stats op• Data kinds: matrix → matrix
• Call: import mathops; mathops.stat_covariance(x) (or opsmath.get("stat_covariance"))
Sample covariance matrix of `(N, D) observations → (D, D)`.
Rows are observations, columns are variables — the `(N, D)` orientation
every Fullseye point/sample API uses (note `np.cov` defaults to the
*transposed* convention). Uses the unbiased `ddof=1` estimator (divides
by `N - 1), hence the N >= 2` requirement. The diagonal holds the
per-variable sample variances; the result is symmetric positive
semi-definite by construction, so it can go straight into
:func:mat_eigh for principal axes (the covariance-ellipse workflow).
HALCON: no public tuple/matrix operator — covariance lives inside HALCON's
calibration and matching internals only.
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
matrix as input)mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_cond · stat_correlation
stats)stat_describe · stat_histogram · 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.