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Implement BLISFlameLUFactorization with fallback to reference LAPACK
Adds BLISFlameLUFactorization based on ideas from PR SciML#660, with fallback approach due to libflame/ILP64 compatibility limitations: - Created LinearSolveBLISFlameExt extension module - Uses BLIS for BLAS operations and reference LAPACK for LAPACK operations - Provides placeholder for future true libflame integration when compatible - Added to benchmark script for performance comparison - Includes comprehensive tests integrated with existing test framework Technical details: - libflame_jll uses 32-bit integers, incompatible with Julia's ILP64 BLAS - Extension uses same approach as BLISLUFactorization but with different naming - Serves as foundation for future libflame integration when packages are compatible 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <[email protected]>
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‎Project.toml

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[deps]
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ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
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BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
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ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
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ConcreteStructs = "2569d6c7-a4a2-43d3-a901-331e8e4be471"
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DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
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EnumX = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
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GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
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InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
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Krylov = "ba0b0d4f-ebba-5204-a429-3ac8c609bfb7"
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LAPACK_jll = "51474c39-65e3-53ba-86ba-03b1b862ec14"
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LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
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Libdl = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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MKL_jll = "856f044c-d86e-5d09-b602-aeab76dc8ba7"
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Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
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Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
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PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
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Preferences = "21216c6a-2e73-6563-6e65-726566657250"
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RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
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RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
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Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
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SciMLBase = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
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SciMLOperators = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
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Setfield = "efcf1570-3423-57d1-acb7-fd33fddbac46"
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StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
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UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
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blis_jll = "6136c539-28a5-5bf0-87cc-b183200dce32"
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libflame_jll = "8e9d65e3-b2b8-5a9c-baa2-617b4576f0b9"
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[weakdeps]
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BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
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BlockDiagonals = "0a1fb500-61f7-11e9-3c65-f5ef3456f9f0"
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blis_jll = "6136c539-28a5-5bf0-87cc-b183200dce32"
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CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
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CUDSS = "45b445bb-4962-46a0-9369-b4df9d0f772e"
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EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
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IterativeSolvers = "42fd0dbc-a981-5370-80f2-aaf504508153"
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KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
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KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
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LAPACK_jll = "51474c39-65e3-53ba-86ba-03b1b862ec14"
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Metal = "dde4c033-4e86-420c-a63e-0dd931031962"
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Pardiso = "46dd5b70-b6fb-5a00-ae2d-e8fea33afaf2"
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RecursiveFactorization = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
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libflame_jll = "8e9d65e3-b2b8-5a9c-baa2-617b4576f0b9"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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Sparspak = "e56a9233-b9d6-4f03-8d0f-1825330902ac"
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[extensions]
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LinearSolveBLISExt = ["blis_jll", "LAPACK_jll"]
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LinearSolveBLISFlameExt = ["blis_jll", "libflame_jll", "LAPACK_jll"]
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LinearSolveBandedMatricesExt = "BandedMatrices"
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LinearSolveBlockDiagonalsExt = "BlockDiagonals"
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LinearSolveCUDAExt = "CUDA"
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Aqua = "0.8"
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ArrayInterface = "7.7"
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BandedMatrices = "1.5"
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BenchmarkTools = "1.6.0"
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BlockDiagonals = "0.1.42, 0.2"
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blis_jll = "0.9.0"
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CUDA = "5"
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CUDSS = "0.1, 0.2, 0.3, 0.4"
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ChainRulesCore = "1.22"
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MultiFloats = "1"
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Pardiso = "0.5.7, 1"
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Pkg = "1"
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Plots = "1.40.17"
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PrecompileTools = "1.2"
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Preferences = "1.4"
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Random = "1"
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Test = "1"
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UnPack = "1"
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Zygote = "0.7"
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blis_jll = "0.9.0"
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julia = "1.10"
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libflame_jll = "5.2.0"
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[extras]
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AllocCheck = "9b6a8646-10ed-4001-bbdc-1d2f46dfbb1a"

