def get_response_content(fs):
# read the query tree
query_tree = NewickIO.parse(fs.query, FelTree.NewickTree)
# read the reference tree
reference_tree = NewickIO.parse(fs.reference, FelTree.NewickTree)
# calculate the loss using the requested loss function
if fs.uniform:
loss_numerator = TreeComparison.get_split_distance(
query_tree, reference_tree)
elif fs.weighted:
loss_numerator = TreeComparison.get_weighted_split_distance(
query_tree, reference_tree)
# do the normalization if requested
if fs.normalize:
if fs.uniform:
loss_denominator = float(
TreeComparison.get_nontrivial_split_count(reference_tree))
elif fs.weighted:
loss_denominator = float(
TreeComparison.get_weighted_split_count(reference_tree))
else:
loss_denominator = 1
# return the response
if loss_denominator:
return str(loss_numerator / loss_denominator) + '\n'
else:
return 'normalization failed\n'
def get_response_content(fs):
# read the query tree
query_tree = NewickIO.parse(fs.query, FelTree.NewickTree)
# read the reference tree
reference_tree = NewickIO.parse(fs.reference, FelTree.NewickTree)
# calculate the loss using the requested loss function
if fs.uniform:
loss_numerator = TreeComparison.get_split_distance(
query_tree, reference_tree)
elif fs.weighted:
loss_numerator = TreeComparison.get_weighted_split_distance(
query_tree, reference_tree)
# do the normalization if requested
if fs.normalize:
if fs.uniform:
loss_denominator = float(
TreeComparison.get_nontrivial_split_count(reference_tree))
elif fs.weighted:
loss_denominator = float(
TreeComparison.get_weighted_split_count(reference_tree))
else:
loss_denominator = 1
# return the response
if loss_denominator:
return str(loss_numerator / loss_denominator) + '\n'
else:
return 'normalization failed\n'
def test_mito_matrix(self):
D = g_mito_matrix
n = len(D)
observed_Q = get_Q_matrix(D)
expected_Q = g_mito_matrix_q
# assert that the diagonal elements of the observed Q matrix are exactly zero
for i, row in enumerate(observed_Q):
self.assertEqual(row[i], 0)
# assert that the observed Q matrix is approximately equal to the expected Q matrix
abs_tol = .001
for i in range(n):
for j in range(n):
abs_delta = abs(observed_Q[i][j] - expected_Q[i][j])
self.failUnless(abs_delta < abs_tol)
# use neighbor joining to reconstruct the tree
observed_tree = make_tree(D, g_mito_states)
# load the expected tree
expected_tree = NewickIO.parse(g_mito_tree_string, FelTree.NewickTree)
# for the observed and expected trees calculate the induced partitions and corresponding branch lengths
observed_partitions_and_lengths = TreeComparison.get_partitions_and_branch_lengths(
observed_tree)
expected_partitions_and_lengths = TreeComparison.get_partitions_and_branch_lengths(
expected_tree)
# the number of partitions should be the same
self.assertEqual(len(observed_partitions_and_lengths),
len(expected_partitions_and_lengths))
# the partitions should be the same
observed_partitions = set(
[part for part, length in observed_partitions_and_lengths])
expected_partitions = set(
[part for part, length in expected_partitions_and_lengths])
observed_only = observed_partitions - expected_partitions
expected_only = expected_partitions - observed_partitions
lines = [
'observed partitions include: ' + str(observed_only),
'expected partitions include: ' + str(expected_only)
]
self.assertEqual(observed_partitions, expected_partitions,
'\n'.join(lines))
# corresponding partitions should have the same lengths
observed_part_to_length = dict(observed_partitions_and_lengths)
expected_part_to_length = dict(expected_partitions_and_lengths)
lines = []
for part in observed_partitions:
observed_length = observed_part_to_length[part]
expected_length = expected_part_to_length[part]
abs_tol = .00001
abs_delta = abs(observed_length - expected_length)
if abs_delta > abs_tol:
lines.append('partition:' + str(part))
lines.append('observed branch length:' + str(observed_length))
lines.append('expected branch length:' + str(expected_length))
error_message = '\n'.join(lines)
self.failIf(error_message, error_message)
def __init__(self, tree, epsilon):
"""
@param tree: a newick tree in the felsenstein-inspired format
@param epsilon: determines whether loadings are considered negligible
"""
# clear some flags that describe events that occur during reconstruction
self.is_negligible = False
self.is_incomplete = False
self.is_conflicting = False
# define the trees
self.tree = tree
self.reconstructed_tree = None
# set the threshold for loading negligibility
self.epsilon = epsilon
# define some arbitrary ordering of tip names
self.ordered_names = [node.get_name() for node in tree.gen_tips()]
