!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright (C) 2000 - 2017  CP2K developers group                                               !
!--------------------------------------------------------------------------------------------------!

! **************************************************************************************************
!> \brief Optimization routines for all ALMO-based SCF methods
!> \par History
!>       2011.05 created [Rustam Z Khaliullin]
!>       2014.10 as a separate file [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
MODULE almo_scf_optimizer
   USE almo_scf_diis_types,             ONLY: almo_scf_diis_extrapolate,&
                                              almo_scf_diis_init,&
                                              almo_scf_diis_push,&
                                              almo_scf_diis_release,&
                                              almo_scf_diis_type
   USE almo_scf_methods,                ONLY: &
        almo_scf_ks_blk_to_tv_blk, almo_scf_ks_to_ks_blk, almo_scf_ks_to_ks_xx, &
        almo_scf_ks_xx_to_tv_xx, almo_scf_p_blk_to_t_blk, almo_scf_t_blk_to_p, &
        almo_scf_t_blk_to_t_blk_orthonormal, almo_scf_t_to_p, apply_domain_operators, &
        apply_projector, construct_domain_preconditioner, construct_domain_r_down, &
        construct_domain_s_inv, construct_domain_s_sqrt, get_overlap, newton_grad_to_step, &
        pseudo_invert_diagonal_blk, xalmo_initial_guess
   USE almo_scf_qs,                     ONLY: almo_scf_dm_to_ks,&
                                              almo_scf_update_ks_energy,&
                                              matrix_qs_to_almo
   USE almo_scf_types,                  ONLY: almo_scf_env_type,&
                                              optimizer_options_type
   USE cp_dbcsr_cholesky,               ONLY: cp_dbcsr_cholesky_decompose,&
                                              cp_dbcsr_cholesky_invert,&
                                              cp_dbcsr_cholesky_restore
   USE cp_dbcsr_diag,                   ONLY: cp_dbcsr_syevd
   USE cp_external_control,             ONLY: external_control
   USE cp_log_handling,                 ONLY: cp_get_default_logger,&
                                              cp_logger_get_default_unit_nr,&
                                              cp_logger_type
   USE cp_output_handling,              ONLY: cp_print_key_finished_output,&
                                              cp_print_key_unit_nr
   USE ct_methods,                      ONLY: analytic_line_search,&
                                              ct_step_execute,&
                                              diagonalize_diagonal_blocks
   USE ct_types,                        ONLY: ct_step_env_clean,&
                                              ct_step_env_get,&
                                              ct_step_env_init,&
                                              ct_step_env_set,&
                                              ct_step_env_type
   USE dbcsr_api,                       ONLY: &
        dbcsr_add, dbcsr_add_on_diag, dbcsr_copy, dbcsr_create, dbcsr_desymmetrize, &
        dbcsr_distribution_get, dbcsr_distribution_type, dbcsr_filter, dbcsr_finalize, &
        dbcsr_frobenius_norm, dbcsr_func_dtanh, dbcsr_func_inverse, dbcsr_func_tanh, &
        dbcsr_function_of_elements, dbcsr_get_diag, dbcsr_get_info, dbcsr_hadamard_product, &
        dbcsr_iterator_blocks_left, dbcsr_iterator_next_block, dbcsr_iterator_start, &
        dbcsr_iterator_stop, dbcsr_iterator_type, dbcsr_multiply, dbcsr_norm, &
        dbcsr_norm_maxabsnorm, dbcsr_p_type, dbcsr_print_block_sum, dbcsr_release, &
        dbcsr_reserve_block2d, dbcsr_scale, dbcsr_set, dbcsr_set_diag, dbcsr_trace, dbcsr_triu, &
        dbcsr_type, dbcsr_type_no_symmetry, dbcsr_work_create
   USE domain_submatrix_methods,        ONLY: add_submatrices,&
                                              construct_submatrices,&
                                              copy_submatrices,&
                                              init_submatrices,&
                                              maxnorm_submatrices,&
                                              release_submatrices
   USE domain_submatrix_types,          ONLY: domain_map_type,&
                                              domain_submatrix_type,&
                                              select_row
   USE input_constants,                 ONLY: &
        almo_scf_diag, almo_scf_dm_sign, cg_dai_yuan, cg_fletcher, cg_fletcher_reeves, &
        cg_hager_zhang, cg_hestenes_stiefel, cg_liu_storey, cg_polak_ribiere, cg_zero, prec_zero, &
        virt_full, xalmo_case_block_diag, xalmo_case_fully_deloc, xalmo_case_normal
   USE input_section_types,             ONLY: section_vals_get_subs_vals,&
                                              section_vals_type
   USE iterate_matrix,                  ONLY: invert_Hotelling,&
                                              matrix_sqrt_Newton_Schulz
   USE kinds,                           ONLY: dp
   USE machine,                         ONLY: m_flush,&
                                              m_walltime
   USE qs_environment_types,            ONLY: get_qs_env,&
                                              qs_environment_type
#include "./base/base_uses.f90"

   IMPLICIT NONE

   PRIVATE

   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'almo_scf_optimizer'

   PUBLIC :: almo_scf_block_diagonal, &
             almo_scf_xalmo_eigensolver, &
             almo_scf_xalmo_pcg

   LOGICAL, PARAMETER :: debug_mode = .FALSE.
   LOGICAL, PARAMETER :: safe_mode = .FALSE.

CONTAINS

! **************************************************************************************************
!> \brief An SCF procedure that optimizes block-diagonal ALMOs using DIIS
!> \param qs_env ...
!> \param almo_scf_env ...
!> \param optimizer ...
!> \par History
!>       2011.06 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE almo_scf_block_diagonal(qs_env, almo_scf_env, optimizer)
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(almo_scf_env_type)                            :: almo_scf_env
      TYPE(optimizer_options_type)                       :: optimizer

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

      INTEGER                                            :: handle, iscf, ispin, nspin, nstrikes, &
                                                            ntolerate, unit_nr
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: local_nocc_of_domain
      LOGICAL                                            :: converged, prepare_to_exit, should_stop, &
                                                            use_diis, use_prev_as_guess
      REAL(KIND=dp)                                      :: energy_diff, energy_new, energy_old, &
                                                            error_norm, error_norm_ispin, &
                                                            prev_error_norm, t1, t2, &
                                                            true_mixing_fraction
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: local_mu
      TYPE(almo_scf_diis_type), ALLOCATABLE, &
         DIMENSION(:)                                    :: almo_diis
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_ks
      TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:)        :: matrix_mixing_old_blk

      CALL timeset(routineN, handle)

      ! get a useful output_unit
      logger => cp_get_default_logger()
      IF (logger%para_env%mepos == logger%para_env%source) THEN
         unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
      ELSE
         unit_nr = -1
      ENDIF

      ! use DIIS, it's superior to simple mixing
      use_diis = .TRUE.
      use_prev_as_guess = .FALSE.

      nspin = almo_scf_env%nspins
      ALLOCATE (local_mu(almo_scf_env%ndomains))
      ALLOCATE (local_nocc_of_domain(almo_scf_env%ndomains))

      ! init mixing matrices
      ALLOCATE (matrix_mixing_old_blk(nspin))
      ALLOCATE (almo_diis(nspin))
      DO ispin = 1, nspin
         CALL dbcsr_create(matrix_mixing_old_blk(ispin), &
                           template=almo_scf_env%matrix_ks_blk(ispin))
         CALL almo_scf_diis_init(diis_env=almo_diis(ispin), &
                                 sample_err=almo_scf_env%matrix_ks_blk(ispin), &
                                 sample_var=almo_scf_env%matrix_s_blk(1), &
                                 error_type=1, &
                                 max_length=optimizer%ndiis)
      ENDDO

      energy_old = 0.0_dp
      iscf = 0
      prepare_to_exit = .FALSE.
      true_mixing_fraction = 0.0_dp
      ! set variables that control diag/pcg switching
      nstrikes = 0
      ntolerate = 3
      error_norm = 1.0E+10_dp ! arbitrary big step

      IF (unit_nr > 0) THEN
         WRITE (unit_nr, '(T2,A,A,A)') REPEAT("-", 20), &
            " Optimization of block-diagonal ALMOs ", REPEAT("-", 21)
         WRITE (unit_nr, *)
         WRITE (unit_nr, '(T2,A13,A6,A23,A14,A14,A9)') "Method", "Iter", &
            "Total Energy", "Change", "Convergence", "Time"
         WRITE (unit_nr, '(T2,A)') REPEAT("-", 79)
      ENDIF

      ! the real SCF loop
      t1 = m_walltime()
      DO

         iscf = iscf+1

         ! get a copy of the current KS matrix
         CALL get_qs_env(qs_env, matrix_ks=matrix_ks)
         DO ispin = 1, nspin
            CALL matrix_qs_to_almo(matrix_ks(ispin)%matrix, &
                                   almo_scf_env%matrix_ks(ispin), &
                                   almo_scf_env, .FALSE.)
            CALL matrix_qs_to_almo(matrix_ks(ispin)%matrix, &
                                   almo_scf_env%matrix_ks_blk(ispin), &
                                   almo_scf_env, .TRUE.)
            CALL dbcsr_filter(almo_scf_env%matrix_ks(ispin), &
                              almo_scf_env%eps_filter)
         ENDDO

         ! obtain projected KS matrix and the DIIS-error vector
         CALL almo_scf_ks_to_ks_blk(almo_scf_env)

         ! inform the DIIS handler about the new KS matrix and its error vector
         IF (use_diis) THEN
            DO ispin = 1, nspin
               CALL almo_scf_diis_push(diis_env=almo_diis(ispin), &
                                       var=almo_scf_env%matrix_ks_blk(ispin), &
                                       err=almo_scf_env%matrix_err_blk(ispin))
            ENDDO
         ENDIF

         ! get error_norm: choose the largest of the two spins
         prev_error_norm = error_norm
         DO ispin = 1, nspin
            !error_norm=dbcsr_frobenius_norm(almo_scf_env%matrix_err_blk(ispin))
            CALL dbcsr_norm(almo_scf_env%matrix_err_blk(ispin), &
                            dbcsr_norm_maxabsnorm, &
                            norm_scalar=error_norm_ispin)
            IF (ispin .EQ. 1) error_norm = error_norm_ispin
            IF (ispin .GT. 1 .AND. error_norm_ispin .GT. error_norm) &
               error_norm = error_norm_ispin
         ENDDO

         IF (error_norm .LT. almo_scf_env%eps_prev_guess) THEN
            use_prev_as_guess = .TRUE.
         ELSE
            use_prev_as_guess = .FALSE.
         ENDIF

         ! check convergence
         converged = .TRUE.
         IF (error_norm .GT. optimizer%eps_error) converged = .FALSE.
         ! check other exit criteria: max SCF steps and timing
         CALL external_control(should_stop, "SCF", &
                               start_time=qs_env%start_time, &
                               target_time=qs_env%target_time)
         IF (should_stop .OR. iscf >= optimizer%max_iter .OR. converged) THEN
            prepare_to_exit = .TRUE.
         ENDIF

         IF (.NOT. prepare_to_exit) THEN ! update the ALMOs and density matrix

            ! perform mixing of KS matrices
            IF (iscf .NE. 1) THEN
               IF (use_diis) THEN ! use diis instead of mixing
                  DO ispin = 1, nspin
                     CALL almo_scf_diis_extrapolate(diis_env=almo_diis(ispin), &
                                                    extr_var=almo_scf_env%matrix_ks_blk(ispin))
                  ENDDO
               ELSE ! use mixing
                  true_mixing_fraction = almo_scf_env%mixing_fraction
                  DO ispin = 1, nspin
                     CALL dbcsr_add(almo_scf_env%matrix_ks_blk(ispin), &
                                    matrix_mixing_old_blk(ispin), &
                                    true_mixing_fraction, &
                                    1.0_dp-true_mixing_fraction)
                  END DO
               ENDIF
            ENDIF
            ! save the new matrix for the future mixing
            DO ispin = 1, nspin
               CALL dbcsr_copy(matrix_mixing_old_blk(ispin), &
                               almo_scf_env%matrix_ks_blk(ispin))
            ENDDO

            ! obtain ALMOs from the new KS matrix
            SELECT CASE (almo_scf_env%almo_update_algorithm)
            CASE (almo_scf_diag)

               CALL almo_scf_ks_blk_to_tv_blk(almo_scf_env)

            CASE (almo_scf_dm_sign)

               ! update the density matrix
               DO ispin = 1, nspin

                  local_nocc_of_domain(:) = almo_scf_env%nocc_of_domain(:, ispin)
                  local_mu(:) = almo_scf_env%mu_of_domain(:, ispin)
                  ! RZK UPDATE! the update algorithm is removed because
                  ! RZK UPDATE! it requires updating core LS_SCF routines
                  ! RZK UPDATE! (the code exists in the CVS version)
                  CPABORT("Density_matrix_sign has not been tested yet")
                  ! RZK UPDATE!  CALL density_matrix_sign(almo_scf_env%matrix_p_blk(ispin),&
                  ! RZK UPDATE!          local_mu,&
                  ! RZK UPDATE!          almo_scf_env%fixed_mu,&
                  ! RZK UPDATE!          almo_scf_env%matrix_ks_blk(ispin),&
                  ! RZK UPDATE!          !matrix_mixing_old_blk(ispin),&
                  ! RZK UPDATE!          almo_scf_env%matrix_s_blk(1), &
                  ! RZK UPDATE!          almo_scf_env%matrix_s_blk_inv(1), &
                  ! RZK UPDATE!          local_nocc_of_domain,&
                  ! RZK UPDATE!          almo_scf_env%eps_filter,&
                  ! RZK UPDATE!          almo_scf_env%domain_index_of_ao)
                  ! RZK UPDATE!
                  almo_scf_env%mu_of_domain(:, ispin) = local_mu(:)

               ENDDO

               ! obtain ALMOs from matrix_p_blk: T_new = P_blk S_blk T_old
               CALL almo_scf_p_blk_to_t_blk(almo_scf_env, ionic=.FALSE.)
               CALL almo_scf_t_blk_to_t_blk_orthonormal(almo_scf_env)

            END SELECT

            ! obtain density matrix from ALMOs
            CALL almo_scf_t_blk_to_p(almo_scf_env, &
                                     use_sigma_inv_guess=use_prev_as_guess)

            ! compute the new KS matrix and new energy
            CALL almo_scf_dm_to_ks(qs_env, almo_scf_env, energy_new)

         ENDIF ! prepare_to_exit

         energy_diff = energy_new-energy_old
         energy_old = energy_new
         almo_scf_env%almo_scf_energy = energy_new

         t2 = m_walltime()
         ! brief report on the current SCF loop
         IF (unit_nr > 0) THEN
            WRITE (unit_nr, '(T2,A13,I6,F23.10,E14.5,F14.9,F9.2)') "ALMO SCF DIIS", &
               iscf, &
               energy_new, energy_diff, error_norm, t2-t1
         ENDIF
         t1 = m_walltime()

         IF (prepare_to_exit) EXIT

      ENDDO ! end scf cycle

      IF (.NOT. converged) THEN
         IF (unit_nr > 0) THEN
            CPABORT("SCF for block-diagonal ALMOs not converged!")
         ENDIF
      ENDIF

      DO ispin = 1, nspin
         CALL dbcsr_release(matrix_mixing_old_blk(ispin))
         CALL almo_scf_diis_release(diis_env=almo_diis(ispin))
      ENDDO
      DEALLOCATE (almo_diis)
      DEALLOCATE (matrix_mixing_old_blk)
      DEALLOCATE (local_mu)
      DEALLOCATE (local_nocc_of_domain)

      CALL timestop(handle)

   END SUBROUTINE almo_scf_block_diagonal

! **************************************************************************************************
!> \brief An eigensolver-based SCF to optimize extended ALMOs (i.e. ALMOs on
!>        overlapping domains)
!> \param qs_env ...
!> \param almo_scf_env ...
!> \param optimizer ...
!> \par History
!>       2013.03 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE almo_scf_xalmo_eigensolver(qs_env, almo_scf_env, optimizer)
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(almo_scf_env_type)                            :: almo_scf_env
      TYPE(optimizer_options_type)                       :: optimizer

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

      INTEGER                                            :: handle, iscf, ispin, nspin, unit_nr
      LOGICAL                                            :: converged, prepare_to_exit, should_stop
      REAL(KIND=dp)                                      :: denergy_tot, energy_diff, energy_new, &
                                                            energy_old, error_norm, error_norm_0, &
                                                            spin_factor, t1, t2
      REAL(KIND=dp), DIMENSION(2)                        :: denergy_spin
      TYPE(almo_scf_diis_type), ALLOCATABLE, &
         DIMENSION(:)                                    :: almo_diis
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_ks
      TYPE(dbcsr_type)                                   :: matrix_p_almo_scf_converged
      TYPE(domain_submatrix_type), ALLOCATABLE, &
         DIMENSION(:, :)                                 :: submatrix_mixing_old_blk

      CALL timeset(routineN, handle)

      ! get a useful output_unit
      logger => cp_get_default_logger()
      IF (logger%para_env%mepos == logger%para_env%source) THEN
         unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
      ELSE
         unit_nr = -1
      ENDIF

      nspin = almo_scf_env%nspins
      IF (nspin == 1) THEN
         spin_factor = 2.0_dp
      ELSE
         spin_factor = 1.0_dp
      ENDIF

      ! RZK-warning domain_s_sqrt and domain_s_sqrt_inv do not have spin
      ! components yet (may be used later)
      ispin = 1
      CALL construct_domain_s_sqrt( &
         matrix_s=almo_scf_env%matrix_s(1), &
         subm_s_sqrt=almo_scf_env%domain_s_sqrt(:, ispin), &
         subm_s_sqrt_inv=almo_scf_env%domain_s_sqrt_inv(:, ispin), &
         dpattern=almo_scf_env%quench_t(ispin), &
         map=almo_scf_env%domain_map(ispin), &
         node_of_domain=almo_scf_env%cpu_of_domain)
      ! TRY: construct s_inv
      !CALL construct_domain_s_inv(&
      !       matrix_s=almo_scf_env%matrix_s(1),&
      !       subm_s_inv=almo_scf_env%domain_s_inv(:,ispin),&
      !       dpattern=almo_scf_env%quench_t(ispin),&
      !       map=almo_scf_env%domain_map(ispin),&
      !       node_of_domain=almo_scf_env%cpu_of_domain)

      ! construct the domain template for the occupied orbitals
      DO ispin = 1, nspin
         ! RZK-warning we need only the matrix structure, not data
         ! replace construct_submatrices with lighter procedure with
         ! no heavy communications
         CALL construct_submatrices( &
            matrix=almo_scf_env%quench_t(ispin), &
            submatrix=almo_scf_env%domain_t(:, ispin), &
            distr_pattern=almo_scf_env%quench_t(ispin), &
            domain_map=almo_scf_env%domain_map(ispin), &
            node_of_domain=almo_scf_env%cpu_of_domain, &
            job_type=select_row)
      ENDDO

      ! init mixing matrices
      ALLOCATE (submatrix_mixing_old_blk(almo_scf_env%ndomains, nspin))
      CALL init_submatrices(submatrix_mixing_old_blk)
      ALLOCATE (almo_diis(nspin))

      ! TRY: construct block-projector
      !ALLOCATE(submatrix_tmp(almo_scf_env%ndomains))
      !DO ispin=1,nspin
      !   CALL init_submatrices(submatrix_tmp)
      !   CALL construct_domain_r_down(&
      !           matrix_t=almo_scf_env%matrix_t_blk(ispin),&
      !           matrix_sigma_inv=almo_scf_env%matrix_sigma_inv(ispin),&
      !           matrix_s=almo_scf_env%matrix_s(1),&
      !           subm_r_down=submatrix_tmp(:),&
      !           dpattern=almo_scf_env%quench_t(ispin),&
      !           map=almo_scf_env%domain_map(ispin),&
      !           node_of_domain=almo_scf_env%cpu_of_domain,&
      !           filter_eps=almo_scf_env%eps_filter)
      !   CALL multiply_submatrices('N','N',1.0_dp,&
      !           submatrix_tmp(:),&
      !           almo_scf_env%domain_s_inv(:,1),0.0_dp,&
      !           almo_scf_env%domain_r_down_up(:,ispin))
      !   CALL release_submatrices(submatrix_tmp)
      !ENDDO
      !DEALLOCATE(submatrix_tmp)

      DO ispin = 1, nspin
         ! use s_sqrt since they are already properly constructed
         ! and have the same distributions as domain_err and domain_ks_xx
         CALL almo_scf_diis_init(diis_env=almo_diis(ispin), &
                                 sample_err=almo_scf_env%domain_s_sqrt(:, ispin), &
                                 error_type=1, &
                                 max_length=optimizer%ndiis)
      ENDDO

      denergy_tot = 0.0_dp
      energy_old = 0.0_dp
      iscf = 0
      prepare_to_exit = .FALSE.

      ! the SCF loop
      t1 = m_walltime()
      DO

         iscf = iscf+1

         ! get a copy of the current KS matrix
         CALL get_qs_env(qs_env, matrix_ks=matrix_ks)
         DO ispin = 1, nspin
            CALL matrix_qs_to_almo(matrix_ks(ispin)%matrix, &
                                   almo_scf_env%matrix_ks(ispin), &
                                   almo_scf_env, .FALSE.)
            CALL matrix_qs_to_almo(matrix_ks(ispin)%matrix, &
                                   almo_scf_env%matrix_ks_blk(ispin), &
                                   almo_scf_env, .TRUE.)
            CALL dbcsr_filter(almo_scf_env%matrix_ks(ispin), &
                              almo_scf_env%eps_filter)
         ENDDO

         ! obtain projected KS matrix and the DIIS-error vector
         CALL almo_scf_ks_to_ks_xx(almo_scf_env)

         ! inform the DIIS handler about the new KS matrix and its error vector
         DO ispin = 1, nspin
            CALL almo_scf_diis_push(diis_env=almo_diis(ispin), &
                                    d_var=almo_scf_env%domain_ks_xx(:, ispin), &
                                    d_err=almo_scf_env%domain_err(:, ispin))
         ENDDO

         ! check convergence
         converged = .TRUE.
         DO ispin = 1, nspin
            !error_norm=dbcsr_frobenius_norm(almo_scf_env%matrix_err_blk(ispin))
            CALL dbcsr_norm(almo_scf_env%matrix_err_xx(ispin), &
                            dbcsr_norm_maxabsnorm, &
                            norm_scalar=error_norm)
            CALL maxnorm_submatrices(almo_scf_env%domain_err(:, ispin), &
                                     norm=error_norm_0)
            IF (error_norm .GT. optimizer%eps_error) THEN
               converged = .FALSE.
               EXIT ! no need to check the other spin
            ENDIF
         ENDDO
         ! check other exit criteria: max SCF steps and timing
         CALL external_control(should_stop, "SCF", &
                               start_time=qs_env%start_time, &
                               target_time=qs_env%target_time)
         IF (should_stop .OR. iscf >= optimizer%max_iter .OR. converged) THEN
            prepare_to_exit = .TRUE.
         ENDIF

         IF (.NOT. prepare_to_exit) THEN ! update the ALMOs and density matrix

            ! perform mixing of KS matrices
            IF (iscf .NE. 1) THEN
               IF (.FALSE.) THEN ! use diis instead of mixing
                  DO ispin = 1, nspin
                     CALL add_submatrices( &
                        almo_scf_env%mixing_fraction, &
                        almo_scf_env%domain_ks_xx(:, ispin), &
                        1.0_dp-almo_scf_env%mixing_fraction, &
                        submatrix_mixing_old_blk(:, ispin), &
                        'N')
                     !CALL dbcsr_add(almo_scf_env%matrix_ks_blk(ispin),&
                     !        matrix_mixing_old_blk(ispin),&
                     !        almo_scf_env%mixing_fraction,&
                     !        1.0_dp-almo_scf_env%mixing_fraction)
                  END DO
               ELSE
                  DO ispin = 1, nspin
                     CALL almo_scf_diis_extrapolate(diis_env=almo_diis(ispin), &
                                                    d_extr_var=almo_scf_env%domain_ks_xx(:, ispin))
                  ENDDO
               ENDIF
            ENDIF
            ! save the new matrix for the future mixing
            DO ispin = 1, nspin
               CALL copy_submatrices( &
                  almo_scf_env%domain_ks_xx(:, ispin), &
                  submatrix_mixing_old_blk(:, ispin), &
                  copy_data=.TRUE.)
            ENDDO

            ! obtain a new set of ALMOs from the updated KS matrix
            CALL almo_scf_ks_xx_to_tv_xx(almo_scf_env)

            ! update the density matrix
            DO ispin = 1, nspin

               ! save the initial density matrix (to get the perturbative energy lowering)
               IF (iscf .EQ. 1) THEN
                  CALL dbcsr_create(matrix_p_almo_scf_converged, &
                                    template=almo_scf_env%matrix_p(ispin))
                  CALL dbcsr_copy(matrix_p_almo_scf_converged, &
                                  almo_scf_env%matrix_p(ispin))
               ENDIF

               ! update now
               CALL almo_scf_t_to_p( &
                  t=almo_scf_env%matrix_t(ispin), &
                  p=almo_scf_env%matrix_p(ispin), &
                  eps_filter=almo_scf_env%eps_filter, &
                  orthog_orbs=.FALSE., &
                  s=almo_scf_env%matrix_s(1), &
                  sigma=almo_scf_env%matrix_sigma(ispin), &
                  sigma_inv=almo_scf_env%matrix_sigma_inv(ispin), &
                  use_guess=.TRUE.)
               CALL dbcsr_scale(almo_scf_env%matrix_p(ispin), spin_factor)

               ! obtain perturbative estimate (at no additional cost)
               ! of the energy lowering relative to the block-diagonal ALMOs
               IF (iscf .EQ. 1) THEN

                  CALL dbcsr_add(matrix_p_almo_scf_converged, &
                                 almo_scf_env%matrix_p(ispin), -1.0_dp, 1.0_dp)
                  CALL dbcsr_trace(almo_scf_env%matrix_ks_0deloc(ispin), &
                                   matrix_p_almo_scf_converged, &
                                   denergy_spin(ispin))

                  CALL dbcsr_release(matrix_p_almo_scf_converged)

                  denergy_tot = denergy_tot+denergy_spin(ispin)

                  ! RZK-warning Energy correction can be evaluated using matrix_x
                  ! as shown in the attempt below and in the PCG procedure.
                  ! Using matrix_x allows immediate decomposition of the energy
                  ! lowering into 2-body components for EDA. However, it does not
                  ! work here because the diagonalization routine does not necessarily
                  ! produce orbitals with the same sign as the block-diagonal ALMOs
                  ! Any fixes?!

                  !CALL dbcsr_init(matrix_x)
                  !CALL dbcsr_create(matrix_x,&
                  !        template=almo_scf_env%matrix_t(ispin))
                  !
                  !CALL dbcsr_init(matrix_tmp_no)
                  !CALL dbcsr_create(matrix_tmp_no,&
                  !        template=almo_scf_env%matrix_t(ispin))
                  !
                  !CALL dbcsr_copy(matrix_x,&
                  !        almo_scf_env%matrix_t_blk(ispin))
                  !CALL dbcsr_add(matrix_x,almo_scf_env%matrix_t(ispin),&
                  !        -1.0_dp,1.0_dp)

                  !CALL dbcsr_trace(matrix_x, almo_scf_env%matrix_err_xx(ispin),denergy)

                  !denergy=denergy*spin_factor

                  !IF (unit_nr>0) THEN
                  !   WRITE(unit_nr,*) "_ENERGY-0: ", almo_scf_env%almo_scf_energy
                  !   WRITE(unit_nr,*) "_ENERGY-D: ", denergy
                  !   WRITE(unit_nr,*) "_ENERGY-F: ", almo_scf_env%almo_scf_energy+denergy
                  !ENDIF
                  !! RZK-warning update will not work since the energy is overwritten almost immediately
                  !!CALL almo_scf_update_ks_energy(qs_env,&
                  !!        almo_scf_env%almo_scf_energy+denergy)
                  !!

                  !! print out the results of the decomposition analysis
                  !CALL dbcsr_hadamard_product(matrix_x,&
                  !        almo_scf_env%matrix_err_xx(ispin),&
                  !        matrix_tmp_no)
                  !CALL dbcsr_scale(matrix_tmp_no,spin_factor)
                  !CALL dbcsr_filter(matrix_tmp_no,almo_scf_env%eps_filter)
                  !
                  !IF (unit_nr>0) THEN
                  !   WRITE(unit_nr,*)
                  !   WRITE(unit_nr,'(T2,A)') "DECOMPOSITION OF THE DELOCALIZATION ENERGY"
                  !ENDIF

                  !mynode=dbcsr_mp_mynode(dbcsr_distribution_mp(&
                  !   dbcsr_distribution(matrix_tmp_no)))
                  !WRITE(mynodestr,'(I6.6)') mynode
                  !mylogfile='EDA.'//TRIM(ADJUSTL(mynodestr))
                  !OPEN (iunit,file=mylogfile,status='REPLACE')
                  !CALL dbcsr_print_block_sum(matrix_tmp_no,iunit)
                  !CLOSE(iunit)
                  !
                  !CALL dbcsr_release(matrix_tmp_no)
                  !CALL dbcsr_release(matrix_x)

               ENDIF ! iscf.eq.1

            ENDDO

            ! print out the energy lowering
            IF (iscf .EQ. 1) THEN
               IF (unit_nr > 0) THEN
                  WRITE (unit_nr, *)
                  WRITE (unit_nr, '(T2,A35,F25.10)') "ENERGY OF BLOCK-DIAGONAL ALMOs:", &
                     almo_scf_env%almo_scf_energy
                  WRITE (unit_nr, '(T2,A35,F25.10)') "ENERGY LOWERING:", &
                     denergy_tot
                  WRITE (unit_nr, '(T2,A35,F25.10)') "CORRECTED ENERGY:", &
                     almo_scf_env%almo_scf_energy+denergy_tot
                  WRITE (unit_nr, *)
               ENDIF
               CALL almo_scf_update_ks_energy(qs_env, &
                                              energy=almo_scf_env%almo_scf_energy, &
                                              energy_singles_corr=denergy_tot)
            ENDIF

            ! compute the new KS matrix and new energy
            IF (.NOT. almo_scf_env%perturbative_delocalization) THEN
               CALL almo_scf_dm_to_ks(qs_env, almo_scf_env, energy_new)
            ENDIF

         ENDIF ! prepare_to_exit

         IF (almo_scf_env%perturbative_delocalization) THEN

            ! exit after the first step if we do not need the SCF procedure
            converged = .TRUE.
            prepare_to_exit = .TRUE.

