Add comprehensive linear algebra operation benchmarks

This commit adds comprehensive benchmarking infrastructure for linear algebra operations, addressing Phase 1 of the performance improvement plan.

**Benchmarks Added:**
- QR Decomposition (10×10, 30×30, 50×50)
- LU Decomposition (10×10, 30×30, 50×50)
- Cholesky Decomposition (10×10, 30×30, 50×50)
- Eigenvalue Decomposition (10×10, 30×30, 50×50)
- Linear System Solving (10×10, 30×30, 50×50)
- Matrix Inverse (10×10, 30×30, 50×50)
- Least Squares (10×10, 30×30, 50×50)

Total: 21 new benchmarks covering fundamental linear algebra operations.

**Files Modified:**
- benchmarks/FsMath.Benchmarks/LinearAlgebra.fs (new file)
- benchmarks/FsMath.Benchmarks/FsMath.Benchmarks.fsproj
- benchmarks/FsMath.Benchmarks/Program.fs

**Test Results:**
✅ All 132 existing tests pass
✅ All 21 new benchmarks compile and run successfully
✅ Benchmarks are discoverable via --list flat

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <[email protected]>

Author: github-actions[bot]

benchmarks/FsMath.Benchmarks/FsMath.Benchmarks.fsproj

@@ -7,6 +7,7 @@
 
   <ItemGroup>
     <Compile Include="Vector.fs" />
+    <Compile Include="LinearAlgebra.fs" />
     <Compile Include="Program.fs" />
   </ItemGroup>
 

