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"))
> This operator's description has not been translated yet. The original text follows as it is.
[0, 1)^dim の低食い違い点列 (n, dim)。
• `"halton"` —— 座標ごとに異なる素数を基数にした van der Corput 列(自前の実装、決定的)。
`skip` 個を読み飛ばす(先頭の 0 を避けるなら 1)。高次元(> 8 程度)では座標間に縞が出るので注意。
• `"sobol" —— scipy.stats.qmc.Sobol(seed` を与えるとスクランブル)。n は 2 の冪が最良。
• `"random" —— 比較用の一様乱数(seed` 必須、再現性のため)。
門: なめらかな関数の積分誤差は乱数の N^{−1/2} より速く減る / 星形食い違い量が乱数より小さい。
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.