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nathanaelbosch / PSDMatrices.jl

Positive semi-definite matrix types in Julia

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Should `choleskify` return `Cholesky` type?

pnkraemer opened this issue · comments

commented

Currently, choleskify_factor turns any PSD matrix into a PSDMatrix, where the factor R is a valid Cholesky factor.

I personally think choleskify_factor should be split into a triangularize_factor() method, which turns any PSDMatrix into one with an UpperTriangular factor, and a choleskify method, which turns a PSDMatrix with an UpperTriangular factor into a Cholesky type. Why?

  • A method that is called choleskify would be easier to understand if it returned a Cholesky type
  • In most of our applications, triangular factors are sufficient, and the extra multiplication that turns upper triangular types into valid Cholesky factors can be avoided

Thoughts, @nathanaelbosch?

commented

I agree with the split into "triangularize_factor" and "choleskify_factor", even just because triangular factors are often sufficient.

I'm a bit unsure about "choleskify" vs "choleskify_factor", where for me the former returns a Cholesky and the latter returns a PSDMatrix with a factor in Cholesky form. Intuitively, I'd have wanted to have the latter too, but I can't really think of any situation. Do you think that we're always fine with getting a Cholesky out of it? Then, maybe the function we're writing isn't actually choleskify, but a new constructor for Cholesky(::PSDMatrix)? What do you think?