LinAlgKit

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!) — 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 n≈8.

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.

This site is open source. Improve this page.