def cycle(length, directed=False):
"""
Produces a cycle of length `length`.
Parameters
----------
length: int
Number of vertices in the cycle
directed: bool, False
Is the cycle directed?
Returns
-------
a Graph object
"""
graph = Graph()
edges = []
for i in range(length - 1):
edges.append((i, i+1))
if not directed:
edges.append((i+1, i))
edges.append((length - 1, 0))
if not directed:
edges.append((0, length - 1))
graph.add_edges(edges)
return graph
def approx_stationary(edges,
logspace=False,
iterations=None,
lim=1e-8,
initial_state=None):
"""
Approximate stationary distributions computed by by sparse matrix
multiplications. Produces correct results and uses little memory but is
likely not the most CPU efficient implementation in general (e.g. an
eigenvector calculator may be better).
Essentially raises the transition probabilities matrix to a large power.
Parameters
-----------
edges: list of tuples
Transition probabilities of the form [(source, target,
transition_probability
logspace: bool False
Carry out the calculation in logspace
iterations: int, None
Maximum number of iterations
lim: float, 1e-13
Approximate algorithm breaks when successive iterations have a
kl_divergence less than lim
initial_state: None
A distribution over the states of the process. If None, the uniform
distribution is used.
"""
g = Graph()
g.add_edges(edges)
cache = Cache(g)
gen = stationary_generator(cache,
logspace=logspace,
initial_state=initial_state)
previous_ranks = None
for i, ranks in enumerate(gen):
if i > 200:
if i % 10:
s = kl_divergence(ranks, previous_ranks)
if s < lim:
break
if iterations:
if i == iterations:
break
previous_ranks = ranks
# Reverse the enumeration
d = dict()
for m, r in enumerate(ranks):
state = cache.inv_enum[m]
d[(state)] = r
return d
def approx_stationary(edges, logspace=False, iterations=None, lim=1e-8,
initial_state=None):
"""
Approximate stationary distributions computed by by sparse matrix
multiplications. Produces correct results and uses little memory but is
likely not the most CPU efficient implementation in general (e.g. an
eigenvector calculator may be better).
Essentially raises the transition probabilities matrix to a large power.
Parameters
-----------
edges: list of tuples
Transition probabilities of the form [(source, target, transition_probability
logspace: bool False
Carry out the calculation in logspace
iterations: int, None
Maximum number of iterations
lim: float, 1e-13
Approximate algorithm breaks when successive iterations have a
kl_divergence less than lim
"""
g = Graph()
g.add_edges(edges)
cache = Cache(g)
gen = stationary_generator(cache, logspace=logspace,
initial_state=initial_state)
previous_ranks = None
for i, ranks in enumerate(gen):
if i > 200:
if i % 10:
s = kl_divergence(ranks, previous_ranks)
if s < lim:
break
if iterations:
if i == iterations:
break
previous_ranks = ranks
# Reverse the enumeration
d = dict()
for m, r in enumerate(ranks):
state = cache.inv_enum[m]
d[(state)] = r
return d
#m = [[1,2], [2,1]]
#m = [[2,1],[1,2]]
#m = [[2,2],[2,1]]
m = [[2, 2], [1, 1]]
print(N, m, mu)
graph = cycle(N)
fitness_landscape = linear_fitness_landscape(m)
incentive = replicator(fitness_landscape)
edge_dict = multivariate_graph_transitions(N,
graph,
incentive,
num_types=2,
mu=mu)
edges = [(v1, v2, t) for ((v1, v2), t) in edge_dict.items()]
g = Graph(edges)
print("There are %s configurations and %s transitions" %
(len(set([x[0] for x in edge_dict.keys()])), len(edge_dict)))
print("Local Maxima:", len(find_extrema_yen(g, extrema="max")))
print("Local Minima:", len(find_extrema_yen(g, extrema="min")))
print("Total States:", 2**N)
exit()
print("Computing stationary")
s = stationary_distribution(edges, lim=1e-8, iterations=1000)
print("Local Maxima:", len(find_extrema_stationary(s, g, extrema="max")))
print("Local Minima:", len(find_extrema_stationary(s, g, extrema="min")))
# Print stationary distribution top 20