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qs_gspace_mixing.F
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qs_gspace_mixing.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
MODULE qs_gspace_mixing
USE cp_control_types, ONLY: dft_control_type
USE kinds, ONLY: dp
USE mathlib, ONLY: invert_matrix
USE message_passing, ONLY: mp_para_env_type
USE pw_env_types, ONLY: pw_env_get,&
pw_env_type
USE pw_methods, ONLY: pw_axpy,&
pw_copy,&
pw_integrate_function,&
pw_scale,&
pw_transfer,&
pw_zero
USE pw_pool_types, ONLY: pw_pool_type
USE pw_types, ONLY: pw_c1d_gs_type,&
pw_r3d_rs_type
USE qs_density_mixing_types, ONLY: broyden_mixing_nr,&
gspace_mixing_nr,&
mixing_storage_type,&
multisecant_mixing_nr,&
pulay_mixing_nr
USE qs_environment_types, ONLY: get_qs_env,&
qs_environment_type
USE qs_rho_atom_types, ONLY: rho_atom_type
USE qs_rho_types, ONLY: qs_rho_get,&
qs_rho_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'qs_gspace_mixing'
PUBLIC :: gspace_mixing
CONTAINS
! **************************************************************************************************
!> \brief Driver for the g-space mixing, calls the proper routine given the
!>requested method
!> \param qs_env ...
!> \param mixing_method ...
!> \param mixing_store ...
!> \param rho ...
!> \param para_env ...
!> \param iter_count ...
!> \par History
!> 05.2009
!> 02.2015 changed input to make g-space mixing available in linear scaling
!> SCF [Patrick Seewald]
!> \author MI
! **************************************************************************************************
SUBROUTINE gspace_mixing(qs_env, mixing_method, mixing_store, rho, para_env, iter_count)
TYPE(qs_environment_type), POINTER :: qs_env
INTEGER :: mixing_method
TYPE(mixing_storage_type), POINTER :: mixing_store
TYPE(qs_rho_type), POINTER :: rho
TYPE(mp_para_env_type), POINTER :: para_env
INTEGER :: iter_count
CHARACTER(len=*), PARAMETER :: routineN = 'gspace_mixing'
INTEGER :: handle, iatom, ig, ispin, natom, ng, &
nimg, nspin
LOGICAL :: gapw
REAL(dp) :: alpha
REAL(KIND=dp), DIMENSION(:), POINTER :: tot_rho_r
TYPE(dft_control_type), POINTER :: dft_control
TYPE(pw_c1d_gs_type) :: rho_tmp
TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER :: rho_g
TYPE(pw_env_type), POINTER :: pw_env
TYPE(pw_pool_type), POINTER :: auxbas_pw_pool
TYPE(pw_r3d_rs_type), DIMENSION(:), POINTER :: rho_r
TYPE(rho_atom_type), DIMENSION(:), POINTER :: rho_atom
CALL timeset(routineN, handle)
CALL get_qs_env(qs_env, dft_control=dft_control, pw_env=pw_env)
IF (.NOT. (dft_control%qs_control%dftb .OR. dft_control%qs_control%xtb .OR. &
dft_control%qs_control%semi_empirical)) THEN
CPASSERT(ASSOCIATED(mixing_store))
NULLIFY (auxbas_pw_pool, rho_atom, rho_g, rho_r, tot_rho_r)
CALL qs_rho_get(rho, rho_g=rho_g, rho_r=rho_r, tot_rho_r=tot_rho_r)
nspin = SIZE(rho_g, 1)
nimg = dft_control%nimages
ng = SIZE(rho_g(1)%pw_grid%gsq)
CPASSERT(ng == SIZE(mixing_store%rhoin(1)%cc))
alpha = mixing_store%alpha
gapw = dft_control%qs_control%gapw
IF (nspin == 2) THEN
CALL pw_env_get(pw_env=pw_env, auxbas_pw_pool=auxbas_pw_pool)
CALL auxbas_pw_pool%create_pw(rho_tmp)
CALL pw_zero(rho_tmp)
CALL pw_copy(rho_g(1), rho_tmp)
CALL pw_axpy(rho_g(2), rho_g(1), 1.0_dp)
CALL pw_axpy(rho_tmp, rho_g(2), -1.0_dp)
CALL pw_scale(rho_g(2), -1.0_dp)
END IF
IF (iter_count + 1 <= mixing_store%nskip_mixing) THEN
! skip mixing
DO ispin = 1, nspin
DO ig = 1, ng
mixing_store%rhoin(ispin)%cc(ig) = rho_g(ispin)%array(ig)
END DO
END DO
IF (mixing_store%gmix_p .AND. gapw) THEN
CALL get_qs_env(qs_env=qs_env, rho_atom_set=rho_atom)
natom = SIZE(rho_atom)
DO ispin = 1, nspin
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
mixing_store%cpc_h_in(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef
mixing_store%cpc_s_in(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef
END IF
END DO
END DO
END IF
mixing_store%iter_method = "NoMix"
IF (nspin == 2) THEN
CALL pw_axpy(rho_g(2), rho_g(1), 1.0_dp)
CALL pw_scale(rho_g(1), 0.5_dp)
CALL pw_axpy(rho_g(1), rho_g(2), -1.0_dp)
CALL pw_scale(rho_g(2), -1.0_dp)
CALL auxbas_pw_pool%give_back_pw(rho_tmp)
END IF
CALL timestop(handle)
RETURN
END IF
IF ((iter_count + 1 - mixing_store%nskip_mixing) <= mixing_store%n_simple_mix) THEN
CALL gmix_potential_only(qs_env, mixing_store, rho)
mixing_store%iter_method = "Kerker"
ELSEIF (mixing_method == gspace_mixing_nr) THEN
CALL gmix_potential_only(qs_env, mixing_store, rho)
mixing_store%iter_method = "Kerker"
ELSEIF (mixing_method == pulay_mixing_nr) THEN
CALL pulay_mixing(qs_env, mixing_store, rho, para_env)
mixing_store%iter_method = "Pulay"
ELSEIF (mixing_method == broyden_mixing_nr) THEN
CALL broyden_mixing(qs_env, mixing_store, rho, para_env)
mixing_store%iter_method = "Broy."
