def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
# Construct nearest neighbour graph
G = np.zeros([n, n])
for i in range(n):
neighbours = np.argsort(D[i])[:self.nn + 1]
for j in neighbours:
G[i, j] = D[i, j]
G[j, i] = D[j, i]
# Compute ISOMAP distances
D = utils.dijkstra(G)
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
D[np.isinf(D)] = D[~np.isinf(D)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.compress(X)
# Solve for the minimizer
z, f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def compress(self, X, n_components, n_neighbours):
n = X.shape[0]
k = self.k
numNeighbours = self.numNeighbours
# find the distances to every other point
euclD = utils.euclidean_dist_squared(X, X)
euclD = np.sqrt(euclD)
knnD = np.zeros((n, n))
# get the KNN of point i
for i in range(n):
# finds numNeighbours smallest distances from obj_i
# +1 because it will always select itself as (distance of 0), and distances are non-negative
minIndexes = np.argsort(euclD[i])[:numNeighbours + 1]
for index in minIndexes:
# add distances of KNN_i to the distance matrix
knnD[i, index] = euclD[i, index]
D = np.zeros((n, n))
# get distance of every other path using only KNN
for i in range(n):
for j in range(n):
if i != j:
D[i, j] = utils.dijkstra(knnD, i, j)
Z = AlternativePCA(k).fit(X).compress(X)
z = find_min(self._fun_obj_z, Z.flatten(), 500, False, D)
Z = z.reshape(n, k)
return Z
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
# TODO: Convert these Euclidean distances into geodesic distances
order = np.argsort(D, axis=1)[:, :self.k + 1]
distance_mask = np.zeros(D.shape)
for i in range(n):
for j in order[i]:
distance_mask[i, j] = 1
distance_mask[j, i] = 1
D = utils.dijkstra(D * distance_mask)
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
D[np.isinf(D)] = D[~np.isinf(D)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.transform(X)
# Solve for the minimizer
z, f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
# Convert these Euclidean distances into geodesic distances
sorted_dist_indices = np.argsort(D)
G = np.zeros((n, n))
for i in range(n):
for j in range(self.nn):
G[i, sorted_dist_indices[i, j]] = D[i, sorted_dist_indices[i,
j]]
G[sorted_dist_indices[i, j], i] = D[sorted_dist_indices[i, j],
i]
D = utils.dijkstra(G)
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
D[np.isinf(D)] = D[~np.isinf(D)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.transform(X)
# Solve for the minimizer
z, f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
sorted_indices = np.argsort(D)
G = np.zeros((n, n))
for i in range(D.shape[0]):
for j in range(self.nn + 1):
G[i, sorted_indices[i, j]] = D[i, sorted_indices[i, j]]
G[sorted_indices[i, j], i] = D[sorted_indices[i, j], i]
dist = utils.dijkstra(G)
dist[np.isinf(dist)] = dist[~np.isinf(dist)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.compress(X)
# Solve for the minimizer
z, f = findMin(self._fun_obj_z, Z.flatten(), 500, dist)
Z = z.reshape(n, self.k)
return Z
def compress(self, X):
n = X.shape[0]
k = self.k
K = self.K
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
nbrs = np.argsort(D, axis=1)[:, 1:K + 1]
G = np.zeros((n, n))
for i in range(n):
for j in nbrs[i]:
G[i, j] = D[i, j]
G[j, i] = D[j, i]
D = utils.dijkstra(G)
D[D == np.inf] = -np.inf
max = np.max(D)
D[D == -np.inf] = max
# Initialize low-dimensional representation with PCA
Z = PCA(k).fit(X).compress(X)
# Solve for the minimizer
z = find_min(self._fun_obj_z, Z.flatten(), 500, False, D)
Z = z.reshape(n, k)
return Z
def compress(self, X):
n = X.shape[0]
# nearest_neighbours = np.zeros((n, self.nn))
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
adjacency_matrix = np.zeros((n, n))
nearest_neighbours = self.knn(X)
for i, j in enumerate(nearest_neighbours):
for neighbour in j:
adjacency_matrix[i, neighbour] = D[i, neighbour]
adjacency_matrix[neighbour, i] = D[neighbour, i]
dijkstra = utils.dijkstra(adjacency_matrix)
dijkstra[np.isinf(dijkstra)] = dijkstra[~np.isinf(dijkstra)].max()
# Initialize low-dimensional representation with PCA
Z = PCA(self.k).fit(X).compress(X)
# Solve for the minimizer
z = find_min(self._fun_obj_z, Z.flatten(), 500, False, dijkstra)
Z = z.reshape(n, self.k)
return Z
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
# D is symmetric matrix
geoD = np.zeros((n, n))
# find nn-neighbours
for i in range(n):
sort = np.argsort(D[:, i])
neigh = np.setdiff1d(sort[0:self.nn + 1], i)
# find the nn+1 smallest indexes that are not i
for j in range(len(neigh)):
t = neigh[j]
geoD[i, t] = D[i, t]
geoD[t, i] = D[t, i]
D = utils.dijkstra(geoD)
# for disconnected vertices (distance is Inf)
# set their dist = max_dist(graph)
# to encourage they are far away from each other
D[np.isinf(D)] = D[~np.isinf(D)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.compress(X)
# Solve for the minimizer
z, f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def find_and_draw_path(self):
if self.is_bi_dir:
self.build_bi_rrt()
else:
self.build_rrt()
shortest_path = utils.dijkstra(self.adj_matrix, self.start, self.goal)
if shortest_path is None:
print("Path not found")
return
self.draw_shortest_path(shortest_path)
plt.show()
return
def shortest(source, destination, city_data, routes):
"""Given a source and destination, find the shortest path."""
