def add_random_delta_distributions(self, k=1):
""" Convenience method that adds random delta distribution
to the Markov chain.
k: Number of distributions to add. Defaults to 1.
"""
self.add_distributions(mkm.random_delta_distributions(self.n, k))
def add_random_delta_distributions(self,k=1): """ Convenience method that adds random delta distribution to the Markov chain. k: Number of distributions to add. Defaults to 1. """ self.add_distributions(mkm.random_delta_distributions(self.n, k))
def nx_graph_analyze_nbrw(G): # pragma: no cover
import networkx as nx
import matplotlib.pyplot as plt
mc = mkm.nx_graph_nbrw(G)
mc.add_distributions(mkm.random_delta_distributions(mc.get_n(), 5))
mc.compute_tv_mixing()
plt.figure()
for i in range(mc.num_distributions()):
(x, tv) = mc.distribution_tv_mixing(i)
plt.plot(x, tv)
plt.xlabel("t")
plt.ylabel("Distance to stationary distribution in total variation")
plt.show()
def nx_graph_analyze_nbrw(G): # pragma: no cover
import networkx as nx
import matplotlib.pyplot as plt
mc = mkm.nx_graph_nbrw(G)
mc.add_distributions(mkm.random_delta_distributions(mc.get_n(),5))
mc.compute_tv_mixing()
plt.figure()
for i in range(mc.num_distributions()):
(x,tv) = mc.distribution_tv_mixing(i)
plt.plot(x, tv)
plt.xlabel("t")
plt.ylabel("Distance to stationary distribution in total variation")
plt.show()
def test_markov_chain():
# initialization and initial state (take n>=10000 to challenge the numerics)
n = 100
mc = MarkovChain(mkm.line_lazy_transition_matrix(n))
assert (mc.get_n() == n)
assert (mc.stationary_distribution_known() == False)
assert (mc.get_stationary_distribution() == None)
assert (mc.num_distributions() == 0)
# distributions
mc.add_distributions(mkm.delta_distribution(n, 0))
assert (mc.get_distribution(0) == mkm.delta_distribution(n, 0)).all()
mc.add_distributions(mkm.random_delta_distributions(n, 2))
mc.add_distributions(mkm.delta_distribution(n, n - 1))
assert (mc.num_distributions() == 4)
# iterations
assert (mc.last_iteration_time(1) == 0)
# iterate
mc.iterate_distributions(
[0], 2) # this one will determine the stationary distribution
assert (mc.last_iteration_time(0) == 2)
assert (mc.next_iteration_time(0, 1) == 2)
mc.iterate_distributions([0, 1, 3], 5)
mc.iterate_distributions_to_stationarity([0, 2])
mc.iterate_all_distributions_to_stationarity()
# stationary distribution
# mixing
(x, tv) = mc.distribution_tv_mixing(1)
mc.compute_tv_mixing()
# print some stuff
mc.print_info()
def test_markov_chain(): # initialization and initial state (take n>=10000 to challenge the numerics) n = 100 mc = MarkovChain(mkm.line_lazy_transition_matrix(n)) assert(mc.get_n() == n) assert(mc.stationary_distribution_known() == False) assert(mc.get_stationary_distribution() == None) assert(mc.num_distributions() == 0) # distributions mc.add_distributions(mkm.delta_distribution(n,0)) assert (mc.get_distribution(0) == mkm.delta_distribution(n,0)).all() mc.add_distributions(mkm.random_delta_distributions(n,2)) mc.add_distributions(mkm.delta_distribution(n,n-1)) assert(mc.num_distributions() == 4) # iterations assert(mc.last_iteration_time(1) == 0) # iterate mc.iterate_distributions([0],2) # this one will determine the stationary distribution assert(mc.last_iteration_time(0) == 2) assert(mc.next_iteration_time(0,1) == 2) mc.iterate_distributions([0,1,3],5) mc.iterate_distributions_to_stationarity([0,2]) mc.iterate_all_distributions_to_stationarity() # stationary distribution # mixing (x,tv) = mc.distribution_tv_mixing(1) mc.compute_tv_mixing() # print some stuff mc.print_info()
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 SRW on the graph from the adjacency matrix
P = mkm.graph_srw_transition_matrix(A)
# Markov chain with the transition marix
mc = mkm.MarkovChain(P)
# stationary distribution of SRW on a graph is deg(x)/2*|E|
mc.set_stationary_distribution(mkm.graph_srw_stationary_distribution(A))
# add a random starting position to the Markov chain
mc.add_distributions(mkm.random_delta_distributions(mc.get_n(),1))
# determine the mixing in total variation
mc.compute_tv_mixing()
# plot the mixing
(x,tv) = mc.distribution_tv_mixing(0)
plt.plot(x, tv)
plt.xlabel("t")
plt.ylabel("Distance to stationary distribution in total variation")
plt.show()
G_3_regular = nx.read_sparse6('3_regular.s6')
def test_iteration(): import numpy, time, random N = 10000 k = 10000 P = mkm.line_lazy_transition_matrix(N) P = P.transpose() P = P.tocsr() # single distribution x = mkm.delta_distribution(N,0) start = time.time() for i in xrange(k): x = P.dot(x) end = time.time() print "Python loop:" print end - start print x x = mkm.delta_distribution(N,0) start = time.time() x = mkm.matrix_vector_iteration_local(P,x,k) end = time.time() print "Python local iteration:" print end - start print x x = mkm.delta_distribution(N,0) start = time.time() x = mkm.matrix_vector_iteration_by_processes(P,x,k) end = time.time() print "Python iterating (multiple processes):" print end - start print x P = P.transpose() x = mkm.delta_distribution(N,0) start = time.time() x = mkm.iterate_distributions(P,x,k) end = time.time() print "Generic Python iteration:" print end - start print x P = P.transpose() # multiple distributions k = 10000 nd = 10 random.seed(0) x = mkm.random_delta_distributions(N,nd).transpose() start = time.time() x = mkm.matrix_vector_iteration_local(P,x,k) end = time.time() print "Python local iteration:" print end - start print x random.seed(0) x = mkm.random_delta_distributions(N,nd).transpose() start = time.time() x = mkm.matrix_vector_iteration_by_processes(P,x,k) end = time.time() print "Python iterating (multiple processes):" print end - start print x random.seed(0) P = P.transpose() x = mkm.random_delta_distributions(N,nd) start = time.time() x = mkm.iterate_distributions(P,x,k).transpose() end = time.time() print "Generic Python iteration:" print end - start print x P = P.transpose()
