Cluster Module
Overview
Finds clusters using a network of neighbors. 

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:
_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 attributecluster_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 1point cluster.Identifying micelles is one usecase 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 attributecluster_keys
, as a list of lists. If keys are not provided, every point is assigned a key corresponding to its index, andcluster_keys
contains the point ids present in each cluster. property cluster_idx
The cluster index for each point.
 Type
(\(N_{points}\))
numpy.ndarray
 compute(self, system, keys=None, neighbors=None)
Compute the clusters for the given set of points.
 Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.keys ((\(N_{points}\))
numpy.ndarray
) – Membership keys, one for each point.neighbors (
freud.locality.NeighborList
or dict, optional) – Either aNeighborList
of neighbor pairs to use in the calculation, or a dictionary of query arguments (Default value: None).
 default_query_args
No default query arguments.
 plot(self, ax=None)
Plot cluster distribution.
 Parameters
ax (
matplotlib.axes.Axes
, optional) – Axis to plot on. IfNone
, make a new figure and axis. (Default value =None
) Returns
Axis with the plot.
 Return type
 class freud.cluster.ClusterProperties
Bases:
_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:Geometric center
Center of mass
Gyration tensor
Moment of inertia tensor
Size (number of points)
Mass (total mass of each cluster)
Note
The center of mass and geometric center for each cluster are computed using the minimum image convention
 property centers
The geometric centers of the clusters, independent of mass and defined as
\[\mathbf{C}_g^k = \frac{1}{N_k} \sum_{i=0}^{N_k} \mathbf{r_i}\]where \(\mathbf{C}_g^k\) is the center of the \(k\) th cluster, \(N_k\) is the number of particles in the \(k\) th cluster and \(\mathbf{r_i}\) are their positions.
 Type
(\(N_{clusters}\), 3)
numpy.ndarray
 property centers_of_mass
The centers of mass of the clusters:
\[\mathbf{C}_m^k = \frac{1}{M_k} \sum_{i=0}^{N_k} m_i \mathbf{r_i}\]where \(\mathbf{C}_m^k\) is the center of mass of the \(k\) th cluster, \(M_k\) is the total mass of particles in the \(k\) th cluster, \(\mathbf{r_i}\) are their positions and \(m_i\) are their masses.
 Type
(\(N_{clusters}\), 3)
numpy.ndarray
 property cluster_masses
The total mass of particles in each cluster.
 Type
(\(N_{clusters}\))
numpy.ndarray
 compute(self, system, cluster_idx, masses=None)
Compute properties of the point clusters. Loops over all points in the given array and determines the geometric center, center of mass, moment of inertia, gyration tensors, and radius of gyration [VymvetalVondravsek11] of each cluster. After calling this method, properties can be accessed via their attributes.
Example:
>>> import freud >>> # Compute clusters using box, positions, and nlist data >>> box, points = freud.data.make_random_system(10, 100) >>> cl = freud.cluster.Cluster() >>> cl.compute((box, points), neighbors={'r_max': 1.0}) freud.cluster.Cluster() >>> # Compute cluster properties based on identified clusters >>> cl_props = freud.cluster.ClusterProperties() >>> cl_props.compute((box, points), cl.cluster_idx) freud.cluster.ClusterProperties()
 Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.cluster_idx ((\(N_{points}\),)
np.ndarray
) – Cluster indexes for each point.masses ((\(N_{points}\), )
numpy.ndarray
) – Masses corresponding to each point, defaulting to 1 if not provided orNone
(Default value =None
).
 property gyrations
The gyration tensors of the clusters. Normalized by particle number:
\[\begin{split}\mathbf{S}_k = \frac{1}{N_k} \begin{bmatrix} \sum_i x_i^2 & \sum_i x_i y_i & \sum_i x_i z_i \\ \sum_i y_i x_i & \sum_i y_i^2 & \sum_i y_i z_i \\ \sum_i z_i x_i & \sum_i z_i y_i & \sum_i z_i^2 \\ \end{bmatrix}\end{split}\]where \(\mathbf{S}_k\) is the gyration tensor of the \(k\) th cluster.
 Type
(\(N_{clusters}\), 3, 3)
numpy.ndarray
 property inertia_tensors
The inertia tensors of the clusters. Neither normalized by mass nor number:
\[\begin{split}\mathbf{I}_k = \begin{bmatrix} \sum_i m_i(y_i^2+z_i^2)& \sum_i m_i(x_iy_i)& \sum_i m_i(x_iz_i)\\ \sum_i m_i(y_ix_i)& \sum_i m_i(x_i^2+z_i^2)& \sum_i m_i(y_iz_i)\\ \sum_i m_i(z_ix_i)& \sum_i m_i(z_iy_i)& \sum_i m_i(y_i^2+x_i^2)\\ \end{bmatrix}\end{split}\]where \(\mathbf{I}_k\) is the inertia tensor of the \(k\) th cluster.
 Type
(\(N_{clusters}\), 3, 3)
numpy.ndarray
 property radii_of_gyration
The radius of gyration of each cluster. Defined by IUPAP as
\[R_g^k = \left(\frac{1}{M} \sum_{i=0}^{N_k} m_i s_i^2 \right)^{1/2}\]where \(s_i\) is the distance of particle \(i\) from the center of mass.
 Type
(\(N_{clusters}\),)
numpy.ndarray
 property sizes
The cluster sizes.
 Type
(\(N_{clusters}\))
numpy.ndarray