Source code for hiphive.core.get_orbits

# Contains the get_orbits function which categorizes clusters into orbits and
# orientation families

from .utilities import BiMap
from .atoms import Atom
from .orbit import Orbit, get_geometrical_radius, get_maximum_distance
from .orientation_family import OrientationFamily
from import logger

import numpy as np

logger = logger.getChild('get_orbits')

# This is the interface accessible for cluster_space
[docs]def get_orbits(cluster_list, atom_list, rotation_matrices, translation_vectors, permutations, prim): """Generate a list of the orbits for the clusters in a supercell configuration. This method requires as input a list of the clusters in a supercell configuration as well as a set of symmetry operations (rotations and translations). From this information it will generate a list of the orbits, i.e. the set of symmetry inequivalent clusters each associated with its respective set of equivalent clusters. Parameters ---------- cluster_list : BiMap object a list of clusters atom_list : BiMap object a list of atoms in a supercell rotation_matrices : list of NumPy (3,3) arrays rotational symmetries to be imposed (e.g., from spglib) translation_vectors : list of NumPy (3) arrays translational symmetries to be imposed (e.g., from spglib) permutations : list of permutations lookup table for permutations prim : hiPhive Atoms object primitive structure Returns ------- list of Orbits objs orbits associated with the list of input clusters """ logger.debug('Preparing input...') atoms = prepare_atoms(atom_list) clusters = prepare_clusters(cluster_list) rotations = prepare_rotations(rotation_matrices) translations = prepare_translations(translation_vectors) permutations = prepare_permutations(permutations) cell = prim.cell basis = prim.basis logger.debug('Creating permutation map...') permutation_map, extended_atoms = \ get_permutation_map(atoms, rotations, translations, basis) logger.debug('Creating orbits...') orbits = _get_orbits(permutation_map, extended_atoms, clusters, basis, cell, rotations, permutations) return orbits
# All prepares are in case we changes some interface stuff
[docs]def prepare_permutations(permutations): perms = BiMap() for p in permutations: perms.append(tuple(p)) return perms
[docs]def prepare_atoms(atom_list): atoms = BiMap() for atom in atom_list: atoms.append(atom) return atoms
[docs]def prepare_clusters(cluster_list): clusters = BiMap() for cluster in cluster_list: clusters.append(tuple(cluster)) return clusters
[docs]def prepare_rotations(rotation_matrices): return rotation_matrices
[docs]def prepare_translations(translation_vectors): return translation_vectors
[docs]def get_permutation_map(atoms, rotations, translations, basis): extended_atoms = atoms.copy() permutation_map = np.zeros((len(atoms), len(rotations)), dtype=int) scaled_positions = [atom.spos(basis) for atom in extended_atoms] for sym_index, (R, T) in enumerate(zip(rotations, translations)): for atom_index, spos in enumerate(scaled_positions): new_spos =, spos) + T new_atom = Atom.spos_to_atom(new_spos, basis) if new_atom not in extended_atoms: extended_atoms.append(new_atom) mapped_atom_index = extended_atoms.index(new_atom) permutation_map[atom_index, sym_index] = mapped_atom_index return permutation_map, extended_atoms
# The internal function doing the outer loop over orbits def _get_orbits(permutation_map, extended_atoms, clusters, basis, cell, rotations, permutations): cluster_is_found = [False] * len(clusters) orbits = [] for cluster_index, cluster in enumerate(clusters): if cluster_is_found[cluster_index]: continue orbit = Orbit() cluster_atoms = [extended_atoms[i] for i in cluster] positions = [atom.pos(basis, cell) for atom in cluster_atoms] orbit.radius = get_geometrical_radius(positions) orbit.maximum_distance = get_maximum_distance(positions) orbit.order = len(cluster) populate_orbit(orbit, permutations, clusters, cluster, permutation_map, extended_atoms, cluster_is_found) orbits.append(orbit) # bar.tick() return orbits # Takes a cluster and generates all equivalent, translated clusters
[docs]def generate_translated_clusters(cluster, extended_atoms): transformed_cluster_atoms = [extended_atoms[i] for i in cluster] tested_offsets = set() for atom in transformed_cluster_atoms: offset = atom.offset if offset in tested_offsets: continue else: tested_offsets.add(offset) translated_cluster = [] for atom in transformed_cluster_atoms: new_offset = np.subtract(atom.offset, offset) new_atom = Atom(, new_offset) translated_cluster.append(extended_atoms.index(new_atom)) yield tuple(translated_cluster)
# Here is the actual categorization
[docs]def populate_orbit(orbit, permutations, clusters, cluster, permutation_map, extended_atoms, cluster_is_found): for sym_index in range(permutation_map.shape[1]): of = OrientationFamily(sym_index) transformed_cluster = permutation_map[cluster, sym_index] for translated_cluster in generate_translated_clusters( transformed_cluster, extended_atoms): argsort = tuple(np.argsort(translated_cluster)) perm_index = permutations.index(argsort) translated_cluster = tuple(sorted(translated_cluster)) translated_cluster_index = clusters.index(translated_cluster) if cluster == translated_cluster: if (sym_index, perm_index) not in orbit.eigensymmetries: orbit.eigensymmetries.append((sym_index, perm_index)) if not cluster_is_found[translated_cluster_index]: cluster_is_found[translated_cluster_index] = True of.cluster_indices.append(translated_cluster_index) of.permutation_indices.append(perm_index) if len(of.cluster_indices) > 0: orbit.orientation_families.append(of) return orbit