Line data Source code
1 : !--------------------------------------------------------------------------------------------------!
2 : ! CP2K: A general program to perform molecular dynamics simulations !
3 : ! Copyright 2000-2026 CP2K developers group <https://cp2k.org> !
4 : ! !
5 : ! SPDX-License-Identifier: GPL-2.0-or-later !
6 : !--------------------------------------------------------------------------------------------------!
7 :
8 : ! **************************************************************************************************
9 : !> \brief GW using RI-RS Approximation for molecules
10 : !> \par History
11 : !> 04.2026 created [Ritaj Tyagi]
12 : ! **************************************************************************************************
13 : MODULE gw_ri_rs_large_cell_Gamma
14 : USE atomic_kind_types, ONLY: atomic_kind_type
15 : USE basis_set_types, ONLY: gto_basis_set_type
16 : USE cell_types, ONLY: cell_type,&
17 : get_cell,&
18 : pbc
19 : USE cp_blacs_env, ONLY: cp_blacs_env_create,&
20 : cp_blacs_env_release,&
21 : cp_blacs_env_type
22 : USE cp_dbcsr_api, ONLY: &
23 : dbcsr_add, dbcsr_binary_read, dbcsr_binary_write, dbcsr_create, dbcsr_distribution_get, &
24 : dbcsr_distribution_new, dbcsr_distribution_release, dbcsr_distribution_type, &
25 : dbcsr_finalize, dbcsr_get_info, dbcsr_p_type, dbcsr_put_block, dbcsr_release, dbcsr_scale, &
26 : dbcsr_set, dbcsr_type, dbcsr_type_no_symmetry
27 : USE cp_dbcsr_operations, ONLY: copy_dbcsr_to_fm,&
28 : copy_fm_to_dbcsr,&
29 : dbcsr_deallocate_matrix_set,&
30 : max_elements_per_block
31 : USE cp_fm_struct, ONLY: cp_fm_struct_type
32 : USE cp_fm_types, ONLY: cp_fm_create,&
33 : cp_fm_release,&
34 : cp_fm_type
35 : USE cp_log_handling, ONLY: cp_get_default_logger,&
36 : cp_logger_type
37 : USE cp_output_handling, ONLY: cp_p_file,&
38 : cp_print_key_should_output
39 : USE gw_ri_rs_compute_Z_lP_utils, ONLY: build_gram_jacobi_blas,&
40 : build_jacobi_diag_from_phi,&
41 : scale_rows_by_diag,&
42 : solve_D_lp_distributed,&
43 : store_Z_lP_columns
44 : USE gw_ri_rs_grid_setup_main, ONLY: setup_ri_rs_grid
45 : USE gw_ri_rs_utils, ONLY: precompute_ri_rs_radii
46 : USE gw_tensor_large_cell_Gamma, ONLY: G_occ_vir,&
47 : compute_QP_energies,&
48 : delete_unnecessary_files,&
49 : fill_fm_Sigma_c_Gamma_time,&
50 : get_W_MIC
51 : USE gw_utils, ONLY: de_init_bs_env
52 : USE gw_utils_compute_integrals, ONLY: build_3c_integral_block_ctx,&
53 : gw_3c_ctx_create,&
54 : gw_3c_ctx_release,&
55 : gw_3c_ctx_type,&
56 : gw_3c_ws_create,&
57 : gw_3c_ws_release,&
58 : gw_3c_ws_type
59 : USE gw_utils_dbcsr, ONLY: dbcsr_contract_ABA,&
60 : hadamard_product
61 : USE gw_utils_fm, ONLY: fm_contract_ABA
62 : USE input_section_types, ONLY: section_vals_type
63 : USE kinds, ONLY: dp
64 : USE machine, ONLY: m_walltime
65 : USE message_passing, ONLY: mp_para_env_type
66 : USE mp2_ri_2c, ONLY: RI_2c_integral_mat
67 : USE orbital_pointers, ONLY: indco,&
68 : ncoset
69 : USE particle_types, ONLY: particle_type
70 : USE post_scf_bandstructure_types, ONLY: post_scf_bandstructure_type
71 : USE qs_environment_types, ONLY: get_qs_env,&
72 : qs_environment_type
73 : #include "./base/base_uses.f90"
74 :
75 : IMPLICIT NONE
76 :
77 : PRIVATE
78 :
79 : CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'gw_ri_rs_large_cell_Gamma'
80 :
81 : PUBLIC :: gw_calc_ri_rs_large_cell_Gamma, &
82 : release_dbcsr_topology_and_matrices, &
83 : setup_square_topology
84 :
85 : CONTAINS
86 :
87 : ! **************************************************************************************************
88 : !> \brief GW calculation using RI-RS formalism for molecules
89 : !> \param qs_env ...
90 : !> \param bs_env Band-structure environment containing GW parameters.
91 : ! **************************************************************************************************
92 :
93 0 : SUBROUTINE gw_calc_ri_rs_large_cell_Gamma(qs_env, bs_env)
94 :
95 : TYPE(qs_environment_type), POINTER :: qs_env
96 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
97 :
98 : CHARACTER(LEN=*), PARAMETER :: routineN = 'gw_calc_ri_rs_large_cell_Gamma'
99 :
100 : INTEGER :: handle
101 0 : TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:) :: fm_Sigma_x_Gamma, fm_W_time
102 0 : TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:, :, :) :: fm_Sigma_c_Gamma_time
103 :
104 0 : CALL timeset(routineN, handle)
105 :
106 : !!========================================================================
107 : !! 0. Precompute AO and RI Radii
108 : !! Per-atom cutoff radii from the most diffuse Gaussian primitives in
109 : !! the AO and RI auxiliary basis sets. Stored in bs_env%ri_rs%
110 : !! radius_ao_per_atom and radius_ri_per_atom, used for sphere-cutoff
111 : !! and phi_local screening.
112 : !!========================================================================
113 0 : CALL precompute_ri_rs_radii(bs_env)
114 :
115 : !!========================================================================
116 : !! 1. Grid Generation for RI-RS
117 : !! (Modified Lebedev grids from Ivan Duchemin and Xavier Blase)
118 : !! Generate flattened 1D array of grid points for RI-RS.
119 : !! Equation: r_g(k) = R_A + r_g(A)
120 : !!========================================================================
121 0 : CALL setup_ri_rs_grid(bs_env, bs_env%ri_rs%grid_points)
122 :
123 : !!========================================================================
124 : !! 2. Atomic Basis Evaluation
125 : !! Compute values of spherical atomic basis functions at grid points.
126 : !! Expression: ϕ_μl = ϕ_μ(r_l) (mat_phi_mu_l)
127 : !!========================================================================
128 : CALL atomic_basis_at_grid_point(bs_env, bs_env%ri_rs%grid_points, &
129 0 : bs_env%ri_rs%mat_phi_mu_l)
130 :
131 : !!========================================================================
132 : !! 3. Compute RI-RS Coefficients (Z_lp)
133 : !! Solve the regularized system for each atom P, where the grid domain
134 : !! is restricted to r_l within a cutoff distance of atom P:
135 : !! a. D_ll' = [ Σ_μ ϕ_μ(r_l) ϕ_μ(r_l') ]^2 (Equation 13)
136 : !! b. D_lP = Σ_{μν} ϕ_μ(r_l) ϕ_ν(r_l) (μν|P) (Equation 15)
137 : !! c. Conditioning:
138 : !! Dvec_l = 1 / sqrt(D_ll) (Diagonal scaling vector)
139 : !! D'_ll' = Dvec_l * D_ll' * Dvec_l' + λδ_ll'
140 : !! D'_lP = Dvec_l * D_lP
141 : !! d. Solve: Σ_l' D'_ll' * Z'_l'P = D'_lP (Equation 14)
142 : !! e. Rescale: Z_lP = Z'_lP * Dvec_l (Z_lP stored in mat_Z_lP)
143 : !!========================================================================
144 : CALL compute_Z_lP(qs_env, bs_env, bs_env%ri_rs%grid_points, &
145 0 : bs_env%ri_rs%mat_phi_mu_l, bs_env%ri_rs%mat_Z_lP)
146 0 : bs_env%ri_rs%grid_built = .TRUE.
147 :
148 : !!========================================================================
149 : !! 4. Compute Independent-Particle Polarizability (χ)
150 : !! G^occ_µλ(i|τ|) = sum_n^occ C_µn e^(-|(ϵ_n-ϵ_F)τ|) C_λn
151 : !! G^vir_µλ(i|τ|) = sum_n^vir C_µn e^(-|(ϵ_n-ϵ_F)τ|) C_λn
152 : !! G^occ_ll'(i|τ|) = sum_µν ϕ_µ(r_l) G^occ_µν ϕ_ν(r_l')
153 : !! G^vir_ll'(i|τ|) = sum_µν ϕ_µ(r_l) G^vir_µν ϕ_ν(r_l')
154 : !! χ_ll'(iτ) = G^occ_ll'(i|τ|) * G^vir_ll'(i|τ|)
155 : !! χ_PQ(iτ) = sum_ll' Z_lP χ_ll'(iτ) Z_l'Q
156 : !!========================================================================
157 : CALL get_mat_chi_Gamma_tau(bs_env, bs_env%mat_chi_Gamma_tau, &
158 0 : bs_env%ri_rs%mat_phi_mu_l, bs_env%ri_rs%mat_Z_lP)
159 :
160 : !!========================================================================
161 : !! 5. Compute Screened Interaction (W^MIC)
162 : !! χ_PQ(iτ) -> χ_PQ(iω) -> ε_PQ(iω) -> W_PQ(iω) -> W^MIC_PQ(iτ)
163 : !!========================================================================
164 0 : CALL get_W_MIC(bs_env, qs_env, bs_env%mat_chi_Gamma_tau, fm_W_time)
165 :
166 : !!========================================================================
167 : !! 6. Compute Exact Exchange Self-Energy (Σ^x)
168 : !! D_µν = sum_n^occ C_µn C_νn
169 : !! D_ll' = sum_µν ϕ_µ(r_l) D_µν ϕ_ν(r_l')
170 : !! V^trunc_ll' = sum_PQ Z_lP V^trunc_PQ Z_l'Q
171 : !! Σ^x_ll' = D_ll' * V^trunc_ll'
172 : !! Σ^x_λσ(k=0) = -sum_ll' ϕ_λ(r_l) Σ^x_ll' ϕ_σ(r_l')
173 : !!========================================================================
174 : CALL compute_Sigma_x(bs_env, qs_env, bs_env%ri_rs%mat_phi_mu_l, &
175 0 : bs_env%ri_rs%mat_Z_lP, fm_Sigma_x_Gamma)
176 :
177 : !!========================================================================
178 : !! 7. Compute Correlation Self-Energy (Σ^c)
179 : !! W^MIC_ll'(iτ) = sum_PQ Z_lP W^MIC_PQ(iτ) Z_l'Q
180 : !! Σ^c_ll'(iτ) = -G^occ_ll'(i|τ|) * W^MIC_ll'(iτ), for τ < 0
181 : !! Σ^c_ll'(iτ) = G^vir_ll'(i|τ|) * W^MIC_ll'(iτ), for τ > 0
182 : !! Σ^c_λσ(iτ) = sum_ll' ϕ_λ(r_l) Σ^c_ll'(iτ) ϕ_σ(r_l')
183 : !!========================================================================
184 : CALL compute_Sigma_c(bs_env, fm_W_time, bs_env%ri_rs%mat_phi_mu_l, &
185 0 : bs_env%ri_rs%mat_Z_lP, fm_Sigma_c_Gamma_time)
186 :
187 : !!========================================================================
188 : !! 8. Compute Quasiparticle Energies
189 : !! Σ^c_λσ(iτ) -> Σ^c_nn(ϵ)
190 : !! ϵ_nk^GW = ϵ_nk^DFT + Σ^c_nn(ϵ) + Σ^x_nn - v^xc_nn
191 : !!========================================================================
192 0 : CALL compute_QP_energies(bs_env, qs_env, fm_Sigma_x_Gamma, fm_Sigma_c_Gamma_time)
193 :
194 0 : CALL de_init_bs_env(qs_env, bs_env)
195 :
196 0 : CALL timestop(handle)
197 :
198 0 : END SUBROUTINE gw_calc_ri_rs_large_cell_Gamma
199 :
200 : ! **************************************************************************************************
201 : !> \brief Evaluates atomic basis functions on a real-space grid and builds a sparse DBCSR matrix.
