def nx_graph_nbrw(G):
import networkx as nx
A = nx.to_scipy_sparse_matrix(G)
P = mkm.graph_nbrw_transition_matrix(A)
mc = mkm.MarkovChain(P)
mc.set_stationary_distribution(mkm.uniform_distribution(mc.get_n()))
return mc
def nx_graph_nbrw(G): import networkx as nx A = nx.to_scipy_sparse_matrix(G) P = mkm.graph_nbrw_transition_matrix(A) mc = mkm.MarkovChain(P) mc.set_stationary_distribution(mkm.uniform_distribution(mc.get_n())) return mc
def nx_graph_nbrw(G): """Returns the Markov chain for the NBRW on the graph G. """ import networkx as nx A = nx.to_scipy_sparse_matrix(G) P = mkm.graph_nbrw_transition_matrix(A) mc = mkm.MarkovChain(P) mc.set_stationary(mkm.uniform_distribution(mc.get_n())) return mc
def nx_graph_nbrw(G):
"""Returns the Markov chain for the NBRW on the graph G.
"""
import networkx as nx
A = nx.to_scipy_sparse_matrix(G)
P = mkm.graph_nbrw_transition_matrix(A)
mc = mkm.MarkovChain(P)
mc.set_stationary(mkm.uniform_distribution(mc.get_n()))
return mc
def tets_transition_matrix(): assert(mkm.is_transition_matrix(numpy.eye(1))) assert(mkm.is_transition_matrix(numpy.eye(5))) assert(mkm.is_transition_matrix(numpy.ones((1,2,3))) == False) assert(mkm.is_transition_matrix(mkm.line_lazy_transition_matrix(100, p = 0.51))) A = numpy.ones((3,3)) numpy.fill_diagonal(A,0) P = mkm.graph_nbrw_transition_matrix(ssp.dok_matrix(A)) assert(mkm.is_transition_matrix(P)) print P
def tets_transition_matrix():
assert (mkm.is_transition_matrix(numpy.eye(1)))
assert (mkm.is_transition_matrix(numpy.eye(5)))
assert (mkm.is_transition_matrix(numpy.ones((1, 2, 3))) == False)
assert (mkm.is_transition_matrix(
mkm.line_lazy_transition_matrix(100, p=0.51)))
A = numpy.ones((3, 3))
numpy.fill_diagonal(A, 0)
P = mkm.graph_nbrw_transition_matrix(ssp.dok_matrix(A))
assert (mkm.is_transition_matrix(P))
print P
def tets_transition_matrix():
assert (mkm.is_transition_matrix(numpy.eye(1)))
assert (mkm.is_transition_matrix(numpy.eye(5)))
assert (mkm.is_transition_matrix(numpy.ones((1, 2, 3))) == False)
assert (mkm.is_transition_matrix(
mkm.line_lazy_transition_matrix(100, p=0.51)))
# graph_nbrw_transition_matrix
A = numpy.ones((3, 3))
numpy.fill_diagonal(A, 0)
P = mkm.graph_nbrw_transition_matrix(A)
assert (mkm.is_transition_matrix(P))
print A
print P
# tree_nbrw_transition_matrix
A = numpy.array([[0, 1, 0, 0, 0], [1, 0, 1, 1, 0], [0, 1, 0, 0, 0],
[0, 1, 0, 0, 1], [0, 0, 0, 1, 0]])
P = mkm.tree_nbrw_transition_matrix(A, 0)
assert (mkm.is_transition_matrix(P))
print A
print P
# plot the total variation mixing
mc.plot_tv_mixing(y_tol=0.01, threshold=1e-5)
####################### NBRW EXAMPLE #########################
import matplotlib.pyplot as plt
# load a 6-regular graph with 50.000 nodes from file
G_6_regular = nx.read_sparse6('6_regular.s6')
# get the adjacency matrix
A = nx.to_scipy_sparse_matrix(G_6_regular)
# transition matrix for NBRW on the graph from the adjacency matrix
P = mkm.graph_nbrw_transition_matrix(A)
# Markov chain with the transition marix
mc = mkm.MarkovChain(P)
# the stationary distribution is uniform
mc.set_stationary(mkm.uniform_distribution(mc.get_n()))
# add a random starting position to the Markov chain
mc.add_random_delta_distributions(1)
# determine the mixing
mc.compute_tv_mixing()
# plot the mixing
(x,tv) = mc.distribution_tv_mixing(0)
