def test_all_or_nothing(self):
# load the data
graph=np.loadtxt('data/braess_graph.csv', delimiter=',', skiprows=1)
g = construct_igraph(graph)
od=np.loadtxt('data/braess_od.csv', delimiter=',', skiprows=1)
od={int(od[0]): ([int(od[1])],[od[2]])}
# all or nothing assignment
L = all_or_nothing(g, od)
self.assertTrue(np.linalg.norm(L - np.array([2., 0., 2., 0., 2.])) < eps)
g.es["weight"] = [1., 1., 1000., 1.0, 0.0]
# modify graph
L = all_or_nothing(g, od)
self.assertTrue(np.linalg.norm(L - np.array([0., 2., 0., 0., 2.])) < eps)
def LA_free_flow_costs(thres, cog_costs):
'''
study aiming at comparing the OD costs of all-or-nothing assignment
between costs = travel times, and costs with multiplicative cognitive costs
'''
net, demand, node, geom = load_LA_2()
g = construct_igraph(net)
g2 = construct_igraph(net)
od = construct_od(demand)
print np.array(g.es["weight"]).dot(all_or_nothing(g, od))/ (np.sum(demand[:,2])*60.)
for K in cog_costs:
net2, small_capacity = multiply_cognitive_cost(net, geom, thres, K)
g2.es["weight"] = net2[:,3]
print np.array(g.es["weight"]).dot(all_or_nothing(g2, od))/ (np.sum(demand[:,2])*60.)
def all_or_nothing_assignment(cost, net, demand):
# given vector of edge costs, graph, and demand, computes the AoN
# assignment
g = construct_igraph(net)
od = construct_od(demand)
g.es["weight"] = cost.tolist()
return all_or_nothing(g, od)
def test_all_or_nothing(self):
# load the data
graph = np.loadtxt('data/braess_graph.csv', delimiter=',', skiprows=1)
g = construct_igraph(graph)
od = np.loadtxt('data/braess_od.csv', delimiter=',', skiprows=1)
od = {int(od[0]): ([int(od[1])], [od[2]])}
# all or nothing assignment
L = all_or_nothing(g, od)
self.assertTrue(
np.linalg.norm(L - np.array([2., 0., 2., 0., 2.])) < eps)
g.es["weight"] = [1., 1., 1000., 1.0, 0.0]
# modify graph
L = all_or_nothing(g, od)
self.assertTrue(
np.linalg.norm(L - np.array([0., 2., 0., 0., 2.])) < eps)
def search_direction(f, graph, g, od):
# computes the Frank-Wolfe step
# g is just a canvas containing the link information and to be updated with
# the most recent edge costs
x = np.power(f.reshape((f.shape[0], 1)), np.array([0, 1, 2, 3, 4]))
grad = np.einsum('ij,ij->i', x, graph[:, 3:])
# print x.shape, graph[:,3:].shape, grad.shape
# print x[0], graph[:,3:][0], grad[0]
g.es['weight'] = grad.tolist()
#start timer
#start_time1 = timeit.default_timer()
L, path_flows = all_or_nothing(g, od)
# print len(path_flows)
# for k in path_flows:
# print k, path_flows[k]
# exit(1)
#end of timer
#elapsed1 = timeit.default_timer() - start_time1
#print ('all_or_nothing took %s seconds' % elapsed1)
return L, grad, path_flows
def LA_free_flow_costs(thres, cog_costs):
'''
study aiming at comparing the OD costs of all-or-nothing assignment
between costs = travel times, and costs with multiplicative cognitive costs
'''
net, demand, node, geom = load_LA_2()
g = construct_igraph(net)
g2 = construct_igraph(net)
od = construct_od(demand)
print np.array(g.es["weight"]).dot(all_or_nothing(
g, od)) / (np.sum(demand[:, 2]) * 60.)
for K in cog_costs:
net2, small_capacity = multiply_cognitive_cost(net, geom, thres, K)
g2.es["weight"] = net2[:, 3]
print np.array(g.es["weight"]).dot(all_or_nothing(
g2, od)) / (np.sum(demand[:, 2]) * 60.)
