LCOV - code coverage report
Current view: top level - src - mp2_ri_2c.F (source / functions) Hit Total Coverage
Test: CP2K Regtests (git:b8e0b09) Lines: 611 642 95.2 %
Date: 2024-08-31 06:31:37 Functions: 16 16 100.0 %

          Line data    Source code
       1             : !--------------------------------------------------------------------------------------------------!
       2             : !   CP2K: A general program to perform molecular dynamics simulations                              !
       3             : !   Copyright 2000-2024 CP2K developers group <https://cp2k.org>                                   !
       4             : !                                                                                                  !
       5             : !   SPDX-License-Identifier: GPL-2.0-or-later                                                      !
       6             : !--------------------------------------------------------------------------------------------------!
       7             : 
       8             : ! **************************************************************************************************
       9             : !> \brief Framework for 2c-integrals for RI
      10             : !> \par History
      11             : !>      06.2012 created [Mauro Del Ben]
      12             : !>      03.2019 separated from mp2_ri_gpw [Frederick Stein]
      13             : ! **************************************************************************************************
      14             : MODULE mp2_ri_2c
      15             :    USE atomic_kind_types,               ONLY: atomic_kind_type,&
      16             :                                               get_atomic_kind_set
      17             :    USE basis_set_types,                 ONLY: gto_basis_set_p_type,&
      18             :                                               gto_basis_set_type
      19             :    USE cell_types,                      ONLY: cell_type,&
      20             :                                               get_cell,&
      21             :                                               plane_distance
      22             :    USE constants_operator,              ONLY: operator_coulomb
      23             :    USE cp_blacs_env,                    ONLY: cp_blacs_env_create,&
      24             :                                               cp_blacs_env_release,&
      25             :                                               cp_blacs_env_type
      26             :    USE cp_cfm_basic_linalg,             ONLY: cp_cfm_scale_and_add_fm
      27             :    USE cp_cfm_types,                    ONLY: cp_cfm_create,&
      28             :                                               cp_cfm_release,&
      29             :                                               cp_cfm_to_fm,&
      30             :                                               cp_cfm_type
      31             :    USE cp_control_types,                ONLY: dft_control_type
      32             :    USE cp_dbcsr_api,                    ONLY: &
      33             :         dbcsr_copy, dbcsr_create, dbcsr_deallocate_matrix, dbcsr_desymmetrize, &
      34             :         dbcsr_distribution_release, dbcsr_distribution_type, dbcsr_p_type, dbcsr_release, &
      35             :         dbcsr_reserve_all_blocks, dbcsr_set, dbcsr_type, dbcsr_type_antisymmetric, &
      36             :         dbcsr_type_no_symmetry, dbcsr_type_symmetric
      37             :    USE cp_dbcsr_cp2k_link,              ONLY: cp_dbcsr_alloc_block_from_nbl
      38             :    USE cp_dbcsr_operations,             ONLY: copy_dbcsr_to_fm,&
      39             :                                               cp_dbcsr_dist2d_to_dist,&
      40             :                                               dbcsr_allocate_matrix_set,&
      41             :                                               dbcsr_deallocate_matrix_set
      42             :    USE cp_eri_mme_interface,            ONLY: cp_eri_mme_param
      43             :    USE cp_fm_basic_linalg,              ONLY: cp_fm_column_scale,&
      44             :                                               cp_fm_triangular_invert
      45             :    USE cp_fm_cholesky,                  ONLY: cp_fm_cholesky_decompose
      46             :    USE cp_fm_diag,                      ONLY: choose_eigv_solver,&
      47             :                                               cp_fm_power,&
      48             :                                               cp_fm_syevx
      49             :    USE cp_fm_struct,                    ONLY: cp_fm_struct_create,&
      50             :                                               cp_fm_struct_release,&
      51             :                                               cp_fm_struct_type
      52             :    USE cp_fm_types,                     ONLY: cp_fm_copy_general,&
      53             :                                               cp_fm_create,&
      54             :                                               cp_fm_get_info,&
      55             :                                               cp_fm_release,&
      56             :                                               cp_fm_set_all,&
      57             :                                               cp_fm_to_fm,&
      58             :                                               cp_fm_type
      59             :    USE distribution_2d_types,           ONLY: distribution_2d_type
      60             :    USE group_dist_types,                ONLY: create_group_dist,&
      61             :                                               get_group_dist,&
      62             :                                               group_dist_d1_type,&
      63             :                                               release_group_dist
      64             :    USE input_constants,                 ONLY: do_eri_gpw,&
      65             :                                               do_eri_mme,&
      66             :                                               do_eri_os,&
      67             :                                               do_potential_coulomb,&
      68             :                                               do_potential_id,&
      69             :                                               do_potential_long,&
      70             :                                               do_potential_truncated
      71             :    USE kinds,                           ONLY: dp
      72             :    USE kpoint_coulomb_2c,               ONLY: build_2c_coulomb_matrix_kp
      73             :    USE kpoint_methods,                  ONLY: kpoint_init_cell_index,&
      74             :                                               rskp_transform
      75             :    USE kpoint_types,                    ONLY: get_kpoint_info,&
      76             :                                               kpoint_type
      77             :    USE libint_2c_3c,                    ONLY: compare_potential_types,&
      78             :                                               libint_potential_type
      79             :    USE machine,                         ONLY: m_flush
      80             :    USE message_passing,                 ONLY: mp_comm_type,&
      81             :                                               mp_para_env_release,&
      82             :                                               mp_para_env_type,&
      83             :                                               mp_request_type
      84             :    USE mp2_eri,                         ONLY: mp2_eri_2c_integrate
      85             :    USE mp2_eri_gpw,                     ONLY: mp2_eri_2c_integrate_gpw
      86             :    USE mp2_types,                       ONLY: integ_mat_buffer_type
      87             :    USE parallel_gemm_api,               ONLY: parallel_gemm
      88             :    USE particle_methods,                ONLY: get_particle_set
      89             :    USE particle_types,                  ONLY: particle_type
      90             :    USE qs_environment_types,            ONLY: get_qs_env,&
      91             :                                               qs_environment_type
      92             :    USE qs_integral_utils,               ONLY: basis_set_list_setup
      93             :    USE qs_interactions,                 ONLY: init_interaction_radii
      94             :    USE qs_kind_types,                   ONLY: get_qs_kind,&
      95             :                                               qs_kind_type
      96             :    USE qs_ks_types,                     ONLY: get_ks_env,&
      97             :                                               set_ks_env
      98             :    USE qs_neighbor_list_types,          ONLY: neighbor_list_set_p_type,&
      99             :                                               release_neighbor_list_sets
     100             :    USE qs_tensors,                      ONLY: build_2c_integrals,&
     101             :                                               build_2c_neighbor_lists
     102             :    USE rpa_communication,               ONLY: communicate_buffer
     103             :    USE rpa_gw_kpoints_util,             ONLY: cp_cfm_power
     104             : 
     105             : !$ USE OMP_LIB, ONLY: omp_get_max_threads, omp_get_thread_num
     106             : #include "./base/base_uses.f90"
     107             : 
     108             :    IMPLICIT NONE
     109             : 
     110             :    PRIVATE
     111             : 
     112             :    CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'mp2_ri_2c'
     113             : 
     114             :    PUBLIC :: get_2c_integrals, trunc_coulomb_for_exchange, RI_2c_integral_mat, &
     115             :              inversion_of_M_and_mult_with_chol_dec_of_V
     116             : 
     117             : CONTAINS
     118             : 
     119             : ! **************************************************************************************************
     120             : !> \brief ...
     121             : !> \param qs_env ...
     122             : !> \param eri_method ...
     123             : !> \param eri_param ...
     124             : !> \param para_env ...
     125             : !> \param para_env_sub ...
     126             : !> \param mp2_memory ...
     127             : !> \param my_Lrows ...
     128             : !> \param my_Vrows ...
     129             : !> \param fm_matrix_PQ ...
     130             : !> \param ngroup ...
     131             : !> \param color_sub ...
     132             : !> \param dimen_RI ...
     133             : !> \param dimen_RI_red reduced RI dimension,  needed if we perform SVD instead of Cholesky
     134             : !> \param kpoints ...
     135             : !> \param my_group_L_size ...
     136             : !> \param my_group_L_start ...
     137             : !> \param my_group_L_end ...
     138             : !> \param gd_array ...
     139             : !> \param calc_PQ_cond_num ...
     140             : !> \param do_svd ...
     141             : !> \param potential ...
     142             : !> \param ri_metric ...
     143             : !> \param fm_matrix_L_kpoints ...
     144             : !> \param fm_matrix_Minv_L_kpoints ...
     145             : !> \param fm_matrix_Minv ...
     146             : !> \param fm_matrix_Minv_Vtrunc_Minv ...
     147             : !> \param do_im_time ...
     148             : !> \param do_kpoints ...
     149             : !> \param mp2_eps_pgf_orb_S ...
     150             : !> \param qs_kind_set ...
     151             : !> \param sab_orb_sub ...
     152             : !> \param calc_forces ...
     153             : !> \param unit_nr ...
     154             : ! **************************************************************************************************
     155         618 :    SUBROUTINE get_2c_integrals(qs_env, eri_method, eri_param, para_env, para_env_sub, mp2_memory, &
     156             :                                my_Lrows, my_Vrows, fm_matrix_PQ, ngroup, color_sub, dimen_RI, dimen_RI_red, &
     157             :                                kpoints, my_group_L_size, my_group_L_start, my_group_L_end, &
     158             :                                gd_array, calc_PQ_cond_num, do_svd, potential, ri_metric, &
     159             :                                fm_matrix_L_kpoints, fm_matrix_Minv_L_kpoints, &
     160             :                                fm_matrix_Minv, fm_matrix_Minv_Vtrunc_Minv, &
     161             :                                do_im_time, do_kpoints, mp2_eps_pgf_orb_S, qs_kind_set, sab_orb_sub, calc_forces, unit_nr)
     162             : 
     163             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     164             :       INTEGER, INTENT(IN)                                :: eri_method
     165             :       TYPE(cp_eri_mme_param), POINTER                    :: eri_param
     166             :       TYPE(mp_para_env_type), POINTER                    :: para_env, para_env_sub
     167             :       REAL(KIND=dp), INTENT(IN)                          :: mp2_memory
     168             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :), &
     169             :          INTENT(OUT)                                     :: my_Lrows, my_Vrows
     170             :       TYPE(cp_fm_type), INTENT(OUT)                      :: fm_matrix_PQ
     171             :       INTEGER, INTENT(IN)                                :: ngroup, color_sub
     172             :       INTEGER, INTENT(OUT)                               :: dimen_RI, dimen_RI_red
     173             :       TYPE(kpoint_type), POINTER                         :: kpoints
     174             :       INTEGER, INTENT(OUT)                               :: my_group_L_size, my_group_L_start, &
     175             :                                                             my_group_L_end
     176             :       TYPE(group_dist_d1_type), INTENT(OUT)              :: gd_array
     177             :       LOGICAL, INTENT(IN)                                :: calc_PQ_cond_num, do_svd
     178             :       TYPE(libint_potential_type)                        :: potential, ri_metric
     179             :       TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:, :)     :: fm_matrix_L_kpoints, &
     180             :                                                             fm_matrix_Minv_L_kpoints, &
     181             :                                                             fm_matrix_Minv, &
     182             :                                                             fm_matrix_Minv_Vtrunc_Minv
     183             :       LOGICAL, INTENT(IN)                                :: do_im_time, do_kpoints
     184             :       REAL(KIND=dp), INTENT(IN)                          :: mp2_eps_pgf_orb_S
     185             :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     186             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
     187             :          POINTER                                         :: sab_orb_sub
     188             :       LOGICAL, INTENT(IN)                                :: calc_forces
     189             :       INTEGER, INTENT(IN)                                :: unit_nr
     190             : 
     191             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'get_2c_integrals'
     192             : 
     193             :       INTEGER                                            :: handle, num_small_eigen
     194             :       REAL(KIND=dp)                                      :: cond_num, eps_pgf_orb_old
