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_cubature(n: 'int', dim: 'int' = 2, a=-1.0, b=1.0) -> 'dict' (to call the implementation directly, import mathnumerics; mathnumerics.gauss_cubature(n: 'int', dim: 'int' = 2, a=-1.0, b=1.0) -> 'dict'; from the registry, opsmath.get("gauss_cubature"))
Nodes (n^dim, dim) and weights for quadrature over the box [a, b]^dim (a, b may also be per axis) by a tensor product of Gauss–Legendre rules.
For pixel averages of images, volume integrals over volumes, and PSF integrals. Integrates products of polynomials up to degree 2n−1 on each axis exactly (gate: x^p y^q with p, q <= 2n−1 is exact; an error if any of them is 2n). The number of points is n^dim, so it grows rapidly in high dimensions (for dim > 6 low-discrepancy sequences are better suited).
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)
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
numerics)erf · erfc · bessel · gauss_quadrature · 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.