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rpa_exchange.F
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rpa_exchange.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 !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Auxiliary routines needed for RPA-exchange
!> given blacs_env to another
!> \par History
!> 09.2016 created [Vladimir Rybkin]
!> 03.2019 Renamed [Frederick Stein]
!> 03.2019 Moved Functions from rpa_ri_gpw.F [Frederick Stein]
!> 04.2024 Added open-shell calculations, SOSEX [Frederick Stein]
!> \author Vladimir Rybkin
! **************************************************************************************************
MODULE rpa_exchange
USE atomic_kind_types, ONLY: atomic_kind_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_copy, dbcsr_create, dbcsr_get_info, dbcsr_init_p, dbcsr_multiply, dbcsr_p_type, &
dbcsr_release, dbcsr_set, dbcsr_trace, dbcsr_type, dbcsr_type_no_symmetry
USE cp_dbcsr_operations, ONLY: dbcsr_allocate_matrix_set
USE cp_fm_basic_linalg, ONLY: cp_fm_column_scale
USE cp_fm_diag, ONLY: choose_eigv_solver
USE cp_fm_struct, ONLY: cp_fm_struct_create,&
cp_fm_struct_p_type,&
cp_fm_struct_release
USE cp_fm_types, ONLY: cp_fm_create,&
cp_fm_get_info,&
cp_fm_release,&
cp_fm_set_all,&
cp_fm_to_fm,&
cp_fm_to_fm_submat_general,&
cp_fm_type
USE group_dist_types, ONLY: create_group_dist,&
get_group_dist,&
group_dist_d1_type,&
group_dist_proc,&
maxsize,&
release_group_dist
USE hfx_admm_utils, ONLY: tddft_hfx_matrix
USE hfx_types, ONLY: hfx_create,&
hfx_release,&
hfx_type
USE input_constants, ONLY: rpa_exchange_axk,&
rpa_exchange_none,&
rpa_exchange_sosex
USE input_section_types, ONLY: section_vals_get_subs_vals,&
section_vals_type
USE kinds, ONLY: dp,&
int_8
USE local_gemm_api, ONLY: LOCAL_GEMM_PU_GPU
USE mathconstants, ONLY: sqrthalf
USE message_passing, ONLY: mp_para_env_type,&
mp_proc_null
USE mp2_types, ONLY: mp2_type
USE parallel_gemm_api, ONLY: parallel_gemm
USE particle_types, ONLY: particle_type
USE qs_environment_types, ONLY: get_qs_env,&
qs_environment_type
USE qs_kind_types, ONLY: qs_kind_type
USE qs_subsys_types, ONLY: qs_subsys_get,&
qs_subsys_type
USE rpa_communication, ONLY: gamma_fm_to_dbcsr
USE rpa_util, ONLY: calc_fm_mat_S_rpa,&
remove_scaling_factor_rpa
USE scf_control_types, ONLY: scf_control_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'rpa_exchange'
PUBLIC :: rpa_exchange_work_type, rpa_exchange_needed_mem
TYPE rpa_exchange_env_type
PRIVATE
TYPE(qs_environment_type), POINTER :: qs_env => NULL()
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: mat_hfx => NULL()
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: dbcsr_Gamma_munu_P => NULL()
TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:) :: dbcsr_Gamma_inu_P
! Workaround GCC 8
TYPE(dbcsr_type), DIMENSION(:), POINTER :: mo_coeff_o => NULL()
TYPE(dbcsr_type), DIMENSION(:), POINTER :: mo_coeff_v => NULL()
TYPE(dbcsr_type) :: work_ao
TYPE(hfx_type), DIMENSION(:, :), POINTER :: x_data => NULL()
TYPE(mp_para_env_type), POINTER :: para_env => NULL()
TYPE(section_vals_type), POINTER :: hfx_sections => NULL()
LOGICAL :: my_recalc_hfx_integrals = .FALSE.
REAL(KIND=dp) :: eps_filter = 0.0_dp
TYPE(cp_fm_struct_p_type), DIMENSION(:), ALLOCATABLE :: struct_Gamma
CONTAINS
PROCEDURE, PASS(exchange_env), NON_OVERRIDABLE :: create => hfx_create_subgroup
!PROCEDURE, PASS(exchange_env), NON_OVERRIDABLE :: integrate => integrate_exchange
PROCEDURE, PASS(exchange_env), NON_OVERRIDABLE :: release => hfx_release_subgroup
END TYPE
TYPE dbcsr_matrix_p_set
TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:) :: matrix_set
END TYPE
TYPE rpa_exchange_work_type
PRIVATE
INTEGER :: exchange_correction = rpa_exchange_none
TYPE(rpa_exchange_env_type) :: exchange_env
INTEGER, DIMENSION(:), ALLOCATABLE :: homo, virtual, dimen_ia
TYPE(group_dist_d1_type) :: aux_func_dist = group_dist_d1_type()
INTEGER, DIMENSION(:), ALLOCATABLE :: aux2send
INTEGER :: dimen_RI = 0
INTEGER :: block_size = 0
INTEGER :: color_sub = 0
INTEGER :: ngroup = 0
TYPE(cp_fm_type) :: fm_mat_Q_tmp = cp_fm_type()
TYPE(cp_fm_type) :: fm_mat_R_half_gemm = cp_fm_type()
TYPE(cp_fm_type) :: fm_mat_U = cp_fm_type()
TYPE(mp_para_env_type), POINTER :: para_env_sub => NULL()
CONTAINS
PROCEDURE, PUBLIC, PASS(exchange_work), NON_OVERRIDABLE :: create => rpa_exchange_work_create
PROCEDURE, PUBLIC, PASS(exchange_work), NON_OVERRIDABLE :: compute => rpa_exchange_work_compute
PROCEDURE, PUBLIC, PASS(exchange_work), NON_OVERRIDABLE :: release => rpa_exchange_work_release
PROCEDURE, PRIVATE, PASS(exchange_work), NON_OVERRIDABLE :: redistribute_into_subgroups
PROCEDURE, PRIVATE, PASS(exchange_work), NON_OVERRIDABLE :: compute_fm => rpa_exchange_work_compute_fm
PROCEDURE, PRIVATE, PASS(exchange_work), NON_OVERRIDABLE :: compute_hfx => rpa_exchange_work_compute_hfx
END TYPE
CONTAINS
! **************************************************************************************************
!> \brief ...
!> \param mp2_env ...
!> \param homo ...
