Line data Source code
1 : !--------------------------------------------------------------------------------------------------!
2 : ! CP2K: A general program to perform molecular dynamics simulations !
3 : ! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
4 : ! !
5 : ! SPDX-License-Identifier: GPL-2.0-or-later !
6 : !--------------------------------------------------------------------------------------------------!
7 :
8 : ! **************************************************************************************************
9 : !> \brief Distribution methods for atoms, particles, or molecules
10 : !> \par History
11 : !> - 1d-distribution of molecules and particles (Sep. 2003, MK)
12 : !> - 2d-distribution for Quickstep updated with molecules (Oct. 2003, MK)
13 : !> \author MK (22.08.2003)
14 : ! **************************************************************************************************
15 : MODULE distribution_methods
16 : USE atomic_kind_types, ONLY: atomic_kind_type,&
17 : get_atomic_kind,&
18 : get_atomic_kind_set
19 : USE basis_set_types, ONLY: get_gto_basis_set,&
20 : gto_basis_set_type
21 : USE cell_types, ONLY: cell_type,&
22 : pbc,&
23 : real_to_scaled,&
24 : scaled_to_real
25 : USE cp_array_utils, ONLY: cp_1d_i_p_type
26 : USE cp_blacs_env, ONLY: cp_blacs_env_type
27 : USE cp_dbcsr_api, ONLY: dbcsr_distribution_get_num_images
28 : USE cp_log_handling, ONLY: cp_get_default_logger,&
29 : cp_logger_get_default_io_unit,&
30 : cp_logger_get_default_unit_nr,&
31 : cp_logger_type
32 : USE cp_min_heap, ONLY: cp_heap_fill,&
33 : cp_heap_get_first,&
34 : cp_heap_new,&
35 : cp_heap_release,&
36 : cp_heap_reset_first,&
37 : cp_heap_type
38 : USE cp_output_handling, ONLY: cp_p_file,&
39 : cp_print_key_finished_output,&
40 : cp_print_key_should_output,&
41 : cp_print_key_unit_nr
42 : USE distribution_1d_types, ONLY: distribution_1d_create,&
43 : distribution_1d_type
44 : USE distribution_2d_types, ONLY: distribution_2d_create,&
45 : distribution_2d_type,&
46 : distribution_2d_write
47 : USE input_constants, ONLY: model_block_count,&
48 : model_block_lmax
49 : USE input_section_types, ONLY: section_vals_get_subs_vals,&
50 : section_vals_type,&
51 : section_vals_val_get
52 : USE kinds, ONLY: dp,&
53 : int_8
54 : USE machine, ONLY: m_flush
55 : USE mathconstants, ONLY: pi
56 : USE mathlib, ONLY: gcd,&
57 : lcm
58 : USE molecule_kind_types, ONLY: get_molecule_kind,&
59 : get_molecule_kind_set,&
60 : molecule_kind_type
61 : USE molecule_types, ONLY: molecule_type
62 : USE parallel_rng_types, ONLY: UNIFORM,&
63 : rng_stream_type
64 : USE particle_types, ONLY: particle_type
65 : USE qs_kind_types, ONLY: get_qs_kind,&
66 : qs_kind_type
67 : USE util, ONLY: sort
68 : #include "./base/base_uses.f90"
69 :
70 : IMPLICIT NONE
71 :
72 : PRIVATE
73 :
74 : ! *** Global parameters (in this module) ***
75 :
76 : CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'distribution_methods'
77 :
78 : ! *** Public subroutines ***
79 :
80 : PUBLIC :: distribute_molecules_1d, &
81 : distribute_molecules_2d
82 :
83 : CONTAINS
84 :
85 : ! **************************************************************************************************
86 : !> \brief Distribute molecules and particles
87 : !> \param atomic_kind_set particle (atomic) kind information
88 : !> \param particle_set particle information
89 : !> \param local_particles distribution of particles created by this routine
90 : !> \param molecule_kind_set molecule kind information
91 : !> \param molecule_set molecule information
92 : !> \param local_molecules distribution of molecules created by this routine
93 : !> \param force_env_section ...
94 : !> \param prev_molecule_kind_set previous molecule kind information, used with
95 : !> prev_local_molecules
96 : !> \param prev_local_molecules previous distribution of molecules, new one will
97 : !> be identical if all the prev_* arguments are present and associated
98 : !> \par History
99 : !> none
100 : !> \author MK (Jun. 2003)
101 : ! **************************************************************************************************
102 10431 : SUBROUTINE distribute_molecules_1d(atomic_kind_set, particle_set, &
103 : local_particles, &
104 : molecule_kind_set, molecule_set, &
105 : local_molecules, force_env_section, &
106 : prev_molecule_kind_set, &
107 : prev_local_molecules)
108 :
109 : TYPE(atomic_kind_type), DIMENSION(:), POINTER :: atomic_kind_set
110 : TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
111 : TYPE(distribution_1d_type), POINTER :: local_particles
112 : TYPE(molecule_kind_type), DIMENSION(:), POINTER :: molecule_kind_set
113 : TYPE(molecule_type), DIMENSION(:), POINTER :: molecule_set
114 : TYPE(distribution_1d_type), POINTER :: local_molecules
115 : TYPE(section_vals_type), POINTER :: force_env_section
116 : TYPE(molecule_kind_type), DIMENSION(:), OPTIONAL, &
117 : POINTER :: prev_molecule_kind_set
118 : TYPE(distribution_1d_type), OPTIONAL, POINTER :: prev_local_molecules
119 :
120 : CHARACTER(len=*), PARAMETER :: routineN = 'distribute_molecules_1d'
121 :
122 : INTEGER :: atom_a, bin, handle, iatom, imolecule, imolecule_kind, imolecule_local, &
123 : imolecule_prev_kind, iparticle_kind, ipe, iw, kind_a, molecule_a, n, natom, nbins, nload, &
124 : nmolecule, nmolecule_kind, nparticle_kind, nsgf, output_unit
125 : INTEGER(int_8) :: bin_price
126 : INTEGER(int_8), ALLOCATABLE, DIMENSION(:) :: workload_count, workload_fill
127 10431 : INTEGER, ALLOCATABLE, DIMENSION(:) :: nmolecule_local, nparticle_local, work
128 10431 : INTEGER, DIMENSION(:), POINTER :: molecule_list
129 : LOGICAL :: found, has_prev_subsys_info, is_local
130 10431 : TYPE(cp_1d_i_p_type), ALLOCATABLE, DIMENSION(:) :: local_molecule
131 : TYPE(cp_heap_type) :: bin_heap_count, bin_heap_fill
132 : TYPE(cp_logger_type), POINTER :: logger
133 : TYPE(molecule_kind_type), POINTER :: molecule_kind
134 :
135 10431 : CALL timeset(routineN, handle)
136 :
137 10431 : has_prev_subsys_info = .FALSE.
138 10431 : IF (PRESENT(prev_local_molecules) .AND. &
139 : PRESENT(prev_molecule_kind_set)) THEN
140 2639 : IF (ASSOCIATED(prev_local_molecules) .AND. &
141 : ASSOCIATED(prev_molecule_kind_set)) THEN
142 44 : has_prev_subsys_info = .TRUE.
143 : END IF
144 : END IF
145 :
146 10431 : logger => cp_get_default_logger()
147 :
148 : ASSOCIATE (group => logger%para_env, mype => logger%para_env%mepos + 1, &
149 : npe => logger%para_env%num_pe)
150 :
151 31293 : ALLOCATE (workload_count(npe))
152 30256 : workload_count(:) = 0
153 :
154 20862 : ALLOCATE (workload_fill(npe))
155 30256 : workload_fill(:) = 0
156 :
157 10431 : nmolecule_kind = SIZE(molecule_kind_set)
158 :
159 31293 : ALLOCATE (nmolecule_local(nmolecule_kind))
160 145468 : nmolecule_local(:) = 0
161 :
162 176761 : ALLOCATE (local_molecule(nmolecule_kind))
163 :
164 10431 : nparticle_kind = SIZE(atomic_kind_set)
165 :
166 31293 : ALLOCATE (nparticle_local(nparticle_kind))
167 36693 : nparticle_local(:) = 0
168 :
169 10431 : nbins = npe
170 :
171 10431 : CALL cp_heap_new(bin_heap_count, nbins)
172 10431 : CALL cp_heap_fill(bin_heap_count, workload_count)
173 :
174 10431 : CALL cp_heap_new(bin_heap_fill, nbins)
175 10431 : CALL cp_heap_fill(bin_heap_fill, workload_fill)
176 :
177 145468 : DO imolecule_kind = 1, nmolecule_kind
178 :
179 135037 : molecule_kind => molecule_kind_set(imolecule_kind)
180 :
181 135037 : NULLIFY (molecule_list)
182 :
183 : ! *** Get the number of molecules and the number of ***
184 : ! *** atoms in each molecule of that molecular kind ***
185 :
186 : CALL get_molecule_kind(molecule_kind=molecule_kind, &
187 : molecule_list=molecule_list, &
188 : natom=natom, &
189 135037 : nsgf=nsgf)
190 :
191 : ! *** Consider the number of atoms or basis ***
192 : ! *** functions which depends on the method ***
193 :
194 135037 : nload = MAX(natom, nsgf)
195 135037 : nmolecule = SIZE(molecule_list)
196 :
197 : ! *** Get the number of local molecules of the current molecule kind ***
198 :
199 438027 : DO imolecule = 1, nmolecule
200 438027 : IF (has_prev_subsys_info) THEN
201 297660 : DO imolecule_prev_kind = 1, SIZE(prev_molecule_kind_set)
202 3188004 : IF (ANY(prev_local_molecules%list(imolecule_prev_kind)%array( &
203 5060 : 1:prev_local_molecules%n_el(imolecule_prev_kind)) == molecule_list(imolecule))) THEN
204 : ! molecule used to be local
205 2530 : nmolecule_local(imolecule_kind) = nmolecule_local(imolecule_kind) + 1
206 : END IF
207 : END DO
208 : ELSE
209 297930 : CALL cp_heap_get_first(bin_heap_count, bin, bin_price, found)
210 297930 : IF (.NOT. found) &
211 0 : CPABORT("No topmost heap element found.")
