Force enable MKL during benchmarking to ensure availability

- Set LoadMKL_JLL=true before loading LinearSolve in autotune module
- This ensures MKL algorithms are available for benchmarking
- Track the original preference to inform user of temporary change
- Final preference is still set based on benchmark results
- Added documentation explaining this behavior

Author: ChrisRackauckas

lib/LinearSolveAutotune/src/LinearSolveAutotune.jl

@@ -1,9 +1,22 @@
 module LinearSolveAutotune
 
-# Note: MKL preference should be set before loading LinearSolve for optimal performance
-# The autotune system will write the appropriate preference based on benchmark results
+# Ensure MKL is available for benchmarking by setting the preference before loading LinearSolve
 using Preferences
 using MKL_jll
+
+# Set MKL preference to true for benchmarking if MKL is available
+# We need to use UUID instead of the module since LinearSolve isn't loaded yet
+const LINEARSOLVE_UUID = Base.UUID("7ed4a6bd-45f5-4d41-b270-4a48e9bafcae")
+if MKL_jll.is_available()
+    # Force load MKL for benchmarking to ensure we can test MKL algorithms
+    # The autotune results will determine the final preference setting
+    current_pref = Preferences.load_preference(LINEARSOLVE_UUID, "LoadMKL_JLL", nothing)
+    if current_pref !== true
+        Preferences.set_preferences!(LINEARSOLVE_UUID, "LoadMKL_JLL" => true; force = true)
+        @info "Temporarily setting LoadMKL_JLL=true for benchmarking (was $(current_pref))"
+    end
+end
+
 using LinearSolve
 using BenchmarkTools
 using DataFrames
@@ -145,6 +158,12 @@ Run a comprehensive benchmark of all available LU factorization methods and opti
   - Set Preferences for optimal algorithm selection
   - Support both CPU and GPU algorithms based on hardware detection
   - Test algorithm compatibility with different element types
+  - Automatically manage MKL loading preference based on performance results
+
+!!! note "MKL Preference Management"
+    During benchmarking, MKL is temporarily enabled (if available) to test MKL algorithms.
+    After benchmarking, the LoadMKL_JLL preference is set based on whether MKL algorithms
+    performed best in any category. This optimizes startup time and memory usage.
 
 # Arguments
 

lib/LinearSolveAutotune/src/preferences.jl

@@ -128,6 +128,8 @@ function set_algorithm_preferences(categories::Dict{String, String})
 
     # Set MKL preference based on whether it was best for any category
     # If MKL wasn't best anywhere, disable it to avoid loading unnecessary dependencies
+    # Note: During benchmarking, MKL is temporarily enabled to test MKL algorithms
+    # This final preference setting determines whether MKL loads in normal usage
     Preferences.set_preferences!(LinearSolve, "LoadMKL_JLL" => mkl_is_best_somewhere; force = true)
 
     if mkl_is_best_somewhere