Coverage for icet/tools/structure_generation.py: 99%
171 statements
« prev ^ index » next coverage.py v7.5.0, created at 2024-05-06 04:14 +0000
1import itertools
2from typing import List, Dict, Tuple, Union
3import numpy as np
4from mchammer.ensembles import TargetClusterVectorAnnealing
5from mchammer.calculators import (TargetVectorCalculator,
6 compare_cluster_vectors)
7from icet.tools import (enumerate_structures,
8 enumerate_supercells)
9from icet import ClusterSpace
10from icet.input_output.logging_tools import logger
11from ase import Atoms
12from ase.data import chemical_symbols as periodic_table
15def generate_target_structure_from_supercells(cluster_space: ClusterSpace,
16 supercells: List[Atoms],
17 target_concentrations: dict,
18 target_cluster_vector: List[float],
19 T_start: float = 5.0,
20 T_stop: float = 0.001,
21 n_steps: int = None,
22 optimality_weight: float = 1.0,
23 random_seed: int = None,
24 random_start: bool = True,
25 tol: float = 1e-5) -> Atoms:
26 """
27 Given a :attr:`cluster_space` and a :attr:`target_cluster_vector` and one
28 or more :attr:`supercells`, generate a structure that as closely as
29 possible matches that cluster vector.
31 Internally the function uses a simulated annealing algorithm and the
32 difference between two cluster vectors is calculated with the
33 measure suggested by A. van de Walle et al. in Calphad **42**, 13-18
34 (2013) [WalTiwJon13]_ (for more information, see
35 :class:`mchammer.calculators.TargetVectorCalculator`).
37 Parameters
38 ----------
39 cluster_space
40 A cluster space defining the lattice to be occupied.
41 supercells
42 List of one or more supercells among which an optimal
43 structure will be searched for.
44 target_concentrations
45 Concentration of each species in the target structure, per
46 sublattice (for example ``{'Au': 0.5, 'Pd': 0.5}`` for a
47 single sublattice Au-Pd structure, or
48 ``{'A': {'Au': 0.5, 'Pd': 0.5}, 'B': {'H': 0.25, 'X': 0.75}}``
49 for a system with two sublattices.
50 The symbols defining sublattices ('A', 'B' etc) can be
51 found by printing the :attr:`cluster_space`.
52 target_cluster_vector
53 Cluster vector that the generated structure should match as
54 closely as possible.
55 T_start
56 Artificial temperature at which the simulated annealing starts.
57 T_stop
58 Artifical temperature at which the simulated annealing stops.
59 n_steps
60 Total number of Monte Carlo steps in the simulation.
61 optimality_weight
62 Controls weighting :math:`L` of perfect correlations, see
63 :class:`mchammer.calculators.TargetVectorCalculator`.
64 random_seed
65 Seed for the random number generator used in the Monte Carlo simulation
66 and used for initializing the occupation of the supercells if
67 random_start is ``True``.
68 random_start
69 Randomly occupy starting structure, can be disabled
70 if the user prefers to pass an initial structure.
71 tol
72 Numerical tolerance.
73 """
74 target_concentrations = _validate_concentrations(target_concentrations, cluster_space)
76 calculators = []
78 # Loop over all supercells and intialize
79 # them with a "random" occupation of symbols that
80 # fulfill the target concentrations
81 valid_supercells = []
82 warning_issued = False
83 for supercell in supercells:
84 supercell_copy = supercell.copy()
85 if random_start: 85 ↛ 96line 85 didn't jump to line 96, because the condition on line 85 was never false
86 try:
87 occupy_structure_randomly(supercell_copy, cluster_space,
88 target_concentrations,
89 random_seed)
90 except ValueError:
91 if not warning_issued:
92 logger.warning('At least one supercell was not commensurate with the specified '
93 'target concentrations.')
