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wilson2.py
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wilson2.py
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#!/usr/bin/env python3
"""
Wilson's algorithm for unweighted STs.
"""
import numpy as np
import networkx as nx
import sys
import os
home = os.getenv('HOME')
sys.path.append(home + '/workspace/networkqit')
import matplotlib.pyplot as plt
import networkqit as nq
import random
import matplotlib
class Wilson:
def __init__(self, G, q):
self.G = G
self.H = nx.DiGraph()
self.nv = G.number_of_nodes()
self.q = q
self.L = nx.laplacian_matrix(self.G).toarray()
# set edge attribute weight with weight 1
self.H.add_weighted_edges_from([(u,v,1.0) for u,v in G.edges()])
self.H.add_weighted_edges_from([(v,u,1.0) for u,v in G.edges()])
# add links from all nodes in the original graph to the root with weight q
self.root = self.nv
self.H.add_weighted_edges_from([(u,self.root, q) for u in G.nodes()])
# Choose an edge from v's adjacency list (randomly)
def random_successor(self, v):
nei = list(self.H.neighbors(v))
weight = np.array([ self.H.get_edge_data(v,u)['weight'] for u in nei], dtype=float)
weight /= weight.sum()
return np.random.choice(nei, p = weight)
def sample(self):
intree = [False] * self.H.number_of_nodes()
successor = {}
# put the additional node
F = nx.DiGraph()
self.roots = set()
root = self.nv
intree[root] = True
successor[root] = None
from random import shuffle
l = [root] + list(range(self.nv))
shuffle(l) # not necessary but nice, since the results do not depend on the order
for i in l:
u = i
while not intree[u]:
successor[u] = self.random_successor(u)
if successor[u] == self.nv: # if the last node of the trajectory is ∆ add it to the roots
self.roots.add(u)
u = successor[u]
u = i # come back to the node it started from
# remove self-loops
while not intree[u]:
intree[u] = True
#if u in successor:
u = successor[u]
# Creates the random forest
for i in range(self.nv):
if i in successor.keys():
neighbor = successor[i]
if neighbor is not None:
F.add_edge(i,neighbor)
if self.nv in self.roots:
self.roots.remove(self.root)
# remove the root node, together with all its links
F.remove_node(self.root)
# save the leaves
# self.leaves = [n for n in F.nodes() if F.degree(n)==1]
return F, list(self.roots)
def s(self):
lambdai = np.linalg.eigvalsh(self.L)
return (self.q/(self.q + lambdai)).sum()
def draw_sampling(G, T, root_nodes=None, **kwargs):
ax = kwargs.get('ax',None)
cmap = kwargs.get('cmap', matplotlib.cm.get_cmap('Set3'))
T = nx.DiGraph(T)
n_trees = nx.number_weakly_connected_components(T)
pos = kwargs.get('pos', nx.spectral_layout(G))
if root_nodes is not None:
nx.draw_networkx_nodes(G, pos=pos, nodelist=root_nodes, node_color='r',node_size=25,linew_width=1,ax=ax)
#nx.draw_networkx_labels(G, pos=pos, labels={i: i for i in range(G.number_of_nodes())})
nx.draw_networkx_nodes(G, pos=pos, node_color='k', node_size=3, lines_width=0.1,ax=ax)
nx.draw_networkx_edges(G, pos, edge_style='dashed', alpha=0.1, edge_color='k', edge_width=0.01, ax=ax)
for i, t in enumerate(nx.weakly_connected_component_subgraphs(T)):
e = nx.number_of_edges(t)
#print('|V|=%d |E|=%d' % (t.number_of_nodes(),t.number_of_edges()))
nx.draw_networkx_edges(t, pos, width=4, edge_cmap=cmap, edge_color=[cmap(float(i)/n_trees)]*e ,ax=ax, arrows=True)
#nx.draw_networkx_edges(t, pos, width=1, edge_color='k', arrows=True,ax=ax)
plt.axis('off')
def trace_estimator(G):
reps = 1
beta_range = np.logspace(-2, 2, 100)
L = nx.laplacian_matrix(G).toarray()
plt.semilogx(beta_range, [np.mean([len(Wilson(G,1/beta).sample()[1]) for _ in range(reps)]) for beta in beta_range], label='E[|R|]')
plt.semilogx(beta_range, [Wilson(G,q=1/beta).s() for beta in beta_range], label='q Tr[(qI+L)^{-1}]' )
plt.legend()
plt.grid(which='both')
plt.show()
def sampling_example(G,pos=None):
q = 0.1
W = Wilson(G, q=q)
F,roots = W.sample()
draw_sampling(G, F, roots, pos=pos)
plt.show()
def quad(x,y):
pos = {}
k = 0
for i in range(x):
for j in range(y):
pos[k] = np.array([i,j])
k = k+1
return pos
if __name__=='__main__':
G = nx.grid_2d_graph(15, 15, periodic=False)
G = nx.from_numpy_array(nx.to_numpy_array(G))
pos = quad(15,15)
#trace_estimator(G)
sampling_example(G)