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mp2_grids.F
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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 Routines to calculate frequency and time grids (integration points and weights)
10!> for correlation methods
11!> \par History
12!> 05.2019 Refactored from rpa_ri_gpw [Frederick Stein]
13! **************************************************************************************************
14MODULE mp2_grids
15 USE cp_fm_types, ONLY: cp_fm_get_info,&
16 cp_fm_type
17 USE input_section_types, ONLY: section_vals_type,&
18 section_vals_val_set
19 USE kinds, ONLY: dp
20 USE kpoint_types, ONLY: get_kpoint_info,&
21 kpoint_env_type,&
22 kpoint_type
23 USE machine, ONLY: m_flush
24 USE mathconstants, ONLY: pi
25 USE message_passing, ONLY: mp_para_env_release,&
26 mp_para_env_type
27 USE minimax_exp, ONLY: get_exp_minimax_coeff
28 USE minimax_exp_gw, ONLY: get_exp_minimax_coeff_gw
29 USE minimax_rpa, ONLY: get_rpa_minimax_coeff,&
30 get_rpa_minimax_coeff_larger_grid
31 USE qs_environment_types, ONLY: get_qs_env,&
32 qs_environment_type
33 USE qs_mo_types, ONLY: get_mo_set,&
34 mo_set_type
35#include "./base/base_uses.f90"
36
37 IMPLICIT NONE
38
39 PRIVATE
40
41 CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'mp2_grids'
42
43 PUBLIC :: get_minimax_grid, get_clenshaw_grid, test_least_square_ft, get_l_sq_wghts_cos_tf_t_to_w, &
44 get_l_sq_wghts_cos_tf_w_to_t, get_l_sq_wghts_sin_tf_t_to_w
45
46CONTAINS
47
48! **************************************************************************************************
49!> \brief ...
50!> \param para_env ...
51!> \param unit_nr ...
52!> \param homo ...
53!> \param Eigenval ...
54!> \param num_integ_points ...
55!> \param do_im_time ...
56!> \param do_ri_sos_laplace_mp2 ...
57!> \param do_print ...
58!> \param tau_tj ...
59!> \param tau_wj ...
60!> \param qs_env ...
61!> \param do_gw_im_time ...
62!> \param do_kpoints_cubic_RPA ...
63!> \param e_fermi ...
64!> \param tj ...
65!> \param wj ...
66!> \param weights_cos_tf_t_to_w ...
67!> \param weights_cos_tf_w_to_t ...
68!> \param weights_sin_tf_t_to_w ...
69!> \param regularization ...
70! **************************************************************************************************
71 SUBROUTINE get_minimax_grid(para_env, unit_nr, homo, Eigenval, num_integ_points, &
72 do_im_time, do_ri_sos_laplace_mp2, do_print, tau_tj, tau_wj, qs_env, do_gw_im_time, &
73 do_kpoints_cubic_RPA, e_fermi, tj, wj, weights_cos_tf_t_to_w, &
74 weights_cos_tf_w_to_t, weights_sin_tf_t_to_w, regularization)
75
76 TYPE(mp_para_env_type), INTENT(IN) :: para_env
77 INTEGER, INTENT(IN) :: unit_nr
78 INTEGER, DIMENSION(:), INTENT(IN) :: homo
79 REAL(kind=dp), DIMENSION(:, :, :), INTENT(IN) :: eigenval
80 INTEGER, INTENT(IN) :: num_integ_points
81 LOGICAL, INTENT(IN) :: do_im_time, do_ri_sos_laplace_mp2, &
82 do_print
83 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
84 INTENT(OUT) :: tau_tj, tau_wj
85 TYPE(qs_environment_type), POINTER :: qs_env
86 LOGICAL, INTENT(IN) :: do_gw_im_time, do_kpoints_cubic_rpa
87 REAL(kind=dp), INTENT(OUT) :: e_fermi
88 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
89 INTENT(INOUT) :: tj, wj
90 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :), &
91 INTENT(OUT) :: weights_cos_tf_t_to_w, &
92 weights_cos_tf_w_to_t, &
93 weights_sin_tf_t_to_w
94 REAL(kind=dp), INTENT(IN), OPTIONAL :: regularization
95
96 CHARACTER(LEN=*), PARAMETER :: routinen = 'get_minimax_grid'
97 INTEGER, PARAMETER :: num_points_per_magnitude = 200
98
99 INTEGER :: handle, ierr, ispin, jquad, nspins
100 LOGICAL :: my_do_kpoints, my_open_shell
101 REAL(kind=dp) :: emax, emin, max_error_min, my_e_range, &
102 my_regularization, scaling
103 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: x_tw
104 TYPE(section_vals_type), POINTER :: input
105
106 CALL timeset(routinen, handle)
107
108 ! Test for spin unrestricted
109 nspins = SIZE(homo)
110 my_open_shell = (nspins == 2)
111
112 ! Test whether all necessary variables are available
113 my_do_kpoints = .false.
114 IF (.NOT. do_ri_sos_laplace_mp2) THEN
115 my_do_kpoints = do_kpoints_cubic_rpa
116 END IF
117
118 my_regularization = 0.0_dp
119 IF (PRESENT(regularization)) THEN
120 my_regularization = regularization
121 END IF
122
123 IF (my_do_kpoints) THEN
124 CALL gap_and_max_eig_diff_kpoints(qs_env, para_env, emin, emax, e_fermi)
125 my_e_range = emax/emin
126 ELSE
127 IF (qs_env%mp2_env%E_range <= 1.0_dp .OR. qs_env%mp2_env%E_gap <= 0.0_dp) THEN
128 emin = huge(dp)
129 emax = 0.0_dp
130 DO ispin = 1, nspins
131 IF (homo(ispin) > 0) THEN
132 emin = min(emin, eigenval(homo(ispin) + 1, 1, ispin) - eigenval(homo(ispin), 1, ispin))
133 emax = max(emax, maxval(eigenval(:, :, ispin)) - minval(eigenval(:, :, ispin)))
134 END IF
135 END DO
136 my_e_range = emax/emin
137 qs_env%mp2_env%e_range = my_e_range
138 qs_env%mp2_env%e_gap = emin
139
140 CALL get_qs_env(qs_env, input=input)
141 CALL section_vals_val_set(input, "DFT%XC%WF_CORRELATION%E_RANGE", r_val=my_e_range)
142 CALL section_vals_val_set(input, "DFT%XC%WF_CORRELATION%E_GAP", r_val=emin)
143 ELSE
144 my_e_range = qs_env%mp2_env%E_range
145 emin = qs_env%mp2_env%E_gap
146 emax = emin*my_e_range
147 END IF
148 END IF
149
150 IF (num_integ_points > 20 .AND. my_e_range < 100.0_dp) THEN
151 IF (unit_nr > 0) &
152 CALL cp_warn(__location__, &
153 "You requested a large minimax grid (> 20 points) for a small minimax range R (R < 100). "// &
154 "That may lead to numerical "// &
155 "instabilities when computing minimax grid weights. You can prevent small ranges by choosing "// &
156 "a larger basis set with higher angular momenta or alternatively using all-electron calculations.")