212 :
213 297930 : ipe = bin
214 297930 : IF (bin_price /= workload_count(ipe)) &
215 0 : CPABORT("inconsistent heap")
216 :
217 297930 : workload_count(ipe) = workload_count(ipe) + nload
218 297930 : IF (ipe == mype) THEN
219 164119 : nmolecule_local(imolecule_kind) = nmolecule_local(imolecule_kind) + 1
220 : END IF
221 :
222 297930 : bin_price = workload_count(ipe)
223 297930 : CALL cp_heap_reset_first(bin_heap_count, bin_price)
224 : END IF
225 : END DO
226 :
227 : ! *** Distribute the molecules ***
228 135037 : n = nmolecule_local(imolecule_kind)
229 :
230 135037 : IF (n > 0) THEN
231 217914 : ALLOCATE (local_molecule(imolecule_kind)%array(n))
232 : ELSE
233 62399 : NULLIFY (local_molecule(imolecule_kind)%array)
234 : END IF
235 :
236 : imolecule_local = 0
237 583495 : DO imolecule = 1, nmolecule
238 302990 : is_local = .FALSE.
239 302990 : IF (has_prev_subsys_info) THEN
240 297660 : DO imolecule_prev_kind = 1, SIZE(prev_molecule_kind_set)
241 3188004 : IF (ANY(prev_local_molecules%list(imolecule_prev_kind)%array( &
242 5060 : 1:prev_local_molecules%n_el(imolecule_prev_kind)) == molecule_list(imolecule))) THEN
243 2530 : is_local = .TRUE.
244 : END IF
245 : END DO
246 : ELSE
247 297930 : CALL cp_heap_get_first(bin_heap_fill, bin, bin_price, found)
248 297930 : IF (.NOT. found) &
249 0 : CPABORT("No topmost heap element found.")
250 :
251 297930 : ipe = bin
252 297930 : IF (bin_price /= workload_fill(ipe)) &
253 0 : CPABORT("inconsistent heap")
254 :
255 297930 : workload_fill(ipe) = workload_fill(ipe) + nload
256 297930 : is_local = (ipe == mype)
257 : END IF
258 302990 : IF (is_local) THEN
259 166649 : imolecule_local = imolecule_local + 1
260 166649 : molecule_a = molecule_list(imolecule)
261 166649 : local_molecule(imolecule_kind)%array(imolecule_local) = molecule_a
262 579909 : DO iatom = 1, natom
263 413260 : atom_a = molecule_set(molecule_a)%first_atom + iatom - 1
264 :
265 : CALL get_atomic_kind(atomic_kind=particle_set(atom_a)%atomic_kind, &
266 413260 : kind_number=kind_a)
267 579909 : nparticle_local(kind_a) = nparticle_local(kind_a) + 1
268 : END DO
269 : END IF
270 438027 : IF (.NOT. has_prev_subsys_info) THEN
271 297930 : bin_price = workload_fill(ipe)
272 297930 : CALL cp_heap_reset_first(bin_heap_fill, bin_price)
273 : END IF
274 : END DO
275 :
276 : END DO
277 :
278 30256 : IF (ANY(workload_fill .NE. workload_count)) &
279 0 : CPABORT("Inconsistent heaps encountered")
280 :
281 10431 : CALL cp_heap_release(bin_heap_count)
282 10431 : CALL cp_heap_release(bin_heap_fill)
283 :
284 : ! *** Create the local molecule structure ***
285 :
286 : CALL distribution_1d_create(local_molecules, &
287 : n_el=nmolecule_local, &
288 10431 : para_env=logger%para_env)
289 :
290 : ! *** Create the local particle structure ***
291 :
292 : CALL distribution_1d_create(local_particles, &
293 : n_el=nparticle_local, &
294 10431 : para_env=logger%para_env)
295 :
296 : ! *** Store the generated local molecule and particle distributions ***
297 :
298 36693 : nparticle_local(:) = 0
299 :
300 145468 : DO imolecule_kind = 1, nmolecule_kind
301 :
302 135037 : IF (nmolecule_local(imolecule_kind) == 0) CYCLE
303 :
304 : local_molecules%list(imolecule_kind)%array(:) = &
305 239287 : local_molecule(imolecule_kind)%array(:)
306 :
307 72638 : molecule_kind => molecule_kind_set(imolecule_kind)
308 :
309 : CALL get_molecule_kind(molecule_kind=molecule_kind, &
310 72638 : natom=natom)
311 :
312 249718 : DO imolecule = 1, nmolecule_local(imolecule_kind)
313 166649 : molecule_a = local_molecule(imolecule_kind)%array(imolecule)
314 714946 : DO iatom = 1, natom
315 413260 : atom_a = molecule_set(molecule_a)%first_atom + iatom - 1
316 : CALL get_atomic_kind(atomic_kind=particle_set(atom_a)%atomic_kind, &
317 413260 : kind_number=kind_a)
318 413260 : nparticle_local(kind_a) = nparticle_local(kind_a) + 1
319 579909 : local_particles%list(kind_a)%array(nparticle_local(kind_a)) = atom_a
320 : END DO
321 : END DO
322 :
323 : END DO
324 :
325 : ! *** Print distribution, if requested ***
326 :
327 10431 : IF (BTEST(cp_print_key_should_output(logger%iter_info, &
328 31293 : force_env_section, "PRINT%DISTRIBUTION1D"), cp_p_file)) THEN
329 :
330 : output_unit = cp_print_key_unit_nr(logger, force_env_section, "PRINT%DISTRIBUTION1D", &
331 130 : extension=".Log")
332 :
333 130 : iw = output_unit
334 130 : IF (output_unit < 0) iw = cp_logger_get_default_unit_nr(logger, LOCAL=.TRUE.)
335 :
336 : ! *** Print molecule distribution ***
337 :
338 390 : ALLOCATE (work(npe))
339 390 : work(:) = 0
340 :
341 416 : work(mype) = SUM(nmolecule_local)
342 130 : CALL group%sum(work)
343 :
344 130 : IF (output_unit > 0) THEN
345 : WRITE (UNIT=output_unit, &
346 : FMT="(/, T2, A, T51, A, /, (T52, I6, T73, I8))") &
347 65 : "DISTRIBUTION OF THE MOLECULES", &
348 65 : "Process Number of molecules", &
349 260 : (ipe - 1, work(ipe), ipe=1, npe)
350 : WRITE (UNIT=output_unit, FMT="(T55, A3, T73, I8)") &
351 195 : "Sum", SUM(work)
352 65 : CALL m_flush(output_unit)
353 : END IF
354 :
355 130 : CALL group%sync()
356 :
357 390 : DO ipe = 1, npe
358 260 : IF (ipe == mype) THEN
359 : WRITE (UNIT=iw, FMT="(/, T3, A)") &
360 130 : "Process Kind Local molecules (global indices)"
361 416 : DO imolecule_kind = 1, nmolecule_kind
362 416 : IF (imolecule_kind == 1) THEN
363 : WRITE (UNIT=iw, FMT="(T4, I6, 2X, I5, (T21, 10I6))") &
364 130 : ipe - 1, imolecule_kind, &
365 330 : (local_molecules%list(imolecule_kind)%array(imolecule), &
366 590 : imolecule=1, nmolecule_local(imolecule_kind))
367 : ELSE
368 : WRITE (UNIT=iw, FMT="(T12, I5, (T21, 10I6))") &
369 156 : imolecule_kind, &
370 234 : (local_molecules%list(imolecule_kind)%array(imolecule), &
371 546 : imolecule=1, nmolecule_local(imolecule_kind))
372 : END IF
373 : END DO
374 : END IF
375 260 : CALL m_flush(iw)
376 390 : CALL group%sync()
377 : END DO
378 :
379 : ! *** Print particle distribution ***
380 :
381 390 : work(:) = 0
382 :
383 436 : work(mype) = SUM(nparticle_local)
384 130 : CALL group%sum(work)
385 :
386 130 : IF (output_unit > 0) THEN
387 : WRITE (UNIT=output_unit, &
388 : FMT="(/, T2, A, T51, A, /, (T52, I6, T73, I8))") &
389 65 : "DISTRIBUTION OF THE PARTICLES", &
390 65 : "Process Number of particles", &
391 260 : (ipe - 1, work(ipe), ipe=1, npe)
392 : WRITE (UNIT=output_unit, FMT="(T55, A3, T73, I8)") &
393 195 : "Sum", SUM(work)
394 65 : CALL m_flush(output_unit)
395 : END IF
396 :
397 130 : CALL group%sync()
398 :
399 390 : DO ipe = 1, npe
400 260 : IF (ipe == mype) THEN
401 : WRITE (UNIT=iw, FMT="(/, T3, A)") &
402 130 : "Process Kind Local particles (global indices)"
403 436 : DO iparticle_kind = 1, nparticle_kind
404 436 : IF (iparticle_kind == 1) THEN
405 : WRITE (UNIT=iw, FMT="(T4, I6, 2X, I5, (T20, 10I6))") &
406 130 : ipe - 1, iparticle_kind, &
407 586 : (local_particles%list(iparticle_kind)%array(iatom), &
408 846 : iatom=1, nparticle_local(iparticle_kind))
409 : ELSE
410 : WRITE (UNIT=iw, FMT="(T12, I5, (T20, 10I6))") &
411 176 : iparticle_kind, &
412 1084 : (local_particles%list(iparticle_kind)%array(iatom), &
413 1436 : iatom=1, nparticle_local(iparticle_kind))
414 : END IF
415 : END DO
416 : END IF
417 260 : CALL m_flush(iw)
418 390 : CALL group%sync()
419 : END DO
420 130 : DEALLOCATE (work)
421 :
422 : CALL cp_print_key_finished_output(output_unit, logger, force_env_section, &
423 130 : "PRINT%DISTRIBUTION1D")
424 : END IF
425 : END ASSOCIATE
426 : ! *** Release work storage ***
427 :
428 10431 : DEALLOCATE (workload_count)
429 :
430 10431 : DEALLOCATE (workload_fill)
431 :
432 10431 : DEALLOCATE (nmolecule_local)
433 :
434 10431 : DEALLOCATE (nparticle_local)
435 :
436 145468 : DO imolecule_kind = 1, nmolecule_kind
437 145468 : IF (ASSOCIATED(local_molecule(imolecule_kind)%array)) THEN
438 72638 : DEALLOCATE (local_molecule(imolecule_kind)%array)
439 : END IF
440 : END DO
441 10431 : DEALLOCATE (local_molecule)
442 :
443 10431 : CALL timestop(handle)
444 :
445 20862 : END SUBROUTINE distribute_molecules_1d
446 :
447 : ! **************************************************************************************************
448 : !> \brief Distributes the particle pairs creating a 2d distribution optimally
449 : !> suited for quickstep
450 : !> \param cell ...
