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dyskstra.py
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190 lines (159 loc) · 6.89 KB
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from __future__ import print_function
import numpy as np
class DistanceMatrix():
def __init__(self, array, labels):
self.array = array
self.labels = labels
def get_index(self, name):
for index, label in enumerate(self.labels):
if label.name == name:
return index
raise ValueError("Label name {} not found".format(name))
def remove_arc(self,label1,label2):
index1 = self.get_index(label1)
index2 = self.get_index(label2)
array[index1,index2]=array[index2,index1] = np.inf
def remove_node(self,label_name):
index = self.get_index(label_name)
#delete the row and column
#re_index
for index,label in enumerate(self.labels):
label.index = index
class VertexLabel():
def __init__(self, name, index):
self.name = name
self.index = index
self.order = None
self.value = None
self.working = [np.inf]
def __str__(self):
return "|{}|{}|{}|\n{}".format(
self.name, self.order, self.value, self.working)
def make_labels(names):
return [VertexLabel(name, i) for i, name in enumerate(names)]
gasexample = np.array(
[
[np.nan, 120, 150, np.inf, 120, 100, np.inf, 70, 180],
[120, np.nan, 60, 60, 90, np.inf, 210, 160, 40],
[150, 60, np.nan, 20, np.inf, 180, 170, np.inf, 50],
[np.inf, 60, 20, np.nan, 40, 160, 150, 140, 60],
[120, 90, np.inf, 40, np.nan, 130, np.inf, 110, np.inf],
[100, np.inf, 180, 160, 130, np.nan, np.inf, 30, np.inf],
[np.inf, 210, 170, 150, np.inf, np.nan, np.inf, 150, 200],
[70, 160, np.inf, 140, 110, 30, 150, np.nan, 200],
[180, 40, 50, 60, np.inf, np.inf, 200, 200, np.nan],
])
gas_labels = make_labels("TABCDEFGH")
gas = DistanceMatrix(gasexample, gas_labels)
book1 = DistanceMatrix(np.array([
[np.nan, 5, 6, 2, np.inf, np.inf],
[5, np.nan, np.inf, np.inf, 4, np.inf],
[6, np.inf, np.nan, 2, 4, 8],
[2, np.inf, 2, np.nan, np.inf, 12],
[np.inf, 4, 4, np.inf, np.nan, 3],
[np.inf, np.inf, 8, 12, 3, np.nan]
]),
make_labels("SABCDT"))
book2 = DistanceMatrix(np.array([
[np.nan, 8, 8, 18, np.inf, np.inf, np.inf, np.inf],
[8, np.nan, np.inf, 7, 15, np.inf, np.inf, np.inf],
[8, np.inf, np.nan, 8, np.inf, 12, np.inf, np.inf],
[18, 7, 8, np.nan, 6, 6, 9, np.inf],
[np.inf, 15, np.inf, 6, np.nan, np.inf, np.inf, 8],
[np.inf, np.inf, 12, 6, np.inf, np.nan, np.inf, 9],
[np.inf, np.inf, np.inf, 9, np.inf, np.inf, np.nan, 8],
[np.inf, np.inf, np.inf, np.inf, 8, 9, 8, np.nan],
]),
make_labels("ABCDEFGH"))
digraph = DistanceMatrix(np.array([
[np.nan, 5, 2, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf],
[5, np.nan, 2, 4, np.inf, np.inf, np.inf, np.inf, np.inf],
[np.inf, 2, np.nan, 3, 5, np.inf, np.inf, np.inf, np.inf],
[np.inf, 4, 3, np.nan, 1, 9, 11, np.inf, np.inf],
[5, np.inf, np.inf, np.inf, np.nan, 8, np.inf, np.inf, 14],
[np.inf, np.inf, np.inf, 9, 8, np.nan, 1, 5, 7],
[np.inf, np.inf, np.inf, 11, np.inf, np.inf, np.nan, 2, np.inf],
[np.inf, np.inf, np.inf, np.inf, np.inf, 5, np.inf, np.nan, 2],