!> \param virtual ...
!> \param dimen_RI ...
!> \param para_env ...
!> \param mem_per_rank ...
!> \param mem_per_repl ...
! **************************************************************************************************
SUBROUTINE rpa_exchange_needed_mem(mp2_env, homo, virtual, dimen_RI, para_env, mem_per_rank, mem_per_repl)
TYPE(mp2_type), INTENT(IN) :: mp2_env
INTEGER, DIMENSION(:), INTENT(IN) :: homo, virtual
INTEGER, INTENT(IN) :: dimen_RI
TYPE(mp_para_env_type), INTENT(IN) :: para_env
REAL(KIND=dp), INTENT(INOUT) :: mem_per_rank, mem_per_repl
INTEGER :: block_size
! We need the block size and if it is unknown, an upper bound
block_size = mp2_env%ri_rpa%exchange_block_size
IF (block_size <= 0) block_size = MAX(1, (dimen_RI + para_env%num_pe - 1)/para_env%num_pe)
! storage of product matrix (upper bound only as it depends on the square of the potential still unknown block size)
mem_per_rank = mem_per_rank + REAL(MAXVAL(homo), KIND=dp)**2*block_size**2*8.0_dp/(1024_dp**2)
! work arrays R (2x) and U, copies of Gamma (2x), communication buffer (as expensive as Gamma)
mem_per_repl = mem_per_repl + 3.0_dp*dimen_RI*dimen_RI*8.0_dp/(1024_dp**2) &
+ 3.0_dp*MAXVAL(homo*virtual)*dimen_RI*8.0_dp/(1024_dp**2)
END SUBROUTINE rpa_exchange_needed_mem
! **************************************************************************************************
!> \brief ...
!> \param exchange_work ...
!> \param qs_env ...
!> \param para_env_sub ...
!> \param mat_munu ...
!> \param dimen_RI ...
!> \param fm_mat_S ...
!> \param fm_mat_Q ...
!> \param fm_mat_Q_gemm ...
!> \param homo ...
!> \param virtual ...
! **************************************************************************************************
SUBROUTINE rpa_exchange_work_create(exchange_work, qs_env, para_env_sub, mat_munu, dimen_RI, &
fm_mat_S, fm_mat_Q, fm_mat_Q_gemm, homo, virtual)
CLASS(rpa_exchange_work_type), INTENT(INOUT) :: exchange_work
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(mp_para_env_type), POINTER, INTENT(IN) :: para_env_sub
TYPE(dbcsr_p_type), INTENT(IN) :: mat_munu
INTEGER, INTENT(IN) :: dimen_RI
TYPE(cp_fm_type), DIMENSION(:), INTENT(IN) :: fm_mat_S
TYPE(cp_fm_type), INTENT(IN) :: fm_mat_Q, fm_mat_Q_gemm
INTEGER, DIMENSION(SIZE(fm_mat_S)), INTENT(IN) :: homo, virtual
INTEGER :: nspins, aux_global, aux_local, my_process_row, proc, ispin
INTEGER, DIMENSION(:), POINTER :: row_indices, aux_distribution_fm
TYPE(cp_blacs_env_type), POINTER :: context
exchange_work%exchange_correction = qs_env%mp2_env%ri_rpa%exchange_correction
IF (exchange_work%exchange_correction == rpa_exchange_none) RETURN
ASSOCIATE (para_env => fm_mat_S(1)%matrix_struct%para_env)
exchange_work%para_env_sub => para_env_sub
exchange_work%ngroup = para_env%num_pe/para_env_sub%num_pe
exchange_work%color_sub = para_env%mepos/para_env_sub%num_pe
END ASSOCIATE
CALL cp_fm_get_info(fm_mat_S(1), row_indices=row_indices, nrow_locals=aux_distribution_fm, context=context)
CALL context%get(my_process_row=my_process_row)
CALL create_group_dist(exchange_work%aux_func_dist, exchange_work%ngroup, dimen_RI)
ALLOCATE (exchange_work%aux2send(0:exchange_work%ngroup - 1))
exchange_work%aux2send = 0
DO aux_local = 1, aux_distribution_fm(my_process_row)
aux_global = row_indices(aux_local)
proc = group_dist_proc(exchange_work%aux_func_dist, aux_global)
exchange_work%aux2send(proc) = exchange_work%aux2send(proc) + 1
END DO
nspins = SIZE(fm_mat_S)
ALLOCATE (exchange_work%homo(nspins), exchange_work%virtual(nspins), exchange_work%dimen_ia(nspins))
exchange_work%homo(:) = homo
exchange_work%virtual(:) = virtual
exchange_work%dimen_ia(:) = homo*virtual
exchange_work%dimen_RI = dimen_RI
exchange_work%block_size = qs_env%mp2_env%ri_rpa%exchange_block_size
IF (exchange_work%block_size <= 0) exchange_work%block_size = dimen_RI
CALL cp_fm_create(exchange_work%fm_mat_U, fm_mat_Q%matrix_struct, name="fm_mat_U")
CALL cp_fm_create(exchange_work%fm_mat_Q_tmp, fm_mat_Q%matrix_struct, name="fm_mat_Q_tmp")
CALL cp_fm_create(exchange_work%fm_mat_R_half_gemm, fm_mat_Q_gemm%matrix_struct)
IF (qs_env%mp2_env%ri_rpa%use_hfx_implementation) THEN
CALL exchange_work%exchange_env%create(qs_env, mat_munu%matrix, para_env_sub, fm_mat_S)
END IF
IF (ASSOCIATED(qs_env%mp2_env%ri_rpa%mo_coeff_o)) THEN
DO ispin = 1, SIZE(qs_env%mp2_env%ri_rpa%mo_coeff_o)
CALL dbcsr_release(qs_env%mp2_env%ri_rpa%mo_coeff_o(ispin))
END DO
DEALLOCATE (qs_env%mp2_env%ri_rpa%mo_coeff_o)
END IF
IF (ASSOCIATED(qs_env%mp2_env%ri_rpa%mo_coeff_v)) THEN
DO ispin = 1, SIZE(qs_env%mp2_env%ri_rpa%mo_coeff_v)
CALL dbcsr_release(qs_env%mp2_env%ri_rpa%mo_coeff_v(ispin))
END DO
DEALLOCATE (qs_env%mp2_env%ri_rpa%mo_coeff_v)
END IF
END SUBROUTINE
! **************************************************************************************************
!> \brief ... Initializes x_data on a subgroup
!> \param exchange_env ...
