Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/flow/mincost.py @ 0:4f3585e2f14b draft default tip
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
author | shellac |
---|---|
date | Mon, 22 Mar 2021 18:12:50 +0000 |
parents | |
children |
rev | line source |
---|---|
0
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
1 """ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
2 Minimum cost flow algorithms on directed connected graphs. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
3 """ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
4 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
5 __all__ = ["min_cost_flow_cost", "min_cost_flow", "cost_of_flow", "max_flow_min_cost"] |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
6 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
7 import networkx as nx |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
8 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
9 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
10 def min_cost_flow_cost(G, demand="demand", capacity="capacity", weight="weight"): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
11 r"""Find the cost of a minimum cost flow satisfying all demands in digraph G. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
12 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
13 G is a digraph with edge costs and capacities and in which nodes |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
14 have demand, i.e., they want to send or receive some amount of |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
15 flow. A negative demand means that the node wants to send flow, a |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
16 positive demand means that the node want to receive flow. A flow on |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
17 the digraph G satisfies all demand if the net flow into each node |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
18 is equal to the demand of that node. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
19 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
20 Parameters |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
21 ---------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
22 G : NetworkX graph |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
23 DiGraph on which a minimum cost flow satisfying all demands is |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
24 to be found. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
25 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
26 demand : string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
27 Nodes of the graph G are expected to have an attribute demand |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
28 that indicates how much flow a node wants to send (negative |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
29 demand) or receive (positive demand). Note that the sum of the |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
30 demands should be 0 otherwise the problem in not feasible. If |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
31 this attribute is not present, a node is considered to have 0 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
32 demand. Default value: 'demand'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
33 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
34 capacity : string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
35 Edges of the graph G are expected to have an attribute capacity |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
36 that indicates how much flow the edge can support. If this |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
37 attribute is not present, the edge is considered to have |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
38 infinite capacity. Default value: 'capacity'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
39 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
40 weight : string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
41 Edges of the graph G are expected to have an attribute weight |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
42 that indicates the cost incurred by sending one unit of flow on |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
43 that edge. If not present, the weight is considered to be 0. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
44 Default value: 'weight'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
45 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
46 Returns |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
47 ------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
48 flowCost : integer, float |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
49 Cost of a minimum cost flow satisfying all demands. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
50 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
51 Raises |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
52 ------ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
53 NetworkXError |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
54 This exception is raised if the input graph is not directed or |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
55 not connected. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
56 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
57 NetworkXUnfeasible |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
58 This exception is raised in the following situations: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
59 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
60 * The sum of the demands is not zero. Then, there is no |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
61 flow satisfying all demands. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
62 * There is no flow satisfying all demand. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
63 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
64 NetworkXUnbounded |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
65 This exception is raised if the digraph G has a cycle of |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
66 negative cost and infinite capacity. Then, the cost of a flow |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
67 satisfying all demands is unbounded below. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
68 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
69 See also |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
70 -------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
71 cost_of_flow, max_flow_min_cost, min_cost_flow, network_simplex |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
72 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
73 Notes |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
74 ----- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
75 This algorithm is not guaranteed to work if edge weights or demands |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
76 are floating point numbers (overflows and roundoff errors can |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
77 cause problems). As a workaround you can use integer numbers by |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
78 multiplying the relevant edge attributes by a convenient |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
79 constant factor (eg 100). |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
80 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
81 Examples |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
82 -------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
83 A simple example of a min cost flow problem. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
84 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
85 >>> G = nx.DiGraph() |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
86 >>> G.add_node("a", demand=-5) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
87 >>> G.add_node("d", demand=5) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
88 >>> G.add_edge("a", "b", weight=3, capacity=4) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
89 >>> G.add_edge("a", "c", weight=6, capacity=10) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
90 >>> G.add_edge("b", "d", weight=1, capacity=9) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
91 >>> G.add_edge("c", "d", weight=2, capacity=5) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
92 >>> flowCost = nx.min_cost_flow_cost(G) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
93 >>> flowCost |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
94 24 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
95 """ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
96 return nx.network_simplex(G, demand=demand, capacity=capacity, weight=weight)[0] |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
97 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
98 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
99 def min_cost_flow(G, demand="demand", capacity="capacity", weight="weight"): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
100 r"""Returns a minimum cost flow satisfying all demands in digraph G. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
101 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
102 G is a digraph with edge costs and capacities and in which nodes |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
103 have demand, i.e., they want to send or receive some amount of |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
104 flow. A negative demand means that the node wants to send flow, a |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
105 positive demand means that the node want to receive flow. A flow on |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
106 the digraph G satisfies all demand if the net flow into each node |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
