qs_fb_env_methods.F

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!--------------------------------------------------------------------------------------------------!
!   CP2K: A general program to perform molecular dynamics simulations                              !
!   Copyright 2000-2026 CP2K developers group <https://cp2k.org>                                   !
!                                                                                                  !
!   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
!--------------------------------------------------------------------------------------------------!
 
MODULE qs_fb_env_methods
 
   USE atomic_kind_types,               ONLY: atomic_kind_type,&
                                              get_atomic_kind
   USE basis_set_types,                 ONLY: get_gto_basis_set,&
                                              gto_basis_set_p_type,&
                                              gto_basis_set_type
   USE cell_types,                      ONLY: cell_type
   USE cp_blacs_env,                    ONLY: cp_blacs_env_type
   USE cp_control_types,                ONLY: dft_control_type
   USE cp_dbcsr_api,                    ONLY: &
        dbcsr_create, dbcsr_finalize, dbcsr_get_info, dbcsr_iterator_blocks_left, &
        dbcsr_iterator_next_block, dbcsr_iterator_readonly_start, dbcsr_iterator_stop, &
        dbcsr_iterator_type, dbcsr_multiply, dbcsr_p_type, dbcsr_release, dbcsr_reserve_blocks, &
        dbcsr_set, dbcsr_type, dbcsr_type_no_symmetry
   USE cp_dbcsr_operations,             ONLY: copy_dbcsr_to_fm,&
                                              dbcsr_allocate_matrix_set,&
                                              dbcsr_deallocate_matrix_set
   USE cp_fm_basic_linalg,              ONLY: cp_fm_gemm,&
                                              cp_fm_symm,&
                                              cp_fm_triangular_invert,&
                                              cp_fm_triangular_multiply,&
                                              cp_fm_uplo_to_full
   USE cp_fm_cholesky,                  ONLY: cp_fm_cholesky_decompose,&
                                              cp_fm_cholesky_reduce,&
                                              cp_fm_cholesky_restore
   USE cp_fm_diag,                      ONLY: choose_eigv_solver,&
                                              cp_fm_power
   USE cp_fm_struct,                    ONLY: cp_fm_struct_create,&
                                              cp_fm_struct_release,&
                                              cp_fm_struct_type
   USE cp_fm_types,                     ONLY: cp_fm_create,&
                                              cp_fm_release,&
                                              cp_fm_set_all,&
                                              cp_fm_to_fm,&
                                              cp_fm_type
   USE cp_log_handling,                 ONLY: cp_get_default_logger,&
                                              cp_logger_type
   USE cp_output_handling,              ONLY: cp_print_key_finished_output,&
                                              cp_print_key_unit_nr
   USE cp_units,                        ONLY: cp_unit_from_cp2k
   USE input_constants,                 ONLY: cholesky_dbcsr,&
                                              cholesky_inverse,&
                                              cholesky_off,&
                                              cholesky_reduce,&
                                              cholesky_restore
   USE input_section_types,             ONLY: section_vals_get_subs_vals,&
                                              section_vals_type,&
                                              section_vals_val_get
   USE kinds,                           ONLY: default_string_length,&
                                              dp
   USE message_passing,                 ONLY: mp_para_env_type
   USE orbital_pointers,                ONLY: nco,&
                                              ncoset
   USE parallel_gemm_api,               ONLY: parallel_gemm
   USE particle_types,                  ONLY: particle_type
   USE qs_density_matrices,             ONLY: calculate_density_matrix
   USE qs_diis,                         ONLY: qs_diis_b_step
   USE qs_environment_types,            ONLY: get_qs_env,&
                                              qs_environment_type
   USE qs_fb_atomic_halo_types,         ONLY: &
        fb_atomic_halo_build_halo_atoms, fb_atomic_halo_cost, fb_atomic_halo_create, &
        fb_atomic_halo_list_create, fb_atomic_halo_list_nullify, fb_atomic_halo_list_obj, &
        fb_atomic_halo_list_set, fb_atomic_halo_list_write_info, &
        fb_atomic_halo_nelectrons_estimate_z, fb_atomic_halo_nullify, fb_atomic_halo_obj, &
        fb_atomic_halo_set, fb_atomic_halo_sort, fb_build_pair_radii
   USE qs_fb_env_types,                 ONLY: fb_env_get,&
                                              fb_env_has_data,&
                                              fb_env_obj,&
                                              fb_env_set
   USE qs_fb_filter_matrix_methods,     ONLY: fb_fltrmat_build,&
                                              fb_fltrmat_build_2
   USE qs_fb_trial_fns_types,           ONLY: fb_trial_fns_create,&
                                              fb_trial_fns_nullify,&
                                              fb_trial_fns_obj,&
                                              fb_trial_fns_set
   USE qs_integral_utils,               ONLY: basis_set_list_setup
   USE qs_kind_types,                   ONLY: get_qs_kind,&
                                              qs_kind_type
   USE qs_mo_occupation,                ONLY: set_mo_occupation
   USE qs_mo_types,                     ONLY: allocate_mo_set,&
                                              deallocate_mo_set,&
                                              get_mo_set,&
                                              init_mo_set,&
                                              mo_set_type,&
                                              set_mo_set
   USE qs_scf_types,                    ONLY: qs_scf_env_type
   USE scf_control_types,               ONLY: scf_control_type
   USE string_utilities,                ONLY: compress,&
                                              uppercase
#include "./base/base_uses.f90"
 
   IMPLICIT NONE
 
   PRIVATE
 
   CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'qs_fb_env_methods'
 
   PUBLIC :: fb_env_do_diag, &
             fb_env_read_input, &
             fb_env_build_rcut_auto, &
             fb_env_build_atomic_halos, &
             fb_env_write_info
 
CONTAINS
 
! **************************************************************************************************
!> \brief Do filtered matrix method diagonalisation
!> \param fb_env : the filter matrix environment
!> \param qs_env : quickstep environment
!> \param matrix_ks : DBCSR system (unfiltered) input KS matrix
!> \param matrix_s  : DBCSR system (unfiltered) input overlap matrix
!> \param scf_section : SCF input section
!> \param diis_step : whether we are doing a DIIS step
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_env_do_diag(fb_env, &
                             qs_env, &
                             matrix_ks, &
                             matrix_s, &
                             scf_section, &
                             diis_step)
      TYPE(fb_env_obj), INTENT(INOUT)                    :: fb_env
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_ks, matrix_s
      TYPE(section_vals_type), POINTER                   :: scf_section
      LOGICAL, INTENT(INOUT)                             :: diis_step
 
      CHARACTER(LEN=*), PARAMETER                        :: routinen = 'fb_env_do_diag'
 
