Locality Module

Overview

`freud.locality.AABBQuery`	Use an Axis-Aligned Bounding Box (AABB) tree [HAN+16] to find neighbors.
`freud.locality.Filter`	Filter an Existing `NeighborList`.
`freud.locality.FilterSANN`	Filter a `NeighborList` via the SANN method.
`freud.locality.LinkCell`	Supports efficiently finding all points in a set within a certain distance from a given point.
`freud.locality.NeighborList`	Class representing bonds between two sets of points.
`freud.locality.NeighborQuery`	Class representing a set of points along with the ability to query for neighbors of these points.
`freud.locality.NeighborQueryResult`	Class encapsulating the output of queries of NeighborQuery objects.
`freud.locality.PeriodicBuffer`	Replicate periodic images of points inside a box.
`freud.locality.Voronoi`	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: NeighborQuery

Use an Axis-Aligned 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: freud.box.Box

classmethod from_system(type cls, system, dimensions=None)

Create a NeighborQuery from any system-like object.

The standard concept of a system in freud is any object that provides a way to access a box-like object (anything that can be coerced to a box by freud.box.Box.from_box()) and an array-like object (according to NumPy’s definition) of particle positions that turns into a \(N\times 3\) array.

Supported types for system include:

AABBQuery
LinkCell
A sequence of (box, points) where box is a Box and points is a numpy.ndarray.
Objects with attributes box and points.
MDAnalysis.coordinates.timestep.Timestep
gsd.hoomd.Snapshot
garnett.trajectory.Frame
ovito.data.DataCollection
hoomd.data snapshot

Parameters

system (system-like 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 of NeighborQuery built from an inferred box and points.

Return type

freud.locality.NeighborQuery

plot(self, ax=None, title=None, *args, **kwargs)

Plot system box and points.

Parameters

ax (matplotlib.axes.Axes) – Axis to plot on. If None, 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() or matplotlib.axes.Axes.plot().
**kwargs – Passed on to mpl_toolkits.mplot3d.Axes3D.plot() or matplotlib.axes.Axes.plot().

Returns

Axis and point data for the plot.

Return type

tuple (matplotlib.axes.Axes, matplotlib.collections.PathCollection)

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

NeighborQueryResult

class freud.locality.Filter

Bases: _PairCompute

Filter an Existing NeighborList.

This class serves as the base class for all NeighborList filtering methods in freud. Filtering a NeighborList requires first computing the unfiltered NeighborList from a system and a set of query arguments. Then, based on the arrangement of particles, their shapes, and other criteria determined by the derived class, some of the neighbors are removed from the unfiltered NeighborList.

The compute method of each Filter class will take a system object along with a neighbors dictionary specifying query arguments. The neighbors dictionary along with the system object will be used to build the unfiltered neighborlist, which will then be filtered according to the filter class. After the calculation, the filtered neighborlist will be available as the property filtered_nlist .

Warning

This class is abstract and should not be instantiated directly.

compute(self, system, neighbors=None, query_points=None)

Filter a Neighborlist.

Parameters

system – Any object that is a valid argument to freud.locality.NeighborQuery.from_system.
neighbors (freud.locality.NeighborList or dict, optional) – Either a NeighborList of neighbor pairs to use for the unfiltered neighbor list, or a dictionary of query arguments. If None, an unfiltered neighborlist will be created such that all pairs of particles are neighbors via NeighborList.all_pairs() (Default value = None).
query_points ((\(N_{query\_points}\), 3) np.ndarray, optional) – Query points used to calculate the unfiltered neighborlist. Uses the system’s points if None (Default value = None).

default_query_args: No default query arguments.

property filtered_nlist

The filtered neighbor list.

Type: NeighborList

property unfiltered_nlist

The unfiltered neighbor list.

Type: NeighborList

class freud.locality.FilterSANN

Bases: Filter

Filter a NeighborList via the SANN method.

The Solid Angle Nearest Neighbor (SANN) method [vMFVF12] is a parameter-free algorithm for the identification of nearest neighbors. The SANN method attributes to each possible neighbor a solid angle and determines the cutoff radius by the requirement that the sum of the solid angles is 4π.

For performance considerations, SANN is implemented as a way of filtering a pre-existing set of neighbors due to the high performance cost of sorting all \(N^2\) particle pairs by distance. For a more in-depth explanation of the neighborlist filter concept in freud, see Filter.

Warning

Due to the above design decision, it is possible that the unfiltered neighborlist will not contain enough neighbors to completely fill the neighbor shell of some particles in the system. The allow_incomplete_shell argument to FilterSANN’s constructor controls whether a warning or exception is raised in these cases.

Note

The filtered_nlist computed by this class will be sorted by distance.

Parameters: allow_incomplete_shell (bool) – Whether particles with incomplete neighbor shells are allowed in the filtered neighborlist. If True, a warning will be raised if there are particles with incomplete neighbors shells in the filtered neighborlist. If False, an exception will be raised in the same case (Default value = False).

compute(self, system, neighbors=None, query_points=None)

Filter a Neighborlist.

Parameters

system – Any object that is a valid argument to freud.locality.NeighborQuery.from_system.
neighbors (freud.locality.NeighborList or dict, optional) – Either a NeighborList of neighbor pairs to use for the unfiltered neighbor list, or a dictionary of query arguments. If None, an unfiltered neighborlist will be created such that all pairs of particles are neighbors via NeighborList.all_pairs() (Default value = None).
query_points ((\(N_{query\_points}\), 3) np.ndarray, optional) – Query points used to calculate the unfiltered neighborlist. Uses the system’s points if None (Default value = None).

default_query_args: No default query arguments.

property filtered_nlist

The filtered neighbor list.

