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almo_scf_optimizer.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2021 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \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_lbfgs_types, ONLY: lbfgs_create,&
lbfgs_get_direction,&
lbfgs_history_type,&
lbfgs_release,&
lbfgs_seed
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_rescaling, &
almo_scf_t_to_proj, apply_domain_operators, apply_projector, &
construct_domain_preconditioner, construct_domain_r_down, construct_domain_s_inv, &
construct_domain_s_sqrt, fill_matrix_with_ones, get_overlap, orthogonalize_mos, &
pseudo_invert_diagonal_blk, xalmo_initial_guess
USE almo_scf_qs, ONLY: almo_dm_to_almo_ks,&
almo_dm_to_qs_env,&
almo_scf_update_ks_energy,&
matrix_qs_to_almo
USE almo_scf_types, ONLY: almo_scf_env_type,&
optimizer_options_type
USE cell_types, ONLY: cell_type
USE cp_blacs_env, ONLY: cp_blacs_env_type
USE cp_dbcsr_cholesky, ONLY: cp_dbcsr_cholesky_decompose,&
cp_dbcsr_cholesky_invert,&
cp_dbcsr_cholesky_restore
USE cp_external_control, ONLY: external_control
USE cp_files, ONLY: close_file,&
open_file
USE cp_log_handling, ONLY: cp_get_default_logger,&
cp_logger_get_default_unit_nr,&
cp_logger_type,&
cp_to_string
USE cp_output_handling, ONLY: cp_print_key_finished_output,&
cp_print_key_unit_nr
USE cp_para_types, ONLY: cp_para_env_type
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_dot, dbcsr_filter, dbcsr_finalize, &
dbcsr_frobenius_norm, dbcsr_func_dtanh, dbcsr_func_inverse, dbcsr_func_tanh, &
dbcsr_function_of_elements, dbcsr_get_block_p, 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_nblkcols_total, dbcsr_nblkrows_total, 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_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, &
op_loc_berry, op_loc_pipek, trustr_cauchy, trustr_dogleg, virt_full, &
xalmo_case_block_diag, xalmo_case_fully_deloc, xalmo_case_normal, xalmo_prec_domain, &
xalmo_prec_full, xalmo_prec_zero
USE input_section_types, ONLY: section_vals_get_subs_vals,&
section_vals_type
USE iterate_matrix, ONLY: determinant,&
invert_Hotelling,&
matrix_sqrt_Newton_Schulz
USE kinds, ONLY: dp
USE machine, ONLY: m_flush,&
m_walltime
USE message_passing, ONLY: mp_sum
USE particle_methods, ONLY: get_particle_set
USE particle_types, ONLY: particle_type
USE qs_energy_types, ONLY: qs_energy_type
USE qs_environment_types, ONLY: get_qs_env,&
qs_environment_type
USE qs_kind_types, ONLY: qs_kind_type
USE qs_loc_utils, ONLY: compute_berry_operator
USE qs_localization_methods, ONLY: initialize_weights
#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_trustr, &
almo_scf_xalmo_pcg, &
almo_scf_construct_nlmos
LOGICAL, PARAMETER :: debug_mode = .FALSE.
LOGICAL, PARAMETER :: safe_mode = .FALSE.
LOGICAL, PARAMETER :: almo_mathematica = .FALSE.
INTEGER, PARAMETER :: hessian_path_reuse = 1, &
hessian_path_assemble = 2
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]
!> 2018.09 smearing support [Ruben Staub]
!> \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), INTENT(INOUT) :: almo_scf_env
TYPE(optimizer_options_type), INTENT(IN) :: optimizer
CHARACTER(len=*), PARAMETER :: routineN = 'almo_scf_block_diagonal'
INTEGER :: handle, iscf, ispin, nspin, 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) :: density_rec, energy_diff, energy_new, energy_old, error_norm, &
error_norm_ispin, kTS_sum, 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_type), ALLOCATABLE, DIMENSION(:) :: matrix_mixing_old_blk
TYPE(qs_energy_type), POINTER :: qs_energy
CALL timeset(routineN, handle)
! get a useful output_unit
logger => cp_get_default_logger()
IF (logger%para_env%ionode) 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
CALL get_qs_env(qs_env, energy=qs_energy)
energy_old = qs_energy%total
iscf = 0
prepare_to_exit = .FALSE.
true_mixing_fraction = 0.0_dp
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
! 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.