451 : !> \param atomic_kind_set ...
452 : !> \param particle_set ...
453 : !> \param qs_kind_set ...
454 : !> \param molecule_kind_set ...
455 : !> \param molecule_set ...
456 : !> \param distribution_2d the distribution that will be created by this
457 : !> method
458 : !> \param blacs_env the parallel environment at the basis of the
459 : !> distribution
460 : !> \param force_env_section ...
461 : !> \par History
462 : !> - local_rows & cols blocksize optimizations (Aug. 2003, MK)
463 : !> - cleanup of distribution_2d (Sep. 2003, fawzi)
464 : !> - update for molecules (Oct. 2003, MK)
465 : !> \author fawzi (Feb. 2003)
466 : !> \note
467 : !> Intermediate generation of a 2d distribution of the molecules, but
468 : !> only the corresponding particle (atomic) distribution is currently
469 : !> used. The 2d distribution of the molecules is deleted, but may easily
470 : !> be recovered (MK).
471 : ! **************************************************************************************************
472 7610 : SUBROUTINE distribute_molecules_2d(cell, atomic_kind_set, particle_set, &
473 : qs_kind_set, molecule_kind_set, molecule_set, &
474 : distribution_2d, blacs_env, force_env_section)
475 : TYPE(cell_type), POINTER :: cell
476 : TYPE(atomic_kind_type), DIMENSION(:), POINTER :: atomic_kind_set
477 : TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
478 : TYPE(qs_kind_type), DIMENSION(:), POINTER :: qs_kind_set
479 : TYPE(molecule_kind_type), DIMENSION(:), POINTER :: molecule_kind_set
480 : TYPE(molecule_type), DIMENSION(:), POINTER :: molecule_set
481 : TYPE(distribution_2d_type), POINTER :: distribution_2d
482 : TYPE(cp_blacs_env_type), POINTER :: blacs_env
483 : TYPE(section_vals_type), POINTER :: force_env_section
484 :
485 : CHARACTER(len=*), PARAMETER :: routineN = 'distribute_molecules_2d'
486 :
487 : INTEGER :: cluster_price, cost_model, handle, iatom, iatom_mol, iatom_one, ikind, imol, &
488 : imolecule, imolecule_kind, iparticle_kind, ipcol, iprow, iw, kind_a, n, natom, natom_mol, &
489 : nclusters, nmolecule, nmolecule_kind, nparticle_kind, nsgf, output_unit
490 7610 : INTEGER, ALLOCATABLE, DIMENSION(:) :: cluster_list, cluster_prices, &
491 7610 : nparticle_local_col, &
492 7610 : nparticle_local_row, work
493 7610 : INTEGER, DIMENSION(:), POINTER :: lmax_basis, molecule_list
494 7610 : INTEGER, DIMENSION(:, :), POINTER :: cluster_col_distribution, &
495 7610 : cluster_row_distribution, &
496 7610 : col_distribution, row_distribution
497 : LOGICAL :: basic_cluster_optimization, basic_optimization, basic_spatial_optimization, &
498 : molecular_distribution, skip_optimization
499 7610 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: coords, pbc_scaled_coords
500 : REAL(KIND=dp), DIMENSION(3) :: center
501 7610 : TYPE(cp_1d_i_p_type), DIMENSION(:), POINTER :: local_particle_col, local_particle_row
502 : TYPE(cp_logger_type), POINTER :: logger
503 : TYPE(gto_basis_set_type), POINTER :: orb_basis_set
504 : TYPE(molecule_kind_type), POINTER :: molecule_kind
505 : TYPE(section_vals_type), POINTER :: distribution_section
506 :
507 : !...
508 :
509 7610 : CALL timeset(routineN, handle)
510 :
511 7610 : logger => cp_get_default_logger()
512 :
513 7610 : distribution_section => section_vals_get_subs_vals(force_env_section, "DFT%QS%DISTRIBUTION")
514 :
515 7610 : CALL section_vals_val_get(distribution_section, "2D_MOLECULAR_DISTRIBUTION", l_val=molecular_distribution)
516 7610 : CALL section_vals_val_get(distribution_section, "SKIP_OPTIMIZATION", l_val=skip_optimization)
517 7610 : CALL section_vals_val_get(distribution_section, "BASIC_OPTIMIZATION", l_val=basic_optimization)
518 7610 : CALL section_vals_val_get(distribution_section, "BASIC_SPATIAL_OPTIMIZATION", l_val=basic_spatial_optimization)
519 7610 : CALL section_vals_val_get(distribution_section, "BASIC_CLUSTER_OPTIMIZATION", l_val=basic_cluster_optimization)
520 :
521 7610 : CALL section_vals_val_get(distribution_section, "COST_MODEL", i_val=cost_model)
522 : !
523 :
524 : ASSOCIATE (group => blacs_env%para_env, myprow => blacs_env%mepos(1) + 1, mypcol => blacs_env%mepos(2) + 1, &
525 : nprow => blacs_env%num_pe(1), npcol => blacs_env%num_pe(2))
526 :
527 7610 : nmolecule_kind = SIZE(molecule_kind_set)
528 7610 : CALL get_molecule_kind_set(molecule_kind_set, nmolecule=nmolecule)
529 :
530 7610 : nparticle_kind = SIZE(atomic_kind_set)
531 7610 : CALL get_atomic_kind_set(atomic_kind_set=atomic_kind_set, natom=natom)
532 :
533 : !
534 : ! we need to generate two representations of the distribution, one as a straight array with global particles
535 : ! one ordered wrt to kinds and only listing the local particles
536 : !
