Make predict_sequence march (integrate once, interpolate per detection)

[matthewholman]

Summary

predict_sequence re-integrated each orbit from its epoch for every requested time. It looped detections calling predict_from_fit_result → predict, and predict does reb_simulation_create … assist_free … reb_simulation_free per call — so predicting an orbit to N times ran N full integrations from the epoch, each with its own IAS15 ramp-up.

residuals_at_state (#406) already solved exactly this for the fit/rejection path with a sorted forward + backward single pass that reuses one sim and lets integrate_or_interpolate interpolate at each detection. predict_sequence simply never got the same treatment. This PR gives it that treatment.

Change

• predict_sequence now marches. It splits detections into those after the epoch (marched forward) and before it (marched backward), each sorted, and runs each pass against a single sim — so the trajectory is integrated once per direction and integrate_light_time → assist_integrate_or_interpolate interpolates at each detection, instead of a fresh integration per detection. Mirrors residuals_at_state/create_sequences.
• Refactored the per-detection geometry + covariance out of predict() into a reusable compute_single_predict(ephem, ax, var, …) that operates on an existing sim. The bound single-observation predict() keeps its own sim create/free and is behavior-unchanged.
• Because each detection carries its own observer position, a single predict_sequence call may now mix observatories (each detection is light-corrected against its own station).

Correctness

integrate_or_interpolate makes the integration independent of the query times (it interpolates at each), so the marching result is bit-identical to the per-detection path:

max |ΔRA|  = 0.000e+00 deg
max |ΔDec| = 0.000e+00 deg
max ellipse rel diff = 0.000e+00

(verified across times both before and after the epoch, i.e. both passes). New test test_predict_sequence_marches_equivalently asserts a one-call multi-time prediction equals per-time predictions to integrator precision.

Impact

Any multi-time prediction benefits — ephemeris generation, the predict CLI over a time grid, and covariance-aware prediction of a catalog to many epochs — turning N integrations per orbit into ~1. No API change (predict / predict_sequence signatures and outputs are unchanged).

🤖 Generated with Claude Code

[kjnapier]

Good