numerics op• Data kinds: none → signal (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.chebyshev_nodes(n: 'int', a: 'float' = -1.0, b: 'float' = 1.0, kind: 'int' = 2) -> 'np.ndarray' (to call the implementation directly, import mathnumerics; mathnumerics.chebyshev_nodes(n: 'int', a: 'float' = -1.0, b: 'float' = 1.0, kind: 'int' = 2) -> 'np.ndarray'; from the registry, opsmath.get("chebyshev_nodes"))
n Chebyshev points on the interval [a, b] (in ascending order).
kind=2 (default) gives the Chebyshev–Lobatto points x_k = cos(kπ/(n−1)) including the endpoints; kind=1 gives the Chebyshev–Gauss points cos((2k+1)π/(2n)) excluding the endpoints. They get denser toward the ends and suppress the wild swings of polynomial interpolation (Runge phenomenon).
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
signal as input)mat_solve · mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · interp_cubic · interp_scattered
numerics)erf · erfc · bessel · gauss_quadrature · gauss_cubature · chebyshev_coeffs_nd · chebyshev_eval_nd · low_discrepancy
*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.