Locality Module¶
Overview
Use an AxisAligned Bounding Box (AABB) tree [HAN+16] to find neighbors. 

Supports efficiently finding all points in a set within a certain distance from a given point. 

Class representing bonds between two sets of points. 

Class representing a set of points along with the ability to query for neighbors of these points. 

Class encapsulating the output of queries of NeighborQuery objects. 

Replicate periodic images of points inside a box. 

Computes Voronoi diagrams using voro++. 
Details
The freud.locality
module contains data structures to efficiently
locate points based on their proximity to other points.

class
freud.locality.
AABBQuery
¶ Bases:
freud.locality.NeighborQuery
Use an AxisAligned Bounding Box (AABB) tree [HAN+16] to find neighbors.
Also available as
freud.AABBQuery
. Parameters
box (
freud.box.Box
) – Simulation box.points ((\(N\), 3)
numpy.ndarray
) – The points to use to build the tree.

box
¶ The box object used by this data structure.
 Type

classmethod
from_system
(type cls, system, dimensions=None)¶ Create a
NeighborQuery
from any systemlike object.The standard concept of a system in freud is any object that provides a way to access a boxlike object (anything that can be coerced to a box by
freud.box.Box.from_box()
) and an arraylike object (according to NumPy’s definition) of particle positions that turns into a \(N\times 3\) array.Supported types for
system
include:A sequence of
(box, points)
wherebox
is aBox
andpoints
is anumpy.ndarray
.Objects with attributes
box
andpoints
.hoomd.data
snapshot
 Parameters
system (systemlike object) – Any object that can be converted to a
NeighborQuery
.dimensions (int) – Whether the object is 2 or 3 dimensional. It may be inferred if not provided, but in some cases inference is not possible, in which case it will default to 3 (Default value = None).
 Returns
The same
NeighborQuery
object if one is given, or an instance ofNeighborQuery
built from an inferredbox
andpoints
. Return type

plot
(self, ax=None, title=None, *args, **kwargs)¶ Plot system box and points.
 Parameters
ax (
matplotlib.axes.Axes
) – Axis to plot on. IfNone
, make a new figure and axis. The axis projection (2D or 3D) must match the dimensionality of the system (Default value =None
).title (str) – Title of the plot (Default value =
None
).*args – Passed on to
mpl_toolkits.mplot3d.Axes3D.plot()
ormatplotlib.axes.Axes.plot()
.**kwargs – Passed on to
mpl_toolkits.mplot3d.Axes3D.plot()
ormatplotlib.axes.Axes.plot()
.
 Returns
Axis with the plot.
 Return type

points
¶ The array of points in this data structure.
 Type
np.ndarray

query
(self, query_points, query_args)¶ Query for nearest neighbors of the provided point.
 Parameters
query_points ((\(N\), 3)
numpy.ndarray
) – Points to query for.query_args (dict) – Query arguments determining how to find neighbors. For information on valid query argument, see the Query API.
 Returns
Results object containing the output of this query.
 Return type

class
freud.locality.
LinkCell
¶ Bases:
freud.locality.NeighborQuery
Supports efficiently finding all points in a set within a certain distance from a given point.
Also available as
freud.LinkCell
. Parameters
box (
freud.box.Box
) – Simulation box.points ((\(N\), 3)
numpy.ndarray
) – The points to bin into the cell list.cell_width (float, optional) – Width of cells. If not provided,
LinkCell
will estimate a cell width based on the number of points and the box size, assuming a constant density of points in the box.

box
¶ The box object used by this data structure.
 Type

classmethod
from_system
(type cls, system, dimensions=None)¶ Create a
NeighborQuery
from any systemlike object.The standard concept of a system in freud is any object that provides a way to access a boxlike object (anything that can be coerced to a box by
freud.box.Box.from_box()
) and an arraylike object (according to NumPy’s definition) of particle positions that turns into a \(N\times 3\) array.Supported types for
system
include:A sequence of
(box, points)
wherebox
is aBox
andpoints
is anumpy.ndarray
.Objects with attributes
box
andpoints
.hoomd.data
snapshot
 Parameters
system (systemlike object) – Any object that can be converted to a
NeighborQuery
.dimensions (int) – Whether the object is 2 or 3 dimensional. It may be inferred if not provided, but in some cases inference is not possible, in which case it will default to 3 (Default value = None).
 Returns
The same
NeighborQuery
object if one is given, or an instance ofNeighborQuery
built from an inferredbox
andpoints
. Return type

