Environment Module¶
Overview
Compute the bond orientational order diagram for the system of particles. 

Compute a set of descriptors (a numerical “fingerprint”) of a particle’s local environment. 

Clusters particles according to whether their local environments match or not, according to various shape matching metrics. 

Find matches between local arrangements of a set of points and a provided motif. 

Calculates the minimum angles of separation between orientations and global orientations. 

Calculates the minimum angles of separation between orientations and query orientations. 

Calculates the maximal projection of nearest neighbor bonds for each particle onto some set of reference vectors, defined in the particles’ local reference frame. 
Details
The freud.environment
module contains functions which characterize the
local environments of particles in the system. These methods use the positions
and orientations of particles in the local neighborhood of a given particle to
characterize the particle environment.

class
freud.environment.
AngularSeparationGlobal
¶ Bases:
freud.util._Compute
Calculates the minimum angles of separation between orientations and global orientations.

property
angles
¶ \(\left(N_{orientations}, N_{global\_orientations}\right)\)
numpy.ndarray
: The global angles in radians.

compute
(self, global_orientations, orientations, equiv_orientations=np.array([[1, 0, 0, 0]]))¶ Calculates the minimum angles of separation between
global_orientations
andorientations
, checking for underlying symmetry as encoded inequiv_orientations
. The result is stored in theglobal_angles
class attribute. Parameters
global_orientations ((\(N_{global}\), 4)
numpy.ndarray
) – Set of global orientations to calculate the order parameter.orientations ((\(N_{particles}\), 4)
numpy.ndarray
) – Orientations to calculate the order parameter.equiv_orientations ((\(N_{equiv}\), 4)
numpy.ndarray
, optional) – The set of all equivalent quaternions that map the particle to itself (the elements of its rotational symmetry group). Important:equiv_orientations
must include both \(q\) and \(q\), for all included quaternions. Note that this calculation assumes that all points in the system share the same set of equivalent orientations. (Default value =[[1, 0, 0, 0]]
)

property

class
freud.environment.
AngularSeparationNeighbor
¶ Bases:
freud.locality._PairCompute
Calculates the minimum angles of separation between orientations and query orientations.

property
angles
¶ The neighbor angles in radians. The angles are stored in the order of the neighborlist object.
 Type
\(\left(N_{bonds}\right)\)
numpy.ndarray

compute
(self, system, orientations, query_points=None, query_orientations=None, equiv_orientations=np.array([[1, 0, 0, 0]]), neighbors=None)¶ Calculates the minimum angles of separation between
orientations
andquery_orientations
, checking for underlying symmetry as encoded inequiv_orientations
. The result is stored in theneighbor_angles
class attribute. Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.orientations ((\(N_{points}\), 4)
numpy.ndarray
) – Orientations associated with system points that are used to calculate bonds.query_points ((\(N_{query\_points}\), 3)
numpy.ndarray
, optional) – Query points used to calculate the correlation function. Uses the system’s points ifNone
(Default value =None
).query_orientations ((\(N_{query\_points}\), 4)
numpy.ndarray
, optional) – Query orientations used to calculate bonds. Usesorientations
ifNone
. (Default value =None
).equiv_orientations ((\(N_{equiv}\), 4)
numpy.ndarray
, optional) – The set of all equivalent quaternions that map the particle to itself (the elements of its rotational symmetry group). Important:equiv_orientations
must include both \(q\) and \(q\), for all included quaternions. Note that this calculation assumes that all points in the system share the same set of equivalent orientations. (Default value =[[1, 0, 0, 0]]
)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.

property
nlist
¶ The neighbor list from the last compute.