94 warning_issued = True
95 continue
96 valid_supercells.append(supercell_copy)
97 calculators.append(TargetVectorCalculator(supercell_copy, cluster_space,
98 target_cluster_vector,
99 optimality_weight=optimality_weight,
100 optimality_tol=tol))
102 if len(valid_supercells) == 0:
103 raise ValueError('No supercells that may host the specified '
104 'target_concentrations were supplied.')
106 ens = TargetClusterVectorAnnealing(structure=valid_supercells, calculators=calculators,
107 T_start=T_start, T_stop=T_stop,
108 random_seed=random_seed)
109 return ens.generate_structure(number_of_trial_steps=n_steps)
112def generate_target_structure(cluster_space: ClusterSpace,
113 max_size: int,
114 target_concentrations: dict,
115 target_cluster_vector: List[float],
116 include_smaller_cells: bool = True,
117 pbc: Union[Tuple[bool, bool, bool], Tuple[int, int, int]] = None,
118 T_start: float = 5.0,
119 T_stop: float = 0.001,
120 n_steps: int = None,
121 optimality_weight: float = 1.0,
122 random_seed: int = None,
123 tol: float = 1e-5) -> Atoms:
124 """
125 Given a :attr:`cluster_space` and a :attr:`target_cluster_vector`, generate
126 a structure that as closely as possible matches that cluster vector.
127 The search is performed among all inequivalent supercells shapes up
128 to a certain size.
130 Internally the function uses a simulated annealing algorithm and the
131 difference between two cluster vectors is calculated with the
132 measure suggested by A. van de Walle et al. in Calphad **42**, 13-18
133 (2013) [WalTiwJon13]_ (for more information, see
134 :class:`mchammer.calculators.TargetVectorCalculator`).
136 Parameters
137 ----------
138 cluster_space
139 Cluster space defining the lattice to be occupied.
140 max_size
141 Maximum supercell size.
142 target_concentrations
143 Concentration of each species in the target structure, per
144 sublattice (for example ``{'Au': 0.5, 'Pd': 0.5}`` for a
145 single sublattice Au-Pd structure, or
146 ``{'A': {'Au': 0.5, 'Pd': 0.5}, 'B': {'H': 0.25, 'X': 0.75}}``
147 for a system with two sublattices.
148 The symbols defining sublattices ('A', 'B' etc) can be
149 found by printing the :attr:`cluster_space`.
150 target_cluster_vector
151 Cluster vector that the generated structure should match as
152 closely as possible.
153 include_smaller_cells
154 If ``True``, search among all supercell sizes including
155 :attr:`max_size`, else search only among those exactly matching
156 :attr:`max_size`
157 pbc
158 Periodic boundary conditions for each direction, e.g.,
159 ``(True, True, False)``. The axes are defined by
160 the cell of :attr:`cluster_space.primitive_structure``.
161 Default is periodic boundary in all directions.
162 T_start
163 Artificial temperature at which the simulated annealing starts.
164 T_stop
165 Artifical temperature at which the simulated annealing stops.
166 n_steps
167 Total number of Monte Carlo steps in the simulation.
168 optimality_weight
169 Controls weighting :math:`L` of perfect correlations, see
170 :class:`mchammer.calculators.TargetVectorCalculator`.
171 random_seed
172 Seed for the random number generator used in the Monte Carlo simulation.
173 tol
174 Numerical tolerance.
175 """
176 target_concentrations = _validate_concentrations(target_concentrations, cluster_space)
178 if pbc is None:
179 pbc = (True, True, True)
181 prim = cluster_space.primitive_structure
182 prim.set_pbc(pbc)
184 supercells = []
185 if include_smaller_cells:
186 sizes = list(range(1, max_size + 1))
187 else:
188 sizes = [max_size]
190 for size in sizes:
191 # For efficiency, make a first check that the current size is
192 # commensurate with all concentrations (example: {'Au': 0.5,
193 # 'Pd': 0.5} would not be commensurate with a supercell with 3
194 # atoms).