plot
(self, ax=None, title=None, *args, **kwargs)¶ Plot system box and points.
 Parameters
ax (
matplotlib.axes.Axes
) – Axis to plot on. IfNone
, make a new figure and axis. The axis projection (2D or 3D) must match the dimensionality of the system (Default value =None
).title (str) – Title of the plot (Default value =
None
).*args – Passed on to
mpl_toolkits.mplot3d.Axes3D.plot()
ormatplotlib.axes.Axes.plot()
.**kwargs – Passed on to
mpl_toolkits.mplot3d.Axes3D.plot()
ormatplotlib.axes.Axes.plot()
.
 Returns
Axis with the plot.
 Return type

points
¶ The array of points in this data structure.
 Type
np.ndarray

query
(self, query_points, query_args)¶ Query for nearest neighbors of the provided point.
 Parameters
query_points ((\(N\), 3)
numpy.ndarray
) – Points to query for.query_args (dict) –
Query arguments determining how to find neighbors. For information on valid query argument, see the Query API.
 Returns
Results object containing the output of this query.
 Return type

class
freud.locality.
NeighborList
¶ Bases:
object
Class representing bonds between two sets of points.
Compute classes contain a set of bonds between two sets of position arrays (“query points” and “points”) and hold a list of index pairs \(\left(i, j\right)\) where \(i < N_{query\_points}, j < N_{points}\) corresponding to neighbor pairs between the two sets.
For efficiency, all bonds must be sorted by the query point index, from least to greatest. Bonds have an query point index \(i\) and a point index \(j\). The first bond index corresponding to a given query point can be found in \(\log(N_{bonds})\) time using
find_first_index()
, because bonds are ordered by the query point index.Note
Typically, there is no need to instantiate this class directly. In most cases, users should manipulate
freud.locality.NeighborList
objects received from a neighbor search algorithm, such asfreud.locality.LinkCell
,freud.locality.AABBQuery
, orfreud.locality.Voronoi
.Also available as
freud.NeighborList
.Example:
# Assume we have position as Nx3 array aq = freud.locality.AABBQuery(box, positions) nlist = aq.query(positions, {'r_max': 3}).toNeighborList() # Get all vectors from central particles to their neighbors rijs = (positions[nlist.point_indices]  positions[nlist.query_point_indices]) rijs = box.wrap(rijs)
The NeighborList can be indexed to access bond particle indices. Example:
for i, j in nlist[:]: print(i, j)

copy
(self, other=None)¶ Create a copy. If other is given, copy its contents into this object. Otherwise, return a copy of this object.
 Parameters
other (
freud.locality.NeighborList
, optional) – A NeighborList to copy into this object (Default value =None
).

distances
¶ The distances for each bond.
 Type
(\(N_{bonds}\))
np.ndarray

filter
(self, filt)¶ Removes bonds that satisfy a boolean criterion.
 Parameters
filt (
np.ndarray
) – Booleanlike array of bonds to keep (True means the bond will not be removed).
Note
This method modifies this object inplace.
Example:
# Keep only the bonds between particles of type A and type B nlist.filter(types[nlist.query_point_indices] != types[nlist.point_indices])

filter_r
(self, float r_max, float r_min=0)¶ Removes bonds that are outside of a given radius range.

find_first_index
(self, unsigned int i)¶ Returns the lowest bond index corresponding to a query particle with an index \(\geq i\).
 Parameters
i (unsigned int) – The particle index.