!> \param qs_env ...
!> \param mat_munu ...
!> \param para_env_sub ...
!> \param fm_mat_S ...
!> \author Vladimir Rybkin
! **************************************************************************************************
SUBROUTINE hfx_create_subgroup(exchange_env, qs_env, mat_munu, para_env_sub, fm_mat_S)
CLASS(rpa_exchange_env_type), INTENT(INOUT) :: exchange_env
TYPE(dbcsr_type), INTENT(IN) :: mat_munu
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(mp_para_env_type), POINTER, INTENT(IN) :: para_env_sub
TYPE(cp_fm_type), DIMENSION(:), INTENT(IN) :: fm_mat_S
CHARACTER(LEN=*), PARAMETER :: routineN = 'hfx_create_subgroup'
INTEGER :: handle, nelectron_total, ispin, &
number_of_aos, nspins, dimen_RI, dimen_ia
TYPE(atomic_kind_type), DIMENSION(:), POINTER :: atomic_kind_set
TYPE(cell_type), POINTER :: my_cell
TYPE(dft_control_type), POINTER :: dft_control
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
TYPE(qs_kind_type), DIMENSION(:), POINTER :: qs_kind_set
TYPE(qs_subsys_type), POINTER :: subsys
TYPE(scf_control_type), POINTER :: scf_control
TYPE(section_vals_type), POINTER :: input
CALL timeset(routineN, handle)
exchange_env%mo_coeff_o => qs_env%mp2_env%ri_rpa%mo_coeff_o
exchange_env%mo_coeff_v => qs_env%mp2_env%ri_rpa%mo_coeff_v
NULLIFY (qs_env%mp2_env%ri_rpa%mo_coeff_o, qs_env%mp2_env%ri_rpa%mo_coeff_v)
nspins = SIZE(exchange_env%mo_coeff_o)
exchange_env%qs_env => qs_env
exchange_env%para_env => para_env_sub
exchange_env%eps_filter = qs_env%mp2_env%mp2_gpw%eps_filter
NULLIFY (my_cell, atomic_kind_set, particle_set, dft_control, qs_kind_set, scf_control)
CALL get_qs_env(qs_env, &
subsys=subsys, &
input=input, &
scf_control=scf_control, &
nelectron_total=nelectron_total)
CALL qs_subsys_get(subsys, &
cell=my_cell, &
atomic_kind_set=atomic_kind_set, &
qs_kind_set=qs_kind_set, &
particle_set=particle_set)
exchange_env%hfx_sections => section_vals_get_subs_vals(input, "DFT%XC%WF_CORRELATION%RI_RPA%HF")
CALL get_qs_env(qs_env, dft_control=dft_control)
! Retrieve particle_set and atomic_kind_set
CALL hfx_create(exchange_env%x_data, para_env_sub, exchange_env%hfx_sections, atomic_kind_set, &
qs_kind_set, particle_set, dft_control, my_cell, orb_basis='ORB', &
nelectron_total=nelectron_total)
exchange_env%my_recalc_hfx_integrals = .TRUE.
CALL dbcsr_allocate_matrix_set(exchange_env%mat_hfx, nspins)
DO ispin = 1, nspins
ALLOCATE (exchange_env%mat_hfx(ispin)%matrix)
CALL dbcsr_init_p(exchange_env%mat_hfx(ispin)%matrix)
CALL dbcsr_create(exchange_env%mat_hfx(ispin)%matrix, template=mat_munu, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_copy(exchange_env%mat_hfx(ispin)%matrix, mat_munu)
END DO
CALL dbcsr_get_info(mat_munu, nfullcols_total=number_of_aos)
CALL dbcsr_create(exchange_env%work_ao, template=mat_munu, &
matrix_type=dbcsr_type_no_symmetry)
ALLOCATE (exchange_env%dbcsr_Gamma_inu_P(nspins))
CALL dbcsr_allocate_matrix_set(exchange_env%dbcsr_Gamma_munu_P, nspins)
DO ispin = 1, nspins
ALLOCATE (exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix)
CALL dbcsr_create(exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix, template=mat_munu, &
matrix_type=dbcsr_type_no_symmetry)
CALL dbcsr_copy(exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix, mat_munu)
CALL dbcsr_set(exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix, 0.0_dp)
CALL dbcsr_create(exchange_env%dbcsr_Gamma_inu_P(ispin), template=exchange_env%mo_coeff_o(ispin))
CALL dbcsr_copy(exchange_env%dbcsr_Gamma_inu_P(ispin), exchange_env%mo_coeff_o(ispin))
CALL dbcsr_set(exchange_env%dbcsr_Gamma_inu_P(ispin), 0.0_dp)
END DO
ALLOCATE (exchange_env%struct_Gamma(nspins))
DO ispin = 1, nspins
CALL cp_fm_get_info(fm_mat_S(ispin), nrow_global=dimen_RI, ncol_global=dimen_ia)
CALL cp_fm_struct_create(exchange_env%struct_Gamma(ispin)%struct, template_fmstruct=fm_mat_S(ispin)%matrix_struct, &
nrow_global=dimen_ia, ncol_global=dimen_RI)
END DO
CALL timestop(handle)
END SUBROUTINE hfx_create_subgroup
! **************************************************************************************************
!> \brief ...
!> \param exchange_work ...
! **************************************************************************************************
SUBROUTINE rpa_exchange_work_release(exchange_work)
CLASS(rpa_exchange_work_type), INTENT(INOUT) :: exchange_work
IF (ALLOCATED(exchange_work%homo)) DEALLOCATE (exchange_work%homo)
IF (ALLOCATED(exchange_work%virtual)) DEALLOCATE (exchange_work%virtual)
IF (ALLOCATED(exchange_work%dimen_ia)) DEALLOCATE (exchange_work%dimen_ia)
NULLIFY (exchange_work%para_env_sub)
CALL release_group_dist(exchange_work%aux_func_dist)
IF (ALLOCATED(exchange_work%aux2send)) DEALLOCATE (exchange_work%aux2send)
CALL cp_fm_release(exchange_work%fm_mat_Q_tmp)
CALL cp_fm_release(exchange_work%fm_mat_U)
CALL cp_fm_release(exchange_work%fm_mat_R_half_gemm)
CALL exchange_work%exchange_env%release()
END SUBROUTINE
! **************************************************************************************************
!> \brief ...
!> \param exchange_env ...
