A simple tool to perform numerical integration using Monte Carlo techniques.

## Project description

========================

Monte Carlo integrator

========================

This package provides a Monte Carlo integrator which can be used to evaluate

multi-dimensional integrals. The results are numerical approximations which are

dependent on the use of random number generation.

Example 1

=========

In this example we compute :math:`\int_0^1 x^2 dx`::

import mcint

import random

def integrand(x): # Describe the function being integrated

return (x**2)

def sampler(): # Describe how Monte Carlo samples are taken

while True:

yield random.random()

result, error = mcint.integrate(integrand, sampler(), measure=1.0, n=100)

print "The integral of x**2 between 0 and 1 is approximately", result

The second argument to the integrate() function should be an iterable

expression, in this case it is a generator. We could do away with this sampler

using the following::

result, error = mcint.integrate(integrand, iter(random.random, -1), measure=1.0, n=100)

This creates an iterable object from the random.random() function which will

continuously call random.random() until it returns -1 (which it will never do as

it returns values between 0.0 and 1.0.

Example 2

=========

In this example we compute :math:`\int_0^1 \int_0^\sqrt{1-y^2} x^2+y^2 dx dy`::

import mcint

import random

import math

def integrand(x):

return (x[0]**2 + x[1]**2)

def sampler():

while True:

y = random.random()

x = random.random()

if x**2+y**2 <= 1:

yield (x,y)

result, error = mcint.integrate(integrand, sampler(), measure=math.pi/4)

Monte Carlo integrator

========================

This package provides a Monte Carlo integrator which can be used to evaluate

multi-dimensional integrals. The results are numerical approximations which are

dependent on the use of random number generation.

Example 1

=========

In this example we compute :math:`\int_0^1 x^2 dx`::

import mcint

import random

def integrand(x): # Describe the function being integrated

return (x**2)

def sampler(): # Describe how Monte Carlo samples are taken

while True:

yield random.random()

result, error = mcint.integrate(integrand, sampler(), measure=1.0, n=100)

print "The integral of x**2 between 0 and 1 is approximately", result

The second argument to the integrate() function should be an iterable

expression, in this case it is a generator. We could do away with this sampler

using the following::

result, error = mcint.integrate(integrand, iter(random.random, -1), measure=1.0, n=100)

This creates an iterable object from the random.random() function which will

continuously call random.random() until it returns -1 (which it will never do as

it returns values between 0.0 and 1.0.

Example 2

=========

In this example we compute :math:`\int_0^1 \int_0^\sqrt{1-y^2} x^2+y^2 dx dy`::

import mcint

import random

import math

def integrand(x):

return (x[0]**2 + x[1]**2)

def sampler():

while True:

y = random.random()

x = random.random()

if x**2+y**2 <= 1:

yield (x,y)

result, error = mcint.integrate(integrand, sampler(), measure=math.pi/4)

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