pybhpt.flux performance

Timing of the gravitational-wave flux computation. See the Performance overview for the methodology and reference machine.

FluxMode(geo, teuk) turns an already-solved TeukolskyMode into the energy, angular momentum, and Carter-constant fluxes at infinity and on the horizon. It runs no solver of its own: it reads the mode amplitudes and forms a fixed algebraic combination of them. So there is no useful flux-specific timing table — the cost of a flux is the cost of the Teukolsky modes that feed it.

Flux is a rounding error on the mode solve

Measured against the solve it consumes, at the same mode (s = -2, a = 0.9):

orbit class	mode (l,m,k,n)	nsamples	solve	flux	flux share
circular–equatorial	(2,2,0,0)	64	0.24 ms	1 µs	0.61%
circular–equatorial	(2,2,0,0)	4096	6.5 ms	4 µs	0.06%
spherical	(2,2,0,0)	64	0.23 ms	1 µs	0.55%
generic	(5,3,-2,3)	512	3.6 ms	1 µs	0.04%
generic	(8,4,2,10)	4096	54.5 ms	4 µs	0.01%

The largest flux share anywhere in the swept grid is 0.61%, at the cheapest mode on the coarsest grid; it drops to a few hundredths of a percent for the expensive modes, because the flux step is essentially constant in nsamples while the solve is not.

Full data: benchmarks/data/teuk_flux.csv, produced by bench_teuk.py alongside the mode-solve benchmarks.

Budgeting a flux calculation

Plan from the pybhpt.teuk numbers instead, and treat the flux itself as free:

wall time ≈ (number of (l, m, k, n) modes summed) × (per-mode solve cost)

with the per-mode cost read off the teuk aggregate table for your orbit class and resolution. Two consequences from that table:

• Orbit class dominates. A generic (eccentric + inclined) orbit costs ~8× a circular–equatorial one at nsamples = 512, because its source integral is a full 2D radial × polar loop.

• The mode count, not the flux algebra, sets the bill. Cost per mode keeps climbing with l and n rather than plateauing, so how deep the mode sum is truncated matters far more than anything on this page.

The one-off KerrGeodesic construction (pybhpt.geo performance) is shared by every mode in the sum and is negligible against it, except for near-polar orbits where the geodesic solve itself costs ~10 ms.