157 END IF
158
159 IF (.NOT. do_ri_sos_laplace_mp2) THEN
160 ALLOCATE (x_tw(2*num_integ_points))
161 x_tw = 0.0_dp
162 ierr = 0
163 IF (num_integ_points .LE. 20) THEN
164 CALL get_rpa_minimax_coeff(num_integ_points, my_e_range, x_tw, ierr)
165 ELSE
166 CALL get_rpa_minimax_coeff_larger_grid(num_integ_points, my_e_range, x_tw)
167 END IF
168
169 ALLOCATE (tj(num_integ_points))
170 tj = 0.0_dp
171
172 ALLOCATE (wj(num_integ_points))
173 wj = 0.0_dp
174
175 DO jquad = 1, num_integ_points
176 tj(jquad) = x_tw(jquad)
177 wj(jquad) = x_tw(jquad + num_integ_points)
178 END DO
179
180 DEALLOCATE (x_tw)
181
182 IF (unit_nr > 0 .AND. do_print) THEN
183 WRITE (unit=unit_nr, fmt="(T3,A,T75,i6)") &
184 "MINIMAX_INFO| Number of integration points:", num_integ_points
185 WRITE (unit=unit_nr, fmt="(T3,A,T66,F15.4)") &
186 "MINIMAX_INFO| Gap for the minimax approximation:", emin
187 WRITE (unit=unit_nr, fmt="(T3,A,T66,F15.4)") &
188 "MINIMAX_INFO| Range for the minimax approximation:", my_e_range
189 WRITE (unit=unit_nr, fmt="(T3,A,T54,A,T72,A)") "MINIMAX_INFO| Minimax parameters:", "Weights", "Abscissas"
190 DO jquad = 1, num_integ_points
191 WRITE (unit=unit_nr, fmt="(T41,F20.10,F20.10)") wj(jquad), tj(jquad)
192 END DO
193 CALL m_flush(unit_nr)
194 END IF
195
196 ! scale the minimax parameters
197 tj(:) = tj(:)*emin
198 wj(:) = wj(:)*emin
199 ELSE
200 ! When we perform SOS-MP2, we need an additional factor of 2 for the energies (compare with mp2_laplace.F)
201 ! We do not need weights etc. for the cosine transform
202 ! We do not scale Emax because it is not needed for SOS-MP2
203 emin = emin*2.0_dp
204 END IF
205
206 ! set up the minimax time grid
207 IF (do_im_time .OR. do_ri_sos_laplace_mp2) THEN
208
209 ALLOCATE (x_tw(2*num_integ_points))
210 x_tw = 0.0_dp
211
212 IF (num_integ_points .LE. 20) THEN
213 CALL get_exp_minimax_coeff(num_integ_points, my_e_range, x_tw)
214 ELSE
215 CALL get_exp_minimax_coeff_gw(num_integ_points, my_e_range, x_tw)
216 END IF
217
218 ! For RPA we include already a factor of two (see later steps)
219 scaling = 2.0_dp
220 IF (do_ri_sos_laplace_mp2) scaling = 1.0_dp
221
222 ALLOCATE (tau_tj(0:num_integ_points))
223 tau_tj = 0.0_dp
224
225 ALLOCATE (tau_wj(num_integ_points))
226 tau_wj = 0.0_dp
227
228 DO jquad = 1, num_integ_points
229 tau_tj(jquad) = x_tw(jquad)/scaling
230 tau_wj(jquad) = x_tw(jquad + num_integ_points)/scaling
231 END DO
232
233 DEALLOCATE (x_tw)
234
235 IF (unit_nr > 0 .AND. do_print) THEN
236 WRITE (unit=unit_nr, fmt="(T3,A,T66,F15.4)") &
237 "MINIMAX_INFO| Range for the minimax approximation:", my_e_range
238 ! For testing the gap
239 WRITE (unit=unit_nr, fmt="(T3,A,T66,F15.4)") &
240 "MINIMAX_INFO| Gap:", emin
241 WRITE (unit=unit_nr, fmt="(T3,A,T54,A,T72,A)") &
242 "MINIMAX_INFO| Minimax parameters of the time grid:", "Weights", "Abscissas"
243 DO jquad = 1, num_integ_points
244 WRITE (unit=unit_nr, fmt="(T41,F20.10,F20.10)") tau_wj(jquad), tau_tj(jquad)
245 END DO
246 CALL m_flush(unit_nr)
247 END IF
248
249 ! scale grid from [1,R] to [Emin,Emax]
250 tau_tj(:) = tau_tj(:)/emin
251 tau_wj(:) = tau_wj(:)/emin
252
253 IF (.NOT. do_ri_sos_laplace_mp2) THEN
254 ALLOCATE (weights_cos_tf_t_to_w(num_integ_points, num_integ_points))
255 weights_cos_tf_t_to_w = 0.0_dp
256
257 CALL get_l_sq_wghts_cos_tf_t_to_w(num_integ_points, tau_tj, weights_cos_tf_t_to_w, tj, &
258 emin, emax, max_error_min, num_points_per_magnitude, &
259 my_regularization)
260
261 ! get the weights for the cosine transform W^c(iw) -> W^c(it)
262 ALLOCATE (weights_cos_tf_w_to_t(num_integ_points, num_integ_points))
263 weights_cos_tf_w_to_t = 0.0_dp
264
265 CALL get_l_sq_wghts_cos_tf_w_to_t(num_integ_points, tau_tj, weights_cos_tf_w_to_t, tj, &
266 emin, emax, max_error_min, num_points_per_magnitude, &
267 my_regularization)
268
269 IF (do_gw_im_time) THEN
270
271 ! get the weights for the sine transform Sigma^sin(it) -> Sigma^sin(iw) (PRB 94, 165109 (2016), Eq. 71)
272 ALLOCATE (weights_sin_tf_t_to_w(num_integ_points, num_integ_points))
273 weights_sin_tf_t_to_w = 0.0_dp
274
275 CALL get_l_sq_wghts_sin_tf_t_to_w(num_integ_points, tau_tj, weights_sin_tf_t_to_w, tj, &
276 emin, emax, max_error_min, num_points_per_magnitude, &
277 my_regularization)
278
279 IF (unit_nr > 0) THEN
280 WRITE (unit=unit_nr, fmt="(T3,A,T66,ES15.2)") &
281 "MINIMAX_INFO| Maximum deviation of the imag. time fit:", max_error_min
282 END IF
283 END IF
284
285 END IF
286
287 END IF
288
289 CALL timestop(handle)
290
291 END SUBROUTINE get_minimax_grid
292
293! **************************************************************************************************
294!> \brief ...
295!> \param para_env ...
296!> \param para_env_RPA ...
297!> \param unit_nr ...
298!> \param homo ...
299!> \param virtual ...
300!> \param Eigenval ...
301!> \param num_integ_points ...
302!> \param num_integ_group ...
303!> \param color_rpa_group ...
304!> \param fm_mat_S ...
305!> \param my_do_gw ...
306!> \param ext_scaling ...
307!> \param a_scaling ...
308!> \param tj ...
309!> \param wj ...
310! **************************************************************************************************
311 SUBROUTINE get_clenshaw_grid(para_env, para_env_RPA, unit_nr, homo, virtual, Eigenval, num_integ_points, &
312 num_integ_group, color_rpa_group, fm_mat_S, my_do_gw, &
313 ext_scaling, a_scaling, tj, wj)
314
315 TYPE(mp_para_env_type), INTENT(IN) :: para_env, para_env_rpa
316 INTEGER, INTENT(IN) :: unit_nr
317 INTEGER, DIMENSION(:), INTENT(IN) :: homo, virtual
318 REAL(kind=dp), DIMENSION(:, :, :), INTENT(IN) :: eigenval
319 INTEGER, INTENT(IN) :: num_integ_points, num_integ_group, &
320 color_rpa_group
321 TYPE(cp_fm_type), DIMENSION(:), INTENT(IN) :: fm_mat_s
322 LOGICAL, INTENT(IN) :: my_do_gw
323 REAL(kind=dp), INTENT(IN) :: ext_scaling
324 REAL(kind=dp), INTENT(OUT) :: a_scaling
325 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
326 INTENT(OUT) :: tj, wj
327
328 CHARACTER(LEN=*), PARAMETER :: routinen = 'get_clenshaw_grid'
329
330 INTEGER :: handle, jquad, nspins
331 LOGICAL :: my_open_shell
332
333 CALL timeset(routinen, handle)
334
335 nspins = SIZE(homo)
336 my_open_shell = (nspins == 2)
337
338 ! Now, start to prepare the different grid
339 ALLOCATE (tj(num_integ_points))
340 tj = 0.0_dp
341
342 ALLOCATE (wj(num_integ_points))
343 wj = 0.0_dp
344
345 DO jquad = 1, num_integ_points - 1
346 tj(jquad) = jquad*pi/(2.0_dp*num_integ_points)
347 wj(jquad) = pi/(num_integ_points*sin(tj(jquad))**2)
348 END DO
349 tj(num_integ_points) = pi/2.0_dp
350 wj(num_integ_points) = pi/(2.0_dp*num_integ_points*sin(tj(num_integ_points))**2)
351
352 IF (my_do_gw .AND. ext_scaling > 0.0_dp) THEN
353 a_scaling = ext_scaling
354 ELSE
355 CALL calc_scaling_factor(a_scaling, para_env, para_env_rpa, homo, virtual, eigenval, &
356 num_integ_points, num_integ_group, color_rpa_group, &
357 tj, wj, fm_mat_s)
358 END IF
359
360 IF (unit_nr > 0) WRITE (unit_nr, '(T3,A,T56,F25.5)') 'INTEG_INFO| Scaling parameter:', a_scaling
361
362 wj(:) = wj(:)*a_scaling
363
364 CALL timestop(handle)
365
366 END SUBROUTINE get_clenshaw_grid
367
368! **************************************************************************************************
369!> \brief ...
370!> \param a_scaling_ext ...
371!> \param para_env ...
372!> \param para_env_RPA ...
373!> \param homo ...
374!> \param virtual ...
375!> \param Eigenval ...
376!> \param num_integ_points ...
377!> \param num_integ_group ...
378!> \param color_rpa_group ...
379!> \param tj_ext ...
380!> \param wj_ext ...
381!> \param fm_mat_S ...