537 22830 : ALLOCATE (row_distribution(natom, 2))
538 15220 : ALLOCATE (col_distribution(natom, 2))
539 : ! Initialize the distributions to -1, as the second dimension only gets set with cluster optimization
540 : ! but the information is needed by dbcsr
541 222718 : row_distribution = -1; col_distribution = -1
542 :
543 37255 : ALLOCATE (local_particle_col(nparticle_kind))
544 29645 : ALLOCATE (local_particle_row(nparticle_kind))
545 22830 : ALLOCATE (nparticle_local_row(nparticle_kind))
546 15220 : ALLOCATE (nparticle_local_col(nparticle_kind))
547 :
548 7610 : IF (basic_optimization .OR. basic_spatial_optimization .OR. basic_cluster_optimization) THEN
549 :
550 7610 : IF (molecular_distribution) THEN
551 2 : nclusters = nmolecule
552 : ELSE
553 : nclusters = natom
554 : END IF
555 :
556 22830 : ALLOCATE (cluster_list(nclusters))
557 15220 : ALLOCATE (cluster_prices(nclusters))
558 22830 : ALLOCATE (cluster_row_distribution(nclusters, 2))
559 15220 : ALLOCATE (cluster_col_distribution(nclusters, 2))
560 230296 : cluster_row_distribution = -1; cluster_col_distribution = -1
561 :
562 : ! Fill in the clusters and their prices
563 7610 : CALL section_vals_val_get(distribution_section, "COST_MODEL", i_val=cost_model)
564 7610 : IF (.NOT. molecular_distribution) THEN
565 53763 : DO iatom = 1, natom
566 46155 : IF (iatom .GT. nclusters) &
567 0 : CPABORT("Bounds error")
568 46155 : CALL get_atomic_kind(particle_set(iatom)%atomic_kind, kind_number=ikind)
569 46155 : cluster_list(iatom) = iatom
570 46155 : SELECT CASE (cost_model)
571 : CASE (model_block_count)
572 46155 : CALL get_qs_kind(qs_kind_set(ikind), nsgf=nsgf)
573 46155 : cluster_price = nsgf
574 : CASE (model_block_lmax)
575 0 : CALL get_qs_kind(qs_kind_set(ikind), basis_set=orb_basis_set)
576 0 : CALL get_gto_basis_set(orb_basis_set, lmax=lmax_basis)
577 0 : cluster_price = MAXVAL(lmax_basis)
578 : CASE default
579 0 : CALL get_qs_kind(qs_kind_set(ikind), basis_set=orb_basis_set)
580 0 : CALL get_gto_basis_set(orb_basis_set, lmax=lmax_basis)
581 46155 : cluster_price = 8 + (MAXVAL(lmax_basis)**2)
582 : END SELECT
583 99918 : cluster_prices(iatom) = cluster_price
584 : END DO
585 : ELSE
586 : imol = 0
587 4 : DO imolecule_kind = 1, nmolecule_kind
588 2 : molecule_kind => molecule_kind_set(imolecule_kind)
589 2 : CALL get_molecule_kind(molecule_kind=molecule_kind, molecule_list=molecule_list, natom=natom_mol)
590 8 : DO imolecule = 1, SIZE(molecule_list)
591 4 : imol = imol + 1
592 4 : cluster_list(imol) = imol
593 4 : cluster_price = 0
594 16 : DO iatom_mol = 1, natom_mol
595 12 : iatom = molecule_set(molecule_list(imolecule))%first_atom + iatom_mol - 1
596 12 : CALL get_atomic_kind(particle_set(iatom)%atomic_kind, kind_number=ikind)
597 16 : SELECT CASE (cost_model)
598 : CASE (model_block_count)
599 12 : CALL get_qs_kind(qs_kind_set(ikind), nsgf=nsgf)
600 12 : cluster_price = cluster_price + nsgf
601 : CASE (model_block_lmax)
602 0 : CALL get_qs_kind(qs_kind_set(ikind), basis_set=orb_basis_set)
603 0 : CALL get_gto_basis_set(orb_basis_set, lmax=lmax_basis)
604 0 : cluster_price = cluster_price + MAXVAL(lmax_basis)
605 : CASE default
606 0 : CALL get_qs_kind(qs_kind_set(ikind), basis_set=orb_basis_set)
607 0 : CALL get_gto_basis_set(orb_basis_set, lmax=lmax_basis)
608 12 : cluster_price = cluster_price + 8 + (MAXVAL(lmax_basis)**2)
609 : END SELECT
610 : END DO
611 6 : cluster_prices(imol) = cluster_price
612 : END DO
613 : END DO
614 : END IF
615 :
616 : ! And distribute
617 7610 : IF (basic_optimization) THEN
618 : CALL make_basic_distribution(cluster_list, cluster_prices, &
619 7440 : nprow, cluster_row_distribution(:, 1), npcol, cluster_col_distribution(:, 1))
620 : ELSE
621 170 : IF (basic_cluster_optimization) THEN
622 4 : IF (molecular_distribution) &
623 0 : CPABORT("clustering and molecular blocking NYI")
624 16 : ALLOCATE (pbc_scaled_coords(3, natom), coords(3, natom))
625 118 : DO iatom = 1, natom
626 114 : CALL real_to_scaled(pbc_scaled_coords(:, iatom), pbc(particle_set(iatom)%r(:), cell), cell)
627 118 : coords(:, iatom) = pbc(particle_set(iatom)%r(:), cell)
628 : END DO
629 : CALL make_cluster_distribution(coords, pbc_scaled_coords, cell, cluster_prices, &
630 4 : nprow, cluster_row_distribution, npcol, cluster_col_distribution)
631 : ELSE ! basic_spatial_optimization
632 498 : ALLOCATE (pbc_scaled_coords(3, nclusters))
633 166 : IF (.NOT. molecular_distribution) THEN
634 : ! just scaled coords
635 2696 : DO iatom = 1, natom
636 2696 : CALL real_to_scaled(pbc_scaled_coords(:, iatom), pbc(particle_set(iatom)%r(:), cell), cell)
637 : END DO
638 : ELSE
639 : ! use scaled coords of geometric center, folding when appropriate
640 : imol = 0
641 0 : DO imolecule_kind = 1, nmolecule_kind
642 0 : molecule_kind => molecule_kind_set(imolecule_kind)
643 0 : CALL get_molecule_kind(molecule_kind=molecule_kind, molecule_list=molecule_list, natom=natom_mol)
644 0 : DO imolecule = 1, SIZE(molecule_list)
645 0 : imol = imol + 1
646 0 : iatom_one = molecule_set(molecule_list(imolecule))%first_atom
647 0 : center = 0.0_dp
648 0 : DO iatom_mol = 1, natom_mol
649 0 : iatom = molecule_set(molecule_list(imolecule))%first_atom + iatom_mol - 1
650 : center = center + &
651 0 : pbc(particle_set(iatom)%r(:) - particle_set(iatom_one)%r(:), cell) + particle_set(iatom_one)%r(:)
652 : END DO
653 0 : center = center/natom_mol
654 0 : CALL real_to_scaled(pbc_scaled_coords(:, imol), pbc(center, cell), cell)
655 : END DO
656 : END DO
657 : END IF
658 :
659 : CALL make_basic_spatial_distribution(pbc_scaled_coords, cluster_prices, &
660 166 : nprow, cluster_row_distribution(:, 1), npcol, cluster_col_distribution(:, 1))
661 :
662 166 : DEALLOCATE (pbc_scaled_coords)
663 : END IF
664 : END IF
665 :
666 : ! And assign back
667 7610 : IF (.NOT. molecular_distribution) THEN
668 230268 : row_distribution = cluster_row_distribution
669 230268 : col_distribution = cluster_col_distribution
670 : ELSE
671 : imol = 0
672 4 : DO imolecule_kind = 1, nmolecule_kind
673 2 : molecule_kind => molecule_kind_set(imolecule_kind)
674 2 : CALL get_molecule_kind(molecule_kind=molecule_kind, molecule_list=molecule_list, natom=natom_mol)
675 8 : DO imolecule = 1, SIZE(molecule_list)
676 4 : imol = imol + 1
677 18 : DO iatom_mol = 1, natom_mol
678 12 : iatom = molecule_set(molecule_list(imolecule))%first_atom + iatom_mol - 1
679 72 : row_distribution(iatom, :) = cluster_row_distribution(imol, :)
680 76 : col_distribution(iatom, :) = cluster_col_distribution(imol, :)
681 : END DO
682 : END DO
683 : END DO
684 : END IF
685 :
686 : ! cleanup
687 7610 : DEALLOCATE (cluster_list)
688 7610 : DEALLOCATE (cluster_prices)
689 7610 : DEALLOCATE (cluster_row_distribution)
690 15220 : DEALLOCATE (cluster_col_distribution)
691 :
692 : ELSE
693 : ! expects nothing else
694 0 : CPABORT("")
695 : END IF
696 :
697 : ! prepare the lists of local particles
698 :
699 : ! count local particles of a given kind
700 22035 : nparticle_local_col = 0
701 22035 : nparticle_local_row = 0
702 53777 : DO iatom = 1, natom
703 46167 : CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, kind_number=kind_a)
704 46167 : IF (row_distribution(iatom, 1) == myprow) nparticle_local_row(kind_a) = nparticle_local_row(kind_a) + 1
705 99944 : IF (col_distribution(iatom, 1) == mypcol) nparticle_local_col(kind_a) = nparticle_local_col(kind_a) + 1
706 : END DO
707 :
708 : ! allocate space
709 22035 : DO iparticle_kind = 1, nparticle_kind
710 14425 : n = nparticle_local_row(iparticle_kind)
711 39110 : ALLOCATE (local_particle_row(iparticle_kind)%array(n))
712 :
713 14425 : n = nparticle_local_col(iparticle_kind)
714 50885 : ALLOCATE (local_particle_col(iparticle_kind)%array(n))
715 : END DO
716 :
717 : ! store
718 22035 : nparticle_local_col = 0
719 22035 : nparticle_local_row = 0
720 53777 : DO iatom = 1, natom
721 46167 : CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, kind_number=kind_a)
722 46167 : IF (row_distribution(iatom, 1) == myprow) THEN
723 24100 : nparticle_local_row(kind_a) = nparticle_local_row(kind_a) + 1
724 24100 : local_particle_row(kind_a)%array(nparticle_local_row(kind_a)) = iatom
725 : END IF
726 99944 : IF (col_distribution(iatom, 1) == mypcol) THEN
727 46167 : nparticle_local_col(kind_a) = nparticle_local_col(kind_a) + 1
