def test_dijkstras(self):
distances = pynet.dijkstras(self.G2, (1, 1))
distance_values = {
(5, 5): 1.625,
(2, 2): 0.125,
(1, 1): 0,
(4, 4): 1.125,
(3, 3): 0.75
}
self.assertEqual(distances, distance_values)
def setUp(self):
self.population = range(5)
self.weights = [0.1, 0.25, 0.1, 0.2, 0.35]
np.random.seed(10)
self.network_file = 'streets.shp'
self.G = pynet.read_network(self.network_file)
self.references = [[i, [n]] for i, n in enumerate(self.G.keys())]
self.scale_set = (0, 1500, 500)
self.network_distances_cache = {}
search_radius = self.scale_set[1]
for i, node in self.references:
n = node[0]
self.network_distances_cache[n] = pynet.dijkstras(self.G, n, search_radius)
self.snapper = pynet.Snapper(self.G)
self.events_file = 'crimes.shp'
points = self.get_points_from_shapefile(self.events_file)
self.events = []
for p in points:
self.events.append(self.snapper.snap(p[0]))
self.test_node = (724587.78057580709, 877802.4281426128)
def test_dijkstras(self):
distances = pynet.dijkstras(self.G2, (1,1))
distance_values = {(5, 5): 1.625, (2, 2): 0.125, (1, 1): 0, (4, 4): 1.125, (3, 3): 0.75}
self.assertEqual(distances, distance_values)
def kernel_density(network, events, bandwidth, orig_nodes, kernel='quadratic'):
"""
This function estimates Kernel densities on a planar undirected network.
It implements the equal-split discontinuous Kernel function developed by Okabe et al. (2009).
Particularly, it computes Kernel densities by using equation 19 and 20
in the paper of Okabe et al. (2009).
Parameters
----------
network: A dictionary of dictionaries like {n1:{n2:d12,...},...}
A planar undirected network
It is assumed that this network is divided by a certain cell size
and is restructured to incorporate the new nodes resulting from the division as well as
events. Therefore, nodes in the network can be classified into three groups:
i) original nodes, 2) event points, and 3) cell points.
events: a list of tuples
a tuple is the network-projected coordinate of an event
that takes the form of (x,y)
bandwidth: a float
Kernel bandwidth
orig_nodes: a list of tuples
a tuple is the coordinate of a node that is part of the original base network
each tuple takes the form of (x,y)
kernel: string
the type of Kernel function
allowed values: 'quadratic', 'gaussian', 'quartic', 'uniform', 'triangular'
Returns
-------
A dictioinary where keys are node and values are their densities
Example: {n1:d1,n2:d2,...}
<tc>#is#kernel_density</tc>
"""
# beginning of step i
density = {}
for n in network:
density[n] = []
# end of step i
# beginning of step ii
def compute_split_multiplier(prev_D, n):
'''
computes the demoninator of the formula 19
Parameters
----------
prev_D: a dictionary storing pathes from n to other nodes in the network
its form is like: {n1:prev_node_of_n1(=n2), n2:prev_node_of_n2(=n3),...}
n: a tuple containing the geographic coordinate of a starting point
its form is like: (x,y)
Returns
-------
An integer
'''
split_multiplier = 1
p = prev_D[n]
while p != None:
if len(network[p]) > 1:
split_multiplier *= (len(network[p]) - 1)
if p not in prev_D:
p = None
else:
p = prev_D[p]
return split_multiplier
# end of step ii
kernel_funcs = {
'triangular': triangular,
'uniform': uniform,
'quadratic': quadratic,
'quartic': quartic,
'gaussian': gaussian
}
#t1 = time.time()
# beginning of step iii
kernel_func = kernel_funcs[kernel]
for e in events:
# beginning of step a
src_D = pynet.dijkstras(network, e, bandwidth, True)
# end of step a
# beginning of step b
density[e].append(kernel_func(0))
# end of step b
# beginning of step c
for n in src_D[
0]: # src_D[0] - a dictionary of nodes whose distance from e is smaller than e
if src_D[0][n] == 0: continue
# src_D[1] - a dictionary from which a path from e to n can be traced
d = src_D[0][n]
if d <= bandwidth:
n_degree = 2.0
if n in events and n in orig_nodes and len(network[n]) > 0:
n_degree = len(network[n])
unsplit_density = kernel_func(d * 1.0 / bandwidth * 1.0)
# src_D[1] - a dictionary from which a path from e to n can be traced
split_multiplier = compute_split_multiplier(src_D[1], n)
density[n].append((1.0 / split_multiplier) * (2.0 / n_degree) *
unsplit_density)
#if str(n[0]) == '724900.335127' and str(n[1]) == '872127.948935':
# print 'event', e
# print 'distance', d
# print 'unsplit_density', unsplit_density
# print 'n_degree', n_degree
# print 'split_multiplier', split_multiplier
# print 'density', (1.0/split_multiplier)*(2.0/n_degree)*unsplit_density
# end of step c
# beginning of step iv
#t1 = time.time()
no_events = len(events)
for node in density:
if len(density[node]) > 0:
#if str(node[0]) == '724900.335127' and str(node[1]) == '872127.948935':
# print density[node]
density[node] = sum(density[node]) / no_events
#density[node] = sum(density[node])*1.0/len(density[node])
else:
density[node] = 0.0
# end of step iv
#for node in events:
# del density[node]
#print 'normalizing density: %s' % (str(time.time() - t1))
return density
def kernel_density(network, events, bandwidth, orig_nodes, kernel='quadratic'):
"""
This function estimates Kernel densities on a planar undirected network.
