Add FastLapackInterface.jl's LU to LinearSolveAutotune

[ChrisRackauckas-Claude]

Summary

This PR adds FastLUFactorization from FastLapackInterface.jl as an optional algorithm for LinearSolveAutotune benchmarking, as documented at https://docs.sciml.ai/LinearSolve/stable/solvers/solvers/#FastLapackInterface.jl

Changes

• Added include_fastlapack parameter to autotune_setup() function (default: false)
• Modified get_available_algorithms() to conditionally include FastLUFactorization
• Updated documentation with usage examples
• FastLapackInterface remains a weak dependency in LinearSolve.jl (no new dependencies added)

Usage

# Default behavior - FastLUFactorization NOT included
results = autotune_setup()

# To include FastLUFactorization in benchmarks:
using FastLapackInterface  # Must load this first
results = autotune_setup(include_fastlapack = true)

Design Rationale

• Opt-in by default: FastLUFactorization is not included unless explicitly requested
• No new dependencies: Keeps FastLapackInterface as a weak dependency
• User control: Users who want to benchmark FastLUFactorization can easily opt-in
• Clear documentation: Usage examples show how to enable the feature

Impact

• No breaking changes - existing code continues to work unchanged
• Users who want to benchmark FastLUFactorization can now do so by:
  1. Loading FastLapackInterface.jl
  2. Setting include_fastlapack = true in autotune_setup()

Testing

The changes have been tested to confirm:

• Default behavior excludes FastLUFactorization
• FastLUFactorization is only included when both conditions are met:
  • FastLapackInterface.jl is loaded
  • include_fastlapack = true is specified
• Clear warning messages when FastLUFactorization is requested but not available

🤖 Generated with Claude Code

Co-Authored-By: Claude [email protected]