numerics op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.chebyshev_coeffs_nd(values, box=None) -> 'dict' (to call the implementation directly, import mathnumerics; mathnumerics.chebyshev_coeffs_nd(values, box=None) -> 'dict'; from the registry, opsmath.get("chebyshev_coeffs_nd"))
> This operator's description has not been translated yet. The original text follows as it is.
テンソル積の Chebyshev–Lobatto 格子で標本化した値から、N 次元の Chebyshev 係数を求める(DCT-I)。
Args:
values: 形 (n1, …, nd) の配列。軸 i の標本は `chebyshev_nodes(n_i, lo_i, hi_i)`(昇順)の上の値。
box: 軸ごとの区間 [(lo, hi), …] (省略で全軸 [−1, 1]、1 組なら全軸に共通)。
Returns:
`coeffs (n1, …, nd): f ≈ Σ c[k] Π T_{k_i}(t_i)(t_i は [−1, 1] に写した座標)、box`、
`decay` = 軸ごとに |c| の最大を次数ごとに並べた列(滑らかな関数は幾何級数的に落ちる = スペクトル収束)、
`tail` = 各軸の最後の 2 次数の |c| の最大(打ち切り誤差の目安。小さいほど点数が足りている)。
門: 次数が各軸 n_i − 1 以下の多項式は厳密に再現する / 1/(a − x) 型の極を持つ関数の係数は
ρ^−k(ρ = a + √(a² − 1)、Bernstein の楕円)で落ちる。画像では、照明むら・反りなどの滑らかな面を
数十の係数で表す(多項式のべき基底は高次で悪条件、Chebyshev は安定)。
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_quadrature · gauss_cubature · 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.