complex op• 資料種類:cimage → rgbimage
• 呼叫: import fullseye as fs; fs.ledger.cplx_domain_colour(field, gamma=1.0, bands=0.0, saturation=1.0)(要直接呼叫實作,import mathops; mathops.cplx_domain_colour(field, gamma=1.0, bands=0.0, saturation=1.0);從台帳取用則 opsmath.get("cplx_domain_colour"))
定義域著色 —— 把複場變成可以讀懂的 RGB 影像。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
Hue carries arg(z) (one full turn of the colour wheel per turn of the argument, red at arg = 0); value carries |z| through the strictly increasing map t/(1+t) with t = |z|**gamma, so a zero is exactly black, |z| = 1 is half brightness and a large modulus saturates at full brightness. The saturation is not dropped far from the origin, so the hue — and with it the argument — stays readable everywhere; pass saturation = 0 for a plain grey ramp of the modulus alone. With bands = 0 (the default) the brightness is monotone in |z|, which means the picture is *invertible*:
the argument comes back out of the hue and the modulus out of the value.
★The picture proves a theorem. Walk a small circle around a zero of order *m* and the hue cycles through the colour wheel exactly *m* times; around a pole of order *m*, *m* times the other way. That is the argument principle, read off the image with no numbers — and this family's cplx_winding_number counts the same integer from the field itself, so the drawing and the arithmetic check each other.
field : complex 2-D array (cimage)
Typically from cplx_rational_field.
gamma : float > 0
Compresses (<1) or stretches (>1) the modulus ramp.
bands : float >= 0
Classic modulus contours: bands shading cycles per decade of
|z|. Non-zero breaks monotonicity (that is the point — it draws
level lines), so the inverse-mapping guarantee above holds only at 0.
saturation : float in [0, 1]
Raises ValueError: not a 2-D complex array; non-finite samples (a pole sampled exactly — see cplx_rational_field); gamma <= 0; bands < 0; saturation outside [0, 1].
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_complex_plane_fields — py -3.11 examples/poc_complex_plane_fields.py
rgbimage 作為輸入)—
complex)cplx_contour_circle · cplx_poly_eval · cplx_contour_integral · cplx_winding_number · cplx_cauchy_value · cplx_argument_principle · cplx_laurent_coeffs · cplx_joukowski
*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.