identifiability op• 資料種類:matrix → table
• 呼叫: import fullseye as fs; fs.ledger.mv_confounding(S=None, names=None, threshold=10.0, log_params=False, max_subset=None) -> 'dict'(要直接呼叫實作,import sensitivity; sensitivity.mv_confounding(S=None, names=None, threshold=10.0, log_params=False, max_subset=None) -> 'dict';從台帳取用則 opsmultivar.get("mv_confounding"))
共線性指數 gamma_K（Brun、Reichert 與 Künsch 2001）：資料能確定哪些參數。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
S is the sensitivity matrix (observations x parameters): column j = the change of every output per change of parameter j (finite differences of a simulation, or a Jacobian), ideally already scaled to be dimensionless (Brun: s_ij = dtheta_j / sc_i * dy_i/dtheta_j). Each column is normalised to unit length, s~_j = s_j / ||s_j||, and for a parameter subset K
gamma_K = 1 / sqrt( min eigenvalue of S~_K^T S~_K ).
gamma_K = 1 for orthogonal columns; it grows when a change in one parameter can be compensated by the others (Brun et al. use 10-15 as the critical range; threshold defaults to 10). Returned: delta_msqr (importance, sqrt(mean s_ij^2) on the given scale), gamma of the full set and of every subset up to max_subset (all subsets for <= 14 parameters), the confounded_pairs (gamma > threshold), the largest identifiable subsets, the undetermined_direction of the full set (eigenvector of the smallest eigenvalue: moving the parameters along it barely changes the output), and per confounded_groups entry (the union of the minimal confounded subsets) the combinations the data determined (eigenvalue of the group's S~^T S~ >= 1/threshold^2) and those undetermined; parameters in no group are determined_individually. With log_params=True (columns are sensitivities to log parameters) the combinations are written as products of powers — e.g. n^1 * d^1 when only the product of refractive index and thickness reaches the data. Columns that are all zero are reported as no_influence and left out of gamma.
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• 演算法的正典(作者、年份)與用途見上面的族使用指南。
• poc_simcal_thin_film — py -3.11 examples/poc_simcal_thin_film.py
• sensitivity_tour — py -3.11 examples/sensitivity_tour.py
table 作為輸入)—
identifiability)*Provenance: sensitivity.py — MULTIVAR 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.