Type: NeighborList

property unfiltered_nlist

The unfiltered neighbor list.

Type: NeighborList

class freud.locality.LinkCell

Bases: 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: freud.box.Box

cell_width

Cell width.

Type: float

classmethod from_system(type cls, system, dimensions=None)

Create a NeighborQuery from any system-like object.

The standard concept of a system in freud is any object that provides a way to access a box-like object (anything that can be coerced to a box by freud.box.Box.from_box()) and an array-like object (according to NumPy’s definition) of particle positions that turns into a \(N\times 3\) array.

Supported types for system include:

AABBQuery
LinkCell
A sequence of (box, points) where box is a Box and points is a numpy.ndarray.
Objects with attributes box and points.
MDAnalysis.coordinates.timestep.Timestep
gsd.hoomd.Snapshot
garnett.trajectory.Frame
ovito.data.DataCollection
hoomd.data snapshot

Parameters

system (system-like 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 of NeighborQuery built from an inferred box and points.

Return type

freud.locality.NeighborQuery

plot(self, ax=None, title=None, *args, **kwargs)

Plot system box and points.

Parameters

ax (matplotlib.axes.Axes) – Axis to plot on. If None, 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() or matplotlib.axes.Axes.plot().
**kwargs – Passed on to mpl_toolkits.mplot3d.Axes3D.plot() or matplotlib.axes.Axes.plot().

Returns

Axis and point data for the plot.

Return type

tuple (matplotlib.axes.Axes, matplotlib.collections.PathCollection)

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

NeighborQueryResult

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 as freud.locality.LinkCell, freud.locality.AABBQuery, or freud.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)

classmethod all_pairs(type cls, system, query_points=None, exclude_ii=True)

Create a NeighborList where all pairs of points are neighbors.

More explicitly, this method returns a NeighborList in which all pairs of points \(i\), \(j\) are neighbors. Pairs such that \(i = j\) can also be excluded using the exclude_ii option. The weight of all neighbors pairs in the returned list will be 1.

Parameters

system – Any object that is valid argument to freud.locality.NeighborQuery.from_system.
query_points ((\(N_{query\_points}\), 3) np.ndarray, optional) – Query points used to create neighbor pairs. Uses the system’s points if None (Default value = None).
exclude_ii (bool) – Whether to exclude pairs of particles with the same point index in the output neighborlist (Default value = True).

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) – Boolean-like array of bonds to keep (True means the bond will not be removed).

Note

This method modifies this object in-place.

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.

Parameters

r_max (float) – Maximum bond distance in the resulting neighbor list.
r_min (float, optional) – Minimum bond distance in the resulting neighbor list (Default value = 0).

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 per-bond weights (if None 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 read-only 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 read-only 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

sort(self, bool by_distance=False)

Sort the entries in the neighborlist.

Parameters: by_distance (bool) – If True, this method sorts the neighborlist entries by query_point_index, then distance, then point_index. If False, this method sorts the NeighborList entries by query_point_index, then point_index, then distance (Default value = False).

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 and LinkCell 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 the NeighborQuery is through the query() and queryBall() 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: freud.box.Box

classmethod from_system(type cls, system, dimensions=None)

Create a NeighborQuery from any system-like object.

The standard concept of a system in freud is any object that provides a way to access a box-like object (anything that can be coerced to a box by freud.box.Box.from_box()) and an array-like object (according to NumPy’s definition) of particle positions that turns into a \(N\times 3\) array.

Supported types for system include:

AABBQuery
LinkCell
A sequence of (box, points) where box is a Box and points is a numpy.ndarray.
Objects with attributes box and points.
MDAnalysis.coordinates.timestep.Timestep
gsd.hoomd.Snapshot
garnett.trajectory.Frame
ovito.data.DataCollection
hoomd.data snapshot

Parameters

system (system-like 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 of NeighborQuery built from an inferred box and points.

Return type

freud.locality.NeighborQuery

plot(self, ax=None, title=None, *args, **kwargs)

Plot system box and points.

Parameters

ax (matplotlib.axes.Axes) – Axis to plot on. If None, 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() or matplotlib.axes.Axes.plot().
**kwargs – Passed on to mpl_toolkits.mplot3d.Axes3D.plot() or matplotlib.axes.Axes.plot().

Returns

Axis and point data for the plot.

Return type

tuple (matplotlib.axes.Axes, matplotlib.collections.PathCollection)

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

NeighborQueryResult

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 of NeighborQuery. The class provides a convenient interface for iterating over query results, and can be transparently converted into a list or a NeighborList 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. If False, 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: NeighborList

class freud.locality.PeriodicBuffer

Bases: _Compute

Replicate periodic images of points inside a box.

property buffer_box

The buffer box, expanded to hold the replicated points.

Type: freud.box.Box

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, include_input_points=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. If True, 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).
include_input_points (bool, optional) – Whether the original points provided by system are included in the buffer, (Default value = False).

class freud.locality.Voronoi

Bases: _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: NeighborList

plot(self, ax=None, color_by_sides=True, cmap=None)

Plot Voronoi diagram.

Parameters

ax (matplotlib.axes.Axes) – Axis to plot on. If None, make a new figure and axis. (Default value = None)
color_by_sides (bool) – If True, color cells by the number of sides. If False, 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

matplotlib.axes.Axes

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