if source not in city_data.keys() or destination not in city_data.keys():
raise KeyError('Both source and destination must be in the database.')
path, distance = utils.dijkstra(source, destination, city_data, routes)
cost = get_cost(path, city_data, routes)
time = get_time(path, city_data, routes)
codes = [ path[0][0] ]
codes.extend([ route[1] for route in path ])
route = ' -> '.join(codes)
return route, distance, time, cost
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X,X)
D = np.sqrt(D)
assert np.allclose(D,D.T)
# TODO: Convert these Euclidean distances into geodesic distances
D_args= np.argsort(D)
D_indx = np.argsort(D_args)
for i in range(n):
for j in range(n):
if D_indx[i,j] <= self.nn:
D_indx[j,i] = D_indx[i,j]
adj = np.zeros((n,n))
for i in range(n):
for j in range(n):
if D_indx[i,j] <= self.nn:
adj[i,j] = 1
if i == j:
adj[i,j] = 0
assert np.allclose(adj,adj.T)
for i in range(n):
for j in range(n):
D[i,j] = utils.dijkstra(adj,i,j)
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
D[np.isinf(D)] = D[~np.isinf(D)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.transform(X)
# Solve for the minimizer
z,f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
# TODO: Convert these Euclidean distances into geodesic distances
# find the neighbours of each point (just re-order in distance)
# initialize GD (0 means no edge)
GD = np.zeros([n, n])
for one_point in range(n):
sorted_indices = np.argsort(D[one_point])
knn_indices = sorted_indices[0:self.nn + 1]
# fill in the geodesic distances
for neighbour in knn_indices:
GD[one_point, neighbour] = D[one_point, neighbour]
GD[neighbour, one_point] = D[neighbour, one_point]
# compute edge weights
# edge weights are just distance and already stored in GD
# compute weighted shortest path via Dijkstra
D = utils.dijkstra(GD)
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
D[np.isinf(D)] = D[~np.isinf(D)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.transform(X)
# Solve for the minimizer
z, f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
np.fill_diagonal(D, np.inf)
########
#"finding the neighbor at each point"
G = np.matrix(np.ones((n, n)) * 0)
for i in range(n):
neighbours = np.argsort(D[:, i])
#want only the k nearest
for j in neighbours[1:self.nn + 1]:
G[i, j] = D[i, j]
G[j, i] = D[j, i]
#weighted shortest path between points (dijksta's)
D = np.zeros((n, n))
for i in range(n):
for j in range(i + 1, n):
D[i, j] = utils.dijkstra(G, i, j)
########
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
D[np.isinf(D)] = D[~np.isinf(D)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.compress(X)
# Solve for the minimizer
z, f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def four_way_path_sum(matrix):
'''
problem 83
'''
dimension = max(matrix)[0]
@memo
def neighbor_function(node):
neighbors = set()
a,b = node
if a+1 <= dimension: neighbors.add((a+1,b))
if a-1 >= 0: neighbors.add((a-1,b))
if b-1 >= 0: neighbors.add((a,b-1))
if b+1 <= dimension: neighbors.add((a,b+1))
return neighbors
def distance_func(first,next):
return matrix[next]
min_path = dijkstra(matrix.keys(),(0,0),(dimension,dimension),neighbor_function,distance_func)
value = sum(matrix[a,b] for a,b in min_path)
return min_path,value
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X, X)
D = np.sqrt(D)
########
# TODO #
G = np.full((n, n), np.inf)
for i in range(n):
for j in range(n):
#temp = np.list(D[i]).sort
temp = sorted(D[i])
#print(self.nn+1)
if D[i][j] in temp[:(self.nn + 1)]:
G[i][j] = D[i][j]
for i in range(n):
for j in range(n):
D[i][j] = utils.dijkstra(G, i, j)
########
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
D[np.isinf(D)] = D[~np.isinf(D)].max()
#G[np.isinf(G)] = G[~np.isinf(G)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.compress(X)
# Solve for the minimizer
z, f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def compress(self, X):
n = X.shape[0]
# Compute Euclidean distances
D = utils.euclidean_dist_squared(X,X)
D = np.sqrt(D)
# TODO: Convert these Euclidean distances into geodesic distances
G = np.zeros((n,n))
for j in range(n):
# Find indices of k + 1 nearest neighbours (including itself)
ind = np.argpartition(D[j,:], (self.nn+1))
ind = ind[:(self.nn + 1)]
print(print(j), print(ind))
for l in ind:
G[j][l] = D[j][l]
G[l][j] = D[l][j]
for j in range(n):
for l in range(j, n):
D[j][l] = utils.dijkstra(G, j, l)
D[l][j] = D[j][l]
