Monte Carlo simulation to estimate the value of Pi

monte-carlo-pi.md

monte-carlo-pi

Monte Carlo simulation to estimate the value of Pi

Runtime

Original Python 2 version

time python monte-carlo-pi.py
3.142226
python monte-carlo-pi.py  85.65s user 0.86s system 96% cpu 1:29.93 total

Python 3 single-processor version

time python monte-carlo-pi.py 
3.1410804
python monte-carlo-pi.py  60.82s user 0.55s system 98% cpu 1:02.55 total

monte-carlo-pi.py

""" Monte Carlo simulation to calculate Pi

Usage:
        monte-carlo-pi.py [--sample-size=<n>] [--seed=<seed>]
        monte-carlo-pi.py [--help]

Options:
    -h --help                 Display this help message.
    -n <n> --sample-size=<n>  The sample size [default: 1e7].
    --seed=<seed>             Random seed for testing purposes.
"""
import docopt
import numpy as np

def main(args):
    if args['--seed']:
        np.random.seed(int(args['--seed']))
    sample_size = int(args['--sample-size'])
    space = np.random.rand(sample_size, 2)
    radius = 1
    num_points_within_radius = sum(1 for x, y in space if np.sqrt(x**2 + y**2) <= radius)
    area_ratio = num_points_within_radius / sample_size
    pi = 4 * area_ratio / radius**2
    print(pi)

if __name__ == "__main__":
    arguments = docopt.docopt(__doc__)
    main(arguments)