ELSEIF (mixing_method == multisecant_mixing_nr) THEN
CPASSERT(.NOT. gapw)
CALL multisecant_mixing(mixing_store, rho, para_env)
mixing_store%iter_method = "MSec."
END IF
IF (nspin == 2) THEN
CALL pw_axpy(rho_g(2), rho_g(1), 1.0_dp)
CALL pw_scale(rho_g(1), 0.5_dp)
CALL pw_axpy(rho_g(1), rho_g(2), -1.0_dp)
CALL pw_scale(rho_g(2), -1.0_dp)
CALL auxbas_pw_pool%give_back_pw(rho_tmp)
END IF
DO ispin = 1, nspin
CALL pw_transfer(rho_g(ispin), rho_r(ispin))
tot_rho_r(ispin) = pw_integrate_function(rho_r(ispin), isign=-1)
END DO
END IF
CALL timestop(handle)
END SUBROUTINE gspace_mixing
! **************************************************************************************************
!> \brief G-space mixing performed via the Kerker damping on the density on the grid
!> thus affecting only the caluclation of the potential, but not the denisity matrix
!> \param qs_env ...
!> \param mixing_store ...
!> \param rho ...
!> \par History
!> 02.2009
!> \author MI
! **************************************************************************************************
SUBROUTINE gmix_potential_only(qs_env, mixing_store, rho)
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(mixing_storage_type), POINTER :: mixing_store
TYPE(qs_rho_type), POINTER :: rho
CHARACTER(len=*), PARAMETER :: routineN = 'gmix_potential_only'
COMPLEX(dp), DIMENSION(:), POINTER :: cc_new
INTEGER :: handle, iatom, ig, ispin, natom, ng, &
nspin
LOGICAL :: gapw
REAL(dp) :: alpha, f_mix
TYPE(dft_control_type), POINTER :: dft_control
TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER :: rho_g
TYPE(rho_atom_type), DIMENSION(:), POINTER :: rho_atom
CPASSERT(ASSOCIATED(mixing_store%rhoin))
CPASSERT(ASSOCIATED(mixing_store%kerker_factor))
CALL timeset(routineN, handle)
NULLIFY (cc_new, dft_control, rho_atom, rho_g)
CALL get_qs_env(qs_env, dft_control=dft_control)
CALL qs_rho_get(rho, rho_g=rho_g)
nspin = SIZE(rho_g, 1)
ng = SIZE(rho_g(1)%pw_grid%gsq)
gapw = dft_control%qs_control%gapw
alpha = mixing_store%alpha
DO ispin = 1, nspin
cc_new => rho_g(ispin)%array
DO ig = 1, mixing_store%ig_max ! ng
f_mix = mixing_store%alpha*mixing_store%kerker_factor(ig)
cc_new(ig) = (1.0_dp - f_mix)*mixing_store%rhoin(ispin)%cc(ig) + f_mix*cc_new(ig)
mixing_store%rhoin(ispin)%cc(ig) = cc_new(ig)
END DO
DO ig = mixing_store%ig_max + 1, ng
f_mix = mixing_store%alpha
cc_new(ig) = (1.0_dp - f_mix)*mixing_store%rhoin(ispin)%cc(ig) + f_mix*cc_new(ig)
mixing_store%rhoin(ispin)%cc(ig) = cc_new(ig)
END DO
END DO
IF (mixing_store%gmix_p .AND. gapw) THEN
CALL get_qs_env(qs_env=qs_env, &
rho_atom_set=rho_atom)
natom = SIZE(rho_atom)
DO ispin = 1, nspin
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
rho_atom(iatom)%cpc_h(ispin)%r_coef = alpha*rho_atom(iatom)%cpc_h(ispin)%r_coef + &
mixing_store%cpc_h_in(iatom, ispin)%r_coef*(1._dp - alpha)
rho_atom(iatom)%cpc_s(ispin)%r_coef = alpha*rho_atom(iatom)%cpc_s(ispin)%r_coef + &
mixing_store%cpc_s_in(iatom, ispin)%r_coef*(1._dp - alpha)
mixing_store%cpc_h_in(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef
mixing_store%cpc_s_in(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef
END IF
END DO
END DO
END IF
CALL timestop(handle)
END SUBROUTINE gmix_potential_only
! **************************************************************************************************
!> \brief Pulay Mixing using as metrics for the residual the Kerer damping factor
!> The mixing is applied directly on the density in reciprocal space,
!> therefore it affects the potentials
!> on the grid but not the density matrix
!> \param qs_env ...
!> \param mixing_store ...
!> \param rho ...
!> \param para_env ...
