add issuccess for CholeskyPivoted

[palday]

Trivial change to add issuccess method for CholeskyPivoted. Let me know if (and where!) I need to add an additional test to cover this.

[ViralBShah]

The test goes in: stdlib/LinearAlgebra/test/cholesky.jl

[ararslan]

Hey Phillip, welcome and thanks for the contribution! Some things to add here:

• At the bottom of the issuccess docstring, something like

  !!! compat "Julia 1.6"
      `issuccess(::CholeskyPivoted)` requires Julia 1.6 or later.
  

• An entry in the LinearAlgebra section of NEWS.md that mentions the addition of this method
• A test for this method in the location Viral pointed out

This functionality looks like a very useful addition!

[palday]

Okay, I think I got everything taken care of. Let me know what I missed. :)

[ViralBShah]

Thanks @palday and welcome!

[andreasnoack]

We discussed this and the possible issues in JuliaLang/LinearAlgebra.jl#720

[ViralBShah]

Anything we should do differently here. Sorry, I wasn't aware of JuliaLang/LinearAlgebra.jl#720.

[andreasnoack]

I think we concluded the definition here was reasonable even though it was argued that the factorization can also be successful when info > 0 and, in fact, that it will always be successful for positive semidefinite matrices. However, it would be good to make these caveats clear in the docs.

[ViralBShah]

@palday Would it be possible for you to review JuliaLang/LinearAlgebra.jl#720 and update the docs accordingly?

[palday]

I also gave some thought to the successful rank-deficient PSD case, but in check=true you would get a RankDeficientException, so the behavior is self-consistent if unfortunately returning false negatives for this case.

[palday]

Ha, it looks like that issue is discussing exactly what I discovered. I'll take a look (might be a few days).