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"))
Computes N-dimensional Chebyshev coefficients from values sampled on a tensor-product Chebyshev–Lobatto grid (DCT-I).
Args:
values: array of shape (n1, …, nd). The samples on axis i are the values on chebyshev_nodes(n_i, lo_i, hi_i) (ascending).
box: interval per axis [(lo, hi), …] (if omitted, [−1, 1] on all axes; 1 pair is shared by all axes).
Returns:
coeffs (n1, …, nd): f ≈ Σ c[k] Π T_{k_i}(t_i) (t_i is the coordinate mapped to [−1, 1]), box,
decay = per axis, the max of |c| listed by degree (for smooth functions it falls geometrically = spectral convergence),
tail = per axis, the max of |c| over the last 2 degrees (a gauge of truncation error; the smaller, the more sufficient the number of points).
Gate: polynomials of degree at most n_i − 1 on each axis are reproduced exactly / for functions with a pole of the form 1/(a − x), the coefficients fall as ρ^−k (ρ = a + √(a² − 1), Bernstein ellipse). For images, smooth surfaces such as uneven illumination or warping are represented with a few dozen coefficients (the polynomial power basis is ill-conditioned at high degree; Chebyshev is stable).
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.