def test_wright_fisher(N=20, lim=1e-10, n=2):
"""Test 2 dimensional Wright-Fisher process."""
for n in [2, 3]:
mu = (n - 1.) / n * 1. / (N + 1)
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
# Wright-Fisher
for low_memory in [True, False]:
edge_func = wright_fisher.multivariate_transitions(
N, incentive, mu=mu, num_types=n, low_memory=low_memory)
states = list(simplex_generator(N, d=n-1))
for logspace in [False, True]:
s = stationary_distribution(
edge_func, states=states, iterations=200, lim=lim,
logspace=logspace)
wf_edges = edge_func_to_edges(edge_func, states)
er = entropy_rate(wf_edges, s)
assert_greater_equal(er, 0)
# Check that the stationary distribution satistifies balance
# conditions
check_detailed_balance(wf_edges, s, places=2)
check_global_balance(wf_edges, s, places=4)
check_eigenvalue(wf_edges, s, places=2)
def test_wright_fisher(N=20, lim=1e-10, n=2):
"""Test 2 dimensional Wright-Fisher process."""
for n in [2, 3]:
mu = (n - 1.) / n * 1. / (N + 1)
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
# Wright-Fisher
for low_memory in [True, False]:
edge_func = wright_fisher.multivariate_transitions(
N, incentive, mu=mu, num_types=n, low_memory=low_memory)
states = list(simplex_generator(N, d=n - 1))
for logspace in [False, True]:
s = stationary_distribution(edge_func,
states=states,
iterations=200,
lim=lim,
logspace=logspace)
wf_edges = edge_func_to_edges(edge_func, states)
er = entropy_rate(wf_edges, s)
assert_greater_equal(er, 0)
# Check that the stationary distribution satistifies balance conditions
check_detailed_balance(wf_edges, s, places=2)
check_global_balance(wf_edges, s, places=4)
check_eigenvalue(wf_edges, s, places=2)
def test_incentive_process_k(lim=1e-14):
"""
Compare stationary distribution computations to known analytic form for
neutral landscape for the Moran process.
"""
for k in [1, 2, 10,]:
for n, N in [(2, 20), (2, 50), (3, 10), (3, 20)]:
mu = (n-1.)/n * 1./(N+1)
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
# Neutral landscape is the default
edges = incentive_process.k_fold_incentive_transitions(
N, incentive, num_types=n, mu=mu, k=k)
stationary_1 = stationary_distribution(edges, lim=lim)
# Check that the stationary distribution satisfies balance
# conditions
check_detailed_balance(edges, stationary_1)
check_global_balance(edges, stationary_1)
check_eigenvalue(edges, stationary_1)
# Also check edge_func calculation
edges = incentive_process.multivariate_transitions(
N, incentive, num_types=n, mu=mu)
states = states_from_edges(edges)
edge_func = power_transitions(edges, k)
stationary_2 = stationary_distribution(
edge_func, states=states, lim=lim)
for key in stationary_1.keys():
assert_almost_equal(
stationary_1[key], stationary_2[key], places=5)
def test_incentive_process(lim=1e-14):
"""
Compare stationary distribution computations to known analytic form for
neutral landscape for the Moran process.
"""
for n, N in [(2, 10), (2, 40), (3, 10), (3, 20), (4, 10)]:
mu = (n - 1.) / n * 1./ (N + 1)
alpha = N * mu / (n - 1. - n * mu)
# Neutral landscape is the default
edges = incentive_process.compute_edges(N, num_types=n,
incentive_func=replicator, mu=mu)
for logspace in [False, True]:
stationary_1 = incentive_process.neutral_stationary(
N, alpha, n, logspace=logspace)
for exact in [False, True]:
stationary_2 = stationary_distribution(
edges, lim=lim, logspace=logspace, exact=exact)
for key in stationary_1.keys():
assert_almost_equal(
stationary_1[key], stationary_2[key], places=4)
# Check that the stationary distribution satisfies balance conditions
check_detailed_balance(edges, stationary_1)
check_global_balance(edges, stationary_1)
check_eigenvalue(edges, stationary_1)
# Test Entropy Rate bounds
er = entropy_rate(edges, stationary_1)
h = (2. * n - 1) / n * numpy.log(n)
assert_less_equal(er, h)
assert_greater_equal(er, 0)
def test_stationary(t1=0.4, t2=0.6):
"""
Test the stationary distribution computations a simple Markov process.
