    character(len=80) :: dirname
    integer :: j, ierr
    complex(real64) :: overlap, prev_overlap
    real(real64), parameter :: WARNING_THRESHOLD = 1.0e-2_real64
 
    push_sub(oct_prop_check)
 
    do j = 1, prop%number_checkpoints + 2
      if (prop%iter(j) == iter) then
        call states_elec_copy(stored_st, psi)
        write(dirname,'(a, i4.4)') trim(prop%dirname), j
        call restart_open_dir(prop%restart_load, dirname, ierr)
        if (ierr == 0) then
          call states_elec_load(prop%restart_load, namespace, space, stored_st, mesh, kpoints, ierr, verbose=.false.)
        end if
        if (ierr /= 0) then
          message(1) = "Unable to read wavefunctions from '"//trim(dirname)//"'."
          call messages_fatal(1, namespace=namespace)
        end if
        call restart_close_dir(prop%restart_load)
        prev_overlap = zstates_elec_mpdotp(namespace, mesh, stored_st, stored_st)
        overlap = zstates_elec_mpdotp(namespace, mesh, stored_st, psi)
        if (abs(overlap - prev_overlap) > warning_threshold) then
          write(message(1), '(a,es13.4)') &
            "Forward-backward propagation produced an error of", abs(overlap-prev_overlap)
          write(message(2), '(a,i8)') "Iter = ", iter
          call messages_warning(2, namespace=namespace)
        end if
        ! Restore state only if the number of checkpoints is larger than zero.
        if (prop%number_checkpoints > 0) then
          call states_elec_end(psi)
          call states_elec_copy(psi, stored_st)
        end if
        call states_elec_end(stored_st)
      end if
    end do
    pop_sub(oct_prop_check)
  end subroutine oct_prop_check
  ! ---------------------------------------------------------
 
 
  ! ---------------------------------------------------------
  subroutine oct_prop_dump_states(prop, space, iter, psi, mesh, kpoints, ierr)
    type(oct_prop_t),    intent(inout) :: prop
    class(space_t),      intent(in)    :: space
    integer,             intent(in)    :: iter
    type(states_elec_t), intent(in)    :: psi
    class(mesh_t),       intent(in)    :: mesh
    type(kpoints_t),     intent(in)    :: kpoints
    integer,             intent(out)   :: ierr
 
    integer :: j, err
    character(len=80) :: dirname
 
    push_sub(oct_prop_dump_states)
 
    ierr = 0
 
    if (restart_skip(prop%restart_dump)) then
      pop_sub(oct_prop_dump_states)
      return
    end if
 
    message(1) = "Debug: Writing OCT propagation states restart."
    call messages_info(1, debug_only=.true.)
 
    do j = 1, prop%number_checkpoints + 2
      if (prop%iter(j) == iter) then
        write(dirname,'(a,i4.4)') trim(prop%dirname), j
        call restart_open_dir(prop%restart_dump, dirname, err)
        if (err == 0) then
          call states_elec_dump(prop%restart_dump, space, psi, mesh, kpoints, err, iter, verbose = .false.)
        end if
        if (err /= 0) then
          message(1) = "Unable to write wavefunctions to '"//trim(dirname)//"'."
          call messages_warning(1)
          ierr = ierr + 2**j
        end if
        call restart_close_dir(prop%restart_dump)
      end if
    end do
 
    message(1) = "Debug: Writing OCT propagation states restart done."
    call messages_info(1, debug_only=.true.)
 
    pop_sub(oct_prop_dump_states)
  end subroutine oct_prop_dump_states
  ! ---------------------------------------------------------
 
 
  ! ---------------------------------------------------------
  subroutine oct_prop_load_states(prop, namespace, space, psi, mesh, kpoints, iter, ierr)
    type(oct_prop_t),    intent(inout) :: prop
    type(namespace_t),   intent(in)    :: namespace
    class(space_t),      intent(in)    :: space
    type(states_elec_t), intent(inout) :: psi
    class(mesh_t),       intent(in)    :: mesh
    type(kpoints_t),     intent(in)    :: kpoints
    integer,             intent(in)    :: iter
    integer,             intent(out)   :: ierr
 
    integer :: j, err
    character(len=80) :: dirname
 
    push_sub(oct_prop_load_states)
 
    ierr = 0
 
    if (restart_skip(prop%restart_load)) then
      ierr = -1
      pop_sub(oct_prop_load_states)
      return
    end if
 
    message(1) = "Debug: Reading OCT propagation states restart."
    call messages_info(1, namespace=namespace, debug_only=.true.)
 
    do j = 1, prop%number_checkpoints + 2
      if (prop%iter(j) == iter) then
        write(dirname,'(a, i4.4)') trim(prop%dirname), j
        call restart_open_dir(prop%restart_load, dirname, err)
        if (err == 0) then
          call states_elec_load(prop%restart_load, namespace, space, psi, mesh, kpoints, err, verbose=.false.)
        end if
        if (err /= 0) then
          message(1) = "Unable to read wavefunctions from '"//trim(dirname)//"'."
          call messages_warning(1, namespace=namespace)
          ierr = ierr + 2**j
        end if
        call restart_close_dir(prop%restart_load)
      end if
    end do
 
    message(1) = "Debug: Reading OCT propagation states restart done."
    call messages_info(1, namespace=namespace, debug_only=.true.)
 
