# Source code for hiphive.core.get_clusters

```
# Contains the get_clusters function which generates clusters
from ase.neighborlist import NeighborList
import numpy as np
import itertools as it
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 object
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 of tuples
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)
for i in range(nPrim):
for order in cutoffs.orders:
cluster = (i,) * order
cluster_dict[order].append(cluster)
for nbody in range(2, cutoffs.max_nbody + 1):
cutoff = cutoffs.max_nbody_cutoff(nbody)
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 cutoff < cutoffs.get_cutoff(nbody=nbody, order=order):
clusters = extend_cluster(cluster, order)
cluster_dict[order].extend(clusters)
cluster_list = BiMap()
for key in sorted(cluster_dict):
for cluster in sorted(cluster_dict[key]):
cluster_list.append(cluster)
return cluster_list
[docs]def generate_geometrical_clusters(atoms, nPrim, cutoff, order):
nm, dm = create_neighbor_matrices(atoms, cutoff)
clusters = []
cutoffs = []
i, j = 0, 0
for tup in it.combinations(range(len(atoms)), r=order):
if tup[0] >= nPrim:
break
if not nm[tup[i], tup[j]]:
continue
for i, j in it.combinations(range(order), r=2):
if not nm[tup[i], tup[j]]:
break
else:
clusters.append(tup)
cutoffs.append(np.max(dm[tup, :][:, tup]))
return clusters, cutoffs
[docs]def create_neighbor_matrices(atoms, cutoff):
atoms = atoms.copy()
atoms.pbc = False
nAtoms = len(atoms)
nl = NeighborList([cutoff / 2] * nAtoms, skin=0, bothways=True)
nl.update(atoms)
neighbor_matrix = np.eye(nAtoms, dtype=bool)
distance_matrix = np.zeros((nAtoms, nAtoms))
for i in range(nAtoms):
indices, _ = nl.get_neighbors(i)
neighbor_matrix[i, indices] = True
distance_matrix[i, indices] = atoms.get_distances(i, indices)
return neighbor_matrix, distance_matrix
[docs]def extend_cluster(cluster, order):
clusters = []
cluster = tuple(cluster)
nbody = len(cluster)
r = order - nbody
for tup in it.combinations_with_replacement(cluster, r):
new_cluster = sorted(cluster + tup)
clusters.append(tuple(new_cluster))
return clusters
```