It implements the equal-split discontinuous Kernel function developed by Okabe et al. (2009).
Particularly, it computes Kernel densities by using equation 19 and 20
in the paper of Okabe et al. (2009).
Parameters
----------
network: A dictionary of dictionaries like {n1:{n2:d12,...},...}
A planar undirected network
It is assumed that this network is divided by a certain cell size
and is restructured to incorporate the new nodes resulting from the division as well as
events. Therefore, nodes in the network can be classified into three groups:
i) original nodes, 2) event points, and 3) cell points.
events: a list of tuples
a tuple is the network-projected coordinate of an event
that takes the form of (x,y)
bandwidth: a float
Kernel bandwidth
orig_nodes: a list of tuples
a tuple is the coordinate of a node that is part of the original base network
each tuple takes the form of (x,y)
kernel: string
the type of Kernel function
allowed values: 'quadratic', 'gaussian', 'quartic', 'uniform', 'triangular'
Returns
-------
A dictioinary where keys are node and values are their densities
Example: {n1:d1,n2:d2,...}
<tc>#is#kernel_density</tc>
"""
# beginning of step i
density = {}
for n in network:
density[n] = []
# end of step i
# beginning of step ii
def compute_split_multiplier(prev_D, n):
'''
computes the demoninator of the formula 19
Parameters
----------
prev_D: a dictionary storing pathes from n to other nodes in the network
its form is like: {n1:prev_node_of_n1(=n2), n2:prev_node_of_n2(=n3),...}
n: a tuple containing the geographic coordinate of a starting point
its form is like: (x,y)
Returns
-------
An integer
'''
split_multiplier = 1
p = prev_D[n]
while p != None:
if len(network[p]) > 1:
split_multiplier *= (len(network[p]) - 1)
if p not in prev_D:
p = None
else:
p = prev_D[p]
return split_multiplier
# end of step ii
kernel_funcs = {'triangular':triangular, 'uniform': uniform,
'quadratic': quadratic, 'quartic':quartic, 'gaussian':gaussian}
#t1 = time.time()
# beginning of step iii
kernel_func = kernel_funcs[kernel]
for e in events:
# beginning of step a
src_D = pynet.dijkstras(network, e, bandwidth, True)
# end of step a
# beginning of step b
density[e].append(kernel_func(0))
# end of step b
# beginning of step c
for n in src_D[0]: # src_D[0] - a dictionary of nodes whose distance from e is smaller than e
if src_D[0][n] == 0: continue
# src_D[1] - a dictionary from which a path from e to n can be traced
d = src_D[0][n]
if d <= bandwidth:
n_degree = 2.0
if n in events and n in orig_nodes and len(network[n]) > 0:
n_degree = len(network[n])
unsplit_density = kernel_func(d*1.0/bandwidth*1.0)
# src_D[1] - a dictionary from which a path from e to n can be traced
split_multiplier = compute_split_multiplier(src_D[1], n)
density[n].append((1.0/split_multiplier)*(2.0/n_degree)*unsplit_density)
#if str(n[0]) == '724900.335127' and str(n[1]) == '872127.948935':
# print 'event', e
# print 'distance', d
# print 'unsplit_density', unsplit_density
# print 'n_degree', n_degree
# print 'split_multiplier', split_multiplier
# print 'density', (1.0/split_multiplier)*(2.0/n_degree)*unsplit_density
# end of step c
# beginning of step iv
#t1 = time.time()
no_events = len(events)
for node in density:
if len(density[node]) > 0:
#if str(node[0]) == '724900.335127' and str(node[1]) == '872127.948935':
# print density[node]
density[node] = sum(density[node])/no_events
#density[node] = sum(density[node])*1.0/len(density[node])
else:
density[node] = 0.0
# end of step iv
#for node in events:
# del density[node]
#print 'normalizing density: %s' % (str(time.time() - t1))
return density