"""
edges = [(0, 1, t1), (0, 0, 1. - t1), (1, 0, t2), (1, 1, 1. - t2)]
s_0 = 1. / (1. + t1 / t2)
exact_stationary = {0: s_0, 1: 1 - s_0}
for logspace in [True, False]:
s = stationary_distribution(edges, logspace=logspace)
# Check that the stationary distribution satisfies balance conditions
check_detailed_balance(edges, s)
check_global_balance(edges, s)
check_eigenvalue(edges, s)
# Check that the approximation converged to the exact distribution
for key in s.keys():
assert_almost_equal(exact_stationary[key], s[key])
def test_stationary(t1=0.4, t2=0.6):
"""
Test the stationary distribution computations a simple Markov process.
"""
edges = [(0, 1, t1), (0, 0, 1. - t1), (1, 0, t2), (1, 1, 1. - t2)]
s_0 = 1./(1. + t1 / t2)
exact_stationary = {0: s_0, 1: 1 - s_0}
for logspace in [True, False]:
s = stationary_distribution(edges, logspace=logspace)
# Check that the stationary distribution satisfies balance conditions
check_detailed_balance(edges, s)
check_global_balance(edges, s)
check_eigenvalue(edges, s)
# Check that the approximation converged to the exact distribution
for key in s.keys():
assert_almost_equal(exact_stationary[key], s[key])
def test_stationary_4():
"""
Test the stationary distribution computations a simple Markov process.
"""
edges = [(0, 0, 1. / 2), (0, 1, 1. / 2), (0, 2, 0), (0, 3, 0),
(1, 0, 1. / 6), (1, 1, 1. / 2), (1, 2, 1. / 3), (1, 3, 0),
(2, 0, 0), (2, 1, 1. / 3), (2, 2, 1. / 2), (2, 3, 1. / 6),
(3, 0, 0), (3, 1, 0), (3, 2, 1. / 2), (3, 3, 1. / 2)]
exact_stationary = {0: 1. / 8, 1: 3. / 8, 2: 3. / 8, 3: 1. / 8}
for logspace in [True, False]:
s = stationary_distribution(edges, logspace=logspace)
# Check that the stationary distribution satisfies balance conditions
check_detailed_balance(edges, s)
check_global_balance(edges, s)
check_eigenvalue(edges, s)
# Check that the approximation converged to the exact distribution
for key in s.keys():
assert_almost_equal(exact_stationary[key], s[key])
def test_stationary_4():
"""
Test the stationary distribution computations a simple Markov process.
"""
edges = [(0, 0, 1./2), (0, 1, 1./2), (0, 2, 0), (0, 3, 0),
(1, 0, 1./6), (1, 1, 1./2), (1, 2, 1./3), (1, 3, 0),
(2, 0, 0), (2, 1, 1./3), (2, 2, 1./2), (2, 3, 1./6),
(3, 0, 0), (3, 1, 0), (3, 2, 1./2), (3, 3, 1./2)]
exact_stationary = {0: 1./8, 1: 3./8, 2: 3./8, 3: 1./8}
for logspace in [True, False]:
s = stationary_distribution(edges, logspace=logspace)
# Check that the stationary distribution satisfies balance conditions
check_detailed_balance(edges, s)
check_global_balance(edges, s)
check_eigenvalue(edges, s)
# Check that the approximation converged to the exact distribution
for key in s.keys():
assert_almost_equal(exact_stationary[key], s[key])
