# 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