johnjax - 3 months ago 14
Python Question

# Optimizing Python distance calculation while accounting for periodic boundary conditions

I have written a Python script to calculate the distance between two points in 3D space while accounting for periodic boundary conditions. The problem is that I need to do this calculation for many, many points and the calculation is quite slow. Here is my function.

``````def PBCdist(coord1,coord2,UC):
dx = coord1[0] - coord2[0]
if (abs(dx) > UC[0]*0.5):
dx = UC[0] - dx
dy = coord1[1] - coord2[1]
if (abs(dy) > UC[1]*0.5):
dy = UC[1] - dy
dz = coord1[2] - coord2[2]
if (abs(dz) > UC[2]*0.5):
dz = UC[2] - dz
dist = np.sqrt(dx**2 + dy**2 + dz**2)
return dist
``````

I then call the function as so

``````for i, coord2 in enumerate(coordlist):
do something with i
``````

Recently I read that I can greatly increase performance by using list comprehension. The following works for the non-PBC case, but not for the PBC case

``````coord_indices = [i for i, y in enumerate([np.sqrt(np.sum((coord2-coord1)**2)) for coord2 in coordlist]) if y < radius]
for i in coord_indices:
do something
``````

Is there some way to do the equivalent of this for the PBC case? Is there an alternative that would work better?

You should write your `distance()` function in a way that you can vectorise the loop over the 5711 points. The following implementation accepts an array of points as either the `x0` or `x1` parameter:

``````def distance(x0, x1, dimensions):
delta = numpy.abs(x0 - x1)
delta = numpy.where(delta > 0.5 * dimensions, delta - dimensions, delta)
return numpy.sqrt((delta ** 2).sum(axis=-1))
``````

Example:

``````>>> dimensions = numpy.array([3.0, 4.0, 5.0])
>>> points = numpy.array([[2.7, 1.5, 4.3], [1.2, 0.3, 4.2]])
>>> distance(points, [1.5, 2.0, 2.5], dimensions)
array([ 2.22036033,  2.42280829])
``````

The result is the array of distances between the points passed as second parameter to `distance()` and each point in `points`.