Woodbury and Bunch Kaufman

[ViralBShah]

I wonder if we should move the Woodbury and Bunch Kaufman out of Base into a LinearAlgebra.jl package. There all kinds of other stuff that could potentially be in there, like all the stuff from Golub and Van Loan.

[JeffBezanson]

Let's just leave them in Base unless they are truly not useful.

[jiahao]

In #2593, @dmbates wrote:

the description of the \ operator is inaccurate. The Hermitian case uses the BunchKaufman factorization, not the Cholesky factor.

Things have probably changed a lot in the intervening months, but I cannot find any evidence that the BunchKaufman factorization is being used in the linear solver polyalgorithm anymore. In fact, I can't find a single use of BunchKaufman anywhere in the base library other than the bkfact and bkfact! functions which compute and return the factorization.

You can still use BunchKaufman factorizations in linear solvers (via A_ldiv_B!) and compute matrix inverses, but that's pretty much it. These functions wrap LAPACK.sytrs! and LAPACK.hetrs!.

[jiahao]

Similarly, Woodbury is entirely self-contained and essentially not referenced outside of base/linalg/woodbury.jl.

[timholy]

It's used in Grid, but there's no reason we can't have Grid load a package.

[jiahao]

Apologies, BunchKaufman is indeed used in the linear solver exactly as @dmbates wrote. \ on Symmetric and Hermitian matrices call bkfact.

[jakebolewski]

Woodbury has been extracted (#10024), BunchKaufman is more useful to have in Base.