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Performance Guide

This page explains the performance characteristics of LinAlgKit and how to reproduce benchmark results.

Determinant algorithms

  • determinant(): Bareiss fraction-free LU with partial pivoting; O(n^3), stable for integer matrices.
  • determinant_naive(): Laplace expansion; O(n!) ā€” only for tiny matrices/testing.

Running benchmarks

Build with benchmarks enabled and run the harness:

mkdir -p ~/matrixlib_build && cd ~/matrixlib_build
cmake -G "Unix Makefiles" -DBUILD_BENCHMARKS=ON /path/to/repo
cmake --build . -j
python3 /path/to/repo/scripts/run_benchmarks.py --build-dir . --csv results.csv --plot results.png

The harness saves a CSV from Google Benchmark and optionally a simple bar plot (if matplotlib is installed).

Interpreting benchmark output

  • real_time is the per-iteration runtime (ns), averaged over repetitions.
  • Determinant (optimized) should scale roughly with O(n^3).
  • Determinant (naive) grows factorially; use only up to nā‰ˆ8.

Tips

  • Build Release for meaningful numbers.
  • Avoid running on a heavily loaded system.
  • For multi-run studies, pin CPU frequency/governor and isolate cores if possible.