Missing function name eigs

[jpfairbanks]

Hi @haampie, is there a reason this package doesn't export a function eigs satisfying the old interface?

it looks like the correct way to use it is

function eigs(A; kwargs)
     schur_to_eigen(partial_schur(A; kwargs...)[1])
end

Is there something else to it?

[haampie]

Hey, yes, I should still write the utility functions. Right now the API is more or less similar to ARPACK (a function for matrix -> schur and one that does some post-processing with partial schur -> eigen). The eigs function in Arpack.jl is actually implemented in Julia itself and does more or less what you have there.

[jpfairbanks]

Here is the version that is working for me in LG.

function eigs(A; kwargs...)
    schr =partialschur(A; kwargs...)
    vals, vectors = partialeigen(schr[1])
    reved = (kwargs[:which] == LR() || kwargs[:which] == LM())
    k = get(kwargs, :nev, length(vals))
    k = min(k, length(vals))
    perm = 1:k
    if vals[1] isa(Real)
        perm = sortperm(vals, rev=reved)
        perm = perm[1:k]
    end
    λ = vals[perm]
    Q = vectors[:, perm]
    return λ, Q
end

I can make a PR. I don't know about the other corner cases. These work for my needs which are mostly limited to Adjacency and Laplacian Matrices of graphs.

[haampie]

So, the order of the eigenvalues has been fixed now when calling partialschur. Also the eigenvalues appear in the PartialSchur struct as decomp.eigenvalues. Further, partialeigen retains the order.

In the end eigs is basically no different from calling partialeigen(partialschur(...)[1]) then. I would be fine with a PR that implements this! Maybe it's good to throw when the method did not converge (?).

[hz-xiaxz]

Hello! Is the eigs function still concerned?

For me, having a eigs function interface will strongly alleviate the burden on using this package. (E.g. For someone just needs a eigs interface, not caring about the implementation details like schur decomposition) Actually, I spent quite a lot of time myself trying to figure out how eigs works in this package. :)