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 ...
http://www.datavis.ca/papers/ellipses-STS402.pdf
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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