# [SciPy-User] random points within an ellipse

nicky van foreest vanforeest@gmail....
Sun Aug 8 16:03:07 CDT 2010

```Hi,

Good idea to include the graphical result.

I must admit that the results of the latest mail by David do not
satisfy my "random intuition". There is a thick cloud around the
origin, which seems unnatural to me.

Just for fun I implemented a rejection method that seems to give good
results. From an algorithmic perspective my implementation is far from
optimal (BTW, I welcome feedback on how to speed up code like this.)
However, the rejection method does not seem that bad, roughly 20% of
the numbers is rejected, and there is no need to compute cosines and
the like. The resulting graph seems ok to me.

I modified the example of DG somewhat for the example below.

Nicky

#!/usr/bin/env python

import numpy as np
from numpy.random import random_sample as random

a = 1.; b = 0.5

def inEllipse(x,y):
return (x/a)**2 + (y/b)**2 < 1.  # taking sqrt is unnecessary

num = 1e4
x = -a + 2*a*random(num)
y = -b + 2*b*random(num)

sample = []
reject = 0
for xx, yy in zip(x,y):
if inEllipse(xx,yy):
sample.append([xx,yy])
else:
reject += 1

print reject
sample = np.array(sample)

import matplotlib.pyplot as plt

fig = plt.figure()

ax.scatter(sample[:,0], sample[:,1])

plt.show() # Figure attached
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```