numerics op• Data kinds: none → matrix (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.low_discrepancy(n: 'int', dim: 'int' = 2, kind: 'str' = 'halton', *, skip: 'int' = 0, seed: 'int | None' = None) -> 'np.ndarray' (to call the implementation directly, import mathnumerics; mathnumerics.low_discrepancy(n: 'int', dim: 'int' = 2, kind: 'str' = 'halton', *, skip: 'int' = 0, seed: 'int | None' = None) -> 'np.ndarray'; from the registry, opsmath.get("low_discrepancy"))
Low-discrepancy point sequence (n, dim) in [0, 1)^dim.
• "halton" —— van der Corput sequences with a different prime base per coordinate (own implementation, deterministic). Skips skip points (1 to avoid the leading 0). Beware: in high dimensions (> 8 or so) stripes appear between coordinates.
• "sobol" —— scipy.stats.qmc.Sobol (scrambled if seed is given). n is best as a power of 2.
• "random" —— uniform random numbers for comparison (seed required, for reproducibility).
Gate: the integration error for smooth functions decreases faster than random's N^{−1/2} / the star discrepancy is smaller than random's.
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
matrix as input)mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_cond · mat_lu · mat_qr
numerics)erf · erfc · bessel · gauss_quadrature · gauss_cubature · chebyshev_coeffs_nd · chebyshev_eval_nd · 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.