         ELSE ! not a perturbative treatment

            energy_diff = energy_new-energy_old
            energy_old = energy_new
            almo_scf_env%almo_scf_energy = energy_new

            t2 = m_walltime()
            ! brief report on the current SCF loop
            IF (unit_nr > 0) THEN
               WRITE (unit_nr, '(T2,A,I6,F20.9,E11.3,E11.3,E11.3,F8.2)') "ALMO SCF", &
                  iscf, &
                  energy_new, energy_diff, error_norm, error_norm_0, t2-t1
            ENDIF
            t1 = m_walltime()

         ENDIF

         IF (prepare_to_exit) EXIT

      ENDDO ! end scf cycle

      IF (.NOT. converged) THEN
         CPABORT("SCF for ALMOs on overlapping domains not converged! ")
      ENDIF

      DO ispin = 1, nspin
         CALL release_submatrices(submatrix_mixing_old_blk(:, ispin))
         CALL almo_scf_diis_release(diis_env=almo_diis(ispin))
      ENDDO
      DEALLOCATE (almo_diis)
      DEALLOCATE (submatrix_mixing_old_blk)

      CALL timestop(handle)

   END SUBROUTINE almo_scf_xalmo_eigensolver

! **************************************************************************************************
!> \brief Optimization of ALMOs using PCG-like minimizers
!> \param qs_env ...
!> \param almo_scf_env ...
!> \param optimizer   controls the optimization algorithm
!> \param quench_t ...
!> \param matrix_t_in ...
!> \param matrix_t_out ...
!> \param assume_t0_q0x - since it is extrememly difficult to converge the iterative
!>                        procedure using T as an optimized variable, assume
!>                        T = T_0 + (1-R_0)*X and optimize X
!>                        T_0 is assumed to be the zero-delocalization reference
!> \param perturbation_only - perturbative (do not update Hamiltonian)
!> \param special_case   to reduce the overhead special cases are implemented:
!>                       xalmo_case_normal - no special case (i.e. xALMOs)
!>                       xalmo_case_block_diag
!>                       xalmo_case_fully_deloc
!> \par History
!>       2011.11 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE almo_scf_xalmo_pcg(qs_env, almo_scf_env, optimizer, quench_t, &
                                 matrix_t_in, matrix_t_out, assume_t0_q0x, perturbation_only, &
                                 special_case)

      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(almo_scf_env_type)                            :: almo_scf_env
      TYPE(optimizer_options_type)                       :: optimizer
      TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:)        :: quench_t, matrix_t_in, matrix_t_out
      LOGICAL, INTENT(IN)                                :: assume_t0_q0x, perturbation_only
      INTEGER, INTENT(IN), OPTIONAL                      :: special_case

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

      CHARACTER(LEN=20)                                  :: iter_type
      INTEGER :: cg_iteration, dim0, eda_unit, fixed_line_search_niter, handle, ispin, iteration, &
         jj, line_search_iteration, max_iter, my_special_case, ncores, ndomains, nspins, occ1, &
         outer_iteration, outer_max_iter, prec_type, precond_domain_projector, unit_nr, &
         zero_neg_eiv
      LOGICAL :: converged, do_md, first_md_iteration, just_started, line_search, &
         md_in_theta_space, optimize_theta, outer_prepare_to_exit, prepare_to_exit, &
         reset_conjugator, skip_grad, use_guess, use_preconditioner
      REAL(kind=dp) :: appr_sec_der, beta, denom, e0, e1, energy_diff, energy_new, energy_old, &
         eps_skip_gradients, g0, g1, grad_norm, grad_norm_frob, kappa, kin_energy, &
         line_search_error, next_step_size_guess, numer, prec_sf_mixing_s, spin_factor, step_size, &
         t1, t2, t_norm, tau, time_step
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:)           :: evals
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(dbcsr_distribution_type)                      :: dist
      TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_ks
      TYPE(dbcsr_type) :: FTsiginv, fvo_0, grad, inv_eiv, m_tmp_nn_1, m_tmp_no_1, m_tmp_no_2, &
         m_tmp_no_3, m_tmp_oo_1, prec_oo, prec_oo_inv, prec_vv, prev_grad, prev_minus_prec_grad, &
         prev_step, siginvTFTsiginv, ST, step, STsiginv_0, velocity
      TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:)        :: m_t_in_local, m_theta
      TYPE(domain_submatrix_type), ALLOCATABLE, &
         DIMENSION(:)                                    :: domain_r_down
      TYPE(section_vals_type), POINTER                   :: almo_print_section, input

      CALL timeset(routineN, handle)

      my_special_case = xalmo_case_normal
      IF (PRESENT(special_case)) my_special_case = special_case

      ! get a useful output_unit
      logger => cp_get_default_logger()
      IF (logger%para_env%mepos == logger%para_env%source) THEN
         unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
      ELSE
         unit_nr = -1
      ENDIF

      IF (unit_nr > 0) THEN
         WRITE (unit_nr, *)
         SELECT CASE (my_special_case)
         CASE (xalmo_case_block_diag)
            WRITE (unit_nr, '(T2,A,A,A)') REPEAT("-", 20), &
               " Optimization of block-diagonal ALMOs ", REPEAT("-", 21)
         CASE (xalmo_case_fully_deloc)
            WRITE (unit_nr, '(T2,A,A,A)') REPEAT("-", 20), &
               " Optimization of fully delocalized MOs ", REPEAT("-", 20)
         CASE (xalmo_case_normal)
            WRITE (unit_nr, '(T2,A,A,A)') REPEAT("-", 27), &
               " Optimization of XALMOs ", REPEAT("-", 28)
         END SELECT
         WRITE (unit_nr, *)
         WRITE (unit_nr, '(T2,A13,A6,A23,A14,A14,A9)') "Method", "Iter", &
            "Objective Function", "Change", "Convergence", "Time"
         WRITE (unit_nr, '(T2,A)') REPEAT("-", 79)
      ENDIF

      ! set local parameters using developer's keywords
      ! RZK-warning: change to normal keywords later
      do_md = almo_scf_env%logical01
      optimize_theta = almo_scf_env%logical05
      prec_sf_mixing_s = almo_scf_env%real04
      eps_skip_gradients = almo_scf_env%real01

      ! preconditioner control
      use_preconditioner = optimizer%preconditioner .NE. prec_zero
      prec_type = 4
      ! RZK-warning: prec_type here is not the same as preconditioner
      ! type in optimizer%preconditioner. change this later
      !prec_type = optimizer%preconditioner
      !if (prec_type.eq.prec_default) prec_type=prec_ks_plus_s

      ! control of the line search
      fixed_line_search_niter = 0 ! init to zero, change when eps is small enough

      CALL dbcsr_get_info(almo_scf_env%matrix_s(1), distribution=dist)
      CALL dbcsr_distribution_get(dist, numnodes=ncores)

      IF (almo_scf_env%nspins == 1) THEN
         spin_factor = 2.0_dp
      ELSE
         spin_factor = 1.0_dp
      ENDIF

      !!!!!! RZK-warning THIS PROCEDURE WILL WORK ONLY FOR CLOSED SHELL SYSTEMS
      !!!!!! TO ADAPT IT FOR UNRESTRICTED ORBITALS - UPDATE KS MATRIX WITH PARTIALLY
      !!!!!! OPTIMIZED ORBITALS - BOTH ALPNA AND BETA
      IF (almo_scf_env%nspins .GT. 1) THEN
         CPABORT("UNRESTRICTED ALMO SCF IS NYI(!)")
      ENDIF

      nspins = almo_scf_env%nspins

      ! create a local copy of matrix_t_in because
      ! matrix_t_in and matrix_t_out can be the same matrix
      ! we need to make sure data in matrix_t_in is intact
      ! after we start writing to matrix_t_out
      ALLOCATE (m_t_in_local(nspins))
      DO ispin = 1, nspins
         CALL dbcsr_create(m_t_in_local(ispin), &
                           template=matrix_t_in(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_copy(m_t_in_local(ispin), matrix_t_in(ispin))
      ENDDO

      ! init matrices for the initial guess
      ALLOCATE (m_theta(nspins))
      DO ispin = 1, nspins
         CALL dbcsr_create(m_theta(ispin), &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
      ENDDO

      ! create initial guess from the initial orbitals
      CALL xalmo_initial_guess(m_guess=m_theta, &
                               m_t_in=m_t_in_local, &
                               m_t0=almo_scf_env%matrix_t_blk, &
                               m_quench_t=quench_t, &
                               m_overlap=almo_scf_env%matrix_s(1), &
                               m_sigma_tmpl=almo_scf_env%matrix_sigma_inv, &
                               nspins=nspins, &
                               xalmo_history=almo_scf_env%xalmo_history, &
                               assume_t0_q0x=assume_t0_q0x, &
                               optimize_theta=optimize_theta, &
                               envelope_amplitude=almo_scf_env%envelope_amplitude, &
                               eps_filter=almo_scf_env%eps_filter, &
                               order_lanczos=almo_scf_env%order_lanczos, &
                               eps_lanczos=almo_scf_env%eps_lanczos, &
                               max_iter_lanczos=almo_scf_env%max_iter_lanczos)

      DO ispin = 1, nspins

         ! init temporary storage
         CALL dbcsr_create(prec_vv, &
                           template=almo_scf_env%matrix_ks(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(prec_oo, &
                           template=almo_scf_env%matrix_sigma(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(prec_oo_inv, &
                           template=almo_scf_env%matrix_sigma(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(m_tmp_oo_1, &
                           template=almo_scf_env%matrix_sigma(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(siginvTFTsiginv, &
                           template=almo_scf_env%matrix_sigma(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(STsiginv_0, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(m_tmp_no_1, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(m_tmp_no_2, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(m_tmp_no_3, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(FTsiginv, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(ST, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(prev_grad, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(grad, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(prev_step, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(step, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)
         CALL dbcsr_create(prev_minus_prec_grad, &
                           template=matrix_t_out(ispin), &
                           matrix_type=dbcsr_type_no_symmetry)

         ndomains = almo_scf_env%ndomains
         ALLOCATE (domain_r_down(ndomains))
         CALL init_submatrices(domain_r_down)

         CALL dbcsr_set(step, 0.0_dp)

         md_in_theta_space = .FALSE. ! turn on later after several minimization steps
         IF (do_md) THEN
            CALL dbcsr_create(velocity, &
                              template=matrix_t_out(ispin))
            CALL dbcsr_copy(velocity, quench_t(ispin))
            CALL dbcsr_set(velocity, 0.0_dp)
            CALL dbcsr_copy(prev_step, quench_t(ispin))
            CALL dbcsr_set(prev_step, 0.0_dp)
            time_step = optimizer%lin_search_step_size_guess
         ENDIF

         ! invert S domains if necessary
         ! RZK-warning must be done outside the spin loop to save time
         IF (my_special_case .EQ. xalmo_case_normal) THEN
            CALL construct_domain_s_inv( &
               matrix_s=almo_scf_env%matrix_s(1), &
               subm_s_inv=almo_scf_env%domain_s_inv(:, ispin), &
               dpattern=quench_t(ispin), &
               map=almo_scf_env%domain_map(ispin), &
               node_of_domain=almo_scf_env%cpu_of_domain)
         ENDIF

         IF (assume_t0_q0x) THEN

            ! save S.T_0.siginv_0
            IF (special_case .EQ. xalmo_case_fully_deloc) THEN
               CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                   almo_scf_env%matrix_s(1), &
                                   almo_scf_env%matrix_t_blk(ispin), &
                                   0.0_dp, ST, &
                                   filter_eps=almo_scf_env%eps_filter)
               CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                   ST, &
                                   almo_scf_env%matrix_sigma_inv_0deloc(ispin), &
                                   0.0_dp, STsiginv_0, &
                                   filter_eps=almo_scf_env%eps_filter)
            ENDIF

            ! construct domain-projector
            IF (my_special_case .EQ. xalmo_case_normal .AND. prec_type .EQ. 4) THEN
               CALL construct_domain_r_down( &
                  matrix_t=almo_scf_env%matrix_t_blk(ispin), &
                  matrix_sigma_inv=almo_scf_env%matrix_sigma_inv(ispin), &
                  matrix_s=almo_scf_env%matrix_s(1), &
                  subm_r_down=domain_r_down(:), &
                  dpattern=quench_t(ispin), &
                  map=almo_scf_env%domain_map(ispin), &
                  node_of_domain=almo_scf_env%cpu_of_domain, &
                  filter_eps=almo_scf_env%eps_filter)
            ENDIF

         ENDIF ! assume_t0_q0x

         IF (assume_t0_q0x) THEN

            ! save S.T_0.siginv_0
            IF (special_case .EQ. xalmo_case_fully_deloc) THEN
               CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                   almo_scf_env%matrix_s(1), &
                                   almo_scf_env%matrix_t_blk(ispin), &
                                   0.0_dp, ST, &
                                   filter_eps=almo_scf_env%eps_filter)
               CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                   ST, &
                                   almo_scf_env%matrix_sigma_inv_0deloc(ispin), &
                                   0.0_dp, STsiginv_0, &
                                   filter_eps=almo_scf_env%eps_filter)
            ENDIF

            ! construct domain-projector
            IF (my_special_case .EQ. xalmo_case_normal .AND. prec_type .EQ. 4) THEN
               CALL construct_domain_r_down( &
                  matrix_t=almo_scf_env%matrix_t_blk(ispin), &
                  matrix_sigma_inv=almo_scf_env%matrix_sigma_inv(ispin), &
                  matrix_s=almo_scf_env%matrix_s(1), &
                  subm_r_down=domain_r_down(:), &
                  dpattern=quench_t(ispin), &
                  map=almo_scf_env%domain_map(ispin), &
                  node_of_domain=almo_scf_env%cpu_of_domain, &
                  filter_eps=almo_scf_env%eps_filter)
            ENDIF

         ENDIF ! assume_t0_q0x

         ! start the outer SCF loop
         outer_max_iter = optimizer%max_iter_outer_loop
         outer_prepare_to_exit = .FALSE.
         outer_iteration = 0
         grad_norm = 0.0_dp
         grad_norm_frob = 0.0_dp
         use_guess = .FALSE.

         DO

            ! start the inner SCF loop
            max_iter = optimizer%max_iter
            prepare_to_exit = .FALSE.
            line_search = .FALSE.
            converged = .FALSE.
            iteration = 0
            cg_iteration = 0
            line_search_iteration = 0
            energy_new = 0.0_dp
            energy_old = 0.0_dp
            line_search_error = 0.0_dp
            t1 = m_walltime()

            DO

               just_started = (iteration .EQ. 0) .AND. (outer_iteration .EQ. 0)

               ! switch to MD after several minimization steps
               IF (iteration .EQ. almo_scf_env%integer01 .AND. do_md) THEN
                  CALL dbcsr_set(velocity, 0.0_dp)
                  CALL dbcsr_set(prev_step, 0.0_dp)
                  md_in_theta_space = .TRUE.
                  first_md_iteration = .TRUE.
               ENDIF

               ! check that all MO coefficients of the guess are less
               ! than the maximum allowed amplitude
               IF (optimize_theta) THEN
                  CALL dbcsr_copy(m_tmp_no_1, m_theta(ispin))
                  CALL dbcsr_norm(m_tmp_no_1, &
                                  dbcsr_norm_maxabsnorm, norm_scalar=t_norm)
                  IF (unit_nr > 0) THEN
                     WRITE (unit_nr, *) "Maximum norm of the initial guess: ", t_norm
                     WRITE (unit_nr, *) "Maximum allowed amplitude: ", &
                        almo_scf_env%envelope_amplitude
                  ENDIF
                  IF (t_norm .GT. almo_scf_env%envelope_amplitude .AND. just_started) THEN
                     CPABORT("Max norm of the initial guess is too large")
                  ENDIF
                  ! use artanh to tame the initial guess
                  CALL dbcsr_function_of_elements(m_tmp_no_1, &
                                                  func=dbcsr_func_tanh, &
                                                  a0=0.0_dp, &
                                                  a1=1.0_dp/almo_scf_env%envelope_amplitude)
                  !CALL dbcsr_function_of_elements(m_guess(ispin), &
                  !                                   func=dbcsr_func_artanh, &
                  !                                   a0=0.0_dp, &
                  !                                   a1=1.0_dp/envelope_amplitude)
                  CALL dbcsr_scale(m_tmp_no_1, &
                                   almo_scf_env%envelope_amplitude)
                  !CALL dbcsr_scale(m_guess(ispin), envelope_amplitude)
               ELSE
                  CALL dbcsr_copy(m_tmp_no_1, m_theta(ispin))
               ENDIF !optimize_theta
               CALL dbcsr_hadamard_product(m_tmp_no_1, quench_t(ispin), &
                                           matrix_t_out(ispin))

               ! project out R_0
               IF (assume_t0_q0x) THEN
                  IF (my_special_case .EQ. xalmo_case_fully_deloc) THEN
                     CALL dbcsr_multiply("T", "N", 1.0_dp, &
                                         STsiginv_0, &
                                         matrix_t_out(ispin), &
                                         0.0_dp, m_tmp_oo_1, &
                                         filter_eps=almo_scf_env%eps_filter)
                     CALL dbcsr_multiply("N", "N", -1.0_dp, &
                                         almo_scf_env%matrix_t_blk(ispin), &
                                         m_tmp_oo_1, &
                                         1.0_dp, matrix_t_out(ispin), &
                                         filter_eps=almo_scf_env%eps_filter)
                  ELSE IF (my_special_case .EQ. xalmo_case_block_diag) THEN
                     CPABORT("cannot use projector with block-daigonal ALMOs")
                  ELSE
                     ! no special case
                     CALL apply_domain_operators( &
                        matrix_in=matrix_t_out(ispin), &
                        matrix_out=m_tmp_no_1, &
                        operator1=domain_r_down(:), &
                        operator2=almo_scf_env%domain_s_inv(:, ispin), &
                        dpattern=quench_t(ispin), &
                        map=almo_scf_env%domain_map(ispin), &
                        node_of_domain=almo_scf_env%cpu_of_domain, &
                        my_action=1, &
                        filter_eps=almo_scf_env%eps_filter, &
                        !matrix_trimmer=,&
                        use_trimmer=.FALSE.)
                     CALL dbcsr_copy(matrix_t_out(ispin), &
                                     m_tmp_no_1)
                  ENDIF ! special case
                  CALL dbcsr_add(matrix_t_out(ispin), &
                                 almo_scf_env%matrix_t_blk(ispin), 1.0_dp, 1.0_dp)
               ENDIF
!IF (just_started) &
!CALL dbcsr_print(matrix_t_out(ispin))
!               CALL dbcsr_filter(matrix_t_out(ispin), &
!                                    eps=almo_scf_env%eps_filter)

               ! compute the density matrix
               CALL almo_scf_t_to_p( &
                  t=matrix_t_out(ispin), &
                  p=almo_scf_env%matrix_p(ispin), &
                  eps_filter=almo_scf_env%eps_filter, &
                  orthog_orbs=.FALSE., &
                  s=almo_scf_env%matrix_s(1), &
                  sigma=almo_scf_env%matrix_sigma(ispin), &
                  sigma_inv=almo_scf_env%matrix_sigma_inv(ispin), &
                  use_guess=use_guess)
               CALL dbcsr_scale(almo_scf_env%matrix_p(ispin), &
                                spin_factor)

               ! update the KS matrix and energy if necessary
               IF (perturbation_only) THEN
                  IF (just_started) THEN
                     CALL dbcsr_copy(almo_scf_env%matrix_ks(ispin), &
                                     almo_scf_env%matrix_ks_0deloc(ispin))
                  ENDIF
               ELSE
                  !!! RZK-warning the KS matrix must be updated outside the spin loop
                  !!! Now the code works only for restricted orbitals
                  CALL almo_scf_dm_to_ks(qs_env, almo_scf_env, energy_new)
                  CALL get_qs_env(qs_env, matrix_ks=matrix_ks)
                  CALL matrix_qs_to_almo(matrix_ks(ispin)%matrix, &
                                         almo_scf_env%matrix_ks(ispin), &
                                         almo_scf_env, .FALSE.)
                  CALL dbcsr_filter(almo_scf_env%matrix_ks(ispin), &
                                    almo_scf_env%eps_filter)
               ENDIF

               CALL compute_frequently_used_matrices( &
                  filter_eps=almo_scf_env%eps_filter, &
                  m_T_in=matrix_t_out(ispin), &
                  m_siginv_in=almo_scf_env%matrix_sigma_inv(ispin), &
                  m_S_in=almo_scf_env%matrix_s(1), &
                  m_F_in=almo_scf_env%matrix_ks(ispin), &
                  m_FTsiginv_out=FTsiginv, &
                  m_siginvTFTsiginv_out=siginvTFTsiginv, &
                  m_ST_out=ST)

               IF (perturbation_only) THEN
                  ! calculate objective function Tr(F_0 R)
                  CALL dbcsr_trace(matrix_t_out(ispin), FTsiginv, energy_new)
                  energy_new = energy_new*spin_factor
               ENDIF

               ! save the previous gradient to compute beta
               ! do it only if the previous grad was computed
               ! for .NOT.line_search
               IF (line_search_iteration .EQ. 0 .AND. iteration .NE. 0) &
                  CALL dbcsr_copy(prev_grad, grad)

               ! compute the energy gradient if necessary
               skip_grad = (iteration .GT. 0 .AND. &
                            fixed_line_search_niter .NE. 0 .AND. &
                            line_search_iteration .NE. fixed_line_search_niter)

               IF (.NOT. skip_grad) THEN

                  CALL compute_gradient( &
                     !m_grad_out=m_tmp_no_2,&
                     m_grad_out=grad, &
                     m_ks=almo_scf_env%matrix_ks(ispin), &
                     m_s=almo_scf_env%matrix_s(1), &
                     m_t=matrix_t_out(ispin), &
                     m_t0=almo_scf_env%matrix_t_blk(ispin), &
                     m_siginv=almo_scf_env%matrix_sigma_inv(ispin), &
                     m_quench_t=quench_t(ispin), &
                     m_FTsiginv=FTsiginv, &
                     m_siginvTFTsiginv=siginvTFTsiginv, &
                     m_ST=ST, &
                     m_STsiginv0=STsiginv_0, &
                     m_theta=m_theta(ispin), &
                     !m_sig_sqrti_ii=m_sig_sqrti_ii(ispin),&
                     domain_s_inv=almo_scf_env%domain_s_inv(:, ispin), &
                     domain_r_down=domain_r_down(:), &
                     cpu_of_domain=almo_scf_env%cpu_of_domain, &
                     domain_map=almo_scf_env%domain_map(ispin), &
                     assume_t0_q0x=assume_t0_q0x, &
                     optimize_theta=optimize_theta, &
                     perturbation_only=perturbation_only, &
                     normalize_orbitals=.FALSE., &
                     penalty_occ_vol=.FALSE., &
                     penalty_occ_vol_prefactor=0.0_dp, &
                     !normalize_orbitals=normalize_orbitals,&
                     !penalty_occ_vol=penalty_occ_vol,&
                     !penalty_occ_vol_prefactor=penalty_occ_vol_g_prefactor,&
                     envelope_amplitude=almo_scf_env%envelope_amplitude, &
                     eps_filter=almo_scf_env%eps_filter, &
                     spin_factor=spin_factor, &
                     special_case=my_special_case)

                  ! RZK-warning:
                  ! some obsolete routines require gradient in m_tmp_no_2
                  ! these must be removed and the line below deleted
                  CALL dbcsr_copy(m_tmp_no_2, grad)

               ENDIF ! skip_grad

               ! check convergence and other exit criteria
               grad_norm_frob = dbcsr_frobenius_norm(grad)
               CALL dbcsr_norm(grad, dbcsr_norm_maxabsnorm, &
                               norm_scalar=grad_norm)
               converged = (grad_norm .LT. optimizer%eps_error)
               IF (converged .OR. (iteration .GE. max_iter)) THEN
                  prepare_to_exit = .TRUE.
               ENDIF
               IF (grad_norm .LT. almo_scf_env%eps_prev_guess) THEN
                  use_guess = .TRUE.
               ENDIF

               IF (md_in_theta_space) THEN

                  IF (.NOT. first_md_iteration) THEN
                     CALL dbcsr_copy(prev_step, step)
                  ENDIF
                  CALL dbcsr_copy(step, grad)
                  CALL dbcsr_scale(step, -1.0_dp)

                  ! update velocities v(i) = v(i-1) + 0.5*dT*(a(i-1) + a(i))
                  IF (.NOT. first_md_iteration) THEN
                     CALL dbcsr_add(velocity, &
                                    step, 1.0_dp, 0.5_dp*time_step)
                     CALL dbcsr_add(velocity, &
                                    prev_step, 1.0_dp, 0.5_dp*time_step)
                  ENDIF
                  kin_energy = dbcsr_frobenius_norm(velocity)
                  kin_energy = 0.5_dp*kin_energy*kin_energy

                  ! update positions theta(i) = theta(i-1) + dT*v(i-1) + 0.5*dT*dT*a(i-1)
                  CALL dbcsr_add(m_theta(ispin), &
                                 velocity, 1.0_dp, time_step)
                  CALL dbcsr_add(m_theta(ispin), &
                                 step, 1.0_dp, 0.5_dp*time_step*time_step)

                  iter_type = "MD"

                  t2 = m_walltime()
                  IF (unit_nr > 0) THEN
                     WRITE (unit_nr, '(T2,A,A2,I5,F16.7,F17.9,F17.9,F17.9,E12.3,F10.3)') &
                        "ALMO SCF ", iter_type, iteration, time_step*iteration, &
                        energy_new, kin_energy, energy_new+kin_energy, grad_norm, &
                        t2-t1
                  ENDIF
                  t1 = m_walltime()

                  IF (first_md_iteration) THEN
                     first_md_iteration = .FALSE.
                  ENDIF

               ELSE ! optimizization (not MD)

                  IF (.NOT. prepare_to_exit) THEN

                     ! check the gradient along the step direction
                     IF (iteration .NE. 0) THEN

                        IF (fixed_line_search_niter .EQ. 0) THEN

                           CALL dbcsr_trace(grad, step, line_search_error)
                           ! normalize the result
                           !IF (unit_nr>0) THEN
                           !   WRITE(unit_nr,*) "Angle between step/grad: ", line_search_error
                           !ENDIF
                           CALL dbcsr_trace(grad, grad, denom)
                           !IF (unit_nr>0) THEN
                           !   WRITE(unit_nr,*) "Frobenius norm of grad:  ", SQRT(denom)
                           !ENDIF
                           line_search_error = line_search_error/SQRT(denom)
                           CALL dbcsr_trace(step, step, denom)
                           !IF (unit_nr>0) THEN
                           !   WRITE(unit_nr,*) "Frobenius norm of step:  ", SQRT(denom)
                           !ENDIF
                           line_search_error = line_search_error/SQRT(denom)
                           IF (ABS(line_search_error) .GT. optimizer%lin_search_eps_error) THEN
                              line_search = .TRUE.
                              line_search_iteration = line_search_iteration+1
                           ELSE
                              line_search = .FALSE.
                              line_search_iteration = 0
                              IF (grad_norm .LT. eps_skip_gradients) THEN
                                 fixed_line_search_niter = ABS(almo_scf_env%integer04)
                              ENDIF
                           ENDIF

                        ELSE ! decision for fixed_line_search_niter

                           IF (.NOT. line_search) THEN
                              line_search = .TRUE.
                              line_search_iteration = line_search_iteration+1
                           ELSE
                              IF (line_search_iteration .EQ. fixed_line_search_niter) THEN
                                 line_search = .FALSE.
                                 line_search_iteration = 0
                                 line_search_iteration = line_search_iteration+1
                              ENDIF
                           ENDIF

                        ENDIF ! fixed_line_search_niter fork
                     ENDIF

                     IF (line_search) THEN
                        energy_diff = 0.0_dp
                     ELSE
                        energy_diff = energy_new-energy_old
                        energy_old = energy_new
                     ENDIF

                     ! update the step direction
                     IF (.NOT. line_search) THEN

                        !IF (unit_nr>0) THEN
                        !   WRITE(unit_nr,*) "....updating step direction...."
                        !ENDIF

                        cg_iteration = cg_iteration+1

                        IF ((just_started .AND. perturbation_only) .OR. &
                            (iteration .EQ. 0 .AND. (.NOT. perturbation_only))) THEN

                           ! compute the preconditioner
                           !IF (unit_nr>0) THEN
                           !   WRITE(unit_nr,*) "....computing preconditioner...."
                           !ENDIF

                           ! calculate (1-R)F(1-R) and S-SRS
                           ! RZK-warning take advantage: some elements will be removed by the quencher
                           ! RZK-warning S operations can be performed outside the spin loop to save time
                           ! IT IS REQUIRED THAT PRECONDITIONER DOES NOT BREAK THE LOCALITY!!!!
                           ! RZK-warning: further optimization is ABSOLUTELY NECESSARY

                           ! First S-SRS
                           !CALL dbcsr_multiply("N","N",1.0_dp,&
                           !        almo_scf_env%matrix_s(1),&
                           !        matrix_t_out(ispin),&
                           !        0.0_dp,m_tmp_no_1,&
                           !        filter_eps=almo_scf_env%eps_filter)
                           CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                               ST, &
                                               almo_scf_env%matrix_sigma_inv(ispin), &
                                               0.0_dp, m_tmp_no_3, &
                                               filter_eps=almo_scf_env%eps_filter)
                           CALL dbcsr_create(m_tmp_nn_1, &
                                             template=almo_scf_env%matrix_s(1), &
                                             matrix_type=dbcsr_type_no_symmetry)
                           CALL dbcsr_desymmetrize(almo_scf_env%matrix_s(1), &
                                                   m_tmp_nn_1)
                           IF (my_special_case .EQ. xalmo_case_fully_deloc) THEN
                              ! use S instead of S-SRS
                           ELSE
                              CALL dbcsr_multiply("N", "T", -1.0_dp, &
                                                  ST, &
                                                  m_tmp_no_3, &
                                                  1.0_dp, m_tmp_nn_1, &
                                                  filter_eps=almo_scf_env%eps_filter)
                           ENDIF

                           ! Second (1-R)F(1-R)
                           !CALL dbcsr_multiply("N","N",1.0_dp,&
                           !        almo_scf_env%matrix_ks(ispin),&
                           !        matrix_t_out(ispin),&
                           !        0.0_dp,m_tmp_no_1,&
                           !        filter_eps=almo_scf_env%eps_filter)
                           ! re-create matrix because desymmetrize is buggy -
                           ! it will create multiple copies of blocks
                           CALL dbcsr_create(prec_vv, &
                                             template=almo_scf_env%matrix_ks(ispin), &
                                             matrix_type=dbcsr_type_no_symmetry)
                           CALL dbcsr_desymmetrize(almo_scf_env%matrix_ks(ispin), &
                                                   prec_vv)
                           CALL dbcsr_multiply("N", "T", -1.0_dp, &
                                               FTsiginv, &
                                               ST, &
                                               1.0_dp, prec_vv, &
                                               filter_eps=almo_scf_env%eps_filter)
                           CALL dbcsr_multiply("N", "T", -1.0_dp, &
                                               ST, &
                                               FTsiginv, &
                                               1.0_dp, prec_vv, &
                                               filter_eps=almo_scf_env%eps_filter)
                           !CALL dbcsr_multiply("T","N",1.0_dp,&
                           !        matrix_t_out(ispin),&
                           !        m_tmp_no_1,&
                           !        0.0_dp,m_tmp_oo_1,&
                           !        filter_eps=almo_scf_env%eps_filter)
                           CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                               ST, &
                                               siginvTFTsiginv, &
                                               0.0_dp, m_tmp_no_3, &
                                               filter_eps=almo_scf_env%eps_filter)
                           CALL dbcsr_multiply("N", "T", 1.0_dp, &
                                               m_tmp_no_3, &
                                               ST, &
                                               1.0_dp, prec_vv, &
                                               filter_eps=almo_scf_env%eps_filter)
                           CALL dbcsr_add(prec_vv, m_tmp_nn_1, &
                                          1.0_dp-prec_sf_mixing_s, &
                                          prec_sf_mixing_s)
                           CALL dbcsr_scale(prec_vv, 2.0_dp*spin_factor)
                           CALL dbcsr_copy(m_tmp_nn_1, prec_vv)

                           ! invert using various algorithms
                           IF (my_special_case .EQ. xalmo_case_block_diag) THEN ! non-overlapping diagonal blocks

                              !precond_domain_projector=0
                              !CALL construct_domain_preconditioner(&
                              !   matrix_main=m_tmp_nn_1,&
                              !   dpattern=quench_t(ispin),&
                              !   map=almo_scf_env%domain_map(ispin),&
                              !   node_of_domain=almo_scf_env%cpu_of_domain,&
                              !   preconditioner=almo_scf_env%domain_preconditioner(:,ispin),&
                              !   use_trimmer=.FALSE.,&
                              !   my_action=precond_domain_projector)
                              CALL pseudo_invert_diagonal_blk(matrix_in=m_tmp_nn_1, &
                                                              matrix_out=prec_vv, &
                                                              nocc=almo_scf_env%nocc_of_domain(:, ispin))

                           ELSE IF (my_special_case .EQ. xalmo_case_fully_deloc) THEN ! the entire system is a block

                              ! invert using cholesky (works with S matrix, will not work with S-SRS matrix)
                              CALL cp_dbcsr_cholesky_decompose(prec_vv, &
                                                               para_env=almo_scf_env%para_env, &
                                                               blacs_env=almo_scf_env%blacs_env)
                              CALL cp_dbcsr_cholesky_invert(prec_vv, &
                                                            para_env=almo_scf_env%para_env, &
                                                            blacs_env=almo_scf_env%blacs_env, &
                                                            upper_to_full=.TRUE.)
                              CALL dbcsr_filter(prec_vv, &
                                                eps=almo_scf_env%eps_filter)
                           ELSE
                              !!! use a sophisticated domain preconditioner
                              IF (assume_t0_q0x) THEN
                                 precond_domain_projector = -1
                              ELSE
                                 precond_domain_projector = 0
                              ENDIF
                              ! for other experimental preconditioner types the inversion is
                              ! done together with applying the preconditioner
                              IF (prec_type .EQ. 4) THEN

                                 CALL construct_domain_preconditioner( &
                                    matrix_main=m_tmp_nn_1, &
                                    subm_s_inv=almo_scf_env%domain_s_inv(:, ispin), &
                                    subm_r_down=domain_r_down(:), &
                                    matrix_trimmer=quench_t(ispin), &
                                    dpattern=quench_t(ispin), &
                                    map=almo_scf_env%domain_map(ispin), &
                                    node_of_domain=almo_scf_env%cpu_of_domain, &
                                    preconditioner=almo_scf_env%domain_preconditioner(:, ispin), &
                                    use_trimmer=.FALSE., &
                                    my_action=precond_domain_projector)
                              ENDIF ! prec type
                           ENDIF

                           ! invert using cholesky (works with S matrix, will not work with S-SRS matrix)
                           !!!CALL cp_dbcsr_cholesky_decompose(prec_vv,&
                           !!!        para_env=almo_scf_env%para_env,&
                           !!!        blacs_env=almo_scf_env%blacs_env)
                           !!!CALL cp_dbcsr_cholesky_invert(prec_vv,&
                           !!!        para_env=almo_scf_env%para_env,&
                           !!!        blacs_env=almo_scf_env%blacs_env,&
                           !!!        upper_to_full=.TRUE.)
                           !!!CALL dbcsr_filter(prec_vv,&
                           !!!        eps=almo_scf_env%eps_filter)
                           !!!

