[Rd] svd for Large Matrix
Radford Neal
r@d|ord @end|ng |rom c@@toronto@edu
Mon Aug 16 17:30:32 CEST 2021
> Dario Strbenac <dstr7320 using 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
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