195 supercell = cluster_space.primitive_structure.repeat((size, 1, 1))
196 if not _concentrations_fit_structure(structure=supercell,
197 cluster_space=cluster_space,
198 concentrations=target_concentrations):
199 continue
201 # Loop over all inequivalent supercells and intialize
202 # them with a "random" occupation of symbols that
203 # fulfill the target concentrations
204 for supercell in enumerate_supercells(prim, [size]):
205 supercell.set_pbc(True)
206 supercells.append(supercell)
208 return generate_target_structure_from_supercells(cluster_space=cluster_space,
209 supercells=supercells,
210 target_concentrations=target_concentrations,
211 target_cluster_vector=target_cluster_vector,
212 T_start=T_start,
213 T_stop=T_stop,
214 n_steps=n_steps,
215 optimality_weight=optimality_weight,
216 random_seed=random_seed,
217 tol=tol)
220def generate_sqs_from_supercells(cluster_space: ClusterSpace,
221 supercells: List[Atoms],
222 target_concentrations: dict,
223 T_start: float = 5.0,
224 T_stop: float = 0.001,
225 n_steps: int = None,
226 optimality_weight: float = 1.0,
227 random_seed: int = None,
228 random_start: bool = True,
229 tol: float = 1e-5) -> Atoms:
230 """
231 Given a :attr:`cluster_space`` and one or more :attr:`supercells`, generate
232 a special quasirandom structure (SQS), i.e., a structure that for
233 the provided supercells size provides the best possible
234 approximation to a random alloy [ZunWeiFer90]_.
236 In the present case, this means that the generated structure will
237 have a cluster vector that as closely as possible matches the
238 cluster vector of an infintely large randomly occupied supercell.
239 Internally the function uses a simulated annealing algorithm and the
240 difference between two cluster vectors is calculated with the
241 measure suggested by A. van de Walle et al. in Calphad **42**, 13-18
242 (2013) [WalTiwJon13]_ (for more information, see
243 :class:`mchammer.calculators.TargetVectorCalculator`).
245 Parameters
246 ----------
247 cluster_space
248 Cluster space defining the lattice to be occupied.
249 supercells
250 List of one or more supercells among which an optimal
251 structure will be searched for.
252 target_concentrations
253 Concentration of each species in the target structure, per
254 sublattice (for example ``{'Au': 0.5, 'Pd': 0.5}`` for a
255 single sublattice Au-Pd structure, or
256 ``{'A': {'Au': 0.5, 'Pd': 0.5}, 'B': {'H': 0.25, 'X': 0.75}}``
257 for a system with two sublattices.
258 The symbols defining sublattices ('A', 'B' etc) can be
259 found by printing the :attr:`cluster_space`.
260 T_start
261 Artificial temperature at which the simulated annealing starts.
262 T_stop
263 Artifical temperature at which the simulated annealing stops.
264 n_steps
265 Total number of Monte Carlo steps in the simulation.
266 optimality_weight
267 Controls weighting :math:`L` of perfect correlations, see
268 :class:`mchammer.calculators.TargetVectorCalculator`.
269 random_seed
270 Seed for the random number generator used in the Monte Carlo simulation
271 and used for initializing the occupation of the supercells if
272 random_start is ``True``.
273 random_start
274 Randomly occupy starting structure, can be disabled
275 if the user prefers to pass an initial structure.
276 tol
277 Numerical tolerance.
278 """
280 sqs_vector = _get_sqs_cluster_vector(cluster_space=cluster_space,
281 target_concentrations=target_concentrations)
282 return generate_target_structure_from_supercells(cluster_space=cluster_space,
283 supercells=supercells,
284 target_concentrations=target_concentrations,
285 target_cluster_vector=sqs_vector,
286 T_start=T_start, T_stop=T_stop,
287 n_steps=n_steps,
288 optimality_weight=optimality_weight,
289 random_seed=random_seed,
290 random_start=random_start,
291 tol=tol)
294def generate_sqs(cluster_space: ClusterSpace,
295 max_size: int,
296 target_concentrations: dict,
297 include_smaller_cells: bool = True,
298 pbc: Union[Tuple[bool, bool, bool], Tuple[int, int, int]] = None,
299 T_start: float = 5.0,
300 T_stop: float = 0.001,
301 n_steps: int = None,
302 optimality_weight: float = 1.0,
303 random_seed: int = None,
304 tol: float = 1e-5) -> Atoms:
305 """
306 Given a :attr:`cluster_space`, generate a special quasirandom structure
307 (SQS), i.e., a structure that for a given supercell size provides
308 the best possible approximation to a random alloy [ZunWeiFer90]_.
