direction opmatrix × table → matriximport fullseye as fs; fs.ledger.fly_t4t5_field(movie, lattice, dt_s, tau_s=0.25, k_e=5.0, k_d=5.0, k_s=10.0, dc=1.0, model='three_arm', tau_hr_s=0.05, reduce='mean') (実装を直接呼ぶなら import flyvision; flyvision.fly_t4t5_field(movie, lattice, dt_s, tau_s=0.25, k_e=5.0, k_d=5.0, k_s=10.0, dc=1.0, model='three_arm', tau_hr_s=0.05, reduce='mean')、台帳から引くなら opsflyvision.get("fly_t4t5_field"))Direction-selective response over the whole eye, in the six hexagonal directions.
T4 (ON) and T5 (OFF) are the first direction-selective cells in the fly, and two mechanisms make them so: preferred-direction enhancement, which is the Hassenstein-Reichardt multiplication, and null-direction suppression, which is the Barlow-Levick division. Haag et al. measured both in one cell and wrote them as three arms reading three adjacent columns — an enhancing arm E one column before the centre, the direct arm D, and a suppressing arm S one column after it::
R = (dc + k_e * LP[E]) * (dc + k_d * D) / (dc + k_s * LP[S])
with first-order low-passes of time constant tau_s on E and S. This op
runs that, or either mechanism alone, at every ommatidium and in all six
lattice directions at once.
movie: (T, n) one polarity channel — the ON or the OFF half of
:func:fly_onoff_split, not both. lattice: a :func:fly_hex_lattice result
(a :func:fly_eye_merge result is refused: its coordinates repeat, so a
neighbour would be looked up in the wrong patch).
dt_s: sample interval, seconds.
model: one of four, the first three sharing the same resting value dc so
that their responses are directly comparable —
"three_arm" — the whole model above (Haag et al., eLife 5:e17421,
2016);"enhance" — the numerator alone, (dc + k_e LP[E])(dc + k_d D)/dc:
preferred-direction enhancement, the Hassenstein-Reichardt
multiplication with no veto;"suppress" — the denominator alone, dc (dc + k_d D)/(dc + k_s
LP[S]): null-direction suppression, the Barlow-Levick division with
no enhancement (Barlow & Levick, J. Physiol. 178:477, 1965);"hr" — the classical opponent correlator LP[E]*D - E*LP[D] with
its own time constant tau_hr_s, which is antisymmetric by construction
and so is direction-selective without either of the two mechanisms above
(Hassenstein & Reichardt, Z. Naturforsch. 11b:513, 1956). It is
:func:fly_emd_response run over the lattice instead of a pair.
tau_s / k_e / k_d / k_s / dc: the three-arm parameters. The defaults are the
paper’s (tau = 250 ms, k = 5/5/10, DC = 1.0). tau_hr_s: the correlator time
constant, used by model="hr" only.
reduce: how the time course becomes one number per direction — "mean"
(the wide-field integration a tangential cell performs), "last" (the
value at the final sample, which is how a transient is read at a chosen
instant) or "max".Returns a (6, n) float64 matrix: row k is the response to motion in
hexagonal direction k (counter-clockwise from +azimuth, see
:data:HEX_STEPS), averaged over time, with the model’s resting value
subtracted so that no stimulus reads exactly 0. It is the (k, n) shape
:func:fly_hs_readout and :func:fly_flow_from_directions take.
Ommatidia at the rim, which have no neighbour on one side, read exactly 0 in that direction: a detector missing an arm has no motion to report, and inventing one at the edge would put a ring of false flow around every eye.
Ground truth, and it is the paper’s claim written as algebra: because the three arms multiply, the direction selectivity of the whole model is the product of the selectivities of its two halves. For any stimulus and any pair of opposite directions,
ratio("three_arm") == ratio("enhance") * ratio("suppress")
exactly, where ratio = R_preferred / R_null taken on R + dc. Two
columns lit in turn, a step of amplitude 1 held for tau, with the paper’s
constants, give R + dc = (dc + k_e(1-1/e))(dc + k_d)/dc = 24.96
preferred and dc(dc + k_d)/(dc + k_s(1-1/e)) = 0.820 null: 4.16 from
enhancement, 7.32 from suppression, 30.46 together. The tests measure all
three and the identity between them.
Raises ValueError: a non-2-D / too-short / non-finite movie, a
column count that is not the lattice’s ommatidium count, a non-positive
dt_s / tau_s / tau_hr_s / dc, a negative gain, an unknown model,
and any malformed lattice.
py -3.11 examples/poc_fly_optomotor_steering.pymatrix を入力に取れる)fly_lamina_filter · fly_onoff_split · fly_flow_from_directions · fly_egomotion_from_flow · fly_hs_readout
direction)Provenance: flyvision.py — FLYVISION operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.