202 : !> \param bs_env ...
203 : !> \param ri_rs_grid_points ...
204 : !> \param mat_phi_mu_l ...
205 : ! **************************************************************************************************
206 :
207 0 : SUBROUTINE atomic_basis_at_grid_point(bs_env, ri_rs_grid_points, mat_phi_mu_l)
208 :
209 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
210 : REAL(KIND=dp), ALLOCATABLE, INTENT(INOUT) :: ri_rs_grid_points(:, :)
211 : TYPE(dbcsr_type), INTENT(OUT) :: mat_phi_mu_l
212 :
213 : CHARACTER(LEN=*), PARAMETER :: routineN = 'atomic_basis_at_grid_point'
214 :
215 : INTEGER :: c_size, chunk_size, handle, i, i_blk, &
216 : iatom, natom, npcol, nprow, &
217 : num_grid_chunks, r_end, r_start
218 0 : INTEGER, DIMENSION(:), POINTER :: col_dist, r_blk_sizes, row_dist, sizes_AO
219 0 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: atom_col_buffer
220 : TYPE(cell_type), POINTER :: cell
221 : TYPE(dbcsr_distribution_type) :: dbcsr_dist_ks, dist
222 : TYPE(mp_para_env_type), POINTER :: para_env
223 0 : TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
224 :
225 0 : CALL timeset(routineN, handle)
226 :
227 : ! Setup Grid Blocking
228 0 : chunk_size = max_elements_per_block
229 :
230 0 : natom = bs_env%n_atom
231 0 : cell => bs_env%ri_rs%cell
232 0 : para_env => bs_env%para_env
233 0 : particle_set => bs_env%ri_rs%particle_set
234 0 : sizes_AO => bs_env%sizes_AO
235 0 : CPASSERT(ASSOCIATED(cell))
236 0 : CPASSERT(ASSOCIATED(para_env))
237 0 : CPASSERT(ASSOCIATED(particle_set))
238 0 : CPASSERT(SIZE(sizes_AO) == natom)
239 0 : CPASSERT(SIZE(ri_rs_grid_points, 2) == bs_env%ri_rs%n_grid_points)
240 :
241 : ! =========================================================================
242 : ! 1. SETUP DBCSR MATRIX TOPOLOGY
243 : ! =========================================================================
244 :
245 : ! B. Define Row Block Sizes (Grid chunks of max size 256)
246 0 : num_grid_chunks = CEILING(REAL(bs_env%ri_rs%n_grid_points, KIND=dp)/REAL(chunk_size, KIND=dp))
247 0 : ALLOCATE (r_blk_sizes(num_grid_chunks))
248 0 : r_blk_sizes = chunk_size
249 0 : IF (MOD(bs_env%ri_rs%n_grid_points, chunk_size) /= 0) THEN
250 0 : r_blk_sizes(num_grid_chunks) = MOD(bs_env%ri_rs%n_grid_points, chunk_size)
251 : END IF
252 :
253 : ! C. Fetch CP2K's Default Process Grid Configuration
254 0 : CALL dbcsr_get_info(bs_env%mat_ao_ao%matrix, distribution=dbcsr_dist_ks)
255 0 : CALL dbcsr_distribution_get(dbcsr_dist_ks, nprows=nprow, npcols=npcol)
256 :
257 : ! D. Build Custom Mappings using Round-Robin across the 2D process grid
258 :
259 0 : ALLOCATE (row_dist(num_grid_chunks))
260 0 : DO i = 1, num_grid_chunks
261 0 : row_dist(i) = MOD(i - 1, nprow)
262 : END DO
263 :
264 0 : ALLOCATE (col_dist(natom))
265 0 : DO i = 1, natom
266 0 : col_dist(i) = MOD(i - 1, npcol)
267 : END DO
268 :
269 : ! E. Create the DBCSR Distribution and Initialize the Matrix
270 : CALL dbcsr_distribution_new(dist, template=dbcsr_dist_ks, &
271 0 : row_dist=row_dist, col_dist=col_dist)
272 :
273 : CALL dbcsr_create(mat_phi_mu_l, name="phi_val_sparse", dist=dist, &
274 : matrix_type=dbcsr_type_no_symmetry, &
275 0 : row_blk_size=r_blk_sizes, col_blk_size=sizes_AO)
276 :
277 : ! =========================================================================
278 : ! 2. STREAM DATA DIRECTLY INTO SPARSE MATRIX
279 : ! =========================================================================
280 : ! Iterate over the atoms assigned to this specific MPI rank
281 0 : DO iatom = para_env%mepos + 1, natom, para_env%num_pe
282 :
283 0 : c_size = sizes_AO(iatom)
284 :
285 : ! Allocate a temporary dense buffer just for this specific atom
286 0 : ALLOCATE (atom_col_buffer(bs_env%ri_rs%n_grid_points, c_size))
287 0 : atom_col_buffer = 0.0_dp
288 :
289 : ! Evaluate the basis functions on the grid. Skip grid points outside the spatial
290 : ! extent of the most diffuse AO Gaussian on iatom; beyond that radius the contribution
291 : ! is guaranteed below eps_filter.
292 : CALL fill_phi_for_atom(atom_col_buffer, ri_rs_grid_points, bs_env%ri_rs%n_grid_points, &
293 : iatom, bs_env, &
294 0 : r2_threshold=bs_env%ri_rs%radius_ao_per_atom(iatom)**2)
295 :
296 : ! Slice the dense column into chunks and insert into DBCSR
297 0 : DO i_blk = 1, num_grid_chunks
298 0 : r_start = (i_blk - 1)*chunk_size + 1
299 0 : r_end = MIN(i_blk*chunk_size, bs_env%ri_rs%n_grid_points)
300 :
301 : ! Apply dynamic sparsity filtering: Only store blocks with physical significance
302 0 : IF (MAXVAL(ABS(atom_col_buffer(r_start:r_end, 1:c_size))) > bs_env%eps_filter) THEN
303 : CALL dbcsr_put_block(mat_phi_mu_l, row=i_blk, col=iatom, &
304 0 : block=atom_col_buffer(r_start:r_end, 1:c_size))
305 : END IF
306 : END DO
307 :
308 0 : DEALLOCATE (atom_col_buffer)
309 :
310 : END DO
311 :
312 : ! Finalize triggers internal MPI communication to route blocks to their correct 2D process owners
313 0 : CALL dbcsr_finalize(mat_phi_mu_l)
314 :
315 0 : IF (bs_env%unit_nr > 0) THEN
316 0 : WRITE (bs_env%unit_nr, *) "Done with evaluation of phi"
317 : END IF
318 :
319 : ! -------------------------------------------------------------------------
320 : ! CLEANUP
321 : ! -------------------------------------------------------------------------
322 0 : DEALLOCATE (r_blk_sizes, row_dist, col_dist)
323 0 : CALL dbcsr_distribution_release(dist)
324 :
325 0 : CALL timestop(handle)
326 :
327 0 : END SUBROUTINE atomic_basis_at_grid_point
328 :
329 : ! **************************************************************************************************
330 : !> \brief Compute value of all basis functions for a single atom across all grid points.
331 : !> Sums contributions from periodic images of `iatom` (loop over (ix, iy, iz) cells gated
332 : !> by `cell%perd`). Each per-image squared distance is compared against `r2_threshold`
333 : !> (per-atom AO Gaussian extent²); images beyond that radius contribute below eps_filter
334 : !> and are skipped.
335 : !> \param phi_val ...
336 : !> \param ri_rs_grid ...
337 : !> \param npts ...
338 : !> \param iatom ...
339 : !> \param bs_env ...
340 : !> \param r2_threshold per-image squared-distance threshold; CYCLE if r² > r2_threshold. Pass
341 : !> HUGE(1.0_dp) to disable.
342 : ! **************************************************************************************************
343 :
344 0 : SUBROUTINE fill_phi_for_atom(phi_val, ri_rs_grid, npts, iatom, bs_env, r2_threshold)
345 :
346 : REAL(KIND=dp), INTENT(INOUT) :: phi_val(:, :)
347 : INTEGER, INTENT(IN) :: npts
348 : REAL(KIND=dp), INTENT(IN) :: ri_rs_grid(3, npts)
349 : INTEGER, INTENT(IN) :: iatom
350 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
351 : REAL(KIND=dp), INTENT(IN) :: r2_threshold
352 :
353 : CHARACTER(LEN=*), PARAMETER :: routineN = 'fill_phi_for_atom'
354 :
355 : INTEGER :: first_sgf, handle, i_pt, ico, iend_co, ikind, ipgf, iset, isgf, ishell, &
356 : istart_co, ix, ix_max, ix_min, iy, iy_max, iy_min, iz, iz_max, iz_min, l, last_sgf, lx, &
357 : ly, lz, n_cart_total, row_idx
358 : REAL(KIND=dp) :: alpha, cell_vector(3), dist_vec(3), &
359 : dist_vec_raw(3), exp_val, poly, r2, &
360 : r_atom(3), weight
361 : REAL(KIND=dp), DIMENSION(3, 3) :: hmat
362 : TYPE(cell_type), POINTER :: cell
363 : TYPE(gto_basis_set_type), POINTER :: orb_basis_set
364 0 : TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
365 :
366 0 : CALL timeset(routineN, handle)
367 :
368 : ! Get Atom Info
369 0 : cell => bs_env%ri_rs%cell
370 0 : particle_set => bs_env%ri_rs%particle_set
371 0 : ikind = particle_set(iatom)%atomic_kind%kind_number
372 0 : orb_basis_set => bs_env%basis_set_AO(ikind)%gto_basis_set
373 0 : CALL get_cell(cell=cell, h=hmat)
374 0 : CPASSERT(ASSOCIATED(orb_basis_set))
375 :
376 0 : IF (cell%perd(1) == 1) THEN; ix_min = -1; ix_max = 1; ELSE; ix_min = 0; ix_max = 0
377 : END IF
378 0 : IF (cell%perd(2) == 1) THEN; iy_min = -1; iy_max = 1; ELSE; iy_min = 0; iy_max = 0
379 : END IF
380 0 : IF (cell%perd(3) == 1) THEN; iz_min = -1; iz_max = 1; ELSE; iz_min = 0; iz_max = 0
381 : END IF
382 :
383 0 : r_atom = particle_set(iatom)%r
384 :
385 : !$OMP PARALLEL DO DEFAULT(NONE) &
386 : !$OMP SHARED(phi_val, ri_rs_grid, npts, orb_basis_set, r_atom, hmat, &
387 : !$OMP ncoset, indco, cell, ix_min, ix_max, &
388 : !$OMP iy_min, iy_max, iz_min, iz_max, r2_threshold) &
389 : !$OMP PRIVATE(i_pt, dist_vec_raw, ix, iy, iz, cell_vector, dist_vec, r2, iset, &
390 : !$OMP n_cart_total, ishell, l, istart_co, iend_co, first_sgf, last_sgf, &
391 : !$OMP ipgf, alpha, exp_val, isgf, ico, row_idx, weight, lx, ly, lz, poly) &
392 0 : !$OMP SCHEDULE(DYNAMIC)
393 :
394 : DO i_pt = 1, npts
395 :
396 : dist_vec_raw = ri_rs_grid(:, i_pt) - r_atom
397 :
398 : DO ix = ix_min, ix_max
399 : DO iy = iy_min, iy_max
400 : DO iz = iz_min, iz_max
401 :
402 : cell_vector(1:3) = MATMUL(hmat, REAL([ix, iy, iz], dp))
403 :
404 : dist_vec = dist_vec_raw - cell_vector
405 :
406 : r2 = DOT_PRODUCT(dist_vec, dist_vec)
407 :
408 : IF (r2 > r2_threshold) CYCLE
409 :
410 : DO iset = 1, orb_basis_set%nset
411 : n_cart_total = ncoset(orb_basis_set%lmax(iset))
412 :
413 : DO ishell = 1, orb_basis_set%nshell(iset)
414 : l = orb_basis_set%l(ishell, iset)
415 : istart_co = ncoset(l - 1) + 1
416 : iend_co = ncoset(l)
417 :
418 : first_sgf = orb_basis_set%first_sgf(ishell, iset)
419 : last_sgf = orb_basis_set%last_sgf(ishell, iset)
420 :
421 : DO ipgf = 1, orb_basis_set%npgf(iset)
422 : alpha = orb_basis_set%zet(ipgf, iset)
423 : exp_val = EXP(-alpha*r2)
424 :
425 : DO isgf = first_sgf, last_sgf
426 : DO ico = istart_co, iend_co
427 : row_idx = (ipgf - 1)*n_cart_total + ico
428 : weight = orb_basis_set%sphi(row_idx, isgf)
429 : lx = indco(1, ico)
430 : ly = indco(2, ico)
431 : lz = indco(3, ico)
432 : poly = (dist_vec(1)**lx)*(dist_vec(2)**ly)*(dist_vec(3)**lz)
433 :
434 : phi_val(i_pt, isgf) = phi_val(i_pt, isgf) + (weight*poly*exp_val)
435 :
436 : END DO
437 : END DO
438 : END DO
439 : END DO
440 : END DO
441 : END DO
442 : END DO
443 : END DO
444 : END DO
445 : !$OMP END PARALLEL DO
446 :
447 0 : CALL timestop(handle)
448 :
449 0 : END SUBROUTINE fill_phi_for_atom
450 :
451 : ! **************************************************************************************************
452 : !> \brief Compute RI-RS Coefficients (Z_lP)
453 : !> \param qs_env ...