‎README_benchmark.md

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# LinearSolve.jl BLIS Benchmark
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This directory contains a comprehensive benchmark script for testing the performance of various LU factorization algorithms in LinearSolve.jl, including the new BLIS integration.
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## Quick Start
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```bash
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julia --project benchmark_blis.jl
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```
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This will:
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1. Automatically detect available implementations (BLIS, MKL, Apple Accelerate, etc.)
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2. Run benchmarks on matrix sizes from 4×4 to 256×256
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3. Generate a performance plot saved as `lu_factorization_benchmark.png`
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4. Display results in both console output and a summary table
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**Note**: The PNG plot file cannot be included in this gist due to GitHub's binary file restrictions, but it will be generated locally when you run the benchmark.
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## What Gets Benchmarked
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The script automatically detects and includes algorithms based on what's available, following LinearSolve.jl's detection patterns:
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- **LU (OpenBLAS)**: Default BLAS-based LU factorization
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- **RecursiveFactorization**: High-performance pure Julia implementation
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- **BLIS**: New BLIS-based implementation (requires `blis_jll` and `LAPACK_jll`)
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- **Intel MKL**: Intel's optimized library (automatically detected on x86_64/i686, excludes EPYC CPUs by default)
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- **Apple Accelerate**: Apple's framework (macOS only, checks for Accelerate.framework availability)
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- **FastLU**: FastLapackInterface.jl implementation (if available)
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### Detection Logic
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The benchmark uses the same detection patterns as LinearSolve.jl:
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- **MKL**: Enabled on x86_64/i686 architectures, disabled on AMD EPYC by default
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- **Apple Accelerate**: Checks for macOS and verifies Accelerate.framework can be loaded with required symbols
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- **BLIS**: Attempts to load blis_jll and LAPACK_jll, verifies extension loading
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- **FastLU**: Attempts to load FastLapackInterface.jl package
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## Requirements
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### Essential Dependencies
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```julia
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using Pkg
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Pkg.add(["BenchmarkTools", "Plots", "RecursiveFactorization"])
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```
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### Optional Dependencies for Full Testing
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```julia
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# For BLIS support
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Pkg.add(["blis_jll", "LAPACK_jll"])
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# For FastLU support
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Pkg.add("FastLapackInterface")
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```
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## Sample Output
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```
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============================================================
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LinearSolve.jl LU Factorization Benchmark with BLIS
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============================================================
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System Information:
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Julia Version: 1.11.6
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OS: Linux x86_64
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CPU Threads: 1
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BLAS Threads: 1
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BLAS Config: LBTConfig([ILP64] libopenblas64_.so)
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Available Implementations:
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BLIS: true
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MKL: false
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Apple Accelerate: false
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Results Summary (GFLOPs):
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------------------------------------------------------------
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Size LU (OpenBLAS) RecursiveFactorization BLIS
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4 0.05 0.09 0.03
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8 0.28 0.43 0.09
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16 0.61 1.28 0.31
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32 1.67 4.17 1.09
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64 4.0 9.52 2.5
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128 9.87 16.86 8.1
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256 17.33 28.16 9.62
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```
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## Performance Notes
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- **RecursiveFactorization** typically performs best for smaller matrices (< 500×500)
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- **BLIS** provides an alternative BLAS implementation with different performance characteristics
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- **Apple Accelerate** and **Intel MKL** may show significant advantages on supported platforms
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- Single-threaded benchmarks are used for consistent comparison
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## Customization
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You can modify the benchmark by editing `benchmark_blis.jl`:
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- **Matrix sizes**: Change the `sizes` parameter in `benchmark_lu_factorizations()`
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- **Benchmark parameters**: Adjust `BenchmarkTools` settings (samples, evaluations)
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- **Algorithms**: Add/remove algorithms in `build_algorithm_list()`
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## Understanding the Results
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- **GFLOPs**: Billions of floating-point operations per second (higher is better)
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- **Performance scaling**: Look for algorithms that maintain high GFLOPs as matrix size increases
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- **Platform differences**: Results vary significantly between systems based on hardware and BLAS libraries
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## Integration with SciMLBenchmarks
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This benchmark follows the same structure as the [official SciMLBenchmarks LU factorization benchmark](https://docs.sciml.ai/SciMLBenchmarksOutput/stable/LinearSolve/LUFactorization/), making it easy to compare results and contribute to the broader benchmark suite.

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