cplx_domain_colour — MATH `complex` op

• 数据种类:cimage → rgbimage

• 调用: import fullseye as fs; fs.ledger.cplx_domain_colour(field, gamma=1.0, bands=0.0, saturation=1.0)(要直接调用实现,import mathops; mathops.cplx_domain_colour(field, gamma=1.0, bands=0.0, saturation=1.0);从台账取用则 opsmath.get("cplx_domain_colour"))

用法

定义域着色 —— 把复场变成可以读懂的 RGB 图像。

> 以下的详细说明为原文 —— 摘要与标题已翻译。

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.

Parameters

----------

field : complex 2-D array (`cimage`)

Typically from :func: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 :func:cplx_rational_field); `gamma <= 0`;

`bands < 0; saturation` outside [0, 1].

HALCON: no operator.

该族通用的输入契约(fail-closed)

mathops 的每个算子都先校验输入再计算(不让任何东西无声通过):

• **complex 输入一律 ValueError** —— 强制转成 float64 会无声丢掉虚部(numpy 只发一个 ComplexWarning,然后返回一个「看着合理却是错的」实数)。请显式写出 .real/.imag/abs(),或改用支持复数的 complexops。

• **含被掩元素的 masked array 一律 ValueError** —— 拒绝「剥掉掩码直接使用下面原值」的隐式转换。请显式选择填充还是丢弃。

• **所有输入中的 NaN/Inf 一律 ValueError**(明确给出个数后拒绝 —— 它会污染整个结果)。

• 形状严格:不对 1-D 与 2-D 做隐式提升或广播(向量槽位收到矩阵、矩阵槽位收到向量都是 ValueError;请显式 reshape)。

• 尺寸上限:接受矩阵的算子与 stat_histogram 的 bins,超过 mathops.MAX_ELEMENTS(2^26 ≈ 6700 万个元素)即 ValueError。

详细使用指南

• math_metrology 族使用指南

参考(示例数据・文献)

• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。

• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。

• 算法的正典(作者・年份)与用途见上面的族使用指南。

可运行的示例(实际调用该算子并已验证的样例)

• poc_complex_plane_fields — py -3.11 examples/poc_complex_plane_fields.py

类型可衔接的下一个算子(可接受 `rgbimage` 作为输入)

—

同类别(`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 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*

cplx_domain_colour — MATH complex op

用法