454 : !> \param bs_env ...
455 : !> \param ri_rs_grid_points ...
456 : !> \param mat_phi_mu_l ...
457 : !> \param mat_Z_lP ...
458 : ! **************************************************************************************************
459 :
460 0 : SUBROUTINE compute_Z_lP(qs_env, bs_env, ri_rs_grid_points, mat_phi_mu_l, mat_Z_lP)
461 :
462 : ! Arguments
463 : TYPE(qs_environment_type), POINTER :: qs_env
464 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
465 : REAL(KIND=dp), ALLOCATABLE, INTENT(INOUT) :: ri_rs_grid_points(:, :)
466 : TYPE(dbcsr_type), INTENT(INOUT) :: mat_phi_mu_l
467 : TYPE(dbcsr_type), INTENT(OUT) :: mat_Z_lP
468 :
469 : CHARACTER(LEN=*), PARAMETER :: key = 'PROPERTIES%BANDSTRUCTURE%GW%PRINT%RESTART', &
470 : routineN = 'compute_Z_lP'
471 :
472 : INTEGER :: atom_j_mepos, atom_j_stride, atom_P, atom_P_start, atom_P_stride, col_end, &
473 : col_start, group_handle, handle, handle_dpotrf, handle_dpotrs, i_blk, ikind, info, j, l, &
474 : loc_idx, max_ao_size, max_loc_ri, my_group, n_ao_total, n_grid_total, n_groups, n_loc_ri, &
475 : n_local_grid, n_procs_per_atom, natom, nkind, npcol_phi, num_grid_chunks, P_loop_atom, &
476 : ri_atom
477 0 : INTEGER, ALLOCATABLE, DIMENSION(:) :: local_grid_idx, row_offset
478 0 : INTEGER, DIMENSION(:), POINTER :: col_dist_ri, r_blk_sizes, ri_blk_sizes, &
479 0 : row_dist_grid
480 : REAL(KIND=dp) :: cutoff_ri, cutoff_ri_2, d_sP, dist2_min, &
481 : r2_threshold, r_c, t1, t2, t3
482 0 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: cutoff_ri_per_atom, cutoff_ri_per_kind, &
483 0 : d_vec_local
484 0 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: D_local, d_lp_local, phi_local, &
485 0 : sphere_grid
486 : REAL(KIND=dp), DIMENSION(3) :: dist_vec_raw, pos_P
487 0 : TYPE(atomic_kind_type), DIMENSION(:), POINTER :: atomic_kind_set
488 : TYPE(cell_type), POINTER :: cell
489 : TYPE(cp_blacs_env_type), POINTER :: blacs_env_sub
490 : TYPE(cp_fm_struct_type), POINTER :: fm_struct_b, fm_struct_D
491 : TYPE(cp_fm_type) :: fm_b, fm_D
492 : TYPE(cp_logger_type), POINTER :: logger
493 : TYPE(dbcsr_distribution_type) :: dist_phi, dist_Z
494 0 : TYPE(gw_3c_ctx_type) :: ctx_3c
495 : TYPE(mp_para_env_type), POINTER :: para_env, para_env_sub
496 0 : TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
497 : TYPE(section_vals_type), POINTER :: input
498 :
499 0 : CALL timeset(routineN, handle)
500 :
501 0 : t1 = m_walltime()
502 :
503 0 : CALL get_qs_env(qs_env, para_env=para_env, particle_set=particle_set, input=input, cell=cell)
504 0 : atomic_kind_set => bs_env%ri_rs%atomic_kind_set
505 :
506 : ! ---------------------------------------------------------------------
507 : ! Subgroup setup. Default G=1 keeps the single-rank BLAS path; G>1 splits
508 : ! ranks into atom-groups so the Cholesky on D_local distributes across G
509 : ! ranks (memory ~1/G) and the compute_d_lp build also splits across the
510 : ! subgroup. G=1 leaves para_env_sub / blacs_env_sub NULL — no subgroup
511 : ! comms created, atom_P loop uses per-rank round-robin, compute_d_lp runs
512 : ! its full atom_j range on each rank, no allreduce.
513 : ! ---------------------------------------------------------------------
514 0 : n_procs_per_atom = MIN(bs_env%ri_rs%n_procs_per_atom_z_lp, para_env%num_pe)
515 0 : IF (n_procs_per_atom < 1) n_procs_per_atom = 1
516 :
517 0 : NULLIFY (para_env_sub, blacs_env_sub)
518 0 : IF (n_procs_per_atom > 1) THEN
519 0 : n_groups = para_env%num_pe/n_procs_per_atom
520 0 : my_group = MIN(para_env%mepos/n_procs_per_atom, n_groups - 1)
521 0 : ALLOCATE (para_env_sub)
522 0 : CALL para_env_sub%from_split(para_env, my_group)
523 0 : CALL cp_blacs_env_create(blacs_env=blacs_env_sub, para_env=para_env_sub)
524 0 : atom_P_start = my_group + 1
525 0 : atom_P_stride = n_groups
526 0 : atom_j_mepos = para_env_sub%mepos
527 0 : atom_j_stride = para_env_sub%num_pe
528 : ELSE
529 0 : atom_P_start = para_env%mepos + 1
530 0 : atom_P_stride = para_env%num_pe
531 0 : atom_j_mepos = 0
532 0 : atom_j_stride = 1
533 : END IF
534 :
535 0 : natom = bs_env%n_atom
536 0 : n_ao_total = bs_env%i_ao_end_from_atom(natom)
537 0 : n_grid_total = bs_env%ri_rs%n_grid_points
538 0 : CPASSERT(SIZE(ri_rs_grid_points, 2) == n_grid_total)
539 :
540 : ! =========================================================================
541 : ! 1. SETUP DBCSR TOPOLOGY & EXACT OFFSETS
542 : ! =========================================================================
543 0 : CALL dbcsr_get_info(mat_phi_mu_l, row_blk_size=r_blk_sizes, distribution=dist_phi)
544 : CALL dbcsr_distribution_get(dist_phi, row_dist=row_dist_grid, &
545 0 : group=group_handle, npcols=npcol_phi)
546 :
547 0 : num_grid_chunks = SIZE(r_blk_sizes)
548 :
549 0 : ALLOCATE (row_offset(num_grid_chunks))
550 0 : row_offset(1) = 0
551 0 : DO i_blk = 2, num_grid_chunks
552 0 : row_offset(i_blk) = row_offset(i_blk - 1) + r_blk_sizes(i_blk - 1)
553 : END DO
554 :
555 0 : ALLOCATE (ri_blk_sizes(natom), col_dist_ri(natom))
556 0 : DO atom_P = 1, natom
557 0 : ri_blk_sizes(atom_P) = bs_env%i_RI_end_from_atom(atom_P) - bs_env%i_RI_start_from_atom(atom_P) + 1
558 0 : col_dist_ri(atom_P) = MOD(atom_P - 1, npcol_phi)
559 : END DO
560 :
561 0 : CALL dbcsr_distribution_new(dist_Z, template=dist_phi, row_dist=row_dist_grid, col_dist=col_dist_ri)
562 :
563 0 : IF (bs_env%ri_rs%Z_lP_exists) THEN
564 : CALL dbcsr_binary_read(filepath=TRIM(bs_env%prefix)//"Z_lP.matrix", &
565 : distribution=dist_Z, &
566 0 : matrix_new=mat_Z_lP)
567 0 : IF (bs_env%unit_nr > 0) THEN
568 : WRITE (bs_env%unit_nr, '(T2,A,T57,A,F7.1,A)') &
569 0 : 'Read Z_lP from file ', ' Execution time', m_walltime() - t1, ' s'
570 0 : WRITE (bs_env%unit_nr, '(A)') ' '
571 : END IF
572 : ELSE
573 :
574 : CALL dbcsr_create(mat_Z_lP, name="mat_Z_lP", dist=dist_Z, &
575 : matrix_type=dbcsr_type_no_symmetry, &
576 0 : row_blk_size=r_blk_sizes, col_blk_size=ri_blk_sizes)
577 :
578 0 : max_ao_size = 0
579 0 : DO j = 1, natom
580 0 : max_ao_size = MAX(max_ao_size, bs_env%i_ao_end_from_atom(j) - bs_env%i_ao_start_from_atom(j) + 1)
581 : END DO
582 0 : max_loc_ri = MAXVAL(ri_blk_sizes)
583 :
584 : ! Per-atom RI-RS integration sphere:
585 : ! cutoff_ri(P) = r_c + r_AO(P)
586 : ! where r_c is the truncated-Coulomb cutoff of the RI metric. The
587 : ! CUTOFF_RADIUS_RI_RS keyword (when > 0) overrides the entire cutoff calculation.
