tb_mat_cond — 2D `typed` op

• Data kinds: matrix → feature

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

tb_mat_cond: input → output

*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*

*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*

*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*

Stages (the ops that come before → this op, left to right):

▸ tb_mat_cond: stages (docs site)

Usage

Spectral (2-norm) condition number `s_max / s_min` — the numerical canary of the whole linalg family.

`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.

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.

Try it in Studio

The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.

img_to_matrix 0.50 0.50
tb_mat_cond 0.50 0.50

▸ Load this pipeline · Load & run

Runnable examples (verified samples that actually call this op)

The examples below call the underlying ledger op mat_cond. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).

• math_metrology — py -3.11 examples/math_metrology.py

Ops the type connects to (they accept `feature` as input)

identity · feature_to_img

Same category (`typed`)

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

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

tb_mat_cond — 2D typed op