107 is equal to the demand of that node. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
108 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
109 Parameters |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
110 ---------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
111 G : NetworkX graph |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
112 DiGraph on which a minimum cost flow satisfying all demands is |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
113 to be found. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
114 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
115 demand : string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
116 Nodes of the graph G are expected to have an attribute demand |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
117 that indicates how much flow a node wants to send (negative |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
118 demand) or receive (positive demand). Note that the sum of the |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
119 demands should be 0 otherwise the problem in not feasible. If |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
120 this attribute is not present, a node is considered to have 0 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
121 demand. Default value: 'demand'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
122 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
123 capacity : string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
124 Edges of the graph G are expected to have an attribute capacity |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
125 that indicates how much flow the edge can support. If this |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
126 attribute is not present, the edge is considered to have |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
127 infinite capacity. Default value: 'capacity'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
128 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
129 weight : string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
130 Edges of the graph G are expected to have an attribute weight |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
131 that indicates the cost incurred by sending one unit of flow on |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
132 that edge. If not present, the weight is considered to be 0. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
133 Default value: 'weight'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
134 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
135 Returns |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
136 ------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
137 flowDict : dictionary |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
138 Dictionary of dictionaries keyed by nodes such that |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
139 flowDict[u][v] is the flow edge (u, v). |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
140 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
141 Raises |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
142 ------ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
143 NetworkXError |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
144 This exception is raised if the input graph is not directed or |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
145 not connected. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
146 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
147 NetworkXUnfeasible |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
148 This exception is raised in the following situations: |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
149 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
150 * The sum of the demands is not zero. Then, there is no |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
151 flow satisfying all demands. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
152 * There is no flow satisfying all demand. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
153 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
154 NetworkXUnbounded |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
155 This exception is raised if the digraph G has a cycle of |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
156 negative cost and infinite capacity. Then, the cost of a flow |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
157 satisfying all demands is unbounded below. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
158 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
159 See also |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
160 -------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
161 cost_of_flow, max_flow_min_cost, min_cost_flow_cost, network_simplex |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
162 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
163 Notes |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
164 ----- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
165 This algorithm is not guaranteed to work if edge weights or demands |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
166 are floating point numbers (overflows and roundoff errors can |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
167 cause problems). As a workaround you can use integer numbers by |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
168 multiplying the relevant edge attributes by a convenient |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
169 constant factor (eg 100). |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
170 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
171 Examples |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
172 -------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
173 A simple example of a min cost flow problem. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
174 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
175 >>> G = nx.DiGraph() |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
176 >>> G.add_node("a", demand=-5) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
177 >>> G.add_node("d", demand=5) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
178 >>> G.add_edge("a", "b", weight=3, capacity=4) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
179 >>> G.add_edge("a", "c", weight=6, capacity=10) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
180 >>> G.add_edge("b", "d", weight=1, capacity=9) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
181 >>> G.add_edge("c", "d", weight=2, capacity=5) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
182 >>> flowDict = nx.min_cost_flow(G) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
183 """ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
184 return nx.network_simplex(G, demand=demand, capacity=capacity, weight=weight)[1] |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
185 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
186 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
187 def cost_of_flow(G, flowDict, weight="weight"): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
188 """Compute the cost of the flow given by flowDict on graph G. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
189 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
190 Note that this function does not check for the validity of the |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
191 flow flowDict. This function will fail if the graph G and the |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
192 flow don't have the same edge set. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
193 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
194 Parameters |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
195 ---------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
196 G : NetworkX graph |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
197 DiGraph on which a minimum cost flow satisfying all demands is |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
198 to be found. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
199 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
200 weight : string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
201 Edges of the graph G are expected to have an attribute weight |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
202 that indicates the cost incurred by sending one unit of flow on |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
203 that edge. If not present, the weight is considered to be 0. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
204 Default value: 'weight'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
205 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
206 flowDict : dictionary |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
207 Dictionary of dictionaries keyed by nodes such that |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
208 flowDict[u][v] is the flow edge (u, v). |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
209 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
210 Returns |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
211 ------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
212 cost : Integer, float |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
213 The total cost of the flow. This is given by the sum over all |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
214 edges of the product of the edge's flow and the edge's weight. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
215 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
216 See also |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
217 -------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
218 max_flow_min_cost, min_cost_flow, min_cost_flow_cost, network_simplex |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
219 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
