complex opcimage → rgbimageimport fullseye as fs; fs.ledger.cplx_domain_colour(field, gamma=1.0, bands=0.0, saturation=1.0) (実装を直接呼ぶなら import mathops; mathops.cplx_domain_colour(field, gamma=1.0, bands=0.0, saturation=1.0)、台帳から引くなら opsmath.get("cplx_domain_colour"))Domain colouring: turn a complex field into an RGB image you can read.
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 :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.
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_complex_plane_fields.pyrgbimage を入力に取れる)—
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 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.