property

class
freud.environment.
BondOrder
¶ Bases:
freud.locality._SpatialHistogram
Compute the bond orientational order diagram for the system of particles.
The bond orientational order diagram (BOOD) is a way of studying the average local environments experienced by particles. In a BOOD, a particle and its nearest neighbors (determined by either a prespecified number of neighbors or simply a cutoff distance) are treated as connected by a bond joining their centers. All of the bonds in the system are then binned by their azimuthal (\(\theta\)) and polar (\(\phi\)) angles to indicate the location of a particle’s neighbors relative to itself. The distance between the particle and its neighbor is only important when determining whether it is counted as a neighbor, but is not part of the BOOD; as such, the BOOD can be viewed as a projection of all bonds onto the unit sphere. The resulting 2D histogram provides insight into how particles are situated relative to oneanother in a system.
This class provides access to the classical BOOD as well as a few useful variants. These variants can be accessed via the
mode
arguments to thecompute()
method. Available modes of calculation are:'bod'
(Bond Order Diagram, default): This mode constructs the default BOOD, which is the 2D histogram containing the number of bonds formed through each azimuthal \(\left( \theta \right)\) and polar \(\left( \phi \right)\) angle.'lbod'
(Local Bond Order Diagram): In this mode, a particle’s neighbors are rotated into the local frame of the particle before the BOOD is calculated, i.e. the directions of bonds are determined relative to the orientation of the particle rather than relative to the global reference frame. An example of when this mode would be useful is when a system is composed of multiple grains of the same crystal; the normal BOOD would show twice as many peaks as expected, but using this mode, the bonds would be superimposed.'obcd'
(Orientation Bond Correlation Diagram): This mode aims to quantify the degree of orientational as well as translational ordering. As a first step, the rotation that would align a particle’s neighbor with the particle is calculated. Then, the neighbor is rotated around the central particle by that amount, which actually changes the direction of the bond. One example of how this mode could be useful is in identifying plastic crystals, which exhibit translational but not orientational ordering. Normally, the BOOD for a plastic crystal would exhibit clear structure since there is translational order, but with this mode, the neighbor positions would actually be modified, resulting in an isotropic (disordered) BOOD.'oocd'
(Orientation Orientation Correlation Diagram): This mode is substantially different from the other modes. Rather than compute the histogram of neighbor bonds, this mode instead computes a histogram of the directors of neighboring particles, where the director is defined as the basis vector \(\hat{z}\) rotated by the neighbor’s quaternion. The directors are then rotated into the central particle’s reference frame. This mode provides insight into the local orientational environment of particles, indicating, on average, how a particle’s neighbors are oriented.
 Parameters
bins (unsigned int or sequence of length 2) – If an unsigned int, the number of bins in \(\theta\) and \(\phi\). If a sequence of two integers, interpreted as
(num_bins_theta, num_bins_phi)
.mode (str, optional) – Mode to calculate bond order. Options are
'bod'
,'lbod'
,'obcd'
, or'oocd'
(Default value ='bod'
).

bin_centers
¶ The centers of each bin in the histogram (has the same shape as the histogram itself).
 Type

property
bin_counts
¶ The bin counts in the histogram.
 Type

bin_edges
¶ The edges of each bin in the histogram (is one element larger in each dimension than the histogram because each bin has a lower and upper bound).
 Type

property
bond_order
¶ Bond order.
 Type
\(\left(N_{\phi}, N_{\theta} \right)\)
numpy.ndarray

bounds
¶ A list of tuples indicating upper and lower bounds of each axis of the histogram.

property
box
¶ Box used in the calculation.
 Type

compute
(self, system, orientations=None, query_points=None, query_orientations=None, neighbors=None, reset=True)¶ Calculates the correlation function and adds to the current histogram.
 Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.orientations ((\(N_{points}\), 4)
numpy.ndarray
) – Orientations associated with system points that are used to calculate bonds. Uses identity quaternions ifNone
(Default value =None
).query_points ((\(N_{query\_points}\), 3)
numpy.ndarray
, optional) – Query points used to calculate the correlation function. Uses the system’s points ifNone
(Default value =None
).query_orientations ((\(N_{query\_points}\), 4)
numpy.ndarray
, optional) – Query orientations used to calculate bonds. Usesorientations
ifNone
. (Default value =None
).neighbors (
freud.locality.NeighborList
or dict, optional) –Either a
NeighborList
of neighbor pairs to use in the calculation, or a dictionary of query arguments (Default value: None).reset (bool) – Whether to erase the previously computed values before adding the new computation; if False, will accumulate data (Default value: True).

default_query_args
¶ No default query arguments.

class
freud.environment.
EnvironmentCluster
¶ Bases:
freud.environment._MatchEnv
Clusters particles according to whether their local environments match or not, according to various shape matching metrics.

property
cluster_environments
¶ \(\left(N_{clusters}, N_{neighbors}, 3\right)\)
numpy.ndarray
): The environments for all clusters.

