ImCoh is documented signed but returns |Im|; ccorr and accorr use opposite sign conventions

[Ramdam17]

Two related sign-convention problems.

1. ImCoh documented signed, implemented as absolute value.

hypyp/sync/imaginary_coh.py:39 and hypyp/analyses.py:504 both write ImCoh = Im(⟨XY*⟩) / √(⟨|X|²⟩⟨|Y|²⟩), with no absolute value. hypyp/sync/README.md likewise. The code takes the magnitude — hypyp/sync/imaginary_coh.py:92:

con = np.abs(np.imag(dphi)) / np.sqrt(...)

Same in numba (:174), torch (:138) and CUDA (cuda_amplitude.py:95, fabs(im)). Measured: no negative value is ever produced.

This discards information. In Nolte et al. 2004 the sign of the imaginary part of coherency carries the lead/lag direction of the interaction; folding it to a magnitude removes the directionality that is a large part of why one reaches for ImCoh in the first place.

2. ccorr and accorr disagree on sign, although presented as variants of the same quantity.

Measured off-diagonal ranges on the same input:

  ccorr    min=+0.001457 max=+0.113029 any_negative=False
  accorr   min=-0.082383 max=+0.078357 any_negative=True
  imcoh    min=+0.001452 max=+0.121609 any_negative=False
  envcorr  min=-0.107288 max=+0.110752 any_negative=True

ccorr takes the absolute value in every backend (numpy ccorr.py:99, numba :236, torch :157, CUDA fabs), while accorr is signed (accorr.py:183, num = r_minus - r_plus with no abs). Both are internally consistent across backends, so neither is a backend bug — but a user comparing ccorr against accorr on the same dataset is comparing a magnitude to a signed quantity.

This is worth resolving deliberately given that ACCorr's reference paper (Zimmermann et al. 2024, Imaging Neuroscience) is specifically about arbitrary methodological decisions skewing inter-brain synchrony estimates.

Suggested fix: decide the intended convention per metric, apply it uniformly across the five backends, and document it explicitly in each class docstring and in sync/README.md. Preserving the sign and letting callers take abs() is the more informative default.