# If two points are disconnected (distance is Inf)
# then set their distance to the maximum
# distance in the graph, to encourage them to be far apart.
D[np.isinf(D)] = D[~np.isinf(D)].max()
# Initialize low-dimensional representation with PCA
pca = PCA(self.k)
pca.fit(X)
Z = pca.transform(X)
# Solve for the minimizer
z,f = findMin(self._fun_obj_z, Z.flatten(), 500, D)
Z = z.reshape(n, self.k)
return Z
def three_way_path_sum(matrix):
'''
problem 82
'''
dimension = max(matrix)[0]
@memo
def neighbor_function(node):
neighbors = set()
a,b = node
if a+1 <= dimension: neighbors.add((a+1,b))
if b-1 >= 0: neighbors.add((a,b-1))
if b+1 <= dimension: neighbors.add((a,b+1))
return neighbors
minimum, min_path, targets = float('inf'), None, tuple((dimension,i) for i in range(dimension))
for j in range(dimension):
source = (0,j)
previous,paths = dijkstra(matrix.keys(),source,None,neighbor_function,lambda x,y:matrix[y]),set()
for a in targets:
if a not in previous or previous[a] in targets:
continue
b,s = a,[]
while previous[b]:
s.append(previous[b])
if previous[b] == source:
break
b = previous[b]
else:
continue
s.reverse()
paths.add(tuple(s+[a]))
path_sums = {path:sum(matrix[p] for p in path) for path in paths}
this_min = min(path_sums.items(),key=lambda x: x[1])
if this_min[1] < minimum:
min_path,minimum = this_min
return minimum,min_path
#!/usr/bin/env python
import sys
import utils
# argv[1] is topology file name
nodes=utils.top2obj(sys.argv[1])
cost = []
tmp = 0
keys = nodes.iterkeys()
for i in keys:
print "start : ", i
tmp = utils.dijkstra(nodes, nodes[i], None)
cost.append(tmp)
print cost
print max(cost)
for i in range(len(chord_sets)):
neighbor_near_list.update(neighbor_near(chord_sets[i]))
for i in range(len(chord_sets)):
neighbor_far_list.update(neighbor_far(chord_sets[i]))
# Create distance table and save it to file.
# Later, we can look up the table to find distance between 2 chords
w1 = 1
w2 = 3
weight_table =[]
count = 0
from datetime import datetime
for chord in named_chords_encode:
print str(datetime.now())
print count
g = Graph()
for i in range(1,4096):
g.add_vertex(i)
for i in range(1,4096):
for j in neighbor_near_list[i]:
g.add_edge(i,j,w1)
for k in neighbor_far_list[i]:
g.add_edge(i,k,w2)
dijkstra(g,g.get_vertex(chord))
for i in range(1,4096):
n = g.get_vertex(i).get_distance()
weight_table.append([chord,i,n])
count = count + 1
pickle.dump(distance_table,open(config.distance_table, "wb" ) )
def _generate_path(self):
self.log.info("Generating path...")
self.path = utils.dijkstra(self.graph, self.origin, self.destination)
self.next_node_idx = 1
self.log.info("Got path: %s", str(self.path))
coodinates = it.product(range(score_kde_fg.shape[0]), range(score_kde_fg.shape[1]))
value = len(tqdm_notebook(coodinates, total=np.prod(score_kde_fg.shape)))
for x, y in tqdm_notebook(coodinates, total=np.prod(score_kde_fg.shape)):
score_kde_fg[x, y] = np.exp(kde_fg.score(img_input[x, y, :].reshape(1, -1)))
score_kde_bg[x, y] = np.exp(kde_bg.score(img_input[x, y, :].reshape(1, -1)))
n = score_kde_fg[x, y] + score_kde_bg[x, y]
if n == 0:
n = 1
likelihood_fg[x, y] = score_kde_fg[x, y]/n
print('Finish!')
# вызываем алгоритм для двух масок
d_fg = dijkstra(xy_fg, likelihood_fg)
d_bg = dijkstra(xy_bg, 1 - likelihood_fg)
print('Finish 2 !')
margin = 1.0
mask = (d_fg < (d_bg + margin)).astype(np.uint8)
cv2.imwrite('face-points6.jpg', mask)
img_fg = img_input.copy()
img_bg = (np.array(Image.open('max.jpg'))/255.0)[:800, :800, :]
x = int(img_bg.shape[0] - img_fg.shape[0])
y = int(img_bg.shape[1]/2 - img_fg.shape[1]/2)
def _generate_path(self):
self.log.info('Generating path...')
self.path = utils.dijkstra(self.graph, self.origin, self.destination)
self.next_node_idx = 1
self.log.info('Got path: %s', str(self.path))