# NA in eigen()

Elizabeth Purdom epurdom at stanford.edu
Fri Mar 3 21:41:53 CET 2006

```Hi,
I am using eigen to get an eigen decomposition of a square, symmetric
matrix. For some reason, I am getting a column in my eigen vectors (the
52nd column out of 601) that is a column of all NAs. I am using the option,
symmetric=T for eigen. I just discovered that I do not get this behavior
when I use the option EISPACK=T. With EISPACK=T, the 52nd eigenvector is
(up to rounding error) a vector of all zeros except for  -0.6714
and  +0.6714 in two locations. The eigenvalues (which are the same with
either one) has the 52nd eigenvalue being exactly 19. I also do not have
the NA problem if I choose symmetric=F.

My main question is whether there is any reason I should not use the
EISPACK option (I do not know that what the EISPACK option really means,
except that its not "preferred")? Or stated another way, should I trust
that the results for EISPACK=T, and just ignore the very odd behavior of
EISPACK=F? Or is there something inherently problematic or unstable about
my eigen decomposition of this matrix -- and if so, is it my matrix or the
program?

I have no idea what's causing it, and I can't get a reproducible example,
other than with my large matrix. My original matrix has no NAs in it. Here
is code, but of course it requires my original, 601x601 symmetric matrix
called mat

> any(is.na(mat))
[1] FALSE
> any(is.na(d))
[1] FALSE
> dim(mat)
[1] 601 601
> length(which(d==0))
[1] 5
> d<-rowSums(mat)
> temp1<-eigen(diag(d)-mat,symmetric=T)
> temp2<-eigen(diag(d)-mat,symmetric=T,EISPACK=T)
> any(is.na(temp1\$vec))
[1] TRUE
> any(is.na(temp1\$vec[,-52]))
[1] FALSE
> any(is.na(temp2\$vec))
[1] FALSE
> all.equal(abs(temp1\$vec[,-52]),abs(temp2\$vec[,-52]))
[1] "Mean relative  difference: 0.3278133"
> all.equal(temp1\$val,temp2\$val)
[1] TRUE
> temp2\$val[52]
[1] 19

Thanks,
Elizabeth

```