220 Notes |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
221 ----- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
222 This algorithm is not guaranteed to work if edge weights or demands |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
223 are floating point numbers (overflows and roundoff errors can |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
224 cause problems). As a workaround you can use integer numbers by |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
225 multiplying the relevant edge attributes by a convenient |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
226 constant factor (eg 100). |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
227 """ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
228 return sum((flowDict[u][v] * d.get(weight, 0) for u, v, d in G.edges(data=True))) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
229 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
230 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
231 def max_flow_min_cost(G, s, t, capacity="capacity", weight="weight"): |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
232 """Returns a maximum (s, t)-flow of minimum cost. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
233 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
234 G is a digraph with edge costs and capacities. There is a source |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
235 node s and a sink node t. This function finds a maximum flow from |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
236 s to t whose total cost is minimized. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
237 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
238 Parameters |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
239 ---------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
240 G : NetworkX graph |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
241 DiGraph on which a minimum cost flow satisfying all demands is |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
242 to be found. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
243 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
244 s: node label |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
245 Source of the flow. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
246 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
247 t: node label |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
248 Destination of the flow. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
249 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
250 capacity: string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
251 Edges of the graph G are expected to have an attribute capacity |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
252 that indicates how much flow the edge can support. If this |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
253 attribute is not present, the edge is considered to have |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
254 infinite capacity. Default value: 'capacity'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
255 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
256 weight: string |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
257 Edges of the graph G are expected to have an attribute weight |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
258 that indicates the cost incurred by sending one unit of flow on |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
259 that edge. If not present, the weight is considered to be 0. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
260 Default value: 'weight'. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
261 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
262 Returns |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
263 ------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
264 flowDict: dictionary |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
265 Dictionary of dictionaries keyed by nodes such that |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
266 flowDict[u][v] is the flow edge (u, v). |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
267 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
268 Raises |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
269 ------ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
270 NetworkXError |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
271 This exception is raised if the input graph is not directed or |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
272 not connected. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
273 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
274 NetworkXUnbounded |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
275 This exception is raised if there is an infinite capacity path |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
276 from s to t in G. In this case there is no maximum flow. This |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
277 exception is also raised if the digraph G has a cycle of |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
278 negative cost and infinite capacity. Then, the cost of a flow |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
279 is unbounded below. |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
280 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
281 See also |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
282 -------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
283 cost_of_flow, min_cost_flow, min_cost_flow_cost, network_simplex |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
284 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
285 Notes |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
286 ----- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
287 This algorithm is not guaranteed to work if edge weights or demands |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
288 are floating point numbers (overflows and roundoff errors can |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
289 cause problems). As a workaround you can use integer numbers by |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
290 multiplying the relevant edge attributes by a convenient |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
291 constant factor (eg 100). |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
292 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
293 Examples |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
294 -------- |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
295 >>> G = nx.DiGraph() |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
296 >>> G.add_edges_from( |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
297 ... [ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
298 ... (1, 2, {"capacity": 12, "weight": 4}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
299 ... (1, 3, {"capacity": 20, "weight": 6}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
300 ... (2, 3, {"capacity": 6, "weight": -3}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
301 ... (2, 6, {"capacity": 14, "weight": 1}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
302 ... (3, 4, {"weight": 9}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
303 ... (3, 5, {"capacity": 10, "weight": 5}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
304 ... (4, 2, {"capacity": 19, "weight": 13}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
305 ... (4, 5, {"capacity": 4, "weight": 0}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
306 ... (5, 7, {"capacity": 28, "weight": 2}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
307 ... (6, 5, {"capacity": 11, "weight": 1}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
308 ... (6, 7, {"weight": 8}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
309 ... (7, 4, {"capacity": 6, "weight": 6}), |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
310 ... ] |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
311 ... ) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
312 >>> mincostFlow = nx.max_flow_min_cost(G, 1, 7) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
313 >>> mincost = nx.cost_of_flow(G, mincostFlow) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
314 >>> mincost |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
315 373 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
316 >>> from networkx.algorithms.flow import maximum_flow |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
317 >>> maxFlow = maximum_flow(G, 1, 7)[1] |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
318 >>> nx.cost_of_flow(G, maxFlow) >= mincost |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
319 True |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
320 >>> mincostFlowValue = sum((mincostFlow[u][7] for u in G.predecessors(7))) - sum( |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
321 ... (mincostFlow[7][v] for v in G.successors(7)) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
322 ... ) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
323 >>> mincostFlowValue == nx.maximum_flow_value(G, 1, 7) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
324 True |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
325 |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
326 """ |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
327 maxFlow = nx.maximum_flow_value(G, s, t, capacity=capacity) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
328 H = nx.DiGraph(G) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
329 H.add_node(s, demand=-maxFlow) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
330 H.add_node(t, demand=maxFlow) |
4f3585e2f14b
"planemo upload commit 60cee0fc7c0cda8592644e1aad72851dec82c959"
shellac
parents:
diff
changeset
|
331 return min_cost_flow(H, capacity=capacity, weight=weight) |