transform op• Data kinds: none → table (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.wavelet_filters(order: 'int' = 2) -> 'dict' (to call the implementation directly, import mathtransforms; mathtransforms.wavelet_filters(order: 'int' = 2) -> 'dict'; from the registry, opsmath.get("wavelet_filters"))
> This operator's description has not been translated yet. The original text follows as it is.
Daubechies の正規直交ウェーブレット dbN のフィルタを、教科書の構成(スペクトル分解)で作る。
|H(ω)|² = cos^{2N}(ω/2)·P(sin²(ω/2))、P(y) = Σ_{k<N} C(N−1+k, k) y^k(Daubechies 1988)。P の根から単位円の
内側の零点を選び、(1 + z⁻¹)^N と掛け合わせる。表を写さないので桁落ちの転記ミスが無い(門が値を確かめる)。
Returns:
`lowpass h(長さ 2N、和 √2)、highpass g[n] = (−1)^n h[2N−1−n]、order`、
`vanishing_moments` = N(次数 N−1 までの多項式を詳細係数で消す)。order=1 は Haar。
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.
• (none yet)
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
transform)abel_transform · abel_inverse · abel_inverse_image · abel_revolve · hankel_transform · tf_poles_zeros · tf_freq_response · tf_impulse_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.