310 In the present case, this means that the generated structure will
311 have a cluster vector that as closely as possible matches the
312 cluster vector of an infintely large randomly occupied supercell.
313 Internally the function uses a simulated annealing algorithm and the
314 difference between two cluster vectors is calculated with the
315 measure suggested by A. van de Walle et al. in Calphad **42**, 13-18
316 (2013) [WalTiwJon13]_ (for more information, see
317 :class:`mchammer.calculators.TargetVectorCalculator`).
319 Parameters
320 ----------
321 cluster_space
322 Cluster space defining the lattice to be occupied.
323 max_size
324 Maximum supercell size.
325 target_concentrations
326 Concentration of each species in the target structure, per
327 sublattice (for example ``{'Au': 0.5, 'Pd': 0.5}`` for a
328 single sublattice Au-Pd structure, or
329 ``{'A': {'Au': 0.5, 'Pd': 0.5}, 'B': {'H': 0.25, 'X': 0.75}}``
330 for a system with two sublattices.
331 The symbols defining sublattices ('A', 'B' etc) can be
332 found by printing the :attr:`cluster_space`.
333 include_smaller_cells
334 If ``True``, search among all supercell sizes including
335 :attr:`max_size`, else search only among those exactly matching
336 :attr:`max_size`
337 pbc
338 Periodic boundary conditions for each direction, e.g.,
339 ``(True, True, False)``. The axes are defined by
340 the cell of ``cluster_space.primitive_structure``.
341 Default is periodic boundary in all directions.
342 T_start
343 Artificial temperature at which the simulated annealing starts.
344 T_stop
345 Artifical temperature at which the simulated annealing stops.
346 n_steps
347 Total number of Monte Carlo steps in the simulation.
348 optimality_weight
349 Controls weighting :math:`L` of perfect correlations, see
350 :class:`mchammer.calculators.TargetVectorCalculator`.
351 random_seed
352 Seed for the random number generator used in the
353 Monte Carlo simulation.
354 tol
355 Numerical tolerance.
356 """
358 sqs_vector = _get_sqs_cluster_vector(cluster_space=cluster_space,
359 target_concentrations=target_concentrations)
360 return generate_target_structure(cluster_space=cluster_space,
361 max_size=max_size,
362 target_concentrations=target_concentrations,
363 target_cluster_vector=sqs_vector,
364 include_smaller_cells=include_smaller_cells,
365 pbc=pbc,
366 T_start=T_start, T_stop=T_stop,
367 n_steps=n_steps,
368 optimality_weight=optimality_weight,
369 random_seed=random_seed,
370 tol=tol)
373def generate_sqs_by_enumeration(cluster_space: ClusterSpace,
374 max_size: int,
375 target_concentrations: dict,
376 include_smaller_cells: bool = True,
377 pbc: Union[Tuple[bool, bool, bool], Tuple[int, int, int]] = None,
378 optimality_weight: float = 1.0,
379 tol: float = 1e-5) -> Atoms:
380 """
381 Given a :attr:`cluster_space`, generate a special quasirandom structure
382 (SQS), i.e., a structure that for a given supercell size provides
383 the best possible approximation to a random alloy [ZunWeiFer90]_.
385 In the present case, this means that the generated structure will
386 have a cluster vector that as closely as possible matches the
387 cluster vector of an infintely large randomly occupied supercell.
388 Internally the function uses a simulated annealing algorithm and the
389 difference between two cluster vectors is calculated with the
390 measure suggested by A. van de Walle et al. in Calphad **42**, 13-18
391 (2013) [WalTiwJon13]_ (for more information, see
392 :class:`mchammer.calculators.TargetVectorCalculator`).
