flow op• 数据种类:matrix → table
• 调用: 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)(要直接调用实现,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);从台账取用则 opsgraph.get("graph_physarum_path"))
在带权图上用黏菌的管道动力学求最短路(Tero et al. 2010)。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
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).
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• 算法的正典(作者、年份)与用途见上面的族使用指南。
• poc_physarum_maze — py -3.11 examples/poc_physarum_maze.py
table 作为输入)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 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.