      CHARACTER(len=2)                                   :: spin_string
      CHARACTER(len=default_string_length)               :: name
      INTEGER :: filtered_nfullrowsorcols_total, handle, homo_filtered, ispin, lfomo_filtered, &
         my_nmo, nao, ndep, nelectron, nmo, nmo_filtered, nspin, original_nfullrowsorcols_total
      INTEGER, DIMENSION(:), POINTER                     :: filtered_roworcol_block_sizes, &
                                                            original_roworcol_block_sizes
      LOGICAL                                            :: collective_com
      REAL(kind=dp) :: diis_error, eps_default, eps_diis, eps_eigval, fermi_level, filter_temp, &
         flexible_electron_count, kts_filtered, maxocc, mu_filtered
      REAL(kind=dp), DIMENSION(:), POINTER               :: eigenvalues, eigenvalues_filtered, occ, &
                                                            occ_filtered
      TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
      TYPE(cp_fm_struct_type), POINTER                   :: filter_fm_struct, fm_struct
      TYPE(cp_fm_type)                                   :: fm_matrix_filter, fm_matrix_filtered_ks, &
                                                            fm_matrix_filtered_s, fm_matrix_ortho, &
                                                            fm_matrix_work
      TYPE(cp_fm_type), POINTER                          :: mo_coeff, mo_coeff_filtered
      TYPE(dbcsr_p_type), DIMENSION(:), POINTER          :: matrix_filter
      TYPE(dbcsr_type)                                   :: matrix_filtered_ks, matrix_filtered_s, &
                                                            matrix_tmp
      TYPE(dbcsr_type), POINTER                          :: matrix_filtered_p
      TYPE(fb_atomic_halo_list_obj)                      :: atomic_halos
      TYPE(fb_trial_fns_obj)                             :: trial_fns
      TYPE(mo_set_type), DIMENSION(:), POINTER           :: mos, mos_filtered
      TYPE(mp_para_env_type), POINTER                    :: para_env
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(qs_scf_env_type), POINTER                     :: scf_env
      TYPE(scf_control_type), POINTER                    :: scf_control
 
! TYPE(neighbor_list_set_p_type), DIMENSION(:), POINTER :: sab_orb
 
      CALL timeset(routinen, handle)
 
      NULLIFY (scf_env, scf_control, para_env, blacs_env, particle_set)
      NULLIFY (eigenvalues, eigenvalues_filtered, occ, occ_filtered)
      NULLIFY (mos, mos_filtered)
      NULLIFY (matrix_filter, matrix_filtered_p)
      NULLIFY (fm_struct, filter_fm_struct)
      NULLIFY (mo_coeff_filtered, mo_coeff)
      ! NULLIFY(sab_orb)
      CALL fb_atomic_halo_list_nullify(atomic_halos)
      CALL fb_trial_fns_nullify(trial_fns)
      NULLIFY (original_roworcol_block_sizes, filtered_roworcol_block_sizes)
 
      ! get qs_env information
      CALL get_qs_env(qs_env=qs_env, &
                      scf_env=scf_env, &
                      scf_control=scf_control, &
                      para_env=para_env, &
                      blacs_env=blacs_env, &
                      particle_set=particle_set, &
                      mos=mos)
 
      nspin = SIZE(matrix_ks)
 
      ! ----------------------------------------------------------------------
      ! DIIS step - based on non-filtered matrices and MOs
      ! ----------------------------------------------------------------------
 
      DO ispin = 1, nspin
         CALL copy_dbcsr_to_fm(matrix_ks(ispin)%matrix, &
                               scf_env%scf_work1(ispin))
      END DO
 
      eps_diis = scf_control%eps_diis
      eps_eigval = epsilon(0.0_dp)
 
      IF (scf_env%iter_count > 1 .AND. .NOT. scf_env%skip_diis) THEN
         CALL qs_diis_b_step(scf_env%scf_diis_buffer, mos, scf_env%scf_work1, &
                             scf_env%scf_work2, scf_env%iter_delta, &
                             diis_error, diis_step, eps_diis, scf_control%nmixing, &
                             s_matrix=matrix_s, scf_section=scf_section)
      ELSE
         diis_step = .false.
      END IF
 
      IF (diis_step) THEN
         scf_env%iter_param = diis_error
         scf_env%iter_method = "DIIS/Filter"
      ELSE
         IF (scf_env%mixing_method == 0) THEN
            scf_env%iter_method = "NoMix/Filter"
         ELSE IF (scf_env%mixing_method == 1) THEN
            scf_env%iter_param = scf_env%p_mix_alpha
            scf_env%iter_method = "P_Mix/Filter"
         ELSE IF (scf_env%mixing_method > 1) THEN
            scf_env%iter_param = scf_env%mixing_store%alpha
            scf_env%iter_method = trim(scf_env%mixing_store%iter_method)//"/Filter"
         END IF
      END IF
 
      ! ----------------------------------------------------------------------
      ! Construct Filter Matrix
      ! ----------------------------------------------------------------------
 
      CALL fb_env_get(fb_env=fb_env, &
                      filter_temperature=filter_temp, &
                      atomic_halos=atomic_halos, &
                      eps_default=eps_default)
 
      ! construct trial functions
      CALL get_mo_set(mo_set=mos(1), maxocc=maxocc)
      CALL fb_env_build_trial_fns_auto(fb_env, qs_env, maxocc)
      CALL fb_env_get(fb_env=fb_env, &
                      trial_fns=trial_fns)
 
      ! allocate filter matrix (matrix_filter(ispin)%matrix are
      ! nullified by dbcsr_allocate_matrix_set)
      CALL dbcsr_allocate_matrix_set(matrix_filter, nspin)
      DO ispin = 1, nspin
         ! get system-wide fermi energy and occupancy, we use this to
         ! define the filter function used for the filter matrix
         CALL get_mo_set(mo_set=mos(ispin), &
                         mu=fermi_level, &
                         maxocc=maxocc)
         ! get filter matrix name
         WRITE (spin_string, fmt="(I1)") ispin
         name = trim("FILTER MATRIX SPIN "//spin_string)
         CALL compress(name)
         CALL uppercase(name)
         ! calculate filter matrix (matrix_s(1) is the overlap, the rest
         ! in the array are its derivatives)
         CALL fb_env_get(fb_env=fb_env, &
                         collective_com=collective_com)
         IF (collective_com) THEN
            CALL fb_fltrmat_build_2(h_mat=matrix_ks(ispin)%matrix, &
                                    s_mat=matrix_s(1)%matrix, &
                                    atomic_halos=atomic_halos, &
                                    trial_fns=trial_fns, &
                                    para_env=para_env, &
                                    particle_set=particle_set, &
                                    fermi_level=fermi_level, &
                                    filter_temp=filter_temp, &
                                    name=name, &
                                    filter_mat=matrix_filter(ispin)%matrix, &
                                    tolerance=eps_default)
         ELSE
            CALL fb_fltrmat_build(h_mat=matrix_ks(ispin)%matrix, &
                                  s_mat=matrix_s(1)%matrix, &
                                  atomic_halos=atomic_halos, &
                                  trial_fns=trial_fns, &
                                  para_env=para_env, &
                                  particle_set=particle_set, &
                                  fermi_level=fermi_level, &
                                  filter_temp=filter_temp, &
                                  name=name, &
                                  filter_mat=matrix_filter(ispin)%matrix, &
                                  tolerance=eps_default)
         END IF
      END DO ! ispin
 
      ! ----------------------------------------------------------------------
      ! Do Filtered Diagonalisation
      ! ----------------------------------------------------------------------
 