     195             :       TYPE(cp_fm_type)                                   :: fm_matrix_L_work, fm_matrix_M_inv_work, &
     196             :                                                             fm_matrix_V
     197             :       TYPE(dft_control_type), POINTER                    :: dft_control
     198             :       TYPE(libint_potential_type)                        :: trunc_coulomb
     199             :       TYPE(mp_para_env_type), POINTER                    :: para_env_L
     200             : 
     201         618 :       CALL timeset(routineN, handle)
     202             : 
     203             :       ! calculate V and store it in fm_matrix_L_work
     204             :       CALL compute_2c_integrals(qs_env, eri_method, eri_param, para_env, para_env_sub, para_env_L, mp2_memory, &
     205             :                                 fm_matrix_L_work, ngroup, color_sub, dimen_RI, &
     206             :                                 my_group_L_size, my_group_L_start, my_group_L_end, &
     207             :                                 gd_array, calc_PQ_cond_num, cond_num, &
     208         618 :                                 num_small_eigen, potential, sab_orb_sub, do_im_time=do_im_time)
     209             : 
     210         618 :       IF (do_im_time .AND. calc_forces) THEN
     211             :          !need a copy of the (P|Q) integrals
     212          50 :          CALL cp_fm_create(fm_matrix_PQ, fm_matrix_L_work%matrix_struct)
     213          50 :          CALL cp_fm_to_fm(fm_matrix_L_work, fm_matrix_PQ)
     214             :       END IF
     215             : 
     216         618 :       dimen_RI_red = dimen_RI
     217             : 
     218         618 :       IF (compare_potential_types(ri_metric, potential) .AND. .NOT. do_im_time) THEN
     219             :          CALL decomp_mat_L(fm_matrix_L_work, do_svd, num_small_eigen, cond_num, .TRUE., gd_array, ngroup, &
     220         448 :                            dimen_RI, dimen_RI_red, para_env)
     221             :       ELSE
     222             : 
     223             :          ! RI-metric matrix (depending on RI metric: Coulomb, overlap or truncated Coulomb)
     224         170 :          IF (do_im_time) THEN
     225         134 :             CALL get_qs_env(qs_env, dft_control=dft_control)
     226             : 
     227             :             ! re-init the radii to be able to generate pair lists with appropriate screening for overlap matrix
     228         134 :             eps_pgf_orb_old = dft_control%qs_control%eps_pgf_orb
     229         134 :             dft_control%qs_control%eps_pgf_orb = mp2_eps_pgf_orb_S
     230         134 :             CALL init_interaction_radii(dft_control%qs_control, qs_kind_set)
     231             : 
     232             :             CALL RI_2c_integral_mat(qs_env, fm_matrix_Minv_L_kpoints, fm_matrix_L_work, dimen_RI, ri_metric, &
     233             :                                     do_kpoints, kpoints, put_mat_KS_env=.TRUE., &
     234         134 :                                     regularization_RI=qs_env%mp2_env%ri_rpa_im_time%regularization_RI)
     235             : 
     236             :             ! re-init the radii to previous values
     237         134 :             dft_control%qs_control%eps_pgf_orb = eps_pgf_orb_old
     238         134 :             CALL init_interaction_radii(dft_control%qs_control, qs_kind_set)
     239             : 
     240             :             ! GPW overlap matrix
     241             :          ELSE
     242             : 
     243          36 :             CALL mp_para_env_release(para_env_L)
     244          36 :             CALL release_group_dist(gd_array)
     245             : 
     246         108 :             ALLOCATE (fm_matrix_Minv_L_kpoints(1, 1))
     247             : 
     248             :             ! Calculate matrix of RI operator (for overlap metric: S), store it in fm_matrix_Minv_L_kpoints
     249             :             CALL compute_2c_integrals(qs_env, eri_method, eri_param, para_env, para_env_sub, para_env_L, mp2_memory, &
     250             :                                       fm_matrix_Minv_L_kpoints(1, 1), ngroup, color_sub, dimen_RI, &
     251             :                                       my_group_L_size, my_group_L_start, my_group_L_end, &
     252             :                                       gd_array, calc_PQ_cond_num, cond_num, &
     253             :                                       num_small_eigen, ri_metric, sab_orb_sub, &
     254          36 :                                       fm_matrix_L_extern=fm_matrix_L_work)
     255             : 
     256             :          END IF
     257             : 
     258         170 :          IF (do_kpoints) THEN
     259             : 
     260             :             ! k-dependent 1/r Coulomb matrix V_PQ(k)
     261          22 :             CALL compute_V_by_lattice_sum(qs_env, fm_matrix_L_kpoints, fm_matrix_Minv_L_kpoints, kpoints)
     262             : 
     263             :             CALL inversion_of_M_and_mult_with_chol_dec_of_V(fm_matrix_Minv_L_kpoints, fm_matrix_L_kpoints, dimen_RI, &
     264          22 :                                                             kpoints, qs_env%mp2_env%ri_rpa_im_time%eps_eigval_S)
     265             : 
     266          22 :             CALL trunc_coulomb_for_exchange(qs_env, trunc_coulomb)
     267             : 
     268             :             ! Gamma-only truncated Coulomb matrix V^tr with cutoff radius = half the unit cell size; for exchange self-energy
     269             :             CALL RI_2c_integral_mat(qs_env, fm_matrix_Minv_Vtrunc_Minv, fm_matrix_L_work, dimen_RI, trunc_coulomb, &
     270          22 :                                     do_kpoints=.FALSE., kpoints=kpoints, put_mat_KS_env=.FALSE., regularization_RI=0.0_dp)
     271             : 
     272             :             ! Gamma-only RI-metric matrix; for computing Gamma-only/MIC self-energy
     273             :             CALL RI_2c_integral_mat(qs_env, fm_matrix_Minv, fm_matrix_L_work, dimen_RI, ri_metric, &
     274          22 :                                     do_kpoints=.FALSE., kpoints=kpoints, put_mat_KS_env=.FALSE., regularization_RI=0.0_dp)
     275             : 
     276             :             CALL Gamma_only_inversion_of_M_and_mult_with_chol_dec_of_Vtrunc(fm_matrix_Minv_Vtrunc_Minv, &
     277          22 :                                                                             fm_matrix_Minv, qs_env)
     278             :          ELSE
     279         148 :             IF (calc_forces .AND. (.NOT. do_im_time)) THEN
     280             :                ! For the gradients, we make a copy of the inverse root of L
     281          12 :                CALL cp_fm_create(fm_matrix_V, fm_matrix_L_work%matrix_struct)
     282          12 :                CALL cp_fm_to_fm(fm_matrix_L_work, fm_matrix_V)
     283             : 
     284             :                CALL decomp_mat_L(fm_matrix_V, do_svd, num_small_eigen, cond_num, .TRUE., gd_array, ngroup, &
     285          12 :                                  dimen_RI, dimen_RI_red, para_env)
     286             :             END IF
     287             : 
     288             :             CALL decomp_mat_L(fm_matrix_L_work, do_svd, num_small_eigen, cond_num, .FALSE., gd_array, ngroup, &
     289         148 :                               dimen_RI, dimen_RI_red, para_env)
     290             : 
     291             :             CALL decomp_mat_L(fm_matrix_Minv_L_kpoints(1, 1), .FALSE., num_small_eigen, cond_num, .TRUE., &
     292         148 :                               gd_array, ngroup, dimen_RI, dimen_RI_red, para_env)
     293             : 
     294         148 :             CALL cp_fm_create(fm_matrix_M_inv_work, fm_matrix_Minv_L_kpoints(1, 1)%matrix_struct)
     295         148 :             CALL cp_fm_set_all(fm_matrix_M_inv_work, 0.0_dp)
     296             : 
     297             :             CALL parallel_gemm('N', 'T', dimen_RI, dimen_RI, dimen_RI, 1.0_dp, fm_matrix_Minv_L_kpoints(1, 1), &
     298         148 :                                fm_matrix_Minv_L_kpoints(1, 1), 0.0_dp, fm_matrix_M_inv_work)
     299             : 
     300         148 :             IF (do_svd) THEN
     301             :                ! We have to reset the size of fm_matrix_Minv_L_kpoints
     302          32 :                CALL reset_size_matrix(fm_matrix_Minv_L_kpoints(1, 1), dimen_RI_red, fm_matrix_L_work%matrix_struct)
     303             : 
     304             :                ! L (=fm_matrix_Minv_L_kpoints) = S^(-1)*chol_dec(V)
     305             :                CALL parallel_gemm('T', 'N', dimen_RI, dimen_RI_red, dimen_RI, 1.0_dp, fm_matrix_M_inv_work, &
     306          32 :                                   fm_matrix_L_work, 0.0_dp, fm_matrix_Minv_L_kpoints(1, 1))
     307             :             ELSE
     308             :                ! L (=fm_matrix_Minv_L_kpoints) = S^(-1)*chol_dec(V)
     309             :                CALL parallel_gemm('T', 'T', dimen_RI, dimen_RI, dimen_RI, 1.0_dp, fm_matrix_M_inv_work, &
     310         116 :                                   fm_matrix_L_work, 0.0_dp, fm_matrix_Minv_L_kpoints(1, 1))
     311             :             END IF
     312             : 
     313             :             ! clean the S_inv matrix
     314         148 :             CALL cp_fm_release(fm_matrix_M_inv_work)
     315             :          END IF
     316             : 
     317         170 :          IF (.NOT. do_im_time) THEN
     318             : 
     319          36 :             CALL cp_fm_to_fm(fm_matrix_Minv_L_kpoints(1, 1), fm_matrix_L_work)
     320          36 :             CALL cp_fm_release(fm_matrix_Minv_L_kpoints)
     321             : 
     322             :          END IF
     323             : 
     324             :       END IF
     325             : 
     326             :       ! If the group distribution changed because of an SVD, we get the new values here
     327         618 :       CALL get_group_dist(gd_array, color_sub, my_group_L_start, my_group_L_end, my_group_L_size)
     328             : 
     329        1102 :       IF (.NOT. do_im_time) THEN
     330         484 :          IF (unit_nr > 0) THEN
     331         242 :             WRITE (UNIT=unit_nr, FMT="(T3,A,T75,i6)") "RI_INFO| Cholesky decomposition group size:", para_env_L%num_pe
     332         242 :             WRITE (UNIT=unit_nr, FMT="(T3,A,T75,i6)") "RI_INFO| Number of groups for auxiliary basis functions", ngroup
     333         242 :             IF (calc_PQ_cond_num .OR. do_svd) THEN
     334             :                WRITE (UNIT=unit_nr, FMT="(T3,A,T67,ES14.5)") &
     335          16 :                   "RI_INFO| Condition number of the (P|Q):", cond_num
     336             :                WRITE (UNIT=unit_nr, FMT="(T3,A,T75,i6)") &
     337          16 :                   "RI_INFO| Number of non-positive Eigenvalues of (P|Q):", num_small_eigen
     338             :             END IF
     339         242 :             CALL m_flush(unit_nr)
     340             :          END IF
     341             : 
     342             :          ! replicate the necessary row of the L^{-1} matrix on each proc
     343         484 :          CALL grep_Lcols(fm_matrix_L_work, my_group_L_start, my_group_L_end, my_group_L_size, my_Lrows)
     344         496 :          IF (calc_forces .AND. .NOT. compare_potential_types(qs_env%mp2_env%ri_metric, &
     345             :                                                              qs_env%mp2_env%potential_parameter)) THEN
     346          12 :             CALL grep_Lcols(fm_matrix_V, my_group_L_start, my_group_L_end, my_group_L_size, my_Vrows)
     347             :          END IF
     348             :       END IF
     349         618 :       CALL cp_fm_release(fm_matrix_L_work)
     350         618 :       IF (calc_forces .AND. .NOT. (do_im_time .OR. compare_potential_types(qs_env%mp2_env%ri_metric, &
     351          12 :                                                                qs_env%mp2_env%potential_parameter))) CALL cp_fm_release(fm_matrix_V)
     352         618 :       CALL mp_para_env_release(para_env_L)
     353             : 
     354         618 :       CALL timestop(handle)
     355             : 
     356         618 :    END SUBROUTINE get_2c_integrals
     357             : 
     358             : ! **************************************************************************************************
     359             : !> \brief ...
     360             : !> \param fm_matrix_L ...
     361             : !> \param do_svd ...
     362             : !> \param num_small_eigen ...
     363             : !> \param cond_num ...
     364             : !> \param do_inversion ...
     365             : !> \param gd_array ...
     366             : !> \param ngroup ...
     367             : !> \param dimen_RI ...
     368             : !> \param dimen_RI_red ...
     369             : !> \param para_env ...
     370             : ! **************************************************************************************************
     371         756 :    SUBROUTINE decomp_mat_L(fm_matrix_L, do_svd, num_small_eigen, cond_num, do_inversion, gd_array, ngroup, &
     372             :                            dimen_RI, dimen_RI_red, para_env)
     373             : 
     374             :       TYPE(cp_fm_type), INTENT(INOUT)                    :: fm_matrix_L
     375             :       LOGICAL, INTENT(IN)                                :: do_svd
     376             :       INTEGER, INTENT(INOUT)                             :: num_small_eigen
     377             :       REAL(KIND=dp), INTENT(INOUT)                       :: cond_num
     378             :       LOGICAL, INTENT(IN)                                :: do_inversion
     379             :       TYPE(group_dist_d1_type), INTENT(INOUT)            :: gd_array
     380             :       INTEGER, INTENT(IN)                                :: ngroup, dimen_RI
     381             :       INTEGER, INTENT(INOUT)                             :: dimen_RI_red
     382             :       TYPE(mp_para_env_type), INTENT(IN)                 :: para_env
     383             : 
     384         756 :       IF (do_svd) THEN
     385          44 :          CALL matrix_root_with_svd(fm_matrix_L, num_small_eigen, cond_num, do_inversion, para_env)
     386             : 
     387          44 :          dimen_RI_red = dimen_RI - num_small_eigen
     388             : 
     389             :          ! We changed the size of fm_matrix_L in matrix_root_with_svd.
     390             :          ! So, we have to get new group sizes
     391          44 :          CALL release_group_dist(gd_array)
     392             : 
     393          44 :          CALL create_group_dist(gd_array, ngroup, dimen_RI_red)
     394             :       ELSE
     395             : 
     396             :          ! calculate Cholesky decomposition L (V=LL^T)
     397         712 :          CALL cholesky_decomp(fm_matrix_L, dimen_RI, do_inversion=do_inversion)
     398             : 
     399         712 :          IF (do_inversion) CALL invert_mat(fm_matrix_L)
     400             :       END IF
     401             : 
     402         756 :    END SUBROUTINE decomp_mat_L
     403             : 
     404             : ! **************************************************************************************************
     405             : !> \brief ...
     406             : !> \param qs_env ...
     407             : !> \param fm_matrix_L_kpoints ...
     408             : !> \param fm_matrix_Minv_L_kpoints ...
     409             : !> \param kpoints ...
