# Compute Classes¶

Calculations in freud are built around the concept of Compute classes, Python objects that encode a given method and expose it through a compute method. In general, these methods operate on a system composed of a triclinic box and a NumPy array of particle positions. The box can be provided as any object that can be interpreted as a freud box (as demonstrated in the examples above). We can look at the freud.order.Hexatic order parameter calculator as an example:

import freud
positions = ...  # Read positions from trajectory file.
op = freud.order.Hexatic(k=6)
op.compute(
system=({'Lx': 5, 'Ly': 5, 'dimensions': 2}, positions),
neighbors=dict(r_max=3)
)

# Plot the value of the order parameter.
from matplotlib import pyplot as plt
plt.hist(np.absolute(op.particle_order))


Here, we are calculating the hexatic order parameter, then using Matplotlib to plot. The freud.order.Hexatic class constructor accepts a single argument k, which represents the periodicity of the calculation. If you’re unfamiliar with this order parameter, the most important piece of information here is that many compute methods in freud require parameters that are provided when the Compute class is constructed.

To calculate the order parameter we call compute, which takes two arguments, a tuple (box, points) and a dict. We first focus on the first argument. The box is any object that can be coerced into a freud.box.Box as described in the previous section; in this case, we use a dictionary to specify a square (2-dimensional) box. The points must be anything that can be coerced into a 2-dimensional NumPy array of shape (N, 3) In general, the points may be provided as anything that can be interpreted as an $$N\times 3$$ list of positions; for more details on valid inputs here, see numpy.asarray(). Note that because the hexatic order parameter is designed for two-dimensional systems, the points must be provided of the form [x, y, 0] (i.e. the z-component must be 0). We’ll go into more detail about the (box, points) tuple soon, but for now, it’s sufficient to just think of it as specifying the system of points we want to work with.

Now let’s return to the neighbors argument to compute, which is a dictionary is used to determine which particle neighbors to use. Many computations in freud (such as the hexatic order parameter) involve the bonds in the system (for example, the average length of bonds or the average number of bonds a given point has). However, the concept of a bond is sufficiently variable between different calculations; for instance, should points be considered bonded if they are within a certain distance of each other? Should every point be considered bonded to a fixed number of other points?

To accommodate this variability, freud offers a very general framework by which bonds can be specified, and we’ll go into more details in the next section. In the example above, we’ve simply informed the Hexatic class that we want it to define bonds as pairs of particles that are less than 3 distance units apart. We then access the computed order parameter as op.particle_order (we use np.absolute() because the output is a complex number and we just want to see its magnitude).

## Accessing Computed Properties¶

In general, Compute classes expose their calculations using properties. Any parameters to the Compute object (e.g. k in the above example) can typically be accessed as soon as the object is constructed:

op = freud.order.Hexatic(k=6)
op.k


Computed quantities can also be accessed in a similar manner, but only after the compute method is called. For example:

op = freud.order.Hexatic(k=6)

# This will raise an exception.
op.particle_order

op.compute(
system=({'Lx': 5, 'Ly': 5, 'dimensions': 2}, positions),
neighbors=dict(r_max=3)
)

# Now you can access this.
op.particle_order


Note

Most (but not all) of freud’s Compute classes are Python wrappers around high-performance implementations in C++. As a result, none of the data or the computations is actually stored in the Python object. Instead, the Python object just stores an instance of the C++ object that actually owns all its data, performs calculations, and returns computed quantities to the user. Python properties provide a nice way to hide this logic so that the Python code involves just a few lines.

Compute objects is that they can be used many times to calculate quantities, and the most recently calculated output can be accessed through the property. If you need to perform a series of calculations and save all the data, you can also easily do that:

# Recall that lists of length 2 automatically convert to 2D freud boxes.
box = [5, 5]

op = freud.order.Hexatic(k=6)

# Assuming that we have a list of Nx3 NumPy arrays that represents a
# simulation trajectory, we can loop over it and calculate the order
# parameter values in sequence.
trajectory  = ...  # Read trajectory file into a list of positions by frame.
hexatic_values = []
for points in trajectory:
op.compute(system=(box, points), neighbors=dict(r_max=3))
hexatic_values.append(op.particle_order)


To make using freud as simple as possible, all Compute classes are designed to return self when compute is called. This feature enables a very concise method-chaining idiom in freud where computed properties are accessed immediately:

particle_order = freud.order.Hexatic(k=6).compute(
system=(box, points)).particle_order