transform op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.dct_transform(x, *, axes=None, inverse: 'bool' = False) -> 'dict' (to call the implementation directly, import mathtransforms; mathtransforms.dct_transform(x, *, axes=None, inverse: 'bool' = False) -> 'dict'; from the registry, opsmath.get("dct_transform"))
> This operator's description has not been translated yet. The original text follows as it is.
正規直交 DCT-II(`inverse=True` で DCT-III = 逆変換)を N 次元で。
Args:
x: 任意次元の実配列(信号・画像・ボリューム)。
axes: 変換する軸(省略で全軸)。
inverse: True なら係数から元に戻す。
Returns:
`coeffs(同じ形)、energy`(Σx²、正規直交なので変換の前後で同じ = Parseval)、
`compaction` = 大きい順に並べた係数のエネルギーの累積割合(先頭 1% で何割を持つか、が JPEG の理由)。
門は定義式 C[k, n] = √(2/N)·c_k·cos(π(2n+1)k / 2N) の行列と一致すること・逆変換で 1e-12 で戻ること。
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 · 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.