Benchmarks

Benchmarks should be read as measurements of rank-one modified workflows, not as claims that cholrot replaces LAPACK, MKL, or OpenBLAS Cholesky factorization. The point is to avoid recomputing or storing objects that are unnecessary for a rank-one modified product or solve.

Dense rank-one benchmark

The dense benchmark compares three routes for computing

\[w = Dv, \qquad D^T D = R^T R - zz^T.\]

  1. build the modified matrix, recompute Cholesky with NumPy, then multiply;

  2. materialize D with cholrot.downdate, then multiply;

  3. compute D @ v directly with cholrot.matvec.

Run the local benchmark with:

python benchmarks/bench_rank1.py --sizes 100 200 400 800 1600 --repeat 5

Save CSV output with:

python benchmarks/bench_rank1.py --csv benchmarks/results/local.csv

Report enough environment information to make the numbers interpretable:

  • CPU model and core/thread count;

  • operating system;

  • Python version;

  • NumPy version and BLAS/LAPACK backend when known;

  • BLAS thread settings, for example OMP_NUM_THREADS or OPENBLAS_NUM_THREADS;

  • cholrot.backend() value;

  • matrix size n;

  • NumPy recompute + matvec time;

  • cholrot materialize + matvec time;

  • cholrot direct matvec time;

  • speedup relative to NumPy recompute.

Threading

The current cholrot C++ kernels are single-threaded. NumPy Cholesky may use multiple BLAS/LAPACK threads depending on the installed backend. For this reason, it is useful to report two benchmark modes:

  • single-threaded BLAS, to compare algorithmic work more directly;

  • default local BLAS settings, to show real-world behavior on the machine used.

Structured identity benchmark

The identity benchmark measures the special case

\[D D^T = I + \alpha zz^T.\]

In this setting cholrot.identity_matvec can avoid scanning a dense input factor because the original Cholesky factor is the identity.

Run it with:

python benchmarks/bench_identity.py --sizes 100 200 400 800 1600 3200 6400 --repeat 5

Scope of public benchmark results

Public benchmark tables should correspond to functions that are part of the published package API: update, downdate, matvec, cholsolve, and identity_matvec. Results from separate private experiments should not be mixed into the public benchmark tables.