ARPACK error in eigs

[timholy]

julia> eigs(ones(2,2), eye(2,2); nev=1)
ERROR: Base.LinAlg.ARPACKException("unspecified ARPACK error: -9999")
Stacktrace:
 [1] aupd_wrapper(::Type{T} where T, ::Base.LinAlg.#matvecA!#98{Array{Float64,2}}, ::Base.LinAlg.##95#102{Array{Float64,2}}, ::Base.LinAlg.##96#103, ::Int64, ::Bool, ::Bool, ::String, ::Int64, ::Int64, ::String, ::Float64, ::Int64, ::Int64, ::Array{Float64,1}) at ./linalg/arpack.jl:52
 [2] #_eigs#91(::Int64, ::Int64, ::Symbol, ::Float64, ::Int64, ::Void, ::Array{Float64,1}, ::Bool, ::Base.LinAlg.#_eigs, ::Array{Float64,2}, ::Array{Float64,2}) at ./linalg/arnoldi.jl:285
 [3] (::Base.LinAlg.#kw##_eigs)(::Array{Any,1}, ::Base.LinAlg.#_eigs, ::Array{Float64,2}, ::Array{Float64,2}) at ./<missing>:0
 [4] #eigs#85(::Array{Any,1}, ::Function, ::Array{Float64,2}, ::Array{Float64,2}) at ./linalg/arnoldi.jl:93
 [5] (::Base.LinAlg.#kw##eigs)(::Array{Any,1}, ::Base.LinAlg.#eigs, ::Array{Float64,2}, ::Array{Float64,2}) at ./<missing>:0

[tkelman]

Did this start happening recently?

[timholy]

Happens on 0.5 too.

[stevengj]

It doesn't like 2x2 matrices:

julia> eigs(randn(2,2), eye(2,2); nev=1)
ERROR: ArgumentError: input matrix A is too small. Use eigfact instead.
Stacktrace:
 [1] #_eigs#91(::Int64, ::Int64, ::Symbol, ::Float64, ::Int64, ::Void, ::Array{Float64,1}, ::Bool, ::Base.LinAlg.#_eigs, ::Array{Float64,2}, ::Array{Float64,2}) at ./linalg/arnoldi.jl:184
 [2] (::Base.LinAlg.#kw##_eigs)(::Array{Any,1}, ::Base.LinAlg.#_eigs, ::Array{Float64,2}, ::Array{Float64,2}) at ./<missing>:0
 [3] #eigs#85(::Array{Any,1}, ::Function, ::Array{Float64,2}, ::Array{Float64,2}) at ./linalg/arnoldi.jl:93
 [4] (::Base.LinAlg.#kw##eigs)(::Array{Any,1}, ::Base.LinAlg.#eigs, ::Array{Float64,2}, ::Array{Float64,2}) at ./<missing>:0

Not sure why ones(2,2) produced a different error.

[stevengj]

(In a quick benchmark, it seems that for anything smaller than 20x20 we'd be better off calling eigfact internally anyway.)

[ViralBShah]

IIRC ARPACK's input doesn't quite work out for these tiny matrices. We should probably just discourage it's use on the small ones. 20x20 seems like a good threshold.

[andreasnoack]

It can be reproduced for much larger matrices, e.g.

julia> LinAlg.eigs(ones(2000,2000), eye(2000); nev=1)
ERROR: LinAlg.ARPACKException("unspecified ARPACK error: -9999")
Stacktrace:
 [1] aupd_wrapper(::Type{T} where T, ::LinAlg.#matvecA!#98{Array{Float64,2}}, ::LinAlg.##95#102{Array{Float64,2}}, ::LinAlg.##96#103, ::Int64, ::Bool, ::Bool, ::String, ::Int64, ::Int64, ::String, ::Float64, ::Int64, ::Int64, ::Array{Float64,1}) at /Users/andreasnoack/julia-dev/base/linalg/arpack.jl:53
 [2] #_eigs#91(::Int64, ::Int64, ::Symbol, ::Float64, ::Int64, ::Void, ::Array{Float64,1}, ::Bool, ::LinAlg.#_eigs, ::Array{Float64,2}, ::Array{Float64,2}) at /Users/andreasnoack/julia-dev/base/linalg/arnoldi.jl:286
 [3] (::LinAlg.#kw##_eigs)(::Array{Any,1}, ::LinAlg.#_eigs, ::Array{Float64,2}, ::Array{Float64,2}) at ./<missing>:0
 [4] #eigs#85(::Array{Any,1}, ::Function, ::Array{Float64,2}, ::Array{Float64,2}) at /Users/andreasnoack/julia-dev/base/linalg/arnoldi.jl:93
 [5] (::LinAlg.#kw##eigs)(::Array{Any,1}, ::LinAlg.#eigs, ::Array{Float64,2}, ::Array{Float64,2}) at ./<missing>:0

but it is still looks like a corner of a corner case since it seems to require that A has a zero eigenvalues and that it is a generalized problem with B=eye(n)*α for some α. The slighest deviation makes the issue go away. E.g. all these work

julia> eigs(ones(2,2), nev = 1)
([2.0], [0.707107; 0.707107], 1, 1, 2, [0.0, 0.0])

julia> eigs(ones(2,2) + eps()*randn(2,2), eye(2), nev = 1)
([2.0], [0.707107; 0.707107], 1, 1, 3, [0.0, 0.0])

julia> eigs(ones(2,2), diagm([1.0, nextfloat(1.0)]), nev = 1)
([2.0], [0.707107; 0.707107], 1, 1, 5, [0.0, 0.0])

So it is probably an issue with ARPACK. I think the right fix is to fix #354.

[andreasnoack]

Actually, it is a duplicate of #354