Change :auto sparse heuristic to size-based threshold#158
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Tests define expected behavior for sparse_threshold parameter: - NonlinearSolverOptions accepts sparse_threshold (default=50) - :auto mode uses M matrix size instead of graph position - Nash games (all leaves) get sparse solve for large M - Small M matrices stay on dense path with high threshold Co-Authored-By: Claude Opus 4.6 <[email protected]>
Replace graph-position-based heuristic (!is_leaf) with size-based heuristic (size(M, 1) >= sparse_threshold). This means leaf players with large M matrices now benefit from sparse factorization too. Key changes: - Add sparse_threshold::Int field to NonlinearSolverOptions (default=50) - Thread sparse_threshold through solve_raw → run_nonlinear_solver → compute_K_evals - Update _merge_options to support sparse_threshold override - Change heuristic: size(M_buf, 1) >= sparse_threshold instead of !is_leaf(graph, ii) The default threshold of 50 rows means: - 3-player chain P3 (24×24 leaf): stays dense (below threshold) - 3-player chain P2 (56×64 leader): uses sparse (above threshold) - 4-player chain all players (60-204 rows): all use sparse Co-Authored-By: Claude Opus 4.6 <[email protected]>
Results show the new :auto (threshold=50) matches :always performance: - 3-player chain: 0.33ms → 0.18ms (-45%), 1238KB → 556KB (-55%) - 4-player chain: 9.56ms → 2.27ms (-76%), 11659KB → 6648KB (-43%) The new :auto even beats :always on allocations for 3-player chain because Player 3 (24×24) stays on dense path, avoiding sparse overhead. Co-Authored-By: Claude Opus 4.6 <[email protected]>
Co-Authored-By: Claude Opus 4.6 <[email protected]>
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Summary
Replace the graph-position-based
:autosparse heuristic (!is_leaf) with a size-based heuristic (size(M, 1) >= sparse_threshold). This means leaf players with large M matrices now benefit from sparse LU factorization, dramatically improving performance for medium-to-large problems.Changes
src/types.jl: Addsparse_threshold::Intfield toNonlinearSolverOptions(default=50), thread throughNonlinearSolverconstructorsrc/nonlinear_kkt.jl: Change heuristic from!is_leaf(graph, ii)tosize(M_buf, 1) >= sparse_thresholdincompute_K_evals; addsparse_thresholdkwarg tocompute_K_evalsandrun_nonlinear_solversrc/solve.jl: Addsparse_thresholdto_merge_options,solve, andsolve_rawtest/test_sparse_threshold.jl: 14 new tests covering options, heuristic behavior, Nash games, and integrationtest/test_tiers.jl,test/test_test_tiers.jl: Register new test filescripts/benchmark_sparse_threshold.jl: Benchmark comparing :never, new :auto, and :alwaysRETROSPECTIVES.md: PR retrospectiveBenchmark Results
New
:automatches:alwaysfor large matrices and beats it on allocations for the 3-player chain because Player 3 (24×24) stays on the faster dense path.Testing
julia --project=. -e 'using Pkg; Pkg.test()')Changelog
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