      ! Obtain matrix dimensions. KS and S matrices are symmetric, so
      ! row_block_sizes and col_block_sizes should be identical. The
      ! same applies to the filtered block sizes. Note that filter
      ! matrix will have row_block_sizes equal to that of the original,
      ! and col_block_sizes equal to that of the filtered.  We assume
      ! also that the matrix dimensions are identical for both spin
      ! channels.
      CALL dbcsr_get_info(matrix_ks(1)%matrix, &
                          row_blk_size=original_roworcol_block_sizes, &
                          nfullrows_total=original_nfullrowsorcols_total)
      CALL dbcsr_get_info(matrix_filter(1)%matrix, &
                          col_blk_size=filtered_roworcol_block_sizes, &
                          nfullcols_total=filtered_nfullrowsorcols_total)
 
      ! filter diagonalisation works on a smaller basis set, and thus
      ! requires a new mo_set (molecular orbitals | eigenvectors) and
      ! the corresponding matrix pools for the eigenvector coefficients
      ALLOCATE (mos_filtered(nspin))
      DO ispin = 1, nspin
         CALL get_mo_set(mo_set=mos(ispin), &
                         maxocc=maxocc, &
                         nelectron=nelectron, &
                         flexible_electron_count=flexible_electron_count)
         CALL allocate_mo_set(mo_set=mos_filtered(ispin), &
                              nao=filtered_nfullrowsorcols_total, &
                              nmo=filtered_nfullrowsorcols_total, &
                              nelectron=nelectron, &
                              n_el_f=real(nelectron, dp), &
                              maxocc=maxocc, &
                              flexible_electron_count=flexible_electron_count)
      END DO ! ispin
 
      ! create DBCSR filtered KS matrix, this is reused for each spin
      ! channel
      ! both row_blk_size and col_blk_size should be that of
      ! col_blk_size of the filter matrix
      CALL dbcsr_create(matrix=matrix_filtered_ks, template=matrix_ks(1)%matrix, &
                        name=trim("FILTERED_KS_MATRIX"), &
                        matrix_type=dbcsr_type_no_symmetry, &
                        row_blk_size=filtered_roworcol_block_sizes, &
                        col_blk_size=filtered_roworcol_block_sizes)
      CALL dbcsr_finalize(matrix_filtered_ks)
 
      ! create DBCSR filtered S (overlap) matrix. Note that
      ! matrix_s(1)%matrix is the original overlap matrix---the rest in
      ! the array are derivatives, and it should not depend on
      ! spin. HOWEVER, since the filter matrix is constructed from KS
      ! matrix, and does depend on spin, the filtered S also becomes
      ! spin dependent. Nevertheless this matrix is reused for each spin
      ! channel
      ! both row_blk_size and col_blk_size should be that of
      ! col_blk_size of the filter matrix
      CALL dbcsr_create(matrix=matrix_filtered_s, template=matrix_s(1)%matrix, &
                        name=trim("FILTERED_S_MATRIX"), &
                        matrix_type=dbcsr_type_no_symmetry, &
                        row_blk_size=filtered_roworcol_block_sizes, &
                        col_blk_size=filtered_roworcol_block_sizes)
      CALL dbcsr_finalize(matrix_filtered_s)
 
      ! create temporary matrix for constructing filtered KS and S
      ! the temporary matrix won't be square
      CALL dbcsr_create(matrix=matrix_tmp, template=matrix_s(1)%matrix, &
                        name=trim("TEMPORARY_MATRIX"), &
                        matrix_type=dbcsr_type_no_symmetry, &
                        row_blk_size=original_roworcol_block_sizes, &
                        col_blk_size=filtered_roworcol_block_sizes)
      CALL dbcsr_finalize(matrix_tmp)
 
      ! create fm format matrices used for diagonalisation
      CALL cp_fm_struct_create(fmstruct=fm_struct, &
                               para_env=para_env, &
                               context=blacs_env, &
                               nrow_global=filtered_nfullrowsorcols_total, &
                               ncol_global=filtered_nfullrowsorcols_total)
      ! both fm_matrix_filtered_s and fm_matrix_filtered_ks are reused
      ! for each spin channel
      CALL cp_fm_create(fm_matrix_filtered_s, &
                        fm_struct, &
                        name="FM_MATRIX_FILTERED_S")
      CALL cp_fm_create(fm_matrix_filtered_ks, &
                        fm_struct, &
                        name="FM_MATRIX_FILTERED_KS")
      ! creaate work matrix
      CALL cp_fm_create(fm_matrix_work, fm_struct, name="FM_MATRIX_WORK")
      CALL cp_fm_create(fm_matrix_ortho, fm_struct, name="FM_MATRIX_ORTHO")
      ! all fm matrices are created, so can release fm_struct
      CALL cp_fm_struct_release(fm_struct)
 
      ! construct filtered KS, S matrix and diagonalise
      DO ispin = 1, nspin
 
         ! construct filtered KS matrix
         CALL dbcsr_multiply("N", "N", 1.0_dp, &
                             matrix_ks(ispin)%matrix, matrix_filter(ispin)%matrix, &
                             0.0_dp, matrix_tmp)
         CALL dbcsr_multiply("T", "N", 1.0_dp, &
                             matrix_filter(ispin)%matrix, matrix_tmp, &
                             0.0_dp, matrix_filtered_ks)
         ! construct filtered S_matrix
         CALL dbcsr_multiply("N", "N", 1.0_dp, &
                             matrix_s(1)%matrix, matrix_filter(ispin)%matrix, &
                             0.0_dp, matrix_tmp)
         CALL dbcsr_multiply("T", "N", 1.0_dp, &
                             matrix_filter(ispin)%matrix, matrix_tmp, &
                             0.0_dp, matrix_filtered_s)
 
         ! now that we have the filtered KS and S matrices for this spin
         ! channel, perform ordinary diagonalisation
 
         ! convert DBCSR matrices to fm format
         CALL copy_dbcsr_to_fm(matrix_filtered_s, fm_matrix_filtered_s)
         CALL copy_dbcsr_to_fm(matrix_filtered_ks, fm_matrix_filtered_ks)
 
         CALL get_mo_set(mos_filtered(ispin), nmo=nmo, nao=nao)
 
         CALL cp_fm_struct_create(fm_struct, nrow_global=nao, &
                                  ncol_global=nmo, para_env=para_env, &
                                  context=blacs_env)
 
         ! setup matrix pools for the molecular orbitals
         CALL init_mo_set(mos_filtered(ispin), &
                          fm_struct=fm_struct, &
                          name="FILTERED_MOS")
         CALL cp_fm_struct_release(fm_struct)
 
         ! now diagonalise
         CALL fb_env_eigensolver(fm_matrix_filtered_ks, &
                                 fm_matrix_filtered_s, &
                                 mos_filtered(ispin), &
                                 fm_matrix_ortho, &
                                 fm_matrix_work, &
                                 eps_eigval, &
                                 ndep, &
                                 scf_env%cholesky_method)
      END DO ! ispin
 
