def get_child_subtrees(root, minima, T):
last = minima
p = T.nodes[minima]['p']
run = 0
subtrees = []
while (last != p):
neighbors = T[p]
#Add all the subtrees with child saddle p
for n in neighbors:
#Check that n is a child and not an ancestor of minima
if (n != last and f_(T.nodes[n]) < f_(T.nodes[p])):
stree = sub_special(T, n)
subtrees.append(stree)
#We've traced back to the root
if (p == root):
return subtrees
last = p #Update the last variable
p = T.nodes[p]['p'] #Move to the next ancestor
run += 1
return subtrees
def match_cost(U, V, mu, su, mv, sv):
#m represents the minima
#s represents the saddle
cost = max(abs(f_(U.nodes[mu]) - f_(V.nodes[mv])),
abs(f_(U.nodes[su]) - f_(V.nodes[sv])))
#print("Match cost: " + str(cost))
return cost
def compute_costs(A, root, costs=None):
if (costs == None):
costs = {}
#Base removal cost
#print("Saddle and Minima in tree: " + str(root in A and A.nodes[root]['p'] in A))
c = remove_cost(A, root, A.nodes[root]['p'])
#Account for the necessary removal of descendants
#Use memoization to speed things up
f = f_(A.nodes[root])
neighbors = A[root]
max_cost = c
for nei in neighbors:
#If nei is a child but its cost hasn't been computed...
if (f_(A.nodes[nei]) < f):
if (nei not in costs):
costs[nei] = compute_costs(A, nei, costs)[nei]
if (costs[nei] > max_cost):
max_cost = costs[nei]
costs[root] = max_cost
return costs
def calc_set_distance(anc, i1, i2, M, distances):
n = list(M.nodes)
#The two nodes corresponding to the given indices.
n1 = n[i1]
node1 = M.nodes[n1]
n2 = n[i2]
node2 = M.nodes[n2]
#Make sure node 1 doesn't have the greater function value
if(f_(node1) > f_(node2)):
n1, n2 = n2, n1
node1, node2 = node1, node2
#The ancestry lines of n1 and n2, respectively
a1 = [n1]
a1.list_append(anc[n1])
a2 = [n2]
a2.list_append(anc[n2])
#Find the common ancestor
for i in range(0, len(a2)):
if(a2[i] in a1):
f = f_(M.nodes[a2[i]])
distances[i1][i2] = f
distances[i2][i1] = f
return f
def on_level_neighbors(G, n):
f = f_(G.nodes[n])
neighbors = G[n]
on_lvl = []
for nei in neighbors:
if(f_(G.nodes[nei]) == f):
on_lvl.append(nei)
return on_lvl
def add_node(n_, G, M):
#The actual node
n = G.nodes[n_]
f = f_(n) #The node's value
#Get all the children
neighbors = G[n_]
true_children = []
for nei in neighbors:
if(f_(G.nodes[nei]) < f): #Is child
true_children.append(nei)
#No children => leaf
if(len(true_children) == 0):
M.add_node(n_) #Create a copy of n in M
n['c'] = n_ #Own inferior
M.nodes[n_]['p'] = n_ #Own superior
M.nodes[n_]['value'] = f #Function value
return
#Get the roots of the children
roots = []
min_root = find_c(true_children[0], G)
for c in true_children:
r = find_c(c, G)
if(r not in roots): #Add the root if it is new
roots.append(r)
if(f_(G.nodes[r]) < f_(G.nodes[min_root])): #Update the min root
min_root = r
#1 child => just update inferior
if(len(roots) == 1):
n['c'] = roots[0]
return
#2 or MORE children => merge
if(len(roots) >= 2):
M.add_node(n_) #Create a copy of n in M
M.nodes[n_]['p'] = n_ #Own parent
M.nodes[n_]['value'] = f #Function value
for r in roots:
p = find_p(r, M) #What we connect to
if(p != n_): #Add Edge
M.add_edge(p, n_)
M.nodes[p]['p'] = n_ #Update the superior
if(f_(M.nodes[p]) == f):
processed = {}
collapse_neighbors(M, n_, processed, merge=True)
#set c as the inferior of n and all other roots
n['c'] = min_root
for r in roots:
G.nodes[r]['c'] = min_root
def median_f(M):
nodes = listify_nodes(M)
nodes.sort(key=f_)
num = len(nodes)
n1 = nodes[math.ceil((num-1)/2)]
n2 = nodes[math.floor((num-1)/2)]
med = (f_(n1)+f_(n2))/2
return med
def find_root(T):
nodes = listify_nodes(T)
max_ = f_(nodes[0])
max_node = nodes[0]
for n in nodes:
if(f_(n) > max_):
max_ = f_(n)
max_node = n
return max_node['name']
def find_on_level(M, roots, f):
for r in roots:
p = find_p(r, M)
if(f_(M.nodes[p]) == f):
return p
return None
def mean_f(M):
nodes = listify_nodes(M)
avg = 0
for n in nodes:
avg += f_(n)
return avg / len(nodes)
def get_child_subtrees_(root, minima, T, subtrees):
last = minima
p = T.nodes[minima]['p']
st = []
while (True):
neighbors = T[p]
#Add all the subtrees with child saddle p
for n in neighbors:
#Check that n is a child and not an ancestor of minima
if (n != last and f_(T.nodes[n]) < f_(T.nodes[p])):
st.append(subtrees[n])
#We've traced back to the root
if (p == root):
return st
last = p #Update the last variable
p = T.nodes[p]['p'] #Move to the next ancestor
def descendants_(G, n, des):
if n in des:
return des[n]
#Add the current node
d = [n]
#Add all the children and their descendants
neighbors = G[n]
for nei in neighbors:
#Check for child
if (f_(G.nodes[nei]) < f_(G.nodes[n])):
#memoize!
if (nei not in des):
des[nei] = descendants_(G, nei, des)
list_append(d, des[nei])
des[n] = d
return d
def remove_cost(A, u, v):
return abs(f_(A.nodes[u]) - f_(A.nodes[v])) / 2