This looks like a variant of the Woodbury formula http://en.wikipedia.org/wiki/Woodbury_matrix_identity
On Thu, Aug 14, 2014 at 2:57 AM, Peter Brady <subscripti...@simonplace.net> wrote: > Hi All, > > I've inherited some R code that I can't work out what they've done. It > appears to work and give sort of reasonable answers, I'm just trying to > work out why they've done what they have. I suspect that this is a > simple vector identity that I've just been staring at too long and have > forgotten... > > The code: > > GGt <- M0 - M1 %*% M0inv %*% t(M1) > svdGG <- svd(GGt) > Gmat <- svdGG$u %*% diag(sqrt(svdGG$d)) > > It is supposed to solve: > > G*G^T = M0 - M1*M0^-1*M1^T > > for G, where G^T is the transpose of G. It is designed to reproduce a > numerical method described in two papers: > > Srikanthan and Pegram, Journal of Hydrology, 371 (2009) 142-153, > Equation A13, who suggest the SVD method but don't describe the > specifics, eg: "...G is found by singular value decomposition..." > > Alternatively, Matalas (1967) Water Resources Research 3 (4) 937-945, > Equation 17, say that the above can be solved using Principle Component > Analysis (PCA). > > I use PCA (specifically POD) and SVD to look at the components after > decomposition, so I'm a bit lost as to how the original matrix G can be > constructed in this case from only the singular values and the left > singular vectors. Like I said earlier, I suspect that this is a simple > array identity that I've forgotten. My Google Fu is letting me down at > this point. > > My questions: > 1) What is the proof, or where can I better find it to satisfy myself, > that the above works? > > 2) Alternatively, can anyone suggest how I could apply PCA in R to > compute the same? > > Thanks in advance, > -pete > > -- > Peter Brady > Email: pdbr...@ans.com.au > Skype: pbrady77 > > ______________________________________________ > 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. ______________________________________________ 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.