588 0 : nkind = SIZE(atomic_kind_set)
589 0 : ALLOCATE (cutoff_ri_per_atom(natom))
590 :
591 0 : IF (bs_env%ri_rs%cutoff_radius_ri_rs > 0.0_dp) THEN
592 0 : cutoff_ri_per_atom(:) = bs_env%ri_rs%cutoff_radius_ri_rs
593 : ELSE
594 0 : r_c = bs_env%ri_metric%cutoff_radius
595 0 : DO P_loop_atom = 1, natom
596 : cutoff_ri_per_atom(P_loop_atom) = &
597 0 : r_c + bs_env%ri_rs%radius_ao_per_atom(P_loop_atom)
598 : END DO
599 : END IF
600 :
601 0 : ALLOCATE (cutoff_ri_per_kind(nkind))
602 0 : cutoff_ri_per_kind(:) = 0.0_dp
603 0 : IF (bs_env%unit_nr > 0) THEN
604 0 : DO P_loop_atom = 1, natom
605 0 : ikind = particle_set(P_loop_atom)%atomic_kind%kind_number
606 : cutoff_ri_per_kind(ikind) = MAX(cutoff_ri_per_kind(ikind), &
607 0 : cutoff_ri_per_atom(P_loop_atom))
608 : END DO
609 0 : WRITE (bs_env%unit_nr, '(T2,A)') 'Per-kind maximum RI-RS sphere cutoff (Bohr):'
610 0 : WRITE (bs_env%unit_nr, '(T4,A4,A14)') 'Kind', 'max cutoff_ri'
611 0 : DO ikind = 1, nkind
612 : WRITE (bs_env%unit_nr, '(T4,A4,F14.4)') &
613 0 : atomic_kind_set(ikind)%element_symbol, &
614 0 : cutoff_ri_per_kind(ikind)
615 : END DO
616 0 : WRITE (bs_env%unit_nr, '(A)') ' '
617 0 : DEALLOCATE (cutoff_ri_per_kind)
618 : END IF
619 :
620 : ! Shared 3c-integral context: hoists libint / t_c_g0 / md_ftable / contracted
621 : ! sphi tables out of the per-triple call so compute_d_lp threads only allocate
622 : ! a lightweight per-thread workspace. MPI-collective; must be outside any
623 : ! OMP region.
624 : CALL gw_3c_ctx_create(ctx_3c, bs_env, bs_env%ri_metric, &
625 : basis_j=bs_env%basis_set_AO, basis_k=bs_env%basis_set_AO, &
626 0 : basis_i=bs_env%basis_set_RI)
627 :
628 : ! =========================================================================
629 : ! 2. MPI LOOP OVER ATOMS (Fully independent, no MPI barriers inside)
630 : ! phi_local for each atom_P's cutoff sphere is built on the fly via
631 : ! fill_phi_for_atom — no dense replicated phi_global, no allreduce.
632 : ! =========================================================================
633 0 : DO atom_P = atom_P_start, natom, atom_P_stride
634 :
635 0 : n_loc_ri = ri_blk_sizes(atom_P)
636 0 : pos_P(:) = particle_set(atom_P)%r(:)
637 :
638 0 : cutoff_ri = cutoff_ri_per_atom(atom_P)
639 0 : cutoff_ri_2 = cutoff_ri**2
640 :
641 : ! ---------------------------------------------------------------------
642 : ! A. Determine Local Grid Domain based on cutoff_ri (PBC distance)
643 : ! ---------------------------------------------------------------------
644 0 : n_local_grid = 0
645 0 : DO l = 1, n_grid_total
646 0 : dist_vec_raw = pbc(ri_rs_grid_points(1:3, l), pos_P(1:3), cell)
647 0 : dist2_min = DOT_PRODUCT(dist_vec_raw, dist_vec_raw)
648 0 : IF (dist2_min <= cutoff_ri_2) n_local_grid = n_local_grid + 1
649 : END DO
650 :
651 0 : ALLOCATE (local_grid_idx(n_local_grid))
652 :
653 0 : n_local_grid = 0
654 0 : DO l = 1, n_grid_total
655 0 : dist_vec_raw = pbc(ri_rs_grid_points(1:3, l), pos_P(1:3), cell)
656 0 : dist2_min = DOT_PRODUCT(dist_vec_raw, dist_vec_raw)
657 0 : IF (dist2_min <= cutoff_ri_2) THEN
658 0 : n_local_grid = n_local_grid + 1
659 0 : local_grid_idx(n_local_grid) = l
660 : END IF
661 : END DO
662 :
663 : ! ---------------------------------------------------------------------
664 : ! B. Build phi_local on the fly via fill_phi_for_atom.
665 : ! Only source atoms whose AO basis can reach the cutoff sphere of
666 : ! atom_P (MIC distance) contribute; the rest are pruned. The
667 : ! periodic fill_phi_for_atom sums over (ix, iy, iz) images of
668 : ! ri_atom internally.
669 : ! ---------------------------------------------------------------------
670 0 : ALLOCATE (sphere_grid(3, n_local_grid))
671 0 : DO loc_idx = 1, n_local_grid
672 0 : sphere_grid(:, loc_idx) = ri_rs_grid_points(:, local_grid_idx(loc_idx))
673 : END DO
674 :
675 0 : ALLOCATE (phi_local(n_local_grid, n_ao_total))
676 0 : phi_local = 0.0_dp
677 :
678 0 : DO ri_atom = 1, natom
679 0 : dist_vec_raw = pbc(particle_set(ri_atom)%r(:), pos_P(:), cell)
680 0 : d_sP = NORM2(dist_vec_raw)
681 0 : IF (d_sP > bs_env%ri_rs%radius_ao_per_atom(ri_atom) + cutoff_ri) CYCLE
682 :
683 0 : col_start = bs_env%i_ao_start_from_atom(ri_atom)
684 0 : col_end = bs_env%i_ao_end_from_atom(ri_atom)
685 0 : r2_threshold = bs_env%ri_rs%radius_ao_per_atom(ri_atom)**2
686 :
687 : CALL fill_phi_for_atom(phi_local(:, col_start:col_end), sphere_grid, &
688 0 : n_local_grid, ri_atom, bs_env, r2_threshold)
689 : END DO
690 :
691 0 : DEALLOCATE (sphere_grid)
692 :
693 : ! ---------------------------------------------------------------------
694 : ! C. Build Local RHS Matrix (d_lp_local) first so the subgroup-
695 : ! distributed compute_d_lp + allreduce is not entangled with the LHS
696 : ! build. compute_d_lp does not depend on D_local or d_vec_local.
697 : ! ---------------------------------------------------------------------
698 0 : ALLOCATE (d_lp_local(n_local_grid, n_loc_ri))
699 0 : d_lp_local = 0.0_dp
700 :
701 0 : t2 = m_walltime()
702 :
703 : CALL compute_d_lp(bs_env, ctx_3c, phi_local, d_lp_local, n_local_grid, &
704 0 : n_loc_ri, atom_P, max_ao_size, atom_j_mepos, atom_j_stride)
705 :
706 : ! Reduce per-subgroup-rank partials into the replicated d_lp_local.
707 : ! Skipped for G=1 (BLAS path): each rank has the full sum locally.
708 0 : IF (n_procs_per_atom > 1) THEN
709 0 : CALL para_env_sub%sum(d_lp_local)
710 : END IF
711 :
712 0 : t3 = m_walltime()
713 :
714 : ! ---------------------------------------------------------------------
715 : ! D. Build d_vec_local (Jacobi diagonal) + LHS — BLAS or ScaLAPACK
716 : ! ---------------------------------------------------------------------
717 0 : ALLOCATE (d_vec_local(n_local_grid))
718 :
719 0 : IF (n_procs_per_atom == 1) THEN
720 : CALL build_gram_jacobi_blas(phi_local, n_local_grid, n_ao_total, &
721 0 : bs_env%ri_rs%tikhonov, D_local, d_vec_local)
722 : ELSE
723 : ! ScaLAPACK path: d_vec computed directly from phi (= 1/||phi_i||^2);
724 : ! solve_D_lp_distributed builds D block-cyclic internally with
725 : ! the squared+scaled values, so no dense D_local on this rank.
726 : CALL build_jacobi_diag_from_phi(phi_local, n_local_grid, n_ao_total, &
727 0 : d_vec_local)
728 : END IF
729 :
730 : ! ---------------------------------------------------------------------
731 : ! E. Pre-scale d_lp by d_vec
732 : ! ---------------------------------------------------------------------
733 0 : CALL scale_rows_by_diag(d_lp_local, d_vec_local, n_local_grid, n_loc_ri)
734 :
735 : ! ---------------------------------------------------------------------
736 : ! F. Solve — BLAS dpotrf/dpotrs or ScaLAPACK pdpotrf/pdpotrs
737 : ! ---------------------------------------------------------------------
738 0 : IF (n_procs_per_atom == 1) THEN
739 0 : CALL timeset(routineN//"_dpotrf", handle_dpotrf)
740 0 : CALL dpotrf('L', n_local_grid, D_local, n_local_grid, info)
741 0 : CALL timestop(handle_dpotrf)
742 0 : IF (info /= 0) CPABORT("RI-RS Cholesky factorization failed")
743 0 : CALL timeset(routineN//"_dpotrs", handle_dpotrs)
744 : CALL dpotrs('L', n_local_grid, n_loc_ri, D_local, n_local_grid, &
745 0 : d_lp_local, n_local_grid, info)
746 0 : CALL timestop(handle_dpotrs)
747 0 : IF (info /= 0) CPABORT("RI-RS Cholesky solve failed")
748 0 : DEALLOCATE (D_local)
749 : ELSE
750 : CALL solve_D_lp_distributed(phi_local, d_vec_local, d_lp_local, &
751 : n_local_grid, n_ao_total, n_loc_ri, &
752 : bs_env%ri_rs%tikhonov, &
753 : para_env_sub, blacs_env_sub, &
754 0 : fm_struct_D, fm_struct_b, fm_D, fm_b, info)
755 0 : IF (info /= 0) CPABORT("Distributed RI-RS Cholesky solve failed")
756 : END IF
757 :
758 : ! ---------------------------------------------------------------------
759 : ! G. Post-scale solution by d_vec (common to both paths)
760 : ! ---------------------------------------------------------------------
761 0 : CALL scale_rows_by_diag(d_lp_local, d_vec_local, n_local_grid, n_loc_ri)
762 :
763 : ! ---------------------------------------------------------------------
764 : ! H. Scatter Local Solution Back to Global DBCSR Matrix.
765 : ! Under ScaLAPACK (G>1) the d_lp_local solution is identical on all
766 : ! G subgroup ranks (gathered via cp_fm_get_submatrix); only the
767 : ! subgroup root writes to mat_Z_lP so each atom column is emitted
768 : ! exactly once. DBCSR routes blocks to their global owner on finalize.
769 : ! local_grid_idx is ascending (built by the ordered scan above), so
770 : ! a single walking pointer over chunks works.
