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 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_known() == False) assert(mc.get_stationary() == 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_random_delta_distributions(2) mc.add_distributions(mkm.delta_distribution(n,n-1)) assert(mc.num_distributions() == 4) # iterations assert(mc.last_iteration_time(1) == 0) assert (mc.closest_iteration_time(0,0) == 0) assert (mc.closest_iteration_time(0,5) == 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() # assert iteration time and prev & next iteration time mc.assert_iteration([0], 99) mc.assert_iteration([0], 101) assert(mc.previous_iteration_time(0,100) == 99) assert(mc.next_iteration_time(0,100) == 101) # stationary distribution # mixing (x,tv) = mc.distribution_tv_mixing(1) mc.compute_tv_mixing() # path sampling path = mc.sample_path(1,10) assert(path[0] == 1) assert(len(path) == 10) # print mc.print_info()
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 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()
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
####################### 50-CYCLE EXAMPLE #########################
# create a graph
G = nx.cycle_graph(50)
# create a MarkovChain that is lazy simple random walk on the graph
mc = mkm.nx_graph_lazy_srw(G)
# plot the total variation mixing
mc.add_random_delta_distributions(1)
mc.plot_tv_mixing(y_tol=0.01, threshold=0.01)
####################### BIASED LINE EXAMPLE #########################
# create the transition matrix
P = mkm.line_lazy_transition_matrix(1000, p=0.51)
# create the MarkovChain with the given transition matrix
mc = mkm.MarkovChain(P)
# add some initial distributions
for i in [0,500,999]:
mc.add_distributions(mkm.delta_distribution(1000,x=i))
# plot the total variation mixing
mc.plot_tv_mixing(y_tol=0.01, threshold=1e-5)
####################### NBRW EXAMPLE #########################
import matplotlib.pyplot as plt
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()