def test_extrema_wf(lim=1e-10):
"""
For small mu, the Wright-Fisher process is minimal in the center.
Test that this happens.
"""
for n, N, mins in [(2, 40, [(20, 20)]), (3, 30, [(10, 10, 10)])]:
mu = 1. / N**3
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edge_func = wright_fisher.multivariate_transitions(N,
incentive,
mu=mu,
num_types=n)
states = list(simplex_generator(N, d=n - 1))
s = stationary_distribution(edge_func,
states=states,
iterations=4 * N,
lim=lim)
s2 = expected_divergence(edge_func, states=states, q_d=0)
assert_equal(find_local_minima(s), set(mins))
er = entropy_rate(edge_func, s, states=states)
assert_greater_equal(er, 0)
def compute_entropy_rate(N=30,
n=2,
m=None,
incentive_func=None,
beta=1.,
mu=None,
exact=False,
lim=1e-13,
logspace=False):
if not m:
m = np.ones((n, n))
if not incentive_func:
incentive_func = incentives.fermi
if not mu:
# mu = (n-1.)/n * 1./(N+1)
mu = 1. / N
fitness_landscape = incentives.linear_fitness_landscape(m)
incentive = incentive_func(fitness_landscape, beta=beta, q=1)
edges = incentive_process.multivariate_transitions(N,
incentive,
num_types=n,
mu=mu)
s = stationary.stationary_distribution(edges,
exact=exact,
lim=lim,
logspace=logspace)
e = stationary.entropy_rate(edges, s)
return e, s
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(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 compute_entropy_rate(N=30, n=2, m=None, incentive_func=None, beta=1.,
mu=None, exact=False, lim=1e-13, logspace=False):
if not m:
m = np.ones((n, n))
if not incentive_func:
incentive_func = incentives.fermi
if not mu:
# mu = (n-1.)/n * 1./(N+1)
mu = 1. / N
fitness_landscape = incentives.linear_fitness_landscape(m)
incentive = incentive_func(fitness_landscape, beta=beta, q=1)
edges = incentive_process.multivariate_transitions(
N, incentive, num_types=n, mu=mu)
s = stationary.stationary_distribution(edges, exact=exact, lim=lim,
logspace=logspace)
e = stationary.entropy_rate(edges, s)
return e, s
def test_extrema_wf(lim=1e-10):
"""
For small mu, the Wright-Fisher process is minimal in the center.
Test that this happens.
"""
for n, N, mins in [(2, 40, [(20, 20)]), (3, 30, [(10, 10, 10)])]:
mu = 1. / N ** 3
m = numpy.ones((n, n)) # neutral landscape
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edge_func = wright_fisher.multivariate_transitions(
N, incentive, mu=mu, num_types=n)
states = list(simplex_generator(N, d=n-1))
s = stationary_distribution(
edge_func, states=states, iterations=4*N, lim=lim)
assert_equal(find_local_minima(s), set(mins))
er = entropy_rate(edge_func, s, states=states)
assert_greater_equal(er, 0)