                           ! re-create the matrix because desymmetrize is buggy -
                           ! it will create multiple copies of blocks
                           !!!DESYM!CALL dbcsr_create(prec_vv,&
                           !!!DESYM!        template=almo_scf_env%matrix_s(1),&
                           !!!DESYM!        matrix_type=dbcsr_type_no_symmetry)
                           !!!DESYM!CALL dbcsr_desymmetrize(almo_scf_env%matrix_s(1),&
                           !!!DESYM!        prec_vv)
                           !CALL dbcsr_multiply("N","N",1.0_dp,&
                           !        almo_scf_env%matrix_s(1),&
                           !        matrix_t_out(ispin),&
                           !        0.0_dp,m_tmp_no_1,&
                           !        filter_eps=almo_scf_env%eps_filter)
                           !CALL dbcsr_multiply("N","N",1.0_dp,&
                           !        m_tmp_no_1,&
                           !        almo_scf_env%matrix_sigma_inv(ispin),&
                           !        0.0_dp,m_tmp_no_3,&
                           !        filter_eps=almo_scf_env%eps_filter)
                           !CALL dbcsr_multiply("N","T",-1.0_dp,&
                           !        m_tmp_no_3,&
                           !        m_tmp_no_1,&
                           !        1.0_dp,prec_vv,&
                           !        filter_eps=almo_scf_env%eps_filter)
                           !CALL dbcsr_add_on_diag(prec_vv,&
                           !        prec_sf_mixing_s)

                           !CALL dbcsr_create(prec_oo,&
                           !        template=almo_scf_env%matrix_sigma(ispin),&
                           !        matrix_type=dbcsr_type_no_symmetry)
                           !CALL dbcsr_desymmetrize(almo_scf_env%matrix_sigma(ispin),&
                           !        matrix_type=dbcsr_type_no_symmetry)
                           !CALL dbcsr_desymmetrize(almo_scf_env%matrix_sigma(ispin),&
                           !        prec_oo)
                           !CALL dbcsr_filter(prec_oo,&
                           !        eps=almo_scf_env%eps_filter)

                           !! invert using cholesky
                           !CALL dbcsr_create(prec_oo_inv,&
                           !        template=prec_oo,&
                           !        matrix_type=dbcsr_type_no_symmetry)
                           !CALL dbcsr_desymmetrize(prec_oo,&
                           !        prec_oo_inv)
                           !CALL cp_dbcsr_cholesky_decompose(prec_oo_inv,&
                           !        para_env=almo_scf_env%para_env,&
                           !        blacs_env=almo_scf_env%blacs_env)
                           !CALL cp_dbcsr_cholesky_invert(prec_oo_inv,&
                           !        para_env=almo_scf_env%para_env,&
                           !        blacs_env=almo_scf_env%blacs_env,&
                           !        upper_to_full=.TRUE.)

                        ENDIF

                        ! save the previous step
                        CALL dbcsr_copy(prev_step, step)

                        ! compute the new step (apply preconditioner if available)
                        IF (use_preconditioner) THEN

                           !IF (unit_nr>0) THEN
                           !   WRITE(unit_nr,*) "....applying preconditioner...."
                           !ENDIF

                           SELECT CASE (prec_type)
                           CASE (1)
                              ! expensive Newton-Raphson step (the Hessian is still approximate)
                              ! RZK-warning THIS PREC HAS NOT BEEN IMPLEMENTED FOR THETA
                              IF (ncores .GT. 1) THEN
                                 CPABORT("serial code only")
                              ENDIF
                              CALL newton_grad_to_step( &
                                 matrix_grad=m_tmp_no_2, &
                                 matrix_step=m_tmp_no_1, &
                                 matrix_s=almo_scf_env%matrix_s(1), &
                                 matrix_ks=almo_scf_env%matrix_ks(ispin), &
                                 matrix_t=matrix_t_out(ispin), &
                                 matrix_sigma_inv=almo_scf_env%matrix_sigma_inv(ispin), &
                                 !matrix_ks=matrix_ks_0,&
                                 !matrix_t=almo_scf_env%matrix_t_blk(ispin),&
                                 !matrix_sigma_inv=matrix_sigma_inv_0,&
                                 quench_t=quench_t(ispin), &
                                 spin_factor=spin_factor, &
                                 eps_filter=almo_scf_env%eps_filter)

                           CASE (3)

                              ! RZK-warning THIS PREC HAS NOT BEEN IMPLEMENTED FOR THETA

                              ! inversion
                              CALL dbcsr_get_info(m_tmp_nn_1, nfullrows_total=dim0)
                              ALLOCATE (evals(dim0))
                              CALL cp_dbcsr_syevd(m_tmp_nn_1, prec_vv, evals, &
                                                  almo_scf_env%para_env, almo_scf_env%blacs_env)
                              ! invert eigenvalues and use eigenvectors to compute the Hessian inverse
                              ! take special care of zero eigenvalues
                              zero_neg_eiv = 0
                              CALL dbcsr_get_info(almo_scf_env%matrix_sigma(ispin), nfullrows_total=occ1)
                              DO jj = 1, dim0
                                 IF (jj .LE. occ1) THEN
                                    evals(jj) = evals(jj)*0.0_dp
                                    zero_neg_eiv = zero_neg_eiv+1
                                 ELSE
                                    evals(jj) = 1.0_dp/evals(jj)
                                 ENDIF
                              ENDDO
                              IF (unit_nr > 0) THEN
                                 WRITE (unit_nr, *) 'ZERO OR NEGATIVE EIGENVALUES: ', zero_neg_eiv
                              ENDIF
                              CALL dbcsr_create(inv_eiv, &
                                                template=m_tmp_nn_1, &
                                                matrix_type=dbcsr_type_no_symmetry)
                              CALL dbcsr_add_on_diag(inv_eiv, 1.0_dp)
                              CALL dbcsr_set_diag(inv_eiv, evals)
                              CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                                  prec_vv, &
                                                  inv_eiv, &
                                                  0.0_dp, m_tmp_nn_1, &
                                                  filter_eps=almo_scf_env%eps_filter)
                              CALL dbcsr_multiply("N", "T", 1.0_dp, &
                                                  m_tmp_nn_1, &
                                                  prec_vv, &
                                                  0.0_dp, inv_eiv, &
                                                  filter_eps=almo_scf_env%eps_filter)
                              CALL dbcsr_copy(prec_vv, inv_eiv)
                              CALL dbcsr_release(inv_eiv)
                              DEALLOCATE (evals)

                              !!CALL dbcsr_copy(step,&
                              !!        quench_t(ispin))
                              !!
                              !!CALL dbcsr_multiply("N","N",1.0_dp,&
                              !!        m_tmp_no_2,&
                              !!        !grad,& - this choice is worse
                              !!        prec_oo,&
                              !!        0.0_dp,step,&
                              !!        !retain_sparsity=.TRUE.,&
                              !!        filter_eps=almo_scf_env%eps_filter)
                              !!
                              CALL dbcsr_copy(m_tmp_no_1, &
                                              quench_t(ispin))
                              !!CALL dbcsr_hadamard_product(&
                              !!        quench_t(ispin),&
                              !!        step,&
                              !!        m_tmp_no_1)
                              !!
                              CALL dbcsr_multiply("N", "N", -1.0_dp, &
                                                  prec_vv, &
                                                  m_tmp_no_2, &
                                                  0.0_dp, m_tmp_no_1, &
                                                  retain_sparsity=.TRUE.)

                           CASE (4)

                              IF (my_special_case .EQ. xalmo_case_block_diag .OR. &
                                  my_special_case .EQ. xalmo_case_fully_deloc) THEN

                                 CALL dbcsr_multiply("N", "N", -1.0_dp, &
                                                     prec_vv, &
                                                     grad, &
                                                     0.0_dp, step, &
                                                     filter_eps=almo_scf_env%eps_filter)

                              ELSE

                                 !!! RZK-warning Currently for non-theta only
                                 IF (optimize_theta) THEN
                                    CPABORT("theta is NYI")
                                 ENDIF

                                 CALL apply_domain_operators( &
                                    matrix_in=grad, &
                                    matrix_out=step, &
                                    operator1=almo_scf_env%domain_preconditioner(:, ispin), &
                                    !operator2=,&
                                    dpattern=quench_t(ispin), &
                                    map=almo_scf_env%domain_map(ispin), &
                                    node_of_domain=almo_scf_env%cpu_of_domain, &
                                    my_action=0, &
                                    filter_eps=almo_scf_env%eps_filter)
                                 !matrix_trimmer=,&
                                 !use_trimmer=.FALSE.,&
                                 CALL dbcsr_scale(step, -1.0_dp)

                                 CALL dbcsr_copy(m_tmp_no_3, &
                                                 quench_t(ispin))
                                 CALL dbcsr_function_of_elements(m_tmp_no_3, &
                                                                 func=dbcsr_func_inverse, &
                                                                 a0=0.0_dp, &
                                                                 a1=1.0_dp)
                                 CALL dbcsr_copy(m_tmp_no_2, step)
                                 CALL dbcsr_hadamard_product( &
                                    m_tmp_no_2, &
                                    m_tmp_no_3, &
                                    step)
                                 CALL dbcsr_copy(m_tmp_no_3, quench_t(ispin))

                                 !CALL dbcsr_create(m_tmp_oo_1,&
                                 !        template=almo_scf_env%matrix_sigma_blk(ispin),&
                                 !        matrix_type=dbcsr_type_no_symmetry)
                                 !CALL dbcsr_desymmetrize(almo_scf_env%matrix_sigma_blk(ispin),m_tmp_oo_1)
                                 !CALL get_overlap(bra=matrix_t_out(ispin),&
                                 !        ket=step,&
                                 !        overlap=m_tmp_oo_1,&
                                 !        metric=almo_scf_env%matrix_s(1),&
                                 !        retain_overlap_sparsity=.TRUE.,&
                                 !        eps_filter=almo_scf_env%eps_filter)
                                 !CALL dbcsr_norm(m_tmp_oo_1,&
                                 !        dbcsr_norm_maxabsnorm, norm_scalar=t_norm)
                                 !IF (unit_nr>0) THEN
                                 !   WRITE(unit_nr,*) "Step block-orthogonality error: ", t_norm
                                 !ENDIF

                              ENDIF ! special case

                           END SELECT ! preconditioner type fork

                        ELSE

                           !!!! NO PRECONDITIONER
                           CALL dbcsr_copy(step, grad)
                           CALL dbcsr_scale(step, -1.0_dp)

                        ENDIF

                        ! check whether we need to reset conjugate directions
                        IF (iteration .EQ. 0) THEN
                           reset_conjugator = .TRUE.
                        ENDIF

                        ! compute the conjugation coefficient - beta
                        IF (.NOT. reset_conjugator) THEN

                           SELECT CASE (optimizer%conjugator)
                           CASE (cg_hestenes_stiefel)
                              CALL dbcsr_copy(m_tmp_no_1, grad)
                              CALL dbcsr_add(m_tmp_no_1, prev_grad, &
                                             1.0_dp, -1.0_dp)
                              CALL dbcsr_trace(m_tmp_no_1, step, numer)
                              CALL dbcsr_trace(m_tmp_no_1, prev_step, denom)
                              beta = -1.0_dp*numer/denom
                           CASE (cg_fletcher_reeves)
                              CALL dbcsr_trace(grad, step, numer)
                              CALL dbcsr_trace(prev_grad, prev_minus_prec_grad, denom)
                              beta = numer/denom
                           CASE (cg_polak_ribiere)
                              CALL dbcsr_trace(prev_grad, prev_minus_prec_grad, denom)
                              CALL dbcsr_copy(m_tmp_no_1, grad)
                              CALL dbcsr_add(m_tmp_no_1, prev_grad, 1.0_dp, -1.0_dp)
                              CALL dbcsr_trace(m_tmp_no_1, step, numer)
                              beta = numer/denom
                           CASE (cg_fletcher)
                              CALL dbcsr_trace(grad, step, numer)
                              CALL dbcsr_trace(prev_grad, prev_step, denom)
                              beta = numer/denom
                           CASE (cg_liu_storey)
                              CALL dbcsr_trace(prev_grad, prev_step, denom)
                              CALL dbcsr_copy(m_tmp_no_1, grad)
                              CALL dbcsr_add(m_tmp_no_1, prev_grad, 1.0_dp, -1.0_dp)
                              CALL dbcsr_trace(m_tmp_no_1, step, numer)
                              beta = numer/denom
                           CASE (cg_dai_yuan)
                              CALL dbcsr_trace(grad, step, numer)
                              CALL dbcsr_copy(m_tmp_no_1, grad)
                              CALL dbcsr_add(m_tmp_no_1, prev_grad, 1.0_dp, -1.0_dp)
                              CALL dbcsr_trace(m_tmp_no_1, prev_step, denom)
                              beta = -1.0_dp*numer/denom
                           CASE (cg_hager_zhang)
                              CALL dbcsr_copy(m_tmp_no_1, grad)
                              CALL dbcsr_add(m_tmp_no_1, prev_grad, 1.0_dp, -1.0_dp)
                              CALL dbcsr_trace(m_tmp_no_1, prev_step, denom)
                              CALL dbcsr_trace(m_tmp_no_1, prev_minus_prec_grad, numer)
                              kappa = -2.0_dp*numer/denom
                              CALL dbcsr_trace(m_tmp_no_1, step, numer)
                              tau = -1.0_dp*numer/denom
                              CALL dbcsr_trace(prev_step, grad, numer)
                              beta = tau-kappa*numer/denom
                           CASE (cg_zero)
                              beta = 0.0_dp
                           CASE DEFAULT
                              CPABORT("illegal conjugator")
                           END SELECT

                           IF (beta .LT. 0.0_dp) THEN
                              IF (unit_nr > 0) THEN
                                 WRITE (unit_nr, *) "Beta is negative: ", beta
                              ENDIF
                              reset_conjugator = .TRUE.
                           ENDIF

                        ENDIF

                        IF (reset_conjugator) THEN

                           beta = 0.0_dp
                           IF (unit_nr > 0 .AND. (.NOT. just_started)) THEN
                              WRITE (unit_nr, *) "(Re)-setting conjugator to zero"
                           ENDIF
                           reset_conjugator = .FALSE.

                        ENDIF

                        ! save the preconditioned gradient (useful for beta)
                        CALL dbcsr_copy(prev_minus_prec_grad, step)

                        !IF (unit_nr>0) THEN
                        !   WRITE(unit_nr,*) "....final beta....", beta
                        !ENDIF

                        ! conjugate the step direction
                        CALL dbcsr_add(step, prev_step, 1.0_dp, beta)

                     ENDIF ! update the step direction

                     ! estimate the step size
                     IF (.NOT. line_search) THEN
                        e0 = energy_new
                        CALL dbcsr_trace(grad, step, g0)
                        ! we just changed the direction and
                        ! we have only E and grad from the current step
                        ! it is not enouhg to compute step_size - just guess it
                        IF (iteration .EQ. 0) THEN
                           step_size = optimizer%lin_search_step_size_guess
                        ELSE
                           IF (next_step_size_guess .LE. 0.0_dp) THEN
                              step_size = optimizer%lin_search_step_size_guess
                           ELSE
                              ! take the last value
                              step_size = next_step_size_guess*1.05_dp
                           ENDIF
                        ENDIF
                        next_step_size_guess = step_size
                     ELSE
                        IF (fixed_line_search_niter .EQ. 0) THEN
                           e1 = energy_new
                           CALL dbcsr_trace(grad, step, g1)
                           ! we have accumulated some points along this direction
                           ! use only the most recent g0 (quadratic approximation)
                           appr_sec_der = (g1-g0)/step_size
                           !IF (unit_nr>0) THEN
                           !   WRITE(unit_nr,'(A2,7F12.5)') &
                           !           "EG",e0,e1,g0,g1,appr_sec_der,step_size,-g1/appr_sec_der
                           !ENDIF
                           step_size = -g1/appr_sec_der
                           e0 = e1
                           g0 = g1
                        ELSE
                           ! use e0, g0 and e1 to compute g1 and make a step
                           ! if the next iteration is also line_search
                           ! use e1 and the calculated g1 as e0 and g0
                           e1 = energy_new
                           appr_sec_der = 2.0*((e1-e0)/step_size-g0)/step_size
                           g1 = appr_sec_der*step_size+g0
                           IF (unit_nr > 0) THEN
                              WRITE (unit_nr, '(A2,7F12.5)') &
                                 "EG", e0, e1, g0, g1, appr_sec_der, step_size, -g1/appr_sec_der
                           ENDIF
                           !appr_sec_der=(g1-g0)/step_size
                           step_size = -g1/appr_sec_der
                           e0 = e1
                           g0 = g1
                        ENDIF
                        next_step_size_guess = next_step_size_guess+step_size
                     ENDIF

                     ! update theta
                     CALL dbcsr_add(m_theta(ispin), step, 1.0_dp, step_size)

                  ENDIF ! not.prepare_to_exit

                  IF (line_search) THEN
                     iter_type = "LS"
                  ELSE
                     iter_type = "CG"
                  ENDIF

                  t2 = m_walltime()
                  IF (unit_nr > 0) THEN
                     iter_type = TRIM("ALMO SCF "//iter_type)
                     WRITE (unit_nr, '(T2,A13,I6,F23.10,E14.5,F14.9,F9.2)') &
                        iter_type, iteration, &
                        energy_new, energy_diff, grad_norm, &
                        t2-t1
                     !WRITE(unit_nr,'(T2,A11,I6,F20.12,E12.3,E12.3,E12.3,F12.5,F10.3)') &
                     !        "ALMO SCF ",iter_type,iteration,&
                     !        energy_new,energy_diff,grad_norm,line_search_error,&
                     !        step_size,t2-t1
                  ENDIF

                  IF (my_special_case .EQ. xalmo_case_block_diag) THEN
                     almo_scf_env%almo_scf_energy = energy_new
                  ENDIF

                  t1 = m_walltime()

               ENDIF ! MD in theta space

               iteration = iteration+1
               IF (prepare_to_exit) EXIT

            ENDDO ! inner SCF loop

            IF (converged .OR. (outer_iteration .GE. outer_max_iter)) THEN
               outer_prepare_to_exit = .TRUE.
            ENDIF

            outer_iteration = outer_iteration+1
            IF (outer_prepare_to_exit) EXIT

         ENDDO ! outer SCF loop

         ! post SCF-loop calculations
         IF (converged) THEN

            ! RZK-warning: must obtain MO coefficients from final theta

            IF (perturbation_only) THEN

               ! compute Fvo for the zero-delocalization state
               CALL dbcsr_create(fvo_0, &
                                 template=matrix_t_out(ispin), &
                                 matrix_type=dbcsr_type_no_symmetry)
               CALL compute_frequently_used_matrices( &
                  filter_eps=almo_scf_env%eps_filter, &
                  m_T_in=almo_scf_env%matrix_t_blk(ispin), &
                  m_siginv_in=almo_scf_env%matrix_sigma_inv_0deloc(ispin), &
                  m_S_in=almo_scf_env%matrix_s(1), &
                  m_F_in=almo_scf_env%matrix_ks_0deloc(ispin), &
                  m_FTsiginv_out=FTsiginv, &
                  m_siginvTFTsiginv_out=siginvTFTsiginv, &
                  m_ST_out=ST)
               CALL dbcsr_copy(fvo_0, quench_t(ispin))
               CALL dbcsr_copy(fvo_0, FTsiginv, keep_sparsity=.TRUE.)
               CALL dbcsr_multiply("N", "N", -1.0_dp, &
                                   ST, &
                                   siginvTFTsiginv, &
                                   1.0_dp, fvo_0, &
                                   retain_sparsity=.TRUE.)

               ! use step matrix to store excitation amplitudes
               CALL dbcsr_copy(step, almo_scf_env%matrix_t_blk(ispin))
               CALL dbcsr_add(step, matrix_t_out(ispin), &
                              -1.0_dp, 1.0_dp)

               CALL dbcsr_scale(fvo_0, spin_factor)
               CALL dbcsr_trace(step, fvo_0, energy_new)

               !CALL dbcsr_add(almo_scf_env%matrix_t_blk(ispin),matrix_t_out(ispin),&
               !        -1.0_dp,1.0_dp)
               !CALL dbcsr_trace(almo_scf_env%matrix_t_blk(ispin),&
               !        fvo_0,energy_new,"T","N")

               ! print out the energy lowering
               IF (unit_nr > 0) THEN
                  WRITE (unit_nr, *)
                  WRITE (unit_nr, '(T2,A35,F25.10)') "ENERGY OF BLOCK-DIAGONAL ALMOs:", &
                     almo_scf_env%almo_scf_energy
                  WRITE (unit_nr, '(T2,A35,F25.10)') "ENERGY LOWERING:", &
                     energy_new
                  WRITE (unit_nr, '(T2,A35,F25.10)') "CORRECTED ENERGY:", &
                     almo_scf_env%almo_scf_energy+energy_new
                  WRITE (unit_nr, *)
               ENDIF
               CALL almo_scf_update_ks_energy(qs_env, &
                                              energy=almo_scf_env%almo_scf_energy, &
                                              energy_singles_corr=energy_new)

               IF (almo_scf_env%almo_analysis%do_analysis) THEN

                  ! energy decomposition analysis (EDA)
                  IF (unit_nr > 0) THEN
                     WRITE (unit_nr, '(T2,A)') "DECOMPOSITION OF THE DELOCALIZATION ENERGY"
                  ENDIF

                  CALL dbcsr_hadamard_product(step, &
                                              fvo_0, m_tmp_no_1)
                  !CALL dbcsr_hadamard_product(almo_scf_env%matrix_t_blk(ispin), &
                  !        fvo_0,m_tmp_no_1)
                  CALL dbcsr_filter(m_tmp_no_1, almo_scf_env%eps_filter)

                  ! open the output file, print and close
                  CALL get_qs_env(qs_env, input=input)
                  almo_print_section => section_vals_get_subs_vals(input, "DFT%ALMO_SCF%ANALYSIS%PRINT")
                  eda_unit = cp_print_key_unit_nr(logger, almo_print_section, &
                                                  "ALMO_EDA_CT", extension=".dat", local=.TRUE.)
                  CALL dbcsr_print_block_sum(m_tmp_no_1, eda_unit)
                  CALL cp_print_key_finished_output(eda_unit, logger, almo_print_section, &
                                                    "ALMO_EDA_CT", local=.TRUE.)

                  ! charge transfer analysis (CTA)
                  IF (unit_nr > 0) THEN
                     WRITE (unit_nr, '(T2,A)') "DECOMPOSITION OF CHARGE TRANSFER TERMS"
                  ENDIF

                  ! first, compute [QR'R]_mu^i = [(S-SRS).X.siginv']_mu^i
                  ! a. STsiginv_0 = S.T0*siginv0
                  CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                      ST, &
                                      almo_scf_env%matrix_sigma_inv_0deloc(ispin), &
                                      0.0_dp, STsiginv_0, &
                                      filter_eps=almo_scf_env%eps_filter)
                  ! c. tmp1 = S.X
                  CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                      almo_scf_env%matrix_s(1), &
                                      step, &
                                      0.0_dp, m_tmp_no_1, &
                                      filter_eps=almo_scf_env%eps_filter)
                  ! d. tmp2 = tr(T0).tmp1 = tr(T0).S.X
                  CALL dbcsr_multiply("T", "N", 1.0_dp, &
                                      almo_scf_env%matrix_t_blk(ispin), &
                                      m_tmp_no_1, &
                                      0.0_dp, m_tmp_oo_1, &
                                      filter_eps=almo_scf_env%eps_filter)
                  ! e. tmp1 = tmp1 - tmp3.tmp2 = S.X - S.T0.siginv0*tr(T0).S.X
                  !         = (1-S.R0).S.X
                  CALL dbcsr_multiply("N", "N", -1.0_dp, &
                                      STsiginv_0, &
                                      m_tmp_oo_1, &
                                      1.0_dp, m_tmp_no_1, &
                                      filter_eps=almo_scf_env%eps_filter)
                  ! f. tmp2 = tmp1*siginv
                  CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                      m_tmp_no_1, &
                                      almo_scf_env%matrix_sigma_inv(ispin), &
                                      0.0_dp, m_tmp_no_2, &
                                      filter_eps=almo_scf_env%eps_filter)
                  ! second, compute traces of blocks [RR'Q]^x_y * [X]^y_x
                  CALL dbcsr_hadamard_product(step, &
                                              m_tmp_no_2, m_tmp_no_1)
                  CALL dbcsr_scale(m_tmp_no_1, spin_factor)
                  CALL dbcsr_filter(m_tmp_no_1, almo_scf_env%eps_filter)

                  eda_unit = cp_print_key_unit_nr(logger, almo_print_section, &
                                                  "ALMO_CTA", extension=".dat", local=.TRUE.)
                  CALL dbcsr_print_block_sum(m_tmp_no_1, eda_unit)
                  CALL cp_print_key_finished_output(eda_unit, logger, almo_print_section, &
                                                    "ALMO_CTA", local=.TRUE.)

               ENDIF ! do ALMO EDA/CTA

               CALL dbcsr_release(fvo_0)

            ELSE

               CALL almo_scf_update_ks_energy(qs_env, &
                                              energy=energy_new)

            ENDIF ! if perturbation only

            !CALL qs_ks_update_qs_env(qs_env, &
            !        calculate_forces=.FALSE., &
            !        just_energy=.TRUE., &
            !        print_active=.TRUE.)

