tb_mat_pinv — 2D typed op

Data kinds: matrixmatrix

Call: fullseye.apply(img, "tb_mat_pinv", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

*No figure: this op takes matrix as input. A Studio program starting from an image cannot reach that type — see the runnable examples below for how it is used.*

Usage

Moore-Penrose pseudo-inverse via SVD, with the cutoff explicit.

Singular values below `rcond * s_max` are treated as zero — that cutoff

*is* the regularisation, so it is a named, documented parameter here

(default `1e-12`) rather than a hidden library default: raising it

discards noisy directions (stabler, more biased), lowering it keeps them

(exact for well-conditioned *A*, explosive near rank deficiency).

Works for any `(m, n): pinv(A) @ b` is the least-squares solution for

`m > n and the minimum-norm solution for m < n`.

HALCON: no direct operator — HALCON reaches the same result through

`svd_matrix` + reciprocal singular values.

Typed bridge of the math op `mat_pinv into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives rcond (default 1e-12); b` is unused.

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

Runnable examples (verified samples that actually call this op)

• (none yet)

Ops the type connects to (they accept matrix as input)

identity · tb_mat_cond · tb_stat_covariance · tb_stat_correlation

Same category (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 operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

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