tb_mat_cond — 2D typed op

数据种类:matrixfeature

调用:fullseye.apply(img, "tb_mat_cond", a=0.5, b=0.5)(2-D 的模型是一张图 + 两个标量旋钮 a,b∈[0,1])

*无图: 该算子以 matrix 为输入。从图像开始的 Studio 程序无法到达该类型,请参见下方的可运行示例。*

用法

谱(2-范数)条件数 `s_max / s_min`——整个线性代数(linalg)算子族的数值健康指标(canary)。

> 以下的详细说明为原文 —— 摘要与标题已翻译。

`cond == 1` for an orthogonal/orthonormal matrix (the best possible);

`inf` (returned, not raised — the question "how conditioned is it?" has

that honest answer) for an exactly singular one. A solve against *A* loses

roughly `log10(cond(A))` significant digits (Golub & Van Loan §2.6):

• `cond ~ 1e3` — comfortable, ~13 digits survive.

• `cond ~ 1e8` — half the digits are gone; residuals may still look

small while parameters are off.

• `cond > 1e12 — **do not trust** :func:mat_solve` here: at best ~3

digits remain. Rescale/centre the problem, or switch to

:func:mat_lstsq / :func:mat_pinv with an honest `rcond`.

Defined for any rectangular `(m, n)` matrix (via its singular values).

HALCON: no direct operator (combine `norm_matrix` of *A* and of its

inverse).

Typed bridge of the math op `mat_cond into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b` are unused.

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。

可运行的示例(实际调用该算子并已验证的样例)

• (暂无)

类型可衔接的下一个算子(可接受 feature 作为输入)

identity

同类别(typed)

tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal


*Provenance: ops.py — 2D 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.