!> \par History
!> 03.2009
!> \author MI
! **************************************************************************************************
SUBROUTINE pulay_mixing(qs_env, mixing_store, rho, para_env)
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(mixing_storage_type), POINTER :: mixing_store
TYPE(qs_rho_type), POINTER :: rho
TYPE(mp_para_env_type), POINTER :: para_env
CHARACTER(len=*), PARAMETER :: routineN = 'pulay_mixing'
COMPLEX(dp), ALLOCATABLE, DIMENSION(:) :: cc_mix
INTEGER :: handle, i, iatom, ib, ibb, ig, ispin, &
jb, n1, n2, natom, nb, nb1, nbuffer, &
ng, nspin
LOGICAL :: gapw
REAL(dp) :: alpha_kerker, alpha_pulay, beta, f_mix, &
inv_err, norm, norm_c_inv, res_norm, &
vol
REAL(dp), ALLOCATABLE, DIMENSION(:) :: alpha_c, ev
REAL(dp), ALLOCATABLE, DIMENSION(:, :) :: a, b, c, c_inv, cpc_h_mix, cpc_s_mix
TYPE(dft_control_type), POINTER :: dft_control
TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER :: rho_g
TYPE(rho_atom_type), DIMENSION(:), POINTER :: rho_atom
CPASSERT(ASSOCIATED(mixing_store%res_buffer))
CPASSERT(ASSOCIATED(mixing_store%rhoin_buffer))
NULLIFY (dft_control, rho_atom, rho_g)
CALL timeset(routineN, handle)
CALL get_qs_env(qs_env, dft_control=dft_control)
CALL qs_rho_get(rho, rho_g=rho_g)
nspin = SIZE(rho_g, 1)
ng = SIZE(mixing_store%res_buffer(1, 1)%cc)
vol = rho_g(1)%pw_grid%vol
alpha_kerker = mixing_store%alpha
beta = mixing_store%pulay_beta
alpha_pulay = mixing_store%pulay_alpha
nbuffer = mixing_store%nbuffer
gapw = dft_control%qs_control%gapw
IF (gapw) THEN
CALL get_qs_env(qs_env=qs_env, rho_atom_set=rho_atom)
natom = SIZE(rho_atom)
END IF
ALLOCATE (cc_mix(ng))
IF (nspin == 2) THEN
CALL pw_axpy(rho_g(1), rho_g(2), 1.0_dp, -1.0_dp)
DO ig = 1, ng
mixing_store%rhoin(2)%cc(ig) = mixing_store%rhoin(1)%cc(ig) - mixing_store%rhoin(2)%cc(ig)
END DO
IF (gapw .AND. mixing_store%gmix_p) THEN
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
rho_atom(iatom)%cpc_h(2)%r_coef = rho_atom(iatom)%cpc_h(1)%r_coef - rho_atom(iatom)%cpc_h(2)%r_coef
rho_atom(iatom)%cpc_s(2)%r_coef = rho_atom(iatom)%cpc_s(1)%r_coef - rho_atom(iatom)%cpc_s(2)%r_coef
mixing_store%cpc_h_in(iatom, 2)%r_coef = mixing_store%cpc_h_in(iatom, 1)%r_coef - &
mixing_store%cpc_h_in(iatom, 2)%r_coef
mixing_store%cpc_s_in(iatom, 2)%r_coef = mixing_store%cpc_s_in(iatom, 1)%r_coef - &
mixing_store%cpc_s_in(iatom, 2)%r_coef
END IF
END DO
END IF
END IF
DO ispin = 1, nspin
ib = MODULO(mixing_store%ncall_p(ispin), nbuffer) + 1
mixing_store%ncall_p(ispin) = mixing_store%ncall_p(ispin) + 1
nb = MIN(mixing_store%ncall_p(ispin), nbuffer)
ibb = MODULO(mixing_store%ncall_p(ispin), nbuffer) + 1
mixing_store%res_buffer(ib, ispin)%cc(:) = CMPLX(0._dp, 0._dp, KIND=dp)
norm = 0.0_dp
IF (nb == 1) mixing_store%rhoin_buffer(1, ispin)%cc = mixing_store%rhoin(ispin)%cc
res_norm = 0.0_dp
DO ig = 1, ng
f_mix = mixing_store%kerker_factor(ig)
mixing_store%res_buffer(ib, ispin)%cc(ig) = f_mix*(rho_g(ispin)%array(ig) - &
mixing_store%rhoin_buffer(ib, ispin)%cc(ig))
res_norm = res_norm + &
REAL(mixing_store%res_buffer(ib, ispin)%cc(ig), dp)*REAL(mixing_store%res_buffer(ib, ispin)%cc(ig), dp) + &
AIMAG(mixing_store%res_buffer(ib, ispin)%cc(ig))*AIMAG(mixing_store%res_buffer(ib, ispin)%cc(ig))
END DO
CALL para_env%sum(res_norm)
res_norm = SQRT(res_norm)
IF (res_norm < 1.E-14_dp) THEN
mixing_store%ncall_p(ispin) = mixing_store%ncall_p(ispin) - 1
ELSE
nb1 = nb + 1
ALLOCATE (a(nb1, nb1))
a = 0.0_dp
ALLOCATE (b(nb1, nb1))
b = 0.0_dp
ALLOCATE (c(nb, nb))
c = 0.0_dp
ALLOCATE (c_inv(nb, nb))
c_inv = 0.0_dp
ALLOCATE (alpha_c(nb))
alpha_c = 0.0_dp
norm_c_inv = 0.0_dp
ALLOCATE (ev(nb1))
ev = 0.0_dp
END IF
DO jb = 1, nb
mixing_store%pulay_matrix(jb, ib, ispin) = 0.0_dp
DO ig = 1, ng
f_mix = mixing_store%special_metric(ig)
mixing_store%pulay_matrix(jb, ib, ispin) = mixing_store%pulay_matrix(jb, ib, ispin) + &
f_mix*(REAL(mixing_store%res_buffer(jb, ispin)%cc(ig), dp) &
*REAL(mixing_store%res_buffer(ib, ispin)%cc(ig), dp) + &
AIMAG(mixing_store%res_buffer(jb, ispin)%cc(ig))* &
AIMAG(mixing_store%res_buffer(ib, ispin)%cc(ig)))
END DO
CALL para_env%sum(mixing_store%pulay_matrix(jb, ib, ispin))
mixing_store%pulay_matrix(jb, ib, ispin) = mixing_store%pulay_matrix(jb, ib, ispin)*vol*vol
mixing_store%pulay_matrix(ib, jb, ispin) = mixing_store%pulay_matrix(jb, ib, ispin)
END DO
IF (nb == 1 .OR. res_norm < 1.E-14_dp) THEN
DO ig = 1, ng
f_mix = alpha_kerker*mixing_store%kerker_factor(ig)
cc_mix(ig) = rho_g(ispin)%array(ig) - &
mixing_store%rhoin_buffer(ib, ispin)%cc(ig)
rho_g(ispin)%array(ig) = f_mix*cc_mix(ig) + &
mixing_store%rhoin_buffer(ib, ispin)%cc(ig)
mixing_store%rhoin_buffer(ibb, ispin)%cc(ig) = rho_g(ispin)%array(ig)
END DO
IF (mixing_store%gmix_p) THEN
IF (gapw) THEN
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
mixing_store%cpc_h_res_buffer(ib, iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef - &
mixing_store%cpc_h_in(iatom, ispin)%r_coef
mixing_store%cpc_s_res_buffer(ib, iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef - &
mixing_store%cpc_s_in(iatom, ispin)%r_coef
rho_atom(iatom)%cpc_h(ispin)%r_coef = alpha_kerker*rho_atom(iatom)%cpc_h(ispin)%r_coef + &
(1.0_dp - alpha_kerker)*mixing_store%cpc_h_in(iatom, ispin)%r_coef
rho_atom(iatom)%cpc_s(ispin)%r_coef = alpha_kerker*rho_atom(iatom)%cpc_s(ispin)%r_coef + &
(1.0_dp - alpha_kerker)*mixing_store%cpc_s_in(iatom, ispin)%r_coef
mixing_store%cpc_h_in_buffer(ib, iatom, ispin)%r_coef = mixing_store%cpc_h_in(iatom, ispin)%r_coef
mixing_store%cpc_s_in_buffer(ib, iatom, ispin)%r_coef = mixing_store%cpc_s_in(iatom, ispin)%r_coef
mixing_store%cpc_h_in_buffer(ibb, iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef
mixing_store%cpc_s_in_buffer(ibb, iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef
END IF
END DO
END IF
END IF
ELSE
b(1:nb, 1:nb) = mixing_store%pulay_matrix(1:nb, 1:nb, ispin)
c(1:nb, 1:nb) = b(1:nb, 1:nb)
b(nb1, 1:nb) = -1.0_dp
b(1:nb, nb1) = -1.0_dp
b(nb1, nb1) = 0.0_dp
CALL invert_matrix(c, c_inv, inv_err, improve=.TRUE.)
