def spatial_outreach(multi,
node_layer='taz',
thru_layers=['streets'],
weight=None,
cost=None,
attrname='outreach'):
'''
Summary:
Compute the spatial outreach of all nodes in a layer according to a specified edge weight (e.g. cost_time_m).
Currently uses area of convex hull to measure outreach.
Args:
layer (TYPE, optional): the layer in which to compute spatial outreach
weight (TYPE, optional): the numeric edge attribute by which to measure path lengths
cost (TYPE, optional): the maximum path length
attrname (str, optional): the base name to use when saving the computed outreach
Returns:
None
'''
from shapely.geometry import MultiPoint
from math import pi
LAT_DIST = 110766.95237186992 / 1000.0 # in km. See http://www.csgnetwork.com/degreelenllavcalc.html
LON_DIST = 101274.42720366278 / 1000.0 # in km. See http://www.csgnetwork.com/degreelenllavcalc.html
def distance_matrix(nodes, weight):
N = len(nodes)
lengths = g.shortest_paths_dijkstra(weights=weight,
source=nodes,
target=nodes)
d = {
nodes[i]: {nodes[j]: lengths[i][j]
for j in range(N)}
for i in range(N)
}
return d
def ego(n, cost, d):
return [j for j in nodes if d[n][j] <= cost]
def area(n, cost, d):
points = [pos[n] for n in ego(n, cost, d)]
return MultiPoint(points).convex_hull.area
g = utility.nx_2_igraph(
multi.layers_as_subgraph(thru_layers + [node_layer]))
nodes = g.vs.select(lambda vertex: vertex['layer'] == node_layer)['name']
pos = {
v['name']: (v['lon'] * LON_DIST, v['lat'] * LAT_DIST)
for v in g.vs.select(lambda v: v['name'] in nodes)
}
d = distance_matrix(nodes, weight)
outreach = {n: sqrt(area(n, cost, d) / pi) for n in nodes}
nx.set_node_attributes(multi.G, attrname, outreach)
def local_intermodality(self, layer=None, thru_layer=None, weight=None):
"""
Summary:
Compute the local intermodality of a set of nodes and save as a node attribute.
Args:
layer (str, optional): the layer for which to compute intermodality
thru_layer (str, optional): the layer through which a path couns as 'intermodal'
weight (str, optional): the numeric edge attribute used to weight paths
Returns:
None
"""
g = utility.nx_2_igraph(self.G)
nodes = g.vs.select(layer=layer)
def intermodality(v, g, nodes=nodes, weight=weight):
paths = g.get_shortest_paths(v, nodes, weights=weight)
total = len(nodes)
intermodal = 0
for p in paths:
if thru_layer in [g.vs[u]['layer'] for u in p]:
intermodal += 1
return intermodal * 1.0 / total
d = {
v['name']: intermodality(v=v, g=g, nodes=nodes, weight=weight)
for v in nodes
}
nx.set_node_attributes(self.G, 'intermodality', d)
def local_intermodality(self, layer = None, thru_layer = None, weight = None):
"""
Summary:
Compute the local intermodality of a set of nodes and save as a node attribute.
Args:
layer (str, optional): the layer for which to compute intermodality
thru_layer (str, optional): the layer through which a path couns as 'intermodal'
weight (str, optional): the numeric edge attribute used to weight paths
Returns:
None
"""
g = utility.nx_2_igraph(self.G)
nodes = g.vs.select(layer=layer)
def intermodality(v, g, nodes = nodes, weight = weight):
paths = g.get_shortest_paths(v, nodes, weights = weight)
total = len(nodes)
intermodal = 0
for p in paths:
if thru_layer in [g.vs[u]['layer'] for u in p]:
intermodal += 1
return intermodal * 1.0 / total
d = {v['name'] : intermodality(v = v, g = g, nodes = nodes, weight = weight)
for v in nodes}
nx.set_node_attributes(self.G, 'intermodality', d)
def spatial_outreach(multi, node_layer = 'taz', thru_layers = ['streets'], weight = None, cost = None, attrname = 'outreach'):
'''
Summary:
Compute the spatial outreach of all nodes in a layer according to a specified edge weight (e.g. cost_time_m).
Currently uses area of convex hull to measure outreach.
Args:
layer (TYPE, optional): the layer in which to compute spatial outreach
weight (TYPE, optional): the numeric edge attribute by which to measure path lengths
cost (TYPE, optional): the maximum path length
attrname (str, optional): the base name to use when saving the computed outreach
Returns:
None
'''
from shapely.geometry import MultiPoint
from math import pi
LAT_DIST = 110766.95237186992 / 1000.0 # in km. See http://www.csgnetwork.com/degreelenllavcalc.html
LON_DIST = 101274.42720366278 / 1000.0 # in km. See http://www.csgnetwork.com/degreelenllavcalc.html
def distance_matrix(nodes, weight):
N = len(nodes)
lengths = g.shortest_paths_dijkstra(weights = weight,
source = nodes,
target = nodes)
d = {nodes[i] : {nodes[j] : lengths[i][j] for j in range(N) }
for i in range(N)}
return d
def ego(n, cost, d):
return [j for j in nodes if d[n][j] <= cost]
def area(n, cost, d):
points = [pos[n] for n in ego(n, cost, d)]
return MultiPoint(points).convex_hull.area
g = utility.nx_2_igraph(multi.layers_as_subgraph(thru_layers + [node_layer]))
nodes = g.vs.select(lambda vertex: vertex['layer'] == node_layer)['name']
pos = {v['name'] : (v['lon'] * LON_DIST, v['lat'] * LAT_DIST)
for v in g.vs.select(lambda v: v['name'] in nodes)}
d = distance_matrix(nodes, weight)
outreach = {n : sqrt(area(n, cost, d)/pi) for n in nodes}
nx.set_node_attributes(multi.G, attrname, outreach)