382! **************************************************************************************************
383 SUBROUTINE calc_scaling_factor(a_scaling_ext, para_env, para_env_RPA, homo, virtual, Eigenval, &
384 num_integ_points, num_integ_group, color_rpa_group, &
385 tj_ext, wj_ext, fm_mat_S)
386 REAL(kind=dp), INTENT(OUT) :: a_scaling_ext
387 TYPE(mp_para_env_type), INTENT(IN) :: para_env, para_env_rpa
388 INTEGER, DIMENSION(:), INTENT(IN) :: homo, virtual
389 REAL(kind=dp), DIMENSION(:, :, :), INTENT(IN) :: eigenval
390 INTEGER, INTENT(IN) :: num_integ_points, num_integ_group, &
391 color_rpa_group
392 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
393 INTENT(IN) :: tj_ext, wj_ext
394 TYPE(cp_fm_type), DIMENSION(:), INTENT(IN) :: fm_mat_s
395
396 CHARACTER(LEN=*), PARAMETER :: routinen = 'calc_scaling_factor'
397
398 INTEGER :: handle, icycle, jquad, ncol_local, &
399 ncol_local_beta, nspins
400 LOGICAL :: my_open_shell
401 REAL(kind=dp) :: a_high, a_low, a_scaling, conv_param, eps, first_deriv, left_term, &
402 right_term, right_term_ref, right_term_ref_beta, step
403 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: cottj, d_ia, d_ia_beta, iaia_ri, &
404 iaia_ri_beta, m_ia, m_ia_beta
405 TYPE(mp_para_env_type), POINTER :: para_env_col, para_env_col_beta
406
407 CALL timeset(routinen, handle)
408
409 nspins = SIZE(homo)
410 my_open_shell = (nspins == 2)
411
412 eps = 1.0e-10_dp
413
414 ALLOCATE (cottj(num_integ_points))
415
416 ! calculate the cotangent of the abscissa tj
417 DO jquad = 1, num_integ_points
418 cottj(jquad) = 1.0_dp/tan(tj_ext(jquad))
419 END DO
420
421 CALL calc_ia_ia_integrals(para_env_rpa, homo(1), virtual(1), ncol_local, right_term_ref, eigenval(:, 1, 1), &
422 d_ia, iaia_ri, m_ia, fm_mat_s(1), para_env_col)
423
424 ! In the open shell case do point 1-2-3 for the beta spin
425 IF (my_open_shell) THEN
426 CALL calc_ia_ia_integrals(para_env_rpa, homo(2), virtual(2), ncol_local_beta, right_term_ref_beta, eigenval(:, 1, 2), &
427 d_ia_beta, iaia_ri_beta, m_ia_beta, fm_mat_s(2), para_env_col_beta)
428
429 right_term_ref = right_term_ref + right_term_ref_beta
430 END IF
431
432 ! bcast the result
433 IF (para_env%mepos == 0) THEN
434 CALL para_env%bcast(right_term_ref, 0)
435 ELSE
436 right_term_ref = 0.0_dp
437 CALL para_env%bcast(right_term_ref, 0)
438 END IF
439
440 ! 5) start iteration for solving the non-linear equation by bisection
441 ! find limit, here step=0.5 seems a good compromise
442 conv_param = 100.0_dp*epsilon(right_term_ref)
443 step = 0.5_dp
444 a_low = 0.0_dp
445 a_high = step
446 right_term = -right_term_ref
447 DO icycle = 1, num_integ_points*2
448 a_scaling = a_high
449
450 CALL calculate_objfunc(a_scaling, left_term, first_deriv, num_integ_points, my_open_shell, &
451 m_ia, cottj, wj_ext, d_ia, d_ia_beta, m_ia_beta, &
452 ncol_local, ncol_local_beta, num_integ_group, color_rpa_group, &
453 para_env, para_env_col, para_env_col_beta)
454 left_term = left_term/4.0_dp/pi*a_scaling
455
456 IF (abs(left_term) > abs(right_term) .OR. abs(left_term + right_term) <= conv_param) EXIT
457 a_low = a_high
458 a_high = a_high + step
459
460 END DO
461
462 IF (abs(left_term + right_term) >= conv_param) THEN
463 IF (a_scaling >= 2*num_integ_points*step) THEN
464 a_scaling = 1.0_dp
465 ELSE
466
467 DO icycle = 1, num_integ_points*2
468 a_scaling = (a_low + a_high)/2.0_dp
469
470 CALL calculate_objfunc(a_scaling, left_term, first_deriv, num_integ_points, my_open_shell, &
471 m_ia, cottj, wj_ext, d_ia, d_ia_beta, m_ia_beta, &
472 ncol_local, ncol_local_beta, num_integ_group, color_rpa_group, &
473 para_env, para_env_col, para_env_col_beta)
474 left_term = left_term/4.0_dp/pi*a_scaling
475
476 IF (abs(left_term) > abs(right_term)) THEN
477 a_high = a_scaling
478 ELSE
479 a_low = a_scaling
480 END IF
481
482 IF (abs(a_high - a_low) < 1.0e-5_dp) EXIT
483
484 END DO
485
486 END IF
487 END IF
488
489 a_scaling_ext = a_scaling
490 CALL para_env%bcast(a_scaling_ext, 0)
491
492 DEALLOCATE (cottj)
493 DEALLOCATE (iaia_ri)
494 DEALLOCATE (d_ia)
495 DEALLOCATE (m_ia)
496 CALL mp_para_env_release(para_env_col)
497
498 IF (my_open_shell) THEN
499 DEALLOCATE (iaia_ri_beta)
500 DEALLOCATE (d_ia_beta)
501 DEALLOCATE (m_ia_beta)
502 CALL mp_para_env_release(para_env_col_beta)
503 END IF
504
505 CALL timestop(handle)
506
507 END SUBROUTINE calc_scaling_factor
508
509! **************************************************************************************************
510!> \brief ...
511!> \param para_env_RPA ...
512!> \param homo ...
513!> \param virtual ...
514!> \param ncol_local ...
515!> \param right_term_ref ...
516!> \param Eigenval ...
517!> \param D_ia ...
518!> \param iaia_RI ...
519!> \param M_ia ...
520!> \param fm_mat_S ...
521!> \param para_env_col ...
522! **************************************************************************************************
523 SUBROUTINE calc_ia_ia_integrals(para_env_RPA, homo, virtual, ncol_local, right_term_ref, Eigenval, &
524 D_ia, iaia_RI, M_ia, fm_mat_S, para_env_col)
525
526 TYPE(mp_para_env_type), INTENT(IN) :: para_env_rpa
527 INTEGER, INTENT(IN) :: homo, virtual
528 INTEGER, INTENT(OUT) :: ncol_local
529 REAL(kind=dp), INTENT(OUT) :: right_term_ref
530 REAL(kind=dp), DIMENSION(:), INTENT(IN) :: eigenval
531 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
532 INTENT(OUT) :: d_ia, iaia_ri, m_ia
533 TYPE(cp_fm_type), INTENT(IN) :: fm_mat_s
534 TYPE(mp_para_env_type), POINTER :: para_env_col
535
536 CHARACTER(LEN=*), PARAMETER :: routinen = 'calc_ia_ia_integrals'
537
538 INTEGER :: avirt, color_col, color_row, handle, &
539 i_global, iib, iocc, nrow_local
540 INTEGER, DIMENSION(:), POINTER :: col_indices, row_indices
541 REAL(kind=dp) :: eigen_diff
542 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: iaia_ri_dp
543 TYPE(mp_para_env_type), POINTER :: para_env_row
544
545 CALL timeset(routinen, handle)
546
547 ! calculate the (ia|ia) RI integrals
548 ! ----------------------------------
549 ! 1) get info fm_mat_S
550 CALL cp_fm_get_info(matrix=fm_mat_s, &
551 nrow_local=nrow_local, &
552 ncol_local=ncol_local, &
553 row_indices=row_indices, &
554 col_indices=col_indices)
555
556 ! allocate the local buffer of iaia_RI integrals (dp kind)
557 ALLOCATE (iaia_ri_dp(ncol_local))
558 iaia_ri_dp = 0.0_dp
559
560 ! 2) perform the local multiplication SUM_K (ia|K)*(ia|K)
561 DO iib = 1, ncol_local
562 iaia_ri_dp(iib) = iaia_ri_dp(iib) + dot_product(fm_mat_s%local_data(:, iib), fm_mat_s%local_data(:, iib))
563 END DO
564
565 ! 3) sum the result with the processes of the RPA_group having the same columns
566 ! _______ia______ _
567 ! | | | | | | |
568 ! --> | 1 | 5 | 9 | 13| SUM --> | |
569 ! |___|__ |___|___| |_|
570 ! | | | | | | |
571 ! --> | 2 | 6 | 10| 14| SUM --> | |
572 ! K |___|___|___|___| |_| (ia|ia)_RI
573 ! | | | | | | |
574 ! --> | 3 | 7 | 11| 15| SUM --> | |
575 ! |___|___|___|___| |_|
576 ! | | | | | | |
577 ! --> | 4 | 8 | 12| 16| SUM --> | |
578 ! |___|___|___|___| |_|
579 !
580
581 color_col = fm_mat_s%matrix_struct%context%mepos(2)
582 ALLOCATE (para_env_col)
583 CALL para_env_col%from_split(para_env_rpa, color_col)
584
585 CALL para_env_col%sum(iaia_ri_dp)
586
587 ! convert the iaia_RI_dp into double-double precision
588 ALLOCATE (iaia_ri(ncol_local))
589 DO iib = 1, ncol_local
590 iaia_ri(iib) = iaia_ri_dp(iib)
591 END DO
592 DEALLOCATE (iaia_ri_dp)
593
594 ! 4) calculate the right hand term, D_ia is the matrix containing the
595 ! orbital energy differences, M_ia is the diagonal of the full RPA 'excitation'
596 ! matrix
597 ALLOCATE (d_ia(ncol_local))
598
599 ALLOCATE (m_ia(ncol_local))
600
601 DO iib = 1, ncol_local
602 i_global = col_indices(iib)
603
604 iocc = max(1, i_global - 1)/virtual + 1
605 avirt = i_global - (iocc - 1)*virtual
606 eigen_diff = eigenval(avirt + homo) - eigenval(iocc)
607
608 d_ia(iib) = eigen_diff
609 END DO
610
611 DO iib = 1, ncol_local
612 m_ia(iib) = d_ia(iib)*d_ia(iib) + 2.0_dp*d_ia(iib)*iaia_ri(iib)
613 END DO
614
615 right_term_ref = 0.0_dp
616 DO iib = 1, ncol_local
617 right_term_ref = right_term_ref + (sqrt(m_ia(iib)) - d_ia(iib) - iaia_ri(iib))
618 END DO
619 right_term_ref = right_term_ref/2.0_dp
620
621 ! sum the result with the processes of the RPA_group having the same row
622 color_row = fm_mat_s%matrix_struct%context%mepos(1)
623 ALLOCATE (para_env_row)
624 CALL para_env_row%from_split(para_env_rpa, color_row)
625
626 ! allocate communication array for rows
627 CALL para_env_row%sum(right_term_ref)
628
629 CALL mp_para_env_release(para_env_row)
630
631 CALL timestop(handle)
632
633 END SUBROUTINE calc_ia_ia_integrals
634
635! **************************************************************************************************
636!> \brief ...
637!> \param a_scaling ...
638!> \param left_term ...
639!> \param first_deriv ...
640!> \param num_integ_points ...
641!> \param my_open_shell ...
642!> \param M_ia ...
643!> \param cottj ...
644!> \param wj ...
645!> \param D_ia ...
646!> \param D_ia_beta ...
647!> \param M_ia_beta ...
648!> \param ncol_local ...
649!> \param ncol_local_beta ...
650!> \param num_integ_group ...
651!> \param color_rpa_group ...
652!> \param para_env ...
653!> \param para_env_col ...
654!> \param para_env_col_beta ...
