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Commit db308330 authored by Tiago Peixoto's avatar Tiago Peixoto
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Improve documentation for flow module

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src/graph_tool/flow/__init__.py
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......@@ -35,6 +35,39 @@ Summary
Contents
++++++++
The following network will be used as an example throughout the documentation.
.. testcode::
from numpy.random import seed, random
from scipy.linalg import norm
seed(42)
points = random((400, 2)) * 10
points[0] = [0, 0]
points[1] = [10, 10]
g, pos = gt.triangulation(points, type="delaunay")
g.set_directed(True)
edges = list(g.edges())
# reciprocate edges
for e in edges:
g.add_edge(e.target(), e.source())
# The capacity will be defined as the inverse euclidian distance
cap = g.new_edge_property("double")
for e in g.edges():
cap[e] = min(1.0 / norm(pos[e.target()].a - pos[e.source()].a), 10)
g.edge_properties["cap"] = cap
g.vertex_properties["pos"] = pos
g.save("flow-example.xml.gz")
gt.graph_draw(g, pos=pos, pin=True, penwidth=cap, output="flow-example.png")
.. figure:: flow-example.png
:align: center
Example network used in the documentation below. The edge capacities are
represented by the edge width.
"""
from .. dl_import import dl_import
......@@ -87,43 +120,25 @@ def edmonds_karp_max_flow(g, source, target, capacity, residual=None):
Examples
--------
>>> from numpy.random import seed, random
>>> seed(43)
>>> g = gt.random_graph(100, lambda: (2,2))
>>> c = g.new_edge_property("double")
>>> c.a = random(len(c.a))
>>> res = gt.edmonds_karp_max_flow(g, g.vertex(0), g.vertex(1), c)
>>> res.a = c.a - res.a # the actual flow
>>> print res.a[0:g.num_edges()]
[ 0.13339096 0.13339096 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0.20608185 0. 0. 0.
0.08000038 0. 0. 0. 0. 0. 0.
0.12608147 0. 0. 0. 0. 0. 0.
0. 0. 0. 0.08000038 0. 0.
0.00730949 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0.13339096 0. 0. 0. 0. 0.
0.08000038 0.08000038 0. 0. 0. 0. 0.
0. 0.12608147 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0.00730949
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0.08000038 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0.08000038 0. 0. 0. 0. 0. 0.
0.00730949 0. 0.12608147 0. 0. 0. 0. ]
>>> g = gt.load_graph("flow-example.xml.gz")
>>> cap = g.edge_properties["cap"]
>>> src, tgt = g.vertex(0), g.vertex(1)
>>> res = gt.edmonds_karp_max_flow(g, src, tgt, cap)
>>> res.a = cap.a - res.a # the actual flow
>>> max_flow = sum(res[e] for e in tgt.in_edges())
>>> print max_flow
6.92759897841
>>> pos = g.vertex_properties["pos"]
>>> gt.graph_draw(g, pos=pos, pin=True, penwidth=res, output="example-edmonds-karp.png")
<...>
.. figure:: example-edmonds-karp.png
:align: center
Edge flows obtained with the Edmonds-Karp algorithm. The source and
target are on the lower left and upper right corners, respectively. The
edge flows are represented by the edge width.
References
----------
......@@ -181,45 +196,25 @@ def push_relabel_max_flow(g, source, target, capacity, residual=None):
Examples
--------
>>> from numpy.random import seed, random
>>> seed(43)
>>> g = gt.random_graph(100, lambda: (2,2))
>>> c = g.new_edge_property("double")
>>> c.a = random(len(c.a))
>>> res = gt.push_relabel_max_flow(g, g.vertex(0), g.vertex(1), c)
>>> res.a = c.a - res.a # the actual flow
>>> print res.a[0:g.num_edges()]
[ 0.00730949 0.0835572 0. 0. 0. 0. 0.
0.06926091 0.06926091 0. 0.07624771 0. 0.03957485
0.05028544 0.05028544 0. 0. 0. 0.07624771
0.07624771 0. 0.07624771 0. 0. 0.07624771
0. 0. 0. 0. 0. 0.20608185
0.03395359 0. 0. 0.06926091 0. 0. 0.
0. 0. 0. 0. 0.06926091 0.
0.03957485 0. 0. 0. 0. 0.
0.02596227 0.05028544 0.12983414 0. 0. 0.
