intermittent failure in sparse test

[JeffBezanson]

E.g. here: https://travis-ci.org/JuliaLang/julia/jobs/285862539

Expression: !(Base.USE_GPL_LIBS) || abs(det(factorize(Symmetric(A)))) ≈ abs(det(factorize(Array(A))))
  MethodError: no method matching logabsdet(::Base.LinAlg.LDLt{Float64,SymTridiagonal{Float64,Array{Float64,1}}})
  Closest candidates are:
    logabsdet(!Matched::Base.LinAlg.UnitUpperTriangular{T,S} where S<:(AbstractArray{T,2} where T)) where T at linalg/triangular.jl:2193
    logabsdet(!Matched::Base.LinAlg.UnitLowerTriangular{T,S} where S<:(AbstractArray{T,2} where T)) where T at linalg/triangular.jl:2194
    logabsdet(!Matched::Union{LowerTriangular{T,S} where S<:(AbstractArray{T,2} where T), UpperTriangular{T,S} where S<:(AbstractArray{T,2} where T)}) where T at linalg/triangular.jl:2198

[JeffBezanson]

https://travis-ci.org/JuliaLang/julia/jobs/285889609

[JeffBezanson]

https://ci.appveyor.com/project/JuliaLang/julia/build/1.0.19831/job/xk3spyg0gavfrmvr

[rfourquet]

@vtjnash may have found a cause here, see also my answer to his comment.

[vtjnash]

../julia runtests.jl sparse/sparse --seed=0xa57677a41a6158abdaf4fc54c55c744c
reproduces it (thanks @rfourquet for the hint)

[vtjnash]

Also linalg/lu: https://travis-ci.org/JuliaLang/julia/jobs/285885653

[andreasnoack]

These shouldn't be hard to fix. We'll need to set more seeds explicitly which is fine. I'll open a PR soon. However, the new seed actually revealed a missing method. The reason for this is that factorize is so type unstable. The new random matrix happens to be symmetric tridiagonal whereas the previous was just symmetric or pd.

[andreasnoack]

However, the LU failure is more problematic. See

julia/test/linalg/lu.jl

Lines 196 to 208 in 10d470d

	@testset "Rational{BigInt} and BigFloat Hilbert Matrix" begin
	## Hilbert Matrix (very ill conditioned)
	## Testing Rational{BigInt} and BigFloat version
	nHilbert = 50
	H = Rational{BigInt}[1//(i+j-1) for i = 1:nHilbert,j = 1:nHilbert]
	Hinv = Rational{BigInt}[(-1)^(i+j)*(i+j-1)*binomial(nHilbert+i-1,nHilbert-j)*
	binomial(nHilbert+j-1,nHilbert-i)*binomial(i+j-2,i-1)^2
	for i = big(1):nHilbert,j=big(1):nHilbert]
	@test inv(H) == Hinv
	setprecision(2^10) do
	@test norm(Array{Float64}(inv(float(H)) - float(Hinv))) < 1e-100
	end
	end

. There shouldn't be anything random in that test so something more serious is going on there.

[andreasnoack]

It looks like Hinv occasionally has a single element set to zero instead the right value (the (36,42) element when I was able to reproduce locally). Notice again that this should be completely deterministic. There are no random numbers here.

[kshyatt]

That line, with all its wrapping, is making me really sad :(

[andreasnoack]

I think the issue is somehow related to the comprehension. If I change the comprehension for to an array allocation and a double loop then I'm unable to get the corruption but with the comprehension it happens quite frequently. Hence, we could probably make the tests pass by avoiding the comprehension but it would probably be good to understand why this can happen at all.

[andreasnoack]

Fixed by #24085. The other issue is genuine and tracked in #24098.