def grg_equilateral(
G, # graph
s, # start node
t, # end node
start_t, # start time
end_t, # end time
i, # recursion level
objective, # objective function class
Xi_pilot,
max_recursions,
):
'''
G - dictionary representing the graph
s - start node (int)
t - end node (int)
start_t - start time (int)
end_t - end time (int)
i - recursion level (int)
objective - objective function class
Xi_pilot - pilot samples (set)
'''
if i == max_recursions:
dbg.printdbg('Top level')
if G.soonest_arrival(s, t, start_t) > end_t:
# impossible to get from node s to node t in the
# alloted time frame
return None, None, None
if end_t - start_t == 0:
# s and t must be the same node. This happens when the budget is
# not a perfect power of 2 - we may recurse one more time than
# necessary. Return a zero length path, and zero gain in the
# objective function.
return [], 0.0, objective
# base case
if i == 0:
if not t in G.edge_dict[s]:
return None, None, None
edge_list = G.edge_dict[s][t]
m_new_best = -np.inf
P_best = None
obj_best = None
# try each edge between these nodes
if objective.value:
obj_without = objective.value
else:
obj_without = objective.f(Xi_pilot, update_dist=True)
for e in edge_list:
if start_t + e.length(start_t) <= end_t:
P = [e]
new_samples = ppas.graph.path_samples(P, start_t)
# print 'Adding %d samples' % len(new_samples)
samples_with = set.union(Xi_pilot, new_samples)
obj_with = objective.f(samples_with, update_dist=True)
m_new = obj_with - obj_without
if m_new > m_new_best:
m_new_best = m_new
P_best = P
return P_best, m_new_best, objective
# recursive case
P = None
m = -np.inf
obj_best = objective
for v in G.nodes:
# assumes edges are all equal lenghth, and time budget is
# a power of two
b = (start_t + end_t) / 2
if i >= max_recursions:
spaces = ' ' * (max_recursions - i)
dbg.printdbg('%s Middle v=%d with b=%d, m=%e' % (spaces, v, b, m))
if G.soonest_arrival(s, v, start_t) > b:
# first half infeasible
continue
if G.soonest_arrival(v, t, b) > end_t:
# second half infeasible
continue
#print ' '*(max_recursions - i), 'Solving first half:', list(Xi_pilot), list(objective.conditioned_on)
P1, m1, objective_new = grg_equilateral(G, s, v, start_t, b, i - 1,
objective.copy(), Xi_pilot,
max_recursions)
if P1 == None:
continue
Xi_pilot_new = set.union(Xi_pilot,
ppas.graph.path_samples(P1, start_t))
#print ' '*(max_recursions - i), 'Solving second half:', list(Xi_pilot_new), list(objective_new.conditioned_on)
P2, m2, objective_new = grg_equilateral(G, v, t, b, end_t, i - 1,
objective_new, Xi_pilot_new,
max_recursions)
if P2 == None:
continue
P_new = P1 + P2
m_new = m1 + m2
if m_new > m:
P = P_new
m = m_new
obj_best = objective_new
return P, m, obj_best
def grg_equilateral(
G, # graph
s, # start node
t, # end node
start_t, # start time
end_t, # end time
i, # recursion level
objective, # objective function class
Xi_pilot,
max_recursions,
):
'''
G - dictionary representing the graph
s - start node (int)
t - end node (int)
start_t - start time (int)
end_t - end time (int)
i - recursion level (int)
objective - objective function class
Xi_pilot - pilot samples (set)
'''
if i == max_recursions:
dbg.printdbg('Top level')
if G.soonest_arrival(s, t, start_t) > end_t:
# impossible to get from node s to node t in the
# alloted time frame
return None, None, None
if end_t - start_t == 0:
# s and t must be the same node. This happens when the budget is
# not a perfect power of 2 - we may recurse one more time than
# necessary. Return a zero length path, and zero gain in the
# objective function.
return [], 0.0, objective
# base case
if i == 0:
if not t in G.edge_dict[s]:
return None, None, None
edge_list = G.edge_dict[s][t]
m_new_best = -np.inf
P_best = None
obj_best = None
# try each edge between these nodes
if objective.value:
obj_without = objective.value
else:
obj_without = objective.f(Xi_pilot, update_dist=True)
for e in edge_list:
if start_t + e.length(start_t) <= end_t:
P = [e]
new_samples = ppas.graph.path_samples(P, start_t)
# print 'Adding %d samples' % len(new_samples)
samples_with = set.union(Xi_pilot, new_samples)
obj_with = objective.f(samples_with, update_dist=True)
m_new = obj_with - obj_without
if m_new > m_new_best:
m_new_best = m_new
P_best = P
return P_best, m_new_best, objective
# recursive case
P = None
m = -np.inf
obj_best = objective
for v in G.nodes:
# assumes edges are all equal lenghth, and time budget is
# a power of two
b = (start_t + end_t)/2
if i >= max_recursions:
spaces = ' ' * (max_recursions - i)
dbg.printdbg(
'%s Middle v=%d with b=%d, m=%e' % (spaces, v, b, m))
if G.soonest_arrival(s, v, start_t) > b:
# first half infeasible
continue
if G.soonest_arrival(v, t, b) > end_t:
# second half infeasible
continue
#print ' '*(max_recursions - i), 'Solving first half:', list(Xi_pilot), list(objective.conditioned_on)
P1, m1, objective_new = grg_equilateral(
G, s, v, start_t, b, i-1, objective.copy(), Xi_pilot, max_recursions)
if P1 == None:
continue
Xi_pilot_new = set.union(Xi_pilot, ppas.graph.path_samples(P1, start_t))
#print ' '*(max_recursions - i), 'Solving second half:', list(Xi_pilot_new), list(objective_new.conditioned_on)
P2, m2, objective_new = grg_equilateral(
G, v, t, b, end_t, i-1, objective_new, Xi_pilot_new, max_recursions)
if P2 == None:
continue
P_new = P1 + P2
m_new = m1 + m2
if m_new > m:
P = P_new
m = m_new
obj_best = objective_new
return P, m, obj_best
def grg_transect(
G, # graph
s, # start node
t, # end node
start_t, # start time
end_t, # end time
i, # recursion level
objective, # objective function class
Xi_pilot,
max_recursions,
):
'''
G - dictionary representing the graph
h - path (list) to sample (set) expansion function
s - start node (int)
t - end node (int)
start_t - start time (int)
end_t - end time (int)
i - recursion level (int)
objective - objective function class
Xi_pilot - pilot samples (set)
'''
if i == max_recursions:
dbg.printdbg('Top level')
if G.soonest_arrival(s, t, start_t) > end_t:
# impossible to get from node s to node t in the
# alloted time frame
return None, None
if end_t - start_t == 0:
# s and t must be the same node. This happens when the budget is
# not a perfect power of 2 - we may recurse one more time than
# necessary. Return a zero length path, and zero gain in the
# objective function.
return [], 0.0
# base case
if i == 0:
if not t in G.edge_dict[s]:
return None, None
edge_list = G.edge_dict[s][t]
m_new_best = -np.inf
P_best = None
obj_best = None
# try each edge between these nodes
obj_without = objective.f(Xi_pilot, update_dist=False)
for e in edge_list:
if start_t + e.length(start_t) <= end_t:
P = [e]
samples_with = set.union(Xi_pilot,
ppas.graph.path_samples(P, start_t))
obj_with = objective.f(samples_with, update_dist=False)
m_new = obj_with - obj_without
if m_new > m_new_best:
m_new_best = m_new
P_best = P
return P_best, m_new_best
# recursive case
m = -np.inf
obj_best = objective
P = None
b_choices = range(start_t, end_t)
# always choose the middle node. assumes nodes are number 0 through n, with 0
# always being the start node, and n always being the end node
v = int((s + t) / 2)
for b in b_choices:
if i >= max_recursions:
spaces = ' ' * (max_recursions - i)
dbg.printdbg('%s Middle v=%d with b=%d, m=%e' % (spaces, v, b, m))
if G.soonest_arrival(s, v, start_t) > b:
# first half infeasible
continue
if G.soonest_arrival(v, t, b) > end_t:
#second half infeasible
continue
P1, m1 = grg_transect(G, s, v, start_t, b, i - 1, objective, Xi_pilot,
max_recursions)
if P1 == None:
continue
Xi_pilot_new = set.union(Xi_pilot,
ppas.graph.path_samples(P1, start_t))
P2, m2 = grg_transect(G, v, t, b, end_t, i - 1, objective,
Xi_pilot_new, max_recursions)
if P2 == None:
continue
P_new = P1 + P2
m_new = m1 + m2
if m_new > m:
P = P_new
m = m_new
return P, m
def grg_transect(
G, # graph
s, # start node
t, # end node
start_t, # start time
end_t, # end time
i, # recursion level
objective, # objective function class
Xi_pilot,
max_recursions,
):
'''
G - dictionary representing the graph
h - path (list) to sample (set) expansion function
s - start node (int)
t - end node (int)
start_t - start time (int)
end_t - end time (int)
i - recursion level (int)
objective - objective function class
Xi_pilot - pilot samples (set)
'''
if i == max_recursions:
dbg.printdbg('Top level')
if G.soonest_arrival(s, t, start_t) > end_t:
# impossible to get from node s to node t in the
# alloted time frame
return None, None
if end_t - start_t == 0:
# s and t must be the same node. This happens when the budget is
# not a perfect power of 2 - we may recurse one more time than
# necessary. Return a zero length path, and zero gain in the
# objective function.
return [], 0.0
# base case
if i == 0:
if not t in G.edge_dict[s]:
return None, None
edge_list = G.edge_dict[s][t]
m_new_best = -np.inf
P_best = None
obj_best = None
# try each edge between these nodes
obj_without = objective.f(Xi_pilot, update_dist=False)
for e in edge_list:
if start_t + e.length(start_t) <= end_t:
P = [e]
samples_with = set.union(Xi_pilot, ppas.graph.path_samples(P, start_t))
obj_with = objective.f(samples_with, update_dist=False)
m_new = obj_with - obj_without
if m_new > m_new_best:
m_new_best = m_new
P_best = P
return P_best, m_new_best
# recursive case
m = -np.inf
obj_best = objective
P = None
b_choices = range(start_t, end_t)
# always choose the middle node. assumes nodes are number 0 through n, with 0
# always being the start node, and n always being the end node
v = int((s + t)/2)
for b in b_choices:
if i >= max_recursions:
spaces = ' ' * (max_recursions - i)
dbg.printdbg(
'%s Middle v=%d with b=%d, m=%e' % (spaces, v, b, m))
if G.soonest_arrival(s, v, start_t) > b:
# first half infeasible
continue
if G.soonest_arrival(v, t, b) > end_t:
#second half infeasible
continue
P1, m1 = grg_transect(
G, s, v, start_t, b, i-1, objective, Xi_pilot, max_recursions)
if P1 == None:
continue
Xi_pilot_new = set.union(Xi_pilot, ppas.graph.path_samples(P1, start_t))
P2, m2 = grg_transect(
G, v, t, b, end_t, i-1, objective, Xi_pilot_new, max_recursions)
if P2 == None:
continue
P_new = P1 + P2
m_new = m1 + m2
if m_new > m:
P = P_new
m = m_new
return P, m