      ! release temporary matrices
      CALL dbcsr_release(matrix_filtered_s)
      CALL dbcsr_release(matrix_filtered_ks)
      CALL cp_fm_release(fm_matrix_filtered_s)
      CALL cp_fm_release(fm_matrix_filtered_ks)
      CALL cp_fm_release(fm_matrix_work)
      CALL cp_fm_release(fm_matrix_ortho)
 
      ! ----------------------------------------------------------------------
      ! Construct New Density Matrix
      ! ----------------------------------------------------------------------
 
      ! calculate filtered molecular orbital occupation numbers and fermi
      ! level etc
      CALL set_mo_occupation(mo_array=mos_filtered, &
                             smear=scf_control%smear)
 
      ! get the filtered density matrix and then convert back to the
      ! full basis version in scf_env ready to be used outside this
      ! subroutine
      ALLOCATE (matrix_filtered_p)
      ! the filtered density matrix should have the same sparse
      ! structure as the original density matrix, we must copy the
      ! sparse structure here, since construction of the density matrix
      ! preserves its sparse form, and therefore matrix_filtered_p must
      ! have its blocks allocated here now. We assume the original
      ! density matrix scf_env%p_mix_new has the same sparse structure
      ! in both spin channels.
      CALL dbcsr_create(matrix=matrix_filtered_p, template=scf_env%p_mix_new(1, 1)%matrix, &
                        name=trim("FILTERED_MATRIX_P"), &
                        row_blk_size=filtered_roworcol_block_sizes, &
                        col_blk_size=filtered_roworcol_block_sizes)
      CALL dbcsr_finalize(matrix_filtered_p)
      CALL fb_dbcsr_copy_sparse_struct(matrix_filtered_p, &
                                       scf_env%p_mix_new(1, 1)%matrix)
      ! old implementation, using sab_orb to allocate the blocks in matrix_filtered_p
      ! CALL get_qs_env(qs_env=qs_env, sab_orb=sab_orb)
      ! CALL cp_dbcsr_alloc_block_from_nbl(matrix_filtered_p, sab_orb)
      CALL dbcsr_set(matrix_filtered_p, 0.0_dp)
 
      DO ispin = 1, nspin
         ! calculate matrix_filtered_p
         CALL calculate_density_matrix(mos_filtered(ispin), &
                                       matrix_filtered_p)
         ! convert back to full basis p
         CALL dbcsr_multiply("N", "N", 1.0_dp, &
                             matrix_filter(ispin)%matrix, matrix_filtered_p, &
                             0.0_dp, matrix_tmp)
         CALL dbcsr_multiply("N", "T", 1.0_dp, &
                             matrix_tmp, matrix_filter(ispin)%matrix, &
                             0.0_dp, scf_env%p_mix_new(ispin, 1)%matrix, &
                             retain_sparsity=.true.)
         ! note that we want to retain the sparse structure of
         ! scf_env%p_mix_new
      END DO ! ispin
 
      ! release temporary matrices
      CALL dbcsr_release(matrix_tmp)
      CALL dbcsr_release(matrix_filtered_p)
      DEALLOCATE (matrix_filtered_p)
 
      ! ----------------------------------------------------------------------
      ! Update MOs
      ! ----------------------------------------------------------------------
 
      ! we still need to convert mos_filtered back to the full basis
      ! version (mos) for this, we need to update mo_coeff (and/or
      ! mo_coeff_b --- the DBCSR version, if used) of mos
 
      ! note also that mo_eigenvalues cannot be fully updated, given
      ! that the eigenvalues are computed in a smaller basis, and thus
      ! do not give the full spectron. Printing of molecular states
      ! (molecular DOS) at each SCF step is therefore not recommended
      ! when using this method. The idea is that if one wants a full
      ! molecular DOS, then one should perform a full diagonalisation
      ! without the filters once the SCF has been achieved.
 
      ! NOTE: from reading the source code, it appears that mo_coeff_b
      ! is actually never used by default (DOUBLE CHECK?!). Even
      ! subroutine eigensolver_dbcsr updates mo_coeff, and not
      ! mo_coeff_b.
 
      ! create FM format filter matrix
      CALL cp_fm_struct_create(fmstruct=filter_fm_struct, &
                               para_env=para_env, &
                               context=blacs_env, &
                               nrow_global=original_nfullrowsorcols_total, &
                               ncol_global=filtered_nfullrowsorcols_total)
      CALL cp_fm_create(fm_matrix_filter, &
                        filter_fm_struct, &
                        name="FM_MATRIX_FILTER")
      CALL cp_fm_struct_release(filter_fm_struct)
 
      DO ispin = 1, nspin
         ! now the full basis mo_set should only contain the reduced
         ! number of eigenvectors and eigenvalues
         CALL get_mo_set(mo_set=mos_filtered(ispin), &
                         homo=homo_filtered, &
                         lfomo=lfomo_filtered, &
                         nmo=nmo_filtered, &
                         eigenvalues=eigenvalues_filtered, &
                         occupation_numbers=occ_filtered, &
                         mo_coeff=mo_coeff_filtered, &
                         kts=kts_filtered, &
                         mu=mu_filtered)
         ! first set all the relevant scalars
         CALL set_mo_set(mo_set=mos(ispin), &
                         homo=homo_filtered, &
                         lfomo=lfomo_filtered, &
                         kts=kts_filtered, &
                         mu=mu_filtered)
         ! now set the arrays and fm_matrices
         CALL get_mo_set(mo_set=mos(ispin), &
                         nmo=nmo, &
                         occupation_numbers=occ, &
                         eigenvalues=eigenvalues, &
                         mo_coeff=mo_coeff)
         ! number of mos in original mo_set may sometimes be less than
         ! nmo_filtered, so we must make sure we do not go out of bounds
         my_nmo = min(nmo, nmo_filtered)
         eigenvalues(:) = 0.0_dp
         eigenvalues(1:my_nmo) = eigenvalues_filtered(1:my_nmo)
         occ(:) = 0.0_dp
         occ(1:my_nmo) = occ_filtered(1:my_nmo)
         ! convert mo_coeff_filtered back to original basis
         CALL cp_fm_set_all(matrix=mo_coeff, alpha=0.0_dp)
         CALL copy_dbcsr_to_fm(matrix_filter(ispin)%matrix, fm_matrix_filter)
         CALL cp_fm_gemm("N", "N", &
                         original_nfullrowsorcols_total, &
                         my_nmo, &
                         filtered_nfullrowsorcols_total, &
                         1.0_dp, fm_matrix_filter, mo_coeff_filtered, &
                         0.0_dp, mo_coeff)
 
      END DO ! ispin
 
      ! release temporary matrices
      CALL cp_fm_release(fm_matrix_filter)
 
      ! ----------------------------------------------------------------------
      ! Final Clean Up
      ! ----------------------------------------------------------------------
 
      DO ispin = 1, nspin
         CALL deallocate_mo_set(mo_set=mos_filtered(ispin))
      END DO
      DEALLOCATE (mos_filtered)
      CALL dbcsr_deallocate_matrix_set(matrix_filter)
 
      CALL timestop(handle)
 
