[R] volume of ellipsoid

Michael Friendly friendly at yorku.ca
Fri Nov 15 15:16:01 CET 2013

On 11/14/2013 9:35 AM, yuanzhi wrote:
> Hi, Carl Witthoft
> yes, it looks like a mathematical question. I will try based on your
> suggestion to calculate the volume of the intersection. But I still want to
> know whether there are some functions in R which can calculate the volume of
> an ellipsoid(area for p=2, hypervolume for p>3) containing X, just like the
> "convhulln" function in "geometry" package which can calculate the volume of
> convex hull containing X.

See the Appendix A.2 in my paper on Elliptical Insights ...

for the properties of ellipsoids and calculation of (hyper)volumes
based on a spectral decomposition.

The intersection of general ellipsoids is mathematically extremely 
complex.  You can approximate it by acceptance sampling -- finding the
proportion of random points in R^p in the bounding box of the ellipsoids 
which are contained in both.

Michael Friendly     Email: friendly AT yorku DOT ca
Professor, Psychology Dept. & Chair, Quantitative Methods
York University      Voice: 416 736-2100 x66249 Fax: 416 736-5814
4700 Keele Street    Web:   http://www.datavis.ca
Toronto, ONT  M3J 1P3 CANADA

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