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"))
Orthonormal DCT-II (with inverse=True, DCT-III = the inverse transform) in N dimensions.
Args:
x: real array of any dimension (signal, image, volume).
axes: axes to transform (all axes if omitted).
inverse: if True, reconstruct from the coefficients.
Returns:
coeffs (same shape), energy (Σx²; orthonormal, so the same before and after the transform = Parseval), compaction = cumulative energy fraction of the coefficients sorted largest first (what fraction the top 1% holds is the reason for JPEG).
Gate: agreement with the matrix of the defining formula C[k, n] = √(2/N)·c_k·cos(π(2n+1)k / 2N), and the inverse transform returning to within 1e-12.
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.