alpha_c = 0.0_dp
DO i = 1, nb
DO jb = 1, nb
alpha_c(i) = alpha_c(i) + c_inv(jb, i)
norm_c_inv = norm_c_inv + c_inv(jb, i)
END DO
END DO
alpha_c(1:nb) = alpha_c(1:nb)/norm_c_inv
cc_mix = CMPLX(0._dp, 0._dp, KIND=dp)
DO jb = 1, nb
DO ig = 1, ng
cc_mix(ig) = cc_mix(ig) + &
alpha_c(jb)*(mixing_store%rhoin_buffer(jb, ispin)%cc(ig) + &
mixing_store%pulay_beta*mixing_store%res_buffer(jb, ispin)%cc(ig))
END DO
END DO
mixing_store%rhoin_buffer(ibb, ispin)%cc = CMPLX(0._dp, 0._dp, KIND=dp)
IF (alpha_pulay > 0.0_dp) THEN
DO ig = 1, ng
f_mix = alpha_pulay*mixing_store%kerker_factor(ig)
rho_g(ispin)%array(ig) = f_mix*rho_g(ispin)%array(ig) + &
(1.0_dp - f_mix)*cc_mix(ig)
mixing_store%rhoin_buffer(ibb, ispin)%cc(ig) = rho_g(ispin)%array(ig)
END DO
ELSE
DO ig = 1, ng
rho_g(ispin)%array(ig) = cc_mix(ig)
mixing_store%rhoin_buffer(ibb, ispin)%cc(ig) = rho_g(ispin)%array(ig)
END DO
END IF
IF (mixing_store%gmix_p .AND. gapw) THEN
CALL get_qs_env(qs_env=qs_env, rho_atom_set=rho_atom)
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
n1 = SIZE(rho_atom(iatom)%cpc_h(ispin)%r_coef, 1)
n2 = SIZE(rho_atom(iatom)%cpc_h(ispin)%r_coef, 2)
ALLOCATE (cpc_h_mix(n1, n2))
ALLOCATE (cpc_s_mix(n1, n2))
mixing_store%cpc_h_res_buffer(ib, iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef - &
mixing_store%cpc_h_in_buffer(ib, iatom, ispin)%r_coef
mixing_store%cpc_s_res_buffer(ib, iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef - &
mixing_store%cpc_s_in_buffer(ib, iatom, ispin)%r_coef
cpc_h_mix = 0.0_dp
cpc_s_mix = 0.0_dp
DO jb = 1, nb
cpc_h_mix(:, :) = cpc_h_mix(:, :) + &
alpha_c(jb)*mixing_store%cpc_h_in_buffer(jb, iatom, ispin)%r_coef(:, :) + &
alpha_c(jb)*beta*mixing_store%cpc_h_res_buffer(jb, iatom, ispin)%r_coef(:, :)
cpc_s_mix(:, :) = cpc_s_mix(:, :) + &
alpha_c(jb)*mixing_store%cpc_s_in_buffer(jb, iatom, ispin)%r_coef(:, :) + &
alpha_c(jb)*beta*mixing_store%cpc_s_res_buffer(jb, iatom, ispin)%r_coef(:, :)
END DO
rho_atom(iatom)%cpc_h(ispin)%r_coef = alpha_pulay*rho_atom(iatom)%cpc_h(ispin)%r_coef + &
(1.0_dp - alpha_pulay)*cpc_h_mix
rho_atom(iatom)%cpc_s(ispin)%r_coef = alpha_pulay*rho_atom(iatom)%cpc_s(ispin)%r_coef + &
(1.0_dp - alpha_pulay)*cpc_s_mix
mixing_store%cpc_h_in_buffer(ibb, iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef
mixing_store%cpc_s_in_buffer(ibb, iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef
DEALLOCATE (cpc_h_mix)
DEALLOCATE (cpc_s_mix)
END IF
END DO
END IF
END IF ! nb==1
IF (res_norm > 1.E-14_dp) THEN
DEALLOCATE (a)
DEALLOCATE (b)
DEALLOCATE (ev)
DEALLOCATE (c, c_inv, alpha_c)
END IF
END DO ! ispin
DEALLOCATE (cc_mix)
IF (nspin == 2) THEN
CALL pw_axpy(rho_g(1), rho_g(2), 1.0_dp, -1.0_dp)
DO ig = 1, ng
mixing_store%rhoin(2)%cc(ig) = mixing_store%rhoin(1)%cc(ig) - mixing_store%rhoin(2)%cc(ig)
END DO
IF (gapw .AND. mixing_store%gmix_p) THEN
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
rho_atom(iatom)%cpc_h(2)%r_coef = rho_atom(iatom)%cpc_h(1)%r_coef - rho_atom(iatom)%cpc_h(2)%r_coef
rho_atom(iatom)%cpc_s(2)%r_coef = rho_atom(iatom)%cpc_s(1)%r_coef - rho_atom(iatom)%cpc_s(2)%r_coef
mixing_store%cpc_h_in(iatom, 2)%r_coef = mixing_store%cpc_h_in(iatom, 1)%r_coef - &
mixing_store%cpc_h_in(iatom, 2)%r_coef
mixing_store%cpc_s_in(iatom, 2)%r_coef = mixing_store%cpc_s_in(iatom, 1)%r_coef - &
mixing_store%cpc_s_in(iatom, 2)%r_coef
END IF
END DO
END IF
END IF
CALL timestop(handle)
END SUBROUTINE pulay_mixing
! **************************************************************************************************
!> \brief Broyden Mixing using as metrics for the residual the Kerer damping factor
!> The mixing is applied directly on the density expansion in reciprocal space
!> \param qs_env ...
