flow op• データ種: matrix → table
• 呼び出し: import fullseye as fs; fs.ledger.graph_physarum_path(lengths, source=0, sink=None, dt=0.1, max_iters=5000, tol=1e-06, frac=0.5) (実装を直接呼ぶなら import physarum_search; physarum_search.graph_physarum_path(lengths, source=0, sink=None, dt=0.1, max_iters=5000, tol=1e-06, frac=0.5)、台帳から引くなら opsgraph.get("graph_physarum_path"))
粘菌(Tero 2010)の管の力学で重み付きグラフの最短路を解く: 単位流量を流し、各管の導電度を |流量| へ寄せる。最短路が一意なら導電度はその指示関数に収束する(Bonifaci 2012)。導電度・流量の行列、道、道の長さ、流れの長さを返す。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
`lengths is a symmetric (n, n) matrix of tube lengths (0` = no tube, diagonal 0).
A unit flow is pushed from `source to sink (default n - 1`) through tubes of
conductance `D_e`; the pressures solve the weighted Laplacian (Kirchhoff), the flow in a
tube is `Q_e = D_e (p_u - p_v) / L_e, and each tube adapts dD_e/dt = |Q_e| - D_e`
(explicit Euler, step `dt`). Bonifaci, Mehlhorn and Varma (2012) prove that with a unique
shortest path the conductances converge to its indicator: `D_e -> 1 on it, 0` off it.
The path is read by following, from the source, the tube that carries the most flow out of
each node (a potential flow has no cycle); it must be at least `frac` of the thickest tube
all along, else the run is refused as not converged.
Returns `conductance and flow ((n, n) matrices, flow antisymmetric), path`
(node indices source → sink), `path_length` (sum of the tube lengths along it),
`flow_length = sum |Q_e| L_e (the length of the unit flow; it is >= path_length`
for every unit flow and equal only when all flow rides shortest paths), `iters`,
`converged (max |dD| fell below tol), history` (max |dD| per iteration).
Raises `ValueError`: matrix not square / symmetric / finite / non-negative, self-loops;
bad node indices or `source == sink; sink unreachable; dt` outside (0, 1]; no path
survived the threshold (not converged).
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• poc_physarum_maze — py -3.11 examples/poc_physarum_maze.py
table を入力に取れる)graph_edge_consensus · graph_core_persistence · tree_morphometry · tree_sholl · tree_run_length
flow)physarum_route · graph_physarum_transport · physarum_transport_image
*Provenance: physarum_search.py — GRAPH operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.