def all_undirected_forest_components(n):
""" Enumerate undirected forests with n nodes. """
# First get all the nondecreasing sequences that add to n
sequences = nondecreasing_sequences_adding_to(n)
# Now for each sequence get all the forests
return flatmap(functools.partial(nondet_map, all_undirected_trees), sequences)
def test_sample_string_for_tree():
t = nx.DiGraph([(0, 1), (1, 2), (2, 3)])
nomi_samples = [
immutably(sample_string_for_tree)(t, [2]) for _ in range(1000)
]
mi_samples = [ # MI 1
immutably(sample_string_for_tree)(t, [0, 1]) for _ in range(1000)
]
# When self-information is high, samples become sparser, so more samples
# are needed to get a distribution with the right MI.
mi_samples2 = [ # MI 1
immutably(sample_string_for_tree)(t, [2, 1]) for _ in range(10000)
]
mi_samples3 = [ # MI 2
immutably(sample_string_for_tree)(t, [0, 2]) for _ in range(1000)
]
assert len(set(mi_samples)) < len(set(nomi_samples))
def is_close(x, y, tol):
return abs(x - y) < tol
import rfutils.entropy
nomi_mi = rfutils.entropy.mutual_information(
Counter(rfutils.flatmap(lambda s: rfutils.sliding(s, 2),
nomi_samples)))
assert is_close(nomi_mi, 0, 0.01)
mi_mi = rfutils.entropy.mutual_information(
Counter(rfutils.flatmap(lambda s: rfutils.sliding(s, 2), mi_samples)))
assert is_close(mi_mi, 1, 0.01)
mi2_mi = rfutils.entropy.mutual_information(
Counter(rfutils.flatmap(lambda s: rfutils.sliding(s, 2), mi_samples2)))
assert is_close(mi2_mi, 1, 0.01)
mi3_mi = rfutils.entropy.mutual_information(
Counter(rfutils.flatmap(lambda s: rfutils.sliding(s, 2), mi_samples3)))
assert is_close(mi3_mi, 2, 0.1)
def bind(self, f):
return Amb(rfutils.flatmap(f, self.values))
def all_head_final_trees(n):
return filter(
tree_is_head_final,
flatmap(directed_trees, all_undirected_trees(n))
)
def all_directed_trees(n):
""" Generate all rooted directed trees with n nodes.
There are n ^ (n - 1) such trees. """
return flatmap(directed_trees, all_undirected_trees(n))
def all_directed_forest_components(n):
forests = all_undirected_forest_components(n)
return flatmap(functools.partial(nondet_map, directed_trees), forests)
def main():
langs = sorted(corpora.sud_langs)
rfutils.write_dicts(sys.stdout, rfutils.flatmap(run, langs))