# get the distance matrix with respect to this ordering
D = tree.get_distance_matrix(self.ordered_names)
# get the Gower doubly centered matrix
G = MatrixUtil.double_centered(np.array(D))
# get the eigendecomposition of the Gower matrix
eigenvalues, eigenvector_transposes = np.linalg.eigh(G)
eigenvectors = eigenvector_transposes.T
self.sorted_eigensystem = list(
reversed(
list(
sorted((abs(w), v)
for w, v in zip(eigenvalues, eigenvectors)))))
# build the tree recursively using the sorted eigensystem
indices = set(range(len(self.ordered_names)))
try:
# try to reconstruct the tree
root = self._build_tree(indices, 0)
root.set_branch_length(None)
output_tree = Newick.NewickTree(root)
# convert the tree to the FelTree format
newick_string = NewickIO.get_newick_string(output_tree)
self.reconstructed_tree = NewickIO.parse(newick_string,
FelTree.NewickTree)
except NegligibleError:
self.is_negligible = True
except IncompleteError:
self.is_incomplete = True
else:
# compare the splits defined by the reconstructed tree
# to splits in the original tree
expected_partitions = TreeComparison.get_nontrivial_partitions(
self.tree)
observed_partitions = TreeComparison.get_nontrivial_partitions(
self.reconstructed_tree)
invalid_partitions = observed_partitions - expected_partitions
if invalid_partitions:
self.is_conflicting = True
def __init__(self, tree, epsilon):
"""
@param tree: a newick tree in the felsenstein-inspired format
@param epsilon: determines whether loadings are considered negligible
"""
# clear some flags that describe events that occur during reconstruction
self.is_negligible = False
self.is_incomplete = False
self.is_conflicting = False
# define the trees
self.tree = tree
self.reconstructed_tree = None
# set the threshold for loading negligibility
self.epsilon = epsilon
# define some arbitrary ordering of tip names
self.ordered_names = [node.get_name() for node in tree.gen_tips()]
# get the distance matrix with respect to this ordering
D = tree.get_distance_matrix(self.ordered_names)
# get the Gower doubly centered matrix
G = MatrixUtil.double_centered(np.array(D))
# get the eigendecomposition of the Gower matrix
eigenvalues, eigenvector_transposes = np.linalg.eigh(G)
eigenvectors = eigenvector_transposes.T
self.sorted_eigensystem = list(reversed(list(sorted((abs(w), v) for w, v in zip(eigenvalues, eigenvectors)))))
# build the tree recursively using the sorted eigensystem
indices = set(range(len(self.ordered_names)))
try:
# try to reconstruct the tree
root = self._build_tree(indices, 0)
root.set_branch_length(None)
output_tree = Newick.NewickTree(root)
# convert the tree to the FelTree format
newick_string = NewickIO.get_newick_string(output_tree)
self.reconstructed_tree = NewickIO.parse(
newick_string, FelTree.NewickTree)
except NegligibleError:
self.is_negligible = True
except IncompleteError:
self.is_incomplete = True
else:
# compare the splits defined by the reconstructed tree
# to splits in the original tree
expected_partitions = TreeComparison.get_nontrivial_partitions(
self.tree)
observed_partitions = TreeComparison.get_nontrivial_partitions(
self.reconstructed_tree)
invalid_partitions = observed_partitions - expected_partitions
if invalid_partitions:
self.is_conflicting = True
def run(self, distance_matrices, ordered_names):
"""
This function stores the losses for each reconstruction.
@param distance_matrices: a sequence of distance matrices
@param ordered_names: order of taxa in the distance matrix
"""
if self.start_time is not None:
msg = 'each simulation object should be run only once'
raise HandlingError(msg)
if not distance_matrices:
raise HandlingErrror('no distance matrices were provided')
tip_name_set = set(node.name for node in self.original_tree.gen_tips())
if tip_name_set != set(ordered_names):
raise HandlingError('leaf name mismatch')
self.start_time = time.time()
# Define the reference tree and its maximum cost
# under different loss functions.
reference_tree = self.original_tree
max_error_count = TreeComparison.get_nontrivial_split_count(
reference_tree)
max_loss_value = TreeComparison.get_weighted_split_count(
reference_tree)
for distance_matrix in distance_matrices:
# create the tree builder
tree_builder = NeighborhoodJoining.TreeBuilder(
distance_matrix, ordered_names, self.splitter)
# set parameters of the validating tree builder
tree_builder.set_fallback_name(self.fallback_name)
# build the tree
try:
query_tree = tree_builder.build()
except NeighborhoodJoining.NeighborhoodJoiningError as e:
raise HandlingError(e)
