wrong permutation for rook-pivoted Bunch–Kaufman

[stevengj]

JuliaLang/julia#14389 by @timholy added support for rook-pivoted Bunch–Kaufman factorization, but it seems like the permutation (p or P) property should have been updated. As reported on discourse, it looks like the wrong permutation. For example:

A = Symmetric([-5 -9 9; -9 4 1; 9 1 2])
B = bunchkaufman(A, true)
B.U * B.D * B.U' ≈ A[B.p, B.p]

gives false. The permutation B.p == [1,3,2], whereas it seems that the correct permuation is [2,1,3] in this case.

JuliaLang/julia#14389 did not change the _ipiv2perm_bk routine that computes the permutation from ipiv, but the documentation for sytrf_rook seems to indicate that its ipiv array has a different meaning than that of sytrf.

[stevengj]

A corrected permutation was posted here: https://discourse.julialang.org/t/bunch-kaufman-with-rook-pivoting/24379/4 by @RalphAS