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*, 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_speed * v_x d_y = timestep * p.ang_speed * v_y p.x += d_x p.y += d_y

We may notice 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 over the time ...

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