         ENDIF ! if converged

         IF (md_in_theta_space) THEN
            CALL dbcsr_release(velocity)
         ENDIF
         CALL dbcsr_release(prec_vv)
         CALL dbcsr_release(prec_oo)
         CALL dbcsr_release(prec_oo_inv)
         CALL dbcsr_release(m_tmp_no_1)
         CALL dbcsr_release(STsiginv_0)
         CALL dbcsr_release(m_tmp_no_2)
         CALL dbcsr_release(m_tmp_no_3)
         CALL dbcsr_release(m_tmp_oo_1)
         CALL dbcsr_release(ST)
         CALL dbcsr_release(FTsiginv)
         CALL dbcsr_release(siginvTFTsiginv)
         CALL dbcsr_release(m_tmp_nn_1)
         CALL dbcsr_release(prev_grad)
         CALL dbcsr_release(prev_step)
         CALL dbcsr_release(grad)
         CALL dbcsr_release(step)
         CALL dbcsr_release(prev_minus_prec_grad)

         IF (.NOT. converged) THEN
            CPABORT("Optimization not converged! ")
         ENDIF

         DEALLOCATE (domain_r_down)

      ENDDO ! ispin

      DO ispin = 1, nspins
         CALL dbcsr_release(m_theta(ispin))
         CALL dbcsr_release(m_t_in_local(ispin))
      ENDDO ! ispin
      DEALLOCATE (m_theta, m_t_in_local)

      CALL timestop(handle)

   END SUBROUTINE almo_scf_xalmo_pcg

! **************************************************************************************************
!> \brief Compute matrices that are used often in various parts of the
!>        optimization procedure
!> \param filter_eps ...
!> \param m_T_in ...
!> \param m_siginv_in ...
!> \param m_S_in ...
!> \param m_F_in ...
!> \param m_FTsiginv_out ...
!> \param m_siginvTFTsiginv_out ...
!> \param m_ST_out ...
!> \par History
!>       2016.12 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE compute_frequently_used_matrices(filter_eps, &
                                               m_T_in, m_siginv_in, m_S_in, m_F_in, m_FTsiginv_out, &
                                               m_siginvTFTsiginv_out, m_ST_out)

      REAL(KIND=dp), INTENT(IN)                          :: filter_eps
      TYPE(dbcsr_type), INTENT(IN)                       :: m_T_in, m_siginv_in, m_S_in, m_F_in
      TYPE(dbcsr_type), INTENT(INOUT)                    :: m_FTsiginv_out, m_siginvTFTsiginv_out, &
                                                            m_ST_out

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

      INTEGER                                            :: handle
      TYPE(dbcsr_type)                                   :: m_tmp_no_1, m_tmp_oo_1

      CALL timeset(routineN, handle)

      CALL dbcsr_create(m_tmp_no_1, &
                        template=m_T_in, &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL dbcsr_create(m_tmp_oo_1, &
                        template=m_siginv_in, &
                        matrix_type=dbcsr_type_no_symmetry)

      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          m_F_in, &
                          m_T_in, &
                          0.0_dp, m_tmp_no_1, &
                          filter_eps=filter_eps)

      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          m_tmp_no_1, &
                          m_siginv_in, &
                          0.0_dp, m_FTsiginv_out, &
                          filter_eps=filter_eps)

      CALL dbcsr_multiply("T", "N", 1.0_dp, &
                          m_T_in, &
                          m_FTsiginv_out, &
                          0.0_dp, m_tmp_oo_1, &
                          filter_eps=filter_eps)

      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          m_siginv_in, &
                          m_tmp_oo_1, &
                          0.0_dp, m_siginvTFTsiginv_out, &
                          filter_eps=filter_eps)

      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          m_S_in, &
                          m_T_in, &
                          0.0_dp, m_ST_out, &
                          filter_eps=filter_eps)

      CALL dbcsr_release(m_tmp_no_1)
      CALL dbcsr_release(m_tmp_oo_1)

      CALL timestop(handle)

   END SUBROUTINE compute_frequently_used_matrices

! **************************************************************************************************
!> \brief Split the matrix of virtual orbitals into two:
!>        retained orbs and discarded
!> \param almo_scf_env ...
!> \par History
!>       2011.09 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE split_v_blk(almo_scf_env)

      TYPE(almo_scf_env_type)                            :: almo_scf_env

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

      INTEGER                                            :: discarded_v, handle, iblock_col, &
                                                            iblock_col_size, iblock_row, &
                                                            iblock_row_size, ispin, retained_v
      REAL(kind=dp), DIMENSION(:, :), POINTER            :: data_p, p_new_block
      TYPE(dbcsr_iterator_type)                          :: iter

      CALL timeset(routineN, handle)

      DO ispin = 1, almo_scf_env%nspins

         CALL dbcsr_work_create(almo_scf_env%matrix_v_blk(ispin), &
                                work_mutable=.TRUE.)
         CALL dbcsr_work_create(almo_scf_env%matrix_v_disc_blk(ispin), &
                                work_mutable=.TRUE.)

         CALL dbcsr_iterator_start(iter, almo_scf_env%matrix_v_full_blk(ispin))

         DO WHILE (dbcsr_iterator_blocks_left(iter))

            CALL dbcsr_iterator_next_block(iter, iblock_row, iblock_col, data_p, &
                                           row_size=iblock_row_size, col_size=iblock_col_size)

            IF (iblock_row .NE. iblock_col) THEN
               CPABORT("off-diagonal block found")
            ENDIF

            retained_v = almo_scf_env%nvirt_of_domain(iblock_col, ispin)
            discarded_v = almo_scf_env%nvirt_disc_of_domain(iblock_col, ispin)
            CPASSERT(retained_v .GT. 0)
            CPASSERT(discarded_v .GT. 0)

            NULLIFY (p_new_block)
            CALL dbcsr_reserve_block2d(almo_scf_env%matrix_v_disc_blk(ispin), &
                                       iblock_row, iblock_col, p_new_block)
            CPASSERT(ASSOCIATED(p_new_block))
            CPASSERT(retained_v+discarded_v .EQ. iblock_col_size)
            p_new_block(:, :) = data_p(:, (retained_v+1):iblock_col_size)

            NULLIFY (p_new_block)
            CALL dbcsr_reserve_block2d(almo_scf_env%matrix_v_blk(ispin), &
                                       iblock_row, iblock_col, p_new_block)
            CPASSERT(ASSOCIATED(p_new_block))
            p_new_block(:, :) = data_p(:, 1:retained_v)

         ENDDO ! iterator
         CALL dbcsr_iterator_stop(iter)

         CALL dbcsr_finalize(almo_scf_env%matrix_v_blk(ispin))
         CALL dbcsr_finalize(almo_scf_env%matrix_v_disc_blk(ispin))

      ENDDO ! ispin

      CALL timestop(handle)

   END SUBROUTINE split_v_blk

! **************************************************************************************************
!> \brief various methods for calculating the Harris-Foulkes correction
!> \param almo_scf_env ...
!> \par History
!>       2011.06 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE harris_foulkes_correction(almo_scf_env)

      TYPE(almo_scf_env_type)                            :: almo_scf_env

      CHARACTER(len=*), PARAMETER :: routineN = 'harris_foulkes_correction', &
         routineP = moduleN//':'//routineN
      INTEGER, PARAMETER                                 :: cayley_transform = 1, dm_ls_step = 2

      INTEGER :: algorithm_id, handle, handle1, handle2, handle3, handle4, handle5, handle6, &
         handle7, handle8, ispin, iteration, n, nmins, nspin, opt_k_max_iter, &
         outer_opt_k_iteration, outer_opt_k_max_iter, unit_nr
      INTEGER, DIMENSION(1)                              :: fake, nelectron_spin_real
      LOGICAL :: converged, line_search, md_in_k_space, outer_opt_k_prepare_to_exit, &
         prepare_to_exit, reset_conjugator, reset_step_size, use_cubic_approximation, &
         use_quadratic_approximation
      REAL(KIND=dp) :: aa, bb, beta, conjugacy_error, conjugacy_error_threshold, &
         delta_obj_function, denom, energy_correction_final, frob_matrix, frob_matrix_base, fun0, &
         fun1, gfun0, gfun1, grad_norm, grad_norm_frob, kappa, kin_energy, line_search_error, &
         line_search_error_threshold, num_threshold, numer, obj_function, quadratic_approx_error, &
         quadratic_approx_error_threshold, safety_multiplier, spin_factor, step_size, &
         step_size_quadratic_approx, step_size_quadratic_approx2, t1, t1a, t1cholesky, t2, t2a, &
         t2cholesky, tau, time_step, x_opt_eps_adaptive, x_opt_eps_adaptive_factor
      REAL(KIND=dp), DIMENSION(1)                        :: local_mu
      REAL(KIND=dp), DIMENSION(2)                        :: energy_correction
      REAL(KIND=dp), DIMENSION(3)                        :: minima
      TYPE(cp_logger_type), POINTER                      :: logger
      TYPE(ct_step_env_type)                             :: ct_step_env
      TYPE(dbcsr_type) :: grad, k_vd_index_down, k_vr_index_down, matrix_k_central, matrix_tmp1, &
         matrix_tmp2, prec, prev_grad, prev_minus_prec_grad, prev_step, sigma_oo_curr, &
         sigma_oo_curr_inv, sigma_vv_sqrt, sigma_vv_sqrt_guess, sigma_vv_sqrt_inv, &
         sigma_vv_sqrt_inv_guess, step, t_curr, tmp1_n_vr, tmp2_n_o, tmp3_vd_vr, tmp4_o_vr, &
         tmp_k_blk, vd_fixed, vd_index_sqrt, vd_index_sqrt_inv, velocity, vr_fixed, vr_index_sqrt, &
         vr_index_sqrt_inv
      TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:)        :: matrix_p_almo_scf_converged

!TYPE(dbcsr_iterator_type)                  :: iter
!TYPE(dbcsr_type) :: tmp11,tmp22,tmp33
!REAL(kind=dp)                            :: k_var1, k_var2
!TYPE(dbcsr_type)                      :: fake_step
!
!TYPE(dbcsr_type)                      :: sigma_dr, sigma_dr2, sigma_rr, sigma_rr2
!TYPE(dbcsr_type)                      :: fake_a,fake_b,fake_k0
!INTEGER                                  :: retained_v,discarded_v,i_row,j_col
!TYPE(dbcsr_type) :: matrix_rst0, matrix_rst1, matrix_rst2, ss_vv
!REAL(KIND=dp)       :: filter_memorize, init_filter, occ_vv
!INTEGER             :: ppp

      CALL timeset(routineN, handle)

      ! get a useful output_unit
      logger => cp_get_default_logger()
      IF (logger%para_env%mepos == logger%para_env%source) THEN
         unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
      ELSE
         unit_nr = -1
      ENDIF

      nspin = almo_scf_env%nspins
      energy_correction_final = 0.0_dp
      IF (nspin .EQ. 1) THEN
         spin_factor = 2.0_dp
      ELSE
         spin_factor = 1.0_dp
      ENDIF

      IF (almo_scf_env%deloc_use_occ_orbs) THEN
         algorithm_id = cayley_transform
      ELSE
         algorithm_id = dm_ls_step
      ENDIF

      t1 = m_walltime()

      SELECT CASE (algorithm_id)
      CASE (cayley_transform)

         ! rescale density matrix by spin factor
         ! so the orbitals and density are consistent with each other
         IF (almo_scf_env%nspins == 1) THEN
            CALL dbcsr_scale(almo_scf_env%matrix_p(1), 1.0_dp/spin_factor)
         ENDIF

         ! transform matrix_t not matrix_t_blk (we might need ALMOs later)
         DO ispin = 1, nspin

            CALL dbcsr_copy(almo_scf_env%matrix_t(ispin), &
                            almo_scf_env%matrix_t_blk(ispin))

            ! obtain orthogonalization matrices for ALMOs
            ! RZK-warning - remove this sqrt(sigma) and inv(sqrt(sigma))
            ! ideally ALMO scf should use sigma and sigma_inv in
            ! the tensor_up_down representation

            IF (unit_nr > 0) THEN
               WRITE (unit_nr, *) "sqrt and inv(sqrt) of MO overlap matrix"
            ENDIF
            CALL dbcsr_create(almo_scf_env%matrix_sigma_sqrt(ispin), &
                              template=almo_scf_env%matrix_sigma(ispin), &
                              matrix_type=dbcsr_type_no_symmetry)
            CALL dbcsr_create(almo_scf_env%matrix_sigma_sqrt_inv(ispin), &
                              template=almo_scf_env%matrix_sigma(ispin), &
                              matrix_type=dbcsr_type_no_symmetry)

            CALL matrix_sqrt_Newton_Schulz(almo_scf_env%matrix_sigma_sqrt(ispin), &
                                           almo_scf_env%matrix_sigma_sqrt_inv(ispin), &
                                           almo_scf_env%matrix_sigma(ispin), &
                                           threshold=almo_scf_env%eps_filter, &
                                           order=almo_scf_env%order_lanczos, &
                                           eps_lanczos=almo_scf_env%eps_lanczos, &
                                           max_iter_lanczos=almo_scf_env%max_iter_lanczos)

            IF (safe_mode) THEN
               CALL dbcsr_create(matrix_tmp1, template=almo_scf_env%matrix_sigma(ispin), &
                                 matrix_type=dbcsr_type_no_symmetry)
               CALL dbcsr_create(matrix_tmp2, template=almo_scf_env%matrix_sigma(ispin), &
                                 matrix_type=dbcsr_type_no_symmetry)

               CALL dbcsr_multiply("N", "N", 1.0_dp, almo_scf_env%matrix_sigma_sqrt_inv(ispin), &
                                   almo_scf_env%matrix_sigma(ispin), &
                                   0.0_dp, matrix_tmp1, filter_eps=almo_scf_env%eps_filter)
               CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_tmp1, &
                                   almo_scf_env%matrix_sigma_sqrt_inv(ispin), &
                                   0.0_dp, matrix_tmp2, filter_eps=almo_scf_env%eps_filter)

               frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp2)
               CALL dbcsr_add_on_diag(matrix_tmp2, -1.0_dp)
               frob_matrix = dbcsr_frobenius_norm(matrix_tmp2)
               IF (unit_nr > 0) THEN
                  WRITE (unit_nr, *) "Error for (inv(sqrt(SIG))*SIG*inv(sqrt(SIG))-I)", frob_matrix/frob_matrix_base
               ENDIF

               CALL dbcsr_release(matrix_tmp1)
               CALL dbcsr_release(matrix_tmp2)
            ENDIF
         ENDDO

         IF (almo_scf_env%almo_update_algorithm .EQ. almo_scf_diag) THEN

            DO ispin = 1, nspin

               t1a = m_walltime()

               line_search_error_threshold = almo_scf_env%real01
               conjugacy_error_threshold = almo_scf_env%real02
               quadratic_approx_error_threshold = almo_scf_env%real03
               x_opt_eps_adaptive_factor = almo_scf_env%real04

               !! the outer loop for k optimization
               outer_opt_k_max_iter = almo_scf_env%opt_k_outer_max_iter
               outer_opt_k_prepare_to_exit = .FALSE.
               outer_opt_k_iteration = 0
               grad_norm = 0.0_dp
               grad_norm_frob = 0.0_dp
               CALL dbcsr_set(almo_scf_env%matrix_x(ispin), 0.0_dp)
               IF (almo_scf_env%deloc_truncate_virt .EQ. virt_full) outer_opt_k_max_iter = 0

               DO

                  ! obtain proper retained virtuals (1-R)|ALMO_vr>
                  CALL apply_projector(psi_in=almo_scf_env%matrix_v_blk(ispin), &
                                       psi_out=almo_scf_env%matrix_v(ispin), &
                                       psi_projector=almo_scf_env%matrix_t_blk(ispin), &
                                       metric=almo_scf_env%matrix_s(1), &
                                       project_out=.TRUE., &
                                       psi_projector_orthogonal=.FALSE., &
                                       proj_in_template=almo_scf_env%matrix_ov(ispin), &
                                       eps_filter=almo_scf_env%eps_filter, &
                                       sig_inv_projector=almo_scf_env%matrix_sigma_inv(ispin))
                  !sig_inv_template=almo_scf_env%matrix_sigma_inv(ispin),&

                  ! save initial retained virtuals
                  CALL dbcsr_create(vr_fixed, &
                                    template=almo_scf_env%matrix_v(ispin))
                  CALL dbcsr_copy(vr_fixed, almo_scf_env%matrix_v(ispin))

                  ! init matrices common for optimized and non-optimized virts
                  CALL dbcsr_create(sigma_vv_sqrt, &
                                    template=almo_scf_env%matrix_sigma_vv(ispin), &
                                    matrix_type=dbcsr_type_no_symmetry)
                  CALL dbcsr_create(sigma_vv_sqrt_inv, &
                                    template=almo_scf_env%matrix_sigma_vv(ispin), &
                                    matrix_type=dbcsr_type_no_symmetry)
                  CALL dbcsr_create(sigma_vv_sqrt_inv_guess, &
                                    template=almo_scf_env%matrix_sigma_vv(ispin), &
                                    matrix_type=dbcsr_type_no_symmetry)
                  CALL dbcsr_create(sigma_vv_sqrt_guess, &
                                    template=almo_scf_env%matrix_sigma_vv(ispin), &
                                    matrix_type=dbcsr_type_no_symmetry)
                  CALL dbcsr_set(sigma_vv_sqrt_guess, 0.0_dp)
                  CALL dbcsr_add_on_diag(sigma_vv_sqrt_guess, 1.0_dp)
                  CALL dbcsr_filter(sigma_vv_sqrt_guess, almo_scf_env%eps_filter)
                  CALL dbcsr_set(sigma_vv_sqrt_inv_guess, 0.0_dp)
                  CALL dbcsr_add_on_diag(sigma_vv_sqrt_inv_guess, 1.0_dp)
                  CALL dbcsr_filter(sigma_vv_sqrt_inv_guess, almo_scf_env%eps_filter)

                  ! do things required to optimize virtuals
                  IF (almo_scf_env%deloc_truncate_virt .NE. virt_full) THEN

                     ! project retained virtuals out of discarded block-by-block
                     ! (1-Q^VR_ALMO)|ALMO_vd>
                     ! this is probably not necessary, do it just to be safe
                     !CALL apply_projector(psi_in=almo_scf_env%matrix_v_disc_blk(ispin),&
                     !        psi_out=almo_scf_env%matrix_v_disc(ispin),&
                     !        psi_projector=almo_scf_env%matrix_v_blk(ispin),&
                     !        metric=almo_scf_env%matrix_s_blk(1),&
                     !        project_out=.TRUE.,&
                     !        psi_projector_orthogonal=.FALSE.,&
                     !        proj_in_template=almo_scf_env%matrix_k_tr(ispin),&
                     !        eps_filter=almo_scf_env%eps_filter,&
                     !        sig_inv_template=almo_scf_env%matrix_sigma_vv(ispin))
                     !CALL dbcsr_copy(almo_scf_env%matrix_v_disc_blk(ispin),&
                     !        almo_scf_env%matrix_v_disc(ispin))

                     ! construct discarded virtuals (1-R)|ALMO_vd>
                     CALL apply_projector(psi_in=almo_scf_env%matrix_v_disc_blk(ispin), &
                                          psi_out=almo_scf_env%matrix_v_disc(ispin), &
                                          psi_projector=almo_scf_env%matrix_t_blk(ispin), &
                                          metric=almo_scf_env%matrix_s(1), &
                                          project_out=.TRUE., &
                                          psi_projector_orthogonal=.FALSE., &
                                          proj_in_template=almo_scf_env%matrix_ov_disc(ispin), &
                                          eps_filter=almo_scf_env%eps_filter, &
                                          sig_inv_projector=almo_scf_env%matrix_sigma_inv(ispin))
                     !sig_inv_template=almo_scf_env%matrix_sigma_inv(ispin),&

                     ! save initial discarded
                     CALL dbcsr_create(vd_fixed, &
                                       template=almo_scf_env%matrix_v_disc(ispin))
                     CALL dbcsr_copy(vd_fixed, almo_scf_env%matrix_v_disc(ispin))

                     !! create the down metric in the retained k-subspace
                     CALL dbcsr_create(k_vr_index_down, &
                                       template=almo_scf_env%matrix_sigma_vv_blk(ispin), &
                                       matrix_type=dbcsr_type_no_symmetry)
                     !CALL dbcsr_copy(k_vr_index_down,&
                     !        almo_scf_env%matrix_sigma_vv_blk(ispin))

                     !CALL get_overlap(bra=almo_scf_env%matrix_v_blk(ispin),&
                     !        ket=almo_scf_env%matrix_v_blk(ispin),&
                     !        overlap=k_vr_index_down,&
                     !        metric=almo_scf_env%matrix_s_blk(1),&
                     !        retain_overlap_sparsity=.FALSE.,&
                     !        eps_filter=almo_scf_env%eps_filter)

                     !! create the up metric in the discarded k-subspace
                     CALL dbcsr_create(k_vd_index_down, &
                                       template=almo_scf_env%matrix_vv_disc_blk(ispin), &
                                       matrix_type=dbcsr_type_no_symmetry)
                     !CALL dbcsr_init(k_vd_index_up)
                     !CALL dbcsr_create(k_vd_index_up,&
                     !        template=almo_scf_env%matrix_vv_disc_blk(ispin),&
                     !        matrix_type=dbcsr_type_no_symmetry)
                     !CALL dbcsr_copy(k_vd_index_down,&
                     !        almo_scf_env%matrix_vv_disc_blk(ispin))

                     !CALL get_overlap(bra=almo_scf_env%matrix_v_disc_blk(ispin),&
                     !        ket=almo_scf_env%matrix_v_disc_blk(ispin),&
                     !        overlap=k_vd_index_down,&
                     !        metric=almo_scf_env%matrix_s_blk(1),&
                     !        retain_overlap_sparsity=.FALSE.,&
                     !        eps_filter=almo_scf_env%eps_filter)

                     !IF (unit_nr>0) THEN
                     !   WRITE(unit_nr,*) "Inverting blocked overlap matrix of discarded virtuals"
                     !ENDIF
                     !CALL invert_Hotelling(k_vd_index_up,&
                     !        k_vd_index_down,&
                     !        almo_scf_env%eps_filter)
                     !IF (safe_mode) THEN
                     !   CALL dbcsr_init(matrix_tmp1)
                     !   CALL dbcsr_create(matrix_tmp1,template=k_vd_index_down,&
                     !                        matrix_type=dbcsr_type_no_symmetry)
                     !   CALL dbcsr_multiply("N","N",1.0_dp,k_vd_index_up,&
                     !                          k_vd_index_down,&
                     !                          0.0_dp, matrix_tmp1,&
                     !                          filter_eps=almo_scf_env%eps_filter)
                     !   frob_matrix_base=dbcsr_frobenius_norm(matrix_tmp1)
                     !   CALL dbcsr_add_on_diag(matrix_tmp1,-1.0_dp)
                     !   frob_matrix=dbcsr_frobenius_norm(matrix_tmp1)
                     !   IF (unit_nr>0) THEN
                     !      WRITE(unit_nr,*) "Error for (inv(SIG)*SIG-I)",&
                     !            frob_matrix/frob_matrix_base
                     !   ENDIF
                     !   CALL dbcsr_release(matrix_tmp1)
                     !ENDIF

                     ! init matrices necessary for optimization of truncated virts
                     ! init blocked gradient before setting K to zero
                     ! otherwise the block structure might be lost
                     CALL dbcsr_create(grad, &
                                       template=almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_copy(grad, almo_scf_env%matrix_k_blk(ispin))

                     ! init MD in the k-space
                     md_in_k_space = almo_scf_env%logical01
                     IF (md_in_k_space) THEN
                        CALL dbcsr_create(velocity, &
                                          template=almo_scf_env%matrix_k_blk(ispin))
                        CALL dbcsr_copy(velocity, almo_scf_env%matrix_k_blk(ispin))
                        CALL dbcsr_set(velocity, 0.0_dp)
                        time_step = almo_scf_env%opt_k_trial_step_size
                     ENDIF

                     CALL dbcsr_create(prev_step, &
                                       template=almo_scf_env%matrix_k_blk(ispin))

                     CALL dbcsr_create(prev_minus_prec_grad, &
                                       template=almo_scf_env%matrix_k_blk(ispin))

                     ! initialize diagonal blocks of the preconditioner to 1.0_dp
                     CALL dbcsr_create(prec, &
                                       template=almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_copy(prec, almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_set(prec, 1.0_dp)

                     ! generate initial K (extrapolate if previous values are available)
                     CALL dbcsr_set(almo_scf_env%matrix_k_blk(ispin), 0.0_dp)
                     ! matrix_k_central stores current k because matrix_k_blk is updated
                     ! during linear search
                     CALL dbcsr_create(matrix_k_central, &
                                       template=almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_copy(matrix_k_central, &
                                     almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_create(tmp_k_blk, &
                                       template=almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_create(step, &
                                       template=almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_set(step, 0.0_dp)
                     CALL dbcsr_create(t_curr, &
                                       template=almo_scf_env%matrix_t(ispin))
                     CALL dbcsr_create(sigma_oo_curr, &
                                       template=almo_scf_env%matrix_sigma(ispin), &
                                       matrix_type=dbcsr_type_no_symmetry)
                     CALL dbcsr_create(sigma_oo_curr_inv, &
                                       template=almo_scf_env%matrix_sigma(ispin), &
                                       matrix_type=dbcsr_type_no_symmetry)
                     CALL dbcsr_create(tmp1_n_vr, &
                                       template=almo_scf_env%matrix_v(ispin))
                     CALL dbcsr_create(tmp3_vd_vr, &
                                       template=almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_create(tmp2_n_o, &
                                       template=almo_scf_env%matrix_t(ispin))
                     CALL dbcsr_create(tmp4_o_vr, &
                                       template=almo_scf_env%matrix_ov(ispin))
                     CALL dbcsr_create(prev_grad, &
                                       template=almo_scf_env%matrix_k_blk(ispin))
                     CALL dbcsr_set(prev_grad, 0.0_dp)

                     !CALL dbcsr_init(sigma_oo_guess)
                     !CALL dbcsr_create(sigma_oo_guess,&
                     !        template=almo_scf_env%matrix_sigma(ispin),&
                     !        matrix_type=dbcsr_type_no_symmetry)
                     !CALL dbcsr_set(sigma_oo_guess,0.0_dp)
                     !CALL dbcsr_add_on_diag(sigma_oo_guess,1.0_dp)
                     !CALL dbcsr_filter(sigma_oo_guess,almo_scf_env%eps_filter)
                     !CALL dbcsr_print(sigma_oo_guess)

                  ENDIF ! done constructing discarded virtuals

                  ! init variables
                  opt_k_max_iter = almo_scf_env%opt_k_max_iter
                  iteration = 0
                  converged = .FALSE.
                  prepare_to_exit = .FALSE.
                  beta = 0.0_dp
                  line_search = .FALSE.
                  obj_function = 0.0_dp
                  conjugacy_error = 0.0_dp
                  line_search_error = 0.0_dp
                  fun0 = 0.0_dp
                  fun1 = 0.0_dp
                  gfun0 = 0.0_dp
                  gfun1 = 0.0_dp
                  step_size_quadratic_approx = 0.0_dp
                  reset_step_size = .TRUE.
                  IF (almo_scf_env%deloc_truncate_virt .EQ. virt_full) opt_k_max_iter = 0

                  ! start cg iterations to optimize matrix_k_blk
                  DO

                     CALL timeset('k_opt_vr', handle1)

                     IF (almo_scf_env%deloc_truncate_virt .NE. virt_full) THEN

                        ! construct k-excited virtuals
                        CALL dbcsr_multiply("N", "N", 1.0_dp, vd_fixed, &
                                            almo_scf_env%matrix_k_blk(ispin), &
                                            0.0_dp, almo_scf_env%matrix_v(ispin), &
                                            filter_eps=almo_scf_env%eps_filter)
                        CALL dbcsr_add(almo_scf_env%matrix_v(ispin), vr_fixed, &
                                       +1.0_dp, +1.0_dp)
                     ENDIF

                     ! decompose the overlap matrix of the current retained orbitals
                     !IF (unit_nr>0) THEN
                     !   WRITE(unit_nr,*) "decompose the active VV overlap matrix"
                     !ENDIF
                     CALL get_overlap(bra=almo_scf_env%matrix_v(ispin), &
                                      ket=almo_scf_env%matrix_v(ispin), &
                                      overlap=almo_scf_env%matrix_sigma_vv(ispin), &
                                      metric=almo_scf_env%matrix_s(1), &
                                      retain_overlap_sparsity=.FALSE., &
                                      eps_filter=almo_scf_env%eps_filter)
                     ! use either cholesky or sqrt
                     !! RZK-warning: strangely, cholesky does not work with k-optimization
                     IF (almo_scf_env%deloc_truncate_virt .EQ. virt_full) THEN
                        CALL timeset('cholesky', handle2)
                        t1cholesky = m_walltime()

                        ! re-create sigma_vv_sqrt because desymmetrize is buggy -
                        ! it will create multiple copies of blocks
                        CALL dbcsr_create(sigma_vv_sqrt, &
                                          template=almo_scf_env%matrix_sigma_vv(ispin), &
                                          matrix_type=dbcsr_type_no_symmetry)
                        CALL dbcsr_desymmetrize(almo_scf_env%matrix_sigma_vv(ispin), &
                                                sigma_vv_sqrt)
                        CALL cp_dbcsr_cholesky_decompose(sigma_vv_sqrt, &
                                                         para_env=almo_scf_env%para_env, &
                                                         blacs_env=almo_scf_env%blacs_env)
                        CALL dbcsr_triu(sigma_vv_sqrt)
                        CALL dbcsr_filter(sigma_vv_sqrt, almo_scf_env%eps_filter)
                        ! apply SOLVE to compute U^(-1) : U*U^(-1)=I
                        CALL dbcsr_get_info(sigma_vv_sqrt, nfullrows_total=n)
                        CALL dbcsr_create(matrix_tmp1, template=almo_scf_env%matrix_sigma_vv(ispin), &
                                          matrix_type=dbcsr_type_no_symmetry)
                        CALL dbcsr_set(matrix_tmp1, 0.0_dp)
                        CALL dbcsr_add_on_diag(matrix_tmp1, 1.0_dp)
                        CALL cp_dbcsr_cholesky_restore(matrix_tmp1, n, sigma_vv_sqrt, &
                                                       sigma_vv_sqrt_inv, op="SOLVE", pos="RIGHT", &
                                                       para_env=almo_scf_env%para_env, &
                                                       blacs_env=almo_scf_env%blacs_env)
                        CALL dbcsr_filter(sigma_vv_sqrt_inv, almo_scf_env%eps_filter)
                        CALL dbcsr_release(matrix_tmp1)
                        IF (safe_mode) THEN
                           CALL dbcsr_create(matrix_tmp1, template=almo_scf_env%matrix_sigma_vv(ispin), &
                                             matrix_type=dbcsr_type_no_symmetry)
                           CALL dbcsr_desymmetrize(almo_scf_env%matrix_sigma_vv(ispin), &
                                                   matrix_tmp1)
                           CALL dbcsr_multiply("T", "N", 1.0_dp, sigma_vv_sqrt, &
                                               sigma_vv_sqrt, &
                                               -1.0_dp, matrix_tmp1, filter_eps=almo_scf_env%eps_filter)
                           frob_matrix = dbcsr_frobenius_norm(matrix_tmp1)
                           CALL dbcsr_add_on_diag(matrix_tmp1, 1.0_dp)
                           frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp1)
                           IF (unit_nr > 0) THEN
                              WRITE (unit_nr, *) "Error for ( U^T * U - Sig )", &
                                 frob_matrix/frob_matrix_base
                           ENDIF
                           CALL dbcsr_multiply("N", "N", 1.0_dp, sigma_vv_sqrt_inv, &
                                               sigma_vv_sqrt, &
                                               0.0_dp, matrix_tmp1, filter_eps=almo_scf_env%eps_filter)
                           frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp1)
                           CALL dbcsr_add_on_diag(matrix_tmp1, -1.0_dp)
                           frob_matrix = dbcsr_frobenius_norm(matrix_tmp1)
                           IF (unit_nr > 0) THEN
                              WRITE (unit_nr, *) "Error for ( inv(U) * U - I )", &
                                 frob_matrix/frob_matrix_base
                           ENDIF
                           CALL dbcsr_release(matrix_tmp1)
                        ENDIF ! safe_mode
                        t2cholesky = m_walltime()
                        IF (unit_nr > 0) THEN
                           WRITE (unit_nr, *) "Cholesky+inverse wall-time: ", t2cholesky-t1cholesky
                        ENDIF
                        CALL timestop(handle2)
                     ELSE
                        CALL matrix_sqrt_Newton_Schulz(sigma_vv_sqrt, &
                                                       sigma_vv_sqrt_inv, &
                                                       almo_scf_env%matrix_sigma_vv(ispin), &
                                                       !matrix_sqrt_inv_guess=sigma_vv_sqrt_inv_guess,&
                                                       !matrix_sqrt_guess=sigma_vv_sqrt_guess,&
                                                       threshold=almo_scf_env%eps_filter, &
                                                       order=almo_scf_env%order_lanczos, &
                                                       eps_lanczos=almo_scf_env%eps_lanczos, &
                                                       max_iter_lanczos=almo_scf_env%max_iter_lanczos)
                        CALL dbcsr_copy(sigma_vv_sqrt_inv_guess, sigma_vv_sqrt_inv)
                        CALL dbcsr_copy(sigma_vv_sqrt_guess, sigma_vv_sqrt)
                        IF (safe_mode) THEN
                           CALL dbcsr_create(matrix_tmp1, template=almo_scf_env%matrix_sigma_vv(ispin), &
                                             matrix_type=dbcsr_type_no_symmetry)
                           CALL dbcsr_create(matrix_tmp2, template=almo_scf_env%matrix_sigma_vv(ispin), &
                                             matrix_type=dbcsr_type_no_symmetry)

