estimation op• Data kinds: signal × signal → measurement
• Call: import fullseye as fs; fs.ledger.hist_distance(p, q, metric: 'str' = 'kl', *, eps: 'float' = 1e-12) -> 'float' (to call the implementation directly, import mathestimation; mathestimation.hist_distance(p, q, metric: 'str' = 'kl', *, eps: 'float' = 1e-12) -> 'float'; from the registry, opsmath.get("hist_distance"))
Distance and divergence between 2 histograms (non-negative, normalized by their sum).
• "kl" —— Kullback–Leibler D(p‖q) = Σ p log(p/q) (asymmetric; infinite where q is 0 and p is positive → floored with eps).
• "js" —— Jensen–Shannon (symmetric, 0..log 2; its square root satisfies the metric axioms).
• "bhattacharyya" —— −log Σ √(pq). "hellinger" —— √(1 − Σ √(pq)) (0..1).
• "chi2" —— ½ Σ (p−q)²/(p+q).
Gate: closed form of the KL between normal distributions / KL ≥ 0 with equality for identical distributions / MI = KL(p_xy ‖ p_x p_y).
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).
• 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.
• (none yet)
measurement as input)—
estimation)assign_hungarian · stat_ttest_paired · stat_ttest_welch · stat_ks_test · stat_chi2_gof · crlb_gaussian · kalman_smooth · mat_expm
*Provenance: mathestimation.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.