stats op• Data kinds: signal → signal
• Call: import mathops; mathops.stat_zscore(x) (or opsmath.get("stat_zscore"))
Standardise a 1-D sample: `(x - mean) / std (population ddof=0`).
The result has mean 0 and standard deviation 1 — the common currency for
comparing residuals across scales and flagging outliers (`|z| > 3`).
**A constant input raises `ValueError`** — the decision, stated: with
zero variance the z-score is 0/0. Returning silent zeros would claim "every
point is perfectly average", which is *a* convention but hides upstream
breakage (a sensor stuck at one value would sail through an outlier gate).
Fail-closed instead; a caller who wants the all-zeros convention can catch
this and substitute deliberately.
HALCON: no direct tuple operator (compose `tuple_mean` +
`tuple_deviation` + arithmetic).
Every mathops op validates its input before computing (nothing slips through silently):
• **complex input raises ValueError** — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• **masked arrays with masked elements raise ValueError** — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• **NaN/Inf raises ValueError on every input** (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• measurement_uncertainty — 計測の不確かさと校正の知識 — 「測れている」を主張するために
• 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.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• math_metrology — py -3.11 examples/math_metrology.py
signal as input)mat_solve · mat_lstsq · stat_describe · stat_histogram · interp_linear · interp_cubic · poly_fit · poly_eval
stats)stat_describe · stat_histogram · stat_covariance · stat_correlation
*Provenance: mathops.py — MATH 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.