771 : ! ---------------------------------------------------------------------
772 0 : IF (n_procs_per_atom == 1 .OR. para_env_sub%mepos == 0) THEN
773 : CALL store_Z_lP_columns(mat_Z_lP, d_lp_local, local_grid_idx, n_local_grid, &
774 : n_loc_ri, atom_P, r_blk_sizes, row_offset, &
775 0 : bs_env%eps_filter)
776 : END IF
777 :
778 0 : DEALLOCATE (d_vec_local, d_lp_local)
779 0 : DEALLOCATE (local_grid_idx, phi_local)
780 :
781 : END DO
782 :
783 0 : DEALLOCATE (cutoff_ri_per_atom)
784 0 : CALL gw_3c_ctx_release(ctx_3c)
785 :
786 0 : CALL dbcsr_finalize(mat_Z_lP)
787 :
788 0 : IF (bs_env%unit_nr > 0) THEN
789 : WRITE (bs_env%unit_nr, '(T2,A,T57,A,F7.1,A)') &
790 0 : 'Computed Z_lP ', ' Execution time', m_walltime() - t1, ' s'
791 0 : WRITE (bs_env%unit_nr, '(A)') ' '
792 : END IF
793 :
794 0 : logger => cp_get_default_logger()
795 :
796 0 : IF (BTEST(cp_print_key_should_output(logger%iter_info, input, key), cp_p_file)) THEN
797 0 : CALL dbcsr_binary_write(matrix=mat_Z_lP, filepath=TRIM(bs_env%prefix)//"Z_lP.matrix")
798 : END IF
799 :
800 : END IF
801 :
802 0 : DEALLOCATE (row_offset, ri_blk_sizes, col_dist_ri)
803 0 : CALL dbcsr_distribution_release(dist_Z)
804 :
805 0 : IF (n_procs_per_atom > 1) THEN
806 0 : CALL cp_blacs_env_release(blacs_env_sub)
807 0 : CALL para_env_sub%free()
808 0 : DEALLOCATE (para_env_sub)
809 : END IF
810 :
811 0 : DEALLOCATE (ri_rs_grid_points)
812 :
813 0 : CALL timestop(handle)
814 :
815 0 : END SUBROUTINE compute_Z_lP
816 :
817 : ! **************************************************************************************************
818 : !> \brief Computes the dense localized RHS d_lp(l,P) = Σ_{μν,R,S} ϕ_μ(r_l)·ϕ_ν(r_l)·(μν|P) for one
819 : !> RI atom P. OMP-threaded over (atom_j, atom_k) AO-pair blocks: per thread, sweep all
820 : !> (cell_R, cell_S) periodic images of (atom_j, atom_k) about atom_P at cell (0,0,0); each
821 : !> 3c block is built by build_3c_integral_block_ctx (cached libint / sphi tables in ctx,
822 : !> kind-radius triangle screen → `screened` short-circuits negligible image triples), and
823 : !> grid-chunked pair densities are contracted into a private d_lp partial that is reduced
824 : !> into d_lp at the end of the parallel region.
825 : !> \param bs_env ...
826 : !> \param ctx shared 3c-integral context (gw_3c_ctx_create)
827 : !> \param phi_val ϕ_μ(r_l) on the local-sphere grid (n_grid_total × n_ao)
828 : !> \param d_lp output (n_grid_total × n_loc_ri), zeroed by the caller, accumulated here
829 : !> \param n_grid_total number of local-sphere grid rows
830 : !> \param n_loc_ri number of RI functions of atom_P
831 : !> \param atom_P RI atom (pinned to cell (0,0,0))
832 : !> \param max_ao_size ...
833 : !> \param atom_j_mepos ...
834 : !> \param atom_j_stride ...
835 : ! **************************************************************************************************
836 :
837 0 : SUBROUTINE compute_d_lp(bs_env, ctx, phi_val, d_lp, n_grid_total, n_loc_ri, atom_P, &
838 : max_ao_size, atom_j_mepos, atom_j_stride)
839 :
840 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
841 : TYPE(gw_3c_ctx_type), INTENT(IN) :: ctx
842 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: phi_val
843 : INTEGER, INTENT(IN) :: n_grid_total, n_loc_ri
844 : REAL(KIND=dp), INTENT(INOUT) :: d_lp(n_grid_total, n_loc_ri)
845 : INTEGER, INTENT(IN) :: atom_P, max_ao_size, atom_j_mepos, &
846 : atom_j_stride
847 :
848 : CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_d_lp'
849 : INTEGER, PARAMETER :: grid_chunk = 1024
850 :
851 : INTEGER :: atom_j, atom_k, c, handle, handle_dgemm, ix_max, ix_min, ix_R, ix_S, iy_max, &
852 : iy_min, iy_R, iy_S, iz_max, iz_min, iz_R, iz_S, j, jk_idx, jsize, jstart, k, ksize, &
853 : kstart, l, l0, natom, ri
854 : INTEGER, DIMENSION(3) :: cell_R_vec, cell_S_vec
855 : LOGICAL :: any_kept, screened
856 0 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: d_lp_prv, int_2d_prv, rho_chunk
857 0 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: int_3c_prv, int_3c_sum
858 0 : TYPE(gw_3c_ws_type) :: ws
859 :
860 0 : CALL timeset(routineN, handle)
861 :
862 0 : natom = bs_env%n_atom
863 :
864 0 : IF (bs_env%ri_rs%cell%perd(1) == 1) THEN; ix_min = -1; ix_max = 1; ELSE; ix_min = 0; ix_max = 0
865 : END IF
866 0 : IF (bs_env%ri_rs%cell%perd(2) == 1) THEN; iy_min = -1; iy_max = 1; ELSE; iy_min = 0; iy_max = 0
867 : END IF
868 0 : IF (bs_env%ri_rs%cell%perd(3) == 1) THEN; iz_min = -1; iz_max = 1; ELSE; iz_min = 0; iz_max = 0
869 : END IF
870 :
871 : !$OMP PARALLEL DEFAULT(NONE) &
872 : !$OMP SHARED(bs_env, ctx, phi_val, d_lp, n_grid_total, n_loc_ri, atom_P, max_ao_size, &
873 : !$OMP natom, ix_min, ix_max, iy_min, iy_max, iz_min, iz_max, &
874 : !$OMP atom_j_mepos, atom_j_stride) &
875 : !$OMP PRIVATE(any_kept, atom_j, atom_k, c, handle_dgemm, j, jk_idx, jsize, jstart, k, &
876 : !$OMP ksize, kstart, l, l0, ri, ix_R, iy_R, iz_R, ix_S, iy_S, iz_S, cell_R_vec, &
877 0 : !$OMP cell_S_vec, screened, d_lp_prv, int_2d_prv, rho_chunk, int_3c_prv, int_3c_sum, ws)
878 :
879 : CALL gw_3c_ws_create(ws, ctx)
880 : ALLOCATE (int_3c_prv(max_ao_size, max_ao_size, n_loc_ri))
881 : ALLOCATE (int_3c_sum(max_ao_size, max_ao_size, n_loc_ri))
882 : ALLOCATE (int_2d_prv(max_ao_size*max_ao_size, n_loc_ri))
883 : ALLOCATE (rho_chunk(grid_chunk, max_ao_size*max_ao_size))
884 : ALLOCATE (d_lp_prv(n_grid_total, n_loc_ri))
885 : d_lp_prv(:, :) = 0.0_dp
886 :
887 : ! atom_P pinned at cell (0,0,0); enumerate (atom_j, cell_R) × (atom_k, cell_S). The ctx
888 : ! integral builder's kind_radius triangle screen sets screened=.TRUE. for the bulk of
889 : ! image triples (one or both AO atoms beyond the truncated-Coulomb reach of atom_P),
890 : ! so the 27 × 27 = 729 candidate cells collapse to "adjacent cells" in practice.
891 : ! MPI-stride atom_j over the subgroup (atom_j_stride = 1 for the BLAS path, > 1 for the
892 : ! ScaLAPACK path). COLLAPSE(2) dropped because the outer stride is non-unit under
893 : ! ScaLAPACK; the inner atom_k loop carries enough work for DYNAMIC.
894 : !$OMP DO SCHEDULE(DYNAMIC)
895 : DO atom_j = atom_j_mepos + 1, natom, atom_j_stride
896 : DO atom_k = 1, natom
897 : jstart = bs_env%i_ao_start_from_atom(atom_j)
898 : jsize = bs_env%i_ao_end_from_atom(atom_j) - jstart + 1
899 : kstart = bs_env%i_ao_start_from_atom(atom_k)
900 : ksize = bs_env%i_ao_end_from_atom(atom_k) - kstart + 1
901 :
902 : int_3c_sum(1:jsize, 1:ksize, 1:n_loc_ri) = 0.0_dp
903 : any_kept = .FALSE.
904 :
905 : DO ix_R = ix_min, ix_max
906 : DO iy_R = iy_min, iy_max
907 : DO iz_R = iz_min, iz_max
908 : cell_R_vec = [ix_R, iy_R, iz_R]
909 : DO ix_S = ix_min, ix_max
910 : DO iy_S = iy_min, iy_max
911 : DO iz_S = iz_min, iz_max
912 : cell_S_vec = [ix_S, iy_S, iz_S]
913 :
914 : int_3c_prv(1:jsize, 1:ksize, 1:n_loc_ri) = 0.0_dp
915 :
916 : CALL build_3c_integral_block_ctx(int_3c_prv( &
917 : 1:jsize, 1:ksize, 1:n_loc_ri), ctx, ws, &
918 : atom_j=atom_j, atom_k=atom_k, atom_i=atom_P, &
919 : cell_j=cell_R_vec, cell_k=cell_S_vec, cell_i=[0, 0, 0], &
920 : screened=screened)
921 : IF (screened) CYCLE
922 :
923 : any_kept = .TRUE.
924 : int_3c_sum(1:jsize, 1:ksize, 1:n_loc_ri) = &
925 : int_3c_sum(1:jsize, 1:ksize, 1:n_loc_ri) + &
926 : int_3c_prv(1:jsize, 1:ksize, 1:n_loc_ri)
927 : END DO
928 : END DO
929 : END DO
930 : END DO
931 : END DO
932 : END DO
933 :
934 : IF (.NOT. any_kept) CYCLE
935 :
936 : ! Flatten 3D B_{μν,P} → 2D B_{(μν),P}
937 : DO ri = 1, n_loc_ri
938 : DO k = 1, ksize
939 : DO j = 1, jsize
940 : jk_idx = (k - 1)*jsize + j
941 : int_2d_prv(jk_idx, ri) = int_3c_sum(j, k, ri)
942 : END DO
943 : END DO
944 : END DO
945 :
946 : ! Pair density ρ(l,μν) = ϕ_μ(r_l)ϕ_ν(r_l) in grid chunks, contracted on the fly:
947 : ! d_{l,P} += ρ(l,μν) B_{(μν),P} (dgemm runs serially inside the parallel region)
948 : DO l0 = 1, n_grid_total, grid_chunk
949 : c = MIN(grid_chunk, n_grid_total - l0 + 1)
950 : DO k = 1, ksize
951 : DO j = 1, jsize
952 : jk_idx = (k - 1)*jsize + j
953 : DO l = 1, c
954 : rho_chunk(l, jk_idx) = phi_val(l0 + l - 1, jstart + j - 1)* &
955 : phi_val(l0 + l - 1, kstart + k - 1)
956 : END DO
957 : END DO
958 : END DO
959 : CALL timeset(routineN//"_dgemm", handle_dgemm)
960 : CALL dgemm("N", "N", c, n_loc_ri, jsize*ksize, &
961 : 1.0_dp, rho_chunk, grid_chunk, &
962 : int_2d_prv, max_ao_size*max_ao_size, &
963 : 1.0_dp, d_lp_prv(l0, 1), n_grid_total)
964 : CALL timestop(handle_dgemm)
965 : END DO
966 : END DO
967 : END DO
968 : !$OMP END DO
969 :
970 : !$OMP CRITICAL (compute_d_lp_reduce)
971 : d_lp(1:n_grid_total, 1:n_loc_ri) = d_lp(1:n_grid_total, 1:n_loc_ri) + &
972 : d_lp_prv(1:n_grid_total, 1:n_loc_ri)
973 : !$OMP END CRITICAL (compute_d_lp_reduce)
974 :
975 : DEALLOCATE (int_3c_prv, int_3c_sum, int_2d_prv, rho_chunk, d_lp_prv)
976 : CALL gw_3c_ws_release(ws)
977 :
978 : !$OMP END PARALLEL
979 :
980 0 : CALL timestop(handle)
981 :
982 0 : END SUBROUTINE compute_d_lp
983 :
984 : ! **************************************************************************************************
985 : !> \brief Computes the χ(iτ, k=0) matrix
986 : !> \param bs_env ...