   END SUBROUTINE fb_env_do_diag
 
! **************************************************************************************************
!> \brief The main parallel eigensolver engine for filter matrix diagonalisation
!> \param fm_KS : the BLACS distributed Kohn-Sham matrix, input only
!> \param fm_S  : the BLACS distributed overlap matrix, input only
!> \param mo_set : upon output contains the molecular orbitals (eigenvectors)
!>                 and eigenvalues
!> \param fm_ortho : one of the work matrices, on output, the BLACS distributed
!>                   matrix for orthogalising the eigen problem. E.g. if using
!>                   Cholesky inversse, then the upper triangle part contains
!>                   the inverse of Cholesky U; if not using Cholesky, then it
!>                   contains the S^-1/2.
!> \param fm_work : work matrix used by eigen solver
!> \param eps_eigval : used for quenching the small numbers when computing S^-1/2
!>                     any values less than eps_eigval is truncated to zero.
!> \param ndep : if the overlap is not positive definite, then ndep > 0,
!>               and equals to the number of linear dependent basis functions
!>               in the filtered basis set
!> \param method : method for solving generalised eigenvalue problem
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_env_eigensolver(fm_KS, fm_S, mo_set, fm_ortho, &
                                 fm_work, eps_eigval, ndep, method)
      TYPE(cp_fm_type), INTENT(IN)                       :: fm_ks, fm_s
      TYPE(mo_set_type), INTENT(IN)                      :: mo_set
      TYPE(cp_fm_type), INTENT(IN)                       :: fm_ortho, fm_work
      REAL(kind=dp), INTENT(IN)                          :: eps_eigval
      INTEGER, INTENT(OUT)                               :: ndep
      INTEGER, INTENT(IN)                                :: method
 
      CHARACTER(len=*), PARAMETER :: routinen = 'fb_env_eigensolver'
 
      CHARACTER(len=8)                                   :: ndep_string
      INTEGER                                            :: handle, info, my_method, nao, nmo
      REAL(kind=dp), DIMENSION(:), POINTER               :: mo_eigenvalues
      TYPE(cp_fm_type), POINTER                          :: mo_coeff
 
      CALL timeset(routinen, handle)
 
      CALL get_mo_set(mo_set=mo_set, &
                      nao=nao, &
                      nmo=nmo, &
                      eigenvalues=mo_eigenvalues, &
                      mo_coeff=mo_coeff)
      my_method = method
      ndep = 0
 
      ! first, obtain orthogonalisation (ortho) matrix
      IF (my_method /= cholesky_off) THEN
         CALL cp_fm_to_fm(fm_s, fm_ortho)
         CALL cp_fm_cholesky_decompose(fm_ortho, info_out=info)
         IF (info /= 0) THEN
            CALL cp_warn(__location__, &
                         "Unable to perform Cholesky decomposition on the overlap "// &
                         "matrix. The new filtered basis may not be linearly "// &
                         "independent set. Revert to using inverse square-root "// &
                         "of the overlap. To avoid this warning, you can try "// &
                         "to use a higher filter termperature.")
            my_method = cholesky_off
         ELSE
            SELECT CASE (my_method)
            CASE (cholesky_dbcsr)
               CALL cp_abort(__location__, &
                             "filter matrix method with CHOLESKY_DBCSR is not yet implemented")
            CASE (cholesky_reduce)
               CALL cp_fm_cholesky_reduce(fm_ks, fm_ortho)
               CALL choose_eigv_solver(fm_ks, fm_work, mo_eigenvalues)
               CALL cp_fm_cholesky_restore(fm_work, nmo, fm_ortho, mo_coeff, "SOLVE")
            CASE (cholesky_restore)
               CALL cp_fm_uplo_to_full(fm_ks, fm_work)
               CALL cp_fm_cholesky_restore(fm_ks, nao, fm_ortho, fm_work, "SOLVE", &
                                           pos="RIGHT")
               CALL cp_fm_cholesky_restore(fm_work, nao, fm_ortho, fm_ks, "SOLVE", &
                                           pos="LEFT", transa="T")
               CALL choose_eigv_solver(fm_ks, fm_work, mo_eigenvalues)
               CALL cp_fm_cholesky_restore(fm_work, nmo, fm_ortho, mo_coeff, "SOLVE")
            CASE (cholesky_inverse)
               CALL cp_fm_triangular_invert(fm_ortho)
               CALL cp_fm_uplo_to_full(fm_ks, fm_work)
               CALL cp_fm_triangular_multiply(fm_ortho, &
                                              fm_ks, &
                                              side="R", &
                                              transpose_tr=.false., &
                                              invert_tr=.false., &
                                              uplo_tr="U", &
                                              n_rows=nao, &
                                              n_cols=nao, &
                                              alpha=1.0_dp)
               CALL cp_fm_triangular_multiply(fm_ortho, &
                                              fm_ks, &
                                              side="L", &
                                              transpose_tr=.true., &
                                              invert_tr=.false., &
                                              uplo_tr="U", &
                                              n_rows=nao, &
                                              n_cols=nao, &
                                              alpha=1.0_dp)
               CALL choose_eigv_solver(fm_ks, fm_work, mo_eigenvalues)
               CALL cp_fm_triangular_multiply(fm_ortho, &
                                              fm_work, &
                                              side="L", &
                                              transpose_tr=.false., &
                                              invert_tr=.false., &
                                              uplo_tr="U", &
                                              n_rows=nao, &
                                              n_cols=nmo, &
                                              alpha=1.0_dp)
               CALL cp_fm_to_fm(fm_work, mo_coeff, nmo, 1, 1)
            END SELECT
         END IF
      END IF
      IF (my_method == cholesky_off) THEN
         ! calculating ortho as S^-1/2 using diagonalisation of S, and
         ! solve accordingly
         CALL cp_fm_to_fm(fm_s, fm_ortho)
         CALL cp_fm_power(fm_ortho, fm_work, -0.5_dp, &
                          eps_eigval, ndep)
         IF (ndep > 0) THEN
            WRITE (ndep_string, fmt="(I8)") ndep
            CALL cp_warn(__location__, &
                         "Number of linearly dependent filtered orbitals: "//ndep_string)
         END IF
         ! solve eigen equatoin using S^-1/2
         CALL cp_fm_symm("L", "U", nao, nao, 1.0_dp, fm_ks, fm_ortho, &
                         0.0_dp, fm_work)
         CALL parallel_gemm("T", "N", nao, nao, nao, 1.0_dp, fm_ortho, &
                            fm_work, 0.0_dp, fm_ks)
         CALL choose_eigv_solver(fm_ks, fm_work, mo_eigenvalues)
         CALL parallel_gemm("N", "N", nao, nmo, nao, 1.0_dp, fm_ortho, &
                            fm_work, 0.0_dp, mo_coeff)
      END IF
 
      CALL timestop(handle)
 
   END SUBROUTINE fb_env_eigensolver
 
! **************************************************************************************************
!> \brief Read input sections for filter matrix method
!> \param fb_env : the filter matrix environment
!> \param scf_section : SCF input section
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_env_read_input(fb_env, scf_section)
 
      TYPE(fb_env_obj), INTENT(INOUT)                    :: fb_env
      TYPE(section_vals_type), POINTER                   :: scf_section
 
