If you’re crossproding X by itself, I think passing symmetric = TRUE to eigen will eke out more speed.
Avi On Mon, Aug 16, 2021 at 6:30 PM Radford Neal <radf...@cs.toronto.edu> wrote: > > Dario Strbenac <dstr7...@uni.sydney.edu.au> writes: > > > > I have a real scenario involving 45 million biological cells > > (samples) and 60 proteins (variables) which leads to a segmentation > > fault for svd. I thought this might be a good example of why it > > might benefit from a long vector upgrade. > > Rather than the full SVD of a 45000000x60 X, my guess is that you > may really only be interested in the eigenvalues and eigenvectors of > X^T X, in which case eigen(t(X)%*%X) would probably be much faster. > (And eigen(crossprod(X)) would be even faster.) > > Note that if you instead want the eigenvalues and eigenvectors of > X X^T (which is an enormous matrix), the eigenvalues of this are the > same as those of X^T X, and the eigenvectors are Xv, where v is an > eigenvector of X^T X. > > For example, with R 4.0.2, and the reference BLAS/LAPACK, I get > > > X<-matrix(rnorm(100000),10000,10) > > system.time(for(i in 1:1000) rs<-svd(X)) > user system elapsed > 2.393 0.008 2.403 > > system.time(for(i in 1:1000) re<-eigen(crossprod(X))) > user system elapsed > 0.609 0.000 0.609 > > rs$d^2 > [1] 10568.003 10431.864 10318.959 10219.961 10138.025 10068.566 > 9931.538 > [8] 9813.841 9703.818 9598.532 > > re$values > [1] 10568.003 10431.864 10318.959 10219.961 10138.025 10068.566 > 9931.538 > [8] 9813.841 9703.818 9598.532 > > Possibly some other LAPACK might implement svd better, though I > suspect that R will allocate more big matrices than really necessary > for the svd even aside from whatever LAPACK is doing. > > Regards, > > Radford Neal > > ______________________________________________ > R-devel@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-devel > -- Sent from Gmail Mobile [[alternative HTML version deleted]] ______________________________________________ R-devel@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