0.06926091 0. 0.20608185 0. 0. 0. 0.
0.12983414 0. 0. 0. 0.04480769 0. 0.
0. 0.06926091 0. 0. 0.06926091 0.03957485
0.06926091 0.05028544 0. 0.06057324 0. 0.
0.00730949 0. 0. 0. 0. 0.02596227
0. 0.03667285 0. 0. 0. 0. 0.
0. 0. 0.0835572 0. 0. 0. 0.
0.07624771 0.12983414 0.12983414 0. 0. 0.
0.02596227 0. 0. 0. 0. 0.05028544
0. 0. 0. 0.04480769 0. 0. 0.
0. 0.00730949 0. 0. 0.06926091 0.
0.05028544 0. 0. 0.03395359 0. 0. 0.
0. 0. 0. 0.06057324 0. 0. 0.
0.03395359 0. 0. 0. 0. 0.01633184
0. 0. 0. 0. 0.02596227 0. 0.
0. 0. 0. 0. 0.03395359 0. 0.
0. 0. 0. 0.00547774 0. 0.12983414
0.03395359 0. 0. 0. 0. 0.00547774
0. 0. 0. 0. 0. 0.03957485
0.03395359 0. 0.06926091 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0.00730949 0.07624771 0.20608185 0. 0. 0. 0. ]
>>> g = gt.load_graph("flow-example.xml.gz")
>>> cap = g.edge_properties["cap"]
>>> src, tgt = g.vertex(0), g.vertex(1)
>>> res = gt.push_relabel_max_flow(g, src, tgt, cap)
>>> res.a = cap.a - res.a # the actual flow
>>> max_flow = sum(res[e] for e in tgt.in_edges())
>>> print max_flow
6.92759897841
>>> pos = g.vertex_properties["pos"]
>>> gt.graph_draw(g, pos=pos, pin=True, penwidth=res, output="example-push-relabel.png")
<...>
.. figure:: example-push-relabel.png
:align: center
Edge flows obtained with the push-relabel algorithm. The source and
target are on the lower left and upper right corners, respectively. The
edge flows are represented by the edge width.
References
----------
......@@ -278,32 +273,28 @@ def boykov_kolmogorov_max_flow(g, source, target, capacity, residual=None):
Examples
--------
>>> from numpy.random import seed, random
>>> seed(43)
>>> g = gt.random_graph(100, lambda: (2,2))
>>> c = g.new_edge_property("double")
>>> c.a = random(len(c.a))
>>> res = gt.boykov_kolmogorov_max_flow(g, g.vertex(0), g.vertex(1), c)
>>> res.a = c.a - res.a # the actual flow
>>> print res.a[0:g.num_edges()]
[ 0.13339096 0.13339096 0. 0. 0. 0. 0.
0. 0.00730949 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0.20608185 0. 0. 0.
0.07269089 0. 0.00730949 0. 0. 0. 0.
0.13339096 0. 0. 0. 0. 0. 0.
0. 0. 0. 0.07269089 0. 0. 0.
0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. ]
>>> g = gt.load_graph("flow-example.xml.gz")
>>> cap = g.edge_properties["cap"]
>>> src, tgt = g.vertex(0), g.vertex(1)
>>> res = gt.boykov_kolmogorov_max_flow(g, src, tgt, cap)
>>> res.a = cap.a - res.a # the actual flow
>>> max_flow = sum(res[e] for e in tgt.in_edges())
>>> print max_flow
6.92759897841
>>> pos = g.vertex_properties["pos"]
>>> gt.graph_draw(g, pos=pos, pin=True, penwidth=res, output="example-kolmogorov.png")
<...>
.. figure:: example-kolmogorov.png
:align: center
Edge flows obtained with the Boykov-Kolmogorov algorithm. The source and
target are on the lower left and upper right corners, respectively. The
edge flows are represented by the edge width.
References
----------
.. [boost-kolmogorov] http://www.boost.org/libs/graph/doc/kolmogorov_max_flow.html
.. [boost-kolmogorov] http://www.boost.org/libs/graph/doc/boykov_kolmogorov_max_flow.html
.. [kolmogorov-graph-2003] Vladimir Kolmogorov, "Graph Based Algorithms for
Scene Reconstruction from Two or More Views", PhD thesis, Cornell
University, September 2003.
......
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