property
cluster_idx
¶ The perparticle index indicating cluster membership.
 Type
\(\left(N_{particles}\right)\)
numpy.ndarray

compute
(self, system, threshold, neighbors=None, env_neighbors=None, registration=False, global_search=False)¶ Determine clusters of particles with matching environments.
In general, it is recommended to specify a number of neighbors rather than just a distance cutoff as part of your neighbor querying when performing this computation. Using a distance cutoff alone could easily lead to situations where a point doesn’t match a cluster because a required neighbor is just outside the cutoff.
 Example::
>>> import freud >>> # Compute clusters of particles with matching environments >>> box, points = freud.data.make_random_system(10, 100, seed=0) >>> env_cluster = freud.environment.EnvironmentCluster() >>> env_cluster.compute( ... system = (box, points), ... threshold=0.2, ... neighbors={'num_neighbors': 6}, ... registration=False, ... global_search=False) freud.environment.EnvironmentCluster()
 Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.threshold (float) – Maximum magnitude of the vector difference between two vectors, below which they are “matching”. Typically, a good choice is between 10% and 30% of the first well in the radial distribution function (this has distance units).
neighbors (
freud.locality.NeighborList
or dict, optional) –Either a
NeighborList
of neighbor pairs to use in the calculation, or a dictionary of query arguments (Default value: None).env_neighbors (
freud.locality.NeighborList
or dict, optional) –Either a
NeighborList
of neighbor pairs to use in the calculation, or a dictionary of query arguments This argument is used to define the neighbors of the environment that motifs are registered against. IfNone
, the value provided forneighbors
will be used. (Default value: None).registration (bool, optional) – If True, first use brute force registration to orient one set of environment vectors with respect to the other set such that it minimizes the RMSD between the two sets. Enabling this option incurs a significant performance penalty. (Default value =
False
)global_search (bool, optional) – If True, do an exhaustive search wherein the environments of every single pair of particles in the simulation are compared. If False, only compare the environments of neighboring particles. Enabling this option incurs a significant performance penalty. (Default value =
False
)

default_query_args
¶ No default query arguments.

property
num_clusters
¶ The number of clusters.
 Type
unsigned int

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

property
point_environments
¶ \(\left(N_{points}, N_{neighbors}, 3\right)\)
numpy.ndarray
: All environments for all points.

property

class
freud.environment.
EnvironmentMotifMatch
¶ Bases:
freud.environment._MatchEnv
Find matches between local arrangements of a set of points and a provided motif.
In general, it is recommended to specify a number of neighbors rather than just a distance cutoff as part of your neighbor querying when performing this computation since it can otherwise be very sensitive. Specifically, it is highly recommended that you choose a number of neighbors query that requests at least as many neighbors as the size of the motif you intend to test against. Otherwise, you will struggle to match the motif. However, this is not currently enforced.

compute
(self, system, motif, threshold, neighbors=None, registration=False)¶ Determine clusters of particles that match the motif provided by motif.
 Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.motif ((\(N_{points}\), 3)
numpy.ndarray
) – Vectors that make up the motif against which we are matching.threshold (float) – Maximum magnitude of the vector difference between two vectors, below which they are “matching”. Typically, a good choice is between 10% and 30% of the first well in the radial distribution function (this has distance units).
neighbors (
freud.locality.NeighborList
or dict, optional) –Either a
NeighborList
of neighbor pairs to use in the calculation, or a dictionary of query arguments (Default value: None).registration (bool, optional) – If True, first use brute force registration to orient one set of environment vectors with respect to the other set such that it minimizes the RMSD between the two sets (Default value = False).

default_query_args
¶ No default query arguments.

property
matches
¶ A boolean array indicating whether each point matches the motif.
 Type
\((N_points, )\)
numpy.ndarray

property
point_environments
¶ \(\left(N_{points}, N_{neighbors}, 3\right)\)
numpy.ndarray
: All environments for all points.


class
freud.environment.
LocalBondProjection
¶ Bases:
freud.locality._PairCompute
Calculates the maximal projection of nearest neighbor bonds for each particle onto some set of reference vectors, defined in the particles’ local reference frame.

