Fixed #38346: Eigen decomposition of Symmetric Matrix containing NaNs now throws exception

[kc611]

Fixes JuliaLang/LinearAlgebra.jl#780.

As suggested by @KlausC in the issue

There seems missing a call to ckfinite or analogous in syevr!

adding a call to 'ckfinite' in 'syevr' is a nice fix for the problem. Since Eigen decomposition for both symmetric and hermitian matrix is making call to 'syevr' function it fixes the issue for both. Diagonal matrices already had such a fail-safe for NaN values

julia/stdlib/LinearAlgebra/src/diagonal.jl

Lines 674 to 676 in af3cd59

	if any(!isfinite, D.diag)
	throw(ArgumentError("matrix contains Infs or NaNs"))
	end

[dkarrasch]

@kc611 Thank you and welcome! Can you please add a test (à la @test_throws ...) to make sure the function throws when it should throw?

[kc611]

It seems that there was already a test present for Eigen of matrices with NaN values. I extended it's functionality to Symmetric, Hermitian and Diagonal(just in case) ones.

[JeffBezanson]

Has comments that need to be addressed.

Missing triangular check

[kc611]

Changed the iterations to column-wise (the loops looks a bit clean and consistent that way) and added one based indexing check and @inbounds as suggested.

Also I was thinking about adding a test case where the code is not supposed to throw exception. But dropped the idea since I could not find any appropriate way for doing that (#18780). Any suggestions?

[KlausC]

To verify, that a test does not throw and exception you could do for example:

@test eigen(...) isa Eigen
or
@test something....   !== []
or
@test something...  !== nothing  (if you expect any return type != nothing

[dkarrasch]

LGTM!

[dkarrasch]

The usual unrelated test failures. Thank you very much @kc611, and sorry that it took a while. Your contribution is much appreciated!