Add OpenBLASLUFactorization implementation

[ChrisRackauckas-Claude]

Summary

• Adds OpenBLASLUFactorization as a new solver that directly calls OpenBLAS_jll
• Provides an alternative to MKLLUFactorization that doesn't require MKL
• Implements the same interface and functionality as MKLLUFactorization

Implementation Details

This PR introduces OpenBLASLUFactorization, which mirrors the existing MKLLUFactorization but uses OpenBLAS_jll directly instead of MKL. Key features:

• Direct OpenBLAS calls: Uses OpenBLAS_jll directly without going through libblastrampoline for optimal performance
• Pre-allocated workspace: Avoids allocations during solving, following the same pattern as MKL implementation
• Type support: Handles Float32, Float64, ComplexF32, and ComplexF64
• Consistent interface: Follows the same AbstractFactorization interface as other solvers

Testing

The implementation has been tested locally with all supported types and produces identical results to the standard LUFactorization:

julia> A = rand(10, 10); b = rand(10);
julia> prob = LinearProblem(A, b);
julia> sol_openblas = solve(prob, OpenBLASLUFactorization());
julia> sol_default = solve(prob, LUFactorization());
julia> norm(sol_openblas.u - sol_default.u)
2.7755575615628914e-17

Use Case

This solver is particularly useful for:

• Systems where MKL is not available or desired
• Environments that prefer open-source BLAS implementations
• Benchmarking and comparison between different BLAS backends

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

Latest Updates

Added preference system for OpenBLAS loading as requested:

• Added LoadOpenBLAS_JLL preference with default value true
• Users can now disable OpenBLAS via preferences, matching the MKL pattern
• The implementation follows the exact same pattern as MKL:

if Preferences.@load_preference("LoadOpenBLAS_JLL", true)
    using OpenBLAS_jll: OpenBLAS_jll
    const useopenblas = OpenBLAS_jll.is_available()
else
    const useopenblas = false
end

This allows users to disable OpenBLAS if they prefer to use their system BLAS or another implementation.

The implementation is now feature-complete and matches the MKL implementation pattern in all aspects:

• Direct BLAS calls bypassing libblastrampoline
• Pre-allocated workspace to avoid allocations
• Preference system for conditional loading
• Full integration with the test suite
• Documentation included

🤖 Generated with Claude Code