Calling ?GEEV with non-finite input leads to memory corruption in ?LASCAL

[martin-frbg]

Description
See OpenMathLib/OpenBLAS#5250 for full context and reproducer
Calling ?GEEV with non-finite input will fail in ?HSEQR. ?GEEV will then invoke ?LASCAL to undo any previous scaling of the input data, using INFO as a reference - with the existing guard for INFO.GT.0 covering only half the invocations.
The trivial fix would be to move the existing check for INFO.GT.0 into the outer if (?CALEA) THEN conditional - or add a check for INFO.GE.0 there. The same problem appears to be present in ?GEEVX, though I have not checked in detail.
Checklist

• I've included a minimal example to reproduce the issue
• I'd be willing to make a PR to solve this issue

[angsch]

Does the reproducer you linked in the issue work for reference-LAPACK on your side? When I execute the reproducer, GEBAL triggers XERBLA ( ** On entry to DGEBAL parameter number 3 had an illegal value), which immediately calls STOP. So everything is fine, no memory corruption, HSEQR is never reached.

Irrespective of the exact cause, I think that the best way of handling Inf and/or NaN in GEEV (and likely quite a few other routines) is to just return if the input matrix does not contains only valid floating point numbers. A natural point to check for Inf/NaN is

lapack/SRC/dgeev.f

Lines 348 to 356 in 2475f7b

	ANRM = DLANGE( 'M', N, N, A, LDA, DUM )
	SCALEA = .FALSE.
	IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN
	SCALEA = .TRUE.
	CSCALE = SMLNUM
	ELSE IF( ANRM.GT.BIGNUM ) THEN
	SCALEA = .TRUE.
	CSCALE = BIGNUM
	END IF

Since problems with Inf/NaN will likely pop up every now and then, should there be a function DISFINITE, inspired by the existing DISNAN, to check for Inf or NaN? Then a possibility is to continue the above code snippet like this:

    ELSE IF( DISFINITE( ANRM) ) THEN
        INFO = ... <new info flag for GEEV that signals that Inf/NaN is encountered>
        CALL XERBLA( 'DGEEV', -INFO)
        RETURN
    END

[langou]

I am reopening this issue because, I think we should, in addition, also work on the suggestion of @angsch

As opposed to DISFINITE, I would have used DISNAN and let GEEV proceeds even if there are infinite entries. I feel some people would expect LAPACK to return INFO = 0 if we input a diagonal matrix with Inf on the diagonal. I do not have a strong opinion though. Note that ANRM can be infinite and A only have finite entries but that would an extreme corner case and I would think that LAPACK can, in general, not handle these matrices.