def alphagamma_from_t(t, prob):
"""
Returns a list of tuples containing each shape obtained from `Shape` sh (assuming sh has probability prob) with
their associate probability under the Alpha-Gamma model.
:param sh: `Shape` instance.
:param prob: `function` instance.
:return: `list` instance.
"""
n = count_leaves(t)
if t.is_leaf():
return [(add_leaf_to_edge(t),
lambda a, c: simplify(prob(a, c) * (1 - a) / (n - a)))]
else:
for i in range(len(t.children)):
k = count_leaves(t.children[i])
if n > 1:
p_times_m = lambda a, c, k=k: simplify(
prob(a, c) * (k - a) / (n - a))
else:
p_times_m = prob
for ti, q in alphagamma_from_t(t.children[i], p_times_m):
ts2 = list(iter_replace_tree_at(t.children, i, ti))
yield (Shape(ts2), q)
yield (add_leaf_to_edge(t),
lambda a, c: simplify(prob(a, c) * c / (n - a)))
k = len(t.children)
if k > 1:
prob2 = lambda a, c, k=k: simplify(
prob(a, c) * ((k - 1) * a - c) / (n - a))
else:
prob2 = prob
yield (add_leaf_to_node(t), prob2)
def var_depths(t):
"""
Given a `Shape` t, it returns the variance of its leaves' depths.
:param t: `Shape` instance.
:return: `float` instance.
"""
n = count_leaves(t)
return (n - 1) / n * variance(get_leaf_depths(t))
def cherry_picking(tree, k):
if tree.is_leaf():
return [tree]
elif tree == Shape.CHERRY:
return [Shape.LEAF]
else:
def go(t, i, d): # for binary eyes only
if d != k and not (t.is_leaf() or t.is_cherry()):
chs = [go(ch, i, d + 1) for ch in t.children]
if any(ch is None for ch in chs):
return None
else:
return PhyloTree(None, sorted(chs))
elif d != k and (t == PhyloTree(
None, [PhyloTree(i), PhyloTree(i + 1)]) or t == PhyloTree(
None,
[PhyloTree(i - 1), PhyloTree(i)])):
return None
elif d == k and (t == PhyloTree(
None, [PhyloTree(i), PhyloTree(i + 1)]) or t == PhyloTree(
None,
[PhyloTree(i - 1), PhyloTree(i)])):
return PhyloTree(i)
elif t == PhyloTree(i):
return None
else:
return t
n = count_leaves(tree)
phyl = shape_to_phylotree(tree, gen=int)
ts = []
for i in range(n):
t = go(phyl, i, 1)
if t:
ts.append(phylotree_to_shape(t))
return unique(sorted(ts))
def normalized_sackin_index(tree):
n = count_leaves(tree)
return sackin_index(tree) / (sackin_index(max_sackin(n)[0]) -
sackin_index(binary_max_balanced(n)))
def normalized_binary_colless_index(tree):
n = count_leaves(tree)
return binary_colless_index(tree) / (binary_colless_index(
max_colless(n)[0]) - binary_colless_index(binary_max_balanced(n)))
def normalized_quartet_index(tree):
n = count_leaves(tree)
return quartet_index(tree) / quartet_index(max_quartet(n)[0])
def normalized_binary_quartet_index(tree):
n = count_leaves(tree)
return binary_quartet_index(tree) / binary_quartet_index(
max_binary_quartet(n)[0])
def normalized_cophenetic_index(tree):
n = count_leaves(tree)
return cophenetic_index(tree) / (cophenetic_index(max_cophenetic(n)[0]) -
cophenetic_index(min_cophenetic(n)[0]))
def normalized_binary_qcolless_index(tree):
n = count_leaves(tree)
return binary_qcolless_index(tree) / (binary_qcolless_index(
max_qcolless(n)[0]) - binary_qcolless_index(min_qcolless(n)[0]))