# Note the number and weight of partition errors
# during the reconstruction.
error_count = TreeComparison.get_split_distance(
query_tree, reference_tree)
loss_value = TreeComparison.get_weighted_split_distance(
query_tree, reference_tree)
# make sure that the summary is internally consistent
assert error_count <= max_error_count, (error_count,
max_error_count)
assert loss_value <= max_loss_value, (loss_value, max_loss_value)
# save the reconstruction characteristics to use later
self.error_counts.append(error_count)
self.loss_values.append(loss_value)
self.max_error_counts.append(max_error_count)
self.max_loss_values.append(max_loss_value)
self.stop_time = time.time()
def test_mito_matrix(self):
D = g_mito_matrix
n = len(D)
observed_Q = get_Q_matrix(D)
expected_Q = g_mito_matrix_q
# assert that the diagonal elements of the observed Q matrix are exactly zero
for i, row in enumerate(observed_Q):
self.assertEqual(row[i], 0)
# assert that the observed Q matrix is approximately equal to the expected Q matrix
abs_tol = .001
for i in range(n):
for j in range(n):
abs_delta = abs(observed_Q[i][j] - expected_Q[i][j])
self.failUnless(abs_delta < abs_tol)
# use neighbor joining to reconstruct the tree
observed_tree = make_tree(D, g_mito_states)
# load the expected tree
expected_tree = NewickIO.parse(g_mito_tree_string, FelTree.NewickTree)
# for the observed and expected trees calculate the induced partitions and corresponding branch lengths
observed_partitions_and_lengths = TreeComparison.get_partitions_and_branch_lengths(observed_tree)
expected_partitions_and_lengths = TreeComparison.get_partitions_and_branch_lengths(expected_tree)
# the number of partitions should be the same
self.assertEqual(len(observed_partitions_and_lengths), len(expected_partitions_and_lengths))
# the partitions should be the same
observed_partitions = set([part for part, length in observed_partitions_and_lengths])
expected_partitions = set([part for part, length in expected_partitions_and_lengths])
observed_only = observed_partitions - expected_partitions
expected_only = expected_partitions - observed_partitions
lines = [
'observed partitions include: ' + str(observed_only),
'expected partitions include: ' + str(expected_only)
]
self.assertEqual(observed_partitions, expected_partitions, '\n'.join(lines))
# corresponding partitions should have the same lengths
observed_part_to_length = dict(observed_partitions_and_lengths)
expected_part_to_length = dict(expected_partitions_and_lengths)
lines = []
for part in observed_partitions:
observed_length = observed_part_to_length[part]
expected_length = expected_part_to_length[part]
abs_tol = .00001
abs_delta = abs(observed_length - expected_length)
if abs_delta > abs_tol:
lines.append('partition:' + str(part))
lines.append('observed branch length:' + str(observed_length))
lines.append('expected branch length:' + str(expected_length))
error_message = '\n'.join(lines)
self.failIf(error_message, error_message)
def __call__(self, tree):
# get the partitions implied by the tree
valid_partitions = TreeComparison.get_partitions(tree)
# Get the partition implied by the Fiedler split
# of the graph derived from the tree.
tip_nodes = list(tree.gen_tips())
D = tree.get_partial_distance_matrix(
[id(node) for node in tip_nodes])
y = get_vector(D).tolist()
name_selection = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y) if elem > 0)
name_complement = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y) if elem <= 0)
name_partition = frozenset((name_selection, name_complement))
if name_partition not in valid_partitions:
msg = '\n'.join([
'invalid partition found:',
'tree:', NewickIO.get_newick_string(tree),
'invalid partition:', name_partition])
if not self.fout:
self.fout = open(self.counterexample_filename, 'wt')
print >> self.fout, msg
print msg
self.ncounterexamples += 1
# do not stop looking, even if a counterexample is found
return False
def __call__(self, tree):
# get the partitions implied by the tree
valid_partitions = TreeComparison.get_partitions(tree)
# Get the partition implied by the Fiedler split
# of the graph derived from the tree.
tip_nodes = list(tree.gen_tips())
D = tree.get_partial_distance_matrix([id(node) for node in tip_nodes])
y = get_vector(D).tolist()
name_selection = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y)
if elem > 0)
name_complement = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y)
if elem <= 0)
name_partition = frozenset((name_selection, name_complement))
if name_partition not in valid_partitions:
msg = '\n'.join([
'invalid partition found:', 'tree:',
NewickIO.get_newick_string(tree), 'invalid partition:',
name_partition
])
if not self.fout:
self.fout = open(self.counterexample_filename, 'wt')
print >> self.fout, msg
print msg
self.ncounterexamples += 1
# do not stop looking, even if a counterexample is found
return False
def get_response_content(fs):