compute
(self, system, orientations, proj_vecs, query_points=None, equiv_orientations=np.array([[1, 0, 0, 0]]), neighbors=None)¶ Calculates the maximal projections of nearest neighbor bonds (between
points
andquery_points
) onto the set of reference vectorsproj_vecs
, defined in the local reference frames of thepoints
as defined by the orientationsorientations
. This computation accounts for the underlying symmetries of the reference frame as encoded inequiv_orientations
. Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.orientations ((\(N_{points}\), 4)
numpy.ndarray
) – Orientations associated with system points that are used to calculate bonds.proj_vecs ((\(N_{vectors}\), 3)
numpy.ndarray
) – The set of projection vectors, defined in the query particles’ reference frame, to calculate maximal local bond projections onto.query_points ((\(N_{query\_points}\), 3)
numpy.ndarray
, optional) – Query points used to calculate the correlation function. Uses the system’s points ifNone
(Default value =None
). (Default value =None
).equiv_orientations ((\(N_{equiv}\), 4)
numpy.ndarray
, optional) – The set of all equivalent quaternions that map the particle to itself (the elements of its rotational symmetry group). Important:equiv_orientations
must include both \(q\) and \(q\), for all included quaternions. Note that this calculation assumes that all points in the system share the same set of equivalent orientations. (Default value =[[1, 0, 0, 0]]
)neighbors (
freud.locality.NeighborList
or dict, optional) –Either a
NeighborList
of neighbor pairs to use in the calculation, or a dictionary of query arguments (Default value: None).

default_query_args
¶ No default query arguments.

property
nlist
¶ The neighbor list from the last compute.

property
normed_projections
¶ \(\left(N_{bonds}, N_{projection\_vecs} \right)\)
numpy.ndarray
: The projection of each bond between query particles and their neighbors onto each of the projection vectors, normalized by the length of the bond.

property
projections
¶ \(\left(N_{bonds}, N_{projection\_vecs} \right)\)
numpy.ndarray
: The projection of each bond between query particles and their neighbors onto each of the projection vectors.


class
freud.environment.
LocalDescriptors
¶ Bases:
freud.locality._PairCompute
Compute a set of descriptors (a numerical “fingerprint”) of a particle’s local environment.
The resulting spherical harmonic array will be a complexvalued array of shape
(num_bonds, num_sphs)
. Spherical harmonic calculation can be restricted to some number of nearest neighbors through themax_num_neighbors
argument; if a particle has more bonds than this number, the last one or more rows of bond spherical harmonics for each particle will not be set. This feature is useful for computing descriptors on the same system but with different subsets of neighbors; afreud.locality.NeighborList
with the correct ordering can then be reused in multiple calls tocompute()
with different values ofmax_num_neighbors
to compute descriptors for different local neighborhoods with maximum efficiency. Parameters
l_max (unsigned int) – Maximum spherical harmonic \(l\) to consider.
negative_m (bool, optional) – True if we should also calculate \(Y_{lm}\) for negative \(m\). (Default value =
True
)mode (str, optional) – Orientation mode to use for environments, either
'neighborhood'
to use the orientation of the local neighborhood,'particle_local'
to use the given particle orientations, or'global'
to not rotate environments (Default value ='neighborhood'
).

compute
(self, system, query_points=None, orientations=None, neighbors=None, max_num_neighbors=0)¶ Calculates the local descriptors of bonds from a set of source points to a set of destination points.
 Parameters
system – Any object that is a valid argument to
freud.locality.NeighborQuery.from_system
.query_points ((\(N_{query\_points}\), 3)
numpy.ndarray
, optional) – Query points used to calculate the correlation function. Uses the system’s points ifNone
(Default value =None
).orientations ((\(N_{points}\), 4)
numpy.ndarray
) – Orientations associated with system points that are used to calculate bonds.neighbors (
freud.locality.NeighborList
or dict, optional) –Either a
NeighborList
of neighbor pairs to use in the calculation, or a dictionary of query arguments (Default value: None).max_num_neighbors (unsigned int, optional) – Hard limit on the maximum number of neighbors to use for each particle for the given neighborfinding algorithm. Uses all neighbors if set to 0 (Default value = 0).

default_query_args
¶ No default query arguments.

l_max
¶ The maximum spherical harmonic \(l\) calculated for.
 Type
unsigned int

mode
¶ Orientation mode to use for environments, either
'neighborhood'
to use the orientation of the local neighborhood,'particle_local'
to use the given particle orientations, or'global'
to not rotate environments. Type

property
nlist
¶ The neighbor list from the last compute.

property
num_sphs
¶ The last number of spherical harmonics computed. This is equal to the number of bonds in the last computation, which is at most the number of
points
multiplied by the lower of thenum_neighbors
arguments passed to the last compute call or the constructor (it may be less if there are not enough neighbors for every particle). Type
unsigned int

property
sph
¶ \(\left(N_{bonds}, \text{SphWidth} \right)\)
numpy.ndarray
: The last computed spherical harmonic array.