Support rook-pivoting in bkfact

[timholy]

LAPACK 3.5 supports alternative rook-pivoting algorithms for Bunch-Kaufman. This PR wraps this functionality.

Best reviewed with ?w=1 appended to the URL.

[andreasnoack]

I think it would be simpler to have a loop for each function given the convoluted code just below.

[andreasnoack]

Looks good to me except for the small style comment, maybe we should wait until #14309 has been merged.

[timholy]

Rebased and updated, including the style change. Curiously, Travis never ran this as a PR (it did run the push), but AppVeyor did, so hopefully we're OK.

[nalimilan]

It would be nice to make a bit more advertisement in the future when raising dependency requirements like that. It took me some time to realize why my EPEL RPM builds where failing.

[timholy]

Since I always build openblas from source, I didn't think about this as a potential problem. Sorry about that, and thanks for fixing!

[nalimilan]

You're welcome @timholy.

[ViralBShah]

Could this have been wrapped in a test for laver()? That would allow us to avoid making the minimum LAPACK at 3.5. The main reason is that users of MKL may not have new versions of LAPACK.

[ViralBShah]

Seems like LAPACK.VERSION[] is the new way to do this.

[ViralBShah]

I seem to recollect that even dgesdd was introduced in 3.5 or perhaps 3.4, and used to be protected with a version check once upon a time.

BTW, I am ok with 3.5 being the minimum, but just wanted to point out the issues.

[eschnett]

One can probably work around missing LAPACK functions in MKL with some linker magic. One needs to link against MKL explicitly (i.e. using an -l flag, not the -mkl flag), then link against a new LAPACK. This will preferably resolve symbols against MKL, and then take any missing symbols from LAPACK.