eigs problem

[xshi19]

Hi Yixuan,

I find a problem with eigs(). I generate a simple Hankel matrix H and define a function myfun() which returns H%*%x. eigs() works well if the first argument is H. But when the first argument becomes myfun() it produces following error:

Warning message:
In eigs.fun(A, k, which, sigma, opts, ..., mattype = "function", :
no converged eigenvalues found

The problem can be solved by setting retvec = FALSE or ncv = nrow(H), but it would be extremely slow if the dimension is high.

Thanks!

Here is my code:

library('rARPACK')
library('igraph')

myfun <- function(x, H) {
return(H %*% x)
}

hankel <- function(x, y = NULL) {

Generate Hankel matrix using outer product

m = length(x)
if (is.null(y)) {
y = rep(0, m)
}
n = length(y)
h = c(x, y[2:n])
H = outer(1:m, 1:n, function(u, v) h[u + v - 1])
return(H)
}

n = 100
h = 1 / sqrt(1:n)
H = hankel(h)
ord = 10

r1 = eigs(H, k = ord)
r2 = arpack(myfun, extra = H, sym = TRUE, options = list(n = n, nev = ord, ncv = 20))
r3 = eigs(myfun, k = ord, n = length(h), args = H)

[yixuan]

Thanks @xshi19 , I'll look into this problem shortly.

[yixuan]

This seems to be a known problem that retvec = TRUE and retvec = FALSE can give different results. It is somewhat related to the ARPACK library, and should be fixed either by updating ARPACK included in the source, or using a rewritten C++ version that I'm working on.
I would try to fix it in the next version of rARPACK. Thanks for your report.

[yixuan]

Hi @xshi19
This issue has been resolved in the development version of rARPACK. I added a symmetric argument in eigs.function() to force using a symmetric eigen solver.

## This will correctly return complex-typed eigenvalues
## with imaginary parts being zero
r3 = eigs(myfun, k = ord, n = length(h), args = H)
## Directly return real-typed eigenvalues since we use a symmetric eigensolver
r4 = eigs(myfun, k = ord, n = length(h), args = H, symmetric = TRUE)

You can install the new version from github or waiting for a CRAN version.