# get the newick trees.
trees = []
for tree_string in iterutils.stripped_lines(StringIO(fs.trees)):
# parse each tree and make sure that it conforms to various requirements
tree = NewickIO.parse(tree_string, FelTree.NewickTree)
tip_names = [tip.get_name() for tip in tree.gen_tips()]
if len(tip_names) < 4:
raise HandlingError('expected at least four tips but found ' +
str(len(tip_names)))
if any(name is None for name in tip_names):
raise HandlingError('each terminal node must be labeled')
if len(set(tip_names)) != len(tip_names):
raise HandlingError('each terminal node label must be unique')
trees.append(tree)
# begin the response
out = StringIO()
# look at each tree
nerrors = 0
ncounterexamples = 0
for tree in trees:
# get the set of valid partitions implied by the tree
valid_parts = TreeComparison.get_partitions(tree)
ordered_tip_names = [tip.get_name() for tip in tree.gen_tips()]
# assert that the partition implied by the correct formula is valid
D = np.array(tree.get_distance_matrix(ordered_tip_names))
loadings = get_principal_coordinate(D)
nonneg_leaf_set = frozenset(
tip for tip, v in zip(ordered_tip_names, loadings) if v >= 0)
neg_leaf_set = frozenset(tip
for tip, v in zip(ordered_tip_names, loadings)
if v < 0)
part = frozenset([nonneg_leaf_set, neg_leaf_set])
if part not in valid_parts:
nerrors += 1
print >> out, 'error: a partition that was supposed to be valid was found to be invalid'
print >> out, 'tree:', NewickIO.get_newick_string(tree)
print >> out, 'invalid partition:', partition_to_string(part)
print >> out
# check the validity of the partition implied by the incorrect formula
Q = D * D
loadings = get_principal_coordinate(Q)
nonneg_leaf_set = frozenset(
tip for tip, v in zip(ordered_tip_names, loadings) if v >= 0)
neg_leaf_set = frozenset(tip
for tip, v in zip(ordered_tip_names, loadings)
if v < 0)
part = frozenset([nonneg_leaf_set, neg_leaf_set])
if part not in valid_parts:
ncounterexamples += 1
print >> out, 'found a counterexample!'
print >> out, 'tree:', NewickIO.get_newick_string(tree)
print >> out, 'invalid partition:', partition_to_string(part)
print >> out
print >> out, 'errors found:', nerrors
print >> out, 'counterexamples found:', ncounterexamples
# return the response
return out.getvalue()
def main():
filename = 'counterexamples.out'
fout = open(filename, 'wt')
print 'Does monotonically transforming the pairwise leaf distances affect the compatibility'
print 'of the split found using principal coordinate analysis?'
print 'I am looking through random trees for a tree that is split incompatibly'
print 'when distances are squared.'
print 'Use control-c to stop the program when you get bored.'
try:
count = 0
ncounterexamples = 0
nerrors = 0
while True:
count += 1
# get a random tree
n_base_leaves = 4
n_expected_extra_leaves = 1
expected_branch_length = 1
tree = TreeSampler.sample_tree(n_base_leaves,
n_expected_extra_leaves,
expected_branch_length)
# get the set of valid partitions implied by the tree
valid_parts = TreeComparison.get_partitions(tree)
ordered_tip_names = [tip.get_name() for tip in tree.gen_tips()]
# assert that the partition implied by the correct formula is valid
D = np.array(tree.get_distance_matrix(ordered_tip_names))
loadings = get_principal_coordinate(D)
nonneg_leaf_set = frozenset(
tip for tip, v in zip(ordered_tip_names, loadings) if v >= 0)
neg_leaf_set = frozenset(
tip for tip, v in zip(ordered_tip_names, loadings) if v < 0)
part = frozenset([nonneg_leaf_set, neg_leaf_set])
if part not in valid_parts:
nerrors += 1
print >> fout, 'error: a partition that was supposed to be valid was found to be invalid'
print >> fout, 'tree:', NewickIO.get_newick_string(tree)
print >> fout, 'invalid partition:', partition_to_string(part)
print >> fout
# check the validity of the partition implied by the incorrect formula
Q = D * D
loadings = get_principal_coordinate(Q)
nonneg_leaf_set = frozenset(
tip for tip, v in zip(ordered_tip_names, loadings) if v >= 0)
neg_leaf_set = frozenset(
tip for tip, v in zip(ordered_tip_names, loadings) if v < 0)
part = frozenset([nonneg_leaf_set, neg_leaf_set])
if part not in valid_parts:
ncounterexamples += 1
print >> fout, 'found a counterexample!'
print >> fout, 'tree:', NewickIO.get_newick_string(tree)
print >> fout, 'invalid partition:', partition_to_string(part)
print >> fout
except KeyboardInterrupt, e:
print 'trees examined:', count
print 'errors:', nerrors
print 'counterexamples:', ncounterexamples
def run(self, distance_matrices, ordered_names):
"""
This function stores the losses for each reconstruction.