655! **************************************************************************************************
656 SUBROUTINE calculate_objfunc(a_scaling, left_term, first_deriv, num_integ_points, my_open_shell, &
657 M_ia, cottj, wj, D_ia, D_ia_beta, M_ia_beta, &
658 ncol_local, ncol_local_beta, num_integ_group, color_rpa_group, &
659 para_env, para_env_col, para_env_col_beta)
660 REAL(kind=dp), INTENT(IN) :: a_scaling
661 REAL(kind=dp), INTENT(INOUT) :: left_term, first_deriv
662 INTEGER, INTENT(IN) :: num_integ_points
663 LOGICAL, INTENT(IN) :: my_open_shell
664 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
665 INTENT(IN) :: m_ia, cottj, wj, d_ia, d_ia_beta, &
666 m_ia_beta
667 INTEGER, INTENT(IN) :: ncol_local, ncol_local_beta, &
668 num_integ_group, color_rpa_group
669 TYPE(mp_para_env_type), INTENT(IN) :: para_env, para_env_col
670 TYPE(mp_para_env_type), POINTER :: para_env_col_beta
671
672 INTEGER :: iib, jquad
673 REAL(kind=dp) :: first_deriv_beta, left_term_beta, omega
674
675 left_term = 0.0_dp
676 first_deriv = 0.0_dp
677 left_term_beta = 0.0_dp
678 first_deriv_beta = 0.0_dp
679 DO jquad = 1, num_integ_points
680 ! parallelize over integration points
681 IF (modulo(jquad, num_integ_group) /= color_rpa_group) cycle
682 omega = a_scaling*cottj(jquad)
683
684 DO iib = 1, ncol_local
685 ! parallelize over ia elements in the para_env_row group
686 IF (modulo(iib, para_env_col%num_pe) /= para_env_col%mepos) cycle
687 ! calculate left_term
688 left_term = left_term + wj(jquad)* &
689 (log(1.0_dp + (m_ia(iib) - d_ia(iib)**2)/(omega**2 + d_ia(iib)**2)) - &
690 (m_ia(iib) - d_ia(iib)**2)/(omega**2 + d_ia(iib)**2))
691 first_deriv = first_deriv + wj(jquad)*cottj(jquad)**2* &
692 ((-m_ia(iib) + d_ia(iib)**2)**2/((omega**2 + d_ia(iib)**2)**2*(omega**2 + m_ia(iib))))
693 END DO
694
695 IF (my_open_shell) THEN
696 DO iib = 1, ncol_local_beta
697 ! parallelize over ia elements in the para_env_row group
698 IF (modulo(iib, para_env_col_beta%num_pe) /= para_env_col_beta%mepos) cycle
699 ! calculate left_term
700 left_term_beta = left_term_beta + wj(jquad)* &
701 (log(1.0_dp + (m_ia_beta(iib) - d_ia_beta(iib)**2)/(omega**2 + d_ia_beta(iib)**2)) - &
702 (m_ia_beta(iib) - d_ia_beta(iib)**2)/(omega**2 + d_ia_beta(iib)**2))
703 first_deriv_beta = &
704 first_deriv_beta + wj(jquad)*cottj(jquad)**2* &
705 ((-m_ia_beta(iib) + d_ia_beta(iib)**2)**2/((omega**2 + d_ia_beta(iib)**2)**2*(omega**2 + m_ia_beta(iib))))
706 END DO
707 END IF
708
709 END DO
710
711 ! sum the contribution from all proc, starting form the row group
712 CALL para_env%sum(left_term)
713 CALL para_env%sum(first_deriv)
714
715 IF (my_open_shell) THEN
716 CALL para_env%sum(left_term_beta)
717 CALL para_env%sum(first_deriv_beta)
718
719 left_term = left_term + left_term_beta
720 first_deriv = first_deriv + first_deriv_beta
721 END IF
722
723 END SUBROUTINE calculate_objfunc
724
725! **************************************************************************************************
726!> \brief Calculate integration weights for the tau grid (in dependency of the omega node)
727!> \param num_integ_points ...
728!> \param tau_tj ...
729!> \param weights_cos_tf_t_to_w ...
730!> \param omega_tj ...
731!> \param E_min ...
732!> \param E_max ...
733!> \param max_error ...
734!> \param num_points_per_magnitude ...
735!> \param regularization ...
736! **************************************************************************************************
737 SUBROUTINE get_l_sq_wghts_cos_tf_t_to_w(num_integ_points, tau_tj, weights_cos_tf_t_to_w, omega_tj, &
738 E_min, E_max, max_error, num_points_per_magnitude, &
739 regularization)
740
741 INTEGER, INTENT(IN) :: num_integ_points
742 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
743 INTENT(IN) :: tau_tj
744 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :), &
745 INTENT(INOUT) :: weights_cos_tf_t_to_w
746 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
747 INTENT(IN) :: omega_tj
748 REAL(kind=dp), INTENT(IN) :: e_min, e_max
749 REAL(kind=dp), INTENT(INOUT) :: max_error
750 INTEGER, INTENT(IN) :: num_points_per_magnitude
751 REAL(kind=dp), INTENT(IN) :: regularization
752
753 CHARACTER(LEN=*), PARAMETER :: routinen = 'get_l_sq_wghts_cos_tf_t_to_w'
754
755 INTEGER :: handle, iii, info, jjj, jquad, lwork, &
756 num_x_nodes
757 INTEGER, ALLOCATABLE, DIMENSION(:) :: iwork
758 REAL(kind=dp) :: multiplicator, omega
759 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: sing_values, tau_wj_work, vec_uty, work, &
760 x_values, y_values
761 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :) :: mat_a, mat_sinvvsinvsigma, &
762 mat_sinvvsinvt, mat_u
763
764 CALL timeset(routinen, handle)
765
766 ! take num_points_per_magnitude points per 10-interval
767 num_x_nodes = (int(log10(e_max/e_min)) + 1)*num_points_per_magnitude
768
769 ! take at least as many x points as integration points to have clear
770 ! input for the singular value decomposition
771 num_x_nodes = max(num_x_nodes, num_integ_points)
772
773 ALLOCATE (x_values(num_x_nodes))
774 x_values = 0.0_dp
775 ALLOCATE (y_values(num_x_nodes))
776 y_values = 0.0_dp
777 ALLOCATE (mat_a(num_x_nodes, num_integ_points))
778 mat_a = 0.0_dp
779 ALLOCATE (tau_wj_work(num_integ_points))
780 tau_wj_work = 0.0_dp
781 ALLOCATE (sing_values(num_integ_points))
782 sing_values = 0.0_dp
783 ALLOCATE (mat_u(num_x_nodes, num_x_nodes))
784 mat_u = 0.0_dp
785 ALLOCATE (mat_sinvvsinvt(num_x_nodes, num_integ_points))
786
787 mat_sinvvsinvt = 0.0_dp
788 ! double the value nessary for 'A' to achieve good performance
789 lwork = 8*num_integ_points*num_integ_points + 12*num_integ_points + 2*num_x_nodes
790 ALLOCATE (work(lwork))
791 work = 0.0_dp
792 ALLOCATE (iwork(8*num_integ_points))
793 iwork = 0
794 ALLOCATE (mat_sinvvsinvsigma(num_integ_points, num_x_nodes))
795 mat_sinvvsinvsigma = 0.0_dp
796 ALLOCATE (vec_uty(num_x_nodes))
797 vec_uty = 0.0_dp
798
799 max_error = 0.0_dp
800
801 ! loop over all omega frequency points
802 DO jquad = 1, num_integ_points
803
804 ! set the x-values logarithmically in the interval [Emin,Emax]
805 multiplicator = (e_max/e_min)**(1.0_dp/(real(num_x_nodes, kind=dp) - 1.0_dp))
806 DO iii = 1, num_x_nodes
807 x_values(iii) = e_min*multiplicator**(iii - 1)
808 END DO
809
810 omega = omega_tj(jquad)
811
812 ! y=2x/(x^2+omega_k^2)
813 DO iii = 1, num_x_nodes
814 y_values(iii) = 2.0_dp*x_values(iii)/((x_values(iii))**2 + omega**2)
815 END DO
816
817 ! calculate mat_A
818 DO jjj = 1, num_integ_points
819 DO iii = 1, num_x_nodes
820 mat_a(iii, jjj) = cos(omega*tau_tj(jjj))*exp(-x_values(iii)*tau_tj(jjj))
821 END DO
822 END DO
823
824 ! Singular value decomposition of mat_A
825 CALL dgesdd('A', num_x_nodes, num_integ_points, mat_a, num_x_nodes, sing_values, mat_u, num_x_nodes, &
826 mat_sinvvsinvt, num_x_nodes, work, lwork, iwork, info)
827
828 cpassert(info == 0)
829
830 ! integration weights = V Sigma U^T y
831 ! 1) V*Sigma
832 DO jjj = 1, num_integ_points
833 DO iii = 1, num_integ_points
834! mat_SinvVSinvSigma(iii, jjj) = mat_SinvVSinvT(jjj, iii)/sing_values(jjj)
835 mat_sinvvsinvsigma(iii, jjj) = mat_sinvvsinvt(jjj, iii)*sing_values(jjj) &
836 /(regularization**2 + sing_values(jjj)**2)
837 END DO
838 END DO
839
840 ! 2) U^T y
841 CALL dgemm('T', 'N', num_x_nodes, 1, num_x_nodes, 1.0_dp, mat_u, num_x_nodes, y_values, num_x_nodes, &
842 0.0_dp, vec_uty, num_x_nodes)
843
844 ! 3) (V*Sigma) * (U^T y)
845 CALL dgemm('N', 'N', num_integ_points, 1, num_x_nodes, 1.0_dp, mat_sinvvsinvsigma, num_integ_points, vec_uty, &
846 num_x_nodes, 0.0_dp, tau_wj_work, num_integ_points)
847
848 weights_cos_tf_t_to_w(jquad, :) = tau_wj_work(:)
849
850 CALL calc_max_error_fit_tau_grid_with_cosine(max_error, omega, tau_tj, tau_wj_work, x_values, &
851 y_values, num_integ_points, num_x_nodes)
852
853 END DO ! jquad
854
855 DEALLOCATE (x_values, y_values, mat_a, tau_wj_work, sing_values, mat_u, mat_sinvvsinvt, &
856 work, iwork, mat_sinvvsinvsigma, vec_uty)
857
858 CALL timestop(handle)
859
860 END SUBROUTINE get_l_sq_wghts_cos_tf_t_to_w
861
862! **************************************************************************************************
863!> \brief Calculate integration weights for the tau grid (in dependency of the omega node)
864!> \param num_integ_points ...
865!> \param tau_tj ...
866!> \param weights_sin_tf_t_to_w ...
867!> \param omega_tj ...
868!> \param E_min ...
869!> \param E_max ...
870!> \param max_error ...
871!> \param num_points_per_magnitude ...
872!> \param regularization ...
