import numpy
from .bo import BondOrientationalDescriptor
from .realspace_wrap import compute
[docs]class LocallyAveragedBondOrientationalDescriptor(BondOrientationalDescriptor):
"""
Locally averaged bond-orientational descriptor.
The complex coefficients :math:`q_{lm}(i)` of particle :math:`i` can be
averaged over its :math:`N_b(i)` nearest neighbors, as suggested by Lechner
and Dellago :cite:`lechner_2008`,
.. math::
\\bar{q}_{lm}(i) = \\frac{1}{N_b(i)+1} \left[ q_{l m}(i) + \\sum_{j=1}^{N_b(i)} q_{l m}(j) \\right],
and then made invariant,
.. math::
\\bar{Q}_{l}(i) = \\sqrt{ \\frac{4\pi}{2l + 1}\\sum_{m=-l}^l |\\bar{q}_{lm(i)}|^2 } ,
to provide an improved descriptor for crystal structure detection.
We then consider :math:`\\bar{Q}_l(i)` for a sequence of orders
:math:`\{ l_n \} = \{ l_\mathrm{min}, \dots, l_\mathrm{max} \}`. The resulting
feature vector for particle :math:`i` is given by
.. math::
X^\mathrm{LABO}(i) = (\: \\bar{Q}_{l_\mathrm{min}}(i) \;\; \dots \;\; \\bar{Q}_{l_\mathrm{max}}(i) \:) .
See the tutorials for more details.
Attributes
----------
trajectory : Trajectory
Trajectory on which the structural descriptor will be computed.
active_filters : list
All the active filters on both groups prior to the computation of the
descriptor.
dimension : int
Spatial dimension of the descriptor (2 or 3).
grid : numpy.ndarray
Grid of orders :math:`\{ l_n \}`.
features : numpy.ndarray
Array of all the structural features for the particles in group=0 in
accordance with the defined filters (if any). This attribute is
initialized when the method ``compute`` is called (default value is ``None``).
groups : tuple
Composition of the groups: ``groups[0]`` and ``groups[1]`` contain lists of all
the ``Particle`` instances in groups 0 and 1 respectively. Each element of
the tuple is a list of ``Particle`` in ``trajectory``, *e.g.* ``groups[0][0]``
is the list of all the particles in the first frame of ``trajectory`` that
belong to group=0.
verbose : bool
Show progress information and warnings about the computation of the
descriptor when verbose is ``True``, and remain silent when verbose is
``False``.
neighbors_boost : float, default: 1.5
Scaling factor to estimate the number of neighbors relative to a
an ideal gas with the same density. This is used internally to set
the dimensions of lists of neighbors. A too small number creates a
risk of overfilling the lists of neighbors, and a too large number
increases memory usage. This only works if the associated ``Trajectory``
has valid cutoffs in the ``Trajectory.nearest_neighbors_cutoffs`` list
attribute. This sets the value of the ``max_num_neighbors`` attribute
during the computation of the descriptor.
max_num_neighbors : int, default: 100
Maximum number of neighbors. This is used internally to set the dimensions
of lists of neighbors. This number is automatically adjusted to limit
memory usage if the associated ``Trajectory`` has valid cutoffs in the
``Trajectory.nearest_neighbors_cutoffs`` list attribute. The
default value ``100`` is used if no cutoffs can be used to estimate a
better value. The default value is sufficient in most cases, otherwise
this number can manually be increased **before** computing the descriptor.
"""
name = 'locally averaged bond-orientational'
symbol = 'labo'
[docs] def __init__(self, trajectory, lmin=1, lmax=8, orders=None,
accept_nans=True, verbose=False):
"""
Parameters
----------
trajectory : Trajectory
Trajectory on which the structural descriptor will be computed.
lmin : int, default: 1
Minimum order :math:`l_\mathrm{min}`. This sets the lower bound of
the grid :math:`\{ l_n \}`.
lmax : int, default: 8
Maximum order :math:`l_\mathrm{max}`. This sets the upper bound of
the grid :math:`\{ l_n \}`. For numerical reasons,
:math:`l_\mathrm{max}` cannot be larger than 16.
orders: list, default: None
Sequence :math:`\{l_n\}` of specific orders to compute, *e.g.*
``orders=[4,6]``. This has the priority over ``lmin`` and ``lmax``.
accept_nans: bool, default: True
If ``False``, discard any row from the array of features that contains a
`NaN` element. If ``True``, keep `NaN` elements in the array of features.
verbose : bool, default: False
Show progress information and warnings about the computation of the
descriptor when verbose is ``True``, and remain silent when verbose
is ``False``.
"""
BondOrientationalDescriptor.__init__(self, trajectory, lmin=lmin,
lmax=lmax, orders=orders,
accept_nans=accept_nans, verbose=verbose)
[docs] def compute(self):
"""
Compute the locally averaged bond-orientational correlations for the particles
in group=0 for the grid of orders :math:`\{ l_n \}`. Returns the data matrix
and also overwrites the ``features`` attribute.
Returns
-------
features : numpy.ndarray
Data matrix with bond-orientational correlations.
"""
# set up
self._set_up(dtype=numpy.float64)
self._manage_nearest_neighbors()
self._filter_neighbors()
self._filter_subsidiary_neighbors()
n_frames = len(self.groups[0])
row = 0
# all relevant arrays
pos_0 = self.dump('position', group=0)
pos_all = self.trajectory.dump('position')
box = self.trajectory.dump('cell.side')
# computation
for n in self._trange(n_frames):
pos_all_n = pos_all[n].T
for i in range(len(self.groups[0][n])):
hist_n_i = numpy.empty_like(self.grid, dtype=numpy.float64)
nn_i = self._neighbors_number[n][i]
for ln, l in enumerate(self.grid):
hist_n_i[ln] = self._qbar_l(l,
self._neighbors[n][i][0:nn_i],
self._subsidiary_neighbors[n][i],
pos_0[n][i], pos_all_n, box[n])
# TODO: improve Fortran calculation for Lechner-Dellago
# hist_n_i[ln] = compute.qbarl(l, numpy.array(neigh_i),
# numpy.array(neigh_neigh_i).T,
# pos_0[n][i], pos_1[n].T, box)
self.features[row] = hist_n_i
row += 1
self._handle_nans()
return self.features
def _qbar_lm(self, l, neigh_i, neigh_neigh_i, pos_i, pos_all, box):
Nbar_b = len(neigh_i) + 1
q_lm_i = compute.qlm(l, neigh_i, pos_i, pos_all, box)
q_lm_k = []
for kn in range(len(neigh_i)):
k = neigh_i[kn]
q_lm_k.append(compute.qlm(l, neigh_neigh_i[kn], pos_all[:,k], pos_all, box))
qbar_lm = q_lm_i + numpy.sum(q_lm_k, axis=0)
return qbar_lm / Nbar_b
def _qbar_l(self, l, neigh_i, neigh_neigh_i, pos_i, pos_all, box):
"""
Rotational invariant of order l for particle `i`.
"""
qbar_lm = self._qbar_lm(l, neigh_i, neigh_neigh_i, pos_i, pos_all, box)
return compute.rotational_invariant(l, qbar_lm)
[docs]class LechnerDellagoDescriptor(LocallyAveragedBondOrientationalDescriptor):
"""
Alias for the class ``AveragedBondOrientationalDescriptor``.
"""
pass