@param distance_matrices: a sequence of distance matrices
@param ordered_names: order of taxa in the distance matrix
"""
if self.start_time is not None:
msg = "each simulation object should be run only once"
raise HandlingError(msg)
if not distance_matrices:
raise HandlingErrror("no distance matrices were provided")
tip_name_set = set(node.name for node in self.original_tree.gen_tips())
if tip_name_set != set(ordered_names):
raise HandlingError("leaf name mismatch")
self.start_time = time.time()
# Define the reference tree and its maximum cost
# under different loss functions.
reference_tree = self.original_tree
max_error_count = TreeComparison.get_nontrivial_split_count(reference_tree)
max_loss_value = TreeComparison.get_weighted_split_count(reference_tree)
for distance_matrix in distance_matrices:
# create the tree builder
tree_builder = NeighborhoodJoining.TreeBuilder(distance_matrix, ordered_names, self.splitter)
# set parameters of the validating tree builder
tree_builder.set_fallback_name(self.fallback_name)
# build the tree
try:
query_tree = tree_builder.build()
except NeighborhoodJoining.NeighborhoodJoiningError as e:
raise HandlingError(e)
# Note the number and weight of partition errors
# during the reconstruction.
error_count = TreeComparison.get_split_distance(query_tree, reference_tree)
loss_value = TreeComparison.get_weighted_split_distance(query_tree, reference_tree)
# make sure that the summary is internally consistent
assert error_count <= max_error_count, (error_count, max_error_count)
assert loss_value <= max_loss_value, (loss_value, max_loss_value)
# save the reconstruction characteristics to use later
self.error_counts.append(error_count)
self.loss_values.append(loss_value)
self.max_error_counts.append(max_error_count)
self.max_loss_values.append(max_loss_value)
self.stop_time = time.time()
def get_response_content(fs):
# get the newick trees.
trees = []
for tree_string in iterutils.stripped_lines(StringIO(fs.trees)):
# parse each tree and make sure that it conforms to various requirements
tree = NewickIO.parse(tree_string, FelTree.NewickTree)
tip_names = [tip.get_name() for tip in tree.gen_tips()]
if len(tip_names) < 4:
raise HandlingError('expected at least four tips but found ' + str(len(tip_names)))
if any(name is None for name in tip_names):
raise HandlingError('each terminal node must be labeled')
if len(set(tip_names)) != len(tip_names):
raise HandlingError('each terminal node label must be unique')
trees.append(tree)
# begin the response
out = StringIO()
# look at each tree
nerrors = 0
ncounterexamples = 0
for tree in trees:
# get the set of valid partitions implied by the tree
valid_parts = TreeComparison.get_partitions(tree)
ordered_tip_names = [tip.get_name() for tip in tree.gen_tips()]
# assert that the partition implied by the correct formula is valid
D = np.array(tree.get_distance_matrix(ordered_tip_names))
loadings = get_principal_coordinate(D)
nonneg_leaf_set = frozenset(tip for tip, v in zip(ordered_tip_names, loadings) if v >= 0)
neg_leaf_set = frozenset(tip for tip, v in zip(ordered_tip_names, loadings) if v < 0)
part = frozenset([nonneg_leaf_set, neg_leaf_set])
if part not in valid_parts:
nerrors += 1
print >> out, 'error: a partition that was supposed to be valid was found to be invalid'
print >> out, 'tree:', NewickIO.get_newick_string(tree)
print >> out, 'invalid partition:', partition_to_string(part)
print >> out
# check the validity of the partition implied by the incorrect formula
Q = D * D
loadings = get_principal_coordinate(Q)
nonneg_leaf_set = frozenset(tip for tip, v in zip(ordered_tip_names, loadings) if v >= 0)
neg_leaf_set = frozenset(tip for tip, v in zip(ordered_tip_names, loadings) if v < 0)
part = frozenset([nonneg_leaf_set, neg_leaf_set])
if part not in valid_parts:
ncounterexamples += 1
print >> out, 'found a counterexample!'
print >> out, 'tree:', NewickIO.get_newick_string(tree)
print >> out, 'invalid partition:', partition_to_string(part)
print >> out
print >> out, 'errors found:', nerrors
print >> out, 'counterexamples found:', ncounterexamples
# return the response
return out.getvalue()
def main():
filename = 'counterexamples.out'
fout = open(filename, 'wt')
print 'Does monotonically transforming the pairwise leaf distances affect the compatibility'
print 'of the split found using principal coordinate analysis?'
print 'I am looking through random trees for a tree that is split incompatibly'
print 'when distances are squared.'
print 'Use control-c to stop the program when you get bored.'