                           CALL dbcsr_multiply("N", "N", 1.0_dp, sigma_vv_sqrt_inv, &
                                               almo_scf_env%matrix_sigma_vv(ispin), &
                                               0.0_dp, matrix_tmp1, filter_eps=almo_scf_env%eps_filter)
                           CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_tmp1, &
                                               sigma_vv_sqrt_inv, &
                                               0.0_dp, matrix_tmp2, filter_eps=almo_scf_env%eps_filter)

                           frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp2)
                           CALL dbcsr_add_on_diag(matrix_tmp2, -1.0_dp)
                           frob_matrix = dbcsr_frobenius_norm(matrix_tmp2)
                           IF (unit_nr > 0) THEN
                              WRITE (unit_nr, *) "Error for (inv(sqrt(SIGVV))*SIGVV*inv(sqrt(SIGVV))-I)", &
                                 frob_matrix/frob_matrix_base
                           ENDIF

                           CALL dbcsr_release(matrix_tmp1)
                           CALL dbcsr_release(matrix_tmp2)
                        ENDIF
                     ENDIF
                     CALL timestop(handle1)

                     ! compute excitation amplitudes (to the current set of retained virtuals)
                     ! set convergence criterion for x-optimization
                     IF ((iteration .EQ. 0) .AND. (.NOT. line_search) .AND. &
                         (outer_opt_k_iteration .EQ. 0)) THEN
                        x_opt_eps_adaptive = &
                           almo_scf_env%deloc_cayley_eps_convergence
                     ELSE
                        x_opt_eps_adaptive = &
                           MAX(ABS(almo_scf_env%deloc_cayley_eps_convergence), &
                               ABS(x_opt_eps_adaptive_factor*grad_norm))
                     ENDIF
                     CALL ct_step_env_init(ct_step_env)
                     CALL ct_step_env_set(ct_step_env, &
                                          para_env=almo_scf_env%para_env, &
                                          blacs_env=almo_scf_env%blacs_env, &
                                          use_occ_orbs=.TRUE., &
                                          use_virt_orbs=.TRUE., &
                                          occ_orbs_orthogonal=.FALSE., &
                                          virt_orbs_orthogonal=.FALSE., &
                                          pp_preconditioner_full=almo_scf_env%deloc_cayley_occ_precond, &
                                          qq_preconditioner_full=almo_scf_env%deloc_cayley_vir_precond, &
                                          tensor_type=almo_scf_env%deloc_cayley_tensor_type, &
                                          neglect_quadratic_term=almo_scf_env%deloc_cayley_linear, &
                                          conjugator=almo_scf_env%deloc_cayley_conjugator, &
                                          max_iter=almo_scf_env%deloc_cayley_max_iter, &
                                          calculate_energy_corr=.TRUE., &
                                          update_p=.FALSE., &
                                          update_q=.FALSE., &
                                          eps_convergence=x_opt_eps_adaptive, &
                                          eps_filter=almo_scf_env%eps_filter, &
                                          !nspins=1,&
                                          q_index_up=sigma_vv_sqrt_inv, &
                                          q_index_down=sigma_vv_sqrt, &
                                          p_index_up=almo_scf_env%matrix_sigma_sqrt_inv(ispin), &
                                          p_index_down=almo_scf_env%matrix_sigma_sqrt(ispin), &
                                          matrix_ks=almo_scf_env%matrix_ks_0deloc(ispin), &
                                          matrix_t=almo_scf_env%matrix_t(ispin), &
                                          matrix_qp_template=almo_scf_env%matrix_vo(ispin), &
                                          matrix_pq_template=almo_scf_env%matrix_ov(ispin), &
                                          matrix_v=almo_scf_env%matrix_v(ispin), &
                                          matrix_x_guess=almo_scf_env%matrix_x(ispin))
                     ! perform calculations
                     CALL ct_step_execute(ct_step_env)
                     ! get the energy correction
                     CALL ct_step_env_get(ct_step_env, &
                                          energy_correction=energy_correction(ispin), &
                                          copy_matrix_x=almo_scf_env%matrix_x(ispin))
                     CALL ct_step_env_clean(ct_step_env)
                     ! RZK-warning matrix_x is being transformed
                     ! back and forth between orth and up_down representations
                     energy_correction(1) = energy_correction(1)*spin_factor

                     IF (opt_k_max_iter .NE. 0) THEN

                        CALL timeset('k_opt_t_curr', handle3)

                        ! construct current occupied orbitals T_blk + V_r*X
                        CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                            almo_scf_env%matrix_v(ispin), &
                                            almo_scf_env%matrix_x(ispin), &
                                            0.0_dp, t_curr, &
                                            filter_eps=almo_scf_env%eps_filter)
                        CALL dbcsr_add(t_curr, almo_scf_env%matrix_t_blk(ispin), &
                                       +1.0_dp, +1.0_dp)

                        ! calculate current occupied overlap
                        !IF (unit_nr>0) THEN
                        !   WRITE(unit_nr,*) "Inverting current occ overlap matrix"
                        !ENDIF
                        CALL get_overlap(bra=t_curr, &
                                         ket=t_curr, &
                                         overlap=sigma_oo_curr, &
                                         metric=almo_scf_env%matrix_s(1), &
                                         retain_overlap_sparsity=.FALSE., &
                                         eps_filter=almo_scf_env%eps_filter)
                        IF (iteration .EQ. 0) THEN
                           CALL invert_Hotelling(sigma_oo_curr_inv, &
                                                 sigma_oo_curr, &
                                                 threshold=almo_scf_env%eps_filter, &
                                                 use_inv_as_guess=.FALSE.)
                        ELSE
                           CALL invert_Hotelling(sigma_oo_curr_inv, &
                                                 sigma_oo_curr, &
                                                 threshold=almo_scf_env%eps_filter, &
                                                 use_inv_as_guess=.TRUE.)
                           !CALL dbcsr_copy(sigma_oo_guess,sigma_oo_curr_inv)
                        ENDIF
                        IF (safe_mode) THEN
                           CALL dbcsr_create(matrix_tmp1, template=sigma_oo_curr, &
                                             matrix_type=dbcsr_type_no_symmetry)
                           CALL dbcsr_multiply("N", "N", 1.0_dp, sigma_oo_curr, &
                                               sigma_oo_curr_inv, &
                                               0.0_dp, matrix_tmp1, &
                                               filter_eps=almo_scf_env%eps_filter)
                           frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp1)
                           CALL dbcsr_add_on_diag(matrix_tmp1, -1.0_dp)
                           frob_matrix = dbcsr_frobenius_norm(matrix_tmp1)
                           !CALL dbcsr_filter(matrix_tmp1,almo_scf_env%eps_filter)
                           !CALL dbcsr_print(matrix_tmp1)
                           IF (unit_nr > 0) THEN
                              WRITE (unit_nr, *) "Error for (SIG*inv(SIG)-I)", &
                                 frob_matrix/frob_matrix_base, frob_matrix_base
                           ENDIF
                           CALL dbcsr_release(matrix_tmp1)
                        ENDIF
                        IF (safe_mode) THEN
                           CALL dbcsr_create(matrix_tmp1, template=sigma_oo_curr, &
                                             matrix_type=dbcsr_type_no_symmetry)
                           CALL dbcsr_multiply("N", "N", 1.0_dp, sigma_oo_curr_inv, &
                                               sigma_oo_curr, &
                                               0.0_dp, matrix_tmp1, &
                                               filter_eps=almo_scf_env%eps_filter)
                           frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp1)
                           CALL dbcsr_add_on_diag(matrix_tmp1, -1.0_dp)
                           frob_matrix = dbcsr_frobenius_norm(matrix_tmp1)
                           !CALL dbcsr_filter(matrix_tmp1,almo_scf_env%eps_filter)
                           !CALL dbcsr_print(matrix_tmp1)
                           IF (unit_nr > 0) THEN
                              WRITE (unit_nr, *) "Error for (inv(SIG)*SIG-I)", &
                                 frob_matrix/frob_matrix_base, frob_matrix_base
                           ENDIF
                           CALL dbcsr_release(matrix_tmp1)
                        ENDIF

                        CALL timestop(handle3)
                        CALL timeset('k_opt_vd', handle4)

                        ! construct current discarded virtuals:
                        ! (1-R_curr)(1-Q^VR_curr)|ALMO_vd_basis> =
                        ! = (1-Q^VR_curr)|ALMO_vd_basis>
                        ! use sigma_vv_sqrt to store the inverse of the overlap
                        ! sigma_vv_inv is computed from sqrt/cholesky
                        CALL dbcsr_multiply("N", "T", 1.0_dp, &
                                            sigma_vv_sqrt_inv, &
                                            sigma_vv_sqrt_inv, &
                                            0.0_dp, sigma_vv_sqrt, &
                                            filter_eps=almo_scf_env%eps_filter)
                        CALL apply_projector(psi_in=almo_scf_env%matrix_v_disc_blk(ispin), &
                                             psi_out=almo_scf_env%matrix_v_disc(ispin), &
                                             psi_projector=almo_scf_env%matrix_v(ispin), &
                                             metric=almo_scf_env%matrix_s(1), &
                                             project_out=.FALSE., &
                                             psi_projector_orthogonal=.FALSE., &
                                             proj_in_template=almo_scf_env%matrix_k_tr(ispin), &
                                             eps_filter=almo_scf_env%eps_filter, &
                                             sig_inv_projector=sigma_vv_sqrt)
                        !sig_inv_template=almo_scf_env%matrix_sigma_vv(ispin),&
                        CALL dbcsr_add(almo_scf_env%matrix_v_disc(ispin), &
                                       vd_fixed, -1.0_dp, +1.0_dp)

                        CALL timestop(handle4)
                        CALL timeset('k_opt_grad', handle5)

                        ! evaluate the gradient from the assembled components
                        ! grad_xx = c0 [ (Vd_curr^tr)*F*T_curr*sigma_oo_curr_inv*(X^tr)]_xx
                        ! save previous gradient to calculate conjugation coef
                        IF (line_search) THEN
                           CALL dbcsr_copy(prev_grad, grad)
                        ENDIF
                        CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                            almo_scf_env%matrix_ks_0deloc(ispin), &
                                            t_curr, &
                                            0.0_dp, tmp2_n_o, &
                                            filter_eps=almo_scf_env%eps_filter)
                        CALL dbcsr_multiply("N", "T", 1.0_dp, &
                                            sigma_oo_curr_inv, &
                                            almo_scf_env%matrix_x(ispin), &
                                            0.0_dp, tmp4_o_vr, &
                                            filter_eps=almo_scf_env%eps_filter)
                        CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                            tmp2_n_o, &
                                            tmp4_o_vr, &
                                            0.0_dp, tmp1_n_vr, &
                                            filter_eps=almo_scf_env%eps_filter)
                        CALL dbcsr_multiply("T", "N", 2.0_dp*spin_factor, &
                                            almo_scf_env%matrix_v_disc(ispin), &
                                            tmp1_n_vr, &
                                            0.0_dp, grad, &
                                            retain_sparsity=.TRUE.)
                        !filter_eps=almo_scf_env%eps_filter,&
                        ! keep tmp2_n_o for the next step
                        ! keep tmp4_o_vr for the preconditioner

                        ! check convergence and other exit criteria
                        grad_norm_frob = dbcsr_frobenius_norm(grad)
                        CALL dbcsr_norm(grad, dbcsr_norm_maxabsnorm, norm_scalar=grad_norm)
                        converged = (grad_norm .LT. almo_scf_env%opt_k_eps_convergence)
                        IF (converged .OR. (iteration .GE. opt_k_max_iter)) THEN
                           prepare_to_exit = .TRUE.
                        ENDIF
                        CALL timestop(handle5)

                        IF (.NOT. prepare_to_exit) THEN

                           CALL timeset('k_opt_energy', handle6)

                           ! compute "energy" c0*Tr[sig_inv_oo*t*F*t]
                           CALL dbcsr_multiply("T", "N", spin_factor, &
                                               t_curr, &
                                               tmp2_n_o, &
                                               0.0_dp, sigma_oo_curr, &
                                               filter_eps=almo_scf_env%eps_filter)
                           delta_obj_function = fun0
                           CALL dbcsr_trace(sigma_oo_curr_inv, sigma_oo_curr, obj_function)
                           delta_obj_function = obj_function-delta_obj_function
                           IF (line_search) THEN
                              fun1 = obj_function
                           ELSE
                              fun0 = obj_function
                           ENDIF

                           CALL timestop(handle6)

                           ! update the step direction
                           IF (.NOT. line_search) THEN

                              CALL timeset('k_opt_step', handle7)

                              IF ((.NOT. md_in_k_space) .AND. &
                                  (iteration .GE. MAX(0, almo_scf_env%opt_k_prec_iter_start) .AND. &
                                   MOD(iteration-almo_scf_env%opt_k_prec_iter_start, &
                                       almo_scf_env%opt_k_prec_iter_freq) .EQ. 0)) THEN

                                 !IF ((iteration.eq.0).AND.(.NOT.md_in_k_space)) THEN

                                 ! compute the preconditioner
                                 IF (unit_nr > 0) THEN
                                    WRITE (unit_nr, *) "Computing preconditioner"
                                 ENDIF
                                 !CALL opt_k_create_preconditioner(prec,&
                                 !        almo_scf_env%matrix_v_disc(ispin),&
                                 !        almo_scf_env%matrix_ks_0deloc(ispin),&
                                 !        almo_scf_env%matrix_x(ispin),&
                                 !        tmp4_o_vr,&
                                 !        almo_scf_env%matrix_s(1),&
                                 !        grad,&
                                 !        !almo_scf_env%matrix_v_disc_blk(ispin),&
                                 !        vd_fixed,&
                                 !        t_curr,&
                                 !        k_vd_index_up,&
                                 !        k_vr_index_down,&
                                 !        tmp1_n_vr,&
                                 !        spin_factor,&
                                 !        almo_scf_env%eps_filter)
                                 CALL opt_k_create_preconditioner_blk(almo_scf_env, &
                                                                      almo_scf_env%matrix_v_disc(ispin), &
                                                                      tmp4_o_vr, &
                                                                      t_curr, &
                                                                      ispin, &
                                                                      spin_factor)

                              ENDIF

                              ! save the previous step
                              CALL dbcsr_copy(prev_step, step)

                              ! compute the new step
                              CALL opt_k_apply_preconditioner_blk(almo_scf_env, &
                                                                  step, grad, ispin)
                              !CALL dbcsr_hadamard_product(prec,grad,step)
                              CALL dbcsr_scale(step, -1.0_dp)

                              ! check whether we need to reset conjugate directions
                              reset_conjugator = .FALSE.
                              ! first check if manual reset is active
                              IF (iteration .LT. MAX(almo_scf_env%opt_k_conj_iter_start, 1) .OR. &
                                  MOD(iteration-almo_scf_env%opt_k_conj_iter_start, &
                                      almo_scf_env%opt_k_conj_iter_freq) .EQ. 0) THEN

                                 reset_conjugator = .TRUE.

                              ELSE

                                 ! check for the errors in the cg algorithm
                                 !CALL dbcsr_hadamard_product(prec,prev_grad,tmp_k_blk)
                                 !CALL dbcsr_trace(grad,tmp_k_blk,numer)
                                 !CALL dbcsr_trace(prev_grad,tmp_k_blk,denom)
                                 CALL dbcsr_trace(grad, prev_minus_prec_grad, numer)
                                 CALL dbcsr_trace(prev_grad, prev_minus_prec_grad, denom)
                                 conjugacy_error = numer/denom

                                 IF (conjugacy_error .GT. MIN(0.5_dp, conjugacy_error_threshold)) THEN
                                    reset_conjugator = .TRUE.
                                    IF (unit_nr > 0) THEN
                                       WRITE (unit_nr, *) "Lack of progress, conjugacy error is ", conjugacy_error
                                    ENDIF
                                 ENDIF

                                 ! check the gradient along the previous direction
                                 IF ((iteration .NE. 0) .AND. (.NOT. reset_conjugator)) THEN
                                    CALL dbcsr_trace(grad, prev_step, numer)
                                    CALL dbcsr_trace(prev_grad, prev_step, denom)
                                    line_search_error = numer/denom
                                    IF (line_search_error .GT. line_search_error_threshold) THEN
                                       reset_conjugator = .TRUE.
                                       IF (unit_nr > 0) THEN
                                          WRITE (unit_nr, *) "Bad line search, line search error is ", line_search_error
                                       ENDIF
                                    ENDIF
                                 ENDIF

                              ENDIF

                              ! compute the conjugation coefficient - beta
                              IF (.NOT. reset_conjugator) THEN

                                 SELECT CASE (almo_scf_env%opt_k_conjugator)
                                 CASE (cg_hestenes_stiefel)
                                    CALL dbcsr_copy(tmp_k_blk, grad)
                                    CALL dbcsr_add(tmp_k_blk, prev_grad, 1.0_dp, -1.0_dp)
                                    CALL dbcsr_trace(tmp_k_blk, step, numer)
                                    CALL dbcsr_trace(tmp_k_blk, prev_step, denom)
                                    beta = -1.0_dp*numer/denom
                                 CASE (cg_fletcher_reeves)
                                    !CALL dbcsr_hadamard_product(prec,prev_grad,tmp_k_blk)
                                    !CALL dbcsr_trace(prev_grad,tmp_k_blk,denom)
                                    !CALL dbcsr_hadamard_product(prec,grad,tmp_k_blk)
                                    !CALL dbcsr_trace(grad,tmp_k_blk,numer)
                                    !beta=numer/denom
                                    CALL dbcsr_trace(grad, step, numer)
                                    CALL dbcsr_trace(prev_grad, prev_minus_prec_grad, denom)
                                    beta = numer/denom
                                 CASE (cg_polak_ribiere)
                                    !CALL dbcsr_hadamard_product(prec,prev_grad,tmp_k_blk)
                                    !CALL dbcsr_trace(prev_grad,tmp_k_blk,denom)
                                    !CALL dbcsr_add(prev_grad,grad,-1.0_dp,1.0_dp)
                                    !CALL dbcsr_hadamard_product(prec,prev_grad,tmp_k_blk)
                                    !CALL dbcsr_trace(tmp_k_blk,grad,numer)
                                    CALL dbcsr_trace(prev_grad, prev_minus_prec_grad, denom)
                                    CALL dbcsr_copy(tmp_k_blk, grad)
                                    CALL dbcsr_add(tmp_k_blk, prev_grad, 1.0_dp, -1.0_dp)
                                    CALL dbcsr_trace(tmp_k_blk, step, numer)
                                    beta = numer/denom
                                 CASE (cg_fletcher)
                                    !CALL dbcsr_hadamard_product(prec,grad,tmp_k_blk)
                                    !CALL dbcsr_trace(grad,tmp_k_blk,numer)
                                    !CALL dbcsr_trace(prev_grad,prev_step,denom)
                                    !beta=-1.0_dp*numer/denom
                                    CALL dbcsr_trace(grad, step, numer)
                                    CALL dbcsr_trace(prev_grad, prev_step, denom)
                                    beta = numer/denom
                                 CASE (cg_liu_storey)
                                    CALL dbcsr_trace(prev_grad, prev_step, denom)
                                    !CALL dbcsr_add(prev_grad,grad,-1.0_dp,1.0_dp)
                                    !CALL dbcsr_hadamard_product(prec,prev_grad,tmp_k_blk)
                                    !CALL dbcsr_trace(tmp_k_blk,grad,numer)
                                    CALL dbcsr_copy(tmp_k_blk, grad)
                                    CALL dbcsr_add(tmp_k_blk, prev_grad, 1.0_dp, -1.0_dp)
                                    CALL dbcsr_trace(tmp_k_blk, step, numer)
                                    beta = numer/denom
                                 CASE (cg_dai_yuan)
                                    !CALL dbcsr_hadamard_product(prec,grad,tmp_k_blk)
                                    !CALL dbcsr_trace(grad,tmp_k_blk,numer)
                                    !CALL dbcsr_add(prev_grad,grad,-1.0_dp,1.0_dp)
                                    !CALL dbcsr_trace(prev_grad,prev_step,denom)
                                    !beta=numer/denom
                                    CALL dbcsr_trace(grad, step, numer)
                                    CALL dbcsr_copy(tmp_k_blk, grad)
                                    CALL dbcsr_add(tmp_k_blk, prev_grad, 1.0_dp, -1.0_dp)
                                    CALL dbcsr_trace(tmp_k_blk, prev_step, denom)
                                    beta = -1.0_dp*numer/denom
                                 CASE (cg_hager_zhang)
                                    !CALL dbcsr_add(prev_grad,grad,-1.0_dp,1.0_dp)
                                    !CALL dbcsr_trace(prev_grad,prev_step,denom)
                                    !CALL dbcsr_hadamard_product(prec,prev_grad,tmp_k_blk)
                                    !CALL dbcsr_trace(tmp_k_blk,prev_grad,numer)
                                    !kappa=2.0_dp*numer/denom
                                    !CALL dbcsr_trace(tmp_k_blk,grad,numer)
                                    !tau=numer/denom
                                    !CALL dbcsr_trace(prev_step,grad,numer)
                                    !beta=tau-kappa*numer/denom
                                    CALL dbcsr_copy(tmp_k_blk, grad)
                                    CALL dbcsr_add(tmp_k_blk, prev_grad, 1.0_dp, -1.0_dp)
                                    CALL dbcsr_trace(tmp_k_blk, prev_step, denom)
                                    CALL dbcsr_trace(tmp_k_blk, prev_minus_prec_grad, numer)
                                    kappa = -2.0_dp*numer/denom
                                    CALL dbcsr_trace(tmp_k_blk, step, numer)
                                    tau = -1.0_dp*numer/denom
                                    CALL dbcsr_trace(prev_step, grad, numer)
                                    beta = tau-kappa*numer/denom
                                 CASE (cg_zero)
                                    beta = 0.0_dp
                                 CASE DEFAULT
                                    CPABORT("illegal conjugator")
                                 END SELECT

                                 IF (beta .LT. 0.0_dp) THEN
                                    IF (unit_nr > 0) THEN
                                       WRITE (unit_nr, *) "Beta is negative, ", beta
                                    ENDIF
                                    reset_conjugator = .TRUE.
                                 ENDIF

                              ENDIF

                              IF (md_in_k_space) THEN
                                 reset_conjugator = .TRUE.
                              ENDIF

                              IF (reset_conjugator) THEN

                                 beta = 0.0_dp
                                 !reset_step_size=.TRUE.

                                 IF (unit_nr > 0) THEN
                                    WRITE (unit_nr, *) "(Re)-setting conjugator to zero"
                                 ENDIF

                              ENDIF

                              ! save the preconditioned gradient
                              CALL dbcsr_copy(prev_minus_prec_grad, step)

                              ! conjugate the step direction
                              CALL dbcsr_add(step, prev_step, 1.0_dp, beta)

                              CALL timestop(handle7)

                              ! update the step direction
                           ELSE ! step update
                              conjugacy_error = 0.0_dp
                           ENDIF

                           ! compute the gradient with respect to the step size in the curr direction
                           IF (line_search) THEN
                              CALL dbcsr_trace(grad, step, gfun1)
                              line_search_error = gfun1/gfun0
                           ELSE
                              CALL dbcsr_trace(grad, step, gfun0)
                           ENDIF

                           ! make a step - update k
                           IF (line_search) THEN

                              ! check if the trial step provides enough numerical accuracy
                              safety_multiplier = 1.0E+1_dp ! must be more than one
                              num_threshold = MAX(EPSILON(1.0_dp), &
                                                  safety_multiplier*(almo_scf_env%eps_filter**2)*almo_scf_env%ndomains)
                              IF (ABS(fun1-fun0-gfun0*step_size) .LT. num_threshold) THEN
                                 IF (unit_nr > 0) THEN
                                    WRITE (unit_nr, '(T3,A,1X,E17.7)') &
                                       "Numerical accuracy is too low to observe non-linear behavior", &
                                       ABS(fun1-fun0-gfun0*step_size)
                                    WRITE (unit_nr, '(T3,A,1X,E17.7,A,1X,E12.3)') "Error computing ", &
                                       ABS(gfun0), &
                                       " is smaller than the threshold", num_threshold
                                 ENDIF
                                 CPABORT("")
                              ENDIF
                              IF (ABS(gfun0) .LT. num_threshold) THEN
                                 IF (unit_nr > 0) THEN
                                    WRITE (unit_nr, '(T3,A,1X,E17.7,A,1X,E12.3)') "Linear gradient", &
                                       ABS(gfun0), &
                                       " is smaller than the threshold", num_threshold
                                 ENDIF
                                 CPABORT("")
                              ENDIF

                              use_quadratic_approximation = .TRUE.
                              use_cubic_approximation = .FALSE.

                              ! find the minimum assuming quadratic form
                              ! use f0, f1, g0
                              step_size_quadratic_approx = -(gfun0*step_size*step_size)/(2.0_dp*(fun1-fun0-gfun0*step_size))
                              ! use f0, f1, g1
                              step_size_quadratic_approx2 = -(fun1-fun0-step_size*gfun1/2.0_dp)/(gfun1-(fun1-fun0)/step_size)

                              IF ((step_size_quadratic_approx .LT. 0.0_dp) .AND. &
                                  (step_size_quadratic_approx2 .LT. 0.0_dp)) THEN
                                 IF (unit_nr > 0) THEN
                                    WRITE (unit_nr, '(T3,A,1X,E17.7,1X,E17.7,1X,A)') &
                                       "Quadratic approximation gives negative steps", &
                                       step_size_quadratic_approx, step_size_quadratic_approx2, &
                                       "trying cubic..."
                                 ENDIF
                                 use_cubic_approximation = .TRUE.
                                 use_quadratic_approximation = .FALSE.
                              ELSE
                                 IF (step_size_quadratic_approx .LT. 0.0_dp) THEN
                                    step_size_quadratic_approx = step_size_quadratic_approx2
                                 ENDIF
                                 IF (step_size_quadratic_approx2 .LT. 0.0_dp) THEN
                                    step_size_quadratic_approx2 = step_size_quadratic_approx
                                 ENDIF
                              ENDIF

                              ! check accuracy of the quadratic approximation
                              IF (use_quadratic_approximation) THEN
                                 quadratic_approx_error = ABS(step_size_quadratic_approx- &
                                                              step_size_quadratic_approx2)/step_size_quadratic_approx
                                 IF (quadratic_approx_error .GT. quadratic_approx_error_threshold) THEN
                                    IF (unit_nr > 0) THEN
                                       WRITE (unit_nr, '(T3,A,1X,E17.7,1X,E17.7,1X,A)') "Quadratic approximation is poor", &
                                          step_size_quadratic_approx, step_size_quadratic_approx2, &
                                          "Try cubic approximation"
                                    ENDIF
                                    use_cubic_approximation = .TRUE.
                                    use_quadratic_approximation = .FALSE.
                                 ENDIF
                              ENDIF

                              ! check if numerics is fine enough to capture the cubic form
                              IF (use_cubic_approximation) THEN

                                 ! if quadratic approximation is not accurate enough
                                 ! try to find the minimum assuming cubic form
                                 ! aa*x**3 + bb*x**2 + cc*x + dd = f(x)
                                 bb = (-step_size*gfun1+3.0_dp*(fun1-fun0)-2.0_dp*step_size*gfun0)/(step_size*step_size)
                                 aa = (gfun1-2.0_dp*step_size*bb-gfun0)/(3.0_dp*step_size*step_size)

                                 IF (ABS(gfun1-2.0_dp*step_size*bb-gfun0) .LT. num_threshold) THEN
                                    IF (unit_nr > 0) THEN
                                       WRITE (unit_nr, '(T3,A,1X,E17.7)') &
                                          "Numerical accuracy is too low to observe cubic behavior", &
                                          ABS(gfun1-2.0_dp*step_size*bb-gfun0)
                                    ENDIF
                                    use_cubic_approximation = .FALSE.
                                    use_quadratic_approximation = .TRUE.
                                 ENDIF
                                 IF (ABS(gfun1) .LT. num_threshold) THEN
                                    IF (unit_nr > 0) THEN
                                       WRITE (unit_nr, '(T3,A,1X,E17.7,A,1X,E12.3)') "Linear gradient", &
                                          ABS(gfun1), &
                                          " is smaller than the threshold", num_threshold
                                    ENDIF
                                    use_cubic_approximation = .FALSE.
                                    use_quadratic_approximation = .TRUE.
                                 ENDIF
                              ENDIF

                              ! find the step assuming cubic approximation
                              IF (use_cubic_approximation) THEN
                                 ! to obtain the minimum of the cubic function solve the quadratic equation
                                 ! 0.0*x**3 + 3.0*aa*x**2 + 2.0*bb*x + cc = 0
                                 CALL analytic_line_search(0.0_dp, 3.0_dp*aa, 2.0_dp*bb, gfun0, minima, nmins)
                                 IF (nmins .LT. 1) THEN
                                    IF (unit_nr > 0) THEN
                                       WRITE (unit_nr, '(T3,A)') &
                                          "Cubic approximation gives zero soultions! Use quadratic approximation"
                                    ENDIF
                                    use_quadratic_approximation = .TRUE.
                                    use_cubic_approximation = .TRUE.
                                 ELSE
                                    step_size = minima(1)
                                    IF (nmins .GT. 1) THEN
                                       IF (unit_nr > 0) THEN
                                          WRITE (unit_nr, '(T3,A)') &
                                             "More than one solution found! Use quadratic approximation"
                                       ENDIF
                                       use_quadratic_approximation = .TRUE.
                                       use_cubic_approximation = .TRUE.
                                    ENDIF
                                 ENDIF
                              ENDIF

                              IF (use_quadratic_approximation) THEN ! use quadratic approximation
                                 IF (unit_nr > 0) THEN
                                    WRITE (unit_nr, '(T3,A)') "Use quadratic approximation"
                                 ENDIF
                                 step_size = (step_size_quadratic_approx+step_size_quadratic_approx2)*0.5_dp
                              ENDIF

                              ! one more check on the step size
                              IF (step_size .LT. 0.0_dp) THEN
                                 CPABORT("Negative step proposed")
                              ENDIF

                              CALL dbcsr_copy(almo_scf_env%matrix_k_blk(ispin), &
                                              matrix_k_central)
                              CALL dbcsr_add(almo_scf_env%matrix_k_blk(ispin), &
                                             step, 1.0_dp, step_size)
                              CALL dbcsr_copy(matrix_k_central, &
                                              almo_scf_env%matrix_k_blk(ispin))
                              line_search = .FALSE.

