Source code for hiphive.core.rotational_constraints

"""
Functionality for enforcing rotational sum rules
"""
from sklearn.linear_model import Ridge
import numpy as np
from scipy.sparse import coo_matrix
from .utilities import SparseMatrix


[docs]def enforce_rotational_sum_rules(cs, parameters, sum_rules, **kwargs): """ Enforces rotational sum rules by projecting parameters. Note ---- The interface to this function might change in future releases. Parameters ---------- cs : ClusterSpace the underlying cluster space parameters : numpy.ndarray parameters to be constrained sum_rules : list(str) type of sum rules to enforce; possible values: 'Huang', 'Born-Huang' ridge_alpha : float hyperparameter to the ridge regression algorithm; keyword argument passed to the optimizer; larger values specify stronger regularization, i.e. less correction but higher stability [default: 1e-6] iterations : int number of iterations to run the projection since each step projects the solution down to each nullspace in serial; keyword argument passed to the optimizer [default: 10] Returns ------- numpy.ndarray constrained parameters Examples -------- The rotational sum rules can be enforced to the parameters before constructing a force constant potential as illustrated by the following snippet:: cs = ClusterSpace(reference_structure, cutoffs) sc = StructureContainer(cs) # add structures to structure container opt = Optimizer(sc.get_fit_data()) opt.train() new_params = enforce_rotational_sum_rules(cs, opt.parameters, sum_rules=['Huang', 'Born-Huang']) fcp = ForceConstantPotential(cs, new_params) """ parameters = parameters.copy() # handle optional kwargs input iterations = kwargs.pop('iterations', 10) ridge_alpha = kwargs.pop('ridge_alpha', 1e-6) if len(kwargs) != 0: raise ValueError('Unrecognised kwargs: {}'.format(kwargs)) # make orbit-parameter index map params = [] n = 0 for orbit_index, orbit in enumerate(cs.orbits): number_params_in_orbit = len(orbit.eigentensors) params.append(list(range(n, n + number_params_in_orbit))) n += number_params_in_orbit # create lookuptable for force constants lookup = {} for orbit_index, orbit in enumerate(cs.orbits): for of in orbit.orientation_families: for cluster_index, perm_index in zip(of.cluster_indices, of.permutation_indices): cluster = cs._cluster_list[cluster_index] perm = cs._permutations[perm_index] lookup[tuple(cluster)] = [et.transpose(perm) for et in of.eigentensors], orbit_index # append the sum rule matrices Ms = [] args = (lookup, params, cs.atom_list, cs._prim) for sum_rule in sum_rules: if sum_rule == 'Huang': Ms.append(_create_Huang_constraint(*args)) elif sum_rule == 'Born-Huang': Ms.append(_create_Born_Huang_constraint(*args)) else: raise ValueError('At least one unknown sum rule: {}' .format(sum_rule)) cvs_trans = cs._cvs for i, M in enumerate(Ms): row, col, data = [], [], [] for r, c, v in M.row_list(): row.append(r) col.append(c) data.append(np.float64(v)) M = coo_matrix((data, (row, col)), shape=M.shape) Ms[i] = M.dot(cvs_trans) for _ in range(iterations): for M in Ms: clf = Ridge(alpha=ridge_alpha) d = M.dot(parameters) clf.fit(M, d) parameters -= clf.coef_ # subtract the correction return parameters
def _create_Huang_constraint(lookup, parameter_map, atom_list, prim): m = SparseMatrix(3**4, parameter_map[-1][-1] + 1, 0) def R(i, j): pi = atom_list[i].pos(prim.basis, prim.cell) pj = atom_list[j].pos(prim.basis, prim.cell) return pi - pj for i in range(len(prim)): for j in range(len(atom_list)): ets, orbit_index = lookup.get(tuple(sorted((i, j))), (None, None)) if ets is None: continue inv_perm = np.argsort(np.argsort((i, j))) et_indices = parameter_map[orbit_index] for et, et_index in zip(ets, et_indices): et = et.transpose(inv_perm) Rij = R(i, j) Cij = np.einsum(et, [0, 1], Rij, [2], Rij, [3]) Cij -= Cij.transpose([2, 3, 0, 1]) for k in range(3**4): m[k, et_index] += Cij.flat[k] return m def _create_Born_Huang_constraint(lookup, parameter_map, atom_list, prim): constraints = [] for i in range(len(prim)): m = SparseMatrix(3**3, parameter_map[-1][-1] + 1, 0) for j in range(len(atom_list)): ets, orbit_index = lookup.get(tuple(sorted((i, j))), (None, None)) if ets is None: continue inv_perm = np.argsort(np.argsort((i, j))) et_indices = parameter_map[orbit_index] R = atom_list[j].pos(prim.basis, prim.cell) for et, et_index in zip(ets, et_indices): et = et.transpose(inv_perm) tmp = np.einsum(et, [0, 1], R, [2]) tmp -= tmp.transpose([0, 2, 1]) for k in range(3**3): m[k, et_index] += tmp.flat[k] constraints.append(m) M = SparseMatrix.vstack(*constraints) return M