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"""Contains a calculator which given an arbitrary list of clusters and 

associated force constants can calculate the energy and forces of a displaced 

system 

""" 

import numpy as np 

import math 

import numba 

from collections import defaultdict as dd 

 

from ase.calculators.calculator import Calculator, all_changes 

from ase.geometry import find_mic 

 

from .numba_calc import cluster_force_contribution 

 

 

@numba.jit(nopython=True) 

def _get_forces(clusters, force_constants, 

atom_indices_list, atom_positions_list, atom_counts_list, 

prefactors_list, 

nbody, order, 

forces, E, 

displacements): 

fc_tmp = np.zeros(3**order) 

fc = np.zeros(3**order) 

forces_tmp = np.zeros(forces.shape) 

f = np.zeros(3) 

for i in range(len(clusters)): 

cluster = clusters[i] 

fc[:] = force_constants[i].flat 

atom_positions = atom_positions_list[i] 

prefactors = prefactors_list[i] 

cluster_force_contribution(atom_positions, prefactors, nbody, 

fc_tmp, fc, order, 

displacements, 

cluster, f, forces_tmp) 

forces += forces_tmp 

E_tmp = 0 

for atom_index in range(len(forces_tmp)): 

E_tmp += np.dot(forces_tmp[atom_index], displacements[atom_index]) 

E -= E_tmp / order 

 

 

class ForceConstantCalculator(Calculator): 

"""This class provides an ASE calculator that can be used in conjunction 

with integrators and optimizers with the `atomic simulation environment 

(ASE) <https://wiki.fysik.dtu.dk/ase/index.html>`_. To initialize an object 

of this class one must provide the ideal atomic configuration along with a 

compatible force constant model. 

 

Parameters 

----------- 

atoms_ideal : ASE Atoms object 

ideal (reference) configuration (i.e. without displacements) 

fcs: ForceConstants object 

the ForceConstants object must be compatible with the ideal 

(reference) configuration 

""" 

 

implemented_properties = ['energy', 'forces'] 

 

def __init__(self, fcs): 

Calculator.__init__(self) 

 

64 ↛ 65line 64 didn't jump to line 65, because the condition on line 64 was never true if fcs.atoms is None: 

raise ValueError('ForceConstants has no atoms object') 

self.atoms_ideal = fcs.atoms.copy() 

 

# Nearest neighbor distance used as maximum displacement allowed, 

# stops exploding MD simulations. 

self.max_allowed_disp = 2 * np.min(sorted(np.unique( 

self.atoms_ideal.get_all_distances(mic=True).round(4)))[1]) 

 

self.clusters = dd(list) 

self.force_constants = dd(list) 

self.atom_indices = dd(list) 

self.atom_positions = dd(list) 

self.atom_counts = dd(list) 

self.prefactors = dd(list) 

# The main idea is to precompute the prefactor and multiplicities of 

# belonging to each cluster 

for cluster, fc in fcs.get_fc_dict().items(): 

argsort = np.argsort(cluster) # TODO: is already True? 

cluster = np.array(sorted(cluster)) 

nbody = len(set(cluster)) 

order = len(cluster) 

key = (nbody, order) 

self.clusters[key].append(cluster) 

assert fc.shape == (3,) * order 

self.force_constants[key].append(fc.transpose(argsort)) 

unique = np.unique(cluster, return_index=True, return_counts=True) 

self.atom_indices[key].append(unique[0]) 

self.atom_positions[key].append(unique[1]) 

self.atom_counts[key].append(unique[2]) 

prefac = [-count/np.prod(list(map(math.factorial, unique[2]))) 

for count in unique[2]] 

self.prefactors[key].append(prefac) 

for d in [self.clusters, 

self.force_constants, 

self.atom_indices, 

self.atom_positions, 

self.atom_counts, 

self.prefactors, 

]: 

for k, v in d.items(): 

d[k] = np.array(v) 

 

def calculate(self, atoms=None, properties=['energy'], 

system_changes=all_changes): 

Calculator.calculate(self, atoms, properties, system_changes) 

self._check_atoms() 

self._compute_displacements() 

 

113 ↛ exitline 113 didn't return from function 'calculate', because the condition on line 113 was never false if 'forces' in properties or 'energy' in properties: 

E, forces = self.compute_energy_and_forces() 

self.results['forces'] = forces 

self.results['energy'] = E 

 

def _check_atoms(self): 

"""Check that the atomic configuration, with which the calculator is 

associated, is compatible with the ideal configuration provided during 

initialization.""" 

122 ↛ 123line 122 didn't jump to line 123, because the condition on line 122 was never true if len(self.atoms) != len(self.atoms_ideal): 

raise ValueError('Length of atoms does not match reference atoms') 

124 ↛ 125line 124 didn't jump to line 125, because the condition on line 124 was never true if not all(self.atoms.numbers == self.atoms_ideal.numbers): 

raise ValueError('Atomic numbers does not match reference atoms') 

 

def _compute_displacements(self): 

"""Evaluate the atomic displacements between the current and the ideal 

(reference) configuration.""" 

displacements = [] 

for pos, ideal_pos in zip(self.atoms.positions, 

self.atoms_ideal.positions): 

v_ij = np.array([pos - ideal_pos]) 

displacements.append(find_mic(v_ij, self.atoms.cell, 

pbc=True)[0][0]) 

self.displacements = np.array(displacements) 

 

# sanity check that displacements are not too large 

max_disp = np.max(np.linalg.norm(self.displacements, axis=1)) 

140 ↛ 141line 140 didn't jump to line 141, because the condition on line 140 was never true if max_disp > self.max_allowed_disp: 

raise ValueError( 

'Displacement {:.5f} larger than maximum allowed displacement' 

' {:.5f}'.format(max_disp, self.max_allowed_disp)) 

 

def compute_energy_and_forces(self): 

"""Compute energy and forces. 

 

Returns 

------- 

float, list of 3-dimensional vectors 

energy and forces 

""" 

E = np.zeros(1) 

forces = np.zeros((len(self.atoms), 3)) 

 

for key in self.clusters.keys(): 

nbody = key[0] 

order = key[1] 

_get_forces(self.clusters[key], 

self.force_constants[key], 

self.atom_indices[key], 

self.atom_positions[key], 

self.atom_counts[key], 

self.prefactors[key], 

nbody, order, 

forces, E, self.displacements) 

return float(E), forces 

 

def __repr__(self): 

fc_dict_str = '{{{}: {}, ...}}'.format( 

self.clusters[0], self.force_constants[0]) 

fcs_str = 'ForceConstants(fc_dict={}, atoms={!r})'.format( 

fc_dict_str, self.atoms_ideal) 

return 'ForceConstantCalculator({})'.format(fcs_str)