dct_transform — MATH 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"))

Usage

> 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。

Family-wide input contract (fail-closed)

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).

Detailed usage guide

• math_metrology family guide

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

• transforms_tour — py -3.11 examples/transforms_tour.py

Ops the type connects to (they accept table as input)

dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd

Same category (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.