pybhpt.geo performance

Timing of KerrGeodesic construction across orbit geometry and grid resolution. See the Performance overview for the methodology and reference machine.

KerrGeodesic(a, p, e, x, nsamples) is solved once per orbit and then reused by every mode, so its cost is amortized over an entire (l, m, k, n) sweep. The cost is set mainly by the orbit geometry and, at large grids, grows roughly linearly in nsamples.

Representative median times (a = 0.9):

orbit class	nsamples = 64	512	4096
circular–equatorial	7 µs	9 µs	28 µs
eccentric–equatorial	0.03–0.04 ms	0.09–0.13 ms	0.6–0.9 ms
spherical (inclined circular)	0.2–11 ms	0.3–12 ms	1–15 ms
generic (eccentric + inclined)	0.3–12 ms	0.4–12 ms	1.7–17 ms

• Circular–equatorial orbits are essentially free — the frequencies and trajectory are closed-form, so there is no grid-dependent solve.

• Eccentric–equatorial orbits scale cleanly with nsamples.

• Inclined orbits (spherical and generic) carry a large fixed cost that is nearly independent of nsamples; the wide range reflects the inclination x (near-polar orbits are the expensive end). Because this cost is paid once per orbit and shared by all modes, it is rarely the bottleneck of a production run.

Construction time across every sampled (a, p, e, x, nsamples), split by orbit class. The classes separate by orders of magnitude, and the two inclined classes are visibly bimodal — the upper cluster is the near-polar sampling.

The bimodality is inclination, not resolution: at x = 0.5 the spherical and generic orbits sit at 0.29 and 0.40 ms median, while at x = 0.1 both jump to ~11.7 ms, a factor of ~30 with everything else held equal. That split is what widens the ranges in the table above, so read those as two populations rather than a spread.

Full data: benchmarks/data/geodesic.csv.