[np.inf, np.inf, np.inf, np.inf, 14, 7, np.inf, 2, np.nan]
]),
make_labels("ABCDEFGHI"))
roadworks = np.array([
[np.nan, 5, 2, np.inf, np.inf, np.inf, np.inf, np.inf, np.inf],
[5, np.nan, 2, 4, np.inf, np.inf, np.inf, np.inf, np.inf],
[np.inf, 2, np.nan, 3, 5, np.inf, np.inf, np.inf, np.inf],
[np.inf, 4, 3, np.nan, 1, 9, 11, np.inf, np.inf],
[5, np.inf, np.inf, np.inf, np.nan, 8, np.inf, np.inf, 14],
[np.inf, np.inf, np.inf, 9, 8, np.nan, 1, 5, 7],
[np.inf, np.inf, np.inf, 11, np.inf, np.inf, np.nan, 2, np.inf],
[np.inf, np.inf, np.inf, np.inf, np.inf, 5, np.inf, np.nan, np.inf],
[np.inf, np.inf, np.inf, np.inf, 14, 7, np.inf, np.inf, np.nan]
])
roadworks_labels = [VertexLabel(name, i) for i, name in enumerate("ABCDEFGHI")]
roadnetwork = DistanceMatrix(
np.array([
[np.nan,2, 14, 10, np.inf, np.inf, np.inf],
[2, np.nan, np.inf, 7, 15, np.inf, np.inf],
[14, np.inf, np.nan, 2, np.inf, 4, 15],
[10, 7, 2, np.nan, 3, 7, np.inf],
[np.inf,15, np.inf, 3, np.nan, 2, 11],
[np.inf,np.inf, 4, 7, 2, np.nan, 5],
[np.inf,np.inf, 15, np.inf, 11, 5, np.nan]]),
make_labels("ABCDEFG"))
def dykstra(distance_matrix,start_vertex=None,end_vertex=None):
graph, graph_labels=distance_matrix.array, distance_matrix.labels
# Give the first vertex a final label of 0, and and order of 1 since it is the
# first to receive its final label
order = 1
if start_vertex:
start_index = distance_matrix.get_index(start_vertex)
else:
start_index = 0
if end_vertex:
end_index = distance_matrix.get_index(end_vertex)
else:
end_index = -1
graph_labels[start_index].order = order
graph_labels[start_index].value = 0
# give working values to those that are directly connected to the
# last vertex to receive a final value
last_complete_index = start_index
while graph_labels[end_index].value is None:
smallest_distance = np.inf
smallest_index = None
for index, distance in enumerate(graph[last_complete_index]):
if graph_labels[index].order is not None:
continue
if np.isfinite(distance):
# shortcut route? is
# graph_labels[last_complete_index].value+distance
if graph_labels[last_complete_index].value + \
distance < graph_labels[index].working[-1]:
# shortcut found
graph_labels[index].working.append(
graph_labels[last_complete_index].value + distance)
if graph_labels[index].working[-1] < smallest_distance:
smallest_distance = graph_labels[index].working[-1]
smallest_index = index
# the smallest working value now becomes a final value
order += 1
graph_labels[smallest_index].order = order
graph_labels[smallest_index].value = graph_labels[
smallest_index].working[-1]
last_complete_index = smallest_index
for v in graph_labels:
print(v, '\n')
print("------------------_")
path = [graph_labels[end_index]]
while path[-1].value != 0:
for index, distance in enumerate(graph[:, path[-1].index]):
if np.isfinite(distance) :
if path[-1].value - distance == graph_labels[index].value:
path.append(graph_labels[index])
break
else:
# none of the arcs seems to fit
raise Exception("Can't find path. ")
for p in reversed(path):
print(p.name, end=', ')
print(path[0].value)
dykstra(roadnetwork)