try:
count = 0
ncounterexamples = 0
nerrors = 0
while True:
count += 1
# get a random tree
n_base_leaves = 4
n_expected_extra_leaves = 1
expected_branch_length = 1
tree = TreeSampler.sample_tree(n_base_leaves, n_expected_extra_leaves, expected_branch_length)
# get the set of valid partitions implied by the tree
valid_parts = TreeComparison.get_partitions(tree)
ordered_tip_names = [tip.get_name() for tip in tree.gen_tips()]
# assert that the partition implied by the correct formula is valid
D = np.array(tree.get_distance_matrix(ordered_tip_names))
loadings = get_principal_coordinate(D)
nonneg_leaf_set = frozenset(tip for tip, v in zip(ordered_tip_names, loadings) if v >= 0)
neg_leaf_set = frozenset(tip for tip, v in zip(ordered_tip_names, loadings) if v < 0)
part = frozenset([nonneg_leaf_set, neg_leaf_set])
if part not in valid_parts:
nerrors += 1
print >> fout, 'error: a partition that was supposed to be valid was found to be invalid'
print >> fout, 'tree:', NewickIO.get_newick_string(tree)
print >> fout, 'invalid partition:', partition_to_string(part)
print >> fout
# check the validity of the partition implied by the incorrect formula
Q = D * D
loadings = get_principal_coordinate(Q)
nonneg_leaf_set = frozenset(tip for tip, v in zip(ordered_tip_names, loadings) if v >= 0)
neg_leaf_set = frozenset(tip for tip, v in zip(ordered_tip_names, loadings) if v < 0)
part = frozenset([nonneg_leaf_set, neg_leaf_set])
if part not in valid_parts:
ncounterexamples += 1
print >> fout, 'found a counterexample!'
print >> fout, 'tree:', NewickIO.get_newick_string(tree)
print >> fout, 'invalid partition:', partition_to_string(part)
print >> fout
except KeyboardInterrupt, e:
print 'trees examined:', count
print 'errors:', nerrors
print 'counterexamples:', ncounterexamples
def examine_mds_splits():
"""
Examine properties of the hyperplane orthogonal to the MDS axis of a hyperellipse.
The hyperellipse is the Steiner circumscribed hyperellipse that intersects
points of the embedded leaves of a tree.
Earlier results show that the hyperplane orthogonal to the principal
axis of this hyperellipse should separate the leaves in a way that is compatible
with the topology of the tree.
Here we investigate the conjecture that this same hyperplane
also splits internal vertices in a way that is compatible with the topology of the tree.
"""
count = 0
ncontrol_noneuclidean_counterexamples = 0
ncontrol_secondary_counterexamples = 0
print 'Does the principal hyperplane of the leaves always intersect the tree at exactly one point?'
print 'Press control-C to stop looking for a counterexample...'
try:
while True:
# pick a random number of taxa to use as leaves in the tree
ntaxa = random.randrange(3, 12)
# sample an xtree with exponentially distributed branch lengths
xtree = TreeSampler.sample_agglomerated_tree(ntaxa)
for branch in xtree.get_branches():
mu = 2.0
branch.length = random.expovariate(1/mu)
# convert the xtree to a FelTree so we can use the internal vertices
tree_string = xtree.get_newick_string()
tree = NewickIO.parse(tree_string, FelTree.NewickTree)
# get the full id splits of the tree, including internal nodes
id_set = set(id(node) for node in tree.preorder())
d = TreeComparison._get_branch_id_to_node_id_set(tree)
full_id_splits = set(frozenset((frozenset(x), frozenset(id_set-x))) for x in d.values())
# get ordered ids and the number of leaves
ordered_ids = get_ordered_ids(tree)
nleaves = len(list(tree.gen_tips()))
# get the projection
D_full = np.array(tree.get_full_distance_matrix(ordered_ids))
projected_points = do_projection(D_full, nleaves)
# get the split implied by the principal hyperplane of the leaves
left_ids = set(i for i, point in zip(ordered_ids, projected_points) if point[0] < 0)
right_ids = id_set - left_ids
split = frozenset((frozenset(left_ids), frozenset(right_ids)))
# if the split is not compatible with the tree then we have found a counterexample
if split not in full_id_splits:
print 'counterexample:'
print tree_string
break
# now do a control where I look at the wrong eigenvector
left_ids = set(i for i, point in zip(ordered_ids, projected_points) if point[1] < 0)
right_ids = id_set - left_ids
split = frozenset((frozenset(left_ids), frozenset(right_ids)))
if split not in full_id_splits:
ncontrol_secondary_counterexamples += 1
# now do a control that should provide the occasional counterexample
D_control = np.sqrt(D_full)
projected_points = do_projection(D_control, nleaves)
left_ids = set(i for i, point in zip(ordered_ids, projected_points) if point[0] < 0)
right_ids = id_set - left_ids
split = frozenset((frozenset(left_ids), frozenset(right_ids)))
if split not in full_id_splits:
ncontrol_noneuclidean_counterexamples += 1
# increment the count
count += 1
except KeyboardInterrupt, e:
print 'Checked', count, 'trees and found no counterexample.'