IF (iscf == 1) energy_new = energy_old
ENDIF
! if early stopping is on do at least one iteration
IF (optimizer%early_stopping_on .AND. iscf .EQ. 1) &
prepare_to_exit = .FALSE.
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.)
DO ispin = 1, almo_scf_env%nspins
CALL orthogonalize_mos(ket=almo_scf_env%matrix_t_blk(ispin), &
overlap=almo_scf_env%matrix_sigma_blk(ispin), &
metric=almo_scf_env%matrix_s_blk(1), &
retain_locality=.TRUE., &
only_normalize=.FALSE., &
nocc_of_domain=almo_scf_env%nocc_of_domain(:, ispin), &
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)
ENDDO
END SELECT
! obtain density matrix from ALMOs
DO ispin = 1, almo_scf_env%nspins
!! Application of an occupation-rescaling trick for smearing, if requested
IF (almo_scf_env%smear) THEN
CALL almo_scf_t_rescaling(matrix_t=almo_scf_env%matrix_t_blk(ispin), &
mo_energies=almo_scf_env%mo_energies(:, ispin), &
mu_of_domain=almo_scf_env%mu_of_domain(:, ispin), &
real_ne_of_domain=almo_scf_env%real_ne_of_domain(:, ispin), &
spin_kTS=almo_scf_env%kTS(ispin), &
smear_e_temp=almo_scf_env%smear_e_temp, &
ndomains=almo_scf_env%ndomains, &
nocc_of_domain=almo_scf_env%nocc_of_domain(:, ispin))
END IF
CALL almo_scf_t_to_proj(t=almo_scf_env%matrix_t_blk(ispin), &
p=almo_scf_env%matrix_p(ispin), &
eps_filter=almo_scf_env%eps_filter, &
orthog_orbs=.FALSE., &
nocc_of_domain=almo_scf_env%nocc_of_domain(:, ispin), &
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_prev_as_guess, &
smear=almo_scf_env%smear, &
algorithm=almo_scf_env%sigma_inv_algorithm, &
inverse_accelerator=almo_scf_env%order_lanczos, &
inv_eps_factor=almo_scf_env%matrix_iter_eps_error_factor, &
eps_lanczos=almo_scf_env%eps_lanczos, &
max_iter_lanczos=almo_scf_env%max_iter_lanczos, &
para_env=almo_scf_env%para_env, &
blacs_env=almo_scf_env%blacs_env)
ENDDO
IF (almo_scf_env%nspins == 1) THEN
CALL dbcsr_scale(almo_scf_env%matrix_p(1), 2.0_dp)
!! Rescaling electronic entropy contribution by spin_factor
IF (almo_scf_env%smear) THEN
almo_scf_env%kTS(1) = almo_scf_env%kTS(1)*2.0_dp
END IF
ENDIF
IF (almo_scf_env%smear) THEN
kTS_sum = SUM(almo_scf_env%kTS)
ELSE
kTS_sum = 0.0_dp
ENDIF
! compute the new KS matrix and new energy
CALL almo_dm_to_almo_ks(qs_env, &
almo_scf_env%matrix_p, &
almo_scf_env%matrix_ks, &
energy_new, &
almo_scf_env%eps_filter, &
almo_scf_env%mat_distr_aos, &
smear=almo_scf_env%smear, &
kTS_sum=kTS_sum)
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
!! Print number of electrons recovered if smearing was requested
IF (almo_scf_env%smear) THEN
DO ispin = 1, nspin
CALL dbcsr_dot(almo_scf_env%matrix_p(ispin), almo_scf_env%matrix_s(1), density_rec)
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T2,A20,F23.10)') "Electrons recovered:", density_rec
END IF
END DO
END IF
IF (.NOT. converged .AND. (.NOT. optimizer%early_stopping_on)) 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]
!> 2018.09 smearing support [Ruben Staub]
!> \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), INTENT(INOUT) :: almo_scf_env
TYPE(optimizer_options_type), INTENT(IN) :: optimizer
CHARACTER(len=*), PARAMETER :: routineN = 'almo_scf_xalmo_eigensolver'
INTEGER :: handle, iscf, ispin, nspin, unit_nr
LOGICAL :: converged, prepare_to_exit, should_stop
REAL(KIND=dp) :: denergy_tot, density_rec, energy_diff, energy_new, energy_old, error_norm, &
error_norm_0, kTS_sum, 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_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%ionode) 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
! 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 early stopping is on do at least one iteration
IF (optimizer%early_stopping_on .AND. iscf .EQ. 1) &
prepare_to_exit = .FALSE.
