Don't try cholesky for Hermitian in factorize

[dkarrasch]

Up for debate/pkgeval testing.

Closes #54717.

[mikmoore]

@doc factorize needs an update to remove the two places (the factorization type table and the sentence immediately after) that refer to Cholesky factorization.

[dkarrasch]

@nanosoldier runtests()

[nanosoldier]

The package evaluation job you requested has completed - possible new issues were detected.
The full report is available.

[dkarrasch]

@nanosoldier runtests(["HTTP", "MCMCDiagnosticTools", "MLJTestIntegration", "Plots", "TMLE", "JointSurvivalModels", "JumpProblemLibrary", "CryoGrid", "SDEProblemLibrary", "PGFPlots", "Catalyst", "HighVoronoi", "Test", "QuantumAnnealingAnalytics", "GasChromatographySystems"])

[nanosoldier]

The package evaluation job you requested has completed - no new issues were detected.
The full report is available.

[dkarrasch]

It's interesting that seemingly no package relied on the previous behavior. This seems to reflect the fact that spd matrices don't pop up in a generic context, and when they occur users call cholesky directly.

Given the above observation, do we need to announce something here? Or is this an "implementation detail"?

[dkarrasch]

Also, I tried hard spotting new typos, and failed, but I also don't understand why the typo check fails. Is it supposed to spit out a concrete typo, or a code line, like in the whitespace check? Not sure who to ping, but I believe @LilithHafner was involved in setting up the typo check.

[fredrikekre]

I think in most cases you know you have an SPD matrix and at a minimum do factorize(Hermitian(A)) if not cholesky(Hermitian(A)). I also think the factorize function is not that common to use to begin with.