! **************************************************************************************************
SUBROUTINE hfx_release_subgroup(exchange_env)
CLASS(rpa_exchange_env_type), INTENT(INOUT) :: exchange_env
INTEGER :: ispin
NULLIFY (exchange_env%para_env, exchange_env%hfx_sections)
IF (ASSOCIATED(exchange_env%x_data)) THEN
CALL hfx_release(exchange_env%x_data)
NULLIFY (exchange_env%x_data)
END IF
CALL dbcsr_release(exchange_env%work_ao)
IF (ASSOCIATED(exchange_env%dbcsr_Gamma_munu_P)) THEN
DO ispin = 1, SIZE(exchange_env%mat_hfx, 1)
CALL dbcsr_release(exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix)
CALL dbcsr_release(exchange_env%mat_hfx(ispin)%matrix)
CALL dbcsr_release(exchange_env%dbcsr_Gamma_inu_P(ispin))
CALL dbcsr_release(exchange_env%mo_coeff_o(ispin))
CALL dbcsr_release(exchange_env%mo_coeff_v(ispin))
DEALLOCATE (exchange_env%mat_hfx(ispin)%matrix)
DEALLOCATE (exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix)
END DO
DEALLOCATE (exchange_env%mat_hfx, exchange_env%dbcsr_Gamma_munu_P)
DEALLOCATE (exchange_env%dbcsr_Gamma_inu_P, exchange_env%mo_coeff_o, exchange_env%mo_coeff_v)
NULLIFY (exchange_env%mat_hfx, exchange_env%dbcsr_Gamma_munu_P)
END IF
IF (ALLOCATED(exchange_env%struct_Gamma)) THEN
DO ispin = 1, SIZE(exchange_env%struct_Gamma)
CALL cp_fm_struct_release(exchange_env%struct_Gamma(ispin)%struct)
END DO
DEALLOCATE (exchange_env%struct_Gamma)
END IF
END SUBROUTINE hfx_release_subgroup
! **************************************************************************************************
!> \brief Main driver for RPA-exchange energies
!> \param exchange_work ...
!> \param fm_mat_Q ...
!> \param eig ...
!> \param fm_mat_S ...
!> \param omega ...
!> \param e_exchange_corr exchange energy correction for a quadrature point
!> \param mp2_env ...
!> \author Vladimir Rybkin, 07/2016
! **************************************************************************************************
SUBROUTINE rpa_exchange_work_compute(exchange_work, fm_mat_Q, eig, fm_mat_S, omega, &
e_exchange_corr, mp2_env)
CLASS(rpa_exchange_work_type), INTENT(INOUT) :: exchange_work
TYPE(cp_fm_type), INTENT(IN) :: fm_mat_Q
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: eig
TYPE(cp_fm_type), DIMENSION(:), INTENT(INOUT) :: fm_mat_S
REAL(KIND=dp), INTENT(IN) :: omega
REAL(KIND=dp), INTENT(INOUT) :: e_exchange_corr
TYPE(mp2_type), INTENT(INOUT) :: mp2_env
CHARACTER(LEN=*), PARAMETER :: routineN = 'rpa_exchange_work_compute'
REAL(KIND=dp), PARAMETER :: thresh = 0.0000001_dp
INTEGER :: handle, nspins, dimen_RI, iiB
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: eigenval
IF (exchange_work%exchange_correction == rpa_exchange_none) RETURN
CALL timeset(routineN, handle)
CALL cp_fm_get_info(fm_mat_Q, ncol_global=dimen_RI)
nspins = SIZE(fm_mat_S)
! Eigenvalues
ALLOCATE (eigenval(dimen_RI))
eigenval = 0.0_dp
CALL cp_fm_set_all(matrix=exchange_work%fm_mat_Q_tmp, alpha=0.0_dp)
CALL cp_fm_set_all(matrix=exchange_work%fm_mat_U, alpha=0.0_dp)
! Copy Q to Q_tmp
CALL cp_fm_to_fm(fm_mat_Q, exchange_work%fm_mat_Q_tmp)
! Diagonalize Q
CALL choose_eigv_solver(exchange_work%fm_mat_Q_tmp, exchange_work%fm_mat_U, eigenval)
! Calculate diagonal matrix for R_half
! Manipulate eigenvalues to get diagonal matrix
IF (exchange_work%exchange_correction == rpa_exchange_axk) THEN
DO iib = 1, dimen_RI
IF (ABS(eigenval(iib)) .GE. thresh) THEN
eigenval(iib) = &
SQRT((1.0_dp/(eigenval(iib)**2))*LOG(1.0_dp + eigenval(iib)) &
- 1.0_dp/(eigenval(iib)*(eigenval(iib) + 1.0_dp)))
ELSE
eigenval(iib) = sqrthalf
END IF
END DO
ELSE IF (exchange_work%exchange_correction == rpa_exchange_sosex) THEN
DO iib = 1, dimen_RI
IF (ABS(eigenval(iib)) .GE. thresh) THEN
eigenval(iib) = &
SQRT(-(1.0_dp/(eigenval(iib)**2))*LOG(1.0_dp + eigenval(iib)) &
+ 1.0_dp/eigenval(iib))
ELSE
eigenval(iib) = sqrthalf
END IF
END DO
ELSE
CPABORT("Unknown RPA exchange correction")
END IF
! fm_mat_U now contains some sqrt of the required matrix-valued function
CALL cp_fm_column_scale(exchange_work%fm_mat_U, eigenval)
! Release memory
DEALLOCATE (eigenval)
! Redistribute fm_mat_U for "rectangular" multiplication: ia*P P*P
CALL cp_fm_set_all(matrix=exchange_work%fm_mat_R_half_gemm, alpha=0.0_dp)
CALL cp_fm_to_fm_submat_general(exchange_work%fm_mat_U, exchange_work%fm_mat_R_half_gemm, dimen_RI, &
dimen_RI, 1, 1, 1, 1, exchange_work%fm_mat_U%matrix_struct%context)
IF (mp2_env%ri_rpa%use_hfx_implementation) THEN
CALL exchange_work%compute_hfx(fm_mat_S, eig, omega, e_exchange_corr)
ELSE
CALL exchange_work%compute_fm(fm_mat_S, eig, omega, e_exchange_corr, mp2_env)
END IF
CALL timestop(handle)
END SUBROUTINE rpa_exchange_work_compute
! **************************************************************************************************
!> \brief Main driver for RPA-exchange energies
!> \param exchange_work ...
