numerics op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.gauss_quadrature(n: 'int', kind: 'str' = 'legendre', a: 'float | None' = None, b: 'float | None' = None) -> 'dict' (to call the implementation directly, import mathnumerics; mathnumerics.gauss_quadrature(n: 'int', kind: 'str' = 'legendre', a: 'float | None' = None, b: 'float | None' = None) -> 'dict'; from the registry, opsmath.get("gauss_quadrature"))
> This operator's description has not been translated yet. The original text follows as it is.
n 点の Gauss 求積の節点と重み。∫ f ≈ Σ w_k f(x_k)。
n 点で 2n−1 次までの多項式を厳密に積分する(等間隔の台形則は 1 次まで)。
`kind="legendre" は区間 [a, b] へ写せる(既定 [−1, 1])。他の kind は重み関数込みの積分(integral` 参照)。
門: 2n−1 次の単項式は厳密、2n 次は厳密でない(両向き)。
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
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
numerics)erf · erfc · bessel · 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.