FastLAPACK

[rayegun]

This is just a basic set of functions I was able/willing to develop on my laptop at sea. I've only tested A*x \approx b for those factorizations right now.

I'll add tests shortly. A few questions:

1. Should we default to this workspace system for QR and LU? Rather than having "FastQRFactorization"
2. Should the workspace be resized when a user uses set_A with a different size matrix? Problematically I triggered a segfault once when playing with the sizing of A this evening, so I'll have to track that down. It's supposed to just error (and mostly does). FastLAPACKInterface.jl doesn't provide a method to resize workspaces as far as I can tell.

[codecov]

Codecov Report

Merging #153 (5854ef0) into main (e4e450d) will decrease coverage by 4.51%.
The diff coverage is 0.00%.

❗ Current head 5854ef0 differs from pull request most recent head 44a9a33. Consider uploading reports for the commit 44a9a33 to get more accurate results

@@            Coverage Diff             @@
##             main     #153      +/-   ##
==========================================
- Coverage   65.28%   60.77%   -4.52%     
==========================================
  Files           9        9              
  Lines         579      622      +43     
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  Hits          378      378              
- Misses        201      244      +43     

Impacted Files	Coverage Δ
src/LinearSolve.jl	75.00% <ø> (ø)
src/factorization.jl	62.68% <0.00%> (-17.07%)	⬇️

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[ChrisRackauckas]

Should we default to this workspace system for QR and LU? Rather than having "FastQRFactorization"

I think the high level types is probably easiest.

Should the workspace be resized when a user uses set_A with a different size matrix? Problematically I triggered a segfault once when playing with the sizing of A this evening, so I'll have to track that down. It's supposed to just error (and mostly does). FastLAPACKInterface.jl doesn't provide a method to resize workspaces as far as I can tell.

That would be cool if possible.

[ChrisRackauckas]

Now for the real test: does it actually end up faster than direct OpenBLAS/MKL?

[rayegun]

Well it just avoids allocations right? That's the only change AFAICT. So it should be fast for resolves

[ChrisRackauckas]

Run the formatter?

[ChrisRackauckas]

Actually, I'll run the formatter. I want to update the docs anyways.

[rayegun]

Oh oops. @ChrisRackauckas just formatted and added a simple set of tests.

[ChrisRackauckas]

oh that's more than fine.