print 'Found', ncontrol_secondary_counterexamples, 'control counterexamples where I use the wrong eigenvector.'
print 'Found', ncontrol_noneuclidean_counterexamples, 'control counterexamples where I use the wrong distance matrix.'
def get_response_content(fs):
# get the newick trees.
trees = []
for tree_string in iterutils.stripped_lines(fs.trees.splitlines()):
# parse each tree and make sure that it conforms to various requirements
tree = NewickIO.parse(tree_string, FelTree.NewickTree)
tip_names = [tip.get_name() for tip in tree.gen_tips()]
if len(tip_names) < 4:
raise HandlingError('expected at least four tips '
'but found ' + str(len(tip_names)))
if any(name is None for name in tip_names):
raise HandlingError('each terminal node must be labeled')
if len(set(tip_names)) != len(tip_names):
raise HandlingError('each terminal node label must be unique')
trees.append(tree)
# create the response
out = StringIO()
same_count = 0
diff_count = 0
for tree in trees:
# make the local paragraph that will be shown if there is an event
local_out = StringIO()
has_event = False
# print the tree
print >> local_out, NewickIO.get_newick_string(tree)
# get the tip nodes and the internal nodes
tip_nodes = []
internal_nodes = []
for node in tree.preorder():
if node.is_tip():
tip_nodes.append(node)
else:
internal_nodes.append(node)
all_nodes = tip_nodes + internal_nodes
# get all tip name partitions implied by the tree topology
valid_partitions = TreeComparison.get_partitions(tree)
# get results from the augmented distance matrix
D_full = tree.get_partial_distance_matrix(
[id(node) for node in all_nodes])
y_full = get_vector(D_full).tolist()
y = y_full[:len(tip_nodes)]
name_selection = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y)
if elem > 0)
name_complement = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y)
if elem <= 0)
name_partition_a = frozenset((name_selection, name_complement))
if name_partition_a not in valid_partitions:
print >> local_out, 'augmented distance matrix split fail:',
print >> local_out, name_partition_a
has_event = True
# get results from the not-augmented distance matrix
D = tree.get_partial_distance_matrix([id(node) for node in tip_nodes])
y = get_vector(D).tolist()
name_selection = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y)
if elem > 0)
name_complement = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y)
if elem <= 0)
name_partition_b = frozenset((name_selection, name_complement))
if name_partition_b not in valid_partitions:
print >> local_out, 'not-augmented distance matrix split fail:',
print >> local_out, name_partition_b
has_event = True
# compare the name partitions
if name_partition_a == name_partition_b:
same_count += 1
else:
diff_count += 1
print >> local_out, 'this tree was split differently '
print >> local_out, 'by the different methods:'
print >> local_out, 'augmented distance matrix split:',
print >> local_out, name_partition_a
print >> local_out, 'not-augmented distance matrix split:',
print >> local_out, name_partition_b
has_event = True
# print a newline between trees
if has_event:
print >> out, local_out.getvalue()
# write the summary
print >> out, 'for this many trees the same split was found:',
print >> out, same_count
print >> out, 'for this many trees different splits were found:',
print >> out, diff_count
# write the response
return out.getvalue()
def get_response_content(fs):
# get the newick trees.
trees = []
for tree_string in iterutils.stripped_lines(fs.trees.splitlines()):
# parse each tree and make sure that it conforms to various requirements
tree = NewickIO.parse(tree_string, FelTree.NewickTree)
tip_names = [tip.get_name() for tip in tree.gen_tips()]
if len(tip_names) < 4:
raise HandlingError(
'expected at least four tips '
'but found ' + str(len(tip_names)))
if any(name is None for name in tip_names):
raise HandlingError('each terminal node must be labeled')
if len(set(tip_names)) != len(tip_names):
raise HandlingError('each terminal node label must be unique')
trees.append(tree)
# create the response
out = StringIO()
same_count = 0
diff_count = 0
for tree in trees:
# make the local paragraph that will be shown if there is an event
local_out = StringIO()
has_event = False
# print the tree
print >> local_out, NewickIO.get_newick_string(tree)
# get the tip nodes and the internal nodes
tip_nodes = []
internal_nodes = []
for node in tree.preorder():
if node.is_tip():
tip_nodes.append(node)
else:
internal_nodes.append(node)
all_nodes = tip_nodes + internal_nodes
# get all tip name partitions implied by the tree topology
valid_partitions = TreeComparison.get_partitions(tree)
# get results from the augmented distance matrix
D_full = tree.get_partial_distance_matrix(
[id(node) for node in all_nodes])
y_full = get_vector(D_full).tolist()
y = y_full[:len(tip_nodes)]
name_selection = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y) if elem > 0)