394 This functions generates SQS cells by exhaustive enumeration, which
395 means that the generated SQS cell is guaranteed to be optimal with
396 regard to the specified measure and cell size.
398 Parameters
399 ----------
400 cluster_space
401 Cluster space defining the lattice to be occupied.
402 max_size
403 Maximum supercell size.
404 target_concentrations
405 Concentration of each species in the target structure, per
406 sublattice (for example ``{'Au': 0.5, 'Pd': 0.5}`` for a
407 single sublattice Au-Pd structure, or
408 ``{'A': {'Au': 0.5, 'Pd': 0.5}, 'B': {'H': 0.25, 'X': 0.75}}``
409 for a system with two sublattices.
410 The symbols defining sublattices ('A', 'B' etc) can be
411 found by printing the :attr:`cluster_space`.
412 include_smaller_cells
413 if ``True`` search among all supercell sizes including
414 :attr:`max_size`, else search only among those exactly matching
415 :attr:`max_size`.
416 pbc
417 Periodic boundary conditions for each direction, e.g.,
418 ``(True, True, False)``. The axes are defined by
419 the cell of ``cluster_space.primitive_structure``.
420 Default is periodic boundary in all directions.
421 optimality_weight
422 Controls weighting :math:`L` of perfect correlations, see
423 :class:`mchammer.calculators.TargetVectorCalculator`.
424 tol
425 Numerical tolerance.
426 """
427 target_concentrations = _validate_concentrations(target_concentrations, cluster_space)
428 sqs_vector = _get_sqs_cluster_vector(cluster_space=cluster_space,
429 target_concentrations=target_concentrations)
430 # Translate concentrations to the format required for concentration
431 # restricted enumeration
432 cr: Dict[str, tuple] = {}
433 sublattices = cluster_space.get_sublattices(cluster_space.primitive_structure)
434 for sl in sublattices:
435 mult_factor = len(sl.indices) / len(cluster_space.primitive_structure)
436 if sl.symbol in target_concentrations:
437 sl_conc = target_concentrations[sl.symbol]
438 else:
439 sl_conc = {sl.chemical_symbols[0]: 1.0}
440 for species, value in sl_conc.items():
441 c = value * mult_factor
442 if species in cr:
443 cr[species] = (cr[species][0] + c,
444 cr[species][1] + c)
445 else:
446 cr[species] = (c, c)
448 # Check to be sure...
449 c_sum = sum(c[0] for c in cr.values())
450 assert abs(c_sum - 1) < tol # Should never happen, but...
452 as_list = cluster_space.as_list
453 best_score = 1e9
455 if include_smaller_cells:
456 sizes = list(range(1, max_size + 1))
457 else:
458 sizes = [max_size]
460 # Prepare primitive structure with the right boundary conditions
461 prim = cluster_space.primitive_structure
462 if pbc is None:
463 pbc = (True, True, True)
464 prim.set_pbc(pbc)
466 # Enumerate and calculate score for each structuer
467 for structure in enumerate_structures(prim,
468 sizes,
469 cluster_space.chemical_symbols,
470 concentration_restrictions=cr):
471 cv = cluster_space.get_cluster_vector(structure)
472 score = compare_cluster_vectors(cv_1=cv, cv_2=sqs_vector,
473 as_list=as_list,
474 optimality_weight=optimality_weight,
475 tol=tol)
477 if score < best_score:
478 best_score = score
479 best_structure = structure
480 return best_structure
483def occupy_structure_randomly(structure: Atoms, cluster_space: ClusterSpace,
484 target_concentrations: dict,
485 random_seed: int = None) -> None:
486 """
487 Occupy a structure with quasirandom order but fulfilling
488 :attr:`target_concentrations`.