873! **************************************************************************************************
874 SUBROUTINE get_l_sq_wghts_sin_tf_t_to_w(num_integ_points, tau_tj, weights_sin_tf_t_to_w, omega_tj, &
875 E_min, E_max, max_error, num_points_per_magnitude, regularization)
876
877 INTEGER, INTENT(IN) :: num_integ_points
878 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
879 INTENT(IN) :: tau_tj
880 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :), &
881 INTENT(INOUT) :: weights_sin_tf_t_to_w
882 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
883 INTENT(IN) :: omega_tj
884 REAL(kind=dp), INTENT(IN) :: e_min, e_max
885 REAL(kind=dp), INTENT(OUT) :: max_error
886 INTEGER, INTENT(IN) :: num_points_per_magnitude
887 REAL(kind=dp), INTENT(IN) :: regularization
888
889 CHARACTER(LEN=*), PARAMETER :: routinen = 'get_l_sq_wghts_sin_tf_t_to_w'
890
891 INTEGER :: handle, iii, info, jjj, jquad, lwork, &
892 num_x_nodes
893 INTEGER, ALLOCATABLE, DIMENSION(:) :: iwork
894 REAL(kind=dp) :: chi2_min_jquad, multiplicator, omega
895 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: sing_values, tau_wj_work, vec_uty, work, &
896 work_array, x_values, y_values
897 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :) :: mat_a, mat_sinvvsinvsigma, &
898 mat_sinvvsinvt, mat_u
899
900 CALL timeset(routinen, handle)
901
902 ! take num_points_per_magnitude points per 10-interval
903 num_x_nodes = (int(log10(e_max/e_min)) + 1)*num_points_per_magnitude
904
905 ! take at least as many x points as integration points to have clear
906 ! input for the singular value decomposition
907 num_x_nodes = max(num_x_nodes, num_integ_points)
908
909 ALLOCATE (x_values(num_x_nodes))
910 x_values = 0.0_dp
911 ALLOCATE (y_values(num_x_nodes))
912 y_values = 0.0_dp
913 ALLOCATE (mat_a(num_x_nodes, num_integ_points))
914 mat_a = 0.0_dp
915 ALLOCATE (tau_wj_work(num_integ_points))
916 tau_wj_work = 0.0_dp
917 ALLOCATE (work_array(2*num_integ_points))
918 work_array = 0.0_dp
919 ALLOCATE (sing_values(num_integ_points))
920 sing_values = 0.0_dp
921 ALLOCATE (mat_u(num_x_nodes, num_x_nodes))
922 mat_u = 0.0_dp
923 ALLOCATE (mat_sinvvsinvt(num_x_nodes, num_integ_points))
924
925 mat_sinvvsinvt = 0.0_dp
926 ! double the value nessary for 'A' to achieve good performance
927 lwork = 8*num_integ_points*num_integ_points + 12*num_integ_points + 2*num_x_nodes
928 ALLOCATE (work(lwork))
929 work = 0.0_dp
930 ALLOCATE (iwork(8*num_integ_points))
931 iwork = 0
932 ALLOCATE (mat_sinvvsinvsigma(num_integ_points, num_x_nodes))
933 mat_sinvvsinvsigma = 0.0_dp
934 ALLOCATE (vec_uty(num_x_nodes))
935 vec_uty = 0.0_dp
936
937 max_error = 0.0_dp
938
939 ! loop over all omega frequency points
940 DO jquad = 1, num_integ_points
941
942 chi2_min_jquad = 100.0_dp
943
944 ! set the x-values logarithmically in the interval [Emin,Emax]
945 multiplicator = (e_max/e_min)**(1.0_dp/(real(num_x_nodes, kind=dp) - 1.0_dp))
946 DO iii = 1, num_x_nodes
947 x_values(iii) = e_min*multiplicator**(iii - 1)
948 END DO
949
950 omega = omega_tj(jquad)
951
952 ! y=2x/(x^2+omega_k^2)
953 DO iii = 1, num_x_nodes
954! y_values(iii) = 2.0_dp*x_values(iii)/((x_values(iii))**2+omega**2)
955 y_values(iii) = 2.0_dp*omega/((x_values(iii))**2 + omega**2)
956 END DO
957
958 ! calculate mat_A
959 DO jjj = 1, num_integ_points
960 DO iii = 1, num_x_nodes
961 mat_a(iii, jjj) = sin(omega*tau_tj(jjj))*exp(-x_values(iii)*tau_tj(jjj))
962 END DO
963 END DO
964
965 ! Singular value decomposition of mat_A
966 CALL dgesdd('A', num_x_nodes, num_integ_points, mat_a, num_x_nodes, sing_values, mat_u, num_x_nodes, &
967 mat_sinvvsinvt, num_x_nodes, work, lwork, iwork, info)
968
969 cpassert(info == 0)
970
971 ! integration weights = V Sigma U^T y
972 ! 1) V*Sigma
973 DO jjj = 1, num_integ_points
974 DO iii = 1, num_integ_points
975! mat_SinvVSinvSigma(iii, jjj) = mat_SinvVSinvT(jjj, iii)/sing_values(jjj)
976 mat_sinvvsinvsigma(iii, jjj) = mat_sinvvsinvt(jjj, iii)*sing_values(jjj) &
977 /(regularization**2 + sing_values(jjj)**2)
978 END DO
979 END DO
980
981 ! 2) U^T y
982 CALL dgemm('T', 'N', num_x_nodes, 1, num_x_nodes, 1.0_dp, mat_u, num_x_nodes, y_values, num_x_nodes, &
983 0.0_dp, vec_uty, num_x_nodes)
984
985 ! 3) (V*Sigma) * (U^T y)
986 CALL dgemm('N', 'N', num_integ_points, 1, num_x_nodes, 1.0_dp, mat_sinvvsinvsigma, num_integ_points, vec_uty, &
987 num_x_nodes, 0.0_dp, tau_wj_work, num_integ_points)
988
989 weights_sin_tf_t_to_w(jquad, :) = tau_wj_work(:)
990
991 CALL calc_max_error_fit_tau_grid_with_sine(max_error, omega, tau_tj, tau_wj_work, x_values, &
992 y_values, num_integ_points, num_x_nodes)
993
994 END DO ! jquad
995
996 DEALLOCATE (x_values, y_values, mat_a, tau_wj_work, work_array, sing_values, mat_u, mat_sinvvsinvt, &
997 work, iwork, mat_sinvvsinvsigma, vec_uty)
998
999 CALL timestop(handle)
1000
1001 END SUBROUTINE get_l_sq_wghts_sin_tf_t_to_w
1002
1003! **************************************************************************************************
1004!> \brief ...
1005!> \param max_error ...
1006!> \param omega ...
1007!> \param tau_tj ...
1008!> \param tau_wj_work ...
1009!> \param x_values ...
1010!> \param y_values ...
1011!> \param num_integ_points ...
1012!> \param num_x_nodes ...
1013! **************************************************************************************************
1014 PURE SUBROUTINE calc_max_error_fit_tau_grid_with_cosine(max_error, omega, tau_tj, tau_wj_work, x_values, &
1015 y_values, num_integ_points, num_x_nodes)
1016
1017 REAL(kind=dp), INTENT(INOUT) :: max_error, omega
1018 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
1019 INTENT(IN) :: tau_tj, tau_wj_work, x_values, y_values
1020 INTEGER, INTENT(IN) :: num_integ_points, num_x_nodes
1021
1022 INTEGER :: kkk
1023 REAL(kind=dp) :: func_val, func_val_temp, max_error_tmp
1024
1025 max_error_tmp = 0.0_dp
1026
1027 DO kkk = 1, num_x_nodes
1028
1029 func_val = 0.0_dp
1030
1031 CALL eval_fit_func_tau_grid_cosine(func_val, x_values(kkk), num_integ_points, tau_tj, tau_wj_work, omega)
1032
1033 IF (abs(y_values(kkk) - func_val) > max_error_tmp) THEN
1034 max_error_tmp = abs(y_values(kkk) - func_val)
1035 func_val_temp = func_val
1036 END IF
1037
1038 END DO
1039
1040 IF (max_error_tmp > max_error) THEN
1041
1042 max_error = max_error_tmp
1043
1044 END IF
1045
1046 END SUBROUTINE calc_max_error_fit_tau_grid_with_cosine
1047
1048! **************************************************************************************************
1049!> \brief Evaluate fit function when calculating tau grid for cosine transform
1050!> \param func_val ...
1051!> \param x_value ...
1052!> \param num_integ_points ...
1053!> \param tau_tj ...
1054!> \param tau_wj_work ...
1055!> \param omega ...
1056! **************************************************************************************************
1057 PURE SUBROUTINE eval_fit_func_tau_grid_cosine(func_val, x_value, num_integ_points, tau_tj, tau_wj_work, omega)
1058
1059 REAL(kind=dp), INTENT(OUT) :: func_val
1060 REAL(kind=dp), INTENT(IN) :: x_value
1061 INTEGER, INTENT(IN) :: num_integ_points
1062 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
1063 INTENT(IN) :: tau_tj, tau_wj_work
1064 REAL(kind=dp), INTENT(IN) :: omega
1065
1066 INTEGER :: iii
1067
1068 func_val = 0.0_dp
1069
1070 DO iii = 1, num_integ_points
1071
1072 ! calculate value of the fit function
1073 func_val = func_val + tau_wj_work(iii)*cos(omega*tau_tj(iii))*exp(-x_value*tau_tj(iii))
1074
1075 END DO
1076
1077 END SUBROUTINE eval_fit_func_tau_grid_cosine
1078
1079! **************************************************************************************************
1080!> \brief Evaluate fit function when calculating tau grid for sine transform
1081!> \param func_val ...
1082!> \param x_value ...
1083!> \param num_integ_points ...
1084!> \param tau_tj ...
1085!> \param tau_wj_work ...
1086!> \param omega ...