!> \param mixing_store ...
!> \param rho ...
!> \param para_env ...
!> \par History
!> 03.2009
!> \author MI
! **************************************************************************************************
SUBROUTINE broyden_mixing(qs_env, mixing_store, rho, para_env)
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(mixing_storage_type), POINTER :: mixing_store
TYPE(qs_rho_type), POINTER :: rho
TYPE(mp_para_env_type), POINTER :: para_env
CHARACTER(len=*), PARAMETER :: routineN = 'broyden_mixing'
COMPLEX(dp) :: cc_mix
COMPLEX(dp), ALLOCATABLE, DIMENSION(:) :: res_rho
INTEGER :: handle, i, iatom, ib, ig, ispin, j, jb, &
kb, n1, n2, natom, nb, nbuffer, ng, &
nspin
LOGICAL :: gapw, only_kerker
REAL(dp) :: alpha, dcpc_h_res, dcpc_s_res, &
delta_norm, f_mix, inv_err, res_norm, &
rho_norm, valh, vals, w0
REAL(dp), ALLOCATABLE, DIMENSION(:) :: c, g
REAL(dp), ALLOCATABLE, DIMENSION(:, :) :: a, b
TYPE(dft_control_type), POINTER :: dft_control
TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER :: rho_g
TYPE(rho_atom_type), DIMENSION(:), POINTER :: rho_atom
CPASSERT(ASSOCIATED(mixing_store%res_buffer))
CPASSERT(ASSOCIATED(mixing_store%rhoin))
CPASSERT(ASSOCIATED(mixing_store%rhoin_old))
CPASSERT(ASSOCIATED(mixing_store%drho_buffer))
NULLIFY (dft_control, rho_atom, rho_g)
CALL timeset(routineN, handle)
CALL get_qs_env(qs_env, dft_control=dft_control)
CALL qs_rho_get(rho, rho_g=rho_g)
nspin = SIZE(rho_g, 1)
ng = SIZE(mixing_store%res_buffer(1, 1)%cc)
alpha = mixing_store%alpha
w0 = mixing_store%broy_w0
nbuffer = mixing_store%nbuffer
gapw = dft_control%qs_control%gapw
ALLOCATE (res_rho(ng))
mixing_store%ncall = mixing_store%ncall + 1
IF (mixing_store%ncall == 1) THEN
only_kerker = .TRUE.
ELSE
only_kerker = .FALSE.
nb = MIN(mixing_store%ncall - 1, nbuffer)
ib = MODULO(mixing_store%ncall - 2, nbuffer) + 1
END IF
IF (gapw) THEN
CALL get_qs_env(qs_env=qs_env, rho_atom_set=rho_atom)
natom = SIZE(rho_atom)
ELSE
natom = 0
END IF
IF (nspin == 2) THEN
CALL pw_axpy(rho_g(1), rho_g(2), 1.0_dp, -1.0_dp)
DO ig = 1, ng
mixing_store%rhoin(2)%cc(ig) = mixing_store%rhoin(1)%cc(ig) - mixing_store%rhoin(2)%cc(ig)
END DO
IF (gapw .AND. mixing_store%gmix_p) THEN
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
rho_atom(iatom)%cpc_h(2)%r_coef = rho_atom(iatom)%cpc_h(1)%r_coef - rho_atom(iatom)%cpc_h(2)%r_coef
rho_atom(iatom)%cpc_s(2)%r_coef = rho_atom(iatom)%cpc_s(1)%r_coef - rho_atom(iatom)%cpc_s(2)%r_coef
mixing_store%cpc_h_in(iatom, 2)%r_coef = mixing_store%cpc_h_in(iatom, 1)%r_coef - &
mixing_store%cpc_h_in(iatom, 2)%r_coef
mixing_store%cpc_s_in(iatom, 2)%r_coef = mixing_store%cpc_s_in(iatom, 1)%r_coef - &
mixing_store%cpc_s_in(iatom, 2)%r_coef
END IF
END DO
END IF
END IF
DO ispin = 1, nspin
res_rho = CMPLX(0.0_dp, 0.0_dp, KIND=dp)
DO ig = 1, ng
res_rho(ig) = rho_g(ispin)%array(ig) - mixing_store%rhoin(ispin)%cc(ig)
END DO
IF (only_kerker) THEN
DO ig = 1, ng
mixing_store%last_res(ispin)%cc(ig) = res_rho(ig)
f_mix = alpha*mixing_store%kerker_factor(ig)
rho_g(ispin)%array(ig) = mixing_store%rhoin(ispin)%cc(ig) + f_mix*res_rho(ig)
mixing_store%rhoin_old(ispin)%cc(ig) = mixing_store%rhoin(ispin)%cc(ig)
mixing_store%rhoin(ispin)%cc(ig) = rho_g(ispin)%array(ig)
END DO
IF (mixing_store%gmix_p) THEN
IF (gapw) THEN
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
mixing_store%cpc_h_lastres(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef - &
mixing_store%cpc_h_in(iatom, ispin)%r_coef
mixing_store%cpc_s_lastres(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef - &
mixing_store%cpc_s_in(iatom, ispin)%r_coef
rho_atom(iatom)%cpc_h(ispin)%r_coef = alpha*rho_atom(iatom)%cpc_h(ispin)%r_coef + &
mixing_store%cpc_h_in(iatom, ispin)%r_coef*(1._dp - alpha)
