Factorization in lower precision

[geoffroyleconte]

Choose the precision of the factorization with Tf. Remove type parameterization of solve functions.

[codecov[bot]]

Codecov Report

Base: 88.23% // Head: 88.20% // Decreases project coverage by -0.03% :warning:

Coverage data is based on head (ad626b2) compared to base (0ab4769). Patch coverage: 100.00% of modified lines in pull request are covered.

:exclamation: Current head ad626b2 differs from pull request most recent head db21f73. Consider uploading reports for the commit db21f73 to get more accurate results

Additional details and impacted files

```diff @@ Coverage Diff @@ ## main #72 +/- ## ========================================== - Coverage 88.23% 88.20% -0.04% ========================================== Files 1 1 Lines 374 373 -1 ========================================== - Hits 330 329 -1 Misses 44 44 ``` | [Impacted Files](https://codecov.io/gh/JuliaSmoothOptimizers/LimitedLDLFactorizations.jl/pull/72?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers) | Coverage Δ | | |---|---|---| | [src/LimitedLDLFactorizations.jl](https://codecov.io/gh/JuliaSmoothOptimizers/LimitedLDLFactorizations.jl/pull/72/diff?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers#diff-c3JjL0xpbWl0ZWRMRExGYWN0b3JpemF0aW9ucy5qbA==) | `88.20% <100.00%> (-0.04%)` | :arrow_down: | Help us with your feedback. Take ten seconds to tell us [how you rate us](https://about.codecov.io/nps?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers). Have a feature suggestion? [Share it here.](https://app.codecov.io/gh/feedback/?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaSmoothOptimizers)

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[tmigot]

Ok, so if I understand the idea is that you can compute a factorization in Tf type while A is of type T? Have you checked the type stability of the example you gave with @code_warntype?

[geoffroyleconte]

@tmigot @dpo there were indeed some type instabilities but I fixed it with my latest commit. I added a new method in case we want a lower-precision factorization. I think I will have to make similar changes in LDLFactorizations.jl.