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')
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
!! Application of an occupation-rescaling trick for smearing, if requested
IF (almo_scf_env%smear) THEN
CALL almo_scf_t_rescaling(matrix_t=almo_scf_env%matrix_t_blk(ispin), &
mo_energies=almo_scf_env%mo_energies(:, ispin), &
mu_of_domain=almo_scf_env%mu_of_domain(:, ispin), &
real_ne_of_domain=almo_scf_env%real_ne_of_domain(:, ispin), &
spin_kTS=almo_scf_env%kTS(ispin), &
smear_e_temp=almo_scf_env%smear_e_temp, &
ndomains=almo_scf_env%ndomains, &
nocc_of_domain=almo_scf_env%nocc_of_domain(:, ispin))
END IF
! update now
CALL almo_scf_t_to_proj( &
t=almo_scf_env%matrix_t(ispin), &
p=almo_scf_env%matrix_p(ispin), &
eps_filter=almo_scf_env%eps_filter, &
orthog_orbs=.FALSE., &
nocc_of_domain=almo_scf_env%nocc_of_domain(:, ispin), &
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., &
smear=almo_scf_env%smear, &
algorithm=almo_scf_env%sigma_inv_algorithm, &
inverse_accelerator=almo_scf_env%order_lanczos, &
inv_eps_factor=almo_scf_env%matrix_iter_eps_error_factor, &
eps_lanczos=almo_scf_env%eps_lanczos, &
max_iter_lanczos=almo_scf_env%max_iter_lanczos, &
para_env=almo_scf_env%para_env, &
blacs_env=almo_scf_env%blacs_env)
CALL dbcsr_scale(almo_scf_env%matrix_p(ispin), spin_factor)
!! Rescaling electronic entropy contribution by spin_factor
IF (almo_scf_env%smear) THEN
almo_scf_env%kTS(ispin) = almo_scf_env%kTS(ispin)*spin_factor
END IF
! 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_dot(almo_scf_env%matrix_ks_0deloc(ispin), &
matrix_p_almo_scf_converged, &
denergy_spin(ispin))
CALL dbcsr_release(matrix_p_almo_scf_converged)
!! RS-WARNING: If smearing ALMO is requested, electronic entropy contribution should probably be included here
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_dot(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
CALL energy_lowering_report( &
unit_nr=unit_nr, &
ref_energy=almo_scf_env%almo_scf_energy, &
energy_lowering=denergy_tot)
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
IF (almo_scf_env%smear) THEN
kTS_sum = SUM(almo_scf_env%kTS)
ELSE
kTS_sum = 0.0_dp
ENDIF
CALL almo_dm_to_almo_ks(qs_env, &
almo_scf_env%matrix_p, &
almo_scf_env%matrix_ks, &
energy_new, &
almo_scf_env%eps_filter, &
almo_scf_env%mat_distr_aos, &
smear=almo_scf_env%smear, &
kTS_sum=kTS_sum)
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
CALL almo_dm_to_qs_env(qs_env, almo_scf_env%matrix_p, almo_scf_env%mat_distr_aos)
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
!! Print number of electrons recovered if smearing was requested
IF (almo_scf_env%smear) THEN
DO ispin = 1, nspin
CALL dbcsr_dot(almo_scf_env%matrix_p(ispin), almo_scf_env%matrix_s(1), density_rec)
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(T2,A20,F23.10)') "Electrons recovered:", density_rec
END IF
END DO
END IF
IF (.NOT. converged .AND. .NOT. optimizer%early_stopping_on) 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 extremely 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), INTENT(INOUT) :: almo_scf_env
TYPE(optimizer_options_type), INTENT(IN) :: optimizer
TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:), &
INTENT(INOUT) :: 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'
CHARACTER(LEN=20) :: iter_type
INTEGER :: cg_iteration, dim_op, fixed_line_search_niter, handle, idim0, ielem, ispin, &
iteration, line_search_iteration, max_iter, my_special_case, ndomains, nmo, nspins, &
