Add forward rules for triangular linear solves

[jlperla]

Summary

• add forward-mode support for high-level triangular solves
• cover vector and matrix RHS cases, including unit triangular and transposed triangular wrappers
• reuse the existing _zero_unused_elements! handling for unit triangular structure
• support batched forward mode

Tests

• julia --project=test test/runtests.jl --verbose rules/internal_rules/linear_algebra_rules

[jlperla]

@wsmoses I added these in. I think this is a better place to fix some of those issues than the tablegen for now (and it is symmetric to the reverses-rules, so not coming out of nowhere).

[wsmoses]

This is fine for now, but I do think this may make sense to do as a tablegen rule. For regular matmul we saw substantial speed ups in doing so. Assuming this directly translates to the blas call [and not a combination of calls], I would expect similar here

[jlperla]

Definitely. If you want any more work on the EnzymeAD/Enzyme#2825 just post comments or a code review and I will tell the AI to do its thing. But while I don't mind using AIs for patching, I am loathe to do so when I don't understand the code.

[codecov]

Codecov Report

❌ Patch coverage is 0% with 26 lines in your changes missing coverage. Please review.
✅ Project coverage is 69.95%. Comparing base (51a2569) to head (f2158ae).

Files with missing lines	Patch %	Lines
src/internal_rules/linalg.jl	0.00%	26 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #3107      +/-   ##
==========================================
- Coverage   70.04%   69.95%   -0.09%     
==========================================
  Files          66       66              
  Lines       21840    21866      +26     
==========================================
  Hits        15297    15297              
- Misses       6543     6569      +26     

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[wsmoses]

I think you still need to address the previous comments there, involving both splitting it up and also just changing the relefvant pieces?

[jlperla]

@wsmoses Sorry, I think a question might have been lost on slack. To clarify, I wasn't sure if you wanted me to split EnzymeAD/Enzyme#2825 into 3 separate PRs for trsv, trsm, and potrs? Or something else?

[wsmoses]

yes that's correct