     410             : ! **************************************************************************************************
     411          22 :    SUBROUTINE compute_V_by_lattice_sum(qs_env, fm_matrix_L_kpoints, fm_matrix_Minv_L_kpoints, kpoints)
     412             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     413             :       TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:, :)     :: fm_matrix_L_kpoints, &
     414             :                                                             fm_matrix_Minv_L_kpoints
     415             :       TYPE(kpoint_type), POINTER                         :: kpoints
     416             : 
     417             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_V_by_lattice_sum'
     418             : 
     419             :       INTEGER                                            :: handle, i_dim, i_real_imag, ikp, nkp, &
     420             :                                                             nkp_extra, nkp_orig
     421             :       INTEGER, DIMENSION(3)                              :: nkp_grid_orig, periodic
     422          22 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
     423             :       TYPE(cell_type), POINTER                           :: cell
     424          22 :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: matrix_s_RI_aux_transl, matrix_v_RI_kp
     425          22 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
     426          22 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     427             : 
     428          22 :       CALL timeset(routineN, handle)
     429             : 
     430          22 :       NULLIFY (matrix_s_RI_aux_transl, particle_set, cell, qs_kind_set)
     431             : 
     432             :       CALL get_qs_env(qs_env=qs_env, &
     433             :                       matrix_s_RI_aux_kp=matrix_s_RI_aux_transl, &
     434             :                       particle_set=particle_set, &
     435             :                       cell=cell, &
     436             :                       qs_kind_set=qs_kind_set, &
     437          22 :                       atomic_kind_set=atomic_kind_set)
     438             : 
     439             :       ! check that we have a 2n x 2m x 2k mesh to guarantee good convergence
     440          22 :       CALL get_cell(cell=cell, periodic=periodic)
     441          88 :       DO i_dim = 1, 3
     442          88 :          IF (periodic(i_dim) == 1) THEN
     443          40 :             CPASSERT(MODULO(kpoints%nkp_grid(i_dim), 2) == 0)
     444             :          END IF
     445             :       END DO
     446             : 
     447          22 :       nkp = kpoints%nkp
     448             : 
     449        1062 :       ALLOCATE (fm_matrix_L_kpoints(nkp, 2))
     450         498 :       DO ikp = 1, nkp
     451        1450 :          DO i_real_imag = 1, 2
     452             :             CALL cp_fm_create(fm_matrix_L_kpoints(ikp, i_real_imag), &
     453         952 :                               fm_matrix_Minv_L_kpoints(1, i_real_imag)%matrix_struct)
     454        1428 :             CALL cp_fm_set_all(fm_matrix_L_kpoints(ikp, i_real_imag), 0.0_dp)
     455             :          END DO
     456             :       END DO
     457             : 
     458          22 :       CALL allocate_matrix_v_RI_kp(matrix_v_RI_kp, matrix_s_RI_aux_transl, nkp)
     459             : 
     460          22 :       IF (qs_env%mp2_env%ri_rpa_im_time%do_extrapolate_kpoints) THEN
     461             : 
     462          18 :          nkp_orig = qs_env%mp2_env%ri_rpa_im_time%nkp_orig
     463          18 :          nkp_extra = qs_env%mp2_env%ri_rpa_im_time%nkp_extra
     464             : 
     465             :          CALL build_2c_coulomb_matrix_kp(matrix_v_RI_kp, kpoints, basis_type="RI_AUX", &
     466             :                                          cell=cell, particle_set=particle_set, qs_kind_set=qs_kind_set, &
     467             :                                          atomic_kind_set=atomic_kind_set, &
     468             :                                          size_lattice_sum=qs_env%mp2_env%mp2_gpw%size_lattice_sum, &
     469          18 :                                          operator_type=operator_coulomb, ikp_start=1, ikp_end=nkp_orig)
     470             : 
     471          72 :          nkp_grid_orig = kpoints%nkp_grid
     472         144 :          kpoints%nkp_grid(1:3) = qs_env%mp2_env%ri_rpa_im_time%kp_grid_extra(1:3)
     473             : 
     474             :          CALL build_2c_coulomb_matrix_kp(matrix_v_RI_kp, kpoints, basis_type="RI_AUX", &
     475             :                                          cell=cell, particle_set=particle_set, qs_kind_set=qs_kind_set, &
     476             :                                          atomic_kind_set=atomic_kind_set, &
     477             :                                          size_lattice_sum=qs_env%mp2_env%mp2_gpw%size_lattice_sum, &
     478          18 :                                          operator_type=operator_coulomb, ikp_start=nkp_orig + 1, ikp_end=nkp)
     479             : 
     480          72 :          kpoints%nkp_grid = nkp_grid_orig
     481             : 
     482             :       ELSE
     483             : 
     484             :          CALL build_2c_coulomb_matrix_kp(matrix_v_RI_kp, kpoints, basis_type="RI_AUX", &
     485             :                                          cell=cell, particle_set=particle_set, qs_kind_set=qs_kind_set, &
     486             :                                          atomic_kind_set=atomic_kind_set, &
     487             :                                          size_lattice_sum=qs_env%mp2_env%mp2_gpw%size_lattice_sum, &
     488           4 :                                          operator_type=operator_coulomb, ikp_start=1, ikp_end=nkp)
     489             : 
     490             :       END IF
     491             : 
     492         498 :       DO ikp = 1, nkp
     493             : 
     494         476 :          CALL copy_dbcsr_to_fm(matrix_v_RI_kp(ikp, 1)%matrix, fm_matrix_L_kpoints(ikp, 1))
     495         498 :          CALL copy_dbcsr_to_fm(matrix_v_RI_kp(ikp, 2)%matrix, fm_matrix_L_kpoints(ikp, 2))
     496             : 
     497             :       END DO
     498             : 
     499          22 :       CALL dbcsr_deallocate_matrix_set(matrix_v_RI_kp)
     500             : 
     501          22 :       CALL timestop(handle)
     502             : 
     503          22 :    END SUBROUTINE compute_V_by_lattice_sum
     504             : 
     505             : ! **************************************************************************************************
     506             : !> \brief ...
     507             : !> \param matrix_v_RI_kp ...
     508             : !> \param matrix_s_RI_aux_transl ...
     509             : !> \param nkp ...
     510             : ! **************************************************************************************************
     511          22 :    SUBROUTINE allocate_matrix_v_RI_kp(matrix_v_RI_kp, matrix_s_RI_aux_transl, nkp)
     512             : 
     513             :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: matrix_v_RI_kp, matrix_s_RI_aux_transl
     514             :       INTEGER                                            :: nkp
     515             : 
     516             :       INTEGER                                            :: ikp
     517             : 
     518          22 :       NULLIFY (matrix_v_RI_kp)
     519          22 :       CALL dbcsr_allocate_matrix_set(matrix_v_RI_kp, nkp, 2)
     520             : 
     521         498 :       DO ikp = 1, nkp
     522             : 
     523         476 :          ALLOCATE (matrix_v_RI_kp(ikp, 1)%matrix)
     524             :          CALL dbcsr_create(matrix_v_RI_kp(ikp, 1)%matrix, template=matrix_s_RI_aux_transl(1, 1)%matrix, &
     525         476 :                            matrix_type=dbcsr_type_no_symmetry)
     526         476 :          CALL dbcsr_reserve_all_blocks(matrix_v_RI_kp(ikp, 1)%matrix)
     527         476 :          CALL dbcsr_set(matrix_v_RI_kp(ikp, 1)%matrix, 0.0_dp)
     528             : 
     529         476 :          ALLOCATE (matrix_v_RI_kp(ikp, 2)%matrix)
     530             :          CALL dbcsr_create(matrix_v_RI_kp(ikp, 2)%matrix, template=matrix_s_RI_aux_transl(1, 1)%matrix, &
     531         476 :                            matrix_type=dbcsr_type_no_symmetry)
     532         476 :          CALL dbcsr_reserve_all_blocks(matrix_v_RI_kp(ikp, 2)%matrix)
     533         498 :          CALL dbcsr_set(matrix_v_RI_kp(ikp, 2)%matrix, 0.0_dp)
     534             : 
     535             :       END DO
     536             : 
     537          22 :    END SUBROUTINE allocate_matrix_v_RI_kp
     538             : 
     539             : ! **************************************************************************************************
     540             : !> \brief ...
     541             : !> \param qs_env ...
     542             : !> \param fm_matrix_Minv_L_kpoints ...
     543             : !> \param fm_matrix_L ...
     544             : !> \param dimen_RI ...
     545             : !> \param ri_metric ...
     546             : !> \param do_kpoints ...
     547             : !> \param kpoints ...
     548             : !> \param put_mat_KS_env ...
     549             : !> \param regularization_RI ...
     550             : !> \param ikp_ext ...
     551             : !> \param do_build_cell_index ...
     552             : ! **************************************************************************************************
     553         468 :    SUBROUTINE RI_2c_integral_mat(qs_env, fm_matrix_Minv_L_kpoints, fm_matrix_L, dimen_RI, ri_metric, &
     554             :                                  do_kpoints, kpoints, put_mat_KS_env, regularization_RI, ikp_ext, &
     555             :                                  do_build_cell_index)
     556             : 
     557             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     558             :       TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:, :)     :: fm_matrix_Minv_L_kpoints
     559             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_matrix_L
     560             :       INTEGER, INTENT(IN)                                :: dimen_RI
     561             :       TYPE(libint_potential_type)                        :: ri_metric
     562             :       LOGICAL, INTENT(IN)                                :: do_kpoints
     563             :       TYPE(kpoint_type), OPTIONAL, POINTER               :: kpoints
     564             :       LOGICAL, OPTIONAL                                  :: put_mat_KS_env
     565             :       REAL(KIND=dp), OPTIONAL                            :: regularization_RI
     566             :       INTEGER, OPTIONAL                                  :: ikp_ext
     567             :       LOGICAL, OPTIONAL                                  :: do_build_cell_index
     568             : 
     569             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'RI_2c_integral_mat'
     570             : 
     571             :       INTEGER                                            :: handle, i_real_imag, i_size, ikp, &
     572             :                                                             ikp_for_xkp, img, n_real_imag, natom, &
     573             :                                                             nimg, nkind, nkp
     574         468 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: sizes_RI
     575         468 :       INTEGER, DIMENSION(:), POINTER                     :: col_bsize, row_bsize
     576         468 :       INTEGER, DIMENSION(:, :, :), POINTER               :: cell_to_index
     577             :       LOGICAL                                            :: my_do_build_cell_index, my_put_mat_KS_env
     578             :       REAL(KIND=dp)                                      :: my_regularization_RI
     579         468 :       REAL(KIND=dp), DIMENSION(:, :), POINTER            :: xkp
     580             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env
     581             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
     582             :       TYPE(cp_fm_type)                                   :: fm_matrix_S_global
     583             :       TYPE(dbcsr_distribution_type)                      :: dbcsr_dist
     584         468 :       TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER       :: matrix_s_RI_aux_transl
     585         468 :       TYPE(dbcsr_type), ALLOCATABLE, DIMENSION(:)        :: mat_2c
     586             :       TYPE(dbcsr_type), POINTER                          :: cmatrix, matrix_s_RI_aux_desymm, &
     587             :                                                             rmatrix, tmpmat
     588             :       TYPE(dft_control_type), POINTER                    :: dft_control
     589             :       TYPE(distribution_2d_type), POINTER                :: dist_2d
     590         468 :       TYPE(gto_basis_set_p_type), DIMENSION(:), POINTER  :: basis_set_RI
     591             :       TYPE(mp_para_env_type), POINTER                    :: para_env
     592             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
     593         468 :          POINTER                                         :: sab_RI
     594         468 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
     595         468 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     596             : 
     597         468 :       CALL timeset(routineN, handle)
     598             : 
     599         468 :       NULLIFY (sab_RI, matrix_s_RI_aux_transl, dist_2d)
     600             : 
     601         468 :       IF (PRESENT(regularization_RI)) THEN
     602         438 :          my_regularization_RI = regularization_RI
     603             :       ELSE
     604          30 :          my_regularization_RI = 0.0_dp
     605             :       END IF
     606             : 
     607         468 :       IF (PRESENT(put_mat_KS_env)) THEN
     608         178 :          my_put_mat_KS_env = put_mat_KS_env
     609             :       ELSE
     610             :          my_put_mat_KS_env = .FALSE.
     611             :       END IF
     612             : 
     613         468 :       IF (PRESENT(do_build_cell_index)) THEN
     614         260 :          my_do_build_cell_index = do_build_cell_index
     615             :       ELSE
     616             :          my_do_build_cell_index = .FALSE.
