Chapter 5, example 2

Here we show how to parallelize a simple Monte-Carlo simulation for estimating pi.

This function counts the number of points within a quarter of disc centered at the origin, among all points randomly sampled within the unit square.



In [1]:

    
def sample(n):
    return (rand(n) ** 2 + rand(n) ** 2 <= 1).sum()

Pi is approximately equal to four times the ratio of points within that quarter of disc.



In [2]:

    
n = 1000000.
4 * sample(n) / n









    Out[2]:





3.1425920000000001

Now, we create a parallel client and import the rand function on all engines.



In [3]:

    
from IPython.parallel import Client
rc = Client()
v = rc[:]
with v.sync_imports():
    from numpy.random import rand









    



importing rand from numpy.random on engine(s)

Finally, we execute the simulation in parallel over all engines (each engine samples n points, and there are nk points in total if there are k engines), and we combine the results (reduce operation).



In [4]:

    
4 * sum(v.map_sync(sample, [n] * len(v))) / (n * len(v))









    Out[4]:





3.1406360000000002