                           ELSE

                              IF (md_in_k_space) THEN

                                 ! update velocities v(i) = v(i-1) + 0.5*dT*(a(i-1) + a(i))
                                 IF (iteration .NE. 0) THEN
                                    CALL dbcsr_add(velocity, &
                                                   step, 1.0_dp, 0.5_dp*time_step)
                                    CALL dbcsr_add(velocity, &
                                                   prev_step, 1.0_dp, 0.5_dp*time_step)
                                 ENDIF
                                 kin_energy = dbcsr_frobenius_norm(velocity)
                                 kin_energy = 0.5_dp*kin_energy*kin_energy

                                 ! update positions k(i) = k(i-1) + dT*v(i-1) + 0.5*dT*dT*a(i-1)
                                 CALL dbcsr_add(almo_scf_env%matrix_k_blk(ispin), &
                                                velocity, 1.0_dp, time_step)
                                 CALL dbcsr_add(almo_scf_env%matrix_k_blk(ispin), &
                                                step, 1.0_dp, 0.5_dp*time_step*time_step)

                              ELSE

                                 IF (reset_step_size) THEN
                                    step_size = almo_scf_env%opt_k_trial_step_size
                                    reset_step_size = .FALSE.
                                 ELSE
                                    step_size = step_size*almo_scf_env%opt_k_trial_step_size_multiplier
                                 ENDIF
                                 CALL dbcsr_copy(almo_scf_env%matrix_k_blk(ispin), &
                                                 matrix_k_central)
                                 CALL dbcsr_add(almo_scf_env%matrix_k_blk(ispin), &
                                                step, 1.0_dp, step_size)
                                 line_search = .TRUE.
                              ENDIF

                           ENDIF

                        ENDIF ! .NOT.prepare_to_exit

                        ! print the status of the optimization
                        t2a = m_walltime()
                        IF (unit_nr > 0) THEN
                           IF (md_in_k_space) THEN
                              WRITE (unit_nr, '(T6,A,1X,I5,1X,E12.3,E16.7,F15.9,F15.9,F15.9,E12.3,F15.9,F15.9,F8.3)') &
                                 "K iter CG", iteration, time_step, time_step*iteration, &
                                 energy_correction(ispin), obj_function, delta_obj_function, grad_norm, &
                                 kin_energy, kin_energy+obj_function, beta
                           ELSE
                              IF (line_search .OR. prepare_to_exit) THEN
                                 WRITE (unit_nr, '(T6,A,1X,I3,1X,E12.3,F16.10,F16.10,E12.3,E12.3,E12.3,F8.3,F8.3,F10.3)') &
                                    "K iter CG", iteration, step_size, &
                                    energy_correction(ispin), delta_obj_function, grad_norm, &
                                    gfun0, line_search_error, beta, conjugacy_error, t2a-t1a
                                 !(flop1+flop2)/(1.0E6_dp*(t2-t1))
                              ELSE
                                 WRITE (unit_nr, '(T6,A,1X,I3,1X,E12.3,F16.10,F16.10,E12.3,E12.3,E12.3,F8.3,F8.3,F10.3)') &
                                    "K iter LS", iteration, step_size, &
                                    energy_correction(ispin), delta_obj_function, grad_norm, &
                                    gfun1, line_search_error, beta, conjugacy_error, t2a-t1a
                                 !(flop1+flop2)/(1.0E6_dp*(t2-t1))
                              ENDIF
                           ENDIF
                           CALL m_flush(unit_nr)
                        ENDIF
                        t1a = m_walltime()

                     ELSE ! opt_k_max_iter .eq. 0
                        prepare_to_exit = .TRUE.
                     ENDIF ! opt_k_max_iter .ne. 0

                     IF (.NOT. line_search) iteration = iteration+1

                     IF (prepare_to_exit) EXIT

                  ENDDO ! end iterations on K

                  IF (converged .OR. (outer_opt_k_iteration .GE. outer_opt_k_max_iter)) THEN
                     outer_opt_k_prepare_to_exit = .TRUE.
                  ENDIF

                  IF (almo_scf_env%deloc_truncate_virt .NE. virt_full) THEN

                     IF (unit_nr > 0) THEN
                        WRITE (unit_nr, *) "Updating ALMO virtuals"
                     ENDIF

                     CALL timeset('k_opt_v0_update', handle8)

                     ! update retained ALMO virtuals to restart the cg iterations
                     CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                         almo_scf_env%matrix_v_disc_blk(ispin), &
                                         almo_scf_env%matrix_k_blk(ispin), &
                                         0.0_dp, vr_fixed, &
                                         filter_eps=almo_scf_env%eps_filter)
                     CALL dbcsr_add(vr_fixed, almo_scf_env%matrix_v_blk(ispin), &
                                    +1.0_dp, +1.0_dp)

                     ! update discarded ALMO virtuals to restart the cg iterations
                     CALL dbcsr_multiply("N", "T", 1.0_dp, &
                                         almo_scf_env%matrix_v_blk(ispin), &
                                         almo_scf_env%matrix_k_blk(ispin), &
                                         0.0_dp, vd_fixed, &
                                         filter_eps=almo_scf_env%eps_filter)
                     CALL dbcsr_add(vd_fixed, almo_scf_env%matrix_v_disc_blk(ispin), &
                                    -1.0_dp, +1.0_dp)

                     ! orthogonalize new orbitals on fragments
                     CALL get_overlap(bra=vr_fixed, &
                                      ket=vr_fixed, &
                                      overlap=k_vr_index_down, &
                                      metric=almo_scf_env%matrix_s_blk(1), &
                                      retain_overlap_sparsity=.FALSE., &
                                      eps_filter=almo_scf_env%eps_filter)
                     CALL dbcsr_create(vr_index_sqrt_inv, template=k_vr_index_down, &
                                       matrix_type=dbcsr_type_no_symmetry)
                     CALL dbcsr_create(vr_index_sqrt, template=k_vr_index_down, &
                                       matrix_type=dbcsr_type_no_symmetry)
                     CALL matrix_sqrt_Newton_Schulz(vr_index_sqrt, &
                                                    vr_index_sqrt_inv, &
                                                    k_vr_index_down, &
                                                    threshold=almo_scf_env%eps_filter, &
                                                    order=almo_scf_env%order_lanczos, &
                                                    eps_lanczos=almo_scf_env%eps_lanczos, &
                                                    max_iter_lanczos=almo_scf_env%max_iter_lanczos)
                     IF (safe_mode) THEN
                        CALL dbcsr_create(matrix_tmp1, template=k_vr_index_down, &
                                          matrix_type=dbcsr_type_no_symmetry)
                        CALL dbcsr_create(matrix_tmp2, template=k_vr_index_down, &
                                          matrix_type=dbcsr_type_no_symmetry)

                        CALL dbcsr_multiply("N", "N", 1.0_dp, vr_index_sqrt_inv, &
                                            k_vr_index_down, &
                                            0.0_dp, matrix_tmp1, filter_eps=almo_scf_env%eps_filter)
                        CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_tmp1, &
                                            vr_index_sqrt_inv, &
                                            0.0_dp, matrix_tmp2, filter_eps=almo_scf_env%eps_filter)

                        frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp2)
                        CALL dbcsr_add_on_diag(matrix_tmp2, -1.0_dp)
                        frob_matrix = dbcsr_frobenius_norm(matrix_tmp2)
                        IF (unit_nr > 0) THEN
                           WRITE (unit_nr, *) "Error for (inv(sqrt(SIGVV))*SIGVV*inv(sqrt(SIGVV))-I)", &
                              frob_matrix/frob_matrix_base
                        ENDIF

                        CALL dbcsr_release(matrix_tmp1)
                        CALL dbcsr_release(matrix_tmp2)
                     ENDIF
                     CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                         vr_fixed, &
                                         vr_index_sqrt_inv, &
                                         0.0_dp, almo_scf_env%matrix_v_blk(ispin), &
                                         filter_eps=almo_scf_env%eps_filter)

                     CALL get_overlap(bra=vd_fixed, &
                                      ket=vd_fixed, &
                                      overlap=k_vd_index_down, &
                                      metric=almo_scf_env%matrix_s_blk(1), &
                                      retain_overlap_sparsity=.FALSE., &
                                      eps_filter=almo_scf_env%eps_filter)
                     CALL dbcsr_create(vd_index_sqrt_inv, template=k_vd_index_down, &
                                       matrix_type=dbcsr_type_no_symmetry)
                     CALL dbcsr_create(vd_index_sqrt, template=k_vd_index_down, &
                                       matrix_type=dbcsr_type_no_symmetry)
                     CALL matrix_sqrt_Newton_Schulz(vd_index_sqrt, &
                                                    vd_index_sqrt_inv, &
                                                    k_vd_index_down, &
                                                    threshold=almo_scf_env%eps_filter, &
                                                    order=almo_scf_env%order_lanczos, &
                                                    eps_lanczos=almo_scf_env%eps_lanczos, &
                                                    max_iter_lanczos=almo_scf_env%max_iter_lanczos)
                     IF (safe_mode) THEN
                        CALL dbcsr_create(matrix_tmp1, template=k_vd_index_down, &
                                          matrix_type=dbcsr_type_no_symmetry)
                        CALL dbcsr_create(matrix_tmp2, template=k_vd_index_down, &
                                          matrix_type=dbcsr_type_no_symmetry)

                        CALL dbcsr_multiply("N", "N", 1.0_dp, vd_index_sqrt_inv, &
                                            k_vd_index_down, &
                                            0.0_dp, matrix_tmp1, filter_eps=almo_scf_env%eps_filter)
                        CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_tmp1, &
                                            vd_index_sqrt_inv, &
                                            0.0_dp, matrix_tmp2, filter_eps=almo_scf_env%eps_filter)

                        frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp2)
                        CALL dbcsr_add_on_diag(matrix_tmp2, -1.0_dp)
                        frob_matrix = dbcsr_frobenius_norm(matrix_tmp2)
                        IF (unit_nr > 0) THEN
                           WRITE (unit_nr, *) "Error for (inv(sqrt(SIGVV))*SIGVV*inv(sqrt(SIGVV))-I)", &
                              frob_matrix/frob_matrix_base
                        ENDIF

                        CALL dbcsr_release(matrix_tmp1)
                        CALL dbcsr_release(matrix_tmp2)
                     ENDIF
                     CALL dbcsr_multiply("N", "N", 1.0_dp, &
                                         vd_fixed, &
                                         vd_index_sqrt_inv, &
                                         0.0_dp, almo_scf_env%matrix_v_disc_blk(ispin), &
                                         filter_eps=almo_scf_env%eps_filter)

                     CALL dbcsr_release(vr_index_sqrt_inv)
                     CALL dbcsr_release(vr_index_sqrt)
                     CALL dbcsr_release(vd_index_sqrt_inv)
                     CALL dbcsr_release(vd_index_sqrt)

                     CALL timestop(handle8)

                  ENDIF ! ne.virt_full

                  ! RZK-warning released outside the outer loop
                  CALL dbcsr_release(sigma_vv_sqrt)
                  CALL dbcsr_release(sigma_vv_sqrt_inv)
                  IF (almo_scf_env%deloc_truncate_virt .NE. virt_full) THEN
                     CALL dbcsr_release(k_vr_index_down)
                     CALL dbcsr_release(k_vd_index_down)
                     !CALL dbcsr_release(k_vd_index_up)
                     CALL dbcsr_release(matrix_k_central)
                     CALL dbcsr_release(vr_fixed)
                     CALL dbcsr_release(vd_fixed)
                     CALL dbcsr_release(grad)
                     CALL dbcsr_release(prec)
                     CALL dbcsr_release(prev_grad)
                     CALL dbcsr_release(tmp3_vd_vr)
                     CALL dbcsr_release(tmp1_n_vr)
                     CALL dbcsr_release(tmp_k_blk)
                     CALL dbcsr_release(t_curr)
                     CALL dbcsr_release(sigma_oo_curr)
                     CALL dbcsr_release(sigma_oo_curr_inv)
                     CALL dbcsr_release(step)
                     CALL dbcsr_release(tmp2_n_o)
                     CALL dbcsr_release(tmp4_o_vr)
                     CALL dbcsr_release(prev_step)
                     CALL dbcsr_release(prev_minus_prec_grad)
                     IF (md_in_k_space) THEN
                        CALL dbcsr_release(velocity)
                     ENDIF

                  ENDIF

                  outer_opt_k_iteration = outer_opt_k_iteration+1
                  IF (outer_opt_k_prepare_to_exit) EXIT

               ENDDO ! outer loop for k

            ENDDO ! ispin

            ! RZK-warning update mo orbitals

         ELSE ! virtual orbitals might not be available use projected AOs

            ! compute sqrt(S) and inv(sqrt(S))
            ! RZK-warning - remove this sqrt(S) and inv(sqrt(S))
            ! ideally ALMO scf should use sigma and sigma_inv in
            ! the tensor_up_down representation
            IF (.NOT. almo_scf_env%s_sqrt_done) THEN

               IF (unit_nr > 0) THEN
                  WRITE (unit_nr, *) "sqrt and inv(sqrt) of AO overlap matrix"
               ENDIF
               CALL dbcsr_create(almo_scf_env%matrix_s_sqrt(1), &
                                 template=almo_scf_env%matrix_s(1), &
                                 matrix_type=dbcsr_type_no_symmetry)
               CALL dbcsr_create(almo_scf_env%matrix_s_sqrt_inv(1), &
                                 template=almo_scf_env%matrix_s(1), &
                                 matrix_type=dbcsr_type_no_symmetry)

               CALL matrix_sqrt_Newton_Schulz(almo_scf_env%matrix_s_sqrt(1), &
                                              almo_scf_env%matrix_s_sqrt_inv(1), &
                                              almo_scf_env%matrix_s(1), &
                                              threshold=almo_scf_env%eps_filter, &
                                              order=almo_scf_env%order_lanczos, &
                                              eps_lanczos=almo_scf_env%eps_lanczos, &
                                              max_iter_lanczos=almo_scf_env%max_iter_lanczos)

               IF (safe_mode) THEN
                  CALL dbcsr_create(matrix_tmp1, template=almo_scf_env%matrix_s(1), &
                                    matrix_type=dbcsr_type_no_symmetry)
                  CALL dbcsr_create(matrix_tmp2, template=almo_scf_env%matrix_s(1), &
                                    matrix_type=dbcsr_type_no_symmetry)

                  CALL dbcsr_multiply("N", "N", 1.0_dp, almo_scf_env%matrix_s_sqrt_inv(1), &
                                      almo_scf_env%matrix_s(1), &
                                      0.0_dp, matrix_tmp1, filter_eps=almo_scf_env%eps_filter)
                  CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_tmp1, almo_scf_env%matrix_s_sqrt_inv(1), &
                                      0.0_dp, matrix_tmp2, filter_eps=almo_scf_env%eps_filter)

                  frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp2)
                  CALL dbcsr_add_on_diag(matrix_tmp2, -1.0_dp)
                  frob_matrix = dbcsr_frobenius_norm(matrix_tmp2)
                  IF (unit_nr > 0) THEN
                     WRITE (unit_nr, *) "Error for (inv(sqrt(S))*S*inv(sqrt(S))-I)", frob_matrix/frob_matrix_base
                  ENDIF

                  CALL dbcsr_release(matrix_tmp1)
                  CALL dbcsr_release(matrix_tmp2)
               ENDIF

               almo_scf_env%s_sqrt_done = .TRUE.

            ENDIF

            DO ispin = 1, nspin

               CALL ct_step_env_init(ct_step_env)
               CALL ct_step_env_set(ct_step_env, &
                                    para_env=almo_scf_env%para_env, &
                                    blacs_env=almo_scf_env%blacs_env, &
                                    use_occ_orbs=.TRUE., &
                                    use_virt_orbs=almo_scf_env%deloc_cayley_use_virt_orbs, &
                                    occ_orbs_orthogonal=.FALSE., &
                                    virt_orbs_orthogonal=almo_scf_env%orthogonal_basis, &
                                    tensor_type=almo_scf_env%deloc_cayley_tensor_type, &
                                    neglect_quadratic_term=almo_scf_env%deloc_cayley_linear, &
                                    calculate_energy_corr=.TRUE., &
                                    update_p=.TRUE., &
                                    update_q=.FALSE., &
                                    pp_preconditioner_full=almo_scf_env%deloc_cayley_occ_precond, &
                                    qq_preconditioner_full=almo_scf_env%deloc_cayley_vir_precond, &
                                    eps_convergence=almo_scf_env%deloc_cayley_eps_convergence, &
                                    eps_filter=almo_scf_env%eps_filter, &
                                    !nspins=almo_scf_env%nspins,&
                                    q_index_up=almo_scf_env%matrix_s_sqrt_inv(1), &
                                    q_index_down=almo_scf_env%matrix_s_sqrt(1), &
                                    p_index_up=almo_scf_env%matrix_sigma_sqrt_inv(ispin), &
                                    p_index_down=almo_scf_env%matrix_sigma_sqrt(ispin), &
                                    matrix_ks=almo_scf_env%matrix_ks_0deloc(ispin), &
                                    matrix_p=almo_scf_env%matrix_p(ispin), &
                                    matrix_qp_template=almo_scf_env%matrix_t(ispin), &
                                    matrix_pq_template=almo_scf_env%matrix_t_tr(ispin), &
                                    matrix_t=almo_scf_env%matrix_t(ispin), &
                                    conjugator=almo_scf_env%deloc_cayley_conjugator, &
                                    max_iter=almo_scf_env%deloc_cayley_max_iter)

               ! perform calculations
               CALL ct_step_execute(ct_step_env)

               ! for now we do not need the new set of orbitals
               ! just get the energy correction
               CALL ct_step_env_get(ct_step_env, &
                                    energy_correction=energy_correction(ispin))
               !copy_da_energy_matrix=matrix_eda(ispin),&
               !copy_da_charge_matrix=matrix_cta(ispin),&

               CALL ct_step_env_clean(ct_step_env)

            ENDDO

            energy_correction(1) = energy_correction(1)*spin_factor

         ENDIF

         ! print the energy correction and exit
         DO ispin = 1, nspin

            IF (unit_nr > 0) THEN
               WRITE (unit_nr, *)
               WRITE (unit_nr, '(T2,A,I6,F20.9)') "ECORR", ispin, &
                  energy_correction(ispin)
               WRITE (unit_nr, *)
            ENDIF
            energy_correction_final = energy_correction_final+energy_correction(ispin)

            !!! print out the results of decomposition analysis
            !!IF (unit_nr>0) THEN
            !!   WRITE(unit_nr,*)
            !!   WRITE(unit_nr,'(T2,A)') "ENERGY DECOMPOSITION"
            !!ENDIF
            !!CALL dbcsr_print_block_sum(eda_matrix(ispin))
            !!IF (unit_nr>0) THEN
            !!   WRITE(unit_nr,*)
            !!   WRITE(unit_nr,'(T2,A)') "CHARGE DECOMPOSITION"
            !!ENDIF
            !!CALL dbcsr_print_block_sum(cta_matrix(ispin))

            ! obtain density matrix from updated MOs
            ! RZK-later sigma and sigma_inv are lost here
            CALL almo_scf_t_to_p(t=almo_scf_env%matrix_t(ispin), &
                                 p=almo_scf_env%matrix_p(ispin), &
                                 eps_filter=almo_scf_env%eps_filter, &
                                 orthog_orbs=.FALSE., &
                                 s=almo_scf_env%matrix_s(1), &
                                 sigma=almo_scf_env%matrix_sigma(ispin), &
                                 sigma_inv=almo_scf_env%matrix_sigma_inv(ispin))

            IF (almo_scf_env%nspins == 1) &
               CALL dbcsr_scale(almo_scf_env%matrix_p(ispin), &
                                spin_factor)

         ENDDO

      CASE (dm_ls_step)

         ! compute the inverse of S
         IF (.NOT. almo_scf_env%s_inv_done) THEN
            IF (unit_nr > 0) THEN
               WRITE (unit_nr, *) "Inverting AO overlap matrix"
            ENDIF
            CALL dbcsr_create(almo_scf_env%matrix_s_inv(1), &
                              template=almo_scf_env%matrix_s(1), &
                              matrix_type=dbcsr_type_no_symmetry)
            IF (.NOT. almo_scf_env%s_sqrt_done) THEN
               CALL invert_Hotelling(almo_scf_env%matrix_s_inv(1), &
                                     almo_scf_env%matrix_s(1), &
                                     threshold=almo_scf_env%eps_filter)
            ELSE
               CALL dbcsr_multiply("N", "N", 1.0_dp, almo_scf_env%matrix_s_sqrt_inv(1), &
                                   almo_scf_env%matrix_s_sqrt_inv(1), &
                                   0.0_dp, almo_scf_env%matrix_s_inv(1), &
                                   filter_eps=almo_scf_env%eps_filter)
            ENDIF

            IF (safe_mode) THEN
               CALL dbcsr_create(matrix_tmp1, template=almo_scf_env%matrix_s(1), &
                                 matrix_type=dbcsr_type_no_symmetry)
               CALL dbcsr_multiply("N", "N", 1.0_dp, almo_scf_env%matrix_s_inv(1), &
                                   almo_scf_env%matrix_s(1), &
                                   0.0_dp, matrix_tmp1, &
                                   filter_eps=almo_scf_env%eps_filter)
               frob_matrix_base = dbcsr_frobenius_norm(matrix_tmp1)
               CALL dbcsr_add_on_diag(matrix_tmp1, -1.0_dp)
               frob_matrix = dbcsr_frobenius_norm(matrix_tmp1)
               IF (unit_nr > 0) THEN
                  WRITE (unit_nr, *) "Error for (inv(S)*S-I)", &
                     frob_matrix/frob_matrix_base
               ENDIF
               CALL dbcsr_release(matrix_tmp1)
            ENDIF

            almo_scf_env%s_inv_done = .TRUE.

         ENDIF

         DO ispin = 1, nspin
            ! RZK-warning the preconditioner is very important
            !       IF (.FALSE.) THEN
            !           CALL apply_matrix_preconditioner(almo_scf_env%matrix_ks(ispin),&
            !                   "forward",almo_scf_env%matrix_s_blk_sqrt(1),&
            !                   almo_scf_env%matrix_s_blk_sqrt_inv(1))
            !       ENDIF
            !CALL dbcsr_filter(almo_scf_env%matrix_ks(ispin),&
            !         almo_scf_env%eps_filter)
         ENDDO

         ALLOCATE (matrix_p_almo_scf_converged(nspin))
         DO ispin = 1, nspin
            CALL dbcsr_create(matrix_p_almo_scf_converged(ispin), &
                              template=almo_scf_env%matrix_p(ispin))
            CALL dbcsr_copy(matrix_p_almo_scf_converged(ispin), &
                            almo_scf_env%matrix_p(ispin))
         ENDDO

         ! update the density matrix
         DO ispin = 1, nspin

            nelectron_spin_real(1) = almo_scf_env%nelectrons_spin(ispin)
            IF (almo_scf_env%nspins == 1) &
               nelectron_spin_real(1) = nelectron_spin_real(1)/2

            local_mu(1) = SUM(almo_scf_env%mu_of_domain(:, ispin))/almo_scf_env%ndomains
            fake(1) = 123523

            ! RZK UPDATE! the update algorithm is removed because
            ! RZK UPDATE! it requires updating core LS_SCF routines
            ! RZK UPDATE! (the code exists in the CVS version)
            CPABORT("CVS only: density_matrix_sign has not been updated in SVN")
            ! RZK UPDATE!CALL density_matrix_sign(almo_scf_env%matrix_p(ispin),&
            ! RZK UPDATE!                     local_mu,&
            ! RZK UPDATE!                     almo_scf_env%fixed_mu,&
            ! RZK UPDATE!                     almo_scf_env%matrix_ks_0deloc(ispin),&
            ! RZK UPDATE!                     almo_scf_env%matrix_s(1), &
            ! RZK UPDATE!                     almo_scf_env%matrix_s_inv(1), &
            ! RZK UPDATE!                     nelectron_spin_real,&
            ! RZK UPDATE!                     almo_scf_env%eps_filter,&
            ! RZK UPDATE!                     fake)
            ! RZK UPDATE!
            almo_scf_env%mu = local_mu(1)

            !IF (almo_scf_env%has_s_preconditioner) THEN
            !    CALL apply_matrix_preconditioner(&
            !             almo_scf_env%matrix_p_blk(ispin),&
            !             "forward",almo_scf_env%matrix_s_blk_sqrt(1),&
            !             almo_scf_env%matrix_s_blk_sqrt_inv(1))
            !ENDIF
            !CALL dbcsr_filter(almo_scf_env%matrix_p(ispin),&
            !        almo_scf_env%eps_filter)

            IF (almo_scf_env%nspins == 1) &
               CALL dbcsr_scale(almo_scf_env%matrix_p(ispin), &
                                spin_factor)

            !CALL dbcsr_trace(almo_scf_env%matrix_ks_0deloc(ispin),&
            !  almo_scf_env%matrix_p(ispin),&
            !  energy_correction(ispin))
            !IF (unit_nr>0) THEN
            !   WRITE(unit_nr,*)
            !   WRITE(unit_nr,'(T2,A,I6,F20.9)') "EFAKE",ispin,&
            !           energy_correction(ispin)
            !   WRITE(unit_nr,*)
            !ENDIF
            CALL dbcsr_add(matrix_p_almo_scf_converged(ispin), &
                           almo_scf_env%matrix_p(ispin), -1.0_dp, 1.0_dp)
            CALL dbcsr_trace(almo_scf_env%matrix_ks_0deloc(ispin), &
                             matrix_p_almo_scf_converged(ispin), &
                             energy_correction(ispin))

            energy_correction_final = energy_correction_final+energy_correction(ispin)

            IF (unit_nr > 0) THEN
               WRITE (unit_nr, *)
               WRITE (unit_nr, '(T2,A,I6,F20.9)') "ECORR", ispin, &
                  energy_correction(ispin)
               WRITE (unit_nr, *)
            ENDIF

         ENDDO

         DO ispin = 1, nspin
            CALL dbcsr_release(matrix_p_almo_scf_converged(ispin))
         ENDDO
         DEALLOCATE (matrix_p_almo_scf_converged)

      END SELECT ! algorithm selection

      t2 = m_walltime()

      IF (unit_nr > 0) THEN
         WRITE (unit_nr, *)
         WRITE (unit_nr, '(T2,A,F18.9,F18.9,F18.9,F12.6)') "ETOT", &
            almo_scf_env%almo_scf_energy, &
            energy_correction_final, &
            almo_scf_env%almo_scf_energy+energy_correction_final, &
            t2-t1
         WRITE (unit_nr, *)
      ENDIF

      CALL timestop(handle)

   END SUBROUTINE harris_foulkes_correction

! **************************************************************************************************
!> \brief Computes a diagonal preconditioner for the cg optimization of k matrix
!> \param prec ...
!> \param vd_prop ...
!> \param f ...
!> \param x ...
!> \param oo_inv_x_tr ...
!> \param s ...
!> \param grad ...
!> \param vd_blk ...
!> \param t ...
!> \param template_vd_vd_blk ...
!> \param template_vr_vr_blk ...
!> \param template_n_vr ...
!> \param spin_factor ...
!> \param eps_filter ...
!> \par History
!>       2011.09 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE opt_k_create_preconditioner(prec, vd_prop, f, x, oo_inv_x_tr, s, grad, &
                                          vd_blk, t, template_vd_vd_blk, template_vr_vr_blk, template_n_vr, &
                                          spin_factor, eps_filter)

      TYPE(dbcsr_type), INTENT(INOUT)                    :: prec
      TYPE(dbcsr_type), INTENT(IN)                       :: vd_prop, f, x, oo_inv_x_tr, s, grad, &
                                                            vd_blk, t, template_vd_vd_blk, &
                                                            template_vr_vr_blk, template_n_vr
      REAL(KIND=dp), INTENT(IN)                          :: spin_factor, eps_filter

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

      INTEGER                                            :: handle, p_nrows, q_nrows
      REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: p_diagonal, q_diagonal
      TYPE(dbcsr_type)                                   :: pp_diag, qq_diag, t1, t2, tmp, &
                                                            tmp1_n_vr, tmp2_n_vr, tmp_n_vd, &
                                                            tmp_vd_vd_blk, tmp_vr_vr_blk

! init diag blocks outside
! init diag blocks otside
!INTEGER                                  :: iblock_row, iblock_col,&
!                                            nblkrows_tot, nblkcols_tot
!REAL(KIND=dp), DIMENSION(:, :), POINTER  :: p_new_block
!INTEGER                                  :: mynode, hold, row, col

      CALL timeset(routineN, handle)

      ! initialize a matrix to 1.0
      CALL dbcsr_create(tmp, template=prec)
      ! in order to use dbcsr_set matrix blocks must exist
      CALL dbcsr_copy(tmp, prec)
      CALL dbcsr_set(tmp, 1.0_dp)

