In this example, we are going to apply a couple of simple tricks and see how they impact the runtime. Assuming you've already defined the spheres in the previous example, you can enter and run the following code in a worksheet cell:
%time
import numpy
collisions_2 = numpy.zeros(num_particles, dtype=numpy.bool)
r_min = 4*radius**2
for i in range(num_particles):
for j in range(0,i):
r_squared = (x[i] - x[j])**2 + (y[i] - y[j])**2 + (z[i] - z[j])**2
if r_squared < r_min:
collisions_2[i] = True
for j in range(i+1,num_particles):
r_squared = (x[i] - x[j])**2 + (y[i] - y[j])**2 + (z[i] - z[j])**2
if r_squared < r_min:
collisions_2[i] = TrueThe code will print the runtime:
It's about twice as fast! Not bad for two minor changes. Now, try this:
%time
import numpy
collisions_3 = numpy.zeros(num_particles, dtype=numpy.bool)
r_min = 4*radius**2
for i in range(num_particles):
for...