Specialize UMFPack initialization

[ChrisRackauckas]

No description provided.

[ChrisRackauckas]

@Wimmerer could you look into the KLU one? This one might finally finish the SciML/OrdinaryDiffEq.jl#1543 PR.

[rayegun]

Yes, but why are we constructing the UMFPACK factorization directly? So that we don't immediately run the symbolic?

[ChrisRackauckas]

Yes, we just want the initialization of the cache without doing any of the work in order to get the types right.

[codecov]

Codecov Report

Merging #74 (0ffb9eb) into main (d443210) will decrease coverage by 0.78%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main      #74      +/-   ##
==========================================
- Coverage   79.24%   78.45%   -0.79%     
==========================================
  Files           7        7              
  Lines         371      376       +5     
==========================================
+ Hits          294      295       +1     
- Misses         77       81       +4     

Impacted Files	Coverage Δ
src/factorization.jl	80.64% <100.00%> (-3.45%)	⬇️

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[rayegun]

I'll also see if I can make a PR to SuiteSparse.jl, it seems really bad that we should be handling finalizers at this level just to defer factorization.