Monte Carlo Method in Python

Question

I've been attempting to use Python to create a script that lets me generate large numbers of points for use in the Monte Carlo method to calculate an estimate to Pi. The script I have so far is this:

import math
import random
random.seed()

n = 10000

for i in range(n):
    x = random.random()
    y = random.random()
    z = (x,y)

    if x**2+y**2 <= 1:
        print z
    else:
        del z

So far, I am able to generate all of the points I need, but what I would like to get is the number of points that are produced when running the script for use in a later calculation. I'm not looking for incredibly precise results, just a good enough estimate. Any suggestions would be greatly appreciated.

Answer 1

If you're doing any kind of heavy duty numerical calculation, considering learning numpy. Your problem is essentially a one-linear with a numpy setup:

import numpy as np

N   = 10000
pts = np.random.random((N,2))

# Select the points according to your condition
idx = (pts**2).sum(axis=1)  < 1.0
print pts[idx], idx.sum()

Giving:

[[ 0.61255615  0.44319463]
 [ 0.48214768  0.69960483]
 [ 0.04735956  0.18509277]
 ..., 
 [ 0.37543094  0.2858077 ]
 [ 0.43304577  0.45903071]
 [ 0.30838206  0.45977162]], 7854

The last number is count of the number of events that counted, i.e. the count of the points whose radius is less than one.