def test_all_or_nothing_2(self):
# load the data
graph=np.loadtxt('data/graph_test.csv', delimiter=',')
g = construct_igraph(graph)
# print graph
od=np.loadtxt('data/od_test.csv', delimiter=',')
od={int(od[0]): ([int(od[1])],[od[2]])}
L = all_or_nothing(g, od)
def search_direction(f, graph, g, od):
# computes the Frank-Wolfe step
# g is just a canvas containing the link information and to be updated with
# the most recent edge costs
x = np.power(f.reshape((f.shape[0], 1)), np.array([0, 1, 2, 3, 4]))
grad = np.einsum('ij,ij->i', x, graph[:, 3:])
g.es["weight"] = grad.tolist()
return all_or_nothing(g, od), grad
def test_all_or_nothing_2(self):
# load the data
graph = np.loadtxt('data/graph_test.csv', delimiter=',')
g = construct_igraph(graph)
# print graph
od = np.loadtxt('data/od_test.csv', delimiter=',')
od = {int(od[0]): ([int(od[1])], [od[2]])}
L = all_or_nothing(g, od)
def search_direction(f, graph, g, od):
# computes the Frank-Wolfe step
# g is just a canvas containing the link information and to be updated with
# the most recent edge costs
x = np.power(f.reshape((f.shape[0],1)), np.array([0,1,2,3,4]))
grad = np.einsum('ij,ij->i', x, graph[:,3:])
g.es["weight"] = grad.tolist()
return all_or_nothing(g, od), grad
def residual(graphs, demands, g, ods, fs):
f = np.sum(fs, axis=1)
x = np.power(f.reshape((graphs[0].shape[0],1)), np.array([0,1,2,3,4]))
r = 0.
for i, (graph, demand, od) in enumerate(zip(graphs, demands, ods)):
grad = np.einsum('ij,ij->i', x, graph[:,3:])
g.es["weight"] = grad.tolist()
L = all_or_nothing(g, od)
r = r + grad.dot(fs[:,i] - L)
return r
def residual(graphs, demands, g, ods, fs):
f = np.sum(fs, axis=1)
x = np.power(f.reshape((graphs[0].shape[0], 1)), np.array([0, 1, 2, 3, 4]))
r = 0.
for i, (graph, demand, od) in enumerate(zip(graphs, demands, ods)):
grad = np.einsum('ij,ij->i', x, graph[:, 3:])
g.es["weight"] = grad.tolist()
L = all_or_nothing(g, od)
r = r + grad.dot(fs[:, i] - L)
return r
def search_direction(f, graph, g, od, features):
# computes the Frank-Wolfe step
# g is just a canvas containing the link information and to be updated with
# the most recent edge costs
x = np.power(f.reshape((f.shape[0], 1)), np.array([0, 1, 2, 3, 4]))
grad = np.einsum('ij,ij->i', x, graph[:, 3:])
g.es["weight"] = grad.tolist()
#start timer
#start_time1 = timeit.default_timer()
L = all_or_nothing(g, od)
#end of timer
#elapsed1 = timeit.default_timer() - start_time1
#print ("all_or_nothing took %s seconds" % elapsed1)
return L, grad
def search_direction_social_optimum(f, graph, g, od):
# computes the Frank-Wolfe step
# g is just a canvas containing the link information and to be updated with
# the most recent edge costs
x = np.power(f.reshape((f.shape[0], 1)), np.array([0, 1, 2, 3, 4]))
#import pdb; pdb.set_trace()
#When we add the price of anarchy, the cost function becomes a0+ 2*a2*x+ 3*a3*x^2+ 4*a4*x^3+ 5*a5*x^4
#Matrix coefficients saves the 1, 2, 3, 4, and 5 coefficients in front of the ai*x terms
coefficients = np.array([1, 2, 3, 4, 5])
onesArray = np.ones((f.shape[0], 5))
coefficients = onesArray * coefficients.transpose()
#y stands for the flow multiplied by the coefficients
#import pdb; pdb.set_trace()
y = np.einsum('ij, ij->ij', x, coefficients)
grad = np.einsum('ij,ij->i', y, graph[:, 3:])
g.es["weight"] = grad.tolist()
#Calculating All_or_nothing
L = all_or_nothing(g, od)
return L, grad
def total_free_flow_cost(g, od):
return np.array(g.es["weight"]).dot(all_or_nothing(g, od))
def all_or_nothing_assignment(cost, net, demand):
# given vector of edge costs, graph, and demand, computes the AoN assignment
g = construct_igraph(net)
od = construct_od(demand)
g.es["weight"] = cost.tolist()
return all_or_nothing(g, od)
def total_free_flow_cost(g, od):
return np.array(g.es["weight"]).dot(all_or_nothing(g, od))
def total_ff_costs_heterogeneous(graphs, g, ods):
cost = 0.
for graph, od in zip(graphs, ods):
g.es["weight"] = graph[:, 3].tolist()
cost = cost + graph[:, 3].dot(all_or_nothing(g, od))
return cost
def total_ff_costs_heterogeneous(graphs, g, ods):
cost = 0.
for graph, od in zip(graphs, ods):
g.es["weight"] = graph[:,3].tolist()
cost = cost + graph[:,3].dot(all_or_nothing(g, od))
return cost
