def EarthMoversDistance( lengraph, supplygraph, length='length', weight1='weight1', weight2='weight2' ) :
# lengraph is a *non*-multi DiGraph
digraph, s, t = FLOW.obtainCapacityNetwork( lengraph, supplygraph, length, weight1, weight2 )
#
flowgraph = FLOW.obtainFlowNetwork( digraph, s, t, capacity='capacity' )
costgraph = FLOW.obtainWeightedCosts( flowgraph, lengraph, weight=length )
# compute optimal flow
FLOW.max_flow_min_cost( flowgraph, costgraph )
return FLOW.totalcost( costgraph ).value
def obtainWassersteinProblem( lengraph, rategraph, length='length', rate='rate' ) :
digraph = nx.DiGraph()
digraph.add_edges_from( lengraph.edges_iter() )
for u in rategraph.nodes_iter() :
u_supply = rategraph.in_degree( u, rate ) - rategraph.out_degree( u, rate )
if u_supply > 0. :
digraph.add_edge( s, u, capacity = u_supply )
elif u_supply < 0. :
digraph.add_edge( u, t, capacity = -u_supply )
flowgraph = FLOW.obtainFlowNetwork( digraph, s, t )
costgraph = FLOW.obtainWeightedCosts( flowgraph, lengraph, weight=length )
return flowgraph, costgraph
def obtainWassersteinProblem( roadnet, length='length', weight1='weight1', weight2='weight2' ) :
"""
input: a road network, with weights on its elements
output:
returns a graph summarizing the network optimization problem instance;
roadnets are multi-digraph, where edge 'keys' are assumed to be unique,
i.e., road names; and should be different from node labels too;
"""
# for convenience
#ROADS = [ key for u,v,key in roadnet.edges_iter( keys=True ) ]
class node : pass
node_s = node() ; node_t = node()
digraph = nx.DiGraph()
digraph.add_node( node_s )
digraph.add_node( node_t )
""" insert supply and demand of roads """
for u,v, road, data in roadnet.edges_iter( keys=True, data=True ) :
roadlen = data.get( length, 1. )
assert roadlen >= 0.
oneway = data.get( 'oneway', False )
surplus = data.get( weight1, 0. ) - data.get( weight2, 0. )
deficit = -surplus
# supply layer
if surplus > 0. :
digraph.add_edge( node_s, road, capacity=surplus )
w = roadlen / surplus
if oneway : ends = [ v ]
else : ends = [ u, v ]
for node in ends :
digraph.add_edge( road, node, decision_weight=w )
# demand layers
if deficit > 0. :
digraph.add_edge( road, node_t, capacity=deficit )
w = roadlen / deficit
if oneway : ends = [ u ]
else : ends = [ u, v ]
for node in ends :
digraph.add_edge( node, road, decision_weight=w )
""" insert supply and demand of nodes """
for u, data in roadnet.nodes_iter( data=True ) :
surplus = data.get( weight1, 0. ) - data.get( weight2, 0. )
deficit = -surplus
# supply layer
if surplus > 0. :
digraph.add_edge( node_s, u, capacity=surplus )
if deficit > 0. :
digraph.add_edge( u, node_t, capacity=deficit )
""" setup the network flow structure """
conns = roadmap_basic.connectivity_graph( roadnet, length_in=length )
for u, v, data in conns.edges_iter( data=True ) :
w = data.get( 'length', 1 )
digraph.add_edge( u, v, weight=w )
#return digraph, node_s, node_t # this *just* produced a flowgraph; no problem
flowgraph = flownets.obtainFlowNetwork( digraph, node_s, node_t )
costgraph = flownets.obtainWeightedCosts( flowgraph, digraph ) # cute trick
#return flowgraph, costgraph
for u,v, data in digraph.edges_iter( data=True ) :
dec_weight = data.get( 'decision_weight', None )
if dec_weight is None : continue
#
fdata = flowgraph.get_edge_data( u, v, 0 ) # key=0, because we have tightly controlled this construction
flow = fdata.get( 'flow' )
cost = .5 * dec_weight * cvxpy.square( flow )
#print dec_weight, flow, cost
cdata = costgraph.get_edge_data( u, v, 0 )
#print cdata
cdata['cost'] = cost
return flowgraph, costgraph