outer_iteration, outer_max_iter, para_group, prec_type, reim, unit_nr
INTEGER, ALLOCATABLE, DIMENSION(:) :: nocc
LOGICAL :: blissful_neglect, converged, just_started, line_search, normalize_orbitals, &
optimize_theta, outer_prepare_to_exit, penalty_occ_local, penalty_occ_vol, &
prepare_to_exit, reset_conjugator, skip_grad, use_guess
REAL(dp), ALLOCATABLE, DIMENSION(:) :: reim_diag, weights, z2
REAL(kind=dp) :: appr_sec_der, beta, denom, denom2, e0, e1, energy_coeff, energy_diff, &
energy_new, energy_old, eps_skip_gradients, fval, g0, g1, grad_norm, grad_norm_frob, &
line_search_error, localiz_coeff, localization_obj_function, next_step_size_guess, &
penalty_amplitude, penalty_func_new, spin_factor, step_size, t1, t2, tempreal
REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: grad_norm_spin, &
penalty_occ_vol_g_prefactor, &
penalty_occ_vol_h_prefactor
TYPE(cell_type), POINTER :: cell
TYPE(cp_logger_type), POINTER :: logger
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: qs_matrix_s
TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER :: op_sm_set_almo, op_sm_set_qs
TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:) :: FTsiginv, grad, m_sig_sqrti_ii, m_t_in_local, &
m_theta, prec_vv, prev_grad, prev_minus_prec_grad, prev_step, siginvTFTsiginv, ST, step, &
STsiginv_0, tempNOcc, tempNOcc_1, tempOccOcc
TYPE(domain_submatrix_type), ALLOCATABLE, &
DIMENSION(:, :) :: bad_modes_projector_down, domain_r_down
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%ionode) THEN
unit_nr = cp_logger_get_default_unit_nr(logger, local=.TRUE.)
ELSE
unit_nr = -1
ENDIF
nspins = almo_scf_env%nspins
! if unprojected XALMOs are optimized
! then we must use the "blissful_neglect" procedure
blissful_neglect = .FALSE.
IF (my_special_case .EQ. xalmo_case_normal .AND. .NOT. assume_t0_q0x) THEN
blissful_neglect = .TRUE.
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)
IF (blissful_neglect) THEN
WRITE (unit_nr, '(T2,A,A,A)') REPEAT("-", 25), &
" LCP optimization of XALMOs ", REPEAT("-", 26)
ELSE
WRITE (unit_nr, '(T2,A,A,A)') REPEAT("-", 27), &
" Optimization of XALMOs ", REPEAT("-", 28)
ENDIF
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
optimize_theta = almo_scf_env%logical05
eps_skip_gradients = almo_scf_env%real01
! penalty amplitude adjusts the strength of volume conservation
energy_coeff = 1.0_dp !optimizer%opt_penalty%energy_coeff
localiz_coeff = 0.0_dp !optimizer%opt_penalty%occ_loc_coeff
penalty_amplitude = 0.0_dp !optimizer%opt_penalty%occ_vol_coeff
penalty_occ_vol = .FALSE. !( optimizer%opt_penalty%occ_vol_method &
!.NE. penalty_type_none .AND. my_special_case .EQ. xalmo_case_fully_deloc )
penalty_occ_local = .FALSE. !( optimizer%opt_penalty%occ_loc_method &
!.NE. penalty_type_none .AND. my_special_case .EQ. xalmo_case_fully_deloc )
normalize_orbitals = penalty_occ_vol .OR. penalty_occ_local
ALLOCATE (penalty_occ_vol_g_prefactor(nspins))
ALLOCATE (penalty_occ_vol_h_prefactor(nspins))
penalty_occ_vol_g_prefactor(:) = 0.0_dp
penalty_occ_vol_h_prefactor(:) = 0.0_dp
penalty_func_new = 0.0_dp
! preconditioner control
prec_type = optimizer%preconditioner
! control of the line search
fixed_line_search_niter = 0 ! init to zero, change when eps is small enough
IF (nspins == 1) THEN
spin_factor = 2.0_dp
ELSE
spin_factor = 1.0_dp
ENDIF
ALLOCATE (grad_norm_spin(nspins))
ALLOCATE (nocc(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
! m_theta contains a set of variational parameters
! that define one-electron orbitals (simple, projected, etc.)