    pop_sub(oct_prop_load_states)
  end subroutine oct_prop_load_states
  ! ---------------------------------------------------------
 
  ! ---------------------------------------------------------
  subroutine vlaser_operator_quadratic(laser, mesh, space, psi, hpsi)
    type(laser_t),       intent(in)    :: laser
    class(mesh_t),       intent(in)    :: mesh
    class(space_t),      intent(in)    :: space
    complex(real64),     intent(inout) :: psi(:,:)
    complex(real64),     intent(inout) :: hpsi(:,:)
 
    integer :: ip
    logical :: vector_potential, magnetic_field
 
    real(real64) :: a_field(3), a_field_prime(3), bb(3), b_prime(3)
    real(real64), allocatable :: aa(:, :), a_prime(:, :)
 
    push_sub(vlaser_operator_quadratic)
 
    a_field = m_zero
 
    vector_potential = .false.
    magnetic_field = .false.
 
    select case (laser_kind(laser))
    case (e_field_electric) ! do nothing
    case (e_field_magnetic)
      if (.not. allocated(aa)) then
        safe_allocate(aa(1:mesh%np_part, 1:space%dim))
        aa = m_zero
        safe_allocate(a_prime(1:mesh%np_part, 1:space%dim))
      end if
      a_prime = m_zero
      call laser_vector_potential(laser, mesh, a_prime)
      aa = aa + a_prime
      b_prime = m_zero
      call laser_field(laser, b_prime(1:space%dim))
      bb = bb + b_prime
      magnetic_field = .true.
    case (e_field_vector_potential)
      a_field_prime = m_zero
      call laser_field(laser, a_field_prime(1:space%dim))
      a_field = a_field + a_field_prime
      vector_potential = .true.
    end select
 
    if (magnetic_field) then
      do ip = 1, mesh%np
        hpsi(ip, :) = hpsi(ip, :) + m_half * &
          dot_product(aa(ip, 1:space%dim), aa(ip, 1:space%dim)) * psi(ip, :) / p_c**2
      end do
      safe_deallocate_a(aa)
      safe_deallocate_a(a_prime)
    end if
    if (vector_potential) then
      do ip = 1, mesh%np
        hpsi(ip, :) = hpsi(ip, :) + m_half * &
          dot_product(a_field(1:space%dim), a_field(1:space%dim))*psi(ip, :) / p_c**2
      end do
    end if
 
    pop_sub(vlaser_operator_quadratic)
  end subroutine vlaser_operator_quadratic
 
  ! ---------------------------------------------------------
  subroutine vlaser_operator_linear(laser, der, std, psi, hpsi, ik, gyromagnetic_ratio, a_static)
    type(laser_t),               intent(in)      :: laser
    type(derivatives_t),         intent(in)      :: der
    type(states_elec_dim_t),     intent(in)      :: std
    complex(real64), contiguous, intent(inout)   :: psi(:,:)
    complex(real64),             intent(inout)   :: hpsi(:,:)
    integer,                     intent(in)      :: ik
    real(real64),                intent(in)      :: gyromagnetic_ratio
    real(real64), optional,      intent(in)      :: a_static(:,:)
 
    integer :: ip, idim
    logical :: electric_field, vector_potential, magnetic_field
    complex(real64), allocatable :: grad(:, :, :), lhpsi(:, :)
 
    real(real64) :: a_field(3), a_field_prime(3), bb(3), b_prime(3)
 
    real(real64), allocatable :: vv(:), pot(:), aa(:, :), a_prime(:, :)
 
    push_sub(vlaser_operator_linear)
 
    a_field = m_zero
 
    electric_field = .false.
    vector_potential = .false.
    magnetic_field = .false.
 
    select case (laser_kind(laser))
    case (e_field_scalar_potential)
      if (.not. allocated(vv)) then
        safe_allocate(vv(1:der%mesh%np))
      end if
      vv = m_zero
      call laser_potential(laser, der%mesh, vv)
      electric_field = .true.
 
    case (e_field_electric)
      if (.not. allocated(vv)) then
        safe_allocate(vv(1:der%mesh%np))
        vv = m_zero
        safe_allocate(pot(1:der%mesh%np))
      end if
      pot = m_zero
      call laser_potential(laser, der%mesh, pot)
      call lalg_axpy(der%mesh%np, m_one, pot, vv)
      electric_field = .true.
      safe_deallocate_a(pot)
 
    case (e_field_magnetic)
      if (.not. allocated(aa)) then
        safe_allocate(aa(1:der%mesh%np_part, 1:der%dim))
        aa = m_zero
        safe_allocate(a_prime(1:der%mesh%np_part, 1:der%dim))
      end if
      a_prime = m_zero
      call laser_vector_potential(laser, der%mesh, a_prime)
      aa = aa + a_prime
      b_prime = m_zero
      call laser_field(laser, b_prime(1:der%dim))
      bb = bb + b_prime
      magnetic_field = .true.
    case (e_field_vector_potential)
      a_field_prime = m_zero
      call laser_field(laser, a_field_prime(1:der%dim))
      a_field = a_field + a_field_prime
      vector_potential = .true.
    end select
 