!> \param fm_mat_S ...
!> \param eig ...
!> \param omega ...
!> \param e_exchange_corr exchange energy correction for a quadrature point
!> \param mp2_env ...
!> \author Frederick Stein, May-June 2024
! **************************************************************************************************
SUBROUTINE rpa_exchange_work_compute_fm(exchange_work, fm_mat_S, eig, omega, &
e_exchange_corr, mp2_env)
CLASS(rpa_exchange_work_type), INTENT(INOUT) :: exchange_work
TYPE(cp_fm_type), DIMENSION(:), INTENT(IN) :: fm_mat_S
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: eig
REAL(KIND=dp), INTENT(IN) :: omega
REAL(KIND=dp), INTENT(INOUT) :: e_exchange_corr
TYPE(mp2_type), INTENT(INOUT) :: mp2_env
CHARACTER(LEN=*), PARAMETER :: routineN = 'rpa_exchange_work_compute_fm'
INTEGER :: handle, ispin, nspins, P, Q, L_size_Gamma, hom, virt, i, &
send_proc, recv_proc, recv_size, max_aux_size, proc_shift, dimen_ia, &
block_size, P_start, P_end, P_size, Q_start, Q_size, Q_end, handle2, my_aux_size, my_virt
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), TARGET :: mat_Gamma_3_3D
REAL(KIND=dp), POINTER, DIMENSION(:), CONTIGUOUS :: mat_Gamma_3_1D
REAL(KIND=dp), POINTER, DIMENSION(:, :), CONTIGUOUS :: mat_Gamma_3_2D
REAL(KIND=dp), ALLOCATABLE, TARGET, DIMENSION(:) :: recv_buffer_1D
REAL(KIND=dp), POINTER, DIMENSION(:, :), CONTIGUOUS :: recv_buffer_2D
REAL(KIND=dp), POINTER, DIMENSION(:, :, :), CONTIGUOUS :: recv_buffer_3D
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: mat_B_iaP
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), TARGET :: product_matrix_1D
REAL(KIND=dp), POINTER, DIMENSION(:, :), CONTIGUOUS :: product_matrix_2D
REAL(KIND=dp), POINTER, DIMENSION(:, :, :, :), CONTIGUOUS :: product_matrix_4D
TYPE(cp_fm_type) :: fm_mat_Gamma_3
TYPE(mp_para_env_type), POINTER :: para_env
TYPE(group_dist_d1_type) :: virt_dist
CALL timeset(routineN, handle)
nspins = SIZE(fm_mat_S)
CALL get_group_dist(exchange_work%aux_func_dist, exchange_work%color_sub, sizes=my_aux_size)
e_exchange_corr = 0.0_dp
max_aux_size = maxsize(exchange_work%aux_func_dist)
! local_gemm_ctx has a very large footprint the first time this routine is
! called.
CALL mp2_env%local_gemm_ctx%create(LOCAL_GEMM_PU_GPU)
CALL mp2_env%local_gemm_ctx%set_op_threshold_gpu(128*128*128*2)
DO ispin = 1, nspins
hom = exchange_work%homo(ispin)
virt = exchange_work%virtual(ispin)
dimen_ia = hom*virt
IF (hom < 1 .OR. virt < 1) CYCLE
CALL cp_fm_get_info(fm_mat_S(ispin), para_env=para_env)
CALL cp_fm_create(fm_mat_Gamma_3, fm_mat_S(ispin)%matrix_struct)
CALL cp_fm_set_all(matrix=fm_mat_Gamma_3, alpha=0.0_dp)
! Update G with a new value of Omega: in practice, it is G*S
! Scale fm_work_iaP
CALL calc_fm_mat_S_rpa(fm_mat_S(ispin), .TRUE., virt, eig(:, ispin), &
hom, omega, 0.0_dp)
! Calculate Gamma_3: Gamma_3 = G*S*R^(1/2) = G*S*R^(1/2)
CALL parallel_gemm(transa="T", transb="N", m=exchange_work%dimen_RI, n=dimen_ia, k=exchange_work%dimen_RI, alpha=1.0_dp, &
matrix_a=exchange_work%fm_mat_R_half_gemm, matrix_b=fm_mat_S(ispin), beta=0.0_dp, &
matrix_c=fm_mat_Gamma_3)
CALL create_group_dist(virt_dist, exchange_work%para_env_sub%num_pe, virt)
! Remove extra factor from S after the multiplication (to return to the original matrix)
CALL remove_scaling_factor_rpa(fm_mat_S(ispin), virt, eig(:, ispin), hom, omega)
CALL exchange_work%redistribute_into_subgroups(fm_mat_Gamma_3, mat_Gamma_3_3D, ispin, virt_dist)
CALL cp_fm_release(fm_mat_Gamma_3)
! We need only the pure matrix
CALL remove_scaling_factor_rpa(fm_mat_S(ispin), virt, eig(:, ispin), hom, omega)
! Reorder matrix from (P, i*a) -> (a, i, P) with P being distributed within subgroups
CALL exchange_work%redistribute_into_subgroups(fm_mat_S(ispin), mat_B_iaP, ispin, virt_dist)
! Return to the original tensor
CALL calc_fm_mat_S_rpa(fm_mat_S(ispin), .TRUE., virt, eig(:, ispin), hom, omega, 0.0_dp)
L_size_Gamma = SIZE(mat_Gamma_3_3D, 3)
my_virt = SIZE(mat_Gamma_3_3D, 1)
block_size = exchange_work%block_size
mat_Gamma_3_1D(1:INT(my_virt, KIND=int_8)*hom*my_aux_size) => mat_Gamma_3_3D(:, :, 1:my_aux_size)
mat_Gamma_3_2D(1:my_virt, 1:hom*my_aux_size) => mat_Gamma_3_1D(1:INT(my_virt, KIND=int_8)*hom*my_aux_size)
ALLOCATE (product_matrix_1D(INT(hom*MIN(block_size, L_size_gamma), KIND=int_8)* &
INT(hom*MIN(block_size, max_aux_size), KIND=int_8)))
ALLOCATE (recv_buffer_1D(INT(virt, KIND=int_8)*hom*max_aux_size))
recv_buffer_2D(1:my_virt, 1:hom*max_aux_size) => recv_buffer_1D(1:INT(virt, KIND=int_8)*hom*max_aux_size)
recv_buffer_3D(1:my_virt, 1:hom, 1:max_aux_size) => recv_buffer_1D(1:INT(virt, KIND=int_8)*hom*max_aux_size)
DO proc_shift = 0, para_env%num_pe - 1, exchange_work%para_env_sub%num_pe
send_proc = MODULO(para_env%mepos + proc_shift, para_env%num_pe)