     617             :       END IF
     618             : 
     619             :       CALL get_qs_env(qs_env=qs_env, &
     620             :                       para_env=para_env, &
     621             :                       blacs_env=blacs_env, &
     622             :                       nkind=nkind, &
     623             :                       distribution_2d=dist_2d, &
     624             :                       qs_kind_set=qs_kind_set, &
     625             :                       particle_set=particle_set, &
     626             :                       dft_control=dft_control, &
     627         468 :                       natom=natom)
     628             : 
     629        1404 :       ALLOCATE (sizes_RI(natom))
     630        2328 :       ALLOCATE (basis_set_RI(nkind))
     631             : 
     632         468 :       CALL basis_set_list_setup(basis_set_RI, 'RI_AUX', qs_kind_set)
     633         468 :       CALL get_particle_set(particle_set, qs_kind_set, nsgf=sizes_RI, basis=basis_set_RI)
     634             : 
     635             :       CALL build_2c_neighbor_lists(sab_RI, basis_set_RI, basis_set_RI, ri_metric, "RPA_2c_nl_RI", qs_env, &
     636         468 :                                    sym_ij=.TRUE., dist_2d=dist_2d)
     637             : 
     638         468 :       CALL cp_dbcsr_dist2d_to_dist(dist_2d, dbcsr_dist)
     639        1404 :       ALLOCATE (row_bsize(SIZE(sizes_RI)))
     640        1404 :       ALLOCATE (col_bsize(SIZE(sizes_RI)))
     641        1716 :       row_bsize(:) = sizes_RI
     642        1716 :       col_bsize(:) = sizes_RI
     643             : 
     644         468 :       IF (do_kpoints) THEN
     645         282 :          CPASSERT(PRESENT(kpoints))
     646         282 :          IF (my_do_build_cell_index) THEN
     647          10 :             CALL kpoint_init_cell_index(kpoints, sab_RI, para_env, dft_control)
     648             :          END IF
     649             :          CALL get_kpoint_info(kpoints, nkp=nkp, xkp=xkp, &
     650         282 :                               cell_to_index=cell_to_index)
     651         282 :          n_real_imag = 2
     652         282 :          nimg = dft_control%nimages
     653             :       ELSE
     654         186 :          nkp = 1
     655         186 :          n_real_imag = 1
     656         186 :          nimg = 1
     657             :       END IF
     658             : 
     659        2990 :       ALLOCATE (mat_2c(nimg))
     660             :       CALL dbcsr_create(mat_2c(1), "(RI|RI)", dbcsr_dist, dbcsr_type_symmetric, &
     661         468 :                         row_bsize, col_bsize)
     662         468 :       DEALLOCATE (row_bsize, col_bsize)
     663             : 
     664        1586 :       DO img = 2, nimg
     665        1586 :          CALL dbcsr_create(mat_2c(img), template=mat_2c(1))
     666             :       END DO
     667             : 
     668             :       CALL build_2c_integrals(mat_2c, 0.0_dp, qs_env, sab_RI, basis_set_RI, basis_set_RI, &
     669             :                               ri_metric, do_kpoints=do_kpoints, ext_kpoints=kpoints, &
     670         468 :                               regularization_RI=my_regularization_RI)
     671             : 
     672         468 :       CALL dbcsr_distribution_release(dbcsr_dist)
     673         468 :       DEALLOCATE (basis_set_RI)
     674             : 
     675         468 :       IF (my_put_mat_KS_env) THEN
     676         134 :          CALL get_ks_env(qs_env%ks_env, matrix_s_RI_aux_kp=matrix_s_RI_aux_transl)
     677         134 :          IF (ASSOCIATED(matrix_s_RI_aux_transl)) CALL dbcsr_deallocate_matrix_set(matrix_s_RI_aux_transl)
     678             :       END IF
     679         468 :       CALL dbcsr_allocate_matrix_set(matrix_s_RI_aux_transl, 1, nimg)
     680        2054 :       DO img = 1, nimg
     681        1586 :          ALLOCATE (matrix_s_RI_aux_transl(1, img)%matrix)
     682        1586 :          CALL dbcsr_copy(matrix_s_RI_aux_transl(1, img)%matrix, mat_2c(img))
     683        2054 :          CALL dbcsr_release(mat_2c(img))
     684             :       END DO
     685             : 
     686         468 :       IF (my_put_mat_KS_env) THEN
     687         134 :          CALL set_ks_env(qs_env%ks_env, matrix_s_RI_aux_kp=matrix_s_RI_aux_transl)
     688             :       END IF
     689             : 
     690         468 :       IF (PRESENT(ikp_ext)) nkp = 1
     691             : 
     692        4280 :       ALLOCATE (fm_matrix_Minv_L_kpoints(nkp, n_real_imag))
     693        1390 :       DO i_size = 1, nkp
     694        3048 :          DO i_real_imag = 1, n_real_imag
     695        1658 :             CALL cp_fm_create(fm_matrix_Minv_L_kpoints(i_size, i_real_imag), fm_matrix_L%matrix_struct)
     696        2580 :             CALL cp_fm_set_all(fm_matrix_Minv_L_kpoints(i_size, i_real_imag), 0.0_dp)
     697             :          END DO
     698             :       END DO
     699             : 
     700         468 :       NULLIFY (fm_struct)
     701             :       CALL cp_fm_struct_create(fm_struct, context=blacs_env, nrow_global=dimen_RI, &
     702         468 :                                ncol_global=dimen_RI, para_env=para_env)
     703             : 
     704         468 :       CALL cp_fm_create(fm_matrix_S_global, fm_struct)
     705         468 :       CALL cp_fm_set_all(fm_matrix_S_global, 0.0_dp)
     706             : 
     707         468 :       IF (do_kpoints) THEN
     708             : 
     709         282 :          ALLOCATE (rmatrix, cmatrix, tmpmat)
     710             :          CALL dbcsr_create(rmatrix, template=matrix_s_RI_aux_transl(1, 1)%matrix, &
     711         282 :                            matrix_type=dbcsr_type_symmetric)
     712             :          CALL dbcsr_create(cmatrix, template=matrix_s_RI_aux_transl(1, 1)%matrix, &
     713         282 :                            matrix_type=dbcsr_type_antisymmetric)
     714             :          CALL dbcsr_create(tmpmat, template=matrix_s_RI_aux_transl(1, 1)%matrix, &
     715         282 :                            matrix_type=dbcsr_type_no_symmetry)
     716         282 :          CALL cp_dbcsr_alloc_block_from_nbl(rmatrix, sab_RI)
     717         282 :          CALL cp_dbcsr_alloc_block_from_nbl(cmatrix, sab_RI)
     718             : 
     719        1018 :          DO ikp = 1, nkp
     720             : 
     721             :             ! s matrix is not spin dependent, double the work
     722         736 :             CALL dbcsr_set(rmatrix, 0.0_dp)
     723         736 :             CALL dbcsr_set(cmatrix, 0.0_dp)
     724             : 
     725         736 :             IF (PRESENT(ikp_ext)) THEN
     726         260 :                ikp_for_xkp = ikp_ext
     727             :             ELSE
     728             :                ikp_for_xkp = ikp
     729             :             END IF
     730             : 
     731             :             CALL rskp_transform(rmatrix=rmatrix, cmatrix=cmatrix, rsmat=matrix_s_RI_aux_transl, ispin=1, &
     732         736 :                                 xkp=xkp(1:3, ikp_for_xkp), cell_to_index=cell_to_index, sab_nl=sab_RI)
     733             : 
     734         736 :             CALL dbcsr_set(tmpmat, 0.0_dp)
     735         736 :             CALL dbcsr_desymmetrize(rmatrix, tmpmat)
     736             : 
     737         736 :             CALL cp_fm_set_all(fm_matrix_S_global, 0.0_dp)
     738         736 :             CALL copy_dbcsr_to_fm(tmpmat, fm_matrix_S_global)
     739         736 :             CALL cp_fm_copy_general(fm_matrix_S_global, fm_matrix_Minv_L_kpoints(ikp, 1), para_env)
     740             : 
     741         736 :             CALL dbcsr_set(tmpmat, 0.0_dp)
     742         736 :             CALL dbcsr_desymmetrize(cmatrix, tmpmat)
     743             : 
     744         736 :             CALL cp_fm_set_all(fm_matrix_S_global, 0.0_dp)
     745         736 :             CALL copy_dbcsr_to_fm(tmpmat, fm_matrix_S_global)
     746        1018 :             CALL cp_fm_copy_general(fm_matrix_S_global, fm_matrix_Minv_L_kpoints(ikp, 2), para_env)
     747             : 
     748             :          END DO
     749             : 
     750         282 :          CALL dbcsr_deallocate_matrix(rmatrix)
     751         282 :          CALL dbcsr_deallocate_matrix(cmatrix)
     752         282 :          CALL dbcsr_deallocate_matrix(tmpmat)
     753             : 
     754             :       ELSE
     755             : 
     756             :          NULLIFY (matrix_s_RI_aux_desymm)
     757         186 :          ALLOCATE (matrix_s_RI_aux_desymm)
     758             :          CALL dbcsr_create(matrix_s_RI_aux_desymm, template=matrix_s_RI_aux_transl(1, 1)%matrix, &
     759         186 :                            name='S_RI non_symm', matrix_type=dbcsr_type_no_symmetry)
     760             : 
     761         186 :          CALL dbcsr_desymmetrize(matrix_s_RI_aux_transl(1, 1)%matrix, matrix_s_RI_aux_desymm)
     762             : 
     763         186 :          CALL copy_dbcsr_to_fm(matrix_s_RI_aux_desymm, fm_matrix_S_global)
     764             : 
     765         186 :          CALL cp_fm_copy_general(fm_matrix_S_global, fm_matrix_Minv_L_kpoints(1, 1), para_env)
     766             : 
     767         186 :          CALL dbcsr_deallocate_matrix(matrix_s_RI_aux_desymm)
     768             : 
     769             :       END IF
     770             : 
     771         468 :       CALL release_neighbor_list_sets(sab_RI)
     772             : 
     773         468 :       CALL cp_fm_struct_release(fm_struct)
     774             : 
     775         468 :       CALL cp_fm_release(fm_matrix_S_global)
     776             : 
     777         468 :       IF (.NOT. my_put_mat_KS_env) THEN
     778         334 :          CALL dbcsr_deallocate_matrix_set(matrix_s_RI_aux_transl)
     779             :       END IF
     780             : 
     781         468 :       CALL timestop(handle)
     782             : 
     783        1872 :    END SUBROUTINE RI_2c_integral_mat
     784             : 
     785             : ! **************************************************************************************************
     786             : !> \brief ...
     787             : !> \param qs_env ...
     788             : !> \param eri_method ...
     789             : !> \param eri_param ...
     790             : !> \param para_env ...
     791             : !> \param para_env_sub ...
     792             : !> \param para_env_L ...
     793             : !> \param mp2_memory ...
     794             : !> \param fm_matrix_L ...
     795             : !> \param ngroup ...
     796             : !> \param color_sub ...
     797             : !> \param dimen_RI ...
     798             : !> \param my_group_L_size ...
     799             : !> \param my_group_L_start ...
     800             : !> \param my_group_L_end ...
     801             : !> \param gd_array ...
     802             : !> \param calc_PQ_cond_num ...
     803             : !> \param cond_num ...
     804             : !> \param num_small_eigen ...
     805             : !> \param potential ...
     806             : !> \param sab_orb_sub ...
     807             : !> \param do_im_time ...
     808             : !> \param fm_matrix_L_extern ...
     809             : ! **************************************************************************************************
     810         654 :    SUBROUTINE compute_2c_integrals(qs_env, eri_method, eri_param, para_env, para_env_sub, para_env_L, mp2_memory, &
     811             :                                    fm_matrix_L, ngroup, color_sub, dimen_RI, &
     812             :                                    my_group_L_size, my_group_L_start, my_group_L_end, &
     813             :                                    gd_array, calc_PQ_cond_num, cond_num, num_small_eigen, potential, &
     814             :                                    sab_orb_sub, do_im_time, fm_matrix_L_extern)
     815             : 
     816             :       TYPE(qs_environment_type), POINTER                 :: qs_env
     817             :       INTEGER, INTENT(IN)                                :: eri_method
     818             :       TYPE(cp_eri_mme_param), POINTER                    :: eri_param
     819             :       TYPE(mp_para_env_type), INTENT(IN)                 :: para_env
     820             :       TYPE(mp_para_env_type), INTENT(IN), POINTER        :: para_env_sub
     821             :       TYPE(mp_para_env_type), INTENT(OUT), POINTER       :: para_env_L
     822             :       REAL(KIND=dp), INTENT(IN)                          :: mp2_memory
     823             :       TYPE(cp_fm_type), INTENT(OUT)                      :: fm_matrix_L
     824             :       INTEGER, INTENT(IN)                                :: ngroup, color_sub
     825             :       INTEGER, INTENT(OUT)                               :: dimen_RI, my_group_L_size, &
     826             :                                                             my_group_L_start, my_group_L_end
     827             :       TYPE(group_dist_d1_type), INTENT(OUT)              :: gd_array
     828             :       LOGICAL, INTENT(IN)                                :: calc_PQ_cond_num
     829             :       REAL(KIND=dp), INTENT(OUT)                         :: cond_num
     830             :       INTEGER, INTENT(OUT)                               :: num_small_eigen
     831             :       TYPE(libint_potential_type), INTENT(IN)            :: potential
     832             :       TYPE(neighbor_list_set_p_type), DIMENSION(:), &
     833             :          POINTER                                         :: sab_orb_sub
     834             :       LOGICAL, INTENT(IN), OPTIONAL                      :: do_im_time
     835             :       TYPE(cp_fm_type), INTENT(IN), OPTIONAL             :: fm_matrix_L_extern
     836             : 
     837             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_2c_integrals'
     838             : 
     839             :       INTEGER :: best_group_size, color_L, group_size, handle, handle2, i_global, iatom, iiB, &
     840             :          ikind, iproc, j_global, jjB, natom, ncol_local, nkind, nrow_local, nsgf, potential_type, &
     841             :          proc_receive, proc_receive_static, proc_send_static, proc_shift, rec_L_end, rec_L_size, &
     842             :          rec_L_start, strat_group_size
     843         654 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: kind_of
     844         654 :       INTEGER, DIMENSION(:), POINTER                     :: col_indices, row_indices
     845             :       LOGICAL                                            :: my_do_im_time
     846             :       REAL(KIND=dp)                                      :: min_mem_for_QK
     847         654 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: egen_L
     848         654 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: L_external_col, L_local_col
     849         654 :       TYPE(atomic_kind_type), DIMENSION(:), POINTER      :: atomic_kind_set
     850             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env_L
     851             :       TYPE(cp_fm_type)                                   :: fm_matrix_L_diag
     852         654 :       TYPE(group_dist_d1_type)                           :: gd_sub_array
     853             :       TYPE(gto_basis_set_type), POINTER                  :: basis_set_a
     854         654 :       TYPE(particle_type), DIMENSION(:), POINTER         :: particle_set
     855         654 :       TYPE(qs_kind_type), DIMENSION(:), POINTER          :: qs_kind_set
     856             : 
     857         654 :       CALL timeset(routineN, handle)
     858             : 
     859         654 :       my_do_im_time = .FALSE.