classmethod
from_arrays
(type cls, num_query_points, num_points, query_point_indices, point_indices, distances, weights=None)¶ Create a NeighborList from a set of bond information arrays.
Example:
import freud import numpy as np box = freud.box.Box(2, 3, 4, 0, 0, 0) query_points = np.array([[0, 0, 0], [0, 0, 1]]) points = np.array([[0, 0, 1], [0.5, 1, 0]]) query_point_indices = np.array([0, 0, 1]) point_indices = np.array([0, 1, 1]) distances = box.compute_distances( query_points[query_point_indices], points[point_indices]) num_query_points = len(query_points) num_points = len(points) nlist = freud.locality.NeighborList.from_arrays( num_query_points, num_points, query_point_indices, point_indices, distances)
 Parameters
num_query_points (int) – Number of query points (corresponding to
query_point_indices
).num_points (int) – Number of points (corresponding to
point_indices
).query_point_indices (
np.ndarray
) – Array of integers corresponding to indices in the set of query points.point_indices (
np.ndarray
) – Array of integers corresponding to indices in the set of points.distances (
np.ndarray
) – Array of distances between corresponding query points and points.weights (
np.ndarray
, optional) – Array of perbond weights (ifNone
is given, use a value of 1 for each weight) (Default value =None
).

neighbor_counts
¶ A neighbor count array indicating the number of neighbors for each query point.
 Type
(\(N_{query\_points}\))
np.ndarray

num_points
¶ The number of points.
All point indices are less than this value.
 Type
unsigned int

num_query_points
¶ The number of query points.
All query point indices are less than this value.
 Type
unsigned int

point_indices
¶ The point indices for each bond. This array is readonly to prevent breakage of
find_first_index()
. Equivalent to indexing with[:, 1]
. Type
(\(N_{bonds}\))
np.ndarray

query_point_indices
¶ The query point indices for each bond. This array is readonly to prevent breakage of
find_first_index()
. Equivalent to indexing with[:, 0]
. Type
(\(N_{bonds}\))
np.ndarray

segments
¶ A segment array indicating the first bond index for each query point.
 Type
(\(N_{query\_points}\))
np.ndarray

weights
¶ The weights for each bond. By default, bonds have a weight of 1.
 Type
(\(N_{bonds}\))
np.ndarray


class
freud.locality.
NeighborQuery
¶ Bases:
object
Class representing a set of points along with the ability to query for neighbors of these points.
Warning
This class should not be instantiated directly. The subclasses
AABBQuery
andLinkCell
provide the intended interfaces.The
NeighborQuery
class represents the abstract interface for neighbor finding. The class contains a set of points and a simulation box, the latter of which is used to define the system and the periodic boundary conditions required for finding neighbors of these points. The primary mode of interacting with theNeighborQuery
is through thequery()
andqueryBall()
functions, which enable finding either the nearest neighbors of a point or all points within a distance cutoff, respectively. Subclasses of NeighborQuery implement these methods based on the nature of the underlying data structure. Parameters
box (
freud.box.Box
) – Simulation box.points ((\(N\), 3)
numpy.ndarray
) – Point coordinates to build the structure.

box
¶ The box object used by this data structure.
 Type

classmethod
from_system
(type cls, system, dimensions=None)¶ Create a
NeighborQuery
from any systemlike object.The standard concept of a system in freud is any object that provides a way to access a boxlike object (anything that can be coerced to a box by
freud.box.Box.from_box()
) and an arraylike object (according to NumPy’s definition) of particle positions that turns into a \(N\times 3\) array.Supported types for
system
include:A sequence of
(box, points)
wherebox
is aBox
andpoints
is anumpy.ndarray
.Objects with attributes
box
andpoints
.hoomd.data
snapshot
 Parameters
system (systemlike object) – Any object that can be converted to a
NeighborQuery
.dimensions (int) – Whether the object is 2 or 3 dimensional. It may be inferred if not provided, but in some cases inference is not possible, in which case it will default to 3 (Default value = None).
 Returns
The same
NeighborQuery
object if one is given, or an instance ofNeighborQuery
built from an inferredbox
andpoints
. Return type

plot
(self, ax=None, title=None, *args, **kwargs)¶ Plot system box and points.
 Parameters
ax (
matplotlib.axes.Axes
) – Axis to plot on. IfNone
, make a new figure and axis. The axis projection (2D or 3D) must match the dimensionality of the system (Default value =None
).title (str) – Title of the plot (Default value =
None
).*args – Passed on to
mpl_toolkits.mplot3d.Axes3D.plot()
ormatplotlib.axes.Axes.plot()
.**kwargs – Passed on to
mpl_toolkits.mplot3d.Axes3D.plot()
ormatplotlib.axes.Axes.plot()
.
 Returns
Axis with the plot.
 Return type