recv_proc = MODULO(para_env%mepos - proc_shift, para_env%num_pe)
CALL get_group_dist(exchange_work%aux_func_dist, recv_proc/exchange_work%para_env_sub%num_pe, sizes=recv_size)
IF (recv_size == 0) recv_proc = mp_proc_null
CALL para_env%sendrecv(mat_B_iaP, send_proc, recv_buffer_3D(:, :, 1:recv_size), recv_proc)
IF (recv_size == 0) CYCLE
DO P_start = 1, L_size_Gamma, block_size
P_end = MIN(L_size_Gamma, P_start + block_size - 1)
P_size = P_end - P_start + 1
DO Q_start = 1, recv_size, block_size
Q_end = MIN(recv_size, Q_start + block_size - 1)
Q_size = Q_end - Q_start + 1
! Reassign product_matrix pointers to enforce contiguity of target array
product_matrix_2D(1:hom*P_size, 1:hom*Q_size) => &
product_matrix_1D(1:INT(hom*P_size, KIND=int_8)*INT(hom*Q_size, KIND=int_8))
product_matrix_4D(1:hom, 1:P_size, 1:hom, 1:Q_size) => &
product_matrix_1D(1:INT(hom*P_size, KIND=int_8)*INT(hom*Q_size, KIND=int_8))
CALL timeset(routineN//"_gemm", handle2)
CALL mp2_env%local_gemm_ctx%gemm("T", "N", hom*P_size, hom*Q_size, my_virt, 1.0_dp, &
mat_Gamma_3_2D(:, hom*(P_start - 1) + 1:hom*P_end), my_virt, &
recv_buffer_2D(:, hom*(Q_start - 1) + 1:hom*Q_end), my_virt, &
0.0_dp, product_matrix_2D, hom*P_size)
CALL timestop(handle2)
CALL timeset(routineN//"_energy", handle2)
!$OMP PARALLEL DO DEFAULT(NONE) SHARED(P_size, Q_size, hom, product_matrix_4D) &
!$OMP COLLAPSE(3) REDUCTION(+: e_exchange_corr) PRIVATE(P, Q, i)
DO P = 1, P_size
DO Q = 1, Q_size
DO i = 1, hom
e_exchange_corr = e_exchange_corr + DOT_PRODUCT(product_matrix_4D(i, P, :, Q), product_matrix_4D(:, P, i, Q))
END DO
END DO
END DO
CALL timestop(handle2)
END DO
END DO
END DO
CALL release_group_dist(virt_dist)
IF (ALLOCATED(mat_B_iaP)) DEALLOCATE (mat_B_iaP)
IF (ALLOCATED(mat_Gamma_3_3D)) DEALLOCATE (mat_Gamma_3_3D)
IF (ALLOCATED(product_matrix_1D)) DEALLOCATE (product_matrix_1D)
IF (ALLOCATED(recv_buffer_1D)) DEALLOCATE (recv_buffer_1D)
END DO
CALL mp2_env%local_gemm_ctx%destroy()
IF (nspins == 2) e_exchange_corr = e_exchange_corr*2.0_dp
IF (nspins == 1) e_exchange_corr = e_exchange_corr*4.0_dp
CALL timestop(handle)
END SUBROUTINE rpa_exchange_work_compute_fm
! **************************************************************************************************
!> \brief Contract RPA-exchange density matrix with HF exchange integrals and evaluate the correction
!> \param exchange_work ...
!> \param fm_mat_S ...
!> \param eig ...
!> \param omega ...
!> \param e_exchange_corr ...
!> \author Vladimir Rybkin, 08/2016
! **************************************************************************************************
SUBROUTINE rpa_exchange_work_compute_hfx(exchange_work, fm_mat_S, eig, omega, e_exchange_corr)
CLASS(rpa_exchange_work_type), INTENT(INOUT) :: exchange_work
TYPE(cp_fm_type), DIMENSION(:), INTENT(INOUT) :: fm_mat_S
REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: eig
REAL(KIND=dp), INTENT(IN) :: omega
REAL(KIND=dp), INTENT(OUT) :: e_exchange_corr
CHARACTER(LEN=*), PARAMETER :: routineN = 'rpa_exchange_work_compute_hfx'
INTEGER :: handle, ispin, my_aux_start, my_aux_end, &
my_aux_size, nspins, L_counter, dimen_ia, hom, virt
REAL(KIND=dp) :: e_exchange_P
TYPE(dbcsr_matrix_p_set), DIMENSION(:), ALLOCATABLE :: dbcsr_Gamma_3
TYPE(cp_fm_type) :: fm_mat_Gamma_3
TYPE(mp_para_env_type), POINTER :: para_env
CALL timeset(routineN, handle)
e_exchange_corr = 0.0_dp
nspins = SIZE(fm_mat_S)
CALL get_group_dist(exchange_work%aux_func_dist, exchange_work%color_sub, my_aux_start, my_aux_end, my_aux_size)
ALLOCATE (dbcsr_Gamma_3(nspins))
DO ispin = 1, nspins
hom = exchange_work%homo(ispin)
virt = exchange_work%virtual(ispin)
dimen_ia = hom*virt
IF (hom < 1 .OR. virt < 1) CYCLE
CALL cp_fm_get_info(fm_mat_S(ispin), para_env=para_env)
CALL cp_fm_create(fm_mat_Gamma_3, exchange_work%exchange_env%struct_Gamma(ispin)%struct)
CALL cp_fm_set_all(matrix=fm_mat_Gamma_3, alpha=0.0_dp)
! Update G with a new value of Omega: in practice, it is G*S
! Scale fm_work_iaP
CALL calc_fm_mat_S_rpa(fm_mat_S(ispin), .TRUE., virt, eig(:, ispin), &
hom, omega, 0.0_dp)
! Calculate Gamma_3: Gamma_3 = G*S*R^(1/2) = G*S*R^(1/2)
CALL parallel_gemm(transa="T", transb="N", m=dimen_ia, n=exchange_work%dimen_RI, &
k=exchange_work%dimen_RI, alpha=1.0_dp, &
matrix_a=fm_mat_S(ispin), matrix_b=exchange_work%fm_mat_R_half_gemm, beta=0.0_dp, &
matrix_c=fm_mat_Gamma_3)
! Remove extra factor from S after the multiplication (to return to the original matrix)
CALL remove_scaling_factor_rpa(fm_mat_S(ispin), virt, eig(:, ispin), hom, omega)
! Copy Gamma_ia_P^3 to dbcsr matrix set
CALL gamma_fm_to_dbcsr(fm_mat_Gamma_3, dbcsr_Gamma_3(ispin)%matrix_set, &
para_env, exchange_work%para_env_sub, hom, virt, &