      ! compute qq = (Vd^tr)*F*Vd
      CALL dbcsr_create(tmp_n_vd, template=vd_prop)
      CALL dbcsr_multiply("N", "N", 1.0_dp, f, vd_prop, &
                          0.0_dp, tmp_n_vd, filter_eps=eps_filter)
      CALL dbcsr_create(tmp_vd_vd_blk, &
                        template=template_vd_vd_blk)
      CALL dbcsr_copy(tmp_vd_vd_blk, template_vd_vd_blk)
      CALL dbcsr_multiply("T", "N", 1.0_dp, vd_prop, tmp_n_vd, &
                          0.0_dp, tmp_vd_vd_blk, &
                          retain_sparsity=.TRUE., &
                          filter_eps=eps_filter)
      ! copy diagonal elements of the result into rows of a matrix
      CALL dbcsr_get_info(tmp_vd_vd_blk, nfullrows_total=q_nrows)
      ALLOCATE (q_diagonal(q_nrows))
      CALL dbcsr_get_diag(tmp_vd_vd_blk, q_diagonal)
      CALL dbcsr_create(qq_diag, &
                        template=template_vd_vd_blk)
      CALL dbcsr_add_on_diag(qq_diag, 1.0_dp)
      CALL dbcsr_set_diag(qq_diag, q_diagonal)
      CALL dbcsr_create(t1, template=prec)
      CALL dbcsr_multiply("N", "N", 1.0_dp, qq_diag, tmp, &
                          0.0_dp, t1, filter_eps=eps_filter)

      ! compute pp = X*sigma_oo_inv*X^tr
      CALL dbcsr_create(tmp_vr_vr_blk, template=template_vr_vr_blk)
      CALL dbcsr_copy(tmp_vr_vr_blk, template_vr_vr_blk)
      CALL dbcsr_multiply("N", "N", 1.0_dp, x, oo_inv_x_tr, &
                          0.0_dp, tmp_vr_vr_blk, &
                          retain_sparsity=.TRUE., &
                          filter_eps=eps_filter)
      ! copy diagonal elements of the result into cols of a matrix
      CALL dbcsr_get_info(tmp_vr_vr_blk, nfullrows_total=p_nrows)
      ALLOCATE (p_diagonal(p_nrows))
      CALL dbcsr_get_diag(tmp_vr_vr_blk, p_diagonal)
      CALL dbcsr_create(pp_diag, template=template_vr_vr_blk)
      CALL dbcsr_add_on_diag(pp_diag, 1.0_dp)
      CALL dbcsr_set_diag(pp_diag, p_diagonal)
      CALL dbcsr_set(tmp, 1.0_dp)
      CALL dbcsr_create(t2, template=prec)
      CALL dbcsr_multiply("N", "N", 1.0_dp, tmp, pp_diag, &
                          0.0_dp, t2, filter_eps=eps_filter)

      CALL dbcsr_hadamard_product(t1, t2, prec)

      ! compute qq = (Vd^tr)*S*Vd
      CALL dbcsr_multiply("N", "N", 1.0_dp, s, vd_prop, &
                          0.0_dp, tmp_n_vd, filter_eps=eps_filter)
      CALL dbcsr_multiply("T", "N", 1.0_dp, vd_prop, tmp_n_vd, &
                          0.0_dp, tmp_vd_vd_blk, &
                          retain_sparsity=.TRUE., &
                          filter_eps=eps_filter)
      ! copy diagonal elements of the result into rows of a matrix
      CALL dbcsr_get_diag(tmp_vd_vd_blk, q_diagonal)
      CALL dbcsr_add_on_diag(qq_diag, 1.0_dp)
      CALL dbcsr_set_diag(qq_diag, q_diagonal)
      CALL dbcsr_set(tmp, 1.0_dp)
      CALL dbcsr_multiply("N", "N", 1.0_dp, qq_diag, tmp, &
                          0.0_dp, t1, filter_eps=eps_filter)

      ! compute pp = X*sig_oo_inv*(T^tr)*F*T*sig_oo_inv*(X^tr)
      CALL dbcsr_create(tmp1_n_vr, template=template_n_vr)
      CALL dbcsr_create(tmp2_n_vr, template=template_n_vr)
      CALL dbcsr_multiply("N", "N", 1.0_dp, t, oo_inv_x_tr, &
                          0.0_dp, tmp1_n_vr, filter_eps=eps_filter)
      CALL dbcsr_multiply("N", "N", 1.0_dp, f, tmp1_n_vr, &
                          0.0_dp, tmp2_n_vr, filter_eps=eps_filter)
      CALL dbcsr_multiply("T", "N", 1.0_dp, tmp1_n_vr, tmp2_n_vr, &
                          0.0_dp, tmp_vr_vr_blk, &
                          retain_sparsity=.TRUE., &
                          filter_eps=eps_filter)
      ! copy diagonal elements of the result into cols of a matrix
      CALL dbcsr_get_diag(tmp_vr_vr_blk, p_diagonal)
      CALL dbcsr_add_on_diag(pp_diag, 1.0_dp)
      CALL dbcsr_set_diag(pp_diag, p_diagonal)
      CALL dbcsr_set(tmp, 1.0_dp)
      CALL dbcsr_multiply("N", "N", 1.0_dp, tmp, pp_diag, &
                          0.0_dp, t2, filter_eps=eps_filter)

      CALL dbcsr_hadamard_product(t1, t2, tmp)
      CALL dbcsr_add(prec, tmp, 1.0_dp, -1.0_dp)
      CALL dbcsr_scale(prec, 2.0_dp*spin_factor)

      ! compute qp = X*sig_oo_inv*(T^tr)*S*Vd
      CALL dbcsr_multiply("N", "N", 1.0_dp, s, vd_blk, &
                          0.0_dp, tmp_n_vd, filter_eps=eps_filter)
      CALL dbcsr_multiply("T", "N", 1.0_dp, tmp_n_vd, tmp1_n_vr, &
                          0.0_dp, tmp, retain_sparsity=.TRUE., &
                          filter_eps=eps_filter)
      CALL dbcsr_hadamard_product(grad, tmp, t1)
      ! gradient already contains 2.0*spin_factor
      CALL dbcsr_scale(t1, -2.0_dp)

      CALL dbcsr_add(prec, t1, 1.0_dp, 1.0_dp)

      CALL dbcsr_function_of_elements(prec, dbcsr_func_inverse)
      CALL dbcsr_filter(prec, eps_filter)

      DEALLOCATE (q_diagonal)
      DEALLOCATE (p_diagonal)
      CALL dbcsr_release(tmp)
      CALL dbcsr_release(qq_diag)
      CALL dbcsr_release(t1)
      CALL dbcsr_release(pp_diag)
      CALL dbcsr_release(t2)
      CALL dbcsr_release(tmp_n_vd)
      CALL dbcsr_release(tmp_vd_vd_blk)
      CALL dbcsr_release(tmp_vr_vr_blk)
      CALL dbcsr_release(tmp1_n_vr)
      CALL dbcsr_release(tmp2_n_vr)

      CALL timestop(handle)

   END SUBROUTINE opt_k_create_preconditioner

! **************************************************************************************************
!> \brief Computes a block-diagonal preconditioner for the optimization of
!>        k matrix
!> \param almo_scf_env ...
!> \param vd_prop ...
!> \param oo_inv_x_tr ...
!> \param t_curr ...
!> \param ispin ...
!> \param spin_factor ...
!> \par History
!>       2011.10 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE opt_k_create_preconditioner_blk(almo_scf_env, vd_prop, oo_inv_x_tr, &
                                              t_curr, ispin, spin_factor)

      TYPE(almo_scf_env_type), INTENT(INOUT)             :: almo_scf_env
      TYPE(dbcsr_type), INTENT(IN)                       :: vd_prop, oo_inv_x_tr, t_curr
      INTEGER, INTENT(IN)                                :: ispin
      REAL(KIND=dp), INTENT(IN)                          :: spin_factor

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

      INTEGER                                            :: handle
      REAL(KIND=dp)                                      :: eps_filter
      TYPE(dbcsr_type)                                   :: opt_k_e_dd, opt_k_e_rr, s_dd_sqrt, &
                                                            s_rr_sqrt, t1, tmp, tmp1_n_vr, &
                                                            tmp2_n_vr, tmp_n_vd, tmp_vd_vd_blk, &
                                                            tmp_vr_vr_blk

! matrices that has been computed outside the routine already

      CALL timeset(routineN, handle)

      eps_filter = almo_scf_env%eps_filter

      ! compute S_qq = (Vd^tr)*S*Vd
      CALL dbcsr_create(tmp_n_vd, template=almo_scf_env%matrix_v_disc(ispin))
      CALL dbcsr_create(tmp_vd_vd_blk, &
                        template=almo_scf_env%matrix_vv_disc_blk(ispin), &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          almo_scf_env%matrix_s(1), &
                          vd_prop, &
                          0.0_dp, tmp_n_vd, filter_eps=eps_filter)
      CALL dbcsr_copy(tmp_vd_vd_blk, &
                      almo_scf_env%matrix_vv_disc_blk(ispin))
      CALL dbcsr_multiply("T", "N", 1.0_dp, vd_prop, tmp_n_vd, &
                          0.0_dp, tmp_vd_vd_blk, &
                          retain_sparsity=.TRUE.)

      CALL dbcsr_create(s_dd_sqrt, &
                        template=almo_scf_env%matrix_vv_disc_blk(ispin), &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL matrix_sqrt_Newton_Schulz(s_dd_sqrt, &
                                     almo_scf_env%opt_k_t_dd(ispin), &
                                     tmp_vd_vd_blk, &
                                     threshold=eps_filter, &
                                     order=almo_scf_env%order_lanczos, &
                                     eps_lanczos=almo_scf_env%eps_lanczos, &
                                     max_iter_lanczos=almo_scf_env%max_iter_lanczos)

      ! compute F_qq = (Vd^tr)*F*Vd
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          almo_scf_env%matrix_ks_0deloc(ispin), &
                          vd_prop, &
                          0.0_dp, tmp_n_vd, filter_eps=eps_filter)
      CALL dbcsr_copy(tmp_vd_vd_blk, &
                      almo_scf_env%matrix_vv_disc_blk(ispin))
      CALL dbcsr_multiply("T", "N", 1.0_dp, vd_prop, tmp_n_vd, &
                          0.0_dp, tmp_vd_vd_blk, &
                          retain_sparsity=.TRUE.)
      CALL dbcsr_release(tmp_n_vd)

      ! bring to the blocked-orthogonalized basis
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          tmp_vd_vd_blk, &
                          almo_scf_env%opt_k_t_dd(ispin), &
                          0.0_dp, s_dd_sqrt, filter_eps=eps_filter)
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          almo_scf_env%opt_k_t_dd(ispin), &
                          s_dd_sqrt, &
                          0.0_dp, tmp_vd_vd_blk, filter_eps=eps_filter)

      ! diagonalize the matrix
      CALL dbcsr_create(opt_k_e_dd, &
                        template=almo_scf_env%matrix_vv_disc_blk(ispin))
      CALL dbcsr_release(s_dd_sqrt)
      CALL dbcsr_create(s_dd_sqrt, &
                        template=almo_scf_env%matrix_vv_disc_blk(ispin), &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL diagonalize_diagonal_blocks(tmp_vd_vd_blk, &
                                       s_dd_sqrt, &
                                       opt_k_e_dd)

      ! obtain the transformation matrix in the discarded subspace
      ! T = S^{-1/2}.U
      CALL dbcsr_copy(tmp_vd_vd_blk, &
                      almo_scf_env%opt_k_t_dd(ispin))
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          tmp_vd_vd_blk, &
                          s_dd_sqrt, &
                          0.0_dp, almo_scf_env%opt_k_t_dd(ispin), &
                          filter_eps=eps_filter)
      CALL dbcsr_release(s_dd_sqrt)
      CALL dbcsr_release(tmp_vd_vd_blk)

      ! copy diagonal elements of the result into rows of a matrix
      CALL dbcsr_create(tmp, &
                        template=almo_scf_env%matrix_k_blk_ones(ispin))
      CALL dbcsr_copy(tmp, &
                      almo_scf_env%matrix_k_blk_ones(ispin))
      CALL dbcsr_create(t1, &
                        template=almo_scf_env%matrix_k_blk_ones(ispin))
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          opt_k_e_dd, tmp, &
                          0.0_dp, t1, filter_eps=eps_filter)
      CALL dbcsr_release(opt_k_e_dd)

      ! compute S_pp = X*sigma_oo_inv*X^tr
      CALL dbcsr_create(tmp_vr_vr_blk, &
                        template=almo_scf_env%matrix_sigma_vv_blk(ispin), &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL dbcsr_copy(tmp_vr_vr_blk, &
                      almo_scf_env%matrix_sigma_vv_blk(ispin))
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          almo_scf_env%matrix_x(ispin), &
                          oo_inv_x_tr, &
                          0.0_dp, tmp_vr_vr_blk, &
                          retain_sparsity=.TRUE.)

      ! obtain the orthogonalization matrix
      CALL dbcsr_create(s_rr_sqrt, &
                        template=almo_scf_env%matrix_sigma_vv_blk(ispin), &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL matrix_sqrt_Newton_Schulz(s_rr_sqrt, &
                                     almo_scf_env%opt_k_t_rr(ispin), &
                                     tmp_vr_vr_blk, &
                                     threshold=eps_filter, &
                                     order=almo_scf_env%order_lanczos, &
                                     eps_lanczos=almo_scf_env%eps_lanczos, &
                                     max_iter_lanczos=almo_scf_env%max_iter_lanczos)

      ! compute F_pp = X*sig_oo_inv*(T^tr)*F*T*sig_oo_inv*(X^tr)
      CALL dbcsr_create(tmp1_n_vr, &
                        template=almo_scf_env%matrix_v(ispin))
      CALL dbcsr_create(tmp2_n_vr, &
                        template=almo_scf_env%matrix_v(ispin))
      CALL dbcsr_multiply("N", "N", 1.0_dp, t_curr, oo_inv_x_tr, &
                          0.0_dp, tmp1_n_vr, filter_eps=eps_filter)
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          almo_scf_env%matrix_ks_0deloc(ispin), &
                          tmp1_n_vr, &
                          0.0_dp, tmp2_n_vr, filter_eps=eps_filter)
      CALL dbcsr_multiply("T", "N", 1.0_dp, tmp1_n_vr, tmp2_n_vr, &
                          0.0_dp, tmp_vr_vr_blk, &
                          retain_sparsity=.TRUE.)
      CALL dbcsr_release(tmp1_n_vr)
      CALL dbcsr_release(tmp2_n_vr)

      ! bring to the blocked-orthogonalized basis
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          tmp_vr_vr_blk, &
                          almo_scf_env%opt_k_t_rr(ispin), &
                          0.0_dp, s_rr_sqrt, filter_eps=eps_filter)
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          almo_scf_env%opt_k_t_rr(ispin), &
                          s_rr_sqrt, &
                          0.0_dp, tmp_vr_vr_blk, filter_eps=eps_filter)

      ! diagonalize the matrix
      CALL dbcsr_create(opt_k_e_rr, &
                        template=almo_scf_env%matrix_sigma_vv_blk(ispin))
      CALL dbcsr_release(s_rr_sqrt)
      CALL dbcsr_create(s_rr_sqrt, &
                        template=almo_scf_env%matrix_sigma_vv_blk(ispin), &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL diagonalize_diagonal_blocks(tmp_vr_vr_blk, &
                                       s_rr_sqrt, &
                                       opt_k_e_rr)

      ! obtain the transformation matrix in the retained subspace
      ! T = S^{-1/2}.U
      CALL dbcsr_copy(tmp_vr_vr_blk, &
                      almo_scf_env%opt_k_t_rr(ispin))
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          tmp_vr_vr_blk, &
                          s_rr_sqrt, &
                          0.0_dp, almo_scf_env%opt_k_t_rr(ispin), &
                          filter_eps=eps_filter)
      CALL dbcsr_release(s_rr_sqrt)
      CALL dbcsr_release(tmp_vr_vr_blk)

      ! copy diagonal elements of the result into cols of a matrix
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          tmp, opt_k_e_rr, &
                          0.0_dp, almo_scf_env%opt_k_denom(ispin), &
                          filter_eps=eps_filter)
      CALL dbcsr_release(opt_k_e_rr)
      CALL dbcsr_release(tmp)

      ! form the denominator matrix
      CALL dbcsr_add(almo_scf_env%opt_k_denom(ispin), t1, &
                     -1.0_dp, 1.0_dp)
      CALL dbcsr_release(t1)
      CALL dbcsr_scale(almo_scf_env%opt_k_denom(ispin), &
                       2.0_dp*spin_factor)

      CALL dbcsr_function_of_elements(almo_scf_env%opt_k_denom(ispin), &
                                      dbcsr_func_inverse)
      CALL dbcsr_filter(almo_scf_env%opt_k_denom(ispin), &
                        eps_filter)

      CALL timestop(handle)

   END SUBROUTINE opt_k_create_preconditioner_blk

! **************************************************************************************************
!> \brief Applies a block-diagonal preconditioner for the optimization of
!>        k matrix (preconditioner matrices must be calculated and stored
!>        beforehand)
!> \param almo_scf_env ...
!> \param step ...
!> \param grad ...
!> \param ispin ...
!> \par History
!>       2011.10 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE opt_k_apply_preconditioner_blk(almo_scf_env, step, grad, ispin)

      TYPE(almo_scf_env_type), INTENT(INOUT)             :: almo_scf_env
      TYPE(dbcsr_type), INTENT(OUT)                      :: step
      TYPE(dbcsr_type), INTENT(IN)                       :: grad
      INTEGER, INTENT(IN)                                :: ispin

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

      INTEGER                                            :: handle
      REAL(KIND=dp)                                      :: eps_filter
      TYPE(dbcsr_type)                                   :: tmp_k

      CALL timeset(routineN, handle)

      eps_filter = almo_scf_env%eps_filter

      CALL dbcsr_create(tmp_k, template=almo_scf_env%matrix_k_blk(ispin))

      ! transform gradient to the correct "diagonal" basis
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          grad, almo_scf_env%opt_k_t_rr(ispin), &
                          0.0_dp, tmp_k, filter_eps=eps_filter)
      CALL dbcsr_multiply("T", "N", 1.0_dp, &
                          almo_scf_env%opt_k_t_dd(ispin), tmp_k, &
                          0.0_dp, step, filter_eps=eps_filter)

      ! apply diagonal preconditioner
      CALL dbcsr_hadamard_product(step, &
                                  almo_scf_env%opt_k_denom(ispin), tmp_k)

      ! back-transform the result to the initial basis
      CALL dbcsr_multiply("N", "N", 1.0_dp, &
                          almo_scf_env%opt_k_t_dd(ispin), tmp_k, &
                          0.0_dp, step, filter_eps=eps_filter)
      CALL dbcsr_multiply("N", "T", 1.0_dp, &
                          step, almo_scf_env%opt_k_t_rr(ispin), &
                          0.0_dp, tmp_k, filter_eps=eps_filter)

      CALL dbcsr_copy(step, tmp_k)

      CALL dbcsr_release(tmp_k)

      CALL timestop(handle)

