shaper_calibrate: speed up SHAPER_CALIBRATE smoother fitting ~2x (bit-identical)

[Hannott]

Summary

Speeds up the CPU-bound find_best_shaper autotune that runs after a resonance sweep — the compute that fits shaper candidates and produces the shaper graph (e.g. via Shake&Tune). End-to-end drops ~2.2× (7.5s → 3.5s on synthetic data) with bit-identical results. Pure performance change; self-contained (no dependency on other PRs).

The bottleneck

Profiling find_best_shaper showed ~81% of the time in _get_smoother_smoothing, called ~153,000 times for a full 9-candidate autotune. find_max_accel bisects the max acceleration for each candidate smoother at each test frequency (~30 evaluations per bisection), and every evaluation rebuilt a 100-point grid, evaluated the smoother polynomial, and ran 5 trapezoid integrations — all of which depend only on the smoother, not on the accel/scv values the bisection varies.

The fix

The smoothing offsets are linear in the accel- and scv-dependent terms, so they decompose into fixed geometry integrals of the smoother kernel:

offset_180  = (accel/2) · I2
offset_90_x = scv·Jp1 + (accel/2)·Jp2
offset_90_y = scv·Jn1 - (accel/2)·Jn2

_calc_smoother_integrals computes I2, Jp1, Jp2, Jn1, Jn2 (integrals of t²·w and t·w over the kernel — full range and each half) once per smoother and caches them; _get_smoother_smoothing evaluates the closed form. The bisection's ~30 evaluations per frequency now share one geometry computation.

The masked half-range integrals (t≥0 / t<0) are split exactly the way the original masked-then-integrate code did, so the decomposition is algebraically exact — not an approximation.

Verification

• Bit-identical: max absolute difference between the closed form and the original computation is 2×10⁻¹⁶ across all 6 smoothers and a wide accel/scv grid. find_best_shaper on synthetic resonance data produces the identical recommended shaper, frequency, vibration, smoothing, and max_accel for every candidate (full result table diff: no differences).
• Per-evaluation microbenchmark: ~62× faster; end-to-end 7.5s → 3.5s.
• ruff check / ruff format pass.

The remaining post-sweep cost is estimate_smoother's convolution, intentionally left untouched: the only ways to speed it are FFT convolution (changes numerics) or reducing grid resolution (changes results), neither worth trading the exact-results guarantee for.

Running ShakeTune CREATE_VIBRATIONS_PROFILE massively reduced calculation time. Tested on RPi 4:

08:37:25 // Machine estimated vibration symmetry: 25.7%
08:36:13 // This may take some time (5-8min)
08:36:13 // Machine vibrations profile generation...

Signed-off-by: Åsmund Collin aakjaergaard@gmail.com

[rogerlz]

Nice speedup — the decomposition is exact (trapz is linear and the t>=0/t<0 masks are applied after the mean-shift, same as before), the cache key correctly captures the smoother geometry, and since ShaperCalibrate is created per command and fit_shaper runs in the background process, cache lifetime is a non-issue.

Two small things before merge: please add a Signed-off-by trailer to the commit per our commit conventions, and drop the Co-Authored-By/Generated-with attribution from the commit and PR description.

The build CI failure is just a Docker Hub pull timeout — rerunning it.

[Hannott]

@rogerlz Done