987 : !> \param mat_chi_Gamma_tau ...
988 : !> \param mat_phi_mu_l ...
989 : !> \param mat_Z_lP ...
990 : ! **************************************************************************************************
991 :
992 0 : SUBROUTINE get_mat_chi_Gamma_tau(bs_env, mat_chi_Gamma_tau, mat_phi_mu_l, mat_Z_lP)
993 :
994 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
995 : TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: mat_chi_Gamma_tau
996 : TYPE(dbcsr_type), INTENT(INOUT) :: mat_phi_mu_l, mat_Z_lP
997 :
998 : CHARACTER(LEN=*), PARAMETER :: routineN = 'get_mat_chi_Gamma_tau'
999 :
1000 : INTEGER :: handle, i, i_t, ispin, npcol
1001 0 : INTEGER, DIMENSION(:), POINTER :: blk_ao, blk_grid, dist_col_grid, &
1002 0 : dist_row_grid
1003 : REAL(KIND=dp) :: t1, tau
1004 : TYPE(dbcsr_distribution_type) :: dist_grid_grid, dist_phi
1005 : TYPE(dbcsr_type) :: matrix_chi_grid, matrix_chi_grid_spin, &
1006 : matrix_G_occ_grid, matrix_G_vir_grid
1007 :
1008 0 : CALL timeset(routineN, handle)
1009 :
1010 : ! =========================================================================
1011 : ! 1. SETUP CORE TOPOLOGIES
1012 : ! =========================================================================
1013 0 : CALL dbcsr_get_info(mat_phi_mu_l, distribution=dist_phi, row_blk_size=blk_grid, col_blk_size=blk_ao)
1014 0 : CALL dbcsr_distribution_get(dist_phi, row_dist=dist_row_grid, npcols=npcol)
1015 :
1016 : ! Build a perfectly safe column distribution for the Grid dimension
1017 0 : ALLOCATE (dist_col_grid(SIZE(blk_grid)))
1018 0 : DO i = 1, SIZE(blk_grid)
1019 0 : dist_col_grid(i) = MOD(i - 1, npcol)
1020 : END DO
1021 :
1022 : CALL dbcsr_distribution_new(dist_grid_grid, template=dist_phi, &
1023 0 : row_dist=dist_row_grid, col_dist=dist_col_grid)
1024 :
1025 0 : CALL dbcsr_create(matrix_G_occ_grid, "G_occ_grid", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1026 0 : CALL dbcsr_create(matrix_G_vir_grid, "G_vir_grid", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1027 0 : CALL dbcsr_create(matrix_chi_grid, "chi_grid", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1028 0 : CALL dbcsr_create(matrix_chi_grid_spin, "chi_grid_spin", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1029 :
1030 : ! =========================================================================
1031 : ! 2. MAIN IMAGINARY TIME LOOP
1032 : ! =========================================================================
1033 0 : DO i_t = 1, bs_env%num_time_freq_points
1034 0 : t1 = m_walltime()
1035 :
1036 0 : tau = bs_env%time_frequency_grid%imaginary_time(i_t)
1037 0 : CALL dbcsr_set(matrix_chi_grid, 0.0_dp)
1038 :
1039 : ! ----------------------------------------------------------------------
1040 : ! A. SPIN LOOP (Allocations safely encapsulated in wrappers)
1041 : ! ----------------------------------------------------------------------
1042 0 : DO ispin = 1, bs_env%n_spin
1043 :
1044 : ! G^occ_µλ(i|τ|,k=0) = sum_n^occ C_µn(k=0) e^(-|(ϵ_nk=0-ϵ_F)τ|) C_λn(k=0)
1045 : ! G^occ_ll'(i|τ|,k=0) = sum_µν ϕ_µ(r_l) G^occ_µν ϕ_ν(r_l')
1046 : CALL build_G_grid(bs_env, tau, ispin, .TRUE., .FALSE., mat_phi_mu_l, &
1047 0 : matrix_G_occ_grid, bs_env%eps_filter)
1048 :
1049 : ! G^vir_µλ(i|τ|,k=0) = sum_n^vir C_µn(k=0) e^(-|(ϵ_nk=0-ϵ_F)τ|) C_λn(k=0)
1050 : ! G^vir_ll'(i|τ|,k=0) = sum_µν ϕ_µ(r_l) G^vir_µν ϕ_ν(r_l')
1051 : CALL build_G_grid(bs_env, tau, ispin, .FALSE., .TRUE., mat_phi_mu_l, &
1052 0 : matrix_G_vir_grid, bs_env%eps_filter)
1053 :
1054 : ! -------------------------------------------------------------------
1055 : ! B. ELEMENT-WISE HADAMARD PRODUCT
1056 : ! -------------------------------------------------------------------
1057 : ! χ_ll'(iτ,k=0) = G^occ_ll'(i|τ|,k=0) * G^vir_ll'(i|τ|,k=0)
1058 0 : CALL hadamard_product(matrix_G_occ_grid, matrix_G_vir_grid, matrix_chi_grid_spin, bs_env%spin_degeneracy)
1059 :
1060 : ! Accumulate spin contributions
1061 0 : CALL dbcsr_add(matrix_chi_grid, matrix_chi_grid_spin, 1.0_dp, 1.0_dp)
1062 :
1063 : END DO ! ispin
1064 :
1065 : ! ----------------------------------------------------------------------
1066 : ! C. TRANSFORM TO AUXILIARY BASIS & EXPORT DIRECTLY
1067 : ! χ_aux = Z^T * χ_grid * Z
1068 : ! χ_PQ(iτ,k=0) = sum_ll' Z_lP χ_ll'(iτ,k=0) Z_l'Q
1069 : ! Result is dumped directly into the final array mat_chi_Gamma_tau!
1070 : ! ----------------------------------------------------------------------
1071 : CALL dbcsr_contract_ABA("T", "N", mat_Z_lP, matrix_chi_grid, &
1072 0 : mat_chi_Gamma_tau(i_t)%matrix, bs_env%eps_filter)
1073 :
1074 0 : IF (bs_env%unit_nr > 0) THEN
1075 : WRITE (bs_env%unit_nr, '(T2,A,I13,A,I3,A,F7.1,A)') &
1076 0 : 'Computed χ(iτ,k=0) for time point', i_t, ' /', bs_env%num_time_freq_points, &
1077 0 : ', Execution time', m_walltime() - t1, ' s'
1078 : END IF
1079 :
1080 : END DO ! i_t
1081 :
1082 : ! =========================================================================
1083 : ! 3. FINAL CLEANUP
1084 : ! =========================================================================
1085 0 : CALL dbcsr_release(matrix_G_occ_grid)
1086 0 : CALL dbcsr_release(matrix_G_vir_grid)
1087 0 : CALL dbcsr_release(matrix_chi_grid)
1088 0 : CALL dbcsr_release(matrix_chi_grid_spin)
1089 0 : CALL dbcsr_distribution_release(dist_grid_grid)
1090 0 : DEALLOCATE (dist_col_grid)
1091 :
1092 0 : IF (bs_env%unit_nr > 0) WRITE (bs_env%unit_nr, '(A)') ' '
1093 :
1094 0 : CALL timestop(handle)
1095 :
1096 0 : END SUBROUTINE get_mat_chi_Gamma_tau
1097 :
1098 : ! **************************************************************************************************
1099 : !> \brief Computes Green's Function in grid basis
1100 : !> \param bs_env ...
1101 : !> \param tau ...
1102 : !> \param ispin ...
1103 : !> \param occ ...
1104 : !> \param vir ...
1105 : !> \param mat_phi_mu_l ...
1106 : !> \param matrix_G_grid ...
1107 : !> \param eps_filter ...
1108 : ! **************************************************************************************************
1109 :
1110 0 : SUBROUTINE build_G_grid(bs_env, tau, ispin, occ, vir, mat_phi_mu_l, matrix_G_grid, eps_filter)
1111 :
1112 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
1113 : REAL(KIND=dp), INTENT(IN) :: tau
1114 : INTEGER, INTENT(IN) :: ispin
1115 : LOGICAL, INTENT(IN) :: occ, vir
1116 : TYPE(dbcsr_type), INTENT(INOUT) :: mat_phi_mu_l, matrix_G_grid
1117 : REAL(KIND=dp), INTENT(IN) :: eps_filter
1118 :
1119 : CHARACTER(LEN=*), PARAMETER :: routineN = 'build_G_grid'
1120 :
1121 : INTEGER :: handle
1122 0 : INTEGER, DIMENSION(:), POINTER :: blk_ao, dist_row_ao
1123 : TYPE(cp_fm_type), POINTER :: fm_G
1124 : TYPE(dbcsr_distribution_type) :: dist_ao_ao
1125 : TYPE(dbcsr_type) :: matrix_G_ao
1126 :
1127 0 : CALL timeset(routineN, handle)
1128 :
1129 : ! 1. Select the correct FM matrix based on occ/vir flags
1130 0 : IF (occ) THEN
1131 0 : fm_G => bs_env%fm_Gocc
1132 : ELSE
1133 0 : fm_G => bs_env%fm_Gvir
1134 : END IF
1135 :
1136 : ! 2. Compute Dense FM Green's Function
1137 : ! G^occ/vir_µλ(i|τ|,k=0) = sum_G^occ/vir_µλn^occ/vir C_µn(k=0) e^(-|(ϵ_nk=0-ϵ_F)τ|) C_λn(k=0)
1138 0 : CALL G_occ_vir(bs_env, tau, fm_G, ispin, occ=occ, vir=vir)
1139 :
1140 : ! 3. Setup AO DBCSR Topology and Create Matrix dynamically
1141 0 : CALL setup_square_topology(mat_phi_mu_l, 'COL', dist_ao_ao, blk_ao, dist_row_ao)
1142 :
1143 : CALL dbcsr_create(matrix_G_ao, name="G_ao", dist=dist_ao_ao, &
1144 : matrix_type=dbcsr_type_no_symmetry, &
1145 0 : row_blk_size=blk_ao, col_blk_size=blk_ao)
1146 :
1147 : ! 4. Convert FM to Sparse DBCSR
1148 0 : CALL copy_fm_to_dbcsr(fm_G, matrix_G_ao, keep_sparsity=.FALSE.)
1149 :
1150 : ! 5. Transform to Grid Basis: G_grid = phi * G_ao * phi^T
1151 : ! G^occ/vir_ll'(i|τ|,k=0) = sum_µν ϕ_µ(r_l) G^occ/vir_µν ϕ_ν(r_l')
1152 : CALL dbcsr_contract_ABA("N", "T", mat_phi_mu_l, matrix_G_ao, matrix_G_grid, &
1153 0 : eps_filter)
1154 :
1155 : ! 6. Release AO matrix and topology
1156 0 : CALL release_dbcsr_topology_and_matrices(dist=dist_ao_ao, mapped_dist=dist_row_ao, m1=matrix_G_ao)
1157 :
1158 0 : CALL timestop(handle)
1159 :
1160 0 : END SUBROUTINE build_G_grid
1161 :
1162 : ! **************************************************************************************************
1163 : !> \brief Computes the exact exchange part of the GW self-energy
1164 : !> \param bs_env ...
1165 : !> \param qs_env ...
1166 : !> \param mat_phi_mu_l ...
1167 : !> \param mat_Z_lP ...
1168 : !> \param fm_Sigma_x_Gamma ...
