Source code for hiphive.core.clusters

# Contains the get_clusters function which generates clusters

import numpy as np
import itertools
from collections import defaultdict

from .utilities import BiMap
from ..io.logging import logger

logger = logger.getChild('get_clusters')


# TODO: This function could be made a bit more general
[docs]def get_clusters(atoms, cutoffs, nPrim, multiplicity=True, use_geometrical_order=False): """Generate a list of all clusters in the atoms object which includes the center atoms with positions within the cell metric. The cutoff determines up to which order and range clusters should be generated. With multiplicity set to True clusters like `[0,0]` and `[3,3,4` etc will be generated. This is useful when doing force constants but not so much for cluster expansions. The geometrical order is the total number of different atoms in the cluster. `[0,0,1]` would have geometrical order 2 and `[1,2,3,4]` would have order 4. If the key word is True the cutoff criteria will be based on the geometrical order of the cluster. This is based on the observation that many body interactions decrease fast with cutoff but anharmonic interactions can be quite long ranged. Parameters ---------- atoms : ase.Atoms can be a general atoms object but must have pbc=False. cutoffs : dict the keys specify the order while the values specify the cutoff radii multiplicity : bool includes clusters where same atom appears more than once geometrical_order : bool specifies if the geometrical order should be used as cutoff_order, otherwise the normal order of the cluster is used Returns ------- list(tuple(int)) a list of clusters where each entry is a tuple of indices, which refer to the atoms in the input supercell """ logger.debug('Generating clusters...') cluster_dict = defaultdict(list) # Generate all on-site clusters of all orders (1-body) for i in range(nPrim): for order in cutoffs.orders: cluster = (i,) * order cluster_dict[order].append(cluster) # Generate all 2-body clusters and above in order for nbody in cutoffs.nbodies: cutoff = cutoffs.max_nbody_cutoff(nbody) # Generate all n-body, order n clusters compatible with the cutoff nbody_clusters, nbody_cutoffs = generate_geometrical_clusters(atoms, nPrim, cutoff, nbody) for order in range(nbody, cutoffs.max_nbody_order(nbody) + 1): for cluster, cutoff in zip(nbody_clusters, nbody_cutoffs): # If the cutoff of the n-body cluster is compatible with order (order > n) then # extend the n-body cluster to higher order (e.g. nbody=3, order=6: ijk -> iijkkk) if cutoff < cutoffs.get_cutoff(nbody=nbody, order=order): cluster_dict[order].extend(extend_cluster(cluster, order)) # The clusters are saved in a BiMap structure which allows for fast lookups cluster_list = BiMap() for key in sorted(cluster_dict): # For each order the clusters are saved in lexicographical order for cluster in sorted(cluster_dict[key]): cluster_list.append(cluster) return cluster_list
[docs]def generate_geometrical_clusters(atoms, n_prim, cutoff, order): neighbor_matrix, distance_matrix = create_neighbor_matrices(atoms, cutoff) clusters, cutoffs = [], [] i, j = 0, 0 # The clusters are generated in lexicographical order for cluster in itertools.combinations(range(len(atoms)), r=order): # If the first atom in the cluster has an index higher or equal to the number of atoms in # the primitive cell then no upcoming cluster will have an atom in the primitive cell, thus # we can break if cluster[0] >= n_prim: break # if the last cluster failed on index i, j we start by checking this index again to speed # things up if not neighbor_matrix[cluster[i], cluster[j]]: continue # loop through all pairs in the cluster and check so that they are neighbors for i, j in itertools.combinations(range(order), r=2): if not neighbor_matrix[cluster[i], cluster[j]]: break else: clusters.append(cluster) # We also note the cutoff each cluster is compatible with cutoffs.append(np.max(distance_matrix[cluster, :][:, cluster])) return clusters, cutoffs
[docs]def create_neighbor_matrices(atoms, cutoff): distance_matrix = atoms.get_all_distances(mic=False) # or True? neighbor_matrix = distance_matrix < cutoff return neighbor_matrix, distance_matrix
[docs]def extend_cluster(cluster, order): clusters = [] cluster = tuple(cluster) nbody = len(cluster) r = order - nbody for tup in itertools.combinations_with_replacement(cluster, r): new_cluster = sorted(cluster + tup) clusters.append(tuple(new_cluster)) return clusters