1087! **************************************************************************************************
1088 PURE SUBROUTINE eval_fit_func_tau_grid_sine(func_val, x_value, num_integ_points, tau_tj, tau_wj_work, omega)
1089
1090 REAL(kind=dp), INTENT(INOUT) :: func_val
1091 REAL(kind=dp), INTENT(IN) :: x_value
1092 INTEGER, INTENT(in) :: num_integ_points
1093 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
1094 INTENT(IN) :: tau_tj, tau_wj_work
1095 REAL(kind=dp), INTENT(IN) :: omega
1096
1097 INTEGER :: iii
1098
1099 func_val = 0.0_dp
1100
1101 DO iii = 1, num_integ_points
1102
1103 ! calculate value of the fit function
1104 func_val = func_val + tau_wj_work(iii)*sin(omega*tau_tj(iii))*exp(-x_value*tau_tj(iii))
1105
1106 END DO
1107
1108 END SUBROUTINE eval_fit_func_tau_grid_sine
1109
1110! **************************************************************************************************
1111!> \brief ...
1112!> \param max_error ...
1113!> \param omega ...
1114!> \param tau_tj ...
1115!> \param tau_wj_work ...
1116!> \param x_values ...
1117!> \param y_values ...
1118!> \param num_integ_points ...
1119!> \param num_x_nodes ...
1120! **************************************************************************************************
1121 PURE SUBROUTINE calc_max_error_fit_tau_grid_with_sine(max_error, omega, tau_tj, tau_wj_work, x_values, &
1122 y_values, num_integ_points, num_x_nodes)
1123
1124 REAL(kind=dp), INTENT(INOUT) :: max_error, omega
1125 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
1126 INTENT(IN) :: tau_tj, tau_wj_work, x_values, y_values
1127 INTEGER, INTENT(IN) :: num_integ_points, num_x_nodes
1128
1129 INTEGER :: kkk
1130 REAL(kind=dp) :: func_val, func_val_temp, max_error_tmp
1131
1132 max_error_tmp = 0.0_dp
1133
1134 DO kkk = 1, num_x_nodes
1135
1136 func_val = 0.0_dp
1137
1138 CALL eval_fit_func_tau_grid_sine(func_val, x_values(kkk), num_integ_points, tau_tj, tau_wj_work, omega)
1139
1140 IF (abs(y_values(kkk) - func_val) > max_error_tmp) THEN
1141 max_error_tmp = abs(y_values(kkk) - func_val)
1142 func_val_temp = func_val
1143 END IF
1144
1145 END DO
1146
1147 IF (max_error_tmp > max_error) THEN
1148
1149 max_error = max_error_tmp
1150
1151 END IF
1152
1153 END SUBROUTINE calc_max_error_fit_tau_grid_with_sine
1154
1155! **************************************************************************************************
1156!> \brief test the singular value decomposition for the computation of integration weights for the
1157!> Fourier transform between time and frequency grid in cubic-scaling RPA
1158!> \param nR ...
1159!> \param iw ...
1160! **************************************************************************************************
1161 SUBROUTINE test_least_square_ft(nR, iw)
1162 INTEGER, INTENT(IN) :: nr, iw
1163
1164 INTEGER :: ierr, ir, jquad, num_integ_points
1165 REAL(kind=dp) :: max_error, multiplicator, rc, rc_max
1166 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: tau_tj, tau_wj, tj, wj, x_tw
1167 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :) :: weights_cos_tf_t_to_w
1168
1169 rc_max = 1.0e+7
1170
1171 multiplicator = rc_max**(1.0_dp/(real(nr, kind=dp) - 1.0_dp))
1172
1173 DO num_integ_points = 1, 20
1174
1175 ALLOCATE (x_tw(2*num_integ_points))
1176 x_tw = 0.0_dp
1177 ALLOCATE (tau_tj(num_integ_points))
1178 tau_tj = 0.0_dp
1179 ALLOCATE (weights_cos_tf_t_to_w(num_integ_points, num_integ_points))
1180 weights_cos_tf_t_to_w = 0.0_dp
1181 ALLOCATE (tau_wj(num_integ_points))
1182 tau_wj = 0.0_dp
1183 ALLOCATE (tj(num_integ_points))
1184 tj = 0.0_dp
1185 ALLOCATE (wj(num_integ_points))
1186 wj = 0.0_dp
1187
1188 DO ir = 0, nr - 1
1189
1190 rc = 2.0_dp*multiplicator**ir
1191
1192 ierr = 0
1193 CALL get_rpa_minimax_coeff(num_integ_points, rc, x_tw, ierr, print_warning=.false.)
1194
1195 DO jquad = 1, num_integ_points
1196 tj(jquad) = x_tw(jquad)
1197 wj(jquad) = x_tw(jquad + num_integ_points)
1198 END DO
1199
1200 x_tw = 0.0_dp
1201
1202 CALL get_exp_minimax_coeff(num_integ_points, rc, x_tw)
1203
1204 DO jquad = 1, num_integ_points
1205 tau_tj(jquad) = x_tw(jquad)/2.0_dp
1206 tau_wj(jquad) = x_tw(jquad + num_integ_points)/2.0_dp
1207 END DO
1208
1209 CALL get_l_sq_wghts_cos_tf_t_to_w(num_integ_points, tau_tj, &
1210 weights_cos_tf_t_to_w, tj, &
1211 1.0_dp, rc, max_error, 200, 0.0_dp)
1212
1213 IF (iw > 0) THEN
1214 WRITE (iw, '(T2, I3, F12.1, ES12.3)') num_integ_points, rc, max_error
1215 END IF
1216
1217 END DO
1218
1219 DEALLOCATE (x_tw, tau_tj, weights_cos_tf_t_to_w, tau_wj, wj, tj)
1220
1221 END DO
1222
1223 END SUBROUTINE test_least_square_ft
1224
1225! **************************************************************************************************
1226!> \brief ...
1227!> \param num_integ_points ...
1228!> \param tau_tj ...
1229!> \param weights_cos_tf_w_to_t ...
1230!> \param omega_tj ...
1231!> \param E_min ...
1232!> \param E_max ...
1233!> \param max_error ...
1234!> \param num_points_per_magnitude ...
1235!> \param regularization ...
1236! **************************************************************************************************
1237 SUBROUTINE get_l_sq_wghts_cos_tf_w_to_t(num_integ_points, tau_tj, weights_cos_tf_w_to_t, omega_tj, &
1238 E_min, E_max, max_error, num_points_per_magnitude, regularization)
1239
1240 INTEGER, INTENT(IN) :: num_integ_points
1241 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
1242 INTENT(IN) :: tau_tj
1243 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :), &
1244 INTENT(INOUT) :: weights_cos_tf_w_to_t
1245 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
1246 INTENT(IN) :: omega_tj
1247 REAL(kind=dp), INTENT(IN) :: e_min, e_max
1248 REAL(kind=dp), INTENT(INOUT) :: max_error
1249 INTEGER, INTENT(IN) :: num_points_per_magnitude
1250 REAL(kind=dp), INTENT(IN) :: regularization
1251
1252 CHARACTER(LEN=*), PARAMETER :: routinen = 'get_l_sq_wghts_cos_tf_w_to_t'
1253
1254 INTEGER :: handle, iii, info, jjj, jquad, lwork, &
1255 num_x_nodes
1256 INTEGER, ALLOCATABLE, DIMENSION(:) :: iwork
1257 REAL(kind=dp) :: chi2_min_jquad, multiplicator, omega, &
1258 tau, x_value
1259 REAL(kind=dp), ALLOCATABLE, DIMENSION(:) :: omega_wj_work, sing_values, vec_uty, &
1260 work, work_array, x_values, y_values
1261 REAL(kind=dp), ALLOCATABLE, DIMENSION(:, :) :: mat_a, mat_sinvvsinvsigma, &
1262 mat_sinvvsinvt, mat_u
1263
1264 CALL timeset(routinen, handle)
1265
1266 ! take num_points_per_magnitude points per 10-interval
1267 num_x_nodes = (int(log10(e_max/e_min)) + 1)*num_points_per_magnitude
1268
1269 ! take at least as many x points as integration points to have clear
1270 ! input for the singular value decomposition
1271 num_x_nodes = max(num_x_nodes, num_integ_points)
1272
1273 ALLOCATE (x_values(num_x_nodes))
1274 x_values = 0.0_dp
1275 ALLOCATE (y_values(num_x_nodes))
1276 y_values = 0.0_dp
1277 ALLOCATE (mat_a(num_x_nodes, num_integ_points))
1278 mat_a = 0.0_dp
1279 ALLOCATE (omega_wj_work(num_integ_points))
1280 omega_wj_work = 0.0_dp
1281 ALLOCATE (work_array(2*num_integ_points))
1282 work_array = 0.0_dp
1283 ALLOCATE (sing_values(num_integ_points))
1284 sing_values = 0.0_dp
1285 ALLOCATE (mat_u(num_x_nodes, num_x_nodes))
1286 mat_u = 0.0_dp
1287 ALLOCATE (mat_sinvvsinvt(num_x_nodes, num_integ_points))
1288
1289 mat_sinvvsinvt = 0.0_dp
1290 ! double the value nessary for 'A' to achieve good performance
1291 lwork = 8*num_integ_points*num_integ_points + 12*num_integ_points + 2*num_x_nodes
1292 ALLOCATE (work(lwork))
1293 work = 0.0_dp
1294 ALLOCATE (iwork(8*num_integ_points))
1295 iwork = 0
1296 ALLOCATE (mat_sinvvsinvsigma(num_integ_points, num_x_nodes))
1297 mat_sinvvsinvsigma = 0.0_dp
1298 ALLOCATE (vec_uty(num_x_nodes))
1299 vec_uty = 0.0_dp
1300
1301 ! set the x-values logarithmically in the interval [Emin,Emax]
1302 multiplicator = (e_max/e_min)**(1.0_dp/(real(num_x_nodes, kind=dp) - 1.0_dp))
1303 DO iii = 1, num_x_nodes
1304 x_values(iii) = e_min*multiplicator**(iii - 1)
1305 END DO
1306
1307 max_error = 0.0_dp
1308
1309 ! loop over all tau time points
1310 DO jquad = 1, num_integ_points
1311
1312 chi2_min_jquad = 100.0_dp
1313
1314 tau = tau_tj(jquad)
1315
1316 ! y=exp(-x*|tau_k|)
1317 DO iii = 1, num_x_nodes
1318 y_values(iii) = exp(-x_values(iii)*tau)
1319 END DO
1320
1321 ! calculate mat_A
1322 DO jjj = 1, num_integ_points
1323 DO iii = 1, num_x_nodes
1324 omega = omega_tj(jjj)
1325 x_value = x_values(iii)
1326 mat_a(iii, jjj) = cos(tau*omega)*2.0_dp*x_value/(x_value**2 + omega**2)
1327 END DO
1328 END DO
1329
1330 ! Singular value decomposition of mat_A
1331 CALL dgesdd('A', num_x_nodes, num_integ_points, mat_a, num_x_nodes, sing_values, mat_u, num_x_nodes, &
1332 mat_sinvvsinvt, num_x_nodes, work, lwork, iwork, info)
1333
1334 cpassert(info == 0)
1335
1336 ! integration weights = V Sigma U^T y
1337 ! 1) V*Sigma
1338 DO jjj = 1, num_integ_points
1339 DO iii = 1, num_integ_points
1340! mat_SinvVSinvSigma(iii, jjj) = mat_SinvVSinvT(jjj, iii)/sing_values(jjj)
1341 mat_sinvvsinvsigma(iii, jjj) = mat_sinvvsinvt(jjj, iii)*sing_values(jjj) &
1342 /(regularization**2 + sing_values(jjj)**2)
1343 END DO
1344 END DO
1345
1346 ! 2) U^T y
1347 CALL dgemm('T', 'N', num_x_nodes, 1, num_x_nodes, 1.0_dp, mat_u, num_x_nodes, y_values, num_x_nodes, &
1348 0.0_dp, vec_uty, num_x_nodes)
1349
1350 ! 3) (V*Sigma) * (U^T y)
1351 CALL dgemm('N', 'N', num_integ_points, 1, num_x_nodes, 1.0_dp, mat_sinvvsinvsigma, num_integ_points, vec_uty, &
1352 num_x_nodes, 0.0_dp, omega_wj_work, num_integ_points)
1353
1354 weights_cos_tf_w_to_t(jquad, :) = omega_wj_work(:)
1355
1356 CALL calc_max_error_fit_omega_grid_with_cosine(max_error, tau, omega_tj, omega_wj_work, x_values, &
1357 y_values, num_integ_points, num_x_nodes)
1358
1359 END DO ! jquad
1360
1361 DEALLOCATE (x_values, y_values, mat_a, omega_wj_work, work_array, sing_values, mat_u, mat_sinvvsinvt, &
1362 work, iwork, mat_sinvvsinvsigma, vec_uty)
1363
1364 CALL timestop(handle)
1365
1366 END SUBROUTINE get_l_sq_wghts_cos_tf_w_to_t
1367
1368! **************************************************************************************************
1369!> \brief ...