728 46167 : local_particle_col(kind_a)%array(nparticle_local_col(kind_a)) = iatom
729 : END IF
730 : END DO
731 :
732 : ! *** Generate the 2d distribution structure but take care of the zero offsets required
733 53777 : row_distribution(:, 1) = row_distribution(:, 1) - 1
734 53777 : col_distribution(:, 1) = col_distribution(:, 1) - 1
735 : CALL distribution_2d_create(distribution_2d, &
736 : row_distribution_ptr=row_distribution, &
737 : col_distribution_ptr=col_distribution, &
738 : local_rows_ptr=local_particle_row, &
739 : local_cols_ptr=local_particle_col, &
740 7610 : blacs_env=blacs_env)
741 :
742 7610 : NULLIFY (local_particle_row)
743 7610 : NULLIFY (local_particle_col)
744 7610 : NULLIFY (row_distribution)
745 7610 : NULLIFY (col_distribution)
746 :
747 : ! *** Print distribution, if requested ***
748 7610 : IF (BTEST(cp_print_key_should_output(logger%iter_info, &
749 7610 : force_env_section, "PRINT%DISTRIBUTION"), cp_p_file)) THEN
750 :
751 : output_unit = cp_print_key_unit_nr(logger, force_env_section, "PRINT%DISTRIBUTION", &
752 80 : extension=".Log")
753 :
754 : ! *** Print row distribution ***
755 :
756 240 : ALLOCATE (work(nprow))
757 236 : work(:) = 0
758 :
759 228 : IF (mypcol == 1) work(myprow) = SUM(distribution_2d%n_local_rows)
760 :
761 80 : CALL group%sum(work)
762 :
763 80 : IF (output_unit > 0) THEN
764 : WRITE (UNIT=output_unit, &
765 : FMT="(/, T2, A, /, T15, A, /, (T16, I10, T41, I10, T71, I10))") &
766 40 : "DISTRIBUTION OF THE PARTICLES (ROWS)", &
767 40 : "Process row Number of particles Number of matrix rows", &
768 158 : (iprow - 1, work(iprow), -1, iprow=1, nprow)
769 : WRITE (UNIT=output_unit, FMT="(T23, A3, T41, I10, T71, I10)") &
770 118 : "Sum", SUM(work), -1
771 40 : CALL m_flush(output_unit)
772 : END IF
773 :
774 80 : DEALLOCATE (work)
775 :
776 : ! *** Print column distribution ***
777 :
778 240 : ALLOCATE (work(npcol))
779 160 : work(:) = 0
780 :
781 156 : IF (myprow == 1) work(mypcol) = SUM(distribution_2d%n_local_cols)
782 :
783 80 : CALL group%sum(work)
784 :
785 80 : IF (output_unit > 0) THEN
786 : WRITE (UNIT=output_unit, &
787 : FMT="(/, T2, A, /, T15, A, /, (T16, I10, T41, I10, T71, I10))") &
788 40 : "DISTRIBUTION OF THE PARTICLES (COLUMNS)", &
789 40 : "Process col Number of particles Number of matrix columns", &
790 120 : (ipcol - 1, work(ipcol), -1, ipcol=1, npcol)
791 : WRITE (UNIT=output_unit, FMT="(T23, A3, T41, I10, T71, I10)") &
792 80 : "Sum", SUM(work), -1
793 40 : CALL m_flush(output_unit)
794 : END IF
795 :
796 80 : DEALLOCATE (work)
797 :
798 : CALL cp_print_key_finished_output(output_unit, logger, force_env_section, &
799 80 : "PRINT%DISTRIBUTION")
800 : END IF
801 : END ASSOCIATE
802 :
803 7610 : IF (BTEST(cp_print_key_should_output(logger%iter_info, &
804 : force_env_section, "PRINT%DISTRIBUTION2D"), cp_p_file)) THEN
805 :
806 70 : iw = cp_logger_get_default_unit_nr(logger, LOCAL=.TRUE.)
807 : CALL distribution_2d_write(distribution_2d, &
808 : unit_nr=iw, &
809 : local=.TRUE., &
810 70 : long_description=.TRUE.)
811 :
812 : END IF
813 :
814 : ! *** Release work storage ***
815 :
816 7610 : DEALLOCATE (nparticle_local_row)
817 :
818 7610 : DEALLOCATE (nparticle_local_col)
819 :
820 7610 : CALL timestop(handle)
821 :
822 22830 : END SUBROUTINE distribute_molecules_2d
823 :
824 : ! **************************************************************************************************
825 : !> \brief Creates a basic distribution
826 : !> \param cluster_list ...
827 : !> \param cluster_prices ...
828 : !> \param nprows ...
829 : !> \param row_distribution ...
830 : !> \param npcols ...
831 : !> \param col_distribution ...
832 : !> \par History
833 : !> - Created 2010-08-06 UB
834 : ! **************************************************************************************************
835 7440 : SUBROUTINE make_basic_distribution(cluster_list, cluster_prices, &
836 7440 : nprows, row_distribution, npcols, col_distribution)
837 : INTEGER, DIMENSION(:), INTENT(INOUT) :: cluster_list, cluster_prices
838 : INTEGER, INTENT(IN) :: nprows
839 : INTEGER, DIMENSION(:), INTENT(OUT) :: row_distribution
840 : INTEGER, INTENT(IN) :: npcols
841 : INTEGER, DIMENSION(:), INTENT(OUT) :: col_distribution
842 :
843 : CHARACTER(len=*), PARAMETER :: routineN = 'make_basic_distribution'
844 :
845 : INTEGER :: bin, cluster, cluster_index, &
846 : cluster_price, nbins, nclusters, pcol, &
847 : pgrid_gcd, prow, timing_handle
848 : INTEGER(int_8) :: bin_price
849 : LOGICAL :: found
850 : TYPE(cp_heap_type) :: bin_heap
851 :
852 : ! ---------------------------------------------------------------------------
853 :
854 7440 : CALL timeset(routineN, timing_handle)
855 7440 : nbins = lcm(nprows, npcols)
856 7440 : pgrid_gcd = gcd(nprows, npcols)
857 7440 : CALL sort(cluster_prices, SIZE(cluster_list), cluster_list)
858 7440 : CALL cp_heap_new(bin_heap, nbins)
859 35792 : CALL cp_heap_fill(bin_heap, (/(0_int_8, bin=1, nbins)/))
860 : !
861 7440 : nclusters = SIZE(cluster_list)
862 : ! Put the most expensive cluster in the bin with the smallest
863 : ! price and repeat.
864 50955 : DO cluster_index = nclusters, 1, -1
865 43515 : cluster = cluster_list(cluster_index)
866 43515 : CALL cp_heap_get_first(bin_heap, bin, bin_price, found)
867 43515 : IF (.NOT. found) &
868 0 : CPABORT("No topmost heap element found.")
869 : !
870 43515 : prow = INT((bin - 1)*pgrid_gcd/npcols)
871 43515 : IF (prow .GE. nprows) &
872 0 : CPABORT("Invalid process row.")
873 43515 : pcol = INT((bin - 1)*pgrid_gcd/nprows)
874 43515 : IF (pcol .GE. npcols) &
875 0 : CPABORT("Invalid process column.")
876 43515 : row_distribution(cluster) = prow + 1
877 43515 : col_distribution(cluster) = pcol + 1
878 : !
879 43515 : cluster_price = cluster_prices(cluster_index)
880 43515 : bin_price = bin_price + cluster_price
881 94470 : CALL cp_heap_reset_first(bin_heap, bin_price)
882 : END DO
883 7440 : CALL cp_heap_release(bin_heap)
884 7440 : CALL timestop(timing_handle)
885 7440 : END SUBROUTINE make_basic_distribution
886 :
887 : ! **************************************************************************************************
888 : !> \brief Creates a basic spatial distribution
889 : !> that tries to make the corresponding blocks as homogeneous as possible
890 : !> \param pbc_scaled_coords ...
891 : !> \param costs ...
892 : !> \param nprows ...
893 : !> \param row_distribution ...
894 : !> \param npcols ...
895 : !> \param col_distribution ...
896 : !> \par History
897 : !> - Created 2010-11-11 Joost VandeVondele
898 : ! **************************************************************************************************
899 166 : SUBROUTINE make_basic_spatial_distribution(pbc_scaled_coords, costs, &
900 166 : nprows, row_distribution, npcols, col_distribution)
901 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: pbc_scaled_coords
902 : INTEGER, DIMENSION(:), INTENT(IN) :: costs
903 : INTEGER, INTENT(IN) :: nprows
904 : INTEGER, DIMENSION(:), INTENT(OUT) :: row_distribution
905 : INTEGER, INTENT(IN) :: npcols
906 : INTEGER, DIMENSION(:), INTENT(OUT) :: col_distribution
907 :
908 : CHARACTER(len=*), PARAMETER :: routineN = 'make_basic_spatial_distribution'
909 :
910 : INTEGER :: handle, iatom, natoms, nbins, pgrid_gcd
911 : INTEGER, ALLOCATABLE, DIMENSION(:) :: bin_costs, distribution
912 :
913 166 : CALL timeset(routineN, handle)
914 :
915 166 : natoms = SIZE(costs)
916 166 : nbins = lcm(nprows, npcols)
917 166 : pgrid_gcd = gcd(nprows, npcols)
918 830 : ALLOCATE (bin_costs(nbins), distribution(natoms))
919 498 : bin_costs = 0
920 :
921 5226 : CALL spatial_recurse(pbc_scaled_coords, costs, (/(iatom, iatom=1, natoms)/), bin_costs, distribution, 0)
922 :
923 : ! WRITE(*, *) "Final bin costs: ", bin_costs
924 :
925 : ! final row_distribution / col_distribution
926 2696 : DO iatom = 1, natoms
927 2530 : row_distribution(iatom) = (distribution(iatom) - 1)*pgrid_gcd/npcols + 1
928 2696 : col_distribution(iatom) = (distribution(iatom) - 1)*pgrid_gcd/nprows + 1
929 : END DO
930 :
931 166 : DEALLOCATE (bin_costs, distribution)
932 :
933 166 : CALL timestop(handle)
934 :
935 166 : END SUBROUTINE make_basic_spatial_distribution
936 :
937 : ! **************************************************************************************************
938 : !> \brief ...
