stats op• Data kinds: signal → table
• Call: import mathops; mathops.stat_describe(x) (or opsmath.get("stat_describe"))
Five-number-plus summary of a 1-D sample, as a plain dict.
Returns `{"n", "mean", "std", "min", "max", "percentiles"}` where
`percentiles is {"p5", "p25", "p50", "p75", "p95"}` (linear
interpolation between order statistics, numpy's default). `std` is the
population standard deviation (`ddof=0` — well-defined down to a
single sample; multiply by `sqrt(n/(n-1))` for the sample estimator,
which is what :func:stat_covariance uses, documented there).
The tails matter in metrology: `mean/std` of residuals say how good
the fit is *on average*; `p5/p95` say how bad the *outliers* are —
report both, a fit can pass on RMS and fail on extremes.
HALCON: `tuple_mean / tuple_deviation / tuple_min` /
`tuple_max` (the percentile row has no single HALCON tuple operator).
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
table as input)—
stats)stat_histogram · stat_covariance · stat_correlation · stat_zscore
*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.