rho_atom(iatom)%cpc_s(ispin)%r_coef = alpha*rho_atom(iatom)%cpc_s(ispin)%r_coef + &
mixing_store%cpc_s_in(iatom, ispin)%r_coef*(1._dp - alpha)
mixing_store%cpc_h_old(iatom, ispin)%r_coef = mixing_store%cpc_h_in(iatom, ispin)%r_coef
mixing_store%cpc_s_old(iatom, ispin)%r_coef = mixing_store%cpc_s_in(iatom, ispin)%r_coef
mixing_store%cpc_h_in(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef
mixing_store%cpc_s_in(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef
END IF
END DO
END IF
END IF
ELSE
ALLOCATE (a(nb, nb))
a = 0.0_dp
ALLOCATE (b(nb, nb))
b = 0.0_dp
ALLOCATE (c(nb))
c = 0.0_dp
ALLOCATE (g(nb))
g = 0.0_dp
delta_norm = 0.0_dp
res_norm = 0.0_dp
rho_norm = 0.0_dp
DO ig = 1, ng
mixing_store%res_buffer(ib, ispin)%cc(ig) = res_rho(ig) - mixing_store%last_res(ispin)%cc(ig)
mixing_store%last_res(ispin)%cc(ig) = res_rho(ig)
res_norm = res_norm + &
REAL(res_rho(ig), dp)*REAL(res_rho(ig), dp) + &
AIMAG(res_rho(ig))*AIMAG(res_rho(ig))
delta_norm = delta_norm + &
REAL(mixing_store%res_buffer(ib, ispin)%cc(ig), dp)* &
REAL(mixing_store%res_buffer(ib, ispin)%cc(ig), dp) + &
AIMAG(mixing_store%res_buffer(ib, ispin)%cc(ig))* &
AIMAG(mixing_store%res_buffer(ib, ispin)%cc(ig))
rho_norm = rho_norm + &
REAL(rho_g(ispin)%array(ig), dp)*REAL(rho_g(ispin)%array(ig), dp) + &
AIMAG(rho_g(ispin)%array(ig))*AIMAG(rho_g(ispin)%array(ig))
END DO
DO ig = 1, ng
mixing_store%drho_buffer(ib, ispin)%cc(ig) = &
mixing_store%rhoin(ispin)%cc(ig) - &
mixing_store%rhoin_old(ispin)%cc(ig)
END DO
CALL para_env%sum(delta_norm)
delta_norm = SQRT(delta_norm)
CALL para_env%sum(res_norm)
res_norm = SQRT(res_norm)
CALL para_env%sum(rho_norm)
rho_norm = SQRT(rho_norm)
IF (res_norm > 1.E-14_dp) THEN
mixing_store%res_buffer(ib, ispin)%cc(:) = mixing_store%res_buffer(ib, ispin)%cc(:)/delta_norm
mixing_store%drho_buffer(ib, ispin)%cc(:) = mixing_store%drho_buffer(ib, ispin)%cc(:)/delta_norm
IF (mixing_store%gmix_p .AND. gapw) THEN
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
n1 = SIZE(mixing_store%cpc_s_in(iatom, ispin)%r_coef, 1)
n2 = SIZE(mixing_store%cpc_s_in(iatom, ispin)%r_coef, 2)
DO i = 1, n2
DO j = 1, n1
mixing_store%dcpc_h_in(ib, iatom, ispin)%r_coef(j, i) = &
(mixing_store%cpc_h_in(iatom, ispin)%r_coef(j, i) - &
mixing_store%cpc_h_old(iatom, ispin)%r_coef(j, i))/delta_norm
dcpc_h_res = ((rho_atom(iatom)%cpc_h(ispin)%r_coef(j, i) - &
mixing_store%cpc_h_in(iatom, ispin)%r_coef(j, i)) - &
mixing_store%cpc_h_lastres(iatom, ispin)%r_coef(j, i))/delta_norm
mixing_store%cpc_h_lastres(iatom, ispin)%r_coef(j, i) = rho_atom(iatom)%cpc_h(ispin)%r_coef(j, i) - &
mixing_store%cpc_h_in(iatom, ispin)%r_coef(j, i)
mixing_store%dcpc_s_in(ib, iatom, ispin)%r_coef(j, i) = &
(mixing_store%cpc_s_in(iatom, ispin)%r_coef(j, i) - &
mixing_store%cpc_s_old(iatom, ispin)%r_coef(j, i))/delta_norm
dcpc_s_res = ((rho_atom(iatom)%cpc_s(ispin)%r_coef(j, i) - &
mixing_store%cpc_s_in(iatom, ispin)%r_coef(j, i)) - &
mixing_store%cpc_s_lastres(iatom, ispin)%r_coef(j, i))/delta_norm
mixing_store%cpc_s_lastres(iatom, ispin)%r_coef(j, i) = rho_atom(iatom)%cpc_s(ispin)%r_coef(j, i) - &
mixing_store%cpc_s_in(iatom, ispin)%r_coef(j, i)
mixing_store%dcpc_h_in(ib, iatom, ispin)%r_coef(j, i) = &
alpha*dcpc_h_res + &
mixing_store%dcpc_h_in(ib, iatom, ispin)%r_coef(j, i)
mixing_store%dcpc_s_in(ib, iatom, ispin)%r_coef(j, i) = &
alpha*dcpc_s_res + &
mixing_store%dcpc_s_in(ib, iatom, ispin)%r_coef(j, i)
END DO
END DO
END IF
END DO
END IF
a(:, :) = 0.0_dp
DO ig = 1, ng
f_mix = alpha*mixing_store%kerker_factor(ig)
mixing_store%drho_buffer(ib, ispin)%cc(ig) = &
f_mix*mixing_store%res_buffer(ib, ispin)%cc(ig) + &
mixing_store%drho_buffer(ib, ispin)%cc(ig)
END DO
DO jb = 1, nb
DO kb = jb, nb