939 : !> \param pbc_scaled_coords ...
940 : !> \param costs ...
941 : !> \param indices ...
942 : !> \param bin_costs ...
943 : !> \param distribution ...
944 : !> \param level ...
945 : ! **************************************************************************************************
946 3206 : RECURSIVE SUBROUTINE spatial_recurse(pbc_scaled_coords, costs, indices, bin_costs, distribution, level)
947 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: pbc_scaled_coords
948 : INTEGER, DIMENSION(:), INTENT(IN) :: costs, indices
949 : INTEGER, DIMENSION(:), INTENT(INOUT) :: bin_costs, distribution
950 : INTEGER, INTENT(IN) :: level
951 :
952 : INTEGER :: iatom, ibin, natoms, nbins, nhalf
953 3206 : INTEGER, ALLOCATABLE, DIMENSION(:) :: atom_costs_sorted, atom_permutation, &
954 3206 : bin_costs_sorted, permutation
955 3206 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:) :: coord
956 :
957 3206 : natoms = SIZE(costs)
958 3206 : nbins = SIZE(bin_costs)
959 3206 : nhalf = (natoms + 1)/2
960 :
961 3206 : IF (natoms <= nbins) THEN
962 : ! assign the most expensive atom to the least costly bin
963 6744 : ALLOCATE (bin_costs_sorted(nbins), permutation(nbins))
964 5058 : bin_costs_sorted(:) = bin_costs
965 1686 : CALL sort(bin_costs_sorted, nbins, permutation)
966 6744 : ALLOCATE (atom_costs_sorted(natoms), atom_permutation(natoms))
967 4216 : atom_costs_sorted(:) = costs
968 1686 : CALL sort(atom_costs_sorted, natoms, atom_permutation)
969 1686 : ibin = 0
970 : ! WRITE(*, *) "Dealing with a new bunch of atoms "
971 4216 : DO iatom = natoms, 1, -1
972 2530 : ibin = ibin + 1
973 : ! WRITE(*, *) "atom", indices(atom_permutation(iatom)), "cost", atom_costs_sorted(iatom), &
974 : ! "bin", permutation(ibin), "its cost", bin_costs(permutation(ibin))
975 : ! WRITE(100, '(A, I0, 3F12.6)') "A", permutation(ibin), pbc_scaled_coords(:, atom_permutation(iatom))
976 2530 : bin_costs(permutation(ibin)) = bin_costs(permutation(ibin)) + atom_costs_sorted(iatom)
977 4216 : distribution(indices(atom_permutation(iatom))) = permutation(ibin)
978 : END DO
979 1686 : DEALLOCATE (bin_costs_sorted, permutation, atom_costs_sorted, atom_permutation)
980 : ELSE
981 : ! divide atoms in two subsets, sorting according to their coordinates, alternatively x, y, z
982 : ! recursively do this for both subsets
983 7600 : ALLOCATE (coord(natoms), permutation(natoms))
984 12354 : coord(:) = pbc_scaled_coords(MOD(level, 3) + 1, :)
985 1520 : CALL sort(coord, natoms, permutation)
986 : CALL spatial_recurse(pbc_scaled_coords(:, permutation(1:nhalf)), costs(permutation(1:nhalf)), &
987 36512 : indices(permutation(1:nhalf)), bin_costs, distribution, level + 1)
988 : CALL spatial_recurse(pbc_scaled_coords(:, permutation(nhalf + 1:)), costs(permutation(nhalf + 1:)), &
989 31532 : indices(permutation(nhalf + 1:)), bin_costs, distribution, level + 1)
990 1520 : DEALLOCATE (coord, permutation)
991 : END IF
992 :
993 3206 : END SUBROUTINE spatial_recurse
994 :
995 : ! **************************************************************************************************
996 : !> \brief creates a distribution placing close by atoms into clusters and
997 : !> putting them on the same processors. Load balancing is
998 : !> performed by balancing sum of the cluster costs per processor
999 : !> \param coords coordinates of the system
1000 : !> \param scaled_coords scaled coordinates
1001 : !> \param cell the cell_type
1002 : !> \param costs costs per atomic block
1003 : !> \param nprows number of precessors per row on the 2d grid
1004 : !> \param row_distribution the resulting distribution over proc_rows of atomic blocks
1005 : !> \param npcols number of precessors per col on the 2d grid
1006 : !> \param col_distribution the resulting distribution over proc_cols of atomic blocks
1007 : ! **************************************************************************************************
1008 4 : SUBROUTINE make_cluster_distribution(coords, scaled_coords, cell, costs, &
1009 4 : nprows, row_distribution, npcols, col_distribution)
1010 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: coords, scaled_coords
1011 : TYPE(cell_type), POINTER :: cell
1012 : INTEGER, DIMENSION(:), INTENT(IN) :: costs
1013 : INTEGER, INTENT(IN) :: nprows
1014 : INTEGER, DIMENSION(:, :), INTENT(OUT) :: row_distribution
1015 : INTEGER, INTENT(IN) :: npcols
1016 : INTEGER, DIMENSION(:, :), INTENT(OUT) :: col_distribution
1017 :
1018 : CHARACTER(len=*), PARAMETER :: routineN = 'make_cluster_distribution'
1019 :
1020 : INTEGER :: handle, i, icluster, level, natom, &
1021 : output_unit
1022 : INTEGER(KIND=int_8) :: ncluster
1023 : INTEGER, ALLOCATABLE, DIMENSION(:) :: atom_to_cluster, cluster_cost, &
1024 4 : cluster_count, cluster_to_col, &
1025 : cluster_to_row, piv_cost, proc_cost, &
1026 4 : sorted_cost
1027 : REAL(KIND=dp) :: fold(3)
1028 4 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: cluster_center, cluster_high, cluster_low
1029 :
1030 4 : CALL timeset(routineN, handle)
1031 :
1032 4 : output_unit = cp_logger_get_default_io_unit()
1033 :
1034 4 : natom = SIZE(costs)
1035 118 : ncluster = dbcsr_distribution_get_num_images(SUM(costs), natom, nprows, npcols)
1036 12 : ALLOCATE (atom_to_cluster(natom))
1037 12 : ALLOCATE (cluster_cost(ncluster))
1038 8 : ALLOCATE (cluster_to_row(ncluster))
1039 8 : ALLOCATE (cluster_to_col(ncluster))
1040 8 : ALLOCATE (sorted_cost(ncluster))
1041 8 : ALLOCATE (piv_cost(ncluster))
1042 16 : cluster_cost(:) = 0
1043 :
1044 4 : icluster = 0
1045 4 : CALL cluster_recurse(coords, scaled_coords, cell, costs, atom_to_cluster, ncluster, icluster, cluster_cost)
1046 :
1047 16 : sorted_cost(:) = cluster_cost(:)
1048 4 : CALL sort(sorted_cost, INT(ncluster), piv_cost)
1049 :
1050 12 : ALLOCATE (proc_cost(nprows))
1051 12 : proc_cost = 0; level = 1
1052 4 : CALL assign_clusters(cluster_cost, piv_cost, proc_cost, cluster_to_row, nprows)
1053 :
1054 12 : DEALLOCATE (proc_cost); ALLOCATE (proc_cost(npcols))
1055 8 : proc_cost = 0; level = 1
1056 4 : CALL assign_clusters(cluster_cost, piv_cost, proc_cost, cluster_to_col, npcols)
1057 :
1058 118 : DO i = 1, natom
1059 114 : row_distribution(i, 1) = cluster_to_row(atom_to_cluster(i))
1060 114 : row_distribution(i, 2) = atom_to_cluster(i)
1061 114 : col_distribution(i, 1) = cluster_to_col(atom_to_cluster(i))
1062 118 : col_distribution(i, 2) = atom_to_cluster(i)
1063 : END DO
1064 :
1065 : ! generate some statistics on clusters
1066 12 : ALLOCATE (cluster_center(3, ncluster))
1067 8 : ALLOCATE (cluster_low(3, ncluster))
1068 8 : ALLOCATE (cluster_high(3, ncluster))
1069 8 : ALLOCATE (cluster_count(ncluster))
1070 16 : cluster_count = 0
1071 118 : DO i = 1, natom
1072 114 : cluster_count(atom_to_cluster(i)) = cluster_count(atom_to_cluster(i)) + 1
1073 460 : cluster_center(:, atom_to_cluster(i)) = coords(:, i)
1074 : END DO
1075 52 : cluster_low = HUGE(0.0_dp)/2
1076 52 : cluster_high = -HUGE(0.0_dp)/2
1077 118 : DO i = 1, natom
