[SciPy-User] random points within an ellipse
Tue Aug 10 11:26:10 CDT 2010
On Tue, Aug 10, 2010 at 12:11 PM, Erin Sheldon <email@example.com> wrote:
> Excerpts from nicky van foreest's message of Sun Aug 08 17:03:07 -0400 2010:
>> 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 -
> I think this version (from my original post) is fairly optimal:
> def get_random_ellipse(n, x0, y0):
> xout = numpy.zeros(n)
> yout = numpy.zeros(n)
> while nkeep < n:
> x=2*x0*(random.random(n-nkeep) - 0.5)
> y=2*y0*(random.random(n-nkeep) - 0.5)
> w,=where( ( (x/x0)**2 + (y/y0)**2 ) < 1 )
> if w.size > 0:
> xout[nkeep:nkeep+w.size] = x[w]
> yout[nkeep:nkeep+w.size] = y[w]
> nkeep += w.size
> return xout,yout
I would oversample if the rejection rate is around 20%
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