transform op• Data kinds: signal × signal → table
• Call: import fullseye as fs; fs.ledger.hankel_transform(r, f, *, r_max: 'float | None' = None, order: 'int' = 0, n: 'int' = 256) -> 'dict' (to call the implementation directly, import mathtransforms; mathtransforms.hankel_transform(r, f, *, r_max: 'float | None' = None, order: 'int' = 0, n: 'int' = 256) -> 'dict'; from the registry, opsmath.get("hankel_transform"))
> This operator's description has not been translated yet. The original text follows as it is.
p 次の Hankel 変換 F(ν) = 2π ∫_0^∞ f(r) J_p(2πνr) r dr を quasi-discrete 法で。
`(r, f) は動径の標本(r は昇順)。標本点 r_k へは線形補間で載せ、r_max`(既定 = r の最大値)の外は 0。
`f に呼び出し可能を渡すと、標本点で直接評価する(r は無視して r_max` を必ず渡す)。
標本点は r_k = j_k R / S(j_k は J_p の k 番目の零点、S = j_{n+1})、周波数 ν_k = j_k / (2πR)。
この変換は核 T が対合(T·T = I)なので、同じ関数で逆変換もできる(`F` を f として渡す)。
門: exp(−π r²) は自己双対(F(ν) = exp(−π ν²))。0 次の Hankel 変換は軸対称な関数の
2 次元フーリエ変換の動径断面に等しい。
返り値: `{"r", "f", "nu", "F", "T_involution_error"}`(最後は ‖T·T − I‖_max)。
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.
• transforms_tour — py -3.11 examples/transforms_tour.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
transform)abel_transform · abel_inverse · abel_inverse_image · abel_revolve · tf_poles_zeros · tf_freq_response · tf_impulse_response · tf_step_response
*Provenance: mathtransforms.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.