1169 : ! **************************************************************************************************
1170 :
1171 0 : SUBROUTINE compute_Sigma_x(bs_env, qs_env, mat_phi_mu_l, mat_Z_lP, fm_Sigma_x_Gamma)
1172 :
1173 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
1174 : TYPE(qs_environment_type), POINTER :: qs_env
1175 : TYPE(dbcsr_type), INTENT(INOUT) :: mat_phi_mu_l, mat_Z_lP
1176 : TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:) :: fm_Sigma_x_Gamma
1177 :
1178 : CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_Sigma_x'
1179 :
1180 : INTEGER :: handle, ispin
1181 0 : INTEGER, DIMENSION(:), POINTER :: blk_aux, blk_grid, dist_col_grid, &
1182 0 : dist_row_aux
1183 : REAL(KIND=dp) :: t1
1184 0 : TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:, :) :: fm_Vtr_Gamma
1185 : TYPE(dbcsr_distribution_type) :: dist_aux_aux, dist_grid_grid
1186 : TYPE(dbcsr_type) :: mat_Sigma_x_Gamma, matrix_D_grid, &
1187 : matrix_Sigma_x_grid, matrix_V_aux, &
1188 : matrix_V_grid
1189 :
1190 0 : CALL timeset(routineN, handle)
1191 :
1192 0 : t1 = m_walltime()
1193 :
1194 0 : ALLOCATE (fm_Sigma_x_Gamma(bs_env%n_spin))
1195 0 : DO ispin = 1, bs_env%n_spin
1196 0 : CALL cp_fm_create(fm_Sigma_x_Gamma(ispin), bs_env%fm_s_Gamma%matrix_struct)
1197 : END DO
1198 :
1199 0 : CALL dbcsr_create(mat_Sigma_x_Gamma, template=bs_env%mat_ao_ao%matrix)
1200 :
1201 : ! =========================================================================
1202 : ! 1. SETUP CORE TOPOLOGIES
1203 : ! =========================================================================
1204 0 : CALL setup_square_topology(mat_phi_mu_l, 'ROW', dist_grid_grid, blk_grid, dist_col_grid)
1205 0 : CALL setup_square_topology(mat_Z_lP, 'COL', dist_aux_aux, blk_aux, dist_row_aux)
1206 :
1207 : ! =========================================================================
1208 : ! 2. COMPUTE V^tr_ll'
1209 : ! =========================================================================
1210 : CALL RI_2c_integral_mat(qs_env, fm_Vtr_Gamma, bs_env%fm_RI_RI, bs_env%n_RI, &
1211 0 : bs_env%trunc_coulomb, do_kpoints=.FALSE.)
1212 :
1213 : ! M^-1(k=0) V^tr(τ) M^-1(k=0) -> fm_Vtr_Gamma
1214 0 : CALL fm_contract_ABA(bs_env%fm_Minv_Gamma, fm_Vtr_Gamma(:, 1))
1215 :
1216 0 : CALL dbcsr_create(matrix_V_aux, "V_aux", dist_aux_aux, dbcsr_type_no_symmetry, blk_aux, blk_aux)
1217 0 : CALL dbcsr_create(matrix_V_grid, "V_grid", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1218 :
1219 0 : CALL copy_fm_to_dbcsr(fm_Vtr_Gamma(1, 1), matrix_V_aux, keep_sparsity=.FALSE.)
1220 :
1221 : ! V^tr_ll' = sum_PQ Z_lP V^trunc_PQ Z_l'Q
1222 : CALL dbcsr_contract_ABA("N", "T", mat_Z_lP, matrix_V_aux, matrix_V_grid, &
1223 0 : bs_env%eps_filter)
1224 0 : CALL dbcsr_release(matrix_V_aux)
1225 :
1226 : ! =========================================================================
1227 : ! 3. SPIN LOOP FOR EXACT EXCHANGE
1228 : ! =========================================================================
1229 0 : DO ispin = 1, bs_env%n_spin
1230 :
1231 : ! Density matrix on grid is essentially G_occ at tau = 0.0
1232 : ! D_µν = sum_n^occ C_µn(k=0) C_νn(k=0)
1233 : ! D_ll' = sum_µν ϕ_µ(r_l) D_µν ϕ_ν(r_l')
1234 0 : CALL dbcsr_create(matrix_D_grid, "D_grid", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1235 0 : CALL build_G_grid(bs_env, 0.0_dp, ispin, .TRUE., .FALSE., mat_phi_mu_l, matrix_D_grid, bs_env%eps_filter)
1236 :
1237 : ! Element-wise Hadamard product: Σ^x_grid = D_grid ◦ V_grid
1238 : ! Σ^x_ll' = D_ll' * V^tr_ll'
1239 0 : CALL dbcsr_create(matrix_Sigma_x_grid, template=matrix_V_grid)
1240 0 : CALL hadamard_product(matrix_D_grid, matrix_V_grid, matrix_Sigma_x_grid, 1.0_dp)
1241 :
1242 0 : CALL dbcsr_release(matrix_D_grid)
1243 :
1244 : ! Transform back to AO basis: Σ^x_ao = -1.0 * phi^T * Σ^x_grid * phi
1245 : ! Σ^x_λσ(k=0) = -sum_ll' ϕ_λ(r_l) Σ^x_ll' ϕ_σ(r_l')
1246 : CALL dbcsr_contract_ABA("T", "N", mat_phi_mu_l, matrix_Sigma_x_grid, &
1247 0 : mat_Sigma_x_Gamma, bs_env%eps_filter)
1248 0 : CALL dbcsr_scale(mat_Sigma_x_Gamma, -1.0_dp)
1249 :
1250 0 : CALL dbcsr_release(matrix_Sigma_x_grid)
1251 :
1252 : ! Data I/O and Export to CP2K Full Matrices
1253 0 : CALL copy_dbcsr_to_fm(mat_Sigma_x_Gamma, fm_Sigma_x_Gamma(ispin))
1254 :
1255 : END DO ! ispin
1256 :
1257 0 : IF (bs_env%unit_nr > 0) THEN
1258 : WRITE (bs_env%unit_nr, '(T2,A,T58,A,F7.1,A)') &
1259 0 : 'Computed Σ^x(k=0),', ' Execution time', m_walltime() - t1, ' s'
1260 0 : WRITE (bs_env%unit_nr, '(A)') ' '
1261 : END IF
1262 :
1263 : ! =========================================================================
1264 : ! 4. CLEANUP
1265 : ! =========================================================================
1266 : CALL release_dbcsr_topology_and_matrices(dist=dist_grid_grid, mapped_dist=dist_col_grid, &
1267 0 : m1=mat_Sigma_x_Gamma, m2=matrix_V_grid)
1268 0 : CALL release_dbcsr_topology_and_matrices(dist=dist_aux_aux, mapped_dist=dist_row_aux)
1269 :
1270 0 : CALL cp_fm_release(fm_Vtr_Gamma)
1271 :
1272 0 : CALL timestop(handle)
1273 :
1274 0 : END SUBROUTINE compute_Sigma_x
1275 :
1276 : ! **************************************************************************************************
1277 : !> \brief Computes the correlation part of the GW self-energy
1278 : !> \param bs_env ...
1279 : !> \param fm_W_time ...
1280 : !> \param mat_phi_mu_l ...
1281 : !> \param mat_Z_lP ...
1282 : !> \param fm_Sigma_c_Gamma_time ...
1283 : ! **************************************************************************************************
1284 :
1285 0 : SUBROUTINE compute_Sigma_c(bs_env, fm_W_time, mat_phi_mu_l, mat_Z_lP, fm_Sigma_c_Gamma_time)
1286 :
1287 : TYPE(post_scf_bandstructure_type), POINTER :: bs_env
1288 : TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:) :: fm_W_time
1289 : TYPE(dbcsr_type), INTENT(INOUT) :: mat_phi_mu_l, mat_Z_lP
1290 : TYPE(cp_fm_type), ALLOCATABLE, DIMENSION(:, :, :) :: fm_Sigma_c_Gamma_time
1291 :
1292 : CHARACTER(LEN=*), PARAMETER :: routineN = 'compute_Sigma_c'
1293 :
1294 : INTEGER :: handle, i_t, ispin
1295 0 : INTEGER, DIMENSION(:), POINTER :: blk_aux, blk_grid, dist_col_grid, &
1296 0 : dist_row_aux
1297 : REAL(KIND=dp) :: t1, tau
1298 : TYPE(dbcsr_distribution_type) :: dist_aux_aux, dist_grid_grid
1299 0 : TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER :: mat_Sigma_neg_tau, mat_Sigma_pos_tau
1300 : TYPE(dbcsr_type) :: matrix_G_occ_grid, matrix_G_vir_grid, matrix_Sigma_neg_grid, &
1301 : matrix_Sigma_pos_grid, matrix_W_aux, matrix_W_grid
1302 :
1303 0 : CALL timeset(routineN, handle)
1304 :
1305 : ! =========================================================================
1306 : ! 1. SETUP CORE TOPOLOGIES AND PRE-ALLOCATE OUTPUT ARRAYS
1307 : ! =========================================================================
1308 0 : CALL setup_square_topology(mat_phi_mu_l, 'ROW', dist_grid_grid, blk_grid, dist_col_grid)
1309 0 : CALL setup_square_topology(mat_Z_lP, 'COL', dist_aux_aux, blk_aux, dist_row_aux)
1310 :
1311 : ! Pre-allocate local DBCSR matrices to act as targets for final output
1312 0 : NULLIFY (mat_Sigma_neg_tau, mat_Sigma_pos_tau)
1313 0 : ALLOCATE (mat_Sigma_neg_tau(bs_env%num_time_freq_points, bs_env%n_spin))
1314 0 : ALLOCATE (mat_Sigma_pos_tau(bs_env%num_time_freq_points, bs_env%n_spin))
1315 :
1316 0 : DO i_t = 1, bs_env%num_time_freq_points
1317 0 : DO ispin = 1, bs_env%n_spin
1318 0 : ALLOCATE (mat_Sigma_neg_tau(i_t, ispin)%matrix)
1319 0 : ALLOCATE (mat_Sigma_pos_tau(i_t, ispin)%matrix)
1320 0 : CALL dbcsr_create(mat_Sigma_neg_tau(i_t, ispin)%matrix, template=bs_env%mat_ao_ao%matrix)
1321 0 : CALL dbcsr_create(mat_Sigma_pos_tau(i_t, ispin)%matrix, template=bs_env%mat_ao_ao%matrix)
1322 : END DO
1323 : END DO
1324 :
1325 : ! =========================================================================
1326 : ! 2. MAIN IMAGINARY TIME LOOP
1327 : ! =========================================================================
1328 0 : DO i_t = 1, bs_env%num_time_freq_points
1329 0 : tau = bs_env%time_frequency_grid%imaginary_time(i_t)
1330 :
1331 : ! -------------------------------------------------------------------
1332 : ! Compute W_grid = Z * W_aux * Z^T
1333 : ! -------------------------------------------------------------------
1334 0 : CALL dbcsr_create(matrix_W_aux, "W_aux", dist_aux_aux, dbcsr_type_no_symmetry, blk_aux, blk_aux)
1335 0 : CALL dbcsr_create(matrix_W_grid, "W_grid", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1336 :
1337 0 : CALL copy_fm_to_dbcsr(fm_W_time(i_t), matrix_W_aux, keep_sparsity=.FALSE.)