490 Parameters
491 ----------
492 structure
493 ASE Atoms object that will be occupied randomly.
494 cluster_space
495 Cluster space (needed as it carries information about sublattices).
496 target_concentrations
497 Concentration of each species in the target structure, per
498 sublattice (for example ``{'Au': 0.5, 'Pd': 0.5}`` for a
499 single sublattice Au-Pd structure, or
500 ``{'A': {'Au': 0.5, 'Pd': 0.5}, 'B': {'H': 0.25, 'X': 0.75}}``
501 for a system with two sublattices.
502 The symbols defining sublattices ('A', 'B' etc) can be
503 found by printing the :attr:`cluster_space`.
504 random_seed
505 Seed for the random number generator.
506 """
507 rng = np.random.default_rng(random_seed)
508 target_concentrations = _validate_concentrations(cluster_space=cluster_space,
509 concentrations=target_concentrations)
511 if not _concentrations_fit_structure(structure, cluster_space, target_concentrations):
512 raise ValueError('Structure with {} atoms cannot accomodate '
513 'target concentrations {}'.format(len(structure),
514 target_concentrations))
516 symbols_all = [''] * len(structure)
517 for sl in cluster_space.get_sublattices(structure):
518 symbols: List[str] = [] # chemical_symbols in one sublattice
519 chemical_symbols = sl.chemical_symbols
520 if len(chemical_symbols) == 1:
521 symbols += [chemical_symbols[0]] * len(sl.indices)
522 else:
523 sl_conc = target_concentrations[sl.symbol]
524 for chemical_symbol in sl.chemical_symbols:
525 n_symbol = int(round(len(sl.indices) * sl_conc[chemical_symbol]))
526 symbols += [chemical_symbol] * n_symbol
528 # Should not happen but you never know
529 assert len(symbols) == len(sl.indices)
531 # Shuffle to introduce randomness
532 rng.shuffle(symbols)
534 # Assign symbols to the right indices
535 for symbol, lattice_site in zip(symbols, sl.indices):
536 symbols_all[lattice_site] = symbol
538 assert symbols_all.count('') == 0
539 structure.set_chemical_symbols(symbols_all)
542def _validate_concentrations(concentrations: dict,
543 cluster_space: ClusterSpace,
544 tol: float = 1e-5) -> dict:
545 """
546 Validates concentration specification against a cluster space
547 (raises `ValueError` if they do not match).
549 Parameters
550 ----------
551 concentrations
552 Concentration specification.
553 cluster_space
554 Cluster space to check against.
555 tol
556 Numerical tolerance.
558 Returns
559 -------
560 An adapted version of concentrations, which is always a dictionary
561 even if there is only one sublattice.
562 """
563 sls = cluster_space.get_sublattices(cluster_space.primitive_structure)
565 if not isinstance(list(concentrations.values())[0], dict):
566 concentrations = {'A': concentrations}
568 # Ensure concentrations sum to 1 at each sublattice
569 for sl_conc in concentrations.values():
570 conc_sum = sum(list(sl_conc.values()))
571 if abs(conc_sum - 1.0) > tol:
572 raise ValueError('Concentrations must sum up '
573 'to 1 for each sublattice (not {})'.format(conc_sum))
575 # Symbols need to match on each sublattice
576 for sl in sls:
577 if sl.symbol not in concentrations:
578 if len(sl.chemical_symbols) > 1:
579 raise ValueError('A sublattice ({}: {}) is missing in '
580 'target_concentrations'.format(sl.symbol,
581 list(sl.chemical_symbols)))
582 else:
583 sl_conc = concentrations[sl.symbol]
584 if tuple(sorted(sl.chemical_symbols)) != tuple(sorted(list(sl_conc.keys()))):
585 raise ValueError('Chemical symbols on a sublattice ({}: {}) are '
586 'not the same as those in the specified '
587 'concentrations {}'.format(sl.symbol, list(sl.chemical_symbols),
588 list(sl_conc.keys())))
590 return concentrations
593def _concentrations_fit_structure(structure: Atoms,
594 cluster_space: ClusterSpace,
595 concentrations: Dict[str, Dict[str, float]],
596 tol: float = 1e-5) -> bool:
597 """
598 Check if specified concentrations are commensurate with a
599 certain supercell (including sublattices).
