def test_extrema_moran_5(lim=1e-16):
"""
Test for extrema of the stationary distribution.
"""
n = 3
N = 60
mu = (3. / 2) * 1. / N
m = [[0, 1, 1], [1, 0, 1], [1, 1, 0]]
maxes = set([(20, 20, 20), (0, 0, 60), (0, 60, 0), (60, 0, 0), (30, 0, 30),
(0, 30, 30), (30, 30, 0)])
fitness_landscape = linear_fitness_landscape(m)
incentive = fermi(fitness_landscape, beta=0.1)
edges = incentive_process.multivariate_transitions(N,
incentive,
num_types=n,
mu=mu)
s = stationary_distribution(edges, lim=lim)
s2 = expected_divergence(edges, q_d=0)
flow = inflow_outflow(edges)
# These sets should all correspond
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s2), set(maxes))
assert_equal(find_local_minima(flow), set(maxes))
# The minima are pathological
assert_equal(find_local_minima(s), set([(3, 3, 54), (3, 54, 3),
(54, 3, 3)]))
assert_equal(find_local_maxima(s2),
set([(4, 52, 4), (4, 4, 52), (52, 4, 4)]))
assert_equal(find_local_maxima(flow),
set([(1, 58, 1), (1, 1, 58), (58, 1, 1)]))
def test_extrema_moran_5(lim=1e-16):
"""
Test for extrema of the stationary distribution.
"""
n = 3
N = 60
mu = (3./2) * 1./N
m = [[0, 1, 1], [1, 0, 1], [1, 1, 0]]
maxes = set([(20, 20, 20), (0, 0, 60), (0, 60, 0), (60, 0, 0),
(30, 0, 30), (0, 30, 30), (30, 30, 0)])
fitness_landscape = linear_fitness_landscape(m)
incentive = fermi(fitness_landscape, beta=0.1)
edges = incentive_process.multivariate_transitions(
N, incentive, num_types=n, mu=mu)
s = stationary_distribution(edges, lim=lim)
s2 = expected_divergence(edges, q_d=0)
flow = inflow_outflow(edges)
# These sets should all correspond
assert_equal(find_local_maxima(s), set(maxes))
assert_equal(find_local_minima(s2), set(maxes))
assert_equal(find_local_minima(flow), set(maxes))
# The minima are pathological
assert_equal(find_local_minima(s),
set([(3, 3, 54), (3, 54, 3), (54, 3, 3)]))
assert_equal(find_local_maxima(s2),
set([(4, 52, 4), (4, 4, 52), (52, 4, 4)]))
assert_equal(find_local_maxima(flow),
set([(1, 58, 1), (1, 1, 58), (58, 1, 1)]))
def full_example(N=60,
m=None,
mu=None,
pickle_filename="inv_enum.pickle",
beta=1.,
filename="enumerated_edges.csv"):
"""
Full example of exporting the stationary calculation to C++.
"""
print "Computing graph of the Markov process."
if not mu:
mu = 3. / 2 * 1. / N
if m is None:
m = [[0, 1, 1], [1, 0, 1], [1, 1, 0]]
iterations = 5 * N
num_types = len(m[0])
fitness_landscape = linear_fitness_landscape(m, normalize=True)
incentive = fermi(fitness_landscape, beta=beta)
edges_gen = incentive_process.multivariate_transitions_gen(
N, incentive, num_types=num_types, mu=mu)
print "Outputting graph to %s" % filename
inv_enum = output_enumerated_edges(N,
num_types,
edges_gen,
filename=filename)
print "Saving inverse enumeration to %s" % pickle_filename
pickle_inv_enumeration(inv_enum, pickle_filename="inv_enum.pickle")
print "Running C++ Calculation"
cwd = os.getcwd()
executable = os.path.join(cwd, "a.out")
subprocess.call([executable, filename, str(iterations)])
print "Loading stationary distribution"
s = stationary_gen(filename="enumerated_stationary.txt",
pickle_filename="inv_enum.pickle")
print "Rendering stationary to SVG"
vmax, vmin = stationary_max_min()
s = stationary_gen(filename="enumerated_stationary.txt",
pickle_filename="inv_enum.pickle")
ternary.svg_heatmap(s,
N,
"stationary.svg",
vmax=vmax,
vmin=vmin,
style='h')
def full_example(N, m, mu, beta=1., pickle_filename="inv_enum.pickle",
filename="enumerated_edges.csv"):
"""
Full example of exporting the stationary calculation to C++.
"""
print("Computing graph of the Markov process.")
if not mu:
mu = 3. / 2 * 1. / N
if m is None:
m = [[0, 1, 1], [1, 0, 1], [1, 1, 0]]
iterations = 200 * N
num_types = len(m[0])
fitness_landscape = linear_fitness_landscape(m)
incentive = fermi(fitness_landscape, beta=beta)
edges_gen = multivariate_transitions_gen(
N, incentive, num_types=num_types, mu=mu)
print("Outputting graph to %s" % filename)
inv_enum = output_enumerated_edges(
N, num_types, edges_gen, filename=filename)
print("Saving inverse enumeration to %s" % pickle_filename)
pickle_inv_enumeration(inv_enum, pickle_filename="inv_enum.pickle")
print("Running C++ Calculation")
cwd = os.getcwd()
executable = os.path.join(cwd, "a.out")
subprocess.call([executable, filename, str(iterations)])
print("Rendering stationary to SVG")
vmax, vmin = stationary_max_min()
s = list(stationary_gen(
filename="enumerated_stationary.txt",
pickle_filename="inv_enum.pickle"))
ternary.svg_heatmap(s, N, "stationary.svg", vmax=vmax, vmin=vmin, style='h')
print("Rendering stationary")
tax = render_stationary(s)
tax.ticks(axis='lbr', linewidth=1, multiple=N//3, offset=0.015)
tax.clear_matplotlib_ticks()
plt.show()
def full_example(N=60, m=None, mu=None, pickle_filename="inv_enum.pickle",
beta=1., filename="enumerated_edges.csv"):
"""
Full example of exporting the stationary calculation to C++.
"""
print "Computing graph of the Markov process."
if not mu:
mu = 3. / 2 * 1. / N
if m is None:
m = [[0,1,1],[1,0,1],[1,1,0]]
iterations = 5 * N
num_types = len(m[0])
fitness_landscape = linear_fitness_landscape(m, normalize=True)
incentive = fermi(fitness_landscape, beta=beta)
edges_gen = incentive_process.multivariate_transitions_gen(N, incentive, num_types=num_types, mu=mu)
print "Outputting graph to %s" % filename
inv_enum = output_enumerated_edges(N, num_types, edges_gen, filename=filename)
print "Saving inverse enumeration to %s" % pickle_filename
pickle_inv_enumeration(inv_enum, pickle_filename="inv_enum.pickle")
print "Running C++ Calculation"
cwd = os.getcwd()
executable = os.path.join(cwd, "a.out")
subprocess.call([executable, filename, str(iterations)])
print "Loading stationary distribution"
s = stationary_gen(filename="enumerated_stationary.txt",
pickle_filename="inv_enum.pickle")
print "Rendering stationary to SVG"
vmax, vmin = stationary_max_min()
s = stationary_gen(filename="enumerated_stationary.txt",
pickle_filename="inv_enum.pickle")
ternary.svg_heatmap(s, N, "stationary.svg", vmax=vmax, vmin=vmin, style='h')