dynsys opなし → signal(引数だけで決まる op —— 画像やデータの入力を取らない)import fullseye as fs; fs.ledger.dynsys_lyapunov_spectrum(system='lorenz', params=None, x0=None, t_end=200.0, dt=0.005, burn_in=20.0) (実装を直接呼ぶなら import mathops; mathops.dynsys_lyapunov_spectrum(system='lorenz', params=None, x0=None, t_end=200.0, dt=0.005, burn_in=20.0)、台帳から引くなら opsmath.get("dynsys_lyapunov_spectrum"))The Lyapunov spectrum by tangent flow + QR — and the sum you can check.
Integrates the state together with an orthonormal frame of tangent vectors
(the variational equation dY/dt = J(x) Y), re-orthonormalising by QR at
every step and accumulating log of the diagonal. The exponents come out
ordered, largest first.
★★Why this earns its place — the trace identity. The sum of the exponents equals the time-average of the divergence of the field:
sum(lambda_i) == <div f>
For Lorenz the divergence is the constant -(sigma + 1 + beta), so the
sum is known in closed form: -13.6667 for the classical parameters. That
is an exact target the attractor picture cannot provide. The published largest
exponent (≈ 0.906 for sigma=10, beta=8/3, rho=28) is a second, independent
check.
Returns a signal: the exponents, descending.
The burn-in uses round(burn_in / dt) steps, and the measured window uses
round((t_end - burn_in) / dt) steps. Thus their actual integrated times
are those step counts multiplied by dt; a measured window rounding to
zero steps is rejected rather than extended past the requested time.
Raises ValueError: unknown system; non-finite input; burn_in not
shorter than t_end; a measured window shorter than one rounded step; a
trajectory that left float range.
Limits: the exponents converge like 1/sqrt(T) — a short window gives a
plausible but wrong spectrum. The trace identity converges much faster and is
the honest gate; the individual exponents need long windows.
HALCON: no operator.
mathops の全 op は入力を検証してから計算する(黙って通さない):
ValueError — float64 への強制変換は虚部を黙って捨てる(numpy は ComplexWarning だけ出して「もっともらしく間違った」実数を返す)。.real/.imag/abs() を明示するか、複素対応の complexops を使う。ValueError — マスクを剥がして下の生値を使う暗黙変換を拒否。埋める/落とすを明示する。ValueError(件数を明示して拒否 — 結果全体に伝播するため)。ValueError。reshape を明示する)。stat_histogram の bins は mathops.MAX_ELEMENTS(2^26 ≈ 6700 万要素)超で ValueError。py -3.11 examples/poc_what_a_picture_cannot_check.pysignal を入力に取れる)mat_solve · mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · interp_cubic · interp_scattered
dynsys)ode_flow_states · ode_vector_field_grid · dynsys_poincare_section · dynsys_bifurcation_map · dynsys_correlation_dimension
Provenance: mathops.py — MATH 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.