# Cluster Module¶

Overview

 freud.cluster.Cluster Finds clusters using a network of neighbors. freud.cluster.ClusterProperties Routines for computing properties of point clusters.

Details

The freud.cluster module aids in finding and computing the properties of clusters of points in a system.

class freud.cluster.Cluster

Bases: freud.locality._PairCompute

Finds clusters using a network of neighbors.

Given a set of points and their neighbors, freud.cluster.Cluster will determine all of the connected components of the network formed by those neighbor bonds. That is, two points are in the same cluster if and only if a path exists between them on the network of bonds. The class attribute cluster_idx holds an array of cluster indices for each point. By the definition of a cluster, points that are not bonded to any other point end up in their own 1-point cluster.

Identifying micelles is one use-case for finding clusters. This operation is somewhat different, though. In a cluster of points, each and every point belongs to one and only one cluster. However, because a string of points belongs to a polymer, that single polymer may be present in more than one cluster. To handle this situation, an optional layer is presented on top of the cluster_idx array. Given a key value per point (e.g. the polymer id), the compute function will process clusters with the key values in mind and provide a list of keys that are present in each cluster in the attribute cluster_keys, as a list of lists. If keys are not provided, every point is assigned a key corresponding to its index, and cluster_keys contains the point ids present in each cluster.

property cluster_idx

The cluster index for each point.

Type

($$N_{points}$$) numpy.ndarray

property cluster_keys

A list of lists of the keys contained in each cluster.

Type

list(list)

compute

Compute the clusters for the given set of points.

Parameters
default_query_args

No default query arguments.

property num_clusters

The number of clusters.

Type

int

plot

Plot cluster distribution.

Parameters

ax (matplotlib.axes.Axes, optional) – Axis to plot on. If None, make a new figure and axis. (Default value = None)

Returns

Axis with the plot.

Return type
class freud.cluster.ClusterProperties

Bases: freud.util._Compute

Routines for computing properties of point clusters.

Given a set of points and cluster ids (from Cluster or another source), this class determines the following properties for each cluster:

• Center of mass

• Gyration tensor

• Size (number of points)

The center of mass for each cluster (properly handling periodic boundary conditions) can be accessed with centers attribute. The $$3 \times 3$$ symmetric gyration tensors $$G$$ can be accessed with gyrations attribute.

property centers

The centers of mass of the clusters.

Type

($$N_{clusters}$$, 3) numpy.ndarray

compute

Compute properties of the point clusters. Loops over all points in the given array and determines the center of mass of the cluster as well as the gyration tensor. These can be accessed after the call to compute() with the centers and gyrations attributes.

Parameters
property gyrations

The gyration tensors of the clusters.

Type

($$N_{clusters}$$, 3, 3) numpy.ndarray

property radii_of_gyration

The radius of gyration of each cluster.

Type

($$N_{clusters}$$,) numpy.ndarray

property sizes

The cluster sizes.

Type

($$N_{clusters}$$) numpy.ndarray