Rewriting the particle simulator in NumPy

In this section, we will optimize our particle simulator by rewriting some parts of it in NumPy. We found, from the profiling we did in Chapter 1, Benchmarking and Profiling, that the slowest part of our program is the following loop contained in the ParticleSimulator.evolve method:

    for i in range(nsteps): 
      for p in self.particles: 

        norm = (p.x**2 + p.y**2)**0.5 
        v_x = (-p.y)/norm 
        v_y = p.x/norm 

        d_x = timestep * p.ang_vel * v_x 
        d_y = timestep * p.ang_vel * v_y 

        p.x += d_x 
        p.y += d_y 

You may have noticed that the body of the loop acts solely on the current particle. If we had an array containing the particle positions and angular speed, we could rewrite the loop using a broadcasted operation. In contrast, the loop's steps depend on the previous step and cannot be parallelized in this way.

It is natural then, to store all the array coordinates in an array of shape (nparticles, 2...