Rewriting the particle simulator in NumPy

In this section, we will optimize our particle simulator by rewriting some parts of it in NumPy. From the profiling we did in Chapter 1, Benchmarking and Profiling, we found that the slowest part of our program is the following loop, which is 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...