def _options_roads_neq( roadnet, road1, road2, length_attr ) :
edge1, data1 = ROAD.obtain_edge( roadnet, road1, data_flag=True )
u1,v1,_ = edge1 ; roadlen1 = data1.get( length_attr, np.inf )
edge2, data2 = ROAD.obtain_edge( roadnet, road2, data_flag=True )
u2,v2,_ = edge2 ; roadlen2 = data2.get( length_attr, np.inf )
x = GLOBAL.x ; y = GLOBAL.y
cost_dict = {
'<-s' : x,
's->' : roadlen1 - x,
'->t' : y,
't<-' : roadlen2 - y
}
options = []
# paths through endpoints
WAYP1 = [ ( 's->', v1 ) ]
if not data1.get( 'oneway', False ) : WAYP1.append( ( '<-s', u1 ) )
WAYP2 = [ ( '->t', u2 ) ]
if not data2.get( 'oneway', False ) : WAYP2.append( ( 't<-', v2 ) )
for s,u in WAYP1 :
p = ROAD.roadify( roadnet, u, length_attr )
for t,v in WAYP2 :
q = ROAD.roadify( roadnet, v, length_attr )
dst = ROAD.distance( roadnet, p, q, length_attr )
cost = cost_dict[s] + dst + cost_dict[t]
options.append( cost )
return options
def _options_roads_eq_yleqx( roadnet, road, length_attr ) :
edge, data = ROAD.obtain_edge( roadnet, road, data_flag=True )
u,v,_ = edge ; roadlen = data.get( length_attr, np.inf )
p = ROAD.roadify( roadnet, u, length_attr )
q = ROAD.roadify( roadnet, v, length_attr )
x = GLOBAL.x ; y = GLOBAL.y
sojourn_cost = roadlen - x + ROAD.distance( roadnet, q, p, length_attr ) + y # a path using the rest of the network
options = [ sojourn_cost ]
if not data.get( 'oneway', False ) :
options.append( x - y )
return options
def measurenx_to_approxnx( roadnet, epsilon, 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;
"""
digraph = nx.DiGraph()
#digraph.add_node('s')
#digraph.add_node('t')
SUPPLY = []
DEMAND = []
""" insert supply and demand of roads """
for u,v, road, data in roadnet.edges_iter( keys=True, data=True ) :
roadlen = float( data.get( length, 1 ) ) # float() just in case
assert roadlen >= 0.
"""
split the road into equal-length segments;
create a node for each segment;
record boundary points, and mass contained
"""
N = int( np.ceil( roadlen / epsilon ) )
eps = roadlen / N
surplus = float( data.get( weight1, 0. ) ) - data.get( weight2, 0. )
deficit = -surplus
bd = np.linspace( 0, roadlen, N+1 )
bd = [ roadmaps.RoadAddress( road, x ) for x in bd ]
for i, boundary in enumerate( zip( bd[:-1], bd[1:] ) ) :
if surplus > 0. :
node = (road,i,'supply')
digraph.add_node( node, boundary=boundary )
digraph.add_edge( 's', node, flow=cvxpy.variable(), minflow=0., maxflow=surplus/N )
SUPPLY.append( node )
if deficit > 0. :
node = (road,i,'demand')
digraph.add_node( node, boundary=boundary )
digraph.add_edge( node, 't', flow=cvxpy.variable(), minflow=0., maxflow=deficit/N )
DEMAND.append( node )
""" ...and nodes """
for u, data in roadnet.nodes_iter( data=True ) :
surplus = data.get( weight1, 0. ) - data.get( weight2, 0. )
deficit = -surplus
if surplus > 0. :
boundary = [ roadmaps.roadify( roadnet, u, weight=length ) ]
node = (u,'supply')
digraph.add_node( node, boundary=boundary )
digraph.add_edge( 's', node, flow=cvxpy.variable(), minflow=0., maxflow=surplus )
SUPPLY.append( node )
if deficit > 0. :
boundary = [ roadmaps.roadify( roadnet, v, weight=length ) ]
node = (u,'demand')
digraph.add_node( node, boundary=boundary )
digraph.add_edge( node, 't', flow=cvxpy.variable(), minflow=0., maxflow=deficit )
DEMAND.append( node )
""" generate bipartite graph b/w SUPPLY and DEMAND """
for u, v in itertools.product( SUPPLY, DEMAND ) :
bd_u = digraph.node[u]['boundary']
bd_v = digraph.node[v]['boundary']
options = [ pair for pair in itertools.product( bd_u, bd_v ) ]
options = [ roadmaps.distance( roadnet, p, q, weight=length ) for p,q in options ]
#options = [ np.inf ]
w = min( options )
W = max( options )
flowvar = cvxpy.variable()
digraph.add_edge( u, v, flow=flowvar, minflow=0., w=w, W=W, cost_lo = w * flowvar, cost_hi = W * flowvar )
nxopt.attach_flownx_constraints( digraph )
return digraph # a flow network