   END SUBROUTINE opt_k_apply_preconditioner_blk

!! **************************************************************************************************
!!> \brief Reduce the number of virtual orbitals by rotating them within
!!>        a domain. The rotation is such that minimizes the frobenius norm of
!!>        the Fov domain-blocks of the discarded virtuals
!!> \par History
!!>       2011.08 created [Rustam Z Khaliullin]
!!> \author Rustam Z Khaliullin
!! **************************************************************************************************
!  SUBROUTINE truncate_subspace_v_blk(qs_env,almo_scf_env)
!
!    TYPE(qs_environment_type), POINTER       :: qs_env
!    TYPE(almo_scf_env_type)                  :: almo_scf_env
!
!    CHARACTER(len=*), PARAMETER :: routineN = 'truncate_subspace_v_blk', &
!      routineP = moduleN//':'//routineN
!
!    INTEGER                                  :: handle, ispin, iblock_row, &
!                                                iblock_col, iblock_row_size, &
!                                                iblock_col_size, retained_v, &
!                                                iteration, line_search_step, &
!                                                unit_nr, line_search_step_last
!    REAL(KIND=dp)                            :: t1, obj_function, grad_norm,&
!                                                c0, b0, a0, obj_function_new,&
!                                                t2, alpha, ff1, ff2, step1,&
!                                                step2,&
!                                                frob_matrix_base,&
!                                                frob_matrix
!    LOGICAL                                  :: safe_mode, converged, &
!                                                prepare_to_exit, failure
!    TYPE(cp_logger_type), POINTER            :: logger
!    TYPE(dbcsr_type)                      :: Fon, Fov, Fov_filtered, &
!                                                temp1_oo, temp2_oo, Fov_original, &
!                                                temp0_ov, U_blk_tot, U_blk, &
!                                                grad_blk, step_blk, matrix_filter, &
!                                                v_full_new,v_full_tmp,&
!                                                matrix_sigma_vv_full,&
!                                                matrix_sigma_vv_full_sqrt,&
!                                                matrix_sigma_vv_full_sqrt_inv,&
!                                                matrix_tmp1,&
!                                                matrix_tmp2
!
!    REAL(kind=dp), DIMENSION(:, :), POINTER  :: data_p, p_new_block
!    TYPE(dbcsr_iterator_type)                  :: iter
!
!
!REAL(kind=dp), DIMENSION(:), ALLOCATABLE     :: eigenvalues, WORK
!REAL(kind=dp), DIMENSION(:,:), ALLOCATABLE   :: data_copy, left_vectors, right_vectors
!INTEGER                                      :: LWORK, INFO
!TYPE(dbcsr_type)                          :: temp_u_v_full_blk
!
!    CALL timeset(routineN,handle)
!
!    safe_mode=.TRUE.
!
!    ! get a useful output_unit
!    logger => cp_get_default_logger()
!    IF (logger%para_env%mepos==logger%para_env%source) THEN
!       unit_nr=cp_logger_get_default_unit_nr(logger,local=.TRUE.)
!    ELSE
!       unit_nr=-1
!    ENDIF
!
!    DO ispin=1,almo_scf_env%nspins
!
!       t1 = m_walltime()
!
!       !!!!!!!!!!!!!!!!!
!       ! 0. Orthogonalize virtuals
!       !    Unfortunately, we have to do it in the FULL V subspace :(
!
!       CALL dbcsr_init(v_full_new)
!       CALL dbcsr_create(v_full_new,&
!               template=almo_scf_env%matrix_v_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!
!       ! project the occupied subspace out
!       CALL almo_scf_p_out_from_v(almo_scf_env%matrix_v_full_blk(ispin),&
!              v_full_new,almo_scf_env%matrix_ov_full(ispin),&
!              ispin,almo_scf_env)
!
!       ! init overlap and its functions
!       CALL dbcsr_init(matrix_sigma_vv_full)
!       CALL dbcsr_init(matrix_sigma_vv_full_sqrt)
!       CALL dbcsr_init(matrix_sigma_vv_full_sqrt_inv)
!       CALL dbcsr_create(matrix_sigma_vv_full,&
!               template=almo_scf_env%matrix_vv_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!       CALL dbcsr_create(matrix_sigma_vv_full_sqrt,&
!               template=almo_scf_env%matrix_vv_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!       CALL dbcsr_create(matrix_sigma_vv_full_sqrt_inv,&
!               template=almo_scf_env%matrix_vv_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!
!       ! construct VV overlap
!       CALL almo_scf_mo_to_sigma(v_full_new,&
!               matrix_sigma_vv_full,&
!               almo_scf_env%matrix_s(1),&
!               almo_scf_env%eps_filter)
!
!       IF (unit_nr>0) THEN
!          WRITE(unit_nr,*) "sqrt and inv(sqrt) of the FULL virtual MO overlap"
!       ENDIF
!
!       ! construct orthogonalization matrices
!       CALL matrix_sqrt_Newton_Schulz(matrix_sigma_vv_full_sqrt,&
!                                      matrix_sigma_vv_full_sqrt_inv,&
!                                      matrix_sigma_vv_full,&
!                                      threshold=almo_scf_env%eps_filter,&
!                                      order=almo_scf_env%order_lanczos,&
!                                      eps_lanczos=almo_scf_env%eps_lanczos,&
!                                      max_iter_lanczos=almo_scf_env%max_iter_lanczos)
!       IF (safe_mode) THEN
!          CALL dbcsr_init(matrix_tmp1)
!          CALL dbcsr_create(matrix_tmp1,template=matrix_sigma_vv_full,&
!                               matrix_type=dbcsr_type_no_symmetry)
!          CALL dbcsr_init(matrix_tmp2)
!          CALL dbcsr_create(matrix_tmp2,template=matrix_sigma_vv_full,&
!                               matrix_type=dbcsr_type_no_symmetry)
!
!          CALL dbcsr_multiply("N","N",1.0_dp,matrix_sigma_vv_full_sqrt_inv,&
!                                 matrix_sigma_vv_full,&
!                                 0.0_dp,matrix_tmp1,filter_eps=almo_scf_env%eps_filter)
!          CALL dbcsr_multiply("N","N",1.0_dp,matrix_tmp1,&
!                                 matrix_sigma_vv_full_sqrt_inv,&
!                                 0.0_dp,matrix_tmp2,filter_eps=almo_scf_env%eps_filter)
!
!          frob_matrix_base=dbcsr_frobenius_norm(matrix_tmp2)
!          CALL dbcsr_add_on_diag(matrix_tmp2,-1.0_dp)
!          frob_matrix=dbcsr_frobenius_norm(matrix_tmp2)
!          IF (unit_nr>0) THEN
!             WRITE(unit_nr,*) "Error for (inv(sqrt(SIGVV))*SIGVV*inv(sqrt(SIGVV))-I)",frob_matrix/frob_matrix_base
!          ENDIF
!
!          CALL dbcsr_release(matrix_tmp1)
!          CALL dbcsr_release(matrix_tmp2)
!       ENDIF
!
!       ! discard unnecessary overlap functions
!       CALL dbcsr_release(matrix_sigma_vv_full)
!       CALL dbcsr_release(matrix_sigma_vv_full_sqrt)
!
!! this can be re-written because we have (1-P)|v>
!
!       !!!!!!!!!!!!!!!!!!!
!       ! 1. Compute F_ov
!       CALL dbcsr_init(Fon)
!       CALL dbcsr_create(Fon,&
!               template=almo_scf_env%matrix_v_full_blk(ispin))
!       CALL dbcsr_init(Fov)
!       CALL dbcsr_create(Fov,&
!               template=almo_scf_env%matrix_ov_full(ispin))
!       CALL dbcsr_init(Fov_filtered)
!       CALL dbcsr_create(Fov_filtered,&
!               template=almo_scf_env%matrix_ov_full(ispin))
!       CALL dbcsr_init(temp1_oo)
!       CALL dbcsr_create(temp1_oo,&
!               template=almo_scf_env%matrix_sigma(ispin),&
!               !matrix_type=dbcsr_type_no_symmetry)
!       CALL dbcsr_init(temp2_oo)
!       CALL dbcsr_create(temp2_oo,&
!               template=almo_scf_env%matrix_sigma(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!
!       CALL dbcsr_multiply("T","N",1.0_dp,almo_scf_env%matrix_t_blk(ispin),&
!               almo_scf_env%matrix_ks_0deloc(ispin),&
!               0.0_dp,Fon,filter_eps=almo_scf_env%eps_filter)
!
!       CALL dbcsr_multiply("N","N",1.0_dp,Fon,&
!               almo_scf_env%matrix_v_full_blk(ispin),&
!               0.0_dp,Fov,filter_eps=almo_scf_env%eps_filter)
!
!       CALL dbcsr_multiply("N","N",1.0_dp,Fon,&
!               almo_scf_env%matrix_t_blk(ispin),&
!               0.0_dp,temp1_oo,filter_eps=almo_scf_env%eps_filter)
!
!       CALL dbcsr_multiply("N","N",1.0_dp,temp1_oo,&
!               almo_scf_env%matrix_sigma_inv(ispin),&
!               0.0_dp,temp2_oo,filter_eps=almo_scf_env%eps_filter)
!       CALL dbcsr_release(temp1_oo)
!
!       CALL dbcsr_multiply("T","N",1.0_dp,almo_scf_env%matrix_t_blk(ispin),&
!               almo_scf_env%matrix_s(1),&
!               0.0_dp,Fon,filter_eps=almo_scf_env%eps_filter)
!
!       CALL dbcsr_multiply("N","N",1.0_dp,Fon,&
!               almo_scf_env%matrix_v_full_blk(ispin),&
!               0.0_dp,Fov_filtered,filter_eps=almo_scf_env%eps_filter)
!       CALL dbcsr_release(Fon)
!
!       CALL dbcsr_multiply("N","N",-1.0_dp,temp2_oo,&
!               Fov_filtered,&
!               1.0_dp,Fov,filter_eps=almo_scf_env%eps_filter)
!       CALL dbcsr_release(temp2_oo)
!
!       CALL dbcsr_multiply("N","N",1.0_dp,almo_scf_env%matrix_sigma_inv(ispin),&
!               Fov,0.0_dp,Fov_filtered,filter_eps=almo_scf_env%eps_filter)
!
!       CALL dbcsr_multiply("N","N",1.0_dp,Fov_filtered,&
!               matrix_sigma_vv_full_sqrt_inv,&
!               0.0_dp,Fov,filter_eps=almo_scf_env%eps_filter)
!       !CALL dbcsr_copy(Fov,Fov_filtered)
!CALL dbcsr_print(Fov)
!
!       IF (safe_mode) THEN
!          CALL dbcsr_init(Fov_original)
!          CALL dbcsr_create(Fov_original,template=Fov)
!          CALL dbcsr_copy(Fov_original,Fov)
!       ENDIF
!
!!! remove diagonal blocks
!!CALL dbcsr_iterator_start(iter,Fov)
!!DO WHILE (dbcsr_iterator_blocks_left(iter))
!!
!!   CALL dbcsr_iterator_next_block(iter,iblock_row,iblock_col,data_p,&
!!           row_size=iblock_row_size,col_size=iblock_col_size)
!!
!!   IF (iblock_row.eq.iblock_col) data_p(:,:)=0.0_dp
!!
!!ENDDO
!!CALL dbcsr_iterator_stop(iter)
!!CALL dbcsr_finalize(Fov)
!
!!! perform svd of blocks
!!!!! THIS ROUTINE WORKS ONLY ON ONE CPU AND ONLY FOR 2 MOLECULES !!!
!!CALL dbcsr_init(temp_u_v_full_blk)
!!CALL dbcsr_create(temp_u_v_full_blk,&
!!        template=almo_scf_env%matrix_vv_full_blk(ispin),&
!!        matrix_type=dbcsr_type_no_symmetry)
!!
!!CALL dbcsr_work_create(temp_u_v_full_blk,&
!!        work_mutable=.TRUE.)
!!CALL dbcsr_iterator_start(iter,Fov)
!!DO WHILE (dbcsr_iterator_blocks_left(iter))
!!
!!   CALL dbcsr_iterator_next_block(iter,iblock_row,iblock_col,data_p,&
!!           row_size=iblock_row_size,col_size=iblock_col_size)
!!
!!   IF (iblock_row.ne.iblock_col) THEN
!!
!!      ! Prepare data
!!      allocate(eigenvalues(min(iblock_row_size,iblock_col_size)))
!!      allocate(data_copy(iblock_row_size,iblock_col_size))
!!      allocate(left_vectors(iblock_row_size,iblock_row_size))
!!      allocate(right_vectors(iblock_col_size,iblock_col_size))
!!      data_copy(:,:)=data_p(:,:)
!!
!!      ! Query the optimal workspace for dgesvd
!!      LWORK = -1
!!      allocate(WORK(MAX(1,LWORK)))
!!      CALL DGESVD('N','A',iblock_row_size,iblock_col_size,data_copy,&
!!              iblock_row_size,eigenvalues,left_vectors,iblock_row_size,&
!!              right_vectors,iblock_col_size,WORK,LWORK,INFO)
!!      LWORK = INT(WORK( 1 ))
!!      deallocate(WORK)
!!
!!      ! Allocate the workspace and perform svd
!!      allocate(WORK(MAX(1,LWORK)))
!!      CALL DGESVD('N','A',iblock_row_size,iblock_col_size,data_copy,&
!!              iblock_row_size,eigenvalues,left_vectors,iblock_row_size,&
!!              right_vectors,iblock_col_size,WORK,LWORK,INFO)
!!      deallocate(WORK)
!!      IF( INFO.NE.0 ) THEN
!!         CPErrorMessage(cp_failure_level,routineP,"DGESVD failed")
!!         CPPrecondition(.FALSE.,cp_failure_level,routineP,failure)
!!      END IF
!!
!!      ! copy right singular vectors into a unitary matrix
!!      NULLIFY (p_new_block)
!!      CALL dbcsr_reserve_block2d(temp_u_v_full_blk,iblock_col,iblock_col,p_new_block)
!!      CPPostcondition(ASSOCIATED(p_new_block),cp_failure_level,routineP,failure)
!!      p_new_block(:,:) = right_vectors(:,:)
!!
!!      deallocate(eigenvalues)
!!      deallocate(data_copy)
!!      deallocate(left_vectors)
!!      deallocate(right_vectors)
!!
!!   ENDIF
!!ENDDO
!!CALL dbcsr_iterator_stop(iter)
!!CALL dbcsr_finalize(temp_u_v_full_blk)
!!!CALL dbcsr_print(temp_u_v_full_blk)
!!CALL dbcsr_multiply("N","T",1.0_dp,Fov,temp_u_v_full_blk,&
!!        0.0_dp,Fov_filtered,filter_eps=almo_scf_env%eps_filter)
!!
!!CALL dbcsr_copy(Fov,Fov_filtered)
!!CALL dbcsr_print(Fov)
!
!       !!!!!!!!!!!!!!!!!!!
!       ! 2. Initialize variables
!
!       ! temp space
!       CALL dbcsr_init(temp0_ov)
!       CALL dbcsr_create(temp0_ov,&
!               template=almo_scf_env%matrix_ov_full(ispin))
!
!       ! current unitary matrix
!       CALL dbcsr_init(U_blk)
!       CALL dbcsr_create(U_blk,&
!               template=almo_scf_env%matrix_vv_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!
!       ! unitary matrix accumulator
!       CALL dbcsr_init(U_blk_tot)
!       CALL dbcsr_create(U_blk_tot,&
!               template=almo_scf_env%matrix_vv_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!       CALL dbcsr_add_on_diag(U_blk_tot,1.0_dp)
!
!!CALL dbcsr_add_on_diag(U_blk,1.0_dp)
!!CALL dbcsr_multiply("N","T",1.0_dp,U_blk,temp_u_v_full_blk,&
!!        0.0_dp,U_blk_tot,filter_eps=almo_scf_env%eps_filter)
!!
!!CALL dbcsr_release(temp_u_v_full_blk)
!
!       ! init gradient
!       CALL dbcsr_init(grad_blk)
!       CALL dbcsr_create(grad_blk,&
!               template=almo_scf_env%matrix_vv_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!
!       ! init step matrix
!       CALL dbcsr_init(step_blk)
!       CALL dbcsr_create(step_blk,&
!               template=almo_scf_env%matrix_vv_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!
!       ! "retain discarded" filter (0.0 - retain, 1.0 - discard)
!       CALL dbcsr_init(matrix_filter)
!       CALL dbcsr_create(matrix_filter,&
!               template=almo_scf_env%matrix_ov_full(ispin))
!       ! copy Fov into the filter matrix temporarily
!       ! so we know which blocks contain significant elements
!       CALL dbcsr_copy(matrix_filter,Fov)
!
!       ! fill out filter elements block-by-block
!       CALL dbcsr_iterator_start(iter,matrix_filter)
!       DO WHILE (dbcsr_iterator_blocks_left(iter))
!
!          CALL dbcsr_iterator_next_block(iter,iblock_row,iblock_col,data_p,&
!                  row_size=iblock_row_size,col_size=iblock_col_size)
!
!          retained_v=almo_scf_env%nvirt_of_domain(iblock_col,ispin)
!
!          data_p(:,1:retained_v)=0.0_dp
!          data_p(:,(retained_v+1):iblock_col_size)=1.0_dp
!
!       ENDDO
!       CALL dbcsr_iterator_stop(iter)
!       CALL dbcsr_finalize(matrix_filter)
!
!       ! apply the filter
!       CALL dbcsr_hadamard_product(Fov,matrix_filter,Fov_filtered)
!
!       !!!!!!!!!!!!!!!!!!!!!
!       ! 3. start iterative minimization of the elements to be discarded
!       iteration=0
!       converged=.FALSE.
!       prepare_to_exit=.FALSE.
!       DO
!
!          iteration=iteration+1
!
!          !!!!!!!!!!!!!!!!!!!!!!!!!
!          ! 4. compute the gradient
!          CALL dbcsr_set(grad_blk,0.0_dp)
!          ! create the diagonal blocks only
!          CALL dbcsr_add_on_diag(grad_blk,1.0_dp)
!
!          CALL dbcsr_multiply("T","N",2.0_dp,Fov_filtered,Fov,&
!                  0.0_dp,grad_blk,retain_sparsity=.TRUE.,&
!                  filter_eps=almo_scf_env%eps_filter)
!          CALL dbcsr_multiply("T","N",-2.0_dp,Fov,Fov_filtered,&
!                  1.0_dp,grad_blk,retain_sparsity=.TRUE.,&
!                  filter_eps=almo_scf_env%eps_filter)
!
!          !!!!!!!!!!!!!!!!!!!!!!!
!          ! 5. check convergence
!          obj_function = 0.5_dp*(dbcsr_frobenius_norm(Fov_filtered))**2
!          grad_norm = dbcsr_frobenius_norm(grad_blk)
!          converged=(grad_norm.lt.almo_scf_env%truncate_v_eps_convergence)
!          IF (converged.OR.(iteration.ge.almo_scf_env%truncate_v_max_iter)) THEN
!             prepare_to_exit=.TRUE.
!          ENDIF
!
!          IF (.NOT.prepare_to_exit) THEN
!
!             !!!!!!!!!!!!!!!!!!!!!!!
!             ! 6. perform steps in the direction of the gradient
!             !    a. first, perform a trial step to "see" the parameters
!             !       of the parabola along the gradient:
!             !       a0 * x^2 + b0 * x + c0
!             !    b. then perform the step to the bottom of the parabola
!
!             ! get c0
!             c0 = obj_function
!             ! get b0 <= d_f/d_alpha along grad
!             !!!CALL dbcsr_multiply("N","N",4.0_dp,Fov,grad_blk,&
!             !!!        0.0_dp,temp0_ov,&
!             !!!        filter_eps=almo_scf_env%eps_filter)
!             !!!CALL dbcsr_trace(Fov_filtered,temp0_ov,b0)
!
!             alpha=almo_scf_env%truncate_v_trial_step_size
!
!             line_search_step_last=3
!             DO line_search_step=1,line_search_step_last
!                CALL dbcsr_copy(step_blk,grad_blk)
!                CALL dbcsr_scale(step_blk,-1.0_dp*alpha)
!                CALL generator_to_unitary(step_blk,U_blk,&
!                        almo_scf_env%eps_filter)
!                CALL dbcsr_multiply("N","N",1.0_dp,Fov,U_blk,0.0_dp,temp0_ov,&
!                        filter_eps=almo_scf_env%eps_filter)
!                CALL dbcsr_hadamard_product(temp0_ov,matrix_filter,&
!                        Fov_filtered)
!
!                obj_function_new = 0.5_dp*(dbcsr_frobenius_norm(Fov_filtered))**2
!                IF (line_search_step.eq.1) THEN
!                   ff1 = obj_function_new
!                   step1 = alpha
!                ELSE IF (line_search_step.eq.2) THEN
!                   ff2 = obj_function_new
!                   step2 = alpha
!                ENDIF
!
!                IF (unit_nr>0.AND.(line_search_step.ne.line_search_step_last)) THEN
!                   WRITE(unit_nr,'(T6,A,1X,I3,1X,F10.3,E12.3,E12.3,E12.3)') &
!                         "JOINT_SVD_lin",&
!                         iteration,&
!                         alpha,&
!                         obj_function,&
!                         obj_function_new,&
!                         obj_function_new-obj_function
!                ENDIF
!
!                IF (line_search_step.eq.1) THEN
!                   alpha=2.0_dp*alpha
!                ENDIF
!                IF (line_search_step.eq.2) THEN
!                   a0 = ((ff1-c0)/step1 - (ff2-c0)/step2) / (step1 - step2)
!                   b0 = (ff1-c0)/step1 - a0*step1
!                   ! step size in to the bottom of "the parabola"
!                   alpha=-b0/(2.0_dp*a0)
!                   ! update the default step size
!                   almo_scf_env%truncate_v_trial_step_size=alpha
!                ENDIF
!                !!!IF (line_search_step.eq.1) THEN
!                !!!   a0 = (obj_function_new - b0 * alpha - c0) / (alpha*alpha)
!                !!!   ! step size in to the bottom of "the parabola"
!                !!!   alpha=-b0/(2.0_dp*a0)
!                !!!   !IF (alpha.gt.10.0_dp) alpha=10.0_dp
!                !!!ENDIF
!
!             ENDDO
!
!             ! update Fov and U_blk_tot (use grad_blk as tmp storage)
!             CALL dbcsr_copy(Fov,temp0_ov)
!             CALL dbcsr_multiply("N","N",1.0_dp,U_blk_tot,U_blk,&
!                     0.0_dp,grad_blk,&
!                     filter_eps=almo_scf_env%eps_filter)
!             CALL dbcsr_copy(U_blk_tot,grad_blk)
!
!          ENDIF
!
!          t2 = m_walltime()
!
!          IF (unit_nr>0) THEN
!             WRITE(unit_nr,'(T6,A,1X,I3,1X,F10.3,E12.3,E12.3,E12.3,E12.3,F10.3)') &
!                   "JOINT_SVD_itr",&
!                   iteration,&
!                   alpha,&
!                   obj_function,&
!                   obj_function_new,&
!                   obj_function_new-obj_function,&
!                   grad_norm,&
!                   t2-t1
!                   !(flop1+flop2)/(1.0E6_dp*(t2-t1))
!             CALL m_flush(unit_nr)
!          ENDIF
!
!          t1 = m_walltime()
!
!          IF (prepare_to_exit) EXIT
!
!       ENDDO ! stop iterations
!
!       IF (safe_mode) THEN
!          CALL dbcsr_multiply("N","N",1.0_dp,Fov_original,&
!                  U_blk_tot,0.0_dp,temp0_ov,&
!                  filter_eps=almo_scf_env%eps_filter)
!CALL dbcsr_print(temp0_ov)
!          CALL dbcsr_hadamard_product(temp0_ov,matrix_filter,&
!                  Fov_filtered)
!          obj_function_new = 0.5_dp*(dbcsr_frobenius_norm(Fov_filtered))**2
!
!          IF (unit_nr>0) THEN
!             WRITE(unit_nr,'(T6,A,1X,E12.3)') &
!                   "SANITY CHECK:",&
!                   obj_function_new
!             CALL m_flush(unit_nr)
!          ENDIF
!
!          CALL dbcsr_release(Fov_original)
!       ENDIF
!
!       CALL dbcsr_release(temp0_ov)
!       CALL dbcsr_release(U_blk)
!       CALL dbcsr_release(grad_blk)
!       CALL dbcsr_release(step_blk)
!       CALL dbcsr_release(matrix_filter)
!       CALL dbcsr_release(Fov)
!       CALL dbcsr_release(Fov_filtered)
!
!       ! compute rotated virtual orbitals
!       CALL dbcsr_init(v_full_tmp)
!       CALL dbcsr_create(v_full_tmp,&
!               template=almo_scf_env%matrix_v_full_blk(ispin),&
!               matrix_type=dbcsr_type_no_symmetry)
!       CALL dbcsr_multiply("N","N",1.0_dp,&
!               v_full_new,&
!               matrix_sigma_vv_full_sqrt_inv,0.0_dp,v_full_tmp,&
!               filter_eps=almo_scf_env%eps_filter)
!       CALL dbcsr_multiply("N","N",1.0_dp,&
!               v_full_tmp,&
!               U_blk_tot,0.0_dp,v_full_new,&
!               filter_eps=almo_scf_env%eps_filter)
!
!       CALL dbcsr_release(matrix_sigma_vv_full_sqrt_inv)
!       CALL dbcsr_release(v_full_tmp)
!       CALL dbcsr_release(U_blk_tot)
!
!!!!! orthogonalized virtuals are not blocked
!       ! copy new virtuals into the truncated matrix
!       !CALL dbcsr_work_create(almo_scf_env%matrix_v_blk(ispin),&
!       CALL dbcsr_work_create(almo_scf_env%matrix_v(ispin),&
!               work_mutable=.TRUE.)
!       CALL dbcsr_iterator_start(iter,v_full_new)
!       DO WHILE (dbcsr_iterator_blocks_left(iter))
!
!          CALL dbcsr_iterator_next_block(iter,iblock_row,iblock_col,data_p,&
!                  row_size=iblock_row_size,col_size=iblock_col_size)
!
!          retained_v=almo_scf_env%nvirt_of_domain(iblock_col,ispin)
!
!          NULLIFY (p_new_block)
!          !CALL dbcsr_reserve_block2d(almo_scf_env%matrix_v_blk(ispin),&
!          CALL dbcsr_reserve_block2d(almo_scf_env%matrix_v(ispin),&
!                  iblock_row,iblock_col,p_new_block)
!          CPPostcondition(ASSOCIATED(p_new_block),cp_failure_level,routineP,failure)
!          CPPrecondition(retained_v.gt.0,cp_failure_level,routineP,failure)
!          p_new_block(:,:) = data_p(:,1:retained_v)
!
!       ENDDO ! iterator
!       CALL dbcsr_iterator_stop(iter)
!       !!CALL dbcsr_finalize(almo_scf_env%matrix_v_blk(ispin))
!       CALL dbcsr_finalize(almo_scf_env%matrix_v(ispin))
!
!       CALL dbcsr_release(v_full_new)
!
!    ENDDO ! ispin
!
!    CALL timestop(handle)
!
!  END SUBROUTINE truncate_subspace_v_blk

! *****************************************************************************
!> \brief Compute the gradient wrt the main variable (e.g. Theta, X)
!> \param m_grad_out ...
!> \param m_ks ...
!> \param m_s ...
!> \param m_t ...
!> \param m_t0 ...
!> \param m_siginv ...
!> \param m_quench_t ...
!> \param m_FTsiginv ...
!> \param m_siginvTFTsiginv ...
!> \param m_ST ...
!> \param m_STsiginv0 ...
!> \param m_theta ...
!> \param domain_s_inv ...
!> \param domain_r_down ...
!> \param cpu_of_domain ...
!> \param domain_map ...
!> \param assume_t0_q0x ...
!> \param optimize_theta ...
!> \param perturbation_only ...
!> \param normalize_orbitals ...
!> \param penalty_occ_vol ...
!> \param penalty_occ_vol_prefactor ...
!> \param envelope_amplitude ...
!> \param eps_filter ...
!> \param spin_factor ...
!> \param special_case ...
!> \param m_sig_sqrti_ii ...
!> \par History
!>       2015.03 created [Rustam Z Khaliullin]
!> \author Rustam Z Khaliullin
! **************************************************************************************************
   SUBROUTINE compute_gradient(m_grad_out, m_ks, m_s, m_t, m_t0, &
                               m_siginv, m_quench_t, m_FTsiginv, m_siginvTFTsiginv, m_ST, m_STsiginv0, &
                               m_theta, domain_s_inv, domain_r_down, &
                               cpu_of_domain, domain_map, assume_t0_q0x, optimize_theta, &
                               perturbation_only, normalize_orbitals, penalty_occ_vol, &
                               penalty_occ_vol_prefactor, envelope_amplitude, eps_filter, spin_factor, &
                               special_case, m_sig_sqrti_ii)

      TYPE(dbcsr_type), INTENT(INOUT)                    :: m_grad_out
      TYPE(dbcsr_type), INTENT(IN)                       :: m_ks, m_s, m_t, m_t0, m_siginv, &
                                                            m_quench_t, m_FTsiginv, &
                                                            m_siginvTFTsiginv, m_ST, m_STsiginv0, &
                                                            m_theta
      TYPE(domain_submatrix_type), DIMENSION(:), &
         INTENT(IN)                                      :: domain_s_inv, domain_r_down
      INTEGER, DIMENSION(:), INTENT(IN)                  :: cpu_of_domain
      TYPE(domain_map_type), INTENT(IN)                  :: domain_map
      LOGICAL, INTENT(IN)                                :: assume_t0_q0x, optimize_theta, &
                                                            perturbation_only, normalize_orbitals, &
                                                            penalty_occ_vol
      REAL(KIND=dp), INTENT(IN)                          :: penalty_occ_vol_prefactor, &
                                                            envelope_amplitude, eps_filter, &
                                                            spin_factor
      INTEGER, INTENT(IN)                                :: special_case
      TYPE(dbcsr_type), INTENT(IN), OPTIONAL             :: m_sig_sqrti_ii

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

      INTEGER                                            :: handle, nao
      REAL(KIND=dp)                                      :: energy_g_norm, penalty_occ_vol_g_norm
      TYPE(dbcsr_type)                                   :: m_tmp_no_1, m_tmp_no_2, m_tmp_no_3, &
                                                            m_tmp_oo_1, m_tmp_oo_2

!TYPE(dbcsr_type), INTENT(INOUT)          :: m_tmp_no_2

      CALL timeset(routineN, handle)

      IF (normalize_orbitals .AND. (.NOT. PRESENT(m_sig_sqrti_ii))) THEN
         CPABORT("Matrix must be present")
      ENDIF

      ! use this otherways unused variables
      CALL dbcsr_get_info(matrix=m_ks, nfullrows_total=nao)
      CALL dbcsr_get_info(matrix=m_s, nfullrows_total=nao)
      CALL dbcsr_get_info(matrix=m_t, nfullrows_total=nao)
      IF (perturbation_only) CPWARN("Unused option")

      CALL dbcsr_create(m_tmp_no_1, &
                        template=m_quench_t, &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL dbcsr_create(m_tmp_no_2, &
                        template=m_quench_t, &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL dbcsr_create(m_tmp_no_3, &
                        template=m_quench_t, &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL dbcsr_create(m_tmp_oo_1, &
                        template=m_siginv, &
                        matrix_type=dbcsr_type_no_symmetry)
      CALL dbcsr_create(m_tmp_oo_2, &
                        template=m_siginv, &
                        matrix_type=dbcsr_type_no_symmetry)

      ! do d_E/d_T first
      !IF (.NOT.PRESENT(m_FTsiginv)) THEN
      !   CALL dbcsr_multiply("N","N",1.0_dp,&
      !           m_ks,&
      !           m_t,&
      !           0.0_dp,m_tmp_no_1,&
      !           filter_eps=eps_filter)
      !   CALL dbcsr_multiply("N","N",1.0_dp,&
      !           m_tmp_no_1,&
      !           m_siginv,&
      !           0.0_dp,m_FTsiginv,&
      !           filter_eps=eps_filter)
      !ENDIF

      CALL dbcsr_copy(m_tmp_no_2, m_quench_t)
      CALL dbcsr_copy(m_tmp_no_2, m_FTsiginv, keep_sparsity=.TRUE.)

      !IF (.NOT.PRESENT(m_siginvTFTsiginv)) THEN
      !   CALL dbcsr_multiply("T","N",1.0_dp,&
      !           m_t,&
      !           m_FTsiginv,&
      !           0.0_dp,m_tmp_oo_1,&
      !           filter_eps=eps_filter)
      !   CALL dbcsr_multiply("N","N",1.0_dp,&
      !           m_siginv,&
      !           m_tmp_oo_1,&
      !           0.0_dp,m_siginvTFTsiginv,&
      !           filter_eps=eps_filter)
      !ENDIF

      !IF (.NOT.PRESENT(m_ST)) THEN
      !   CALL dbcsr_multiply("N","N",1.0_dp,&
      !           m_s,&
      !           m_t,&
      !           0.0_dp,m_ST,&
      !           filter_eps=eps_filter)
      !ENDIF

      CALL dbcsr_multiply("N", "N", -1.0_dp, &
                          m_ST, &
                          m_siginvTFTsiginv, &
                          1.0_dp, m_tmp_no_2, &
                          retain_sparsity=.TRUE.)
      CALL dbcsr_scale(m_tmp_no_2, 2.0_dp*spin_factor)

      ! add penalty on the occupied volume: det(sigma)
      IF (penalty_occ_vol) THEN
         !RZK-warning CALL dbcsr_multiply("N","N",&
         !RZK-warning         penalty_occ_vol_prefactor,&
         !RZK-warning         m_ST,&
         !RZK-warning         m_siginv,&
         !RZK-warning         1.0_dp,m_tmp_no_2,&
         !RZK-warning         retain_sparsity=.TRUE.,&
         !RZK-warning         )
         CALL dbcsr_copy(m_tmp_no_1, m_quench_t)
         CALL dbcsr_multiply("N", "N", &
                             penalty_occ_vol_prefactor, &
                             m_ST, &
                             m_siginv, &
                             0.0_dp, m_tmp_no_1, &
                             retain_sparsity=.TRUE.)
! this norm does not contain the normalization factors
         CALL dbcsr_norm(m_tmp_no_1, dbcsr_norm_maxabsnorm, &
                         norm_scalar=penalty_occ_vol_g_norm)
         CALL dbcsr_norm(m_tmp_no_2, dbcsr_norm_maxabsnorm, &
                         norm_scalar=energy_g_norm)
         !WRITE (*, "(A30,2F20.10)") "Energy/penalty g norms (no norm): ", energy_g_norm, penalty_occ_vol_g_norm
         CALL dbcsr_add(m_tmp_no_2, m_tmp_no_1, 1.0_dp, 1.0_dp)
      ENDIF

      ! take into account the factor from the normalization constraint
      IF (normalize_orbitals) THEN

         ! G = ( G - ST.[tr(T).G]_ii ) . [sig_sqrti]_ii
         ! this expression can be simplified to
         ! G = ( G - c0*ST ) . [sig_sqrti]_ii
         ! where c0 = penalty_occ_vol_prefactor
         ! This is because tr(T).G_Energy = 0 and
         !                 tr(T).G_Penalty = c0*I
         CALL dbcsr_copy(m_tmp_no_1, m_quench_t)
         CALL dbcsr_copy(m_tmp_no_1, m_ST, keep_sparsity=.TRUE.)
         CALL dbcsr_add(m_tmp_no_2, m_tmp_no_1, 1.0_dp, -penalty_occ_vol_prefactor)
         CALL dbcsr_copy(m_tmp_no_1, m_quench_t)
         CALL dbcsr_multiply("N", "N", 1.0_dp, &
                             m_tmp_no_2, &
                             m_sig_sqrti_ii, &
                             0.0_dp, m_tmp_no_1, &
                             retain_sparsity=.TRUE.)

         !!! slower way of taking the norm into account
         !!CALL dbcsr_copy(m_tmp_no_1,m_tmp_no_2,)
         !!CALL dbcsr_multiply("N","N",1.0_dp,&
         !!        m_tmp_no_2,&
         !!        m_sig_sqrti_ii,&
         !!        0.0_dp,m_tmp_no_1,&
         !!        retain_sparsity=.TRUE.,&
         !!        )
         !!
         !!! get [tr(T).G]_ii
         !!CALL dbcsr_copy(m_tmp_oo_1,m_sig_sqrti_ii,)
         !!CALL dbcsr_multiply("T","N",1.0_dp,&
         !!        m_t,&
         !!        m_tmp_no_2,&
         !!        0.0_dp,m_tmp_oo_1,&
         !!        retain_sparsity=.TRUE.,&
         !!        )
         !!CALL dbcsr_get_info(m_sig_sqrti_ii, nfullrows_total=dim0 )
         !!ALLOCATE(tg_diagonal(dim0))
         !!CALL dbcsr_get_diag(m_tmp_oo_1,tg_diagonal,)
         !!CALL dbcsr_set(m_tmp_oo_1,0.0_dp,)
         !!CALL dbcsr_set_diag(m_tmp_oo_1,tg_diagonal,)
         !!DEALLOCATE(tg_diagonal)
         !!
         !!CALL dbcsr_multiply("N","N",1.0_dp,&
         !!        m_sig_sqrti_ii,&
         !!        m_tmp_oo_1,&
         !!        0.0_dp,m_tmp_oo_2,&
         !!        filter_eps=eps_filter,&
         !!        )
         !!CALL dbcsr_multiply("N","N",-1.0_dp,&
         !!        m_ST,&
         !!        m_tmp_oo_2,&
         !!        1.0_dp,m_tmp_no_1,&
         !!        retain_sparsity=.TRUE.,&
         !!        )

      ELSE

         CALL dbcsr_copy(m_tmp_no_1, m_tmp_no_2)

      ENDIF ! normalize_orbitals

      ! project out the occupied space from the gradient
      IF (assume_t0_q0x) THEN
         IF (special_case .EQ. xalmo_case_fully_deloc) THEN
            CALL dbcsr_copy(m_grad_out, m_tmp_no_1)
            CALL dbcsr_multiply("T", "N", 1.0_dp, &
                                m_t0, &
                                m_grad_out, &
                                0.0_dp, m_tmp_oo_1, &
                                filter_eps=eps_filter)
            CALL dbcsr_multiply("N", "N", -1.0_dp, &
                                m_STsiginv0, &
                                m_tmp_oo_1, &
                                1.0_dp, m_grad_out, &
                                filter_eps=eps_filter)
         ELSE IF (special_case .EQ. xalmo_case_block_diag) THEN
            CPABORT("Cannot project the zero-order space from itself")
         ELSE
            ! no special case: normal xALMOs
            CALL apply_domain_operators( &
               matrix_in=m_tmp_no_1, &
               matrix_out=m_grad_out, &
               operator2=domain_r_down(:), &
               operator1=domain_s_inv(:), &
               dpattern=m_quench_t, &
               map=domain_map, &
               node_of_domain=cpu_of_domain, &
               my_action=1, &
               filter_eps=eps_filter, &
               !matrix_trimmer=,&
               use_trimmer=.FALSE.)
         ENDIF ! my_special_case
         CALL dbcsr_copy(m_tmp_no_1, m_grad_out)
      ENDIF

      !! check whether the gradient lies entirely in R or Q
      !CALL dbcsr_multiply("T","N",1.0_dp,&
      !        m_t,&
      !        m_tmp_no_1,&
      !        0.0_dp,m_tmp_oo_1,&
      !        filter_eps=eps_filter,&
      !        )
      !CALL dbcsr_multiply("N","N",1.0_dp,&
      !        m_siginv,&
      !        m_tmp_oo_1,&
      !        0.0_dp,m_tmp_oo_2,&
      !        filter_eps=eps_filter,&
      !        )
      !CALL dbcsr_copy(m_tmp_no_2,m_tmp_no_1,)
      !CALL dbcsr_multiply("N","N",-1.0_dp,&
      !        m_ST,&
      !        m_tmp_oo_2,&
      !        1.0_dp,m_tmp_no_2,&
      !        retain_sparsity=.TRUE.,&
      !        )
      !CALL dbcsr_norm(m_tmp_no_2, dbcsr_norm_maxabsnorm,&
      !        norm_scalar=penalty_occ_vol_g_norm, )
      !WRITE(*,"(A50,2F20.10)") "Virtual-space projection of the gradient", penalty_occ_vol_g_norm
      !CALL dbcsr_add(m_tmp_no_2,m_tmp_no_1,1.0_dp,-1.0_dp,)
      !CALL dbcsr_norm(m_tmp_no_2, dbcsr_norm_maxabsnorm,&
      !        norm_scalar=penalty_occ_vol_g_norm, )
      !WRITE(*,"(A50,2F20.10)") "Occupied-space projection of the gradient", penalty_occ_vol_g_norm
      !CALL dbcsr_norm(m_tmp_no_1, dbcsr_norm_maxabsnorm,&
      !        norm_scalar=penalty_occ_vol_g_norm, )
      !WRITE(*,"(A50,2F20.10)") "Full gradient", penalty_occ_vol_g_norm

      ! transform d_E/d_T to d_E/d_theta
      IF (optimize_theta) THEN
         CALL dbcsr_copy(m_tmp_no_2, m_theta)
         CALL dbcsr_function_of_elements(m_tmp_no_2, &
                                         !func=dbcsr_func_cos,&
                                         func=dbcsr_func_dtanh, &
                                         a0=0.0_dp, &
                                         a1=1.0_dp/envelope_amplitude)
         CALL dbcsr_scale(m_tmp_no_2, &
                          envelope_amplitude)
         CALL dbcsr_set(m_tmp_no_3, 0.0_dp)
         CALL dbcsr_filter(m_tmp_no_3, eps=eps_filter)
         CALL dbcsr_hadamard_product(m_tmp_no_1, &
                                     m_tmp_no_2, &
                                     m_tmp_no_3, &
                                     b_assume_value=1.0_dp)
         CALL dbcsr_hadamard_product(m_tmp_no_3, &
                                     m_quench_t, &
                                     m_grad_out)
      ELSE ! simply copy
         CALL dbcsr_hadamard_product(m_tmp_no_1, &
                                     m_quench_t, &
                                     m_grad_out)
      ENDIF
      CALL dbcsr_filter(m_grad_out, eps=eps_filter)

      CALL dbcsr_release(m_tmp_no_1)
      CALL dbcsr_release(m_tmp_no_2)
      CALL dbcsr_release(m_tmp_no_3)
      CALL dbcsr_release(m_tmp_oo_1)
      CALL dbcsr_release(m_tmp_oo_2)

      CALL timestop(handle)

   END SUBROUTINE compute_gradient

END MODULE almo_scf_optimizer