DO ig = 1, mixing_store%ig_max !ng
a(kb, jb) = a(kb, jb) + mixing_store%p_metric(ig)*( &
REAL(mixing_store%res_buffer(jb, ispin)%cc(ig), dp)* &
REAL(mixing_store%res_buffer(kb, ispin)%cc(ig), dp) + &
AIMAG(mixing_store%res_buffer(jb, ispin)%cc(ig))* &
AIMAG(mixing_store%res_buffer(kb, ispin)%cc(ig)))
END DO
a(jb, kb) = a(kb, jb)
END DO
END DO
CALL para_env%sum(a)
C = 0.0_dp
DO jb = 1, nb
a(jb, jb) = w0 + a(jb, jb)
DO ig = 1, mixing_store%ig_max !ng
c(jb) = c(jb) + mixing_store%p_metric(ig)*( &
REAL(mixing_store%res_buffer(jb, ispin)%cc(ig), dp)*REAL(res_rho(ig), dp) + &
AIMAG(mixing_store%res_buffer(jb, ispin)%cc(ig))*AIMAG(res_rho(ig)))
END DO
END DO
CALL para_env%sum(c)
CALL invert_matrix(a, b, inv_err)
CALL dgemv('T', nb, nb, 1.0_dp, B, nb, C, 1, 0.0_dp, G, 1)
ELSE
G = 0.0_dp
END IF
DO ig = 1, ng
cc_mix = CMPLX(0.0_dp, 0.0_dp, kind=dp)
DO jb = 1, nb
cc_mix = cc_mix - G(jb)*mixing_store%drho_buffer(jb, ispin)%cc(ig)
END DO
f_mix = alpha*mixing_store%kerker_factor(ig)
IF (res_norm > 1.E-14_dp) rho_g(ispin)%array(ig) = mixing_store%rhoin(ispin)%cc(ig) + &
f_mix*res_rho(ig) + cc_mix
mixing_store%rhoin_old(ispin)%cc(ig) = mixing_store%rhoin(ispin)%cc(ig)
mixing_store%rhoin(ispin)%cc(ig) = rho_g(ispin)%array(ig)
END DO
IF (mixing_store%gmix_p) THEN
IF (gapw) THEN
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
n1 = SIZE(mixing_store%cpc_s_in(iatom, ispin)%r_coef, 1)
n2 = SIZE(mixing_store%cpc_s_in(iatom, ispin)%r_coef, 2)
DO i = 1, n2
DO j = 1, n1
valh = 0.0_dp
vals = 0.0_dp
DO jb = 1, nb
valh = valh - G(jb)*mixing_store%dcpc_h_in(jb, iatom, ispin)%r_coef(j, i)
vals = vals - G(jb)*mixing_store%dcpc_s_in(jb, iatom, ispin)%r_coef(j, i)
END DO
IF (res_norm > 1.E-14_dp) THEN
rho_atom(iatom)%cpc_h(ispin)%r_coef(j, i) = &
alpha*rho_atom(iatom)%cpc_h(ispin)%r_coef(j, i) + &
mixing_store%cpc_h_in(iatom, ispin)%r_coef(j, i)*(1._dp - alpha) + valh
rho_atom(iatom)%cpc_s(ispin)%r_coef(j, i) = &
alpha*rho_atom(iatom)%cpc_s(ispin)%r_coef(j, i) + &
mixing_store%cpc_s_in(iatom, ispin)%r_coef(j, i)*(1._dp - alpha) + vals
END IF
END DO
END DO
mixing_store%cpc_h_old(iatom, ispin)%r_coef = mixing_store%cpc_h_in(iatom, ispin)%r_coef
mixing_store%cpc_s_old(iatom, ispin)%r_coef = mixing_store%cpc_s_in(iatom, ispin)%r_coef
mixing_store%cpc_h_in(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_h(ispin)%r_coef
mixing_store%cpc_s_in(iatom, ispin)%r_coef = rho_atom(iatom)%cpc_s(ispin)%r_coef
END IF
END DO
END IF
END IF
DEALLOCATE (a, b, c, g)
END IF
END DO ! ispin
IF (nspin == 2) THEN
CALL pw_axpy(rho_g(1), rho_g(2), 1.0_dp, -1.0_dp)
DO ig = 1, ng
mixing_store%rhoin(2)%cc(ig) = mixing_store%rhoin(1)%cc(ig) - mixing_store%rhoin(2)%cc(ig)
END DO
IF (gapw .AND. mixing_store%gmix_p) THEN
DO iatom = 1, natom
IF (mixing_store%paw(iatom)) THEN
rho_atom(iatom)%cpc_h(2)%r_coef = rho_atom(iatom)%cpc_h(1)%r_coef - rho_atom(iatom)%cpc_h(2)%r_coef
rho_atom(iatom)%cpc_s(2)%r_coef = rho_atom(iatom)%cpc_s(1)%r_coef - rho_atom(iatom)%cpc_s(2)%r_coef
mixing_store%cpc_h_in(iatom, 2)%r_coef = mixing_store%cpc_h_in(iatom, 1)%r_coef - &
mixing_store%cpc_h_in(iatom, 2)%r_coef
mixing_store%cpc_s_in(iatom, 2)%r_coef = mixing_store%cpc_s_in(iatom, 1)%r_coef - &
mixing_store%cpc_s_in(iatom, 2)%r_coef
END IF
END DO
END IF
END IF
DEALLOCATE (res_rho)
CALL timestop(handle)
END SUBROUTINE broyden_mixing
! **************************************************************************************************
!> \brief Multisecant scheme to perform charge density Mixing
!> as preconditioner we use the Kerker damping factor
!> The mixing is applied directly on the density in reciprocal space,
!> therefore it affects the potentials
!> on the grid but not the density matrix
!> \param mixing_store ...
