Add package version tracking and correctness checks to LinearSolveAutotune

[ChrisRackauckas-Claude]

Summary

• Add comprehensive package version tracking to autotune telemetry output
• Implement correctness checks against LUFactorization baseline
• Improve reproducibility and debugging of benchmark results

Motivation

Fixes #669 - Improves the autotune results collection by including exact versions of all solver dependencies and ensuring result correctness.

Changes

1. Package Version Tracking

• Added get_package_versions() function in gpu_detection.jl that collects versions of:
  • LinearSolve.jl and LinearSolveAutotune.jl
  • All solver dependencies (RecursiveFactorization.jl, CUDA.jl, Metal.jl)
  • BLAS libraries (MKL_jll, blis_jll, OpenBLAS_jll, LAPACK_jll)
  • Other relevant packages (Krylov, SparseArrays, etc.)
• Versions are now displayed in telemetry output under a "Package Versions" section
• Added Pkg as a dependency to LinearSolveAutotune

2. Correctness Checks

• Added optional correctness checking in benchmark_algorithms()
• Each algorithm's solution is compared against LUFactorization baseline
• Algorithms that fail correctness check (relative error > tolerance) are:
  • Warned with detailed error information
  • Excluded from benchmark results
• Default tolerance is 1e-2 (very lenient) to catch only major issues
• Can be configured via correctness_tol parameter

3. Testing

• Created test script verifying both features work correctly
• Tests pass with expected output showing:
  • Package versions collected successfully
  • Correctness checks functioning as intended

Example Output

### Package Versions
- **BLAS_lib**: libopenblas64_.so
- **CUDA**: 5.8.3
- **LinearSolve**: 3.27.0
- **Metal**: 1.7.0
- **MKL_jll**: 2025.2.0+0
- **RecursiveFactorization**: 0.2.23
...

Test Plan

• Run local tests with test_autotune_improvements.jl
• Verify package versions are collected and displayed
• Verify correctness checks work and exclude failing algorithms
• Format code with JuliaFormatter (SciMLStyle)
• CI tests should pass

This improves the reliability and reproducibility of LinearSolveAutotune benchmark results.

🤖 Generated with Claude Code

Co-Authored-By: Claude [email protected]