construct op• 資料種類:pairs → signal
• 呼叫: import fullseye as fs; fs.ledger.neighbour_index_gaps(points, k=6)(要直接呼叫實作,import mathops; mathops.neighbour_index_gaps(points, k=6);從台帳取用則 opsmath.get("neighbour_index_gaps"))
最近鄰之間在編號上相距多遠 —— 把斜列(parastichy)變成數。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
In a phyllotactic pattern the visible spirals (parastichies) are not drawn
by anything; they are an illusion of which florets happen to sit next to each
other. This op replaces the illusion with a count: for every point, take its
*k* nearest neighbours in space and record the difference of their
ordering indices. The histogram of those differences is returned, index
`g holding how many neighbour pairs were g` apart.
★Why this earns its place: with the golden angle the peaks land on
Fibonacci numbers (8, 13, 21, 34, 55 ...), and with any other angle they
do not. That is a statement about the arrangement which can be checked
without looking at the picture — which is the whole point, because the
spirals look convincing at every angle.
Parameters
----------
points : (N, 2) array
Ordered points — the order is the data here, not a convenience.
k : int >= 1
Neighbours per point (6 is the natural choice: a well-packed planar
arrangement is locally hexagonal).
Returns a `signal: counts[g]` = number of neighbour pairs whose index
difference is `g (counts[0]` is always 0 — a point is not its own
neighbour).
Raises `ValueError: not an (N, 2) array; fewer than k + 1` points;
`k` below 1; non-finite coordinates.
Limits: the first points of a spiral sit near the centre where the packing
is degenerate, so the histogram has a low-index tail that carries no
parastichy information. Compare *peaks*, not the raw tail.
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_theorems_as_pictures — py -3.11 examples/poc_theorems_as_pictures.py
signal 作為輸入)mat_solve · mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · interp_cubic · interp_scattered
construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · ifs_fractal · ifs_similarity_dimension · space_filling_curve · curve_locality
*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.