Performance & benchmarks

Performance notes

A few rules of thumb when scattering calculations get expensive:

  • Cost grows with the size parameter. The truncation order needed for convergence scales roughly with $x = 2\pi r/\lambda$, and the dense linear algebra is super-linear in that order. Large particles are intrinsically costly.
  • Reach for stable before raising precision on high-aspect spheroids. For an elongated spheroid in Float64, Iterative(EBCM; stable = true) is both more accurate and faster than bumping the element type to Double64 without it; see Usage → High-aspect-ratio spheroids.
  • Extended precision is several times slower. Double64/Arb buy headroom against round-off and larger size parameters, but at a real runtime cost. Use them when accuracy demands it, not by default.
  • Reuse a preparation for parameter sweeps. When you need one shape at many wavelengths or refractive indices, prepare_sh / ShMatrix amortise the geometry quadrature across all points.
  • Multithreading. Several kernels use threads; start Julia with julia --threads=auto (or set JULIA_NUM_THREADS) to use them.

The benchmark suite

The repository ships a benchmark suite built on BenchmarkTools.jl, in benchmark/. It follows the standard Julia convention — benchmark/benchmarks.jl defines a single global const SUITE::BenchmarkGroup — so it works unchanged with both PkgBenchmark.jl and AirspeedVelocity.jl.

Benchmark groups:

  • special_functions — Riccati–Bessel and Wigner-d recursions (inner kernels).
  • ebcm — EBCM blocks, fixed-order solves, and end-to-end auto-convergence.
  • iitm — invariant-imbedding T-matrix (axisymmetric and N-fold).
  • postprocessing — far-field observables from a precomputed T-matrix.
  • linearization — the analytical EBCM Jacobian.
  • precision — Float64 vs Double64 on the same EBCM block.

Running

The simplest path uses the repository's justfile:

just bench            # instantiate the env and run the whole suite

Or directly, in the isolated benchmark/ environment:

julia --project=benchmark -e 'using Pkg; Pkg.develop(path="."); Pkg.instantiate()'
julia --project=benchmark benchmark/runbenchmarks.jl results-baseline.json

Absolute timings are machine-specific, so no numbers are reproduced here; the suite is meant for tracking relative changes (regressions and speed-ups) between revisions. See benchmark/README.md for the full layout.