name_complement = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y) if elem <= 0)
name_partition_a = frozenset((name_selection, name_complement))
if name_partition_a not in valid_partitions:
print >> local_out, 'augmented distance matrix split fail:',
print >> local_out, name_partition_a
has_event = True
# get results from the not-augmented distance matrix
D = tree.get_partial_distance_matrix([id(node) for node in tip_nodes])
y = get_vector(D).tolist()
name_selection = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y) if elem > 0)
name_complement = frozenset(node.get_name()
for node, elem in zip(tip_nodes, y) if elem <= 0)
name_partition_b = frozenset((name_selection, name_complement))
if name_partition_b not in valid_partitions:
print >> local_out, 'not-augmented distance matrix split fail:',
print >> local_out, name_partition_b
has_event = True
# compare the name partitions
if name_partition_a == name_partition_b:
same_count += 1
else:
diff_count += 1
print >> local_out, 'this tree was split differently '
print >> local_out, 'by the different methods:'
print >> local_out, 'augmented distance matrix split:',
print >> local_out, name_partition_a
print >> local_out, 'not-augmented distance matrix split:',
print >> local_out, name_partition_b
has_event = True
# print a newline between trees
if has_event:
print >> out, local_out.getvalue()
# write the summary
print >> out, 'for this many trees the same split was found:',
print >> out, same_count
print >> out, 'for this many trees different splits were found:',
print >> out, diff_count
# write the response
return out.getvalue()
def examine_mds_splits():
"""
Examine properties of the hyperplane orthogonal to the MDS axis of a hyperellipse.
The hyperellipse is the Steiner circumscribed hyperellipse that intersects
points of the embedded leaves of a tree.
Earlier results show that the hyperplane orthogonal to the principal
axis of this hyperellipse should separate the leaves in a way that is compatible
with the topology of the tree.
Here we investigate the conjecture that this same hyperplane
also splits internal vertices in a way that is compatible with the topology of the tree.
"""
count = 0
ncontrol_noneuclidean_counterexamples = 0
ncontrol_secondary_counterexamples = 0
print 'Does the principal hyperplane of the leaves always intersect the tree at exactly one point?'
print 'Press control-C to stop looking for a counterexample...'
try:
while True:
# pick a random number of taxa to use as leaves in the tree
ntaxa = random.randrange(3, 12)
# sample an xtree with exponentially distributed branch lengths
xtree = TreeSampler.sample_agglomerated_tree(ntaxa)
for branch in xtree.get_branches():
mu = 2.0
branch.length = random.expovariate(1 / mu)
# convert the xtree to a FelTree so we can use the internal vertices
tree_string = xtree.get_newick_string()
tree = NewickIO.parse(tree_string, FelTree.NewickTree)
# get the full id splits of the tree, including internal nodes
id_set = set(id(node) for node in tree.preorder())
d = TreeComparison._get_branch_id_to_node_id_set(tree)
full_id_splits = set(
frozenset((frozenset(x), frozenset(id_set - x)))
for x in d.values())
# get ordered ids and the number of leaves
ordered_ids = get_ordered_ids(tree)
nleaves = len(list(tree.gen_tips()))
# get the projection
D_full = np.array(tree.get_full_distance_matrix(ordered_ids))
projected_points = do_projection(D_full, nleaves)
# get the split implied by the principal hyperplane of the leaves
left_ids = set(i for i, point in zip(ordered_ids, projected_points)
if point[0] < 0)
right_ids = id_set - left_ids
split = frozenset((frozenset(left_ids), frozenset(right_ids)))
# if the split is not compatible with the tree then we have found a counterexample
if split not in full_id_splits:
print 'counterexample:'
print tree_string
break
# now do a control where I look at the wrong eigenvector
left_ids = set(i for i, point in zip(ordered_ids, projected_points)
if point[1] < 0)
right_ids = id_set - left_ids
split = frozenset((frozenset(left_ids), frozenset(right_ids)))
if split not in full_id_splits:
ncontrol_secondary_counterexamples += 1
# now do a control that should provide the occasional counterexample
D_control = np.sqrt(D_full)
projected_points = do_projection(D_control, nleaves)
left_ids = set(i for i, point in zip(ordered_ids, projected_points)
if point[0] < 0)
right_ids = id_set - left_ids
split = frozenset((frozenset(left_ids), frozenset(right_ids)))
if split not in full_id_splits:
ncontrol_noneuclidean_counterexamples += 1
# increment the count
count += 1
except KeyboardInterrupt, e:
print 'Checked', count, 'trees and found no counterexample.'
print 'Found', ncontrol_secondary_counterexamples, 'control counterexamples where I use the wrong eigenvector.'
print 'Found', ncontrol_noneuclidean_counterexamples, 'control counterexamples where I use the wrong distance matrix.'
