estimation op• Data kinds: signal → matrix
• Call: import fullseye as fs; fs.ledger.se3_exp(xi) -> 'np.ndarray' (to call the implementation directly, import mathestimation; mathestimation.se3_exp(xi) -> 'np.ndarray'; from the registry, opsmath.get("se3_exp"))
> This operator's description has not been translated yet. The original text follows as it is.
SE(3) の指数写像: 6 次元のねじれ ξ = (v, ω)(並進速度 v、回転ベクトル ω)→ 4×4 の剛体変換。
閉じた式(Rodrigues + 左ヤコビアン): R = I + sinθ/θ ω̂ + (1−cosθ)/θ² ω̂²、t = V v、
V = I + (1−cosθ)/θ² ω̂ + (θ−sinθ)/θ³ ω̂²。θ → 0 は級数で。門: 4×4 の生成元の mat_expm と一致。
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.
• estimation_tour — py -3.11 examples/estimation_tour.py
matrix as input)mat_solve · mat_lstsq · mat_svd · mat_eigh · mat_pinv · mat_cond · mat_lu · mat_qr
estimation)assign_hungarian · hist_distance · stat_ttest_paired · stat_ttest_welch · stat_ks_test · stat_chi2_gof · crlb_gaussian · kalman_smooth
*Provenance: mathestimation.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.