!> \param rho ...
!> \param para_env ...
!> \par History
!> 05.2009
!> \author MI
! **************************************************************************************************
SUBROUTINE multisecant_mixing(mixing_store, rho, para_env)
TYPE(mixing_storage_type), POINTER :: mixing_store
TYPE(qs_rho_type), POINTER :: rho
TYPE(mp_para_env_type), POINTER :: para_env
CHARACTER(len=*), PARAMETER :: routineN = 'multisecant_mixing'
COMPLEX(KIND=dp), PARAMETER :: cmone = (-1.0_dp, 0.0_dp), &
cone = (1.0_dp, 0.0_dp), &
czero = (0.0_dp, 0.0_dp)
COMPLEX(dp) :: saa, yaa
COMPLEX(dp), ALLOCATABLE, DIMENSION(:) :: gn_global, pgn, res_matrix_global, &
tmp_vec, ugn
COMPLEX(dp), ALLOCATABLE, DIMENSION(:, :) :: a_matrix, res_matrix, sa, step_matrix, ya
COMPLEX(dp), DIMENSION(:), POINTER :: gn
INTEGER :: handle, ib, ib_next, ib_prev, ig, &
ig_global, iig, ispin, jb, kb, nb, &
nbuffer, ng, ng_global, nspin
LOGICAL :: use_zgemm, use_zgemm_rev
REAL(dp) :: alpha, f_mix, gn_norm, gn_norm_old, inv_err, n_low, n_up, pgn_norm, prec, &
r_step, reg_par, sigma_max, sigma_tilde, step_size
REAL(dp), ALLOCATABLE, DIMENSION(:) :: norm_res, norm_res_low, norm_res_up
REAL(dp), ALLOCATABLE, DIMENSION(:, :) :: b_matrix, binv_matrix
REAL(dp), DIMENSION(:), POINTER :: g2
REAL(dp), SAVE :: sigma_old = 1.0_dp
TYPE(pw_c1d_gs_type), DIMENSION(:), POINTER :: rho_g
CPASSERT(ASSOCIATED(mixing_store))
CALL timeset(routineN, handle)
NULLIFY (gn, rho_g)
use_zgemm = .FALSE.
use_zgemm_rev = .TRUE.
! prepare the parameters
CALL qs_rho_get(rho, rho_g=rho_g)
nspin = SIZE(rho_g, 1)
! not implemented for large grids.
CPASSERT(rho_g(1)%pw_grid%ngpts < HUGE(ng_global))
ng_global = INT(rho_g(1)%pw_grid%ngpts)
ng = SIZE(mixing_store%rhoin_buffer(1, 1)%cc)
alpha = mixing_store%alpha
sigma_max = mixing_store%sigma_max
reg_par = mixing_store%reg_par
r_step = mixing_store%r_step
nbuffer = mixing_store%nbuffer
! determine the step number, and multisecant iteration
nb = MIN(mixing_store%ncall, nbuffer - 1)
ib = MODULO(mixing_store%ncall, nbuffer) + 1
IF (mixing_store%ncall > 0) THEN
ib_prev = MODULO(mixing_store%ncall - 1, nbuffer) + 1
ELSE
ib_prev = 0
END IF
mixing_store%ncall = mixing_store%ncall + 1
ib_next = MODULO(mixing_store%ncall, nbuffer) + 1
! compute the residual gn and its norm gn_norm
DO ispin = 1, nspin
gn => mixing_store%res_buffer(ib, ispin)%cc
gn_norm = 0.0_dp
DO ig = 1, ng
gn(ig) = (rho_g(ispin)%array(ig) - mixing_store%rhoin_buffer(ib, ispin)%cc(ig))
gn_norm = gn_norm + &
REAL(gn(ig), dp)*REAL(gn(ig), dp) + AIMAG(gn(ig))*AIMAG(gn(ig))
END DO
CALL para_env%sum(gn_norm)
gn_norm = SQRT(gn_norm)
mixing_store%norm_res_buffer(ib, ispin) = gn_norm
END DO
IF (nb == 0) THEN
!simple mixing
DO ispin = 1, nspin
DO ig = 1, ng
f_mix = alpha*mixing_store%kerker_factor(ig)
rho_g(ispin)%array(ig) = mixing_store%rhoin_buffer(1, ispin)%cc(ig) + &
f_mix*mixing_store%res_buffer(1, ispin)%cc(ig)
mixing_store%rhoin_buffer(ib_next, ispin)%cc(ig) = rho_g(ispin)%array(ig)
END DO
END DO
CALL timestop(handle)
RETURN
END IF
! allocate temporary arrays
! step_matrix S ngxnb
ALLOCATE (step_matrix(ng, nb))
! res_matrix Y ngxnb
ALLOCATE (res_matrix(ng, nb))
! matrix A nbxnb
ALLOCATE (a_matrix(nb, ng_global))
! PSI nb vector of norms
ALLOCATE (norm_res(nb))
ALLOCATE (norm_res_low(nb))
ALLOCATE (norm_res_up(nb))
! matrix B nbxnb
ALLOCATE (b_matrix(nb, nb))
! matrix B_inv nbxnb
ALLOCATE (binv_matrix(nb, nb))
ALLOCATE (gn_global(ng_global))
ALLOCATE (res_matrix_global(ng_global))
IF (use_zgemm) THEN
ALLOCATE (sa(ng, ng_global))
ALLOCATE (ya(ng, ng_global))
END IF
IF (use_zgemm_rev) THEN
ALLOCATE (tmp_vec(nb))
END IF
ALLOCATE (pgn(ng))
ALLOCATE (ugn(ng))
DO ispin = 1, nspin