dynsys opなし → table(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.ode_flow_states(system='lorenz', params=None, x0=None, t_end=40.0, dt=0.005, method='rk4') (実装を直接呼ぶなら import mathops; mathops.ode_flow_states(system='lorenz', params=None, x0=None, t_end=40.0, dt=0.005, method='rk4')、台帳から引くなら opsmath.get("ode_flow_states"))Integrate a named vector field — the trajectory, with the order you paid for.
Explicit Runge-Kutta on one of the named systems (lorenz, rossler,
harmonic, linear). method="rk4" is the classical 4th-order step;
method="euler" is there as a control group — the same picture comes out
of both, and only the error tells them apart.
For a linear system the classical RK4 polynomial update matrix is formed once and reused. It is deliberately not the matrix exponential: the expected fifth-order one-step difference remains observable.
★Why the field is a name, not a function: the typed ledger registers inputs
by sort and the chain fuzzer builds arguments from data, so a callable can
never be reached from there. A name (or, for linear, the matrix itself in
params) keeps every op in this family reachable from the ledger.
★Why this earns its place: for system="linear" the exact solution is
expm(A t) x0, so the error is known in closed form — and halving dt
divides it by 16, which is what “4th order” means. A drawing of an
attractor cannot be checked; this can.
system : str
One of DYNSYS_SYSTEMS.
params : floats or None
System parameters (defaults in DYNSYS_SYSTEMS). For linear this is
the matrix A in row-major order (n*n numbers).
x0 : floats or None
Initial state (default: a point on the attractor / unit first coordinate).
t_end, dt : float
Integration window and step. t_end / dt must stay under 4,000,000.
method : “rk4” | “euler”
Returns a states table: t (S,) and one (S,) column per state,
named x0, x1, … .
Raises ValueError: unknown system or method; wrong parameter count;
non-finite input; dt not positive; a step count over the cap; a trajectory
that left float range (the field diverged — reported, never silently clipped).
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.pytable を入力に取れる)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
dynsys)ode_vector_field_grid · dynsys_poincare_section · dynsys_lyapunov_spectrum · 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.