# Copyright (c) 2010-2020 The Regents of the University of Michigan
# This file is from the freud project, released under the BSD 3-Clause License.
R"""
The :class:`freud.data` module provides certain sample data sets and utility
functions that are useful for testing and examples.
.. rubric:: Stability
:mod:`freud.data` is **unstable**. When upgrading from version 2.x to 2.y (y >
x), existing freud scripts may need to be updated. The API will be finalized in
a future release.
"""
import numpy as np
import freud
[docs]class UnitCell(object):
"""Class to represent the unit cell of a crystal structure.
This class represents the unit cell of a crystal structure, which is
defined by a lattice and a basis. It provides the basic attributes of the
unit cell as well as enabling the generation of systems of points
(optionally with some noise) from the unit cell.
Args:
box:
A box-like object (see :meth:`~freud.box.Box.from_box`) containing
the lattice vectors of the unit cell.
basis_positions ((:math:`N_{points}`, 3) :class:`numpy.ndarray`):
The basis of the unit cell in fractional coordinates
(Default value = ``[[0, 0, 0]]``).
"""
def __init__(self, box, basis_positions=[[0, 0, 0]]):
self._box = freud.box.Box.from_box(box)
self._basis_positions = basis_positions
[docs] def generate_system(self, num_replicas=1, scale=1, sigma_noise=0,
seed=None):
"""Generate a system from the unit cell.
The box and the positions are expanded by ``scale``, and then Gaussian
noise with standard deviation ``sigma_noise`` is added to the
positions. All points are wrapped back into the box before being
returned.
Args:
num_replicas (:class:`tuple` or int):
If provided as a single number, the number of replicas in all
dimensions. If a tuple, the number of times replicated in each
dimension. Must be of the form ``(nx, ny, 1)`` for 2D boxes
(Default value = 1).
scale (float):
Factor by which to scale the unit cell (Default value = 1).
sigma_noise (float):
The standard deviation of the normal distribution used to add
noise to the positions in the system (Default value = 0).
seed (int):
If provided, used to seed the random noise generation. Not used
unless ``sigma_noise`` > 0 (Default value = :code:`None`).
Returns:
tuple (:class:`freud.box.Box`, :class:`np.ndarray`):
A system-like object (see
:class:`~freud.locality.NeighborQuery.from_system`).
"""
try:
nx, ny, nz = num_replicas
except TypeError:
nx = ny = num_replicas
nz = 1 if self.box.is2D else num_replicas
if not all((int(n) == n and n > 0 for n in (nx, ny, nz))):
raise ValueError("The number of replicas must be a positive "
"integer in each dimension.")
if self.box.is2D and nz != 1:
raise ValueError("The number of replicas in z must be 1 for a "
"2D unit cell.")
if any([n > 1 for n in (nx, ny, nz)]):
pbuff = freud.locality.PeriodicBuffer()
abs_positions = self.box.make_absolute(self.basis_positions)
pbuff.compute((self.box, abs_positions),
buffer=(nx-1, ny-1, nz-1),
images=True)
box = pbuff.buffer_box*scale
positions = np.concatenate((abs_positions, pbuff.buffer_points))
else:
box = self.box*scale
positions = self.box.make_absolute(self.basis_positions)
# Even numbers of repeats shift the box by L/2
shift_vec = (np.array([nx, ny, nz]) + 1) % 2
positions += shift_vec * self.box.make_absolute([1, 1, 1])
positions *= scale
positions = box.wrap(positions)
if sigma_noise != 0:
rs = np.random.RandomState(seed)
mean = [0]*3
var = sigma_noise*sigma_noise
cov = np.diag([var, var, var if self.dimensions == 3 else 0])
positions += rs.multivariate_normal(
mean, cov, size=positions.shape[:-1])
positions = box.wrap(positions)
return box, positions
@property
def box(self):
""":class:`freud.box.Box`: The box instance containing the lattice
vectors."""
return self._box
@property
def lattice_vectors(self):
""":math:`(3, 3)` :class:`np.ndarray`: The matrix of lattice
vectors."""
return self.box.to_matrix()
@property
def basis_positions(self):
""":math:`(N_{points}, 3)` :class:`np.ndarray`: The basis positions."""
return self._basis_positions
@property
def a1(self):
""":math:`(3, )` :class:`np.ndarray`: The first lattice vector."""
return self.box.to_matrix()[:, 0]
@property
def a2(self):
""":math:`(3, )` :class:`np.ndarray`: The second lattice vector."""
return self.box.to_matrix()[:, 1]
@property
def a3(self):
""":math:`(3, )` :class:`np.ndarray`: The third lattice vector."""
return self.box.to_matrix()[:, 2]
@property
def dimensions(self):
"""int: The dimensionality of the unit cell."""
return self.box.dimensions
[docs] @classmethod
def fcc(cls):
"""Create a face-centered cubic (fcc) unit cell.
Returns:
:class:`~.UnitCell`: A face-centered cubic unit cell.
"""
fractions = np.array([[.5, .5, 0],
[.5, 0, .5],
[0, .5, .5],
[0, 0, 0]])
return cls([1, 1, 1], fractions)
[docs] @classmethod
def bcc(cls):
"""Create a body-centered cubic (bcc) unit cell.
Returns:
:class:`~.UnitCell`: A body-centered cubic unit cell.
"""
fractions = np.array([[.5, .5, .5],
[0, 0, 0]])
return cls([1, 1, 1], fractions)
[docs] @classmethod
def sc(cls):
"""Create a simple cubic (sc) unit cell.
Returns:
:class:`~.UnitCell`: A simple cubic unit cell.
"""
fractions = np.array([[0, 0, 0]])
return cls([1, 1, 1], fractions)
[docs] @classmethod
def square(cls):
"""Create a square unit cell.
Returns:
:class:`~.UnitCell`: A square unit cell.
"""
fractions = np.array([[0, 0, 0]])
return cls([1, 1], fractions)
[docs] @classmethod
def hex(cls):
"""Create a hexagonal unit cell.
Returns:
:class:`~.UnitCell`: A hexagonal unit cell.
"""
fractions = np.array([[0, 0, 0], [0.5, 0.5, 0]])
return cls([1, np.sqrt(3)], fractions)
[docs]def make_random_system(box_size, num_points, is2D=False, seed=None):
R"""Helper function to make random points with a cubic or square box.
Args:
box_size (float): Size of box.
num_points (int): Number of points.
is2D (bool): If true, creates a 2D system.
(Default value = :code:`False`).
seed (int): Random seed to use. (Default value = :code:`None`).
Returns:
tuple (:class:`freud.box.Box`, :math:`\left(num\_points, 3\right)` :class:`numpy.ndarray`):
Generated box and points.
""" # noqa: E501
rs = np.random.RandomState(seed)
fractional_coords = rs.random_sample((num_points, 3))
if is2D:
box = freud.box.Box.square(box_size)
fractional_coords[:, 2] = 0
else:
box = freud.box.Box.cube(box_size)
points = box.make_absolute(fractional_coords)
return box, points