Michael Friendly wrote > 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 > > ______________________________________________
> R-help@ > mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. Thank you for your reply. I think it is a good idea to calculate the volume in Monte-Carlo method. So the the problem change to be have to quantify whether a point is inside or outside of a region. Yes, it is easy to determine a point inside or outside a ellipsoid by seeing whether (x-x0)'Σ^(-1)(x-x0)-χ2p(α) is greater or smaller than zero, where x0 the point we want to test. but how can we test whether a point in other shapes of region(like the bounding box(R^p) as you said or the smallest convex hull(R^p) of X)? Finally, I aslo want to know how calculate the hypervolume of the bounding box (when P>3)? Thank you again. -- View this message in context: http://r.789695.n4.nabble.com/volume-of-ellipsoid-tp4680409p4680631.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