exchange_work%exchange_env%mo_coeff_o(ispin), &
exchange_work%ngroup, my_aux_start, my_aux_end, my_aux_size)
END DO
DO L_counter = 1, my_aux_size
DO ispin = 1, nspins
! Do dbcsr multiplication: transform the virtual index
CALL dbcsr_multiply("N", "T", 1.0_dp, exchange_work%exchange_env%mo_coeff_v(ispin), &
dbcsr_Gamma_3(ispin)%matrix_set(L_counter), &
0.0_dp, exchange_work%exchange_env%dbcsr_Gamma_inu_P(ispin), &
filter_eps=exchange_work%exchange_env%eps_filter)
CALL dbcsr_release(dbcsr_Gamma_3(ispin)%matrix_set(L_counter))
! Do dbcsr multiplication: transform the occupied index
CALL dbcsr_multiply("N", "T", 0.5_dp, exchange_work%exchange_env%dbcsr_Gamma_inu_P(ispin), &
exchange_work%exchange_env%mo_coeff_o(ispin), &
0.0_dp, exchange_work%exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix, &
filter_eps=exchange_work%exchange_env%eps_filter)
CALL dbcsr_multiply("N", "T", 0.5_dp, exchange_work%exchange_env%mo_coeff_o(ispin), &
exchange_work%exchange_env%dbcsr_Gamma_inu_P(ispin), &
1.0_dp, exchange_work%exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix, &
filter_eps=exchange_work%exchange_env%eps_filter)
CALL dbcsr_set(exchange_work%exchange_env%mat_hfx(ispin)%matrix, 0.0_dp)
END DO
CALL tddft_hfx_matrix(exchange_work%exchange_env%mat_hfx, exchange_work%exchange_env%dbcsr_Gamma_munu_P, &
exchange_work%exchange_env%qs_env, .FALSE., &
exchange_work%exchange_env%my_recalc_hfx_integrals, &
exchange_work%exchange_env%hfx_sections, exchange_work%exchange_env%x_data, &
exchange_work%exchange_env%para_env)
exchange_work%exchange_env%my_recalc_hfx_integrals = .FALSE.
DO ispin = 1, nspins
CALL dbcsr_multiply("N", "T", 1.0_dp, exchange_work%exchange_env%mat_hfx(ispin)%matrix, &
exchange_work%exchange_env%dbcsr_Gamma_munu_P(ispin)%matrix, &
0.0_dp, exchange_work%exchange_env%work_ao, filter_eps=exchange_work%exchange_env%eps_filter)
CALL dbcsr_trace(exchange_work%exchange_env%work_ao, e_exchange_P)
e_exchange_corr = e_exchange_corr - e_exchange_P
END DO
END DO
IF (nspins == 2) e_exchange_corr = e_exchange_corr
IF (nspins == 1) e_exchange_corr = e_exchange_corr*4.0_dp
CALL timestop(handle)
END SUBROUTINE rpa_exchange_work_compute_hfx
! **************************************************************************************************
!> \brief ...
!> \param exchange_work ...
!> \param fm_mat ...
!> \param mat ...
!> \param ispin ...
!> \param virt_dist ...
! **************************************************************************************************
SUBROUTINE redistribute_into_subgroups(exchange_work, fm_mat, mat, ispin, virt_dist)
CLASS(rpa_exchange_work_type), INTENT(IN) :: exchange_work
TYPE(cp_fm_type), INTENT(IN) :: fm_mat
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :), &
INTENT(OUT) :: mat
INTEGER, INTENT(IN) :: ispin
TYPE(group_dist_d1_type), INTENT(IN) :: virt_dist
CHARACTER(LEN=*), PARAMETER :: routineN = 'redistribute_into_subgroups'
INTEGER :: aux_counter, aux_global, aux_local, aux_proc, avirt, dimen_RI, handle, handle2, &
ia_global, ia_local, iocc, max_number_recv, max_number_send, my_aux_end, my_aux_size, &
my_aux_start, my_process_column, my_process_row, my_virt_end, my_virt_size, &
my_virt_start, proc, proc_shift, recv_proc, send_proc, virt_counter, virt_proc, group_size
INTEGER, ALLOCATABLE, DIMENSION(:) :: data2send, recv_col_indices, &
recv_row_indices, send_aux_indices, send_virt_indices, virt2send
INTEGER, DIMENSION(2) :: recv_shape
INTEGER, DIMENSION(:), POINTER :: aux_distribution_fm, col_indices, &
ia_distribution_fm, row_indices
INTEGER, DIMENSION(:, :), POINTER :: mpi2blacs
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:), TARGET :: recv_buffer, send_buffer
REAL(KIND=dp), CONTIGUOUS, DIMENSION(:, :), &
POINTER :: recv_ptr, send_ptr
TYPE(cp_blacs_env_type), POINTER :: context
TYPE(mp_para_env_type), POINTER :: para_env
CALL timeset(routineN, handle)
CALL cp_fm_get_info(matrix=fm_mat, &
nrow_locals=aux_distribution_fm, &
col_indices=col_indices, &
row_indices=row_indices, &
ncol_locals=ia_distribution_fm, &
context=context, &
nrow_global=dimen_RI, &
para_env=para_env)
IF (exchange_work%homo(ispin) <= 0 .OR. exchange_work%virtual(ispin) <= 0) THEN
CALL get_group_dist(virt_dist, exchange_work%para_env_sub%mepos, my_virt_start, my_virt_end, my_virt_size)
ALLOCATE (mat(exchange_work%homo(ispin), my_virt_size, dimen_RI))
CALL timestop(handle)
RETURN
END IF
group_size = exchange_work%para_env_sub%num_pe
CALL timeset(routineN//"_prep", handle2)
CALL get_group_dist(exchange_work%aux_func_dist, exchange_work%color_sub, my_aux_start, my_aux_end, my_aux_size)
CALL get_group_dist(virt_dist, exchange_work%para_env_sub%mepos, my_virt_start, my_virt_end, my_virt_size)
