`eigfact` on `NaN`-filled `Symmetric` matrix returns empty eigenvalue vector

[jrevels]

I'm not super-qualified to suggest a course of action here (or whether it's even a real problem), but it seems worthy of an issue.

If I call eigvals on a NaN-filled Symmetric matrix, it errors:

julia> eigvals(Symmetric(fill(NaN, 5, 5)))[:values]
ERROR: Base.LinAlg.LAPACKException(1)
Stacktrace:
 [1] chklapackerror(::Int64) at ./linalg/lapack.jl:34
 [2] syevr!(::Char, ::Char, ::Char, ::Array{Float64,2}, ::Float64, ::Float64, ::Int64, ::Int64, ::Float64) at ./linalg/lapack.jl:4855
 [3] eigvals! at ./linalg/symmetric.jl:310 [inlined]
 [4] eigvals(::Symmetric{Float64,Array{Float64,2}}) at ./linalg/symmetric.jl:312

However, if I use eigfact instead of eigvals, it doesn't error. Instead, it returns an empty eigenvalue vector:

julia> eigfact(Symmetric(fill(NaN, 5, 5)))
Base.LinAlg.Eigen{Float64,Float64,Array{Float64,2},Array{Float64,1}}(Float64[], Array{Float64}(5,0))

julia> ans[:values]
0-element Array{Float64,1}

I would've expected the above two examples to behave consistently (preferring that both throw an error).

julia> versioninfo()
Julia Version 0.6.0-dev.2899
Commit 61a291b (2017-02-22 04:15 UTC)
Platform Info:
  OS: macOS (x86_64-apple-darwin13.4.0)
  CPU: Intel(R) Core(TM) i5-4288U CPU @ 2.60GHz
  WORD_SIZE: 64
  BLAS: libopenblas (USE64BITINT DYNAMIC_ARCH NO_AFFINITY Haswell)
  LAPACK: libopenblas64_
  LIBM: libopenlibm
  LLVM: libLLVM-3.9.1 (ORCJIT, haswell)

[andreasnoack]

LAPACK seems to have pretty inconsistent behavior when the input matrices have NaNs. For this matrix, the RRR solver returns a non-zero info value when only the values are queries but it returns with zero info value (indicating normal execution) when vectors are queried as well. However, the number of eigenpairs found encoded in the variable m is zero. That is the reason why the arrays are empty. I tried out the DnC and QR solvers as well and they don't seem consistent either.

Possible solutions:

1. Check the inputs for NaNs as we do for the non-symmetric solvers
2. Check that m[1]==n when all pairs of a matrix are queried. However, this would still give a different error message in eigvals/eigfact for the same input matrix.

Right now, I think 1. is the better solution.

[randy3k]

There is a perhaps related issue.

julia> s = Symmetric(eye(2))
2×2 Symmetric{Float64,Array{Float64,2}}:
 1.0  0.0
 0.0  1.0

julia> eigvecs(s)
ERROR: MethodError: no method matching eigfact(::Symmetric{Float64,Array{Float64,2}}; permute=true, scale=true)
Closest candidates are:
  eigfact(::Union{Hermitian{Complex{T},S}, Hermitian{T,S}, Symmetric{T,S}} where S where T<:Real) at linalg/symmetric.jl:326 got unsupported keyword arguments "permute", "scale"
  eigfact(::Union{Hermitian{Complex{T},S}, Hermitian{T,S}, Symmetric{T,S}} where S where T<:Real, ::UnitRange) at linalg/symmetric.jl:349 got unsupported keyword arguments "permute", "scale"
  eigfact(::AbstractArray{TA,2}, ::AbstractArray{TB,2}) where {TA, TB} at linalg/eigen.jl:327 got unsupported keyword arguments "permute", "scale"
  ...
Stacktrace:
 [1] eigvecs(::Symmetric{Float64,Array{Float64,2}}) at ./linalg/eigen.jl:157

[fredrikekre]

Woops, this should not have been closed in JuliaLang/julia#22453

[ArunS-tack]

I guess this issue can be closed now, both eigen(eigfact) and eigvals behave similarly and throw errors.

[Seelengrab]

Bump - this can be closed, as mentioned earlier. Both eigen and eigvals throw the same error:

julia> using LinearAlgebra

julia> eigvals(Symmetric(fill(NaN, 5, 5)))
ERROR: ArgumentError: matrix contains Infs or NaNs
Stacktrace:
    [...]

julia> eigen(Symmetric(fill(NaN, 5, 5)))
ERROR: ArgumentError: matrix contains Infs or NaNs
Stacktrace:
    [...]