1078 798 : fold = pbc(coords(:, i) - cluster_center(:, atom_to_cluster(i)), cell) + cluster_center(:, atom_to_cluster(i))
1079 456 : cluster_low(:, atom_to_cluster(i)) = MIN(cluster_low(:, atom_to_cluster(i)), fold(:))
1080 460 : cluster_high(:, atom_to_cluster(i)) = MAX(cluster_high(:, atom_to_cluster(i)), fold(:))
1081 : END DO
1082 4 : IF (output_unit > 0) THEN
1083 2 : WRITE (output_unit, *)
1084 2 : WRITE (output_unit, '(T2,A)') "Cluster distribution information"
1085 2 : WRITE (output_unit, '(T2,A,T48,I8)') "Number of atoms", natom
1086 2 : WRITE (output_unit, '(T2,A,T48,I8)') "Number of clusters", ncluster
1087 8 : WRITE (output_unit, '(T2,A,T48,I8)') "Largest cluster in atoms", MAXVAL(cluster_count)
1088 8 : WRITE (output_unit, '(T2,A,T48,I8)') "Smallest cluster in atoms", MINVAL(cluster_count)
1089 2 : WRITE (output_unit, '(T2,A,T48,F8.3,I8)') "Largest cartesian extend [a.u.]/cluster x=", &
1090 10 : MAXVAL(cluster_high(1, :) - cluster_low(1, :), MASK=(cluster_count > 0)), &
1091 14 : MAXLOC(cluster_high(1, :) - cluster_low(1, :), MASK=(cluster_count > 0))
1092 2 : WRITE (output_unit, '(T2,A,T48,F8.3,I8)') "Largest cartesian extend [a.u.]/cluster y=", &
1093 10 : MAXVAL(cluster_high(2, :) - cluster_low(2, :), MASK=(cluster_count > 0)), &
1094 14 : MAXLOC(cluster_high(2, :) - cluster_low(2, :), MASK=(cluster_count > 0))
1095 2 : WRITE (output_unit, '(T2,A,T48,F8.3,I8)') "Largest cartesian extend [a.u.]/cluster z=", &
1096 10 : MAXVAL(cluster_high(3, :) - cluster_low(3, :), MASK=(cluster_count > 0)), &
1097 14 : MAXLOC(cluster_high(3, :) - cluster_low(3, :), MASK=(cluster_count > 0))
1098 : END IF
1099 :
1100 4 : DEALLOCATE (atom_to_cluster, cluster_cost, cluster_to_row, cluster_to_col, sorted_cost, piv_cost, proc_cost)
1101 4 : CALL timestop(handle)
1102 :
1103 8 : END SUBROUTINE make_cluster_distribution
1104 :
1105 : ! **************************************************************************************************
1106 : !> \brief assigns the clusters to processors, tryimg to balance the cost on the nodes
1107 : !> \param cluster_cost vector with the cost of each cluster
1108 : !> \param piv_cost pivoting vector sorting the cluster_cost
1109 : !> \param proc_cost cost per processor, on input 0 everywhere
1110 : !> \param cluster_assign assgnment of clusters on proc
1111 : !> \param nproc number of processor over which clusters are distributed
1112 : ! **************************************************************************************************
1113 8 : SUBROUTINE assign_clusters(cluster_cost, piv_cost, proc_cost, cluster_assign, nproc)
1114 : INTEGER, ALLOCATABLE, DIMENSION(:) :: cluster_cost, piv_cost, proc_cost, &
1115 : cluster_assign
1116 : INTEGER :: nproc
1117 :
1118 : CHARACTER(len=*), PARAMETER :: routineN = 'assign_clusters'
1119 :
1120 : INTEGER :: handle, i, ilevel, offset, &
1121 16 : piv_pcost(nproc), sort_proc_cost(nproc)
1122 :
1123 8 : CALL timeset(routineN, handle)
1124 :
1125 26 : DO ilevel = 1, SIZE(cluster_cost)/nproc
1126 42 : sort_proc_cost(:) = proc_cost(:)
1127 18 : CALL sort(sort_proc_cost, nproc, piv_pcost)
1128 :
1129 18 : offset = (SIZE(cluster_cost)/nproc - ilevel + 1)*nproc + 1
1130 50 : DO i = 1, nproc
1131 24 : cluster_assign(piv_cost(offset - i)) = piv_pcost(i)
1132 42 : proc_cost(piv_pcost(i)) = proc_cost(piv_pcost(i)) + cluster_cost(piv_cost(offset - i))
1133 : END DO
1134 : END DO
1135 :
1136 8 : CALL timestop(handle)
1137 :
1138 8 : END SUBROUTINE assign_clusters
1139 :
1140 : ! **************************************************************************************************
1141 : !> \brief recursive routine to cluster atoms.
1142 : !> Low level uses a modified KMEANS algorithm
1143 : !> recursion is used to reduce cost.
1144 : !> each level will subdivide a cluster into smaller clusters
1145 : !> If only a single split is necessary atoms are assigned to the current cluster
1146 : !> \param coord coordinates of the system
1147 : !> \param scaled_coord scaled coordinates
1148 : !> \param cell the cell_type
1149 : !> \param costs costs per atomic block
1150 : !> \param cluster_inds the atom_to cluster mapping
1151 : !> \param ncluster number of clusters still to be created on a given recursion level
1152 : !> \param icluster the index of the current cluster to be created
1153 : !> \param fin_cluster_cost total cost of the final clusters
1154 : ! **************************************************************************************************
1155 16 : RECURSIVE SUBROUTINE cluster_recurse(coord, scaled_coord, cell, costs, cluster_inds, ncluster, icluster, fin_cluster_cost)
1156 : REAL(KIND=dp), DIMENSION(:, :), INTENT(IN) :: coord, scaled_coord
1157 : TYPE(cell_type), POINTER :: cell
1158 : INTEGER, DIMENSION(:), INTENT(IN) :: costs
1159 : INTEGER, DIMENSION(:), INTENT(INOUT) :: cluster_inds
1160 : INTEGER(KIND=int_8), INTENT(INOUT) :: ncluster
1161 : INTEGER, INTENT(INOUT) :: icluster
1162 : INTEGER, DIMENSION(:), INTENT(INOUT) :: fin_cluster_cost
1163 :
1164 : INTEGER :: i, ibeg, iend, maxv(1), min_seed, &
1165 : natoms, nleft, nsplits, seed, tot_cost
1166 16 : INTEGER(KIND=int_8), ALLOCATABLE, DIMENSION(:) :: ncluster_new
1167 16 : INTEGER, ALLOCATABLE, DIMENSION(:) :: cluster_cost, inds_tmp, nat_cluster, piv
1168 : LOGICAL :: found
1169 : REAL(KIND=dp) :: balance, balance_new, conv
1170 :
1171 16 : natoms = SIZE(coord, 2)
1172 : ! This is a bit of an arbitrary choice, simply a try to avoid too many clusters on large systems and too few for balancing on
1173 : ! small systems or subclusters
1174 16 : IF (natoms .LE. 1) THEN
1175 2 : nsplits = 1
1176 : ELSE
1177 14 : nsplits = MIN(INT(MIN(INT(MAX(6, INT(60.00/LOG(REAL(natoms, KIND=dp)))), KIND=int_8), ncluster)), natoms)
1178 : END IF
1179 16 : IF (nsplits == 1) THEN
1180 12 : icluster = icluster + 1
1181 126 : cluster_inds = icluster
1182 126 : fin_cluster_cost(icluster) = SUM(costs)
1183 : ELSE
1184 36 : ALLOCATE (cluster_cost(nsplits), ncluster_new(nsplits), inds_tmp(natoms), piv(natoms), nat_cluster(nsplits))
1185 : ! initialise some values
1186 16 : cluster_cost = 0; seed = 300; found = .TRUE.; min_seed = seed
1187 4 : CALL kmeans(nsplits, coord, scaled_coord, cell, cluster_inds, nat_cluster, seed, conv)
1188 36 : balance = MAXVAL(REAL(nat_cluster, KIND=dp))/MINVAL(REAL(nat_cluster, KIND=dp))
1189 :
1190 : ! If the system is small enough try to do better in terms of balancing number of atoms per cluster
1191 : ! by changing the seed for the initial guess
1192 4 : IF (natoms .LT. 1000 .AND. balance .GT. 1.1) THEN
1193 24 : found = .FALSE.
1194 24 : DO i = 1, 5
1195 24 : IF (balance .GT. 1.1) THEN
1196 20 : CALL kmeans(nsplits, coord, scaled_coord, cell, cluster_inds, nat_cluster, seed + i*40, conv)
1197 160 : balance_new = MAXVAL(REAL(nat_cluster, KIND=dp))/MINVAL(REAL(nat_cluster, KIND=dp))
1198 20 : IF (balance_new .LT. balance) THEN
1199 0 : balance = balance_new
1200 0 : min_seed = seed + i*40;
1201 : END IF
1202 : ELSE
1203 : found = .TRUE.
