def get_splits(initial_distance_matrix,
split_function,
update_function,
on_label_split=None):
"""
This is the most external of the functions in this module.
Get the set of splits implied by the tree that would be reconstructed.
@param initial_distance_matrix: a distance matrix
@param split_function: takes a distance matrix and returns an index split
@param update_function: takes a distance matrix and an index subset and returns a distance matrix
@param on_label_split: notifies the caller of the label split induced by an index split
@return: a set of splits
"""
n = len(initial_distance_matrix)
# keep a stack of (label_set_per_vertex, distance_matrix) pairs
initial_state = ([set([i]) for i in range(n)], initial_distance_matrix)
stack = [initial_state]
# process the stack in a depth first manner, building the split set
label_split_set = set()
while stack:
label_sets, D = stack.pop()
# if the matrix is small then we are done
if len(D) < 4:
continue
# split the indices using the specified function
try:
index_split = split_function(D)
# convert the index split to a label split
label_split = index_split_to_label_split(index_split, label_sets)
# notify the caller if a callback is requested
if on_label_split:
on_label_split(label_split)
# add the split to the master set of label splits
label_split_set.add(label_split)
# for large matrices create the new label sets and the new conformant distance matrices
a, b = index_split
for index_selection, index_complement in ((a, b), (b, a)):
if len(index_complement) > 2:
next_label_sets = SchurAlgebra.vmerge(
label_sets, index_selection)
next_D = update_function(D, index_selection)
next_state = (next_label_sets, next_D)
stack.append(next_state)
except DegenerateSplitException, e:
# we cannot recover from a degenerate split unless there are more than four indices
if len(D) <= 4:
continue
# with more than four indices we can fall back to partial splits
index_set = set([e.index])
# get the next label sets
next_label_sets = SchurAlgebra.vdelete(label_sets, index_set)
# get the next conformant distance matrix by schur complementing out the offending index
L = Euclid.edm_to_laplacian(D)
L_small = SchurAlgebra.mschur(L, index_set)
next_D = Euclid.laplacian_to_edm(L_small)
next_state = (next_label_sets, next_D)
stack.append(next_state)
def get_splits(initial_distance_matrix, split_function, update_function, on_label_split=None):
"""
This is the most external of the functions in this module.
Get the set of splits implied by the tree that would be reconstructed.
@param initial_distance_matrix: a distance matrix
@param split_function: takes a distance matrix and returns an index split
@param update_function: takes a distance matrix and an index subset and returns a distance matrix
@param on_label_split: notifies the caller of the label split induced by an index split
@return: a set of splits
"""
n = len(initial_distance_matrix)
# keep a stack of (label_set_per_vertex, distance_matrix) pairs
initial_state = ([set([i]) for i in range(n)], initial_distance_matrix)
stack = [initial_state]
# process the stack in a depth first manner, building the split set
label_split_set = set()
while stack:
label_sets, D = stack.pop()
# if the matrix is small then we are done
if len(D) < 4:
continue
# split the indices using the specified function
try:
index_split = split_function(D)
# convert the index split to a label split
label_split = index_split_to_label_split(index_split, label_sets)
# notify the caller if a callback is requested
if on_label_split:
on_label_split(label_split)
# add the split to the master set of label splits
label_split_set.add(label_split)
# for large matrices create the new label sets and the new conformant distance matrices
a, b = index_split
for index_selection, index_complement in ((a, b), (b, a)):
if len(index_complement) > 2:
next_label_sets = SchurAlgebra.vmerge(label_sets, index_selection)
next_D = update_function(D, index_selection)
next_state = (next_label_sets, next_D)
stack.append(next_state)
except DegenerateSplitException, e:
# we cannot recover from a degenerate split unless there are more than four indices
if len(D) <= 4:
continue
# with more than four indices we can fall back to partial splits
index_set = set([e.index])
# get the next label sets
next_label_sets = SchurAlgebra.vdelete(label_sets, index_set)
# get the next conformant distance matrix by schur complementing out the offending index
L = Euclid.edm_to_laplacian(D)
L_small = SchurAlgebra.mschur(L, index_set)
next_D = Euclid.laplacian_to_edm(L_small)
next_state = (next_label_sets, next_D)
stack.append(next_state)
def get_subtree_messages(D, eigensplit, ordered_tip_names):
"""
@param D: the matrix of pairwise distances among tips of the tree
@param eigensplit: the split induced by the fiedler vector
@param ordered_tip_names: names of the tips of the tree conformant to v and D
@return: a multi-line string
"""
out = StringIO()
n = len(D)
ordered_label_sets = [set([i]) for i in range(n)]
all_labels = set(range(n))
for i, child in enumerate(eigensplit):
complement = all_labels - child
D_child = MatrixUtil.get_principal_submatrix(D, list(sorted(child)))
child_label_sets = SchurAlgebra.vdelete(ordered_label_sets, complement)
v_child = BuildTreeTopology.edm_to_fiedler(D_child)
print >> out, 'the Fiedler split of Schur complements of subtree', i + 1
for label_set, value in zip(child_label_sets, v_child):
s = label_set_to_string(label_set, ordered_tip_names)
print >> out, s, ':', value
print >> out
return out.getvalue().strip()
def get_subtree_messages(D, eigensplit, ordered_tip_names):
"""
@param D: the matrix of pairwise distances among tips of the tree
@param eigensplit: the split induced by the fiedler vector
@param ordered_tip_names: names of the tips of the tree conformant to v and D
@return: a multi-line string
"""
out = StringIO()
n = len(D)
ordered_label_sets = [set([i]) for i in range(n)]
all_labels = set(range(n))
for i, child in enumerate(eigensplit):
complement = all_labels - child
D_child = MatrixUtil.get_principal_submatrix(D, list(sorted(child)))
child_label_sets = SchurAlgebra.vdelete(ordered_label_sets, complement)
v_child = BuildTreeTopology.edm_to_fiedler(D_child)
print >> out, 'the Fiedler split of Schur complements of subtree', i+1
for label_set, value in zip(child_label_sets, v_child):
s = label_set_to_string(label_set, ordered_tip_names)
print >> out, s, ':', value
print >> out
return out.getvalue().strip()