benchmarks/FsMath.Benchmarks/LinearAlgebra.fs

@@ -0,0 +1,171 @@
+namespace FsMath.Benchmarks
+
+open BenchmarkDotNet.Attributes
+open FsMath
+open FsMath.Algebra
+
+/// <summary>
+/// Benchmarks for linear algebra operations (QR, LU, Cholesky, EVD).
+/// These operations are fundamental to scientific computing and their performance
+/// is critical for applications in statistics, machine learning, and numerical analysis.
+/// </summary>
+[<MemoryDiagnoser>]
+type LinearAlgebraBenchmarks() =
+
+    let mutable smallMatrix: Matrix<float> = Matrix.zeroCreate 10 10
+    let mutable mediumMatrix: Matrix<float> = Matrix.zeroCreate 30 30
+    let mutable largeMatrix: Matrix<float> = Matrix.zeroCreate 50 50
+
+    let mutable smallSymmetric: Matrix<float> = Matrix.zeroCreate 10 10
+    let mutable mediumSymmetric: Matrix<float> = Matrix.zeroCreate 30 30
+    let mutable largeSymmetric: Matrix<float> = Matrix.zeroCreate 50 50
+
+    let mutable smallVector: Vector<float> = Vector.zeroCreate 10
+    let mutable mediumVector: Vector<float> = Vector.zeroCreate 30
+    let mutable largeVector: Vector<float> = Vector.zeroCreate 50
+
+    /// Create a random positive-definite symmetric matrix for Cholesky/EVD benchmarks
+    let createSymmetricPositiveDefinite (n: int) =
+        let random = System.Random(42)
+        // Create a random matrix A
+        let a = Matrix.init n n (fun i j -> random.NextDouble())
+        // Make it symmetric positive-definite: A^T * A
+        let at = Matrix.transpose a
+        at * a
+
+    /// Create a random matrix for general decompositions
+    let createRandomMatrix (rows: int) (cols: int) =
+        let random = System.Random(42)
+        Matrix.init rows cols (fun i j -> random.NextDouble())
+
+    /// Create a random vector
+    let createRandomVector (n: int) =
+        let random = System.Random(42)
+        Vector.init n (fun i -> random.NextDouble())
+
+    [<GlobalSetup>]
+    member _.Setup() =
+        // Initialize matrices with proper random data
+        smallMatrix <- createRandomMatrix 10 10
+        mediumMatrix <- createRandomMatrix 30 30
+        largeMatrix <- createRandomMatrix 50 50
+
+        smallSymmetric <- createSymmetricPositiveDefinite 10
+        mediumSymmetric <- createSymmetricPositiveDefinite 30
+        largeSymmetric <- createSymmetricPositiveDefinite 50
+
+        smallVector <- createRandomVector 10
+        mediumVector <- createRandomVector 30
+        largeVector <- createRandomVector 50
+
+    // ============================================
+    // QR Decomposition Benchmarks
+    // ============================================
+
+    [<Benchmark>]
+    member _.QR_10x10() =
+        LinearAlgebra.qrDecompose smallMatrix
+
+    [<Benchmark>]
+    member _.QR_30x30() =
+        LinearAlgebra.qrDecompose mediumMatrix
+
+    [<Benchmark>]
+    member _.QR_50x50() =
+        LinearAlgebra.qrDecompose largeMatrix
+
+    // ============================================
+    // LU Decomposition Benchmarks
+    // ============================================
+
+    [<Benchmark>]
+    member _.LU_10x10() =
+        LinearAlgebra.luDecompose smallMatrix
+
+    [<Benchmark>]
+    member _.LU_30x30() =
+        LinearAlgebra.luDecompose mediumMatrix
+
+    [<Benchmark>]
+    member _.LU_50x50() =
+        LinearAlgebra.luDecompose largeMatrix
+
+    // ============================================
+    // Cholesky Decomposition Benchmarks
+    // ============================================
+
+    [<Benchmark>]
+    member _.Cholesky_10x10() =
+        LinearAlgebra.cholesky smallSymmetric
+
+    [<Benchmark>]
+    member _.Cholesky_30x30() =
+        LinearAlgebra.cholesky mediumSymmetric
+
+    [<Benchmark>]
+    member _.Cholesky_50x50() =
+        LinearAlgebra.cholesky largeSymmetric
+
+    // ============================================
+    // Eigenvalue Decomposition Benchmarks
+    // ============================================
+
+    [<Benchmark>]
+    member _.EVD_10x10() =
+        LinearAlgebra.symmetricEigenspectrum smallSymmetric
+
+    [<Benchmark>]
+    member _.EVD_30x30() =
+        LinearAlgebra.symmetricEigenspectrum mediumSymmetric
+
+    [<Benchmark>]
+    member _.EVD_50x50() =
+        LinearAlgebra.symmetricEigenspectrum largeSymmetric
+
+    // ============================================
+    // Linear System Solving Benchmarks
+    // ============================================
+
+    [<Benchmark>]
+    member _.SolveLinearSystem_10x10() =
+        LinearAlgebra.solveLinearSystem smallMatrix smallVector
+
+    [<Benchmark>]
+    member _.SolveLinearSystem_30x30() =
+        LinearAlgebra.solveLinearSystem mediumMatrix mediumVector
+
+    [<Benchmark>]
+    member _.SolveLinearSystem_50x50() =
+        LinearAlgebra.solveLinearSystem largeMatrix largeVector
+
+    // ============================================
+    // Matrix Inverse Benchmarks
+    // ============================================
+
+    [<Benchmark>]
+    member _.Inverse_10x10() =
+        LinearAlgebra.inverse smallMatrix
+
+    [<Benchmark>]
+    member _.Inverse_30x30() =
+        LinearAlgebra.inverse mediumMatrix
+
+    [<Benchmark>]
+    member _.Inverse_50x50() =
+        LinearAlgebra.inverse largeMatrix
+
+    // ============================================
+    // Least Squares Benchmarks
+    // ============================================
+
+    [<Benchmark>]
+    member _.LeastSquares_10x10() =
+        LinearAlgebra.leastSquares smallMatrix smallVector
+
+    [<Benchmark>]
+    member _.LeastSquares_30x30() =
+        LinearAlgebra.leastSquares mediumMatrix mediumVector
+
+    [<Benchmark>]
+    member _.LeastSquares_50x50() =
+        LinearAlgebra.leastSquares largeMatrix largeVector

benchmarks/FsMath.Benchmarks/Program.fs

@@ -5,8 +5,9 @@ open FsMath.Benchmarks
 [<EntryPoint>]
 let Main args =
     // Register multiple benchmark classes
-    let switcher = BenchmarkSwitcher [| 
+    let switcher = BenchmarkSwitcher [|
         typeof<VectorBenchmarks>
+        typeof<LinearAlgebraBenchmarks>
     |]
     switcher.Run args |> ignore
     0