points
¶ The array of points in this data structure.
 Type
np.ndarray

query
(self, query_points, query_args)¶ Query for nearest neighbors of the provided point.
 Parameters
query_points ((\(N\), 3)
numpy.ndarray
) – Points to query for.query_args (dict) –
Query arguments determining how to find neighbors. For information on valid query argument, see the Query API.
 Returns
Results object containing the output of this query.
 Return type

class
freud.locality.
NeighborQueryResult
¶ Bases:
object
Class encapsulating the output of queries of NeighborQuery objects.
Warning
This class should not be instantiated directly, it is the return value of the
query()
method ofNeighborQuery
. The class provides a convenient interface for iterating over query results, and can be transparently converted into a list or aNeighborList
object.The
NeighborQueryResult
makes it easy to work with the results of queries and convert them to various natural objects. Additionally, the result is a generator, making it easy for users to lazily iterate over the object.
toNeighborList
(self, sort_by_distance=False)¶ Convert query result to a freud
NeighborList
. Parameters
sort_by_distance (bool) – If
True
, sort neighboring bonds by distance. IfFalse
, sort neighboring bonds by point index (Default value =False
). Returns
A
NeighborList
containing all neighbor pairs found by the query generating this result object. Return type


class
freud.locality.
PeriodicBuffer
¶ Bases:
freud.util._Compute
Replicate periodic images of points inside a box.

property
buffer_box
¶ The buffer box, expanded to hold the replicated points.
 Type

property
buffer_ids
¶ The buffer point ids.
 Type
\(\left(N_{buffer}\right)\)
numpy.ndarray

property
buffer_points
¶ The buffer point positions.
 Type
\(\left(N_{buffer}, 3\right)\)
numpy.ndarray

compute
(self, system, buffer, bool images=False)¶ Compute the periodic buffer.
 Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.buffer (float or list of 3 floats) – Buffer distance for replication outside the box.
images (bool, optional) – If
False
,buffer
is a distance. IfTrue
,buffer
is a number of images to replicate in each dimension. Note that one image adds half of a box length to each side, meaning that one image doubles the box side lengths, two images triples the box side lengths, and so on. (Default value =False
).

property

class
freud.locality.
Voronoi
¶ Bases:
freud.util._Compute
Computes Voronoi diagrams using voro++.
Voronoi diagrams (Wikipedia) are composed of convex polytopes (polyhedra in 3D, polygons in 2D) called cells, corresponding to each input point. The cells bound a region of Euclidean space for which all contained points are closer to a corresponding input point than any other input point. A ridge is defined as a boundary between cells, which contains points equally close to two or more input points.
The voro++ library [Ryc09] is used for fast computations of the Voronoi diagram.

compute
(self, system)¶ Compute Voronoi diagram.
 Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.

property
nlist
¶ Returns the computed
NeighborList
.The
NeighborList
computed by this class is weighted. In 2D systems, the bond weight is the length of the ridge (boundary line) between the neighboring points’ Voronoi cells. In 3D systems, the bond weight is the area of the ridge (boundary polygon) between the neighboring points’ Voronoi cells. The weights are not normalized, and the weights for each query point sum to the surface area (perimeter in 2D) of the polytope.It is possible for pairs of points to appear multiple times in the neighbor list. For example, in a small unit cell, points may neighbor one another on multiple sides because of periodic boundary conditions.
 Returns
Neighbor list.
 Return type

plot
(self, ax=None, color_by_sides=True, cmap=None)¶ Plot Voronoi diagram.
 Parameters
ax (
matplotlib.axes.Axes
) – Axis to plot on. IfNone
, make a new figure and axis. (Default value =None
)
 color_by_sides (bool):
If
True
, color cells by the number of sides. IfFalse
, random colors are used for each cell. (Default value =True
) cmap (str):
Colormap name to use (Default value =
None
).
 Returns
Axis with the plot.
 Return type

property
polytopes
¶ A list of
numpy.ndarray
defining Voronoi polytope vertices for each cell. Type
list[
numpy.ndarray
]

property
volumes
¶ Returns an array of Voronoi cell volumes (areas in 2D).
 Type
\(\left(N_{points} \right)\)
numpy.ndarray