1204 : EXIT
1205 : END IF
1206 : END DO
1207 : END IF
1208 : !If we do not match the convergence than recompute at least the best assignment
1209 4 : IF (.NOT. found) CALL kmeans(nsplits, coord, scaled_coord, cell, cluster_inds, nat_cluster, min_seed, conv)
1210 :
1211 : ! compute the cost of each cluster to decide how many splits have to be performed on the next lower level
1212 118 : DO i = 1, natoms
1213 118 : cluster_cost(cluster_inds(i)) = cluster_cost(cluster_inds(i)) + costs(i)
1214 : END DO
1215 16 : tot_cost = SUM(cluster_cost)
1216 : ! compute new splitting, can be done more elegant
1217 16 : ncluster_new(:) = ncluster*cluster_cost(:)/tot_cost
1218 16 : nleft = INT(ncluster - SUM(ncluster_new))
1219 : ! As we won't have empty clusters, we can not have 0 as new size, so we correct for this at first
1220 16 : DO i = 1, nsplits
1221 16 : IF (ncluster_new(i) == 0) THEN
1222 6 : ncluster_new(i) = 1
1223 6 : nleft = nleft - 1
1224 : END IF
1225 : END DO
1226 : ! now comes the next part that the number of clusters will not match anymore, so try to correct in a meaningful way without
1227 : ! introducing 0 sized blocks again
1228 4 : IF (nleft .NE. 0) THEN
1229 0 : DO i = 1, ABS(nleft)
1230 0 : IF (nleft < 0) THEN
1231 0 : maxv = MINLOC(cluster_cost/ncluster_new)
1232 0 : IF (ncluster_new(maxv(1)) .NE. 1) THEN
1233 0 : ncluster_new(maxv) = ncluster_new(maxv) - 1
1234 : ELSE
1235 0 : maxv = MAXLOC(ncluster_new)
1236 0 : ncluster_new(maxv) = ncluster_new(maxv) - 1
1237 : END IF
1238 : ELSE
1239 0 : maxv = MAXLOC(cluster_cost/ncluster_new)
1240 0 : ncluster_new(maxv) = ncluster_new(maxv) + 1
1241 : END IF
1242 : END DO
1243 : END IF
1244 :
1245 : !Now get the permutations to sort the atoms in the nsplits clusters for the next level of iteration
1246 118 : inds_tmp(:) = cluster_inds(:)
1247 4 : CALL sort(inds_tmp, natoms, piv)
1248 :
1249 4 : ibeg = 1; iend = 0
1250 16 : DO i = 1, nsplits
1251 12 : IF (nat_cluster(i) == 0) CYCLE
1252 12 : iend = iend + nat_cluster(i)
1253 : CALL cluster_recurse(coord(:, piv(ibeg:iend)), scaled_coord(:, piv(ibeg:iend)), cell, costs(piv(ibeg:iend)), &
1254 1038 : inds_tmp(ibeg:iend), ncluster_new(i), icluster, fin_cluster_cost)
1255 16 : ibeg = ibeg + nat_cluster(i)
1256 : END DO
1257 : ! copy the sorted cluster IDs on the old layout, inds_tmp gets set at the lowest level of recursion
1258 118 : cluster_inds(piv(:)) = inds_tmp
1259 4 : DEALLOCATE (cluster_cost, ncluster_new, inds_tmp, piv, nat_cluster)
1260 :
1261 : END IF
1262 :
1263 16 : END SUBROUTINE cluster_recurse
1264 :
1265 : ! **************************************************************************************************
1266 : !> \brief A modified version of the kmeans algorithm.
1267 : !> The assignment has a penalty function in case clusters become
1268 : !> larger than average. Like this more even sized clusters are created
1269 : !> trading it for locality
1270 : !> \param ncent number of centers to be created
1271 : !> \param coord coordinates
1272 : !> \param scaled_coord scaled coord
1273 : !> \param cell the cell_type
1274 : !> \param cluster atom to cluster assignment
1275 : !> \param nat_cl atoms per cluster
1276 : !> \param seed seed for the RNG. Algorithm might need multiple tries to deliver best results
1277 : !> \param tot_var the total variance of the clusters around the centers
1278 : ! **************************************************************************************************
1279 28 : SUBROUTINE kmeans(ncent, coord, scaled_coord, cell, cluster, nat_cl, seed, tot_var)
1280 : INTEGER :: ncent
1281 : REAL(KIND=dp), DIMENSION(:, :) :: coord, scaled_coord
1282 : TYPE(cell_type), POINTER :: cell
1283 : INTEGER, DIMENSION(:) :: cluster, nat_cl
1284 : INTEGER :: seed
1285 : REAL(KIND=dp) :: tot_var
1286 :
1287 : CHARACTER(len=*), PARAMETER :: routineN = 'kmeans'
1288 :
1289 : INTEGER :: handle, i, ind, itn, j, nat, oldc
1290 : LOGICAL :: changed
1291 56 : REAL(KIND=dp) :: average(3, ncent, 2), cent_coord(3, ncent), devi, deviat(ncent), dist, &
1292 56 : dvec(3), old_var, rn, scaled_cent(3, ncent), var_cl(ncent)
1293 28 : REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: dmat
1294 : REAL(KIND=dp), DIMENSION(3, 2) :: initial_seed
1295 : TYPE(rng_stream_type) :: rng_stream
1296 :
1297 28 : CALL timeset(routineN, handle)
1298 :
1299 252 : initial_seed = REAL(seed, dp); nat = SIZE(coord, 2)
1300 112 : ALLOCATE (dmat(ncent, nat))
1301 :
1302 : rng_stream = rng_stream_type(name="kmeans uniform distribution [0,1]", &
1303 28 : distribution_type=UNIFORM, seed=initial_seed)
1304 :
1305 : ! try to find a clever initial guess with centers being somewhat distributed
1306 28 : rn = rng_stream%next()
1307 28 : ind = CEILING(rn*nat)
1308 112 : cent_coord(:, 1) = coord(:, ind)
1309 84 : DO i = 2, ncent
1310 28 : DO
1311 928 : rn = rng_stream%next()
1312 928 : ind = CEILING(rn*nat)
1313 3712 : cent_coord(:, i) = coord(:, ind)
1314 : devi = HUGE(1.0_dp)
1315 2004 : DO j = 1, i - 1
1316 1076 : dvec = pbc(cent_coord(:, j), cent_coord(:, i), cell)
1317 4304 : dist = SQRT(DOT_PRODUCT(dvec, dvec))
1318 2004 : IF (dist .LT. devi) devi = dist
1319 : END DO
1320 928 : rn = rng_stream%next()
1321 928 : IF (rn .LT. devi**2/169.0) EXIT
1322 : END DO
1323 : END DO
1324 :
1325 : ! Now start the KMEANS but penalise it in case it starts packing too many atoms into a single set
1326 : ! Unfoirtunatelz as this is dependent on what happened before it cant be parallel
1327 826 : cluster = 0; old_var = HUGE(1.0_dp)
1328 106 : DO itn = 1, 1000
1329 1210 : changed = .FALSE.; var_cl = 0.0_dp; tot_var = 0.0_dp; nat_cl = 0; deviat = 0.0_dp
1330 : ! !$OMP PARALLEL DO PRIVATE(i,j,dvec)
1331 4402 : DO i = 1, nat
1332 21418 : DO j = 1, ncent
1333 17016 : dvec = pbc(cent_coord(:, j), coord(:, i), cell)
1334 72360 : dmat(j, i) = DOT_PRODUCT(dvec, dvec)
1335 : END DO
1336 : END DO
1337 4402 : DO i = 1, nat
1338 4296 : devi = HUGE(1.0_dp); oldc = cluster(i)
1339 21312 : DO j = 1, ncent
1340 17016 : dist = dmat(j, i) + MAX(nat_cl(j)**2/nat*ncent, nat/ncent)
1341 21312 : IF (dist .LT. devi) THEN
1342 8760 : devi = dist; cluster(i) = j
1343 : END IF
1344 : END DO
1345 4296 : deviat(cluster(i)) = deviat(cluster(i)) + SQRT(devi)
1346 4296 : nat_cl(cluster(i)) = nat_cl(cluster(i)) + 1
1347 4296 : tot_var = tot_var + devi
1348 4402 : IF (oldc .NE. cluster(i)) changed = .TRUE.
1349 : END DO
1350 : ! get the update of the centers done, add a new one in case one center lost all its atoms
1351 : ! the algorithm would survive, but its nice to really create what you demand
1352 106 : IF (tot_var .GE. old_var) EXIT
1353 106 : IF (changed) THEN
1354 : ! Here misery of computing the center of geometry of the clusters in PBC.
1355 : ! The mapping on the unit circle allows to circumvent all problems
1356 2506 : average = 0.0_dp
1357 3576 : DO i = 1, SIZE(coord, 2)
1358 13992 : average(:, cluster(i), 1) = average(:, cluster(i), 1) + COS(scaled_coord(:, i)*2.0_dp*pi)
1359 14070 : average(:, cluster(i), 2) = average(:, cluster(i), 2) + SIN(scaled_coord(:, i)*2.0_dp*pi)
1360 : END DO
1361 :
1362 362 : DO i = 1, ncent
1363 362 : IF (nat_cl(i) == 0) THEN
1364 0 : rn = rng_stream%next()
1365 0 : scaled_cent(:, i) = scaled_coord(:, CEILING(rn*nat))
1366 : ELSE
1367 1136 : average(:, i, 1) = average(:, i, 1)/REAL(nat_cl(i), dp)
1368 1136 : average(:, i, 2) = average(:, i, 2)/REAL(nat_cl(i), dp)
1369 1136 : scaled_cent(:, i) = (ATAN2(-average(:, i, 2), -average(:, i, 1)) + pi)/(2.0_dp*pi)
1370 284 : CALL scaled_to_real(cent_coord(:, i), scaled_cent(:, i), cell)
1371 : END IF
1372 : END DO
1373 : ELSE
1374 : EXIT
1375 : END IF
1376 : END DO
1377 :
1378 28 : CALL timestop(handle)
1379 :
1380 728 : END SUBROUTINE kmeans
1381 :
1382 : END MODULE distribution_methods
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