stats op• Data kinds: signal → pairs
• Call: import mathops; mathops.stat_histogram(x, bins=10, range=None, density=False) (or opsmath.get("stat_histogram"))
Histogram of a 1-D sample with the binning explicit.
*bins* is a positive integer count of equal-width bins; *range* is an
explicit `(lo, hi) (finite, lo < hi) or None` to span the data
(values exactly at `hi` land in the last bin, numpy's convention; with an
explicit *range*, values outside it are excluded from every bin — they
simply do not count, which is why passing *range* explicitly is the honest
choice when comparing histograms across datasets). With `density=False`
(default) *counts* are occurrence frequencies (int64, summing to the
number of in-range samples); with `density=True` they form a
probability density (float64, integrating to 1 over the range).
A *range* that excludes every sample raises `ValueError` under
`density=True` (the density would be 0/0 — silent NaNs refused) while
`density=False` honestly returns all-zero counts. *bins* is capped at
`MAX_ELEMENTS` (the edge/count arrays are allocations too).
Returns `(counts, edges) — edges has bins + 1` entries;
bin *i* is `[edges[i], edges[i+1])`.
HALCON: `tuple_histo_range (and gray_histo` for whole images).
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
pairs as input)—
stats)stat_describe · 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.