numerics op• Data kinds: signal → signal
• Call: import fullseye as fs; fs.ledger.erf(x) -> 'np.ndarray' (to call the implementation directly, import mathnumerics; mathnumerics.erf(x) -> 'np.ndarray'; from the registry, opsmath.get("erf"))
Error function erf(x) = (2/√π) ∫_0^x e^{−t²} dt.
The cumulative normal distribution, and the very shape of a blurred edge (a step convolved with a Gaussian): a step blurred by a Gaussian of width σ is ½(1 + erf(x / (σ√2))). Gate: odd function, erf(∞) = 1, derivative = (2/√π) e^{−x²}, agrees with the integral by Gauss quadrature.
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.
• numerics_tour — py -3.11 examples/numerics_tour.py
• poc_battery_electrode_breathing — py -3.11 examples/poc_battery_electrode_breathing.py
• poc_change_detection_misreg — py -3.11 examples/poc_change_detection_misreg.py
• poc_crack_width_timeseries — py -3.11 examples/poc_crack_width_timeseries.py
• poc_dic_strain — py -3.11 examples/poc_dic_strain.py
• poc_die_tilt_tsv_overlay — py -3.11 examples/poc_die_tilt_tsv_overlay.py
• poc_dimensional_inspection — py -3.11 examples/poc_dimensional_inspection.py
• poc_exoplanet_transit — py -3.11 examples/poc_exoplanet_transit.py
• poc_fresco_craquelure — py -3.11 examples/poc_fresco_craquelure.py
• poc_mri_bias_field — py -3.11 examples/poc_mri_bias_field.py
• poc_search_sweep_width — py -3.11 examples/poc_search_sweep_width.py
• poc_settlement_significance — py -3.11 examples/poc_settlement_significance.py
• poc_star_astrometry — py -3.11 examples/poc_star_astrometry.py
• representation_roundtrip — py -3.11 examples/representation_roundtrip.py
signal as input)mat_solve · mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · interp_cubic · interp_scattered
numerics)erfc · bessel · gauss_quadrature · gauss_cubature · chebyshev_coeffs_nd · chebyshev_eval_nd · low_discrepancy · chebyshev_nodes
*Provenance: mathnumerics.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.