     860         654 :       IF (PRESENT(do_im_time)) THEN
     861         618 :          my_do_im_time = do_im_time
     862             :       END IF
     863             : 
     864             :       ! get stuff
     865             :       CALL get_qs_env(qs_env, atomic_kind_set=atomic_kind_set, qs_kind_set=qs_kind_set, &
     866         654 :                       particle_set=particle_set)
     867             : 
     868         654 :       nkind = SIZE(qs_kind_set)
     869         654 :       natom = SIZE(particle_set)
     870             : 
     871         654 :       CALL get_atomic_kind_set(atomic_kind_set, kind_of=kind_of)
     872             : 
     873        1858 :       DO ikind = 1, nkind
     874        1204 :          CALL get_qs_kind(qs_kind=qs_kind_set(ikind), basis_set=basis_set_a, basis_type="RI_AUX")
     875        1858 :          CPASSERT(ASSOCIATED(basis_set_a))
     876             :       END DO
     877             : 
     878         654 :       dimen_RI = 0
     879        2580 :       DO iatom = 1, natom
     880        1926 :          ikind = kind_of(iatom)
     881        1926 :          CALL get_qs_kind(qs_kind=qs_kind_set(ikind), nsgf=nsgf, basis_type="RI_AUX")
     882        2580 :          dimen_RI = dimen_RI + nsgf
     883             :       END DO
     884             : 
     885             :       ! check that very small systems are not running on too many processes
     886         654 :       IF (dimen_RI < ngroup) THEN
     887             :          CALL cp_abort(__LOCATION__, "Product of block size and number "// &
     888           0 :                        "of RI functions should not exceed total number of processes")
     889             :       END IF
     890             : 
     891         654 :       CALL create_group_dist(gd_array, ngroup, dimen_RI)
     892             : 
     893         654 :       CALL get_group_dist(gd_array, color_sub, my_group_L_start, my_group_L_end, my_group_L_size)
     894             : 
     895         654 :       CALL timeset(routineN//"_loop_lm", handle2)
     896             : 
     897        2616 :       ALLOCATE (L_local_col(dimen_RI, my_group_L_size))
     898     2256612 :       L_local_col = 0.0_dp
     899             : 
     900         654 :       potential_type = potential%potential_type
     901             : 
     902             :       IF ((eri_method .EQ. do_eri_mme .OR. eri_method .EQ. do_eri_os) &
     903         654 :           .AND. potential_type .EQ. do_potential_coulomb .OR. &
     904             :           (eri_method .EQ. do_eri_mme .AND. potential_type .EQ. do_potential_long)) THEN
     905             : 
     906             :          CALL mp2_eri_2c_integrate(eri_param, potential, para_env_sub, qs_env, &
     907             :                                    basis_type_a="RI_AUX", basis_type_b="RI_AUX", &
     908             :                                    hab=L_local_col, first_b=my_group_L_start, last_b=my_group_L_end, &
     909         280 :                                    eri_method=eri_method)
     910             : 
     911             :       ELSEIF (eri_method .EQ. do_eri_gpw .OR. &
     912             :               (potential_type == do_potential_long .AND. qs_env%mp2_env%eri_method == do_eri_os) &
     913         374 :               .OR. (potential_type == do_potential_id .AND. qs_env%mp2_env%eri_method == do_eri_mme)) THEN
     914             : 
     915             :          CALL mp2_eri_2c_integrate_gpw(qs_env, para_env_sub, my_group_L_start, my_group_L_end, &
     916         374 :                                        natom, potential, sab_orb_sub, L_local_col, kind_of)
     917             : 
     918             :       ELSE
     919           0 :          CPABORT("unknown ERI method")
     920             :       END IF
     921             : 
     922         654 :       CALL timestop(handle2)
     923             : 
     924             :       ! split the total number of proc in a subgroup of the size of ~1/10 of the
     925             :       ! total num of proc
     926         654 :       best_group_size = para_env%num_pe
     927             : 
     928         654 :       strat_group_size = MAX(1, para_env%num_pe/10)
     929             : 
     930         654 :       min_mem_for_QK = REAL(dimen_RI, KIND=dp)*dimen_RI*3.0_dp*8.0_dp/1024_dp/1024_dp
     931             : 
     932         654 :       group_size = strat_group_size - 1
     933         688 :       DO iproc = strat_group_size, para_env%num_pe
     934         688 :          group_size = group_size + 1
     935             :          ! check that group_size is a multiple of sub_group_size and a divisor of
     936             :          ! the total num of proc
     937         688 :          IF (MOD(para_env%num_pe, group_size) /= 0 .OR. MOD(group_size, para_env_sub%num_pe) /= 0) CYCLE
     938             : 
     939             :          ! check for memory
     940         654 :          IF (REAL(group_size, KIND=dp)*mp2_memory < min_mem_for_QK) CYCLE
     941             : 
     942             :          best_group_size = group_size
     943          34 :          EXIT
     944             :       END DO
     945             : 
     946         654 :       IF (my_do_im_time) THEN
     947             :          ! para_env_L is the para_env for im. time to avoid bug
     948         134 :          best_group_size = para_env%num_pe
     949             :       END IF
     950             : 
     951             :       ! create the L group
     952         654 :       color_L = para_env%mepos/best_group_size
     953         654 :       ALLOCATE (para_env_L)
     954         654 :       CALL para_env_L%from_split(para_env, color_L)
     955             : 
     956             :       ! create the blacs_L
     957         654 :       NULLIFY (blacs_env_L)
     958         654 :       CALL cp_blacs_env_create(blacs_env=blacs_env_L, para_env=para_env_L)
     959             : 
     960             :       ! create the full matrix L defined in the L group
     961         654 :       CALL create_matrix_L(fm_matrix_L, blacs_env_L, dimen_RI, para_env_L, "fm_matrix_L", fm_matrix_L_extern)
     962             : 
     963         654 :       IF (my_do_im_time .AND. para_env%num_pe > 1) THEN
     964             : 
     965             :          CALL fill_fm_L_from_L_loc_non_blocking(fm_matrix_L, L_local_col, para_env, &
     966             :                                                 my_group_L_start, my_group_L_end, &
     967         134 :                                                 dimen_RI)
     968             : 
     969             :       ELSE
     970         520 :          BLOCK
     971             :             TYPE(mp_comm_type) :: comm_exchange
     972             : 
     973         520 :             CALL comm_exchange%from_split(para_env_L, para_env_sub%mepos)
     974             : 
     975             :             CALL create_group_dist(gd_sub_array, my_group_L_start, &
     976         520 :                                    my_group_L_end, my_group_L_size, comm_exchange)
     977             : 
     978             :             CALL cp_fm_get_info(matrix=fm_matrix_L, &
     979             :                                 nrow_local=nrow_local, &
     980             :                                 ncol_local=ncol_local, &
     981             :                                 row_indices=row_indices, &
     982         520 :                                 col_indices=col_indices)
     983             : 
     984       39392 :             DO jjB = 1, ncol_local
     985       38872 :                j_global = col_indices(jjB)
     986       39392 :                IF (j_global >= my_group_L_start .AND. j_global <= my_group_L_end) THEN
     987     1602166 :                   DO iiB = 1, nrow_local
     988     1581610 :                      i_global = row_indices(iiB)
     989     1602166 :                      fm_matrix_L%local_data(iiB, jjB) = L_local_col(i_global, j_global - my_group_L_start + 1)
     990             :                   END DO
     991             :                END IF
     992             :             END DO
     993             : 
     994         520 :             proc_send_static = MODULO(comm_exchange%mepos + 1, comm_exchange%num_pe)
     995         520 :             proc_receive_static = MODULO(comm_exchange%mepos - 1, comm_exchange%num_pe)
     996             : 
     997         520 :             DO proc_shift = 1, comm_exchange%num_pe - 1
     998           0 :                proc_receive = MODULO(comm_exchange%mepos - proc_shift, comm_exchange%num_pe)
     999             : 
    1000           0 :                CALL get_group_dist(gd_sub_array, proc_receive, rec_L_start, rec_L_end, rec_L_size)
    1001             : 
    1002           0 :                ALLOCATE (L_external_col(dimen_RI, rec_L_size))
    1003           0 :                L_external_col = 0.0_dp
    1004             : 
    1005           0 :                CALL comm_exchange%sendrecv(L_local_col, proc_send_static, L_external_col, proc_receive_static)
    1006             : 
    1007           0 :                DO jjB = 1, ncol_local
    1008           0 :                   j_global = col_indices(jjB)
    1009           0 :                   IF (j_global >= rec_L_start .AND. j_global <= rec_L_end) THEN
    1010           0 :                      DO iiB = 1, nrow_local
    1011           0 :                         i_global = row_indices(iiB)
    1012           0 :                         fm_matrix_L%local_data(iiB, jjB) = L_external_col(i_global, j_global - rec_L_start + 1)
    1013             :                      END DO
    1014             :                   END IF
    1015             :                END DO
    1016             : 
    1017         520 :                CALL MOVE_ALLOC(L_external_col, L_local_col)
    1018             :             END DO
    1019             : 
    1020         520 :             CALL release_group_dist(gd_sub_array)
    1021        1040 :             CALL comm_exchange%free()
    1022             :          END BLOCK
    1023             :       END IF
    1024             : 
    1025         654 :       DEALLOCATE (L_local_col)
    1026             : 
    1027             :       ! create the new group for the sum of the local data over all processes
    1028             :       BLOCK
    1029             :          TYPE(mp_comm_type) :: comm_exchange
    1030         654 :          comm_exchange = fm_matrix_L%matrix_struct%context%interconnect(para_env)
    1031         654 :          CALL comm_exchange%sum(fm_matrix_L%local_data)
    1032        1308 :          CALL comm_exchange%free()
    1033             :       END BLOCK
    1034             : 
    1035         654 :       cond_num = 1.0_dp
    1036         654 :       num_small_eigen = 0
    1037         654 :       IF (calc_PQ_cond_num) THEN
    1038             :          ! calculate the condition number of the (P|Q) matrix
    1039             :          ! create a copy of the matrix
    1040             : 
    1041           0 :          CALL create_matrix_L(fm_matrix_L_diag, blacs_env_L, dimen_RI, para_env_L, "fm_matrix_L_diag", fm_matrix_L_extern)
    1042             : 
    1043           0 :          CALL cp_fm_to_fm(source=fm_matrix_L, destination=fm_matrix_L_diag)
    1044             : 
    1045           0 :          ALLOCATE (egen_L(dimen_RI))
    1046             : 
    1047           0 :          egen_L = 0.0_dp
    1048           0 :          CALL cp_fm_syevx(matrix=fm_matrix_L_diag, eigenvalues=egen_L)
    1049             : 
    1050           0 :          num_small_eigen = 0
    1051           0 :          DO iiB = 1, dimen_RI
    1052           0 :             IF (ABS(egen_L(iiB)) < 0.001_dp) num_small_eigen = num_small_eigen + 1
    1053             :          END DO
    1054             : 
    1055           0 :          cond_num = MAXVAL(ABS(egen_L))/MINVAL(ABS(egen_L))
    1056             : 
    1057           0 :          CALL cp_fm_release(fm_matrix_L_diag)
    1058             : 
    1059           0 :          DEALLOCATE (egen_L)
    1060             :       END IF
    1061             : 
    1062             :       ! release blacs_env
    1063         654 :       CALL cp_blacs_env_release(blacs_env_L)
    1064             : 
    1065         654 :       CALL timestop(handle)
    1066             : 
    1067        3270 :    END SUBROUTINE compute_2c_integrals
    1068             : 
    1069             : ! **************************************************************************************************
    1070             : !> \brief ...
    1071             : !> \param matrix ...
    1072             : !> \param num_small_evals ...
    1073             : !> \param cond_num ...
    1074             : !> \param do_inversion ...
    1075             : !> \param para_env ...
    1076             : ! **************************************************************************************************
    1077          44 :    SUBROUTINE matrix_root_with_svd(matrix, num_small_evals, cond_num, do_inversion, para_env)
    1078             :       TYPE(cp_fm_type), INTENT(INOUT)                    :: matrix
    1079             :       INTEGER, INTENT(OUT)                               :: num_small_evals
    1080             :       REAL(KIND=dp), INTENT(OUT)                         :: cond_num
    1081             :       LOGICAL, INTENT(IN)                                :: do_inversion
    1082             :       TYPE(mp_para_env_type), INTENT(IN)                 :: para_env
    1083             : 
    1084             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'matrix_root_with_svd'
    1085             : 
    1086             :       INTEGER                                            :: group_size_L, handle, ii, needed_evals, &
    1087             :                                                             nrow, pos_max(1)
    1088          44 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: num_eval
    1089             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:)           :: evals
    1090             :       TYPE(cp_fm_type)                                   :: evecs
    1091             :       TYPE(mp_comm_type)                                 :: comm_exchange
    1092             : 
    1093          44 :       CALL timeset(routineN, handle)
    1094             : 
    1095             :       ! Create arrays carrying eigenvalues and eigenvectors later
    1096          44 :       CALL cp_fm_get_info(matrix=matrix, nrow_global=nrow)
    1097             : 
    1098         132 :       ALLOCATE (evals(nrow))
    1099        3724 :       evals = 0
    1100             : 
    1101          44 :       CALL cp_fm_create(evecs, matrix%matrix_struct)
    1102             : 
    1103             :       ! Perform the EVD (=SVD of a positive semidefinite matrix)
    1104          44 :       CALL choose_eigv_solver(matrix, evecs, evals)
    1105             : 
    1106             :       ! Determine the number of neglectable eigenvalues assuming that the eigenvalues are in ascending order
    1107          44 :       num_small_evals = 0
    1108         202 :       DO ii = 1, nrow
    1109         202 :          IF (evals(ii) > 0.0_dp) THEN
    1110          44 :             num_small_evals = ii - 1
    1111          44 :             EXIT
    1112             :          END IF
    1113             :       END DO
    1114          44 :       needed_evals = nrow - num_small_evals
    1115             : 
    1116             :       ! Get the condition number w.r.t. considered eigenvalues
    1117          44 :       cond_num = evals(nrow)/evals(num_small_evals + 1)
    1118             : 
    1119             :       ! Determine the eigenvalues of the request matrix root or its inverse
    1120         202 :       evals(1:num_small_evals) = 0.0_dp
    1121          44 :       IF (do_inversion) THEN
    1122        1008 :          evals(num_small_evals + 1:nrow) = 1.0_dp/SQRT(evals(num_small_evals + 1:nrow))
    1123             :       ELSE
    1124        2558 :          evals(num_small_evals + 1:nrow) = SQRT(evals(num_small_evals + 1:nrow))
    1125             :       END IF
    1126             : 
    1127          44 :       CALL cp_fm_column_scale(evecs, evals)
    1128             : 
    1129             :       ! As it turns out, the results in the subgroups differ.
    1130             :       ! Thus, we have to equilibrate the results.
    1131             :       ! Step 1: Get a communicator connecting processes with same id within subgroups
    1132             :       ! use that group_size_L is divisible by the total number of processes (see above)
    1133          44 :       group_size_L = para_env%num_pe/matrix%matrix_struct%para_env%num_pe
    1134          44 :       comm_exchange = matrix%matrix_struct%context%interconnect(para_env)
    1135             : 
    1136         132 :       ALLOCATE (num_eval(0:group_size_L - 1))
    1137          44 :       CALL comm_exchange%allgather(num_small_evals, num_eval)
    1138             : 
    1139         118 :       num_small_evals = MINVAL(num_eval)
    1140             : 
    1141         118 :       IF (num_small_evals /= MAXVAL(num_eval)) THEN
    1142             :          ! Step 2: Get position of maximum value
    1143           0 :          pos_max = MAXLOC(num_eval)
    1144           0 :          num_small_evals = num_eval(pos_max(1))
    1145           0 :          needed_evals = nrow - num_small_evals
    1146             : 
    1147             :          ! Step 3: Broadcast your local data to all other processes
    1148           0 :          CALL comm_exchange%bcast(evecs%local_data, pos_max(1))
    1149           0 :          CALL comm_exchange%bcast(cond_num, pos_max(1))
    1150             :       END IF
    1151             : 
    1152          44 :       DEALLOCATE (num_eval)
    1153             : 
    1154          44 :       CALL comm_exchange%free()
    1155             : 
    1156          44 :       CALL reset_size_matrix(matrix, needed_evals, matrix%matrix_struct)
    1157             : 
    1158             :       ! Copy the needed eigenvectors
    1159          44 :       CALL cp_fm_to_fm(evecs, matrix, needed_evals, num_small_evals + 1)
    1160             : 
    1161          44 :       CALL cp_fm_release(evecs)
    1162             : 
    1163          44 :       CALL timestop(handle)
    1164             : 
    1165         132 :    END SUBROUTINE matrix_root_with_svd
    1166             : 
    1167             : ! **************************************************************************************************
    1168             : !> \brief ...
    1169             : !> \param matrix ...
    1170             : !> \param new_size ...
    1171             : !> \param fm_struct_template ...
    1172             : ! **************************************************************************************************
    1173         152 :    SUBROUTINE reset_size_matrix(matrix, new_size, fm_struct_template)
    1174             :       TYPE(cp_fm_type), INTENT(INOUT)                    :: matrix
    1175             :       INTEGER, INTENT(IN)                                :: new_size
    1176             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct_template
    1177             : 
    1178             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'reset_size_matrix'
    1179             : 
    1180             :       INTEGER                                            :: handle
    1181             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    1182             : 
    1183          76 :       CALL timeset(routineN, handle)
    1184             : 
    1185             :       ! Choose the block sizes as large as in the template for the later steps
    1186          76 :       NULLIFY (fm_struct)
    1187          76 :       CALL cp_fm_struct_create(fm_struct, ncol_global=new_size, template_fmstruct=fm_struct_template, force_block=.TRUE.)
    1188             : 
    1189          76 :       CALL cp_fm_release(matrix)
    1190             : 
    1191          76 :       CALL cp_fm_create(matrix, fm_struct)
    1192          76 :       CALL cp_fm_set_all(matrix, 0.0_dp)
    1193             : 
    1194          76 :       CALL cp_fm_struct_release(fm_struct)
    1195             : 
    1196          76 :       CALL timestop(handle)
    1197             : 
    1198          76 :    END SUBROUTINE reset_size_matrix
    1199             : 
    1200             : ! **************************************************************************************************
    1201             : !> \brief ...
    1202             : !> \param fm_matrix_L ...
    1203             : !> \param L_local_col ...
    1204             : !> \param para_env ...
    1205             : !> \param my_group_L_start ...
    1206             : !> \param my_group_L_end ...
    1207             : !> \param dimen_RI ...
    1208             : ! **************************************************************************************************
    1209         134 :    SUBROUTINE fill_fm_L_from_L_loc_non_blocking(fm_matrix_L, L_local_col, para_env, my_group_L_start, &
    1210             :                                                 my_group_L_end, dimen_RI)
    1211             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_matrix_L
    1212             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :), &
    1213             :          INTENT(IN)                                      :: L_local_col
    1214             :       TYPE(mp_para_env_type), INTENT(IN)                 :: para_env
    1215             :       INTEGER, INTENT(IN)                                :: my_group_L_start, my_group_L_end, &
    1216             :                                                             dimen_RI
    1217             : 
    1218             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'fill_fm_L_from_L_loc_non_blocking'
    1219             : 
    1220             :       INTEGER :: dummy_proc, handle, handle2, i_entry_rec, i_row, i_row_global, iproc, j_col, &
    1221             :          j_col_global, LLL, MMM, ncol_local, nrow_local, proc_send, send_pcol, send_prow
    1222         134 :       INTEGER, ALLOCATABLE, DIMENSION(:)                 :: entry_counter, num_entries_rec, &
    1223             :                                                             num_entries_send
    1224         134 :       INTEGER, DIMENSION(:), POINTER                     :: col_indices, row_indices
    1225             :       TYPE(integ_mat_buffer_type), ALLOCATABLE, &
    1226         134 :          DIMENSION(:)                                    :: buffer_rec, buffer_send
    1227         134 :       TYPE(mp_request_type), DIMENSION(:, :), POINTER    :: req_array
    1228             : 
    1229         134 :       CALL timeset(routineN, handle)
    1230             : 
    1231         134 :       CALL timeset(routineN//"_1", handle2)
    1232             : 
    1233             :       ! get info for the dest
    1234             :       CALL cp_fm_get_info(matrix=fm_matrix_L, &
    1235             :                           nrow_local=nrow_local, &
    1236             :                           ncol_local=ncol_local, &
    1237             :                           row_indices=row_indices, &
    1238         134 :                           col_indices=col_indices)
    1239             : 
    1240         402 :       ALLOCATE (num_entries_rec(0:para_env%num_pe - 1))
    1241         268 :       ALLOCATE (num_entries_send(0:para_env%num_pe - 1))
    1242             : 
    1243         402 :       num_entries_rec(:) = 0
    1244         402 :       num_entries_send(:) = 0
    1245             : 
    1246         134 :       dummy_proc = 0
    1247             : 
    1248             :       ! get the process, where the elements from L_local_col have to be sent
    1249       11380 :       DO LLL = 1, dimen_RI
    1250             : 
    1251       11246 :          send_prow = fm_matrix_L%matrix_struct%g2p_row(LLL)
    1252             : 
    1253      561929 :          DO MMM = my_group_L_start, my_group_L_end
    1254             : 
    1255      550549 :             send_pcol = fm_matrix_L%matrix_struct%g2p_col(MMM)
    1256             : 
    1257      550549 :             proc_send = fm_matrix_L%matrix_struct%context%blacs2mpi(send_prow, send_pcol)
    1258             : 
    1259      561795 :             num_entries_send(proc_send) = num_entries_send(proc_send) + 1
    1260             : 
    1261             :          END DO
    1262             : 
    1263             :       END DO
    1264             : 
    1265         134 :       CALL timestop(handle2)
    1266             : 
    1267         134 :       CALL timeset(routineN//"_2", handle2)
    1268             : 
    1269         134 :       CALL para_env%alltoall(num_entries_send, num_entries_rec, 1)
    1270             : 
    1271         134 :       CALL timestop(handle2)
    1272             : 
    1273         134 :       CALL timeset(routineN//"_3", handle2)
    1274             : 
    1275             :       ! allocate buffers to send the entries and the information of the entries
    1276         670 :       ALLOCATE (buffer_rec(0:para_env%num_pe - 1))
    1277         536 :       ALLOCATE (buffer_send(0:para_env%num_pe - 1))
    1278             : 
    1279             :       ! allocate data message and corresponding indices
    1280         402 :       DO iproc = 0, para_env%num_pe - 1
    1281             : 
    1282         804 :          ALLOCATE (buffer_rec(iproc)%msg(num_entries_rec(iproc)))
    1283      550951 :          buffer_rec(iproc)%msg = 0.0_dp
    1284             : 
    1285             :       END DO
    1286             : 
    1287         134 :       CALL timestop(handle2)
    1288             : 
    1289         134 :       CALL timeset(routineN//"_4", handle2)
    1290             : 
    1291         402 :       DO iproc = 0, para_env%num_pe - 1
    1292             : 
    1293         804 :          ALLOCATE (buffer_send(iproc)%msg(num_entries_send(iproc)))
    1294      550951 :          buffer_send(iproc)%msg = 0.0_dp
    1295             : 
    1296             :       END DO
    1297             : 
    1298         134 :       CALL timestop(handle2)
    1299             : 
    1300         134 :       CALL timeset(routineN//"_5", handle2)
    1301             : 
    1302         402 :       DO iproc = 0, para_env%num_pe - 1
    1303             : 
    1304         804 :          ALLOCATE (buffer_rec(iproc)%indx(num_entries_rec(iproc), 2))
    1305     1102036 :          buffer_rec(iproc)%indx = 0
    1306             : 
    1307             :       END DO
    1308             : 
    1309         134 :       CALL timestop(handle2)
    1310             : 
    1311         134 :       CALL timeset(routineN//"_6", handle2)
    1312             : 
    1313         402 :       DO iproc = 0, para_env%num_pe - 1
    1314             : 
    1315         804 :          ALLOCATE (buffer_send(iproc)%indx(num_entries_send(iproc), 2))
    1316     1102036 :          buffer_send(iproc)%indx = 0
    1317             : 
    1318             :       END DO
    1319             : 
    1320         134 :       CALL timestop(handle2)
    1321             : 
    1322         134 :       CALL timeset(routineN//"_7", handle2)
    1323             : 
    1324         268 :       ALLOCATE (entry_counter(0:para_env%num_pe - 1))
    1325         402 :       entry_counter(:) = 0
    1326             : 
    1327             :       ! get the process, where the elements from L_local_col have to be sent and
    1328             :       ! write the data and the info to buffer_send
    1329       11380 :       DO LLL = 1, dimen_RI
    1330             : 
    1331       11246 :          send_prow = fm_matrix_L%matrix_struct%g2p_row(LLL)
    1332             : 
    1333      561929 :          DO MMM = my_group_L_start, my_group_L_end
    1334             : 
    1335      550549 :             send_pcol = fm_matrix_L%matrix_struct%g2p_col(MMM)
    1336             : 
    1337      550549 :             proc_send = fm_matrix_L%matrix_struct%context%blacs2mpi(send_prow, send_pcol)
    1338             : 
    1339      550549 :             entry_counter(proc_send) = entry_counter(proc_send) + 1
    1340             : 
    1341             :             buffer_send(proc_send)%msg(entry_counter(proc_send)) = &
    1342      550549 :                L_local_col(LLL, MMM - my_group_L_start + 1)
    1343             : 
    1344      550549 :             buffer_send(proc_send)%indx(entry_counter(proc_send), 1) = LLL
    1345      561795 :             buffer_send(proc_send)%indx(entry_counter(proc_send), 2) = MMM
    1346             : 
    1347             :          END DO
    1348             : 
    1349             :       END DO
    1350             : 
    1351        2010 :       ALLOCATE (req_array(1:para_env%num_pe, 4))
    1352             : 
    1353         134 :       CALL timestop(handle2)
    1354             : 
    1355         134 :       CALL timeset(routineN//"_8", handle2)
    1356             : 
    1357             :       ! communicate the buffer
    1358             :       CALL communicate_buffer(para_env, num_entries_rec, num_entries_send, buffer_rec, &
    1359         134 :                               buffer_send, req_array)
    1360             : 
    1361      534373 :       fm_matrix_L%local_data = 0.0_dp
    1362             : 
    1363         134 :       CALL timestop(handle2)
    1364             : 
    1365         134 :       CALL timeset(routineN//"_9", handle2)
    1366             : 
    1367             :       ! fill fm_matrix_L with the entries from buffer_rec
    1368         402 :       DO iproc = 0, para_env%num_pe - 1
    1369             : 
    1370      550951 :          DO i_entry_rec = 1, num_entries_rec(iproc)
    1371             : 
    1372    31219430 :             DO i_row = 1, nrow_local
    1373             : 
    1374    30668613 :                i_row_global = row_indices(i_row)
    1375             : 
    1376  4667031343 :                DO j_col = 1, ncol_local
    1377             : 
    1378  4635812181 :                   j_col_global = col_indices(j_col)
    1379             : 
    1380  4635812181 :                   IF (i_row_global == buffer_rec(iproc)%indx(i_entry_rec, 1) .AND. &
    1381    30668613 :                       j_col_global == buffer_rec(iproc)%indx(i_entry_rec, 2)) THEN
    1382             : 
    1383      550549 :                      fm_matrix_L%local_data(i_row, j_col) = buffer_rec(iproc)%msg(i_entry_rec)
    1384             : 
    1385             :                   END IF
    1386             : 
    1387             :                END DO
    1388             : 
    1389             :             END DO
    1390             : 
    1391             :          END DO
    1392             : 
    1393             :       END DO
    1394             : 
    1395         134 :       CALL timestop(handle2)
    1396             : 
    1397         134 :       CALL timeset(routineN//"_10", handle2)
    1398             : 
    1399         402 :       DO iproc = 0, para_env%num_pe - 1
    1400         268 :          DEALLOCATE (buffer_rec(iproc)%msg)
    1401         268 :          DEALLOCATE (buffer_rec(iproc)%indx)
    1402         268 :          DEALLOCATE (buffer_send(iproc)%msg)
    1403         402 :          DEALLOCATE (buffer_send(iproc)%indx)
    1404             :       END DO
    1405             : 
    1406         670 :       DEALLOCATE (buffer_rec, buffer_send)
    1407         134 :       DEALLOCATE (req_array)
    1408         134 :       DEALLOCATE (entry_counter)
    1409         134 :       DEALLOCATE (num_entries_rec, num_entries_send)
    1410             : 
    1411         134 :       CALL timestop(handle2)
    1412             : 
    1413         134 :       CALL timestop(handle)
    1414             : 
    1415        1340 :    END SUBROUTINE fill_fm_L_from_L_loc_non_blocking
    1416             : 
    1417             : ! **************************************************************************************************
    1418             : !> \brief ...
    1419             : !> \param fm_matrix_L ...
    1420             : !> \param dimen_RI ...
    1421             : !> \param do_inversion ...
    1422             : ! **************************************************************************************************
    1423        1468 :    SUBROUTINE cholesky_decomp(fm_matrix_L, dimen_RI, do_inversion)
    1424             : 
    1425             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_matrix_L
    1426             :       INTEGER, INTENT(IN)                                :: dimen_RI
    1427             :       LOGICAL, INTENT(IN)                                :: do_inversion
    1428             : 
    1429             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'cholesky_decomp'
    1430             : 
    1431             :       INTEGER                                            :: handle, i_global, iiB, info_chol, &
    1432             :                                                             j_global, jjB, ncol_local, nrow_local
    1433         734 :       INTEGER, DIMENSION(:), POINTER                     :: col_indices, row_indices
    1434             : 
    1435         734 :       CALL timeset(routineN, handle)
    1436             : 
    1437             :       ! do cholesky decomposition
    1438         734 :       CALL cp_fm_cholesky_decompose(matrix=fm_matrix_L, n=dimen_RI, info_out=info_chol)
    1439         734 :       CPASSERT(info_chol == 0)
    1440             : 
    1441         734 :       IF (.NOT. do_inversion) THEN
    1442             :          ! clean the lower part of the L^{-1} matrix (just to not have surprises afterwards)
    1443             :          CALL cp_fm_get_info(matrix=fm_matrix_L, &
    1444             :                              nrow_local=nrow_local, &
    1445             :                              ncol_local=ncol_local, &
    1446             :                              row_indices=row_indices, &
    1447         116 :                              col_indices=col_indices)
    1448        5803 :          DO iiB = 1, nrow_local
    1449        5687 :             i_global = row_indices(iiB)
    1450      538330 :             DO jjB = 1, ncol_local
    1451      532527 :                j_global = col_indices(jjB)
    1452      538214 :                IF (j_global < i_global) fm_matrix_L%local_data(iiB, jjB) = 0.0_dp
    1453             :             END DO
    1454             :          END DO
    1455             : 
    1456             :       END IF
    1457             : 
    1458         734 :       CALL timestop(handle)
    1459             : 
    1460         734 :    END SUBROUTINE cholesky_decomp
    1461             : 
    1462             : ! **************************************************************************************************
    1463             : !> \brief ...
    1464             : !> \param fm_matrix_Minv_L_kpoints ...
    1465             : !> \param fm_matrix_L_kpoints ...
    1466             : !> \param dimen_RI ...
    1467             : !> \param kpoints ...
    1468             : !> \param eps_eigval_S ...
    1469             : ! **************************************************************************************************
    1470          22 :    SUBROUTINE inversion_of_M_and_mult_with_chol_dec_of_V(fm_matrix_Minv_L_kpoints, fm_matrix_L_kpoints, &
    1471             :                                                          dimen_RI, kpoints, eps_eigval_S)
    1472             : 
    1473             :       TYPE(cp_fm_type), DIMENSION(:, :), INTENT(IN)      :: fm_matrix_Minv_L_kpoints, &
    1474             :                                                             fm_matrix_L_kpoints
    1475             :       INTEGER, INTENT(IN)                                :: dimen_RI
    1476             :       TYPE(kpoint_type), POINTER                         :: kpoints
    1477             :       REAL(KIND=dp), INTENT(IN)                          :: eps_eigval_S
    1478             : 
    1479             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'inversion_of_M_and_mult_with_chol_dec_of_V'
    1480             :       COMPLEX(KIND=dp), PARAMETER :: cone = CMPLX(1.0_dp, 0.0_dp, KIND=dp), &
    1481             :          czero = CMPLX(0.0_dp, 0.0_dp, KIND=dp), ione = CMPLX(0.0_dp, 1.0_dp, KIND=dp)
    1482             : 
    1483             :       INTEGER                                            :: handle, ikp, nkp
    1484             :       TYPE(cp_cfm_type)                                  :: cfm_matrix_K_tmp, cfm_matrix_M_tmp, &
    1485             :                                                             cfm_matrix_V_tmp, cfm_matrix_Vtrunc_tmp
    1486             :       TYPE(cp_fm_struct_type), POINTER                   :: matrix_struct
    1487             : 
    1488          22 :       CALL timeset(routineN, handle)
    1489             : 
    1490          22 :       CALL cp_fm_get_info(fm_matrix_Minv_L_kpoints(1, 1), matrix_struct=matrix_struct)
    1491             : 
    1492          22 :       CALL cp_cfm_create(cfm_matrix_M_tmp, matrix_struct)
    1493          22 :       CALL cp_cfm_create(cfm_matrix_V_tmp, matrix_struct)
    1494          22 :       CALL cp_cfm_create(cfm_matrix_K_tmp, matrix_struct)
    1495          22 :       CALL cp_cfm_create(cfm_matrix_Vtrunc_tmp, matrix_struct)
    1496             : 
    1497          22 :       CALL get_kpoint_info(kpoints, nkp=nkp)
    1498             : 
    1499         498 :       DO ikp = 1, nkp
    1500             : 
    1501         476 :          CALL cp_cfm_scale_and_add_fm(czero, cfm_matrix_M_tmp, cone, fm_matrix_Minv_L_kpoints(ikp, 1))
    1502         476 :          CALL cp_cfm_scale_and_add_fm(cone, cfm_matrix_M_tmp, ione, fm_matrix_Minv_L_kpoints(ikp, 2))
    1503             : 
    1504         476 :          CALL cp_cfm_scale_and_add_fm(czero, cfm_matrix_V_tmp, cone, fm_matrix_L_kpoints(ikp, 1))
    1505         476 :          CALL cp_cfm_scale_and_add_fm(cone, cfm_matrix_V_tmp, ione, fm_matrix_L_kpoints(ikp, 2))
    1506             : 
    1507         476 :          CALL cp_cfm_power(cfm_matrix_M_tmp, threshold=eps_eigval_S, exponent=-1.0_dp)
    1508             : 
    1509         476 :          CALL cp_cfm_power(cfm_matrix_V_tmp, threshold=0.0_dp, exponent=0.5_dp)
    1510             : 
    1511             :          ! save L(k) = SQRT(V(k))
    1512         476 :          CALL cp_cfm_to_fm(cfm_matrix_V_tmp, fm_matrix_L_kpoints(ikp, 1), fm_matrix_L_kpoints(ikp, 2))
    1513             : 
    1514             :          ! get K = M^(-1)*L, where L is the Cholesky decomposition of V = L^T*L
    1515             :          CALL parallel_gemm("N", "C", dimen_RI, dimen_RI, dimen_RI, cone, cfm_matrix_M_tmp, cfm_matrix_V_tmp, &
    1516         476 :                             czero, cfm_matrix_K_tmp)
    1517             : 
    1518             :          ! move
    1519         498 :          CALL cp_cfm_to_fm(cfm_matrix_K_tmp, fm_matrix_Minv_L_kpoints(ikp, 1), fm_matrix_Minv_L_kpoints(ikp, 2))
    1520             : 
    1521             :       END DO
    1522             : 
    1523          22 :       CALL cp_cfm_release(cfm_matrix_M_tmp)
    1524          22 :       CALL cp_cfm_release(cfm_matrix_V_tmp)
    1525          22 :       CALL cp_cfm_release(cfm_matrix_K_tmp)
    1526          22 :       CALL cp_cfm_release(cfm_matrix_Vtrunc_tmp)
    1527             : 
    1528          22 :       CALL timestop(handle)
    1529             : 
    1530          22 :    END SUBROUTINE inversion_of_M_and_mult_with_chol_dec_of_V
    1531             : 
    1532             : ! **************************************************************************************************
    1533             : !> \brief ...
    1534             : !> \param fm_matrix_Minv_Vtrunc_Minv ...
    1535             : !> \param fm_matrix_Minv ...
    1536             : !> \param qs_env ...
    1537             : ! **************************************************************************************************
    1538          88 :    SUBROUTINE Gamma_only_inversion_of_M_and_mult_with_chol_dec_of_Vtrunc(fm_matrix_Minv_Vtrunc_Minv, &
    1539          22 :                                                                          fm_matrix_Minv, qs_env)
    1540             : 
    1541             :       TYPE(cp_fm_type), DIMENSION(:, :)                  :: fm_matrix_Minv_Vtrunc_Minv, &
    1542             :                                                             fm_matrix_Minv
    1543             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1544             : 
    1545             :       CHARACTER(LEN=*), PARAMETER :: &
    1546             :          routineN = 'Gamma_only_inversion_of_M_and_mult_with_chol_dec_of_Vtrunc'
    1547             : 
    1548             :       INTEGER                                            :: dimen_RI, handle, ndep
    1549             :       REAL(KIND=dp)                                      :: eps_eigval_S_Gamma
    1550             :       TYPE(cp_fm_type)                                   :: fm_matrix_RI_metric_inv_work, fm_work
    1551             : 
    1552          22 :       CALL timeset(routineN, handle)
    1553             : 
    1554          22 :       CALL cp_fm_create(fm_work, fm_matrix_Minv(1, 1)%matrix_struct)
    1555          22 :       CALL cp_fm_set_all(fm_work, 0.0_dp)
    1556             : 
    1557          22 :       CALL cp_fm_create(fm_matrix_RI_metric_inv_work, fm_matrix_Minv(1, 1)%matrix_struct)
    1558          22 :       CALL cp_fm_set_all(fm_matrix_RI_metric_inv_work, 0.0_dp)
    1559             : 
    1560          22 :       CALL cp_fm_get_info(matrix=fm_matrix_Minv(1, 1), nrow_global=dimen_RI)
    1561             : 
    1562          22 :       eps_eigval_S_Gamma = qs_env%mp2_env%ri_rpa_im_time%eps_eigval_S_Gamma
    1563             : 
    1564          22 :       IF (eps_eigval_S_Gamma > 1.0E-18) THEN
    1565             : 
    1566             :          ! remove small eigenvalues
    1567             :          CALL cp_fm_power(fm_matrix_Minv(1, 1), fm_matrix_RI_metric_inv_work, -0.5_dp, &
    1568           0 :                           eps_eigval_S_Gamma, ndep)
    1569             : 
    1570             :       ELSE
    1571             : 
    1572          22 :          CALL cholesky_decomp(fm_matrix_Minv(1, 1), dimen_RI, do_inversion=.TRUE.)
    1573             : 
    1574          22 :          CALL invert_mat(fm_matrix_Minv(1, 1))
    1575             : 
    1576             :       END IF
    1577             : 
    1578             :       CALL parallel_gemm('N', 'T', dimen_RI, dimen_RI, dimen_RI, 1.0_dp, fm_matrix_Minv(1, 1), &
    1579          22 :                          fm_matrix_Minv(1, 1), 0.0_dp, fm_matrix_RI_metric_inv_work)
    1580             : 
    1581          22 :       CALL cp_fm_to_fm(fm_matrix_RI_metric_inv_work, fm_matrix_Minv(1, 1))
    1582             : 
    1583             :       CALL parallel_gemm('N', 'N', dimen_RI, dimen_RI, dimen_RI, 1.0_dp, fm_matrix_RI_metric_inv_work, &
    1584          22 :                          fm_matrix_Minv_Vtrunc_Minv(1, 1), 0.0_dp, fm_work)
    1585             : 
    1586             :       CALL parallel_gemm('N', 'N', dimen_RI, dimen_RI, dimen_RI, 1.0_dp, fm_work, &
    1587          22 :                          fm_matrix_RI_metric_inv_work, 0.0_dp, fm_matrix_Minv_Vtrunc_Minv(1, 1))
    1588             : 
    1589          22 :       CALL cp_fm_release(fm_work)
    1590          22 :       CALL cp_fm_release(fm_matrix_RI_metric_inv_work)
    1591             : 
    1592          22 :       CALL timestop(handle)
    1593             : 
    1594          22 :    END SUBROUTINE Gamma_only_inversion_of_M_and_mult_with_chol_dec_of_Vtrunc
    1595             : 
    1596             : ! **************************************************************************************************
    1597             : !> \brief ...
    1598             : !> \param qs_env ...
    1599             : !> \param trunc_coulomb ...
    1600             : !> \param rel_cutoff_trunc_coulomb_ri_x ...
    1601             : !> \param cell_grid ...
    1602             : !> \param do_BvK_cell ...
    1603             : ! **************************************************************************************************
    1604          44 :    SUBROUTINE trunc_coulomb_for_exchange(qs_env, trunc_coulomb, rel_cutoff_trunc_coulomb_ri_x, &
    1605             :                                          cell_grid, do_BvK_cell)
    1606             :       TYPE(qs_environment_type), POINTER                 :: qs_env
    1607             :       TYPE(libint_potential_type), OPTIONAL              :: trunc_coulomb
    1608             :       REAL(KIND=dp), OPTIONAL                            :: rel_cutoff_trunc_coulomb_ri_x
    1609             :       INTEGER, DIMENSION(3), OPTIONAL                    :: cell_grid
    1610             :       LOGICAL, OPTIONAL                                  :: do_BvK_cell
    1611             : 
    1612             :       CHARACTER(LEN=*), PARAMETER :: routineN = 'trunc_coulomb_for_exchange'
    1613             : 
    1614             :       INTEGER                                            :: handle, i_dim
    1615             :       INTEGER, DIMENSION(3)                              :: periodic
    1616             :       LOGICAL                                            :: my_do_BvK_cell
    1617             :       REAL(KIND=dp) :: kp_fac, kp_fac_idim, my_rel_cutoff_trunc_coulomb_ri_x, &
    1618             :          shortest_dist_cell_planes
    1619             :       TYPE(cell_type), POINTER                           :: cell
    1620             :       TYPE(kpoint_type), POINTER                         :: kpoints_scf
    1621             : 
    1622          44 :       CALL timeset(routineN, handle)
    1623             : 
    1624          44 :       NULLIFY (cell)
    1625          44 :       CALL get_qs_env(qs_env, cell=cell, kpoints=kpoints_scf)
    1626          44 :       CALL get_cell(cell=cell, periodic=periodic)
    1627             : 
    1628          44 :       my_do_BvK_cell = .FALSE.
