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Topic: uniform sampling in multi-dimensional ellipsoid
Replies: 1   Last Post: Aug 2, 2013 2:40 PM

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Hossein

Posts: 1
Registered: 5/4/12
uniform sampling in multi-dimensional ellipsoid
Posted: May 4, 2012 9:30 AM
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I'm looking for a method to uniformly sample within an ellipsoid in an n-dimensional space given by:
(x-m)^T * (R^-1) * (x-m) <= 1
where m is the vector specifying the center of the ellipsoid and R is a positive semi-definite matrix specifying how and in what directions the ellipsoid will be stretched (determined by eigenvalues and eigenvectors).

I'm also looking for a method not based on rejection sampling, since in higher dimensions the number of rejected points will increase dramatically.



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