1338 :
1339 : ! W^MIC_ll'(iτ,k=0) = sum_PQ Z_lP W^MIC_PQ(iτ) Z_l'Q
1340 : CALL dbcsr_contract_ABA("N", "T", mat_Z_lP, matrix_W_aux, matrix_W_grid, &
1341 0 : bs_env%eps_filter)
1342 :
1343 0 : CALL dbcsr_release(matrix_W_aux) ! Clean up aux basis immediately
1344 :
1345 0 : DO ispin = 1, bs_env%n_spin
1346 0 : t1 = m_walltime()
1347 :
1348 : ! -------------------------------------------------------------------
1349 : ! A. Transform Green's Functions to the Grid
1350 : ! -------------------------------------------------------------------
1351 0 : CALL dbcsr_create(matrix_G_occ_grid, "G_occ_grid", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1352 0 : CALL dbcsr_create(matrix_G_vir_grid, "G_vir_grid", dist_grid_grid, dbcsr_type_no_symmetry, blk_grid, blk_grid)
1353 :
1354 : ! G^occ_µλ(i|τ|,k=0) = sum_G^occ_µλn^occ C_µn(k=0) e^(-|(ϵ_nk=0-ϵ_F)τ|) C_λn(k=0)
1355 : ! G^occ_ll'(i|τ|,k=0) = sum_µν ϕ_µ(r_l) G^occ_µν ϕ_ν(r_l')
1356 0 : CALL build_G_grid(bs_env, tau, ispin, .TRUE., .FALSE., mat_phi_mu_l, matrix_G_occ_grid, bs_env%eps_filter)
1357 :
1358 : ! G^vir_µλ(i|τ|,k=0) = sum_n^vir C_µn(k=0) e^(-|(ϵ_nk=0-ϵ_F)τ|) C_λn(k=0)
1359 : ! G^vir_ll'(i|τ|,k=0) = sum_µν ϕ_µ(r_l) G^vir_µν ϕ_ν(r_l')
1360 0 : CALL build_G_grid(bs_env, tau, ispin, .FALSE., .TRUE., mat_phi_mu_l, matrix_G_vir_grid, bs_env%eps_filter)
1361 :
1362 : ! -------------------------------------------------------------------
1363 : ! B. Element-wise Hadamard Products for Sigma_c on Grid
1364 : ! Σ_neg_grid = G_occ_grid ◦ W_grid
1365 : ! Σ_pos_grid = G_vir_grid ◦ W_grid
1366 : ! -------------------------------------------------------------------
1367 0 : CALL dbcsr_create(matrix_Sigma_neg_grid, template=matrix_W_grid)
1368 0 : CALL dbcsr_create(matrix_Sigma_pos_grid, template=matrix_W_grid)
1369 :
1370 : ! Σ^c_ll'(iτ,k=0) = -G^occ_ll'(i|τ|,k=0) * W^MIC_ll'(iτ,k=0), for τ < 0
1371 0 : CALL hadamard_product(matrix_G_occ_grid, matrix_W_grid, matrix_Sigma_neg_grid, 1.0_dp)
1372 :
1373 : ! Σ^c_ll'(iτ,k=0) = G^vir_ll'(i|τ|,k=0) * W^MIC_ll'(iτ,k=0), for τ > 0
1374 0 : CALL hadamard_product(matrix_G_vir_grid, matrix_W_grid, matrix_Sigma_pos_grid, 1.0_dp)
1375 :
1376 : ! Instantly purge massive G_grid arrays to save memory
1377 0 : CALL dbcsr_release(matrix_G_occ_grid)
1378 0 : CALL dbcsr_release(matrix_G_vir_grid)
1379 :
1380 : ! -------------------------------------------------------------------
1381 : ! C. Transform Sigma back to AO Basis
1382 : ! Σ_AO = phi^T * Σ_grid * phi
1383 : ! -------------------------------------------------------------------
1384 :
1385 : ! Σ^c_λσ(iτ,k=0) = sum_ll' ϕ_λ(r_l) Σ^c_ll'(iτ,k=0) ϕ_σ(r_l'), for τ < 0
1386 : CALL dbcsr_contract_ABA("T", "N", mat_phi_mu_l, matrix_Sigma_neg_grid, &
1387 0 : mat_Sigma_neg_tau(i_t, ispin)%matrix, bs_env%eps_filter)
1388 0 : CALL dbcsr_scale(mat_Sigma_neg_tau(i_t, ispin)%matrix, -1.0_dp)
1389 :
1390 : ! Σ^c_λσ(iτ,k=0) = sum_ll' ϕ_λ(r_l) Σ^c_ll'(iτ,k=0) ϕ_σ(r_l'), for τ > 0
1391 : CALL dbcsr_contract_ABA("T", "N", mat_phi_mu_l, matrix_Sigma_pos_grid, &
1392 0 : mat_Sigma_pos_tau(i_t, ispin)%matrix, bs_env%eps_filter)
1393 :
1394 : ! Purge Grid Sigma arrays
1395 0 : CALL dbcsr_release(matrix_Sigma_neg_grid)
1396 0 : CALL dbcsr_release(matrix_Sigma_pos_grid)
1397 :
1398 0 : IF (bs_env%unit_nr > 0) THEN
1399 : WRITE (bs_env%unit_nr, '(T2,A,I10,A,I3,A,F7.1,A)') &
1400 0 : 'Computed Σ^c(iτ,k=0) for time point ', i_t, ' /', bs_env%num_time_freq_points, &
1401 0 : ', Execution time', m_walltime() - t1, ' s'
1402 : END IF
1403 :
1404 : END DO ! ispin
1405 :
1406 : ! Release the W_grid for this time point
1407 0 : CALL dbcsr_release(matrix_W_grid)
1408 :
1409 : END DO ! i_t
1410 :
1411 0 : IF (bs_env%unit_nr > 0) WRITE (bs_env%unit_nr, '(A)') ' '
1412 :
1413 : ! -------------------------------------------------------------------------
1414 : ! 3. FINALIZE AND CLEANUP
1415 : ! -------------------------------------------------------------------------
1416 : CALL fill_fm_Sigma_c_Gamma_time(fm_Sigma_c_Gamma_time, bs_env, &
1417 0 : mat_Sigma_pos_tau, mat_Sigma_neg_tau)
1418 :
1419 0 : CALL cp_fm_release(fm_W_time)
1420 :
1421 0 : CALL dbcsr_deallocate_matrix_set(mat_Sigma_neg_tau)
1422 0 : CALL dbcsr_deallocate_matrix_set(mat_Sigma_pos_tau)
1423 :
1424 0 : CALL release_dbcsr_topology_and_matrices(dist=dist_grid_grid, mapped_dist=dist_col_grid)
1425 0 : CALL release_dbcsr_topology_and_matrices(dist=dist_aux_aux, mapped_dist=dist_row_aux)
1426 :
1427 0 : CALL delete_unnecessary_files(bs_env)
1428 0 : CALL timestop(handle)
1429 :
1430 0 : END SUBROUTINE compute_Sigma_c
1431 :
1432 : ! **************************************************************************************************
1433 : !> \brief DBCSR Topology Generation
1434 : !> \param matrix_template ...
1435 : !> \param dim_type ...
1436 : !> \param square_dist ...
1437 : !> \param blk_sizes ...
1438 : !> \param mapped_dist ...
1439 : ! **************************************************************************************************
1440 :
1441 26880 : SUBROUTINE setup_square_topology(matrix_template, dim_type, square_dist, blk_sizes, mapped_dist)
1442 :
1443 : TYPE(dbcsr_type), INTENT(IN) :: matrix_template
1444 : CHARACTER(LEN=*), INTENT(IN) :: dim_type
1445 : TYPE(dbcsr_distribution_type), INTENT(OUT) :: square_dist
1446 : INTEGER, DIMENSION(:), INTENT(OUT), POINTER :: blk_sizes, mapped_dist
1447 :
1448 : CHARACTER(LEN=*), PARAMETER :: routineN = 'setup_square_topology'
1449 :
1450 : INTEGER :: handle, i, np, npcols, nprows
1451 8960 : INTEGER, DIMENSION(:), POINTER :: col_blk, col_dist, row_blk, row_dist
1452 : TYPE(dbcsr_distribution_type) :: dist_template
1453 :
1454 8960 : CALL timeset(routineN, handle)
1455 :
1456 : CALL dbcsr_get_info(matrix_template, distribution=dist_template, &
1457 8960 : row_blk_size=row_blk, col_blk_size=col_blk)
1458 : CALL dbcsr_distribution_get(dist_template, row_dist=row_dist, col_dist=col_dist, &
1459 8960 : nprows=nprows, npcols=npcols)
1460 :
1461 8960 : IF (TRIM(dim_type) == 'ROW') THEN
1462 : ! Creates ROW x ROW (e.g., Grid x Grid from mat_phi_mu_l)
1463 600 : blk_sizes => row_blk
1464 600 : np = npcols
1465 1800 : ALLOCATE (mapped_dist(SIZE(blk_sizes)))
1466 6960 : DO i = 1, SIZE(blk_sizes)
1467 6960 : mapped_dist(i) = MOD(i - 1, np)
1468 : END DO
1469 : CALL dbcsr_distribution_new(square_dist, template=dist_template, &
1470 600 : row_dist=row_dist, col_dist=mapped_dist)
1471 :
1472 8360 : ELSE IF (TRIM(dim_type) == 'COL') THEN
1473 : ! Creates COL x COL (e.g., Aux x Aux from mat_Z_lP)
1474 8360 : blk_sizes => col_blk
1475 8360 : np = nprows
1476 25080 : ALLOCATE (mapped_dist(SIZE(blk_sizes)))
1477 25080 : DO i = 1, SIZE(blk_sizes)
1478 25080 : mapped_dist(i) = MOD(i - 1, np)
1479 : END DO
1480 : CALL dbcsr_distribution_new(square_dist, template=dist_template, &
1481 8360 : row_dist=mapped_dist, col_dist=col_dist)
1482 : END IF
1483 :
1484 8960 : CALL timestop(handle)
1485 :
1486 8960 : END SUBROUTINE setup_square_topology
1487 :
1488 : ! **************************************************************************************************
1489 : !> \brief DBCSR matrices deallocation
1490 : !> \param dist ...
1491 : !> \param mapped_dist ...
1492 : !> \param m1 ...
1493 : !> \param m2 ...
1494 : !> \param m3 ...
1495 : !> \param m4 ...
1496 : ! **************************************************************************************************
1497 :
1498 13560 : SUBROUTINE release_dbcsr_topology_and_matrices(dist, mapped_dist, m1, m2, m3, m4)
1499 :
1500 : TYPE(dbcsr_distribution_type), INTENT(INOUT), &
1501 : OPTIONAL :: dist
1502 : INTEGER, DIMENSION(:), INTENT(INOUT), OPTIONAL, &
1503 : POINTER :: mapped_dist
1504 : TYPE(dbcsr_type), INTENT(INOUT), OPTIONAL :: m1, m2, m3, m4
1505 :
1506 : CHARACTER(LEN=*), PARAMETER :: routineN = 'release_dbcsr_topology_and_matrices'
1507 :
1508 : INTEGER :: handle
1509 :
1510 13560 : CALL timeset(routineN, handle)
1511 :
1512 13560 : IF (PRESENT(dist)) CALL dbcsr_distribution_release(dist)
1513 13560 : IF (PRESENT(mapped_dist)) THEN
1514 8960 : IF (ASSOCIATED(mapped_dist)) THEN
1515 8960 : DEALLOCATE (mapped_dist)
1516 : NULLIFY (mapped_dist)
1517 : END IF
1518 : END IF
1519 13560 : IF (PRESENT(m1)) CALL dbcsr_release(m1)
1520 13560 : IF (PRESENT(m2)) CALL dbcsr_release(m2)
1521 13560 : IF (PRESENT(m3)) CALL dbcsr_release(m3)
1522 13560 : IF (PRESENT(m4)) CALL dbcsr_release(m4)
1523 :
1524 13560 : CALL timestop(handle)
1525 :
1526 13560 : END SUBROUTINE release_dbcsr_topology_and_matrices
1527 :
1528 : END MODULE gw_ri_rs_large_cell_Gamma
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