    if (electric_field) then
      do idim = 1, std%dim
        hpsi(1:der%mesh%np, idim)= hpsi(1:der%mesh%np, idim) + vv(1:der%mesh%np) * psi(1:der%mesh%np, idim)
      end do
      safe_deallocate_a(vv)
    end if
 
    if (magnetic_field) then
      safe_allocate(grad(1:der%mesh%np_part, 1:der%dim, 1:std%dim))
 
      do idim = 1, std%dim
        call zderivatives_grad(der, psi(:, idim), grad(:, :, idim))
      end do
 
      ! If there is a static magnetic field, its associated vector potential is coupled with
      ! the time-dependent one defined as a "laser" (ideally one should just add them all and
      ! do the calculation only once...). Note that h%ep%a_static already has been divided
      ! by P_c, and therefore here we only divide by P_c, and not P_c**2.
      !
      ! We put a minus sign, since for the moment vector potential for
      ! lasers and for the static magnetic field use a different
      ! convetion.
      if (present(a_static)) then
        do ip = 1, der%mesh%np
          hpsi(ip, :) = hpsi(ip, :) - dot_product(aa(ip, 1:der%dim), a_static(ip, 1:der%dim)) * psi(ip, :) / p_c
        end do
      end if
 
      select case (std%ispin)
      case (unpolarized, spin_polarized)
        do ip = 1, der%mesh%np
          hpsi(ip, 1) = hpsi(ip, 1) - m_zi * dot_product(aa(ip, 1:der%dim), grad(ip, 1:der%dim, 1)) / p_c
        end do
      case (spinors)
        do ip = 1, der%mesh%np
          do idim = 1, std%dim
            hpsi(ip, idim) = hpsi(ip, idim) - m_zi * &
              dot_product(aa(ip, 1:der%dim), grad(ip, 1:der%dim, idim)) / p_c
          end do
        end do
      end select
 
 
      select case (std%ispin)
      case (spin_polarized)
        safe_allocate(lhpsi(1:der%mesh%np, 1:std%dim))
        if (modulo(ik+1, 2) == 0) then ! we have a spin down
          lhpsi(1:der%mesh%np, 1) = - m_half / p_c * norm2(bb) * psi(1:der%mesh%np, 1)
        else
          lhpsi(1:der%mesh%np, 1) = + m_half / p_c * norm2(bb) * psi(1:der%mesh%np, 1)
        end if
        hpsi(1:der%mesh%np, :) = hpsi(1:der%mesh%np, :) + (gyromagnetic_ratio * m_half) * lhpsi(1:der%mesh%np, :)
        safe_deallocate_a(lhpsi)
 
      case (spinors)
        safe_allocate(lhpsi(1:der%mesh%np, 1:std%dim))
        lhpsi(1:der%mesh%np, 1) = m_half / p_c * (bb(3) * psi(1:der%mesh%np, 1) &
          + cmplx(bb(1), -bb(2), real64) * psi(1:der%mesh%np, 2))
        lhpsi(1:der%mesh%np, 2) = m_half / p_c * (-bb(3) * psi(1:der%mesh%np, 2) &
          + cmplx(bb(1), bb(2), real64) * psi(1:der%mesh%np, 1))
        hpsi(1:der%mesh%np, :) = hpsi(1:der%mesh%np, :) + (gyromagnetic_ratio * m_half) * lhpsi(1:der%mesh%np, :)
        safe_deallocate_a(lhpsi)
      end select
 
      safe_deallocate_a(grad)
      safe_deallocate_a(aa)
      safe_deallocate_a(a_prime)
    end if
 
    if (vector_potential) then
      safe_allocate(grad(1:der%mesh%np_part, 1:der%dim, 1:std%dim))
 
      do idim = 1, std%dim
        call zderivatives_grad(der, psi(:, idim), grad(:, :, idim))
      end do
 
      select case (std%ispin)
      case (unpolarized, spin_polarized)
        do ip = 1, der%mesh%np
          hpsi(ip, 1) = hpsi(ip, 1) - m_zi * dot_product(a_field(1:der%dim), grad(ip, 1:der%dim, 1)) / p_c
        end do
      case (spinors)
        do ip = 1, der%mesh%np
          do idim = 1, std%dim
            hpsi(ip, idim) = hpsi(ip, idim) - m_zi * &
              dot_product(a_field(1:der%dim), grad(ip, 1:der%dim, idim)) / p_c
          end do
        end do
      end select
      safe_deallocate_a(grad)
    end if
 
    pop_sub(vlaser_operator_linear)
  end subroutine vlaser_operator_linear
 
 
end module propagation_oct_m
 
!! Local Variables:
!! mode: f90
!! coding: utf-8
!! End: