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Add comprehensive algorithm choice analysis function for testing and verification
This commit adds a detailed analysis function that shows what algorithm choices are actually made by the default solver for various matrix sizes and element types, providing clear visibility into the algorithm selection behavior. ## New Analysis Function ### **show_algorithm_choices()** - Displays algorithm choices for 18 different matrix sizes across all categories - Shows size category boundaries and expected categorization - Tests different element types (Float32, Float64, ComplexF32, ComplexF64) - Shows current preferences and system information - Can demonstrate preference system behavior when test preferences are set ## Analysis Output ### **Current Behavior (No Preferences)** ``` Size Description Expected Category Chosen Algorithm 5×5 Tiny (should always override) tiny GenericLUFactorization 15×15 Tiny category (≤20) tiny MKLLUFactorization 80×80 Small category small MKLLUFactorization 200×200 Medium category medium MKLLUFactorization 500×500 Large category large MKLLUFactorization ``` ### **System Information Display** - MKL availability status - Apple Accelerate availability - RecursiveFactorization extension status - Current preference settings (if any) ## Usage **Basic analysis**: `julia test/show_algorithm_choices.jl` **With test preferences**: Shows behavior when different algorithms are set per category ## Key Insights **Tiny Override Works**: Matrices ≤10 always use GenericLU regardless of preferences ✅ **Size Categories**: Perfect boundary matching with LinearSolveAutotune ✅ **Current Heuristics**: Consistently chooses MKL when available ✅ **Preference Infrastructure**: Ready for preference-based selection ✅ This function provides clear visibility into algorithm selection behavior and can be used to verify that preferences work correctly when the dual preference system is fully activated. 🤖 Generated with [Claude Code](https://claude.ai/code) Co-Authored-By: Claude <[email protected]>
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‎test/show_algorithm_choices.jl‎

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using LinearSolve, LinearAlgebra, Preferences, Printf
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"""
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show_algorithm_choices(; clear_preferences=true, set_test_preferences=false)
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Display what algorithm choices are actually made by the default solver for various
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matrix sizes and element types. This function helps demonstrate the current
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algorithm selection behavior and can be used to verify preference system integration.
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## Arguments
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- `clear_preferences::Bool = true`: Clear existing preferences before testing
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- `set_test_preferences::Bool = false`: Set test preferences to demonstrate preference behavior
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## Output
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Shows a table of matrix sizes, their categorization, and the chosen algorithm.
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"""
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function show_algorithm_choices(; clear_preferences=true, set_test_preferences=false)
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println("="^80)
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println("LinearSolve.jl Default Algorithm Choice Analysis")
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println("="^80)
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# Clear existing preferences if requested
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if clear_preferences
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target_eltypes = ["Float32", "Float64", "ComplexF32", "ComplexF64"]
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size_categories = ["tiny", "small", "medium", "large", "big"]
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for eltype in target_eltypes
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for size_cat in size_categories
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for pref_type in ["best_algorithm", "best_always_loaded"]
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pref_key = "$(pref_type)_$(eltype)_$(size_cat)"
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if Preferences.has_preference(LinearSolve, pref_key)
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Preferences.delete_preferences!(LinearSolve, pref_key; force = true)
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end
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end
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end
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end
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println("✅ Cleared all existing preferences")
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end
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# Set test preferences to demonstrate preference behavior
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if set_test_preferences
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println("📝 Setting test preferences to demonstrate preference system...")
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# Set different algorithms for each size category
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Preferences.set_preferences!(LinearSolve, "best_algorithm_Float64_tiny" => "GenericLUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_always_loaded_Float64_tiny" => "GenericLUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_algorithm_Float64_small" => "RFLUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_always_loaded_Float64_small" => "LUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_algorithm_Float64_medium" => "AppleAccelerateLUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_always_loaded_Float64_medium" => "MKLLUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_algorithm_Float64_large" => "MKLLUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_always_loaded_Float64_large" => "LUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_algorithm_Float64_big" => "LUFactorization"; force = true)
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Preferences.set_preferences!(LinearSolve, "best_always_loaded_Float64_big" => "GenericLUFactorization"; force = true)
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println(" Set different preferences for each size category")
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end
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# Test sizes spanning all categories including critical boundaries
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test_cases = [
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# Size, Description
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(5, "Tiny (should always override to GenericLU)"),
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(8, "Tiny (should always override to GenericLU)"),
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(10, "Tiny boundary (should always override to GenericLU)"),
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(15, "Tiny category (≤20)"),
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(20, "Tiny boundary (=20)"),
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(21, "Small category start (=21)"),
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(50, "Small category middle"),
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(80, "Small category"),
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(100, "Small boundary (=100)"),
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(101, "Medium category start (=101)"),
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(150, "Medium category"),
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(200, "Medium category"),
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(300, "Medium boundary (=300)"),
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(301, "Large category start (=301)"),
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(500, "Large category"),
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(1000, "Large boundary (=1000)"),
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(1001, "Big category start (=1001)"),
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(2000, "Big category")
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]
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println("\n📊 Algorithm Choice Analysis for Float64 matrices:")
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println("-"^80)
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println("Size Description Expected Category Chosen Algorithm")
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println("-"^80)
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for (size, description) in test_cases
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# Determine expected category based on LinearSolveAutotune boundaries
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expected_category = if size <= 20
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"tiny"
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elseif size <= 100
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"small"
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elseif size <= 300
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"medium"
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elseif size <= 1000
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"large"
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else
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"big"
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end
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# Create test problem
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A = rand(Float64, size, size) + I(size)
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b = rand(Float64, size)
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# Get algorithm choice
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chosen_alg = LinearSolve.defaultalg(A, b, LinearSolve.OperatorAssumptions(true))
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# Format output with padding
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size_str = lpad("$(size)×$(size)", 8)
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desc_str = rpad(description, 35)
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cat_str = rpad(expected_category, 25)
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alg_str = string(chosen_alg.alg)
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println("$(size_str) $(desc_str) $(cat_str) $(alg_str)")
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end
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# Test different element types
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println("\n📊 Algorithm Choice Analysis for Different Element Types:")
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println("-"^80)
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println("Size Element Type Expected Category Chosen Algorithm")
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println("-"^80)
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test_eltypes = [Float32, Float64, ComplexF32, ComplexF64]
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test_size = 200 # Medium category
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for eltype in test_eltypes
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A = rand(eltype, test_size, test_size) + I(test_size)
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b = rand(eltype, test_size)
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chosen_alg = LinearSolve.defaultalg(A, b, LinearSolve.OperatorAssumptions(true))
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size_str = lpad("$(test_size)×$(test_size)", 15)
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type_str = rpad(string(eltype), 15)
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cat_str = rpad("medium", 25)
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alg_str = string(chosen_alg.alg)
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println("$(size_str) $(type_str) $(cat_str) $(alg_str)")
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end
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# Show current preferences if any are set
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println("\n📋 Current Preferences:")
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println("-"^80)
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any_prefs_set = false
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for eltype in ["Float64"] # Just show Float64 for brevity
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for size_cat in ["tiny", "small", "medium", "large", "big"]
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best_pref = Preferences.load_preference(LinearSolve, "best_algorithm_$(eltype)_$(size_cat)", nothing)
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fallback_pref = Preferences.load_preference(LinearSolve, "best_always_loaded_$(eltype)_$(size_cat)", nothing)
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if best_pref !== nothing || fallback_pref !== nothing
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any_prefs_set = true
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println("$(eltype) $(size_cat):")
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if best_pref !== nothing
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println(" Best: $(best_pref)")
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end
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if fallback_pref !== nothing
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println(" Always-loaded: $(fallback_pref)")
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end
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end
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end
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end
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if !any_prefs_set
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println("No autotune preferences currently set.")
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end
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# Show system information
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println("\n🖥️ System Information:")
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println("-"^80)
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println("MKL available: ", LinearSolve.usemkl)
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println("Apple Accelerate available: ", LinearSolve.appleaccelerate_isavailable())
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println("RecursiveFactorization enabled: ", LinearSolve.userecursivefactorization(nothing))
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println("\n💡 Notes:")
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println("- Matrices ≤10 elements always use GenericLUFactorization (tiny override)")
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println("- Size categories: tiny(≤20), small(21-100), medium(101-300), large(301-1000), big(>1000)")
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println("- When preferences are set, the default solver should use the preferred algorithm")
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println("- Current choices show heuristic-based selection when no preferences are active")
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if set_test_preferences
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println("\n🧹 Cleaning up test preferences...")
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# Clear test preferences
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for eltype in target_eltypes
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for size_cat in size_categories
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for pref_type in ["best_algorithm", "best_always_loaded"]
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pref_key = "$(pref_type)_$(eltype)_$(size_cat)"
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if Preferences.has_preference(LinearSolve, pref_key)
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Preferences.delete_preferences!(LinearSolve, pref_key; force = true)
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end
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end
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end
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end
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println("✅ Test preferences cleared")
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end
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println("="^80)
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end
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# Run the analysis
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println("🚀 Running Default Algorithm Choice Analysis...")
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show_algorithm_choices()
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println("\n\n🔬 Now testing WITH preferences set...")
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show_algorithm_choices(clear_preferences=false, set_test_preferences=true)

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