      CHARACTER(len=*), PARAMETER                        :: routinen = 'fb_env_read_input'
 
      INTEGER                                            :: handle
      LOGICAL                                            :: l_val
      REAL(kind=dp)                                      :: r_val
      TYPE(section_vals_type), POINTER                   :: fb_section
 
      CALL timeset(routinen, handle)
 
      NULLIFY (fb_section)
      fb_section => section_vals_get_subs_vals(scf_section, &
                                               "DIAGONALIZATION%FILTER_MATRIX")
      ! filter_temperature
      CALL section_vals_val_get(fb_section, "FILTER_TEMPERATURE", &
                                r_val=r_val)
      CALL fb_env_set(fb_env=fb_env, &
                      filter_temperature=r_val)
      ! auto_cutoff_scale
      CALL section_vals_val_get(fb_section, "AUTO_CUTOFF_SCALE", &
                                r_val=r_val)
      CALL fb_env_set(fb_env=fb_env, &
                      auto_cutoff_scale=r_val)
      ! communication model
      CALL section_vals_val_get(fb_section, "COLLECTIVE_COMMUNICATION", &
                                l_val=l_val)
      CALL fb_env_set(fb_env=fb_env, &
                      collective_com=l_val)
      ! eps_default
      CALL section_vals_val_get(fb_section, "EPS_FB", &
                                r_val=r_val)
      CALL fb_env_set(fb_env=fb_env, &
                      eps_default=r_val)
 
      CALL timestop(handle)
 
   END SUBROUTINE fb_env_read_input
 
! **************************************************************************************************
!> \brief Automatically generate the cutoff radii of atoms used for
!>        constructing the atomic halos, based on basis set cutoff
!>        ranges for each kind
!> \param fb_env : the filter matrix environment
!> \param qs_env : quickstep environment
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_env_build_rcut_auto(fb_env, qs_env)
      TYPE(fb_env_obj), INTENT(INOUT)                    :: fb_env
      TYPE(qs_environment_type), POINTER                 :: qs_env
 
      CHARACTER(len=*), PARAMETER :: routinen = 'fb_env_build_rcut_auto'
 
      INTEGER                                            :: handle, ikind, nkinds
      REAL(kind=dp)                                      :: auto_cutoff_scale, kind_radius
      REAL(kind=dp), DIMENSION(:), POINTER               :: rcut
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(gto_basis_set_p_type), DIMENSION(:), POINTER  :: basis_set_list
      TYPE(gto_basis_set_type), POINTER                  :: basis_set
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
 
      CALL timeset(routinen, handle)
 
      NULLIFY (rcut, qs_kind_set, dft_control)
 
      CALL get_qs_env(qs_env=qs_env, &
                      qs_kind_set=qs_kind_set, &
                      dft_control=dft_control)
      CALL fb_env_get(fb_env=fb_env, &
                      auto_cutoff_scale=auto_cutoff_scale)
 
      nkinds = SIZE(qs_kind_set)
      ALLOCATE (rcut(nkinds))
 
      ! reading from the other parts of the code, it seemed that
      ! aux_fit_basis_set is only used when do_admm is TRUE. This can be
      ! seen from the calls to generate_qs_task_list subroutine in
      ! qs_create_task_list, found in qs_environment_methods.F:
      ! basis_type is only set as input parameter for do_admm
      ! calculations, and if not set, the task list is generated using
      ! the default basis_set="ORB".
      ALLOCATE (basis_set_list(nkinds))
      IF (dft_control%do_admm) THEN
         CALL basis_set_list_setup(basis_set_list, "AUX_FIT", qs_kind_set)
      ELSE
         CALL basis_set_list_setup(basis_set_list, "ORB", qs_kind_set)
      END IF
 
      DO ikind = 1, nkinds
         basis_set => basis_set_list(ikind)%gto_basis_set
         CALL get_gto_basis_set(gto_basis_set=basis_set, kind_radius=kind_radius)
         rcut(ikind) = kind_radius*auto_cutoff_scale
      END DO
 
      CALL fb_env_set(fb_env=fb_env, &
                      rcut=rcut)
 
      ! cleanup
      DEALLOCATE (basis_set_list)
 
      CALL timestop(handle)
 
   END SUBROUTINE fb_env_build_rcut_auto
 
! **************************************************************************************************
!> \brief Builds an fb_atomic_halo_list object using information
!>        from fb_env
!> \param fb_env the fb_env object
!> \param qs_env : quickstep environment (need this to access particle)
!>                 positions and their kinds as well as which particles
!>                 are local to this process
!> \param scf_section : SCF input section, for printing output
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_env_build_atomic_halos(fb_env, qs_env, scf_section)
      TYPE(fb_env_obj), INTENT(INOUT)                    :: fb_env
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(section_vals_type), POINTER                   :: scf_section
 
      CHARACTER(len=*), PARAMETER :: routinen = 'fb_env_build_atomic_halos'
 
      INTEGER :: handle, iatom, ihalo, max_natoms_local, natoms_global, natoms_local, nelectrons, &
         nhalo_atoms, nkinds_global, owner_id_in_halo
      INTEGER, DIMENSION(:), POINTER                     :: halo_atoms, local_atoms
      REAL(kind=dp)                                      :: cost
      REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :)        :: pair_radii
      REAL(kind=dp), DIMENSION(:), POINTER               :: rcut
      TYPE(cell_type), POINTER                           :: cell
      TYPE(fb_atomic_halo_list_obj)                      :: atomic_halos
      TYPE(fb_atomic_halo_obj), DIMENSION(:), POINTER    :: halos
      TYPE(mp_para_env_type), POINTER                    :: para_env
      TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
 
      CALL timeset(routinen, handle)
 
      cpassert(fb_env_has_data(fb_env))
 
      NULLIFY (cell, halos, halo_atoms, rcut, particle_set, para_env, &
               qs_kind_set, local_atoms)
      CALL fb_atomic_halo_list_nullify(atomic_halos)
 
      ! get relevant data from fb_env
      CALL fb_env_get(fb_env=fb_env, &
                      rcut=rcut, &
                      local_atoms=local_atoms, &
                      nlocal_atoms=natoms_local)
 
      ! create atomic_halos
      CALL fb_atomic_halo_list_create(atomic_halos)
 
      ! get the number of atoms and kinds:
      CALL get_qs_env(qs_env=qs_env, &
                      natom=natoms_global, &
                      particle_set=particle_set, &
                      qs_kind_set=qs_kind_set, &
                      nkind=nkinds_global, &
                      para_env=para_env, &
                      cell=cell)
 
      ! get the maximum number of local atoms across the procs.
      max_natoms_local = natoms_local
      CALL para_env%max(max_natoms_local)
 