1370!> \param max_error ...
1371!> \param tau ...
1372!> \param omega_tj ...
1373!> \param omega_wj_work ...
1374!> \param x_values ...
1375!> \param y_values ...
1376!> \param num_integ_points ...
1377!> \param num_x_nodes ...
1378! **************************************************************************************************
1379 SUBROUTINE calc_max_error_fit_omega_grid_with_cosine(max_error, tau, omega_tj, omega_wj_work, x_values, &
1380 y_values, num_integ_points, num_x_nodes)
1381
1382 REAL(kind=dp), INTENT(INOUT) :: max_error
1383 REAL(kind=dp), INTENT(IN) :: tau
1384 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
1385 INTENT(IN) :: omega_tj, omega_wj_work, x_values, &
1386 y_values
1387 INTEGER, INTENT(IN) :: num_integ_points, num_x_nodes
1388
1389 CHARACTER(LEN=*), PARAMETER :: routinen = 'calc_max_error_fit_omega_grid_with_cosine'
1390
1391 INTEGER :: handle, kkk
1392 REAL(kind=dp) :: func_val, func_val_temp, max_error_tmp
1393
1394 CALL timeset(routinen, handle)
1395
1396 max_error_tmp = 0.0_dp
1397
1398 DO kkk = 1, num_x_nodes
1399
1400 func_val = 0.0_dp
1401
1402 CALL eval_fit_func_omega_grid_cosine(func_val, x_values(kkk), num_integ_points, omega_tj, omega_wj_work, tau)
1403
1404 IF (abs(y_values(kkk) - func_val) > max_error_tmp) THEN
1405 max_error_tmp = abs(y_values(kkk) - func_val)
1406 func_val_temp = func_val
1407 END IF
1408
1409 END DO
1410
1411 IF (max_error_tmp > max_error) THEN
1412
1413 max_error = max_error_tmp
1414
1415 END IF
1416
1417 CALL timestop(handle)
1418
1419 END SUBROUTINE calc_max_error_fit_omega_grid_with_cosine
1420
1421! **************************************************************************************************
1422!> \brief ...
1423!> \param func_val ...
1424!> \param x_value ...
1425!> \param num_integ_points ...
1426!> \param omega_tj ...
1427!> \param omega_wj_work ...
1428!> \param tau ...
1429! **************************************************************************************************
1430 PURE SUBROUTINE eval_fit_func_omega_grid_cosine(func_val, x_value, num_integ_points, omega_tj, omega_wj_work, tau)
1431 REAL(kind=dp), INTENT(OUT) :: func_val
1432 REAL(kind=dp), INTENT(IN) :: x_value
1433 INTEGER, INTENT(IN) :: num_integ_points
1434 REAL(kind=dp), ALLOCATABLE, DIMENSION(:), &
1435 INTENT(IN) :: omega_tj, omega_wj_work
1436 REAL(kind=dp), INTENT(IN) :: tau
1437
1438 INTEGER :: iii
1439 REAL(kind=dp) :: omega
1440
1441 func_val = 0.0_dp
1442
1443 DO iii = 1, num_integ_points
1444
1445 ! calculate value of the fit function
1446 omega = omega_tj(iii)
1447 func_val = func_val + omega_wj_work(iii)*cos(tau*omega)*2.0_dp*x_value/(x_value**2 + omega**2)
1448
1449 END DO
1450
1451 END SUBROUTINE eval_fit_func_omega_grid_cosine
1452
1453! **************************************************************************************************
1454!> \brief ...
1455!> \param qs_env ...
1456!> \param para_env ...
1457!> \param gap ...
1458!> \param max_eig_diff ...
1459!> \param e_fermi ...
1460! **************************************************************************************************
1461 SUBROUTINE gap_and_max_eig_diff_kpoints(qs_env, para_env, gap, max_eig_diff, e_fermi)
1462
1463 TYPE(qs_environment_type), POINTER :: qs_env
1464 TYPE(mp_para_env_type), INTENT(IN) :: para_env
1465 REAL(kind=dp), INTENT(OUT) :: gap, max_eig_diff, e_fermi
1466
1467 CHARACTER(LEN=*), PARAMETER :: routinen = 'gap_and_max_eig_diff_kpoints'
1468
1469 INTEGER :: handle, homo, ikpgr, ispin, kplocal, &
1470 nmo, nspin
1471 INTEGER, DIMENSION(2) :: kp_range
1472 REAL(kind=dp) :: e_homo, e_homo_temp, e_lumo, e_lumo_temp
1473 REAL(kind=dp), DIMENSION(3) :: tmp
1474 REAL(kind=dp), DIMENSION(:), POINTER :: eigenvalues
1475 TYPE(kpoint_env_type), POINTER :: kp
1476 TYPE(kpoint_type), POINTER :: kpoint
1477 TYPE(mo_set_type), POINTER :: mo_set
1478
1479 CALL timeset(routinen, handle)
1480
1481 CALL get_qs_env(qs_env, &
1482 kpoints=kpoint)
1483
1484 mo_set => kpoint%kp_env(1)%kpoint_env%mos(1, 1)
1485 CALL get_mo_set(mo_set, nmo=nmo)
1486
1487 CALL get_kpoint_info(kpoint, kp_range=kp_range)
1488 kplocal = kp_range(2) - kp_range(1) + 1
1489
1490 gap = 1000.0_dp
1491 max_eig_diff = 0.0_dp
1492 e_homo = -1000.0_dp
1493 e_lumo = 1000.0_dp
1494
1495 DO ikpgr = 1, kplocal
1496 kp => kpoint%kp_env(ikpgr)%kpoint_env
1497 nspin = SIZE(kp%mos, 2)
1498 DO ispin = 1, nspin
1499 mo_set => kp%mos(1, ispin)
1500 CALL get_mo_set(mo_set, eigenvalues=eigenvalues, homo=homo)
1501 e_homo_temp = eigenvalues(homo)
1502 e_lumo_temp = eigenvalues(homo + 1)
1503
1504 IF (e_homo_temp > e_homo) e_homo = e_homo_temp
1505 IF (e_lumo_temp < e_lumo) e_lumo = e_lumo_temp
1506 IF (eigenvalues(nmo) - eigenvalues(1) > max_eig_diff) max_eig_diff = eigenvalues(nmo) - eigenvalues(1)
1507
1508 END DO
1509 END DO
1510
1511 ! Collect all three numbers in an array
1512 ! Reverse sign of lumo to reduce number of MPI calls
1513 tmp(1) = e_homo
1514 tmp(2) = -e_lumo
1515 tmp(3) = max_eig_diff
1516 CALL para_env%max(tmp)
1517
1518 gap = -tmp(2) - tmp(1)
1519 e_fermi = (tmp(1) - tmp(2))*0.5_dp
1520 max_eig_diff = tmp(3)
1521
1522 CALL timestop(handle)
1523
1524 END SUBROUTINE
1525
1526END MODULE mp2_grids
modulo
static GRID_HOST_DEVICE int modulo(int a, int m)
Equivalent of Fortran's MODULO, which always return a positive number. https://gcc....
Definition grid_common.h:117
dgemm
static void dgemm(const char transa, const char transb, const int m, const int n, const int k, const double alpha, const double *a, const int lda, const double *b, const int ldb, const double beta, double *c, const int ldc)
Convenient wrapper to hide Fortran nature of dgemm_, swapping a and b.
