Rfast hd.eigen() returns NAs but base eigen() does not

问题

I am having problems with hd.eigen in Rfast. It gives extremely close results to eigen with most data, but sometimes hd.eign returns an empty $vector, NAs, or other undesirable results. For example:

> set.seed(123)
> bigm <- matrix(rnorm(2000*2000,mean=0,sd = 3), 2000, 2000)
> 
> e3 = eigen(bigm)
> length(e3$values)
[1] 2000
> length(e3$vectors)
[1] 4000000
> sum(is.na(e3$vectors) == TRUE)
[1] 0
> sum(is.na(e3$vectors) == FALSE)
[1] 4000000
> 
> e4 = hd.eigen(bigm, vectors = TRUE)
> length(e4$values)
[1] 2000
> length(e4$vectors)
[1] 4000000
> sum(is.na(e4$vectors) == TRUE)
[1] 2000
> sum(is.na(e4$vectors) == FALSE)
[1] 3998000

Other than the fact that it breaks my script, do these NAs indicate a deeper problem with my data? Or is hd.eig not able to handle some situations that the stock eigen() can? Is one better than the other?

Edit: As per Ralf's suggestion, I checked my BLAS versions, and it does seem like maybe R is looking for the wrong version/in the wrong place:

~ $ ldd /usr/lib64/R/bin/exec/R
        linux-vdso.so.1 (0x00007ffeec3b9000)
        libR.so => not found
        libRblas.so => not found
        libgomp.so.1 => /usr/lib64/libgomp.so.1 (0x00007feb27ef2000)
        libpthread.so.0 => /usr/lib64/libpthread.so.0 (0x00007feb27ecf000)
        libc.so.6 => /usr/lib64/libc.so.6 (0x00007feb27cdb000)
        /lib64/ld-linux-x86-64.so.2 => /usr/lib64/ld-linux-x86-64.so.2 (0x00007feb27f7b000)

Also, I am unclear on whether openBLAS is equivalent to the BLAS that is installed by default in other distros.

> sessionInfo()
R version 3.6.1 (2019-07-05)
Platform: x86_64-generic-linux-gnu (64-bit)
Running under: Clear Linux OS

Matrix products: default
BLAS/LAPACK: /usr/lib64/libopenblas_nehalemp-r0.3.6.so

edit 2: I tried the same example on a CentOS-based HPC system, and did not get any NA's. There, sessionInfo() reveals:

BLAS/LAPACK: /hpc/packages/minerva-centos7/intel/parallel_studio_xe_2019/compilers_and_libraries_2019.0.117/linux/mkl/lib/intel64_lin/libmkl_gf_lp64.so

Edit 3: The expression in hd.eign that produces the NAs is

vectors <- tcrossprod(y, t(FF) * L^(-0.5))

specifically, L^(-0.5) produces NaN at index 2000

> L[2000]
[1] -1.136237e-12

However, on the two machines where no NAs are returned L[2000] is positive (although slightly different, 5.822884e-14 on the HPC system and 3.022511e-12 on my Windows machine running Microsoft build of R.

Edit 4: The difference appears to originate in the base eigen() function, which returns one negative value from the crossprod() matrix xx on the problem machine but not not the other two. I saved the xx object and opened between computers, so I know that the input to eigen() was exactly the same.

Edit 5: I drilled one level deeper and found that the original negative value comes from this statement in eigen()

    z <- if (!complex.x) 
      .Internal(La_rs(x, only.values))
    else .Internal(La_rs_cmplx(x, only.values))

Edit 6: If I save as a CSV and then re-open, the problem computer does not produce negative eigenvalues.

> load("/home/james/nfs-cloud/PanosLab/CircRNA/input_to_La_rs.Rdata")
> r <- .Internal(La_rs(as.matrix(x), only.values = FALSE))
> sum(r$values < 0)
[1] 1
> write.csv(x, "test_for_internal.csv", row.names = FALSE)
> x <- read.csv("test_for_internal.csv")
> r <- .Internal(La_rs(as.matrix(x), only.values = FALSE))
> sum(r$values < 0)
[1] 0

Does that give anyone a clue? Is this a bug?

回答1:

The hd.eigen function in Rfast is designed for the case of n smaller than p only.

来源：https://stackoverflow.com/questions/57935571/rfast-hd-eigen-returns-nas-but-base-eigen-does-not

标签

eigenvector

matrix-decomposition