CALL context%get(my_process_column=my_process_column, my_process_row=my_process_row, mpi2blacs=mpi2blacs)
! Determine the number of columns to send
ALLOCATE (send_aux_indices(MAXVAL(exchange_work%aux2send)))
ALLOCATE (virt2send(0:group_size - 1))
virt2send = 0
DO ia_local = 1, ia_distribution_fm(my_process_column)
ia_global = col_indices(ia_local)
avirt = MOD(ia_global - 1, exchange_work%virtual(ispin)) + 1
proc = group_dist_proc(virt_dist, avirt)
virt2send(proc) = virt2send(proc) + 1
END DO
ALLOCATE (data2send(0:para_env%num_pe - 1))
DO aux_proc = 0, exchange_work%ngroup - 1
DO virt_proc = 0, group_size - 1
data2send(aux_proc*group_size + virt_proc) = exchange_work%aux2send(aux_proc)*virt2send(virt_proc)
END DO
END DO
ALLOCATE (send_virt_indices(MAXVAL(virt2send)))
max_number_send = MAXVAL(data2send)
ALLOCATE (send_buffer(INT(max_number_send, KIND=int_8)*exchange_work%homo(ispin)))
max_number_recv = max_number_send
CALL para_env%max(max_number_recv)
ALLOCATE (recv_buffer(max_number_recv))
ALLOCATE (mat(my_virt_size, exchange_work%homo(ispin), my_aux_size))
CALL timestop(handle2)
CALL timeset(routineN//"_own", handle2)
! Start with own data
DO aux_local = 1, aux_distribution_fm(my_process_row)
aux_global = row_indices(aux_local)
IF (aux_global < my_aux_start .OR. aux_global > my_aux_end) CYCLE
DO ia_local = 1, ia_distribution_fm(my_process_column)
ia_global = fm_mat%matrix_struct%col_indices(ia_local)
iocc = (ia_global - 1)/exchange_work%virtual(ispin) + 1
avirt = MOD(ia_global - 1, exchange_work%virtual(ispin)) + 1
IF (my_virt_start > avirt .OR. my_virt_end < avirt) CYCLE
mat(avirt - my_virt_start + 1, iocc, aux_global - my_aux_start + 1) = fm_mat%local_data(aux_local, ia_local)
END DO
END DO
CALL timestop(handle2)
DO proc_shift = 1, para_env%num_pe - 1
send_proc = MODULO(para_env%mepos + proc_shift, para_env%num_pe)
recv_proc = MODULO(para_env%mepos - proc_shift, para_env%num_pe)
CALL timeset(routineN//"_pack_buffer", handle2)
send_ptr(1:virt2send(MOD(send_proc, group_size)), &
1:exchange_work%aux2send(send_proc/group_size)) => &
send_buffer(1:INT(virt2send(MOD(send_proc, group_size)), KIND=int_8)* &
exchange_work%aux2send(send_proc/group_size))
! Pack send buffer
aux_counter = 0
DO aux_local = 1, aux_distribution_fm(my_process_row)
aux_global = row_indices(aux_local)
proc = group_dist_proc(exchange_work%aux_func_dist, aux_global)
IF (proc /= send_proc/group_size) CYCLE
aux_counter = aux_counter + 1
virt_counter = 0
DO ia_local = 1, ia_distribution_fm(my_process_column)
ia_global = col_indices(ia_local)
avirt = MOD(ia_global - 1, exchange_work%virtual(ispin)) + 1
proc = group_dist_proc(virt_dist, avirt)
IF (proc /= MOD(send_proc, group_size)) CYCLE
virt_counter = virt_counter + 1
send_ptr(virt_counter, aux_counter) = fm_mat%local_data(aux_local, ia_local)
send_virt_indices(virt_counter) = ia_global
END DO
send_aux_indices(aux_counter) = aux_global
END DO
CALL timestop(handle2)
CALL timeset(routineN//"_ex_size", handle2)
recv_shape = [1, 1]
CALL para_env%sendrecv(SHAPE(send_ptr), send_proc, recv_shape, recv_proc)
CALL timestop(handle2)
IF (SIZE(send_ptr) == 0) send_proc = mp_proc_null
IF (PRODUCT(recv_shape) == 0) recv_proc = mp_proc_null
CALL timeset(routineN//"_ex_idx", handle2)
ALLOCATE (recv_row_indices(recv_shape(1)), recv_col_indices(recv_shape(2)))
CALL para_env%sendrecv(send_virt_indices(1:virt_counter), send_proc, recv_row_indices, recv_proc)
CALL para_env%sendrecv(send_aux_indices(1:aux_counter), send_proc, recv_col_indices, recv_proc)
CALL timestop(handle2)
! Prepare pointer to recv buffer (consider transposition while packing the send buffer)
recv_ptr(1:recv_shape(1), 1:MAX(1, recv_shape(2))) => recv_buffer(1:recv_shape(1)*MAX(1, recv_shape(2)))
CALL timeset(routineN//"_sendrecv", handle2)
! Perform communication
CALL para_env%sendrecv(send_ptr, send_proc, recv_ptr, recv_proc)
CALL timestop(handle2)
IF (recv_proc == mp_proc_null) THEN
DEALLOCATE (recv_row_indices, recv_col_indices)
CYCLE
END IF
CALL timeset(routineN//"_unpack", handle2)
! Unpack receive buffer
DO aux_local = 1, SIZE(recv_col_indices)
aux_global = recv_col_indices(aux_local)
DO ia_local = 1, SIZE(recv_row_indices)
ia_global = recv_row_indices(ia_local)
iocc = (ia_global - 1)/exchange_work%virtual(ispin) + 1
avirt = MOD(ia_global - 1, exchange_work%virtual(ispin)) + 1
mat(avirt - my_virt_start + 1, iocc, aux_global - my_aux_start + 1) = recv_ptr(ia_local, aux_local)
END DO
END DO
CALL timestop(handle2)
IF (ALLOCATED(recv_row_indices)) DEALLOCATE (recv_row_indices)
IF (ALLOCATED(recv_col_indices)) DEALLOCATE (recv_col_indices)
END DO
DEALLOCATE (send_aux_indices, send_virt_indices)
CALL timestop(handle)
END SUBROUTINE redistribute_into_subgroups
END MODULE rpa_exchange