601 Parameters
602 ----------
603 structure
604 Atomic configuration to be checked.
605 cluster_space
606 Corresponding cluster space.
607 concentrations
608 Which concentrations, per sublattice, e.g., ``{'A': {'Ag': 0.3, 'Au': 0.7}}``.
609 tol
610 Numerical tolerance.
611 """
612 # Check that concentrations are OK in each sublattice
613 for sublattice in cluster_space.get_sublattices(structure):
614 if sublattice.symbol in concentrations:
615 sl_conc = concentrations[sublattice.symbol]
616 for conc in sl_conc.values():
617 n_symbol = conc * len(sublattice.indices)
618 if abs(int(round(n_symbol)) - n_symbol) > tol:
619 return False
620 return True
623def _get_sqs_cluster_vector(cluster_space: ClusterSpace,
624 target_concentrations: Dict[str, Dict[str, float]]) -> np.ndarray:
625 """
626 Get the SQS vector for a certain cluster space and certain
627 concentration. Here SQS vector refers to the cluster vector of an
628 infintely large supercell with random occupation.
630 Parameters
631 ----------
632 cluster_space
633 The kind of lattice to be occupied.
634 target_concentrations
635 Concentration of each species in the target structure,
636 per sublattice (for example `{'A': {'Ag': 0.5, 'Pd': 0.5}}`).
637 """
638 target_concentrations = _validate_concentrations(concentrations=target_concentrations,
639 cluster_space=cluster_space)
641 sublattice_to_index = {letter: index for index,
642 letter in enumerate('ABCDEFGHIJKLMNOPQRSTUVWXYZ')}
643 all_sublattices = cluster_space.get_sublattices(
644 cluster_space.primitive_structure)
646 # Make a map from chemical symbol to integer, later on used
647 # for evaluating cluster functions.
648 # Internally, icet sorts species according to atomic numbers.
649 # Also check that each symbol only occurs in one sublattice.
650 symbol_to_integer_map = {}
651 found_species: List[str] = []
652 for sublattice in all_sublattices:
653 if len(sublattice.chemical_symbols) < 2:
654 continue
655 atomic_numbers = [periodic_table.index(sym) for sym in sublattice.chemical_symbols]
656 for i, species in enumerate(sorted(atomic_numbers)):
657 found_species.append(species)
658 symbol_to_integer_map[periodic_table[species]] = i
660 # Target concentrations refer to all atoms, but probabilities only
661 # to the sublattice.
662 probabilities = {}
663 for sl_conc in target_concentrations.values():
664 if len(sl_conc) == 1:
665 continue
666 for symbol in sl_conc.keys():
667 probabilities[symbol] = sl_conc[symbol]
669 # For every orbit, calculate average cluster function
670 cv = [1.0]
671 for orbit in cluster_space.as_list:
672 if orbit['order'] < 1:
673 continue
675 # What sublattices are there in this orbit?
676 sublattices = [all_sublattices[sublattice_to_index[letter]]
677 for letter in orbit['sublattices']]
679 # What chemical symbols do these sublattices refer to?
680 symbol_groups = [sublattice.chemical_symbols for sublattice in sublattices]
682 # How many allowed species in each of those sublattices?
683 nbr_of_allowed_species = [len(symbol_group)
684 for symbol_group in symbol_groups]
686 # Calculate contribution from every possible combination of
687 # symbols weighted with their probability
688 cluster_product_average = 0
689 for symbols in itertools.product(*symbol_groups):
690 cluster_product = 1
691 for i, symbol in enumerate(symbols):
692 mc_vector_component = orbit['multicomponent_vector'][i]
693 species_i = symbol_to_integer_map[symbol]
694 prod = cluster_space.evaluate_cluster_function(nbr_of_allowed_species[i],
695 mc_vector_component,
696 species_i)
697 cluster_product *= probabilities[symbol] * prod
698 cluster_product_average += cluster_product
699 cv.append(cluster_product_average)
700 return np.array(cv)