You could save the space required to store the inverse of A by repeating solve(A,column) for each column of an identity matrix the size of A, and store just the relevant element of the result. E.g.,
> diag(solve(A)) [1] 0.39576620 0.12064108 0.20705171 0.10067892 0.03191425 0.05857497 0.10749426 0.03868911 0.08550176 > sapply(seq_len(nrow(A)), function(i)solve(A, seq_len(nrow(A))==i)[i]) [1] 0.39576620 0.12064108 0.20705171 0.10067892 0.03191425 0.05857497 0.10749426 0.03868911 0.08550176 It may take more time that you would like. Bill Dunlap Spotfire, TIBCO Software wdunlap tibco.com > -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On > Behalf > Of Camarda, Carlo Giovanni > Sent: Monday, April 22, 2013 1:51 AM > To: Greg Snow > Cc: r-h...@stat.math.ethz.ch > Subject: Re: [R] extracting the diagonal of an inverse matrix > > Dear Greg, > > thanks a lot for your prompt reply. I was aware of the link and the > associated papers. > In my previous mail I was wondering whether there was already an R-routine > for coping > with this issue. > > I add below a testable example which reproduces my problem. > > Thanks again, > Giancarlo > > ## dimensions (my actual dimensions are much larger and I use sparse matrices) > m <- 3 > n <- 3 > ## building A > ## diagonal part > d <- 1:(m*n) > D <- diag(d) > ## additional ~dense part (:penalty term) > P1 <- diff(diag(m), diff=2) > P2 <- diff(diag(n), diff=2) > P1a <- kronecker(diag(n), t(P1)%*%P1) > P2a <- kronecker(t(P2)%*%P2, diag(m)) > P <- 1000 * P1a + 1000 * P2a > ## final matrix A > A <- D + P > ## solving A > B <- solve(A) > ## what I just actually need > diag(B) > > > ________________________________________ > From: Greg Snow [538...@gmail.com] > Sent: Saturday, April 20, 2013 12:16 AM > To: Camarda, Carlo Giovanni > Cc: r-h...@stat.math.ethz.ch > Subject: Re: [R] extracting the diagonal of an inverse matrix > > This link > http://math.stackexchange.com/questions/18488/diagonal-of-an-inverse-of-a- > sparse-matrix might help. It is about sparse matrices, but the general idea > should be able > to be extended to non-sparse matrices as well. > > > On Fri, Apr 19, 2013 at 8:13 AM, Camarda, Carlo Giovanni > <cama...@demogr.mpg.de<mailto:cama...@demogr.mpg.de>> wrote: > Dear R-users, > > I would like to know whether there is a way to extract a diagonal of an > inverse matrix > without computing the inverse of the matrix itself. The size of my matrices > are really > huge and, also using sparse matrix, computing the inverse leads to storage > problems and > low speed. > > In other words, given a square matrix A, I aim to know diag(B), where > B=solve(A), > without computing solve(A). > > Accidentally (I do not know whether it helps), I could write the matrix A as > follows: > A <- D + P > where D is a diagonal matrix. > > I read there are methods around, but, before implementing one of them by > myself, could > you please inform whether there is already an R-routine for this issue? > > Thanks in advance for the help you could provide, > Carlo Giovanni Camarda > ---------- > This mail has been sent through the MPI for Demographic ...{{dropped:19}} > > ______________________________________________ > 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.