Definition grid_cpu_task_list.c:195
cp_fm_types
represent a full matrix distributed on many processors
Definition cp_fm_types.F:15
cp_fm_types::cp_fm_get_info
subroutine, public cp_fm_get_info(matrix, name, nrow_global, ncol_global, nrow_block, ncol_block, nrow_local, ncol_local, row_indices, col_indices, local_data, context, nrow_locals, ncol_locals, matrix_struct, para_env)
returns all kind of information about the full matrix
Definition cp_fm_types.F:1016
input_section_types
objects that represent the structure of input sections and the data contained in an input section
Definition input_section_types.F:15
input_section_types::section_vals_val_set
subroutine, public section_vals_val_set(section_vals, keyword_name, i_rep_section, i_rep_val, val, l_val, i_val, r_val, c_val, l_vals_ptr, i_vals_ptr, r_vals_ptr, c_vals_ptr)
sets the requested value
Definition input_section_types.F:1216
kinds
Defines the basic variable types.
Definition kinds.F:23
kinds::dp
integer, parameter, public dp
Definition kinds.F:34
kpoint_types
Types and basic routines needed for a kpoint calculation.
Definition kpoint_types.F:15
kpoint_types::get_kpoint_info
subroutine, public get_kpoint_info(kpoint, kp_scheme, nkp_grid, kp_shift, symmetry, verbose, full_grid, use_real_wfn, eps_geo, parallel_group_size, kp_range, nkp, xkp, wkp, para_env, blacs_env_all, para_env_kp, para_env_inter_kp, blacs_env, kp_env, kp_aux_env, mpools, iogrp, nkp_groups, kp_dist, cell_to_index, index_to_cell, sab_nl, sab_nl_nosym)
Retrieve information from a kpoint environment.
Definition kpoint_types.F:333
machine
Machine interface based on Fortran 2003 and POSIX.
Definition machine.F:17
machine::m_flush
subroutine, public m_flush(lunit)
flushes units if the &GLOBAL flag is set accordingly
Definition machine.F:106
mathconstants
Definition of mathematical constants and functions.
Definition mathconstants.F:16
mathconstants::pi
real(kind=dp), parameter, public pi
Definition mathconstants.F:110
message_passing
Interface to the message passing library MPI.
Definition message_passing.F:23
message_passing::mp_para_env_release
subroutine, public mp_para_env_release(para_env)
releases the para object (to be called when you don't want anymore the shared copy of this object)
Definition message_passing.F:2027
minimax_exp_gw
Routines to calculate the minimax coefficients in order to approximate 1/x as a sum over exponential ...
Definition minimax_exp_gw.F:17
minimax_exp_gw::get_exp_minimax_coeff_gw
subroutine, public get_exp_minimax_coeff_gw(k, e_range, aw)
...
Definition minimax_exp_gw.F:38
minimax_exp
Routines to calculate the minimax coefficients in order to approximate 1/x as a sum over exponential ...
Definition minimax_exp.F:29
minimax_exp::get_exp_minimax_coeff
subroutine, public get_exp_minimax_coeff(k, rc, aw, mm_error, which_coeffs)
Get best minimax approximation for given input parameters. Automatically chooses the most exact set o...
Definition minimax_exp.F:127
minimax_rpa
Routines to calculate the minimax coefficients for approximating 1/x as 1/x ~ 1/pi SUM_{i}^{K} w_i x^...
Definition minimax_rpa.F:14
minimax_rpa::get_rpa_minimax_coeff_larger_grid
subroutine, public get_rpa_minimax_coeff_larger_grid(k, e_range, aw)
...
Definition minimax_rpa.F:10122
minimax_rpa::get_rpa_minimax_coeff
subroutine, public get_rpa_minimax_coeff(k, e_range, aw, ierr, print_warning)
The a_i and w_i coefficient are stored in aw such that the first 1:K elements correspond to a_i and t...
Definition minimax_rpa.F:41
mp2_grids
Routines to calculate frequency and time grids (integration points and weights) for correlation metho...
Definition mp2_grids.F:14
mp2_grids::get_minimax_grid
subroutine, public get_minimax_grid(para_env, unit_nr, homo, eigenval, num_integ_points, do_im_time, do_ri_sos_laplace_mp2, do_print, tau_tj, tau_wj, qs_env, do_gw_im_time, do_kpoints_cubic_rpa, e_fermi, tj, wj, weights_cos_tf_t_to_w, weights_cos_tf_w_to_t, weights_sin_tf_t_to_w, regularization)
...
Definition mp2_grids.F:75
mp2_grids::get_l_sq_wghts_cos_tf_w_to_t
subroutine, public get_l_sq_wghts_cos_tf_w_to_t(num_integ_points, tau_tj, weights_cos_tf_w_to_t, omega_tj, e_min, e_max, max_error, num_points_per_magnitude, regularization)
...
Definition mp2_grids.F:1239
mp2_grids::get_l_sq_wghts_cos_tf_t_to_w
subroutine, public get_l_sq_wghts_cos_tf_t_to_w(num_integ_points, tau_tj, weights_cos_tf_t_to_w, omega_tj, e_min, e_max, max_error, num_points_per_magnitude, regularization)
Calculate integration weights for the tau grid (in dependency of the omega node)
Definition mp2_grids.F:740
mp2_grids::get_l_sq_wghts_sin_tf_t_to_w
subroutine, public get_l_sq_wghts_sin_tf_t_to_w(num_integ_points, tau_tj, weights_sin_tf_t_to_w, omega_tj, e_min, e_max, max_error, num_points_per_magnitude, regularization)
Calculate integration weights for the tau grid (in dependency of the omega node)
Definition mp2_grids.F:876
mp2_grids::test_least_square_ft
subroutine, public test_least_square_ft(nr, iw)
test the singular value decomposition for the computation of integration weights for the Fourier tran...
Definition mp2_grids.F:1162
mp2_grids::get_clenshaw_grid
subroutine, public get_clenshaw_grid(para_env, para_env_rpa, unit_nr, homo, virtual, eigenval, num_integ_points, num_integ_group, color_rpa_group, fm_mat_s, my_do_gw, ext_scaling, a_scaling, tj, wj)
...
Definition mp2_grids.F:314
qs_environment_types
Definition qs_environment_types.F:14
qs_environment_types::get_qs_env
subroutine, public get_qs_env(qs_env, atomic_kind_set, qs_kind_set, cell, super_cell, cell_ref, use_ref_cell, kpoints, dft_control, mos, sab_orb, sab_all, qmmm, qmmm_periodic, sac_ae, sac_ppl, sac_lri, sap_ppnl, sab_vdw, sab_scp, sap_oce, sab_lrc, sab_se, sab_xtbe, sab_tbe, sab_core, sab_xb, sab_xtb_nonbond, sab_almo, sab_kp, sab_kp_nosym, particle_set, energy, force, matrix_h, matrix_h_im, matrix_ks, matrix_ks_im, matrix_vxc, run_rtp, rtp, matrix_h_kp, matrix_h_im_kp, matrix_ks_kp, matrix_ks_im_kp, matrix_vxc_kp, kinetic_kp, matrix_s_kp, matrix_w_kp, matrix_s_ri_aux_kp, matrix_s, matrix_s_ri_aux, matrix_w, matrix_p_mp2, matrix_p_mp2_admm, rho, rho_xc, pw_env, ewald_env, ewald_pw, active_space, mpools, input, para_env, blacs_env, scf_control, rel_control, kinetic, qs_charges, vppl, rho_core, rho_nlcc, rho_nlcc_g, ks_env, ks_qmmm_env, wf_history, scf_env, local_particles, local_molecules, distribution_2d, dbcsr_dist, molecule_kind_set, molecule_set, subsys, cp_subsys, oce, local_rho_set, rho_atom_set, task_list, task_list_soft, rho0_atom_set, rho0_mpole, rhoz_set, ecoul_1c, rho0_s_rs, rho0_s_gs, do_kpoints, has_unit_metric, requires_mo_derivs, mo_derivs, mo_loc_history, nkind, natom, nelectron_total, nelectron_spin, efield, neighbor_list_id, linres_control, xas_env, virial, cp_ddapc_env, cp_ddapc_ewald, outer_scf_history, outer_scf_ihistory, x_data, et_coupling, dftb_potential, results, se_taper, se_store_int_env, se_nddo_mpole, se_nonbond_env, admm_env, lri_env, lri_density, exstate_env, ec_env, dispersion_env, gcp_env, vee, rho_external, external_vxc, mask, mp2_env, bs_env, kg_env, wanniercentres, atprop, ls_scf_env, do_transport, transport_env, v_hartree_rspace, s_mstruct_changed, rho_changed, potential_changed, forces_up_to_date, mscfg_env, almo_scf_env, gradient_history, variable_history, embed_pot, spin_embed_pot, polar_env, mos_last_converged, rhs)
Get the QUICKSTEP environment.
Definition qs_environment_types.F:502
qs_mo_types
Definition and initialisation of the mo data type.
Definition qs_mo_types.F:22
qs_mo_types::get_mo_set
subroutine, public get_mo_set(mo_set, maxocc, homo, lfomo, nao, nelectron, n_el_f, nmo, eigenvalues, occupation_numbers, mo_coeff, mo_coeff_b, uniform_occupation, kts, mu, flexible_electron_count)
Get the components of a MO set data structure.
Definition qs_mo_types.F:397
cp_fm_types::cp_fm_type
represent a full matrix
Definition cp_fm_types.F:116
input_section_types::section_vals_type
stores the values of a section
Definition input_section_types.F:126
kpoint_types::kpoint_env_type
Keeps information about a specific k-point.
Definition kpoint_types.F:72
kpoint_types::kpoint_type
Contains information about kpoints.
Definition kpoint_types.F:138
message_passing::mp_para_env_type
stores all the informations relevant to an mpi environment
Definition message_passing.F:763
qs_environment_types::qs_environment_type
Definition qs_environment_types.F:215
qs_mo_types::mo_set_type
Definition qs_mo_types.F:46