LinearAlgebra: eigen decomposition of Symmetric Matrix containing NaNs never throws. It just runs forever.

[s-baumann]

On my (Windows) PC the following runs forever without ever throwing or finishing. The error seems to come from inside LAPACK. The key elements seems to be that the matrix is Symmetric and contains a NaN.
using LinearAlgebra aa = [1 2 3; 2 NaN 4; 3 4 5] bb = Symmetric(aa) eigen(bb)

[s-baumann]

using LinearAlgebra
aa = [1 2 3; 2 NaN 4; 3 4 5]
bb = Symmetric(aa)
eigen(bb)

[antoine-levitt]

Can't reproduce here (using MKL). Probably an OpenBLAS issue.

[KlausC]

Could reproduce on Linux. Produced the following stack trace, when interrupted:

eigen(bb)
^C^C^C^C^C^CWARNING: Force throwing a SIGINT
ERROR: InterruptException:
Stacktrace:
 [1] syevr!(jobz::Char, range::Char, uplo::Char, A::Matrix{Float64}, vl::Float64, vu::Float64, il::Int64, iu::Int64, abstol::Float64)
   @ LinearAlgebra.LAPACK /home/julia/julia/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/lapack.jl:5055
 [2] #eigen!#95
   @ /home/julia/julia/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/symmetric.jl:672 [inlined]
 [3] #eigen#96
   @ /home/julia/julia/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/symmetric.jl:677 [inlined]
 [4] eigen(A::Symmetric{Float64, Matrix{Float64}})
   @ LinearAlgebra /home/julia/julia/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/symmetric.jl:675
 [5] top-level scope
   @ REPL[5]:1

There seems missing a call to ckfinite or analogous in syevr!, as can be seen here:

julia> eigen(aa)
ERROR: ArgumentError: matrix contains Infs or NaNs
Stacktrace:
 [1] chkfinite(A::Matrix{Float64})
   @ LinearAlgebra.LAPACK /home/julia/julia/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/lapack.jl:92
 [2] geevx!(balanc::Char, jobvl::Char, jobvr::Char, sense::Char, A::Matrix{Float64})
   @ LinearAlgebra.LAPACK /home/julia/julia/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/lapack.jl:2025
 [3] eigen!(A::Matrix{Float64}; permute::Bool, scale::Bool, sortby::typeof(LinearAlgebra.eigsortby))

[s-baumann]

This is also a problem with Hermitian matrices. No issue with Diagonal matrices though.

diag = Diagonal(aa)
eigen(diag) # This is fine.
herm = Hermitian(aa)
eigen(herm) # This runs forever

[andreasnoack]

The LAPACK world is free from Infs and NaNs. It is assumed that the inputs don't include these values and LAPACK promises not to produce them. Instead, LAPACK returns non-zero info values.