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Numerical Integration using random sampling (Python recipe) by FB36
ActiveState Code (http://code.activestate.com/recipes/577276/)

Numerical Integration using random sampling.

Python, 21 lines
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# Numerical Integration using random sampling
# FB - 201006292
import math
import random

# define any function here!
def f(x):
    return math.sin(x)

# define any xmin-xmax interval here! (xmin < xmax)
xmin = 0.0
xmax = math.pi

numPoints = 1000000 # bigger the better but slower!
sumy = 0.0
for j in range(numPoints):
    x = xmin + (xmax - xmin) * random.random()
    sumy += f(x)

numInt = (xmax - xmin) * sumy / numPoints     
print "Numerical integral = " + str(numInt)
Tags: math, random

3 comments

Dieter Kadelka 13 years, 9 months ago  # | flag

What is this? Is it a try to find the worst numerical integration algorithm? If you replace random.random() by equidistant 1.0*j/numPoints you get the integral 2.0. Not to mention the almost trivial Simpson algorithm and much more better more sophisticated algorithms.

FB36 (author) 13 years, 9 months ago  # | flag

I never claimed my algorithm is the best. I only post this thinking some people may find it interesting, that's all.

I also think it would be better if you post the best algorithm code, instead of simply criticizing others!

Dieter Kadelka 13 years, 9 months ago  # | flag

If you have interest in good algorithms in python, give pygsl and the gsl library in gnu a chance