dynsys op• 資料種類:無 → table(僅由參數決定的運算子 —— 不接受影像或資料輸入)
• 呼叫: import fullseye as fs; fs.ledger.ode_flow_states(system='lorenz', params=None, x0=None, t_end=40.0, dt=0.005, method='rk4')(要直接呼叫實作,import mathops; mathops.ode_flow_states(system='lorenz', params=None, x0=None, t_end=40.0, dt=0.005, method='rk4');從台帳取用則 opsmath.get("ode_flow_states"))
對具名向量場做積分 —— 軌道,以及你所付出的階數。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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.
★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 x (S, n).
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 的每個運算子都先檢驗輸入再計算(不讓任何東西無聲通過):
• complex 輸入一律 ValueError —— 強制轉成 float64 會無聲丟掉虛部(numpy 只發一個 ComplexWarning,然後回傳一個「看似合理卻是錯的」實數)。請明確寫出 .real/.imag/abs(),或改用支援複數的 complexops。
• 含被遮罩元素的 masked array 一律 ValueError —— 拒絕「剝掉遮罩直接使用下面原值」的隱式轉換。請明確選擇填補還是丟棄。
• 所有輸入中的 NaN/Inf 一律 ValueError(明確給出個數後拒絕 —— 它會汙染整個結果)。
• 形狀嚴格:不對 1-D 與 2-D 做隱式提升或廣播(向量槽位收到矩陣、矩陣槽位收到向量都是 ValueError;請明確 reshape)。
• 尺寸上限:接受矩陣的運算子與 stat_histogram 的 bins,超過 mathops.MAX_ELEMENTS(2^26 ≈ 6700 萬個元素)即 ValueError。
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
• poc_what_a_picture_cannot_check — py -3.11 examples/poc_what_a_picture_cannot_check.py
table 作為輸入)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 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.