      ! create the halos, one for each local atom
      ALLOCATE (halos(natoms_local))
      DO ihalo = 1, natoms_local
         CALL fb_atomic_halo_nullify(halos(ihalo))
         CALL fb_atomic_halo_create(halos(ihalo))
      END DO
      CALL fb_atomic_halo_list_set(atomic_halos=atomic_halos, &
                                   nhalos=natoms_local, &
                                   max_nhalos=max_natoms_local)
      ! build halos
      ALLOCATE (pair_radii(nkinds_global, nkinds_global))
      CALL fb_build_pair_radii(rcut, nkinds_global, pair_radii)
      ihalo = 0
      DO iatom = 1, natoms_local
         ihalo = ihalo + 1
         CALL fb_atomic_halo_build_halo_atoms(local_atoms(iatom), &
                                              particle_set, &
                                              cell, &
                                              pair_radii, &
                                              halo_atoms, &
                                              nhalo_atoms, &
                                              owner_id_in_halo)
         CALL fb_atomic_halo_set(atomic_halo=halos(ihalo), &
                                 owner_atom=local_atoms(iatom), &
                                 owner_id_in_halo=owner_id_in_halo, &
                                 natoms=nhalo_atoms, &
                                 halo_atoms=halo_atoms)
         ! prepare halo_atoms for another halo, do not deallocate, as
         ! original data is being pointed at by the atomic halo data
         ! structure
         NULLIFY (halo_atoms)
         ! calculate the number of electrons in each halo
         nelectrons = fb_atomic_halo_nelectrons_estimate_z(halos(ihalo), &
                                                           particle_set)
         ! calculate cost
         cost = fb_atomic_halo_cost(halos(ihalo), particle_set, qs_kind_set)
         CALL fb_atomic_halo_set(atomic_halo=halos(ihalo), &
                                 nelectrons=nelectrons, &
                                 cost=cost)
         ! sort atomic halo
         CALL fb_atomic_halo_sort(halos(ihalo))
      END DO ! iatom
      DEALLOCATE (pair_radii)
 
      ! finalise
      CALL fb_atomic_halo_list_set(atomic_halos=atomic_halos, &
                                   halos=halos)
      CALL fb_env_set(fb_env=fb_env, &
                      atomic_halos=atomic_halos)
 
      ! print info
      CALL fb_atomic_halo_list_write_info(atomic_halos, &
                                          para_env, &
                                          scf_section)
 
      CALL timestop(handle)
 
   END SUBROUTINE fb_env_build_atomic_halos
 
! **************************************************************************************************
!> \brief Automatically construct the trial functiosn used for generating
!>        the filter matrix. It tries to use the single zeta subset from
!>        the system GTO basis set as the trial functions
!> \param fb_env : the filter matrix environment
!> \param qs_env : quickstep environment
!> \param maxocc : maximum occupancy for an orbital
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_env_build_trial_fns_auto(fb_env, qs_env, maxocc)
 
      TYPE(fb_env_obj), INTENT(INOUT)                    :: fb_env
      TYPE(qs_environment_type), POINTER                 :: qs_env
      REAL(kind=dp), INTENT(IN)                          :: maxocc
 
      CHARACTER(len=*), PARAMETER :: routinen = 'fb_env_build_trial_fns_auto'
 
      INTEGER                                            :: counter, handle, icgf, ico, ikind, iset, &
                                                            ishell, itrial, lshell, max_n_trial, &
                                                            nkinds, nset, old_lshell
      INTEGER, DIMENSION(:), POINTER                     :: lmax, nfunctions, nshell
      INTEGER, DIMENSION(:, :), POINTER                  :: functions
      REAL(kind=dp)                                      :: zeff
      TYPE(dft_control_type), POINTER                    :: dft_control
      TYPE(fb_trial_fns_obj)                             :: trial_fns
      TYPE(gto_basis_set_p_type), DIMENSION(:), POINTER  :: basis_set_list
      TYPE(gto_basis_set_type), POINTER                  :: basis_set
      TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
 
      CALL timeset(routinen, handle)
 
      cpassert(fb_env_has_data(fb_env))
      NULLIFY (nfunctions, functions, basis_set, basis_set_list, qs_kind_set, dft_control)
      CALL fb_trial_fns_nullify(trial_fns)
 
      ! create a new trial_fn object
      CALL fb_trial_fns_create(trial_fns)
 
      CALL get_qs_env(qs_env=qs_env, &
                      qs_kind_set=qs_kind_set, &
                      dft_control=dft_control)
 
      nkinds = SIZE(qs_kind_set)
 
      ! reading from the other parts of the code, it seemed that
      ! aux_fit_basis_set is only used when do_admm is TRUE. This can be
      ! seen from the calls to generate_qs_task_list subroutine in
      ! qs_create_task_list, found in qs_environment_methods.F:
      ! basis_type is only set as input parameter for do_admm
      ! calculations, and if not set, the task list is generated using
      ! the default basis_set="ORB".
      ALLOCATE (basis_set_list(nkinds))
      IF (dft_control%do_admm) THEN
         CALL basis_set_list_setup(basis_set_list, "AUX_FIT", qs_kind_set)
      ELSE
         CALL basis_set_list_setup(basis_set_list, "ORB", qs_kind_set)
      END IF
 
      ALLOCATE (nfunctions(nkinds))
      nfunctions = 0
 
      DO ikind = 1, nkinds
         ! "gto = gaussian type orbital"
         basis_set => basis_set_list(ikind)%gto_basis_set
         CALL get_gto_basis_set(gto_basis_set=basis_set, &
                                nset=nset, &
                                lmax=lmax, &
                                nshell=nshell)
         CALL get_qs_kind(qs_kind=qs_kind_set(ikind), &
                          zeff=zeff)
 
         bset1: DO iset = 1, nset
!          old_lshell = lmax(iset)
            old_lshell = -1
            DO ishell = 1, nshell(iset)
               lshell = basis_set%l(ishell, iset)
               counter = 0
               ! loop over orbitals within the same l
               DO ico = ncoset(lshell - 1) + 1, ncoset(lshell)
                  counter = counter + 1
                  ! only include the first zeta orbitals
                  IF ((lshell > old_lshell) .AND. (counter <= nco(lshell))) THEN
                     nfunctions(ikind) = nfunctions(ikind) + 1
                  END IF
               END DO
               ! we have got enough trial functions when we have enough
               ! basis functions to accommodate the number of electrons,
               ! AND that that we have included all the first zeta
               ! orbitals of an angular momentum quantum number l
               IF (((lshell > old_lshell) .OR. (lshell == lmax(iset))) .AND. &
                   (maxocc*real(nfunctions(ikind), dp) >= zeff)) THEN
                  EXIT bset1
               END IF
               old_lshell = lshell
            END DO
         END DO bset1
      END DO ! ikind
 
