Add trim tests for LUFactorization, MKLLUFactorization, and RFLUFactorization

[ChrisRackauckas-Claude]

Summary

Add trimming tests to LinearSolve.jl, similar to PR #734 in NonlinearSolve.jl.

This PR adds tests for Julia's trimming feature (available in Julia 1.12+) to verify that LinearSolve can be successfully trimmed when using pre-initialized caches with different LU factorization algorithms.

Changes

• Add test/trim/ directory with infrastructure for testing trimming
• Add trim tests for three factorization methods:
  • LUFactorization - Julia's built-in LU factorization
  • MKLLUFactorization - MKL-based LU factorization
  • RFLUFactorization - RecursiveFactorization-based LU factorization
• Add "Trim" test group to CI configuration
• Tests only run on Julia 1.12+ (when trimming was introduced)

Test Structure

The tests verify:

1. Each factorization works correctly with pre-initialized cache
2. Each implementation can be successfully compiled with juliac --trim

Each test creates a module with:

• const pre-initialized problem, algorithm, and cache
• A function that reuses the cache for solving with different parameters
• A main entry point for juliac compilation

Notes

• Trim tests only run on Julia 1.12+
• CI excludes trim tests on LTS and pre-release versions
• Tests use a custom environment in test/trim/ to avoid conflicts
• Each factorization is tested separately to ensure independent trimming

Related

• Similar to NonlinearSolve.jl PR Fix Pardiso memory leak by adding finalizer #734
• Addresses trimming support for LinearSolve algorithms

🤖 Generated with Claude Code

Co-Authored-By: Claude noreply@anthropic.com

[ChrisRackauckas-Claude]

Fixed: Removed JuliaFormatter from dependencies (it was incorrectly added during formatting and should not be a package dependency)

[ChrisRackauckas-Claude]

Fixed: Changed reinit!(cache, b_new) to reinit!(cache; b = b_new) to use proper keyword argument syntax

[ChrisRackauckas-Claude]

Fixed: Changed to return the solution object from solve!(cache) instead of returning the cache itself

[ChrisRackauckas-Claude]

Fixed test failures:

1. Changed test assertions: Instead of checking retcode, tests now verify the solution values directly using @test sol.u ≈ expected_values
2. Made MKL tests conditional: MKL tests now only run when MKL is available using LinearSolve.usemkl(nothing) check. This prevents failures on CI runners without MKL binaries.

Tests should now pass on CI.

[ChrisRackauckas-Claude]

Fixed: Changed LinearSolve.usemkl(nothing) to LinearSolve.usemkl - usemkl is a constant boolean, not a function. This fixes the "MethodError: objects of type Bool are not callable" error.