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)