      ! now that we have the number of trial functions get the trial
      ! functions
      max_n_trial = maxval(nfunctions)
      ALLOCATE (functions(max_n_trial, nkinds))
      functions(:, :) = 0
      ! redo the loops to get the trial function indices within the basis set
      DO ikind = 1, nkinds
         ! "gto = gaussian type orbital"
         basis_set => basis_set_list(ikind)%gto_basis_set
         CALL get_gto_basis_set(gto_basis_set=basis_set, &
                                nset=nset, &
                                lmax=lmax, &
                                nshell=nshell)
         CALL get_qs_kind(qs_kind=qs_kind_set(ikind), &
                          zeff=zeff)
         icgf = 0
         itrial = 0
         bset2: DO iset = 1, nset
            old_lshell = -1
            DO ishell = 1, nshell(iset)
               lshell = basis_set%l(ishell, iset)
               counter = 0
               ! loop over orbitals within the same l
               DO ico = ncoset(lshell - 1) + 1, ncoset(lshell)
                  icgf = icgf + 1
                  counter = counter + 1
                  ! only include the first zeta orbitals
                  IF ((lshell > old_lshell) .AND. (counter <= nco(lshell))) THEN
                     itrial = itrial + 1
                     functions(itrial, ikind) = icgf
                  END IF
               END DO
               ! we have got enough trial functions when we have more
               ! basis functions than the number of electrons (obtained
               ! from atomic z), AND that that we have included all the
               ! first zeta orbitals of an angular momentum quantum
               ! number l
               IF (((lshell > old_lshell) .OR. (lshell == lmax(iset))) .AND. &
                   (maxocc*real(itrial, dp) >= zeff)) THEN
                  EXIT bset2
               END IF
               old_lshell = lshell
            END DO
         END DO bset2
      END DO ! ikind
 
      ! set trial_functions
      CALL fb_trial_fns_set(trial_fns=trial_fns, &
                            nfunctions=nfunctions, &
                            functions=functions)
      ! set fb_env
      CALL fb_env_set(fb_env=fb_env, &
                      trial_fns=trial_fns)
 
      ! cleanup
      DEALLOCATE (basis_set_list)
 
      CALL timestop(handle)
 
   END SUBROUTINE fb_env_build_trial_fns_auto
 
! **************************************************************************************************
!> \brief Copy the sparse structure of a DBCSR matrix to another, this
!>        means the other matrix will have the same number of blocks
!>        and their corresponding logical locations allocated, although
!>        the blocks does not have to be the same size as the original
!> \param matrix_out : DBCSR matrix whose blocks are to be allocated
!> \param matrix_in  : DBCSR matrix with existing sparse structure that
!>                     is to be copied
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_dbcsr_copy_sparse_struct(matrix_out, matrix_in)
 
      TYPE(dbcsr_type), INTENT(INOUT)                    :: matrix_out
      TYPE(dbcsr_type), INTENT(IN)                       :: matrix_in
 
      INTEGER                                            :: iatom, jatom, nblkcols_total, &
                                                            nblkrows_total, nblks
      INTEGER, ALLOCATABLE, DIMENSION(:)                 :: cols, rows
      TYPE(dbcsr_iterator_type)                          :: iter
 
      CALL dbcsr_get_info(matrix=matrix_in, &
                          nblkrows_total=nblkrows_total, &
                          nblkcols_total=nblkcols_total)
 
      nblks = nblkrows_total*nblkcols_total
      ALLOCATE (rows(nblks))
      ALLOCATE (cols(nblks))
      rows(:) = 0
      cols(:) = 0
      nblks = 0
      CALL dbcsr_iterator_readonly_start(iter, matrix_in)
      DO WHILE (dbcsr_iterator_blocks_left(iter))
         CALL dbcsr_iterator_next_block(iter, iatom, jatom)
         nblks = nblks + 1
         rows(nblks) = iatom
         cols(nblks) = jatom
      END DO
      CALL dbcsr_iterator_stop(iter)
      CALL dbcsr_reserve_blocks(matrix_out, rows(1:nblks), cols(1:nblks))
      CALL dbcsr_finalize(matrix_out)
 
      ! cleanup
      DEALLOCATE (rows)
      DEALLOCATE (cols)
 
   END SUBROUTINE fb_dbcsr_copy_sparse_struct
 
! **************************************************************************************************
!> \brief Write out parameters used for the filter matrix method to
!>        output
!> \param fb_env : the filter matrix environment
!> \param qs_env : quickstep environment
!> \param scf_section : SCF input section
!> \author Lianheng Tong (LT) lianheng.tong@kcl.ac.uk
! **************************************************************************************************
   SUBROUTINE fb_env_write_info(fb_env, qs_env, scf_section)
      TYPE(fb_env_obj), INTENT(IN)                       :: fb_env
      TYPE(qs_environment_type), POINTER                 :: qs_env
      TYPE(section_vals_type), POINTER                   :: scf_section
 
      CHARACTER(len=*), PARAMETER                        :: routinen = 'fb_env_write_info'
 
      CHARACTER(LEN=2)                                   :: element_symbol
      INTEGER                                            :: handle, ikind, nkinds, unit_nr
      LOGICAL                                            :: collective_com
      REAL(kind=dp)                                      :: auto_cutoff_scale, filter_temperature
      REAL(kind=dp), DIMENSION(:), POINTER               :: rcut
      TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
      TYPE(cp_logger_type), POINTER                      :: logger
 
      CALL timeset(routinen, handle)
 
      NULLIFY (rcut, atomic_kind_set, logger)
 
      CALL get_qs_env(qs_env=qs_env, &
                      atomic_kind_set=atomic_kind_set)
      CALL fb_env_get(fb_env=fb_env, &
                      filter_temperature=filter_temperature, &
                      auto_cutoff_scale=auto_cutoff_scale, &
                      rcut=rcut, &
                      collective_com=collective_com)
 
      nkinds = SIZE(atomic_kind_set)
 
      logger => cp_get_default_logger()
      unit_nr = cp_print_key_unit_nr(logger, scf_section, &
                                     "PRINT%FILTER_MATRIX", &
                                     extension="")
      IF (unit_nr > 0) THEN
         IF (collective_com) THEN
            WRITE (unit=unit_nr, fmt="(/,A,T71,A)") &
               " FILTER_MAT_DIAG| MPI communication method:", &
               "Collective"
         ELSE
            WRITE (unit=unit_nr, fmt="(/,A,T71,A)") &
               " FILTER_MAT_DIAG| MPI communication method:", &
               "At each step"
         END IF
         WRITE (unit=unit_nr, fmt="(A,T71,g10.4)") &
            " FILTER_MAT_DIAG| Filter temperature [K]:", &
            cp_unit_from_cp2k(filter_temperature, "K")
         WRITE (unit=unit_nr, fmt="(A,T71,f10.4)") &
            " FILTER_MAT_DIAG| Filter temperature [a.u.]:", &
            filter_temperature
         WRITE (unit=unit_nr, fmt="(A,T71,f10.4)") &
            " FILTER_MAT_DIAG| Auto atomic cutoff radius scale:", &
            auto_cutoff_scale
         WRITE (unit=unit_nr, fmt="(A)") &
            " FILTER_MAT_DIAG| atomic cutoff radii [a.u.]"
         DO ikind = 1, nkinds
            CALL get_atomic_kind(atomic_kind=atomic_kind_set(ikind), &
                                 element_symbol=element_symbol)
            WRITE (unit=unit_nr, fmt="(A,A,T71,f10.4)") &
               " FILTER_MAT_DIAG|   ", element_symbol, rcut(ikind)
         END DO ! ikind
      END IF
      CALL cp_print_key_finished_output(unit_nr, logger, scf_section, &
                                        "PRINT%FILTER_MATRIX")
 
      CALL timestop(handle)
 
   END SUBROUTINE fb_env_write_info
 
END MODULE qs_fb_env_methods