    1629          44 :       IF (PRESENT(do_BvK_cell)) my_do_BvK_cell = do_BvK_cell
    1630          22 :       IF (my_do_BvK_cell) THEN
    1631             :          kp_fac = 1.0E10_dp
    1632          24 :          DO i_dim = 1, 3
    1633             :             ! look for smallest k-point mesh in periodic direction
    1634          24 :             IF (periodic(i_dim) == 1) THEN
    1635          12 :                IF (PRESENT(cell_grid)) THEN
    1636          12 :                   kp_fac_idim = REAL(cell_grid(i_dim), KIND=dp)
    1637             :                ELSE
    1638           0 :                   kp_fac_idim = REAL(kpoints_scf%nkp_grid(i_dim), KIND=dp)
    1639             :                END IF
    1640          12 :                IF (kp_fac > kp_fac_idim) kp_fac = kp_fac_idim
    1641             :             END IF
    1642             :          END DO
    1643             :       ELSE
    1644             :          kp_fac = 1.0_dp
    1645             :       END IF
    1646             : 
    1647          44 :       shortest_dist_cell_planes = 1.0E4_dp
    1648          44 :       IF (periodic(1) == 1) THEN
    1649          16 :          IF (shortest_dist_cell_planes > plane_distance(1, 0, 0, cell)) THEN
    1650          16 :             shortest_dist_cell_planes = plane_distance(1, 0, 0, cell)
    1651             :          END IF
    1652             :       END IF
    1653          44 :       IF (periodic(2) == 1) THEN
    1654          36 :          IF (shortest_dist_cell_planes > plane_distance(0, 1, 0, cell)) THEN
    1655          24 :             shortest_dist_cell_planes = plane_distance(0, 1, 0, cell)
    1656             :          END IF
    1657             :       END IF
    1658          44 :       IF (periodic(3) == 1) THEN
    1659          32 :          IF (shortest_dist_cell_planes > plane_distance(0, 0, 1, cell)) THEN
    1660           8 :             shortest_dist_cell_planes = plane_distance(0, 0, 1, cell)
    1661             :          END IF
    1662             :       END IF
    1663             : 
    1664          44 :       IF (PRESENT(rel_cutoff_trunc_coulomb_ri_x)) THEN
    1665          22 :          my_rel_cutoff_trunc_coulomb_ri_x = rel_cutoff_trunc_coulomb_ri_x
    1666             :       ELSE
    1667          22 :          my_rel_cutoff_trunc_coulomb_ri_x = qs_env%mp2_env%ri_rpa_im_time%rel_cutoff_trunc_coulomb_ri_x
    1668             :       END IF
    1669             : 
    1670          44 :       IF (PRESENT(trunc_coulomb)) THEN
    1671          44 :          trunc_coulomb%potential_type = do_potential_truncated
    1672             :          trunc_coulomb%cutoff_radius = shortest_dist_cell_planes* &
    1673             :                                        my_rel_cutoff_trunc_coulomb_ri_x* &
    1674          44 :                                        kp_fac
    1675          44 :          trunc_coulomb%filename = "t_c_g.dat"
    1676             :          ! dummy
    1677          44 :          trunc_coulomb%omega = 0.0_dp
    1678             :       END IF
    1679             : 
    1680          44 :       CALL timestop(handle)
    1681             : 
    1682          44 :    END SUBROUTINE trunc_coulomb_for_exchange
    1683             : 
    1684             : ! **************************************************************************************************
    1685             : !> \brief ...
    1686             : !> \param fm_matrix_L ...
    1687             : ! **************************************************************************************************
    1688        1236 :    SUBROUTINE invert_mat(fm_matrix_L)
    1689             : 
    1690             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_matrix_L
    1691             : 
    1692             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'invert_mat'
    1693             : 
    1694             :       INTEGER                                            :: handle, i_global, iiB, j_global, jjB, &
    1695             :                                                             ncol_local, nrow_local
    1696         618 :       INTEGER, DIMENSION(:), POINTER                     :: col_indices, row_indices
    1697             : 
    1698         618 :       CALL timeset(routineN, handle)
    1699             : 
    1700         618 :       CALL cp_fm_triangular_invert(matrix_a=fm_matrix_L, uplo_tr='U')
    1701             : 
    1702             :       ! clean the lower part of the L^{-1} matrix (just to not have surprises afterwards)
    1703             :       CALL cp_fm_get_info(matrix=fm_matrix_L, &
    1704             :                           nrow_local=nrow_local, &
    1705             :                           ncol_local=ncol_local, &
    1706             :                           row_indices=row_indices, &
    1707         618 :                           col_indices=col_indices)
    1708       41060 :       DO iiB = 1, nrow_local
    1709       40442 :          i_global = row_indices(iiB)
    1710     3383046 :          DO jjB = 1, ncol_local
    1711     3341986 :             j_global = col_indices(jjB)
    1712     3382428 :             IF (j_global < i_global) fm_matrix_L%local_data(iiB, jjB) = 0.0_dp
    1713             :          END DO
    1714             :       END DO
    1715             : 
    1716         618 :       CALL timestop(handle)
    1717             : 
    1718         618 :    END SUBROUTINE invert_mat
    1719             : 
    1720             : ! **************************************************************************************************
    1721             : !> \brief ...
    1722             : !> \param fm_matrix_L ...
    1723             : !> \param blacs_env_L ...
    1724             : !> \param dimen_RI ...
    1725             : !> \param para_env_L ...
    1726             : !> \param name ...
    1727             : !> \param fm_matrix_L_extern ...
    1728             : ! **************************************************************************************************
    1729         654 :    SUBROUTINE create_matrix_L(fm_matrix_L, blacs_env_L, dimen_RI, para_env_L, name, fm_matrix_L_extern)
    1730             :       TYPE(cp_fm_type), INTENT(OUT)                      :: fm_matrix_L
    1731             :       TYPE(cp_blacs_env_type), POINTER                   :: blacs_env_L
    1732             :       INTEGER, INTENT(IN)                                :: dimen_RI
    1733             :       TYPE(mp_para_env_type), POINTER                    :: para_env_L
    1734             :       CHARACTER(LEN=*), INTENT(IN)                       :: name
    1735             :       TYPE(cp_fm_type), INTENT(IN), OPTIONAL             :: fm_matrix_L_extern
    1736             : 
    1737             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'create_matrix_L'
    1738             : 
    1739             :       INTEGER                                            :: handle
    1740             :       TYPE(cp_fm_struct_type), POINTER                   :: fm_struct
    1741             : 
    1742         654 :       CALL timeset(routineN, handle)
    1743             : 
    1744             :       ! create the full matrix L defined in the L group
    1745         654 :       IF (PRESENT(fm_matrix_L_extern)) THEN
    1746          36 :          CALL cp_fm_create(fm_matrix_L, fm_matrix_L_extern%matrix_struct, name=name)
    1747             :       ELSE
    1748         618 :          NULLIFY (fm_struct)
    1749             :          CALL cp_fm_struct_create(fm_struct, context=blacs_env_L, nrow_global=dimen_RI, &
    1750         618 :                                   ncol_global=dimen_RI, para_env=para_env_L)
    1751             : 
    1752         618 :          CALL cp_fm_create(fm_matrix_L, fm_struct, name=name)
    1753             : 
    1754         618 :          CALL cp_fm_struct_release(fm_struct)
    1755             :       END IF
    1756             : 
    1757         654 :       CALL cp_fm_set_all(matrix=fm_matrix_L, alpha=0.0_dp)
    1758             : 
    1759         654 :       CALL timestop(handle)
    1760             : 
    1761         654 :    END SUBROUTINE create_matrix_L
    1762             : 
    1763             : ! **************************************************************************************************
    1764             : !> \brief ...
    1765             : !> \param fm_matrix_L ...
    1766             : !> \param my_group_L_start ...
    1767             : !> \param my_group_L_end ...
    1768             : !> \param my_group_L_size ...
    1769             : !> \param my_Lrows ...
    1770             : ! **************************************************************************************************
    1771         496 :    SUBROUTINE grep_Lcols(fm_matrix_L, &
    1772             :                          my_group_L_start, my_group_L_end, my_group_L_size, my_Lrows)
    1773             :       TYPE(cp_fm_type), INTENT(IN)                       :: fm_matrix_L
    1774             :       INTEGER, INTENT(IN)                                :: my_group_L_start, my_group_L_end, &
    1775             :                                                             my_group_L_size
    1776             :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :), &
    1777             :          INTENT(OUT)                                     :: my_Lrows
    1778             : 
    1779             :       CHARACTER(LEN=*), PARAMETER                        :: routineN = 'grep_Lcols'
    1780             : 
    1781             :       INTEGER :: dimen_RI, handle, handle2, i_global, iiB, j_global, jjB, max_row_col_local, &
    1782             :          ncol_local, ncol_rec, nrow_local, nrow_rec, proc_receive_static, proc_send_static, &
    1783             :          proc_shift
    1784         496 :       INTEGER, ALLOCATABLE, DIMENSION(:, :)              :: local_col_row_info, rec_col_row_info
    1785         496 :       INTEGER, DIMENSION(:), POINTER                     :: col_indices, col_indices_rec, &
    1786         496 :                                                             row_indices, row_indices_rec
    1787         496 :       REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :)        :: local_L, rec_L
    1788             :       REAL(KIND=dp), CONTIGUOUS, DIMENSION(:, :), &
    1789         496 :          POINTER                                         :: local_L_internal
    1790             :       TYPE(mp_para_env_type), POINTER                    :: para_env
    1791             : 
    1792         496 :       CALL timeset(routineN, handle)
    1793             : 
    1794             :       CALL cp_fm_get_info(matrix=fm_matrix_L, &
    1795             :                           nrow_local=nrow_local, &
    1796             :                           ncol_local=ncol_local, &
    1797             :                           row_indices=row_indices, &
    1798             :                           col_indices=col_indices, &
    1799             :                           nrow_global=dimen_RI, &
    1800             :                           local_data=local_L_internal, &
    1801         496 :                           para_env=para_env)
    1802             : 
    1803        1984 :       ALLOCATE (my_Lrows(dimen_RI, my_group_L_size))
    1804     1598968 :       my_Lrows = 0.0_dp
    1805             : 
    1806        1984 :       ALLOCATE (local_L(nrow_local, ncol_local))
    1807     2928436 :       local_L(:, :) = local_L_internal(1:nrow_local, 1:ncol_local)
    1808             : 
    1809         496 :       max_row_col_local = MAX(nrow_local, ncol_local)
    1810         496 :       CALL para_env%max(max_row_col_local)
    1811             : 
    1812        1984 :       ALLOCATE (local_col_row_info(0:max_row_col_local, 2))
    1813       76116 :       local_col_row_info = 0
    1814             :       ! 0,1 nrows
    1815         496 :       local_col_row_info(0, 1) = nrow_local
    1816       36311 :       local_col_row_info(1:nrow_local, 1) = row_indices(1:nrow_local)
    1817             :       ! 0,2 ncols
    1818         496 :       local_col_row_info(0, 2) = ncol_local
    1819       37204 :       local_col_row_info(1:ncol_local, 2) = col_indices(1:ncol_local)
    1820             : 
    1821         992 :       ALLOCATE (rec_col_row_info(0:max_row_col_local, 2))
    1822             : 
    1823             :       ! accumulate data on my_Lrows starting from myself
    1824       37204 :       DO jjB = 1, ncol_local
    1825       36708 :          j_global = col_indices(jjB)
    1826       37204 :          IF (j_global >= my_group_L_start .AND. j_global <= my_group_L_end) THEN
    1827     1509484 :             DO iiB = 1, nrow_local
    1828     1490110 :                i_global = row_indices(iiB)
    1829     1509484 :                my_Lrows(i_global, j_global - my_group_L_start + 1) = local_L(iiB, jjB)
    1830             :             END DO
    1831             :          END IF
    1832             :       END DO
    1833             : 
    1834         496 :       proc_send_static = MODULO(para_env%mepos + 1, para_env%num_pe)
    1835         496 :       proc_receive_static = MODULO(para_env%mepos - 1, para_env%num_pe)
    1836             : 
    1837         496 :       CALL timeset(routineN//"_comm", handle2)
    1838             : 
    1839         520 :       DO proc_shift = 1, para_env%num_pe - 1
    1840             :          ! first exchange information on the local data
    1841        4200 :          rec_col_row_info = 0
    1842          24 :          CALL para_env%sendrecv(local_col_row_info, proc_send_static, rec_col_row_info, proc_receive_static)
    1843          24 :          nrow_rec = rec_col_row_info(0, 1)
    1844          24 :          ncol_rec = rec_col_row_info(0, 2)
    1845             : 
    1846          72 :          ALLOCATE (row_indices_rec(nrow_rec))
    1847        1061 :          row_indices_rec = rec_col_row_info(1:nrow_rec, 1)
    1848             : 
    1849          72 :          ALLOCATE (col_indices_rec(ncol_rec))
    1850        2064 :          col_indices_rec = rec_col_row_info(1:ncol_rec, 2)
    1851             : 
    1852          96 :          ALLOCATE (rec_L(nrow_rec, ncol_rec))
    1853       91052 :          rec_L = 0.0_dp
    1854             : 
    1855             :          ! then send and receive the real data
    1856          24 :          CALL para_env%sendrecv(local_L, proc_send_static, rec_L, proc_receive_static)
    1857             : 
    1858             :          ! accumulate the received data on my_Lrows
    1859        2064 :          DO jjB = 1, ncol_rec
    1860        2040 :             j_global = col_indices_rec(jjB)
    1861        2064 :             IF (j_global >= my_group_L_start .AND. j_global <= my_group_L_end) THEN
    1862       91028 :                DO iiB = 1, nrow_rec
    1863       88988 :                   i_global = row_indices_rec(iiB)
    1864       91028 :                   my_Lrows(i_global, j_global - my_group_L_start + 1) = rec_L(iiB, jjB)
    1865             :                END DO
    1866             :             END IF
    1867             :          END DO
    1868             : 
    1869        4200 :          local_col_row_info(:, :) = rec_col_row_info
    1870          24 :          CALL MOVE_ALLOC(rec_L, local_L)
    1871             : 
    1872          24 :          DEALLOCATE (col_indices_rec)
    1873         520 :          DEALLOCATE (row_indices_rec)
    1874             :       END DO
    1875         496 :       CALL timestop(handle2)
    1876             : 
    1877         496 :       DEALLOCATE (local_col_row_info)
    1878         496 :       DEALLOCATE (rec_col_row_info)
    1879         496 :       DEALLOCATE (local_L)
    1880             : 
    1881         496 :       CALL timestop(handle)
    1882             : 
    1883        1488 :    END SUBROUTINE grep_Lcols
    1884             : 
    1885             : END MODULE mp2_ri_2c

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