def get_response_content(fs):
# define the requested physical size of the images (in pixels)
physical_size = (640, 480)
# get the directed edges and the branch lengths and vertex names
R, B, N = FtreeIO.newick_to_RBN(fs.tree_string)
# get the requested undirected edge
edge = get_edge(R, N, fs.branch_name)
# get the undirected tree topology
T = Ftree.R_to_T(R)
# get the leaves and the vertices of articulation
leaves = Ftree.T_to_leaves(T)
internal = Ftree.T_to_internal_vertices(T)
vertices = leaves + internal
nleaves = len(leaves)
v_to_index = Ftree.invseq(vertices)
# get the requested indices
x_index = fs.x_axis - 1
y_index = fs.y_axis - 1
if x_index >= nleaves - 1 or y_index >= nleaves - 1:
raise ValueError(
'projection indices must be smaller than the number of leaves')
# adjust the branch length
initial_length = B[edge]
t = sigmoid(fs.frame_progress)
B[edge] = (1 - t) * initial_length + t * fs.final_length
# get the points
w, v = Ftree.TB_to_harmonic_extension(T, B, leaves, internal)
X_full = np.dot(v, np.diag(np.reciprocal(np.sqrt(w))))
X = np.vstack([X_full[:, x_index], X_full[:, y_index]]).T
# draw the image
ext = Form.g_imageformat_to_ext[fs.imageformat]
return get_animation_frame(ext, physical_size, fs.scale, v_to_index, T, X,
w)
def test_leaf_distn_a(self):
# Read the example tree.
example_tree = '(a:2, (b:1, c:1, d:1, e:1)x:1)y;'
R, B, N = FtreeIO.newick_to_RBN(example_tree)
T = Ftree.R_to_T(R)
r = Ftree.R_to_root(R)
# Get the leaf distribution associated with the root.
internal_to_leaf_distn = get_internal_vertex_to_leaf_distn(T, B)
r_to_leaf_distn = internal_to_leaf_distn[r]
leaves = Ftree.T_to_leaves(T)
observed_name_weight_pairs = [
(N[v], r_to_leaf_distn[v]) for v in leaves]
# Set up the expectation for the test.
n = 5.0
expected_name_weight_pairs = []
expected_first_value = n / (3*n - 2)
expected_non_first_value = 2 / (3*n - 2)
expected_name_weight_pairs.append(('a', expected_first_value))
for name in list('bcde'):
expected_name_weight_pairs.append((name, expected_non_first_value))
# Do the comparison for testing.
expected_d = dict(expected_name_weight_pairs)
observed_d = dict(observed_name_weight_pairs)
for v in leaves:
name = N[v]
expected_value = expected_d[name]
observed_value = observed_d[name]
self.assertTrue(np.allclose(expected_value, observed_value))
def get_leaf_distn_acl(R, B):
"""
This is a possibly equivalent formulation.
It is based on Felsenstein weights.
"""
# Get the vertex order.
T = Ftree.R_to_T(R)
r = Ftree.R_to_root(R)
leaves = Ftree.T_to_leaves(T)
non_r_internal = [v for v in Ftree.T_to_internal_vertices(T) if v != r]
vertices = leaves + non_r_internal + [r]
# Get the pseudoinverse of the Laplacian.
# This is also the doubly centered covariance matrix.
L = Ftree.TB_to_L_principal(T, B, vertices)
HSH = np.linalg.pinv(L)
# Decenter the covariance matrix using the root.
# This should give the rooted covariance matrix
# which is M in the appendix of Weights for Data Related by a Tree
# by Altschul, Carroll, and Lipman, 1989.
e = np.ones_like(HSH[-1])
J = np.ones_like(HSH)
M = HSH - np.outer(e, HSH[-1]) - np.outer(HSH[-1], e) + HSH[-1,-1]*J
# Pick out the part corresponding to leaves.
nleaves = len(leaves)
S = M[:nleaves, :nleaves]
S_pinv = np.linalg.pinv(S)
# Normalized row or column sums of inverse of M gives the leaf distribution.
w = S_pinv.sum(axis=0) / S_pinv.sum()
return dict((v, w[i]) for i, v in enumerate(leaves))
def newick_to_TN(s):
"""
Everything to do with branch lengths is ignored.
@param s: newick string
@return: undirected topology, vertex name map
"""
tree = NewickIO.parse_simple(s, _IO_Tree())
return Ftree.R_to_T(tree.R), tree.v_to_name
def test_topo_b_from_newick(self):
s = '((1:1, 2:0.5)6:1, (3:0.33333333333, 4:0.5)7:1, 5:1)8;'
observed_T, observed_B = newick_to_TB(s, int)
expected_T = Ftree.R_to_T(set([
(8,7), (8,6), (8,5), (7,4), (7,3), (6,2), (6,1)]))
self.assertEqual(observed_T, expected_T)
observed_leaves = Ftree.T_to_leaves(observed_T)
expected_leaves = [1, 2, 3, 4, 5]
self.assertEqual(observed_leaves, expected_leaves)
def newick_to_TBN(s):
"""
@param s: newick string
@return: undirected topology, branch lengths, vertex name map
"""
tree = NewickIO.parse_simple(s, _IO_Tree())
T = Ftree.R_to_T(tree.R)
Ftree.TB_assert_branch_lengths(T, tree.B)
return T, tree.B, tree.v_to_name
def get_response_content(fs):
# read the tree
T, B, N = FtreeIO.newick_to_TBN(fs.tree)
leaves = Ftree.T_to_leaves(T)
internal = Ftree.T_to_internal_vertices(T)
# get the distinguished vertex of articulation
r = get_unique_vertex(N, fs.vertex)
if r not in internal:
raise ValueError(
'the distinguished vertex should have degree at least two')
# Partition the leaves with respect to the given root.
# Each set of leaves will eventually define a connected component.
R = Ftree.T_to_R_specific(T, r)
v_to_sinks = Ftree.R_to_v_to_sinks(R)
# break some edges
R_pruned = set(R)
neighbors = Ftree.T_to_v_to_neighbors(T)[r]
for adj in neighbors:
R_pruned.remove((r, adj))
T_pruned = Ftree.R_to_T(R_pruned)
# get the leaf partition
ordered_leaves = []
leaf_lists = []
for adj in neighbors:
R_subtree = Ftree.T_to_R_specific(T_pruned, adj)
C = sorted(b for a, b in R_subtree if b not in v_to_sinks)
ordered_leaves.extend(C)
leaf_lists.append(C)
# define the vertices to keep and those to remove
keepers = ordered_leaves + [r]
# get the schur complement
L_schur = Ftree.TB_to_L_schur(T, B, keepers)
# get principal submatrices of the schur complement
principal_matrices = []
accum = 0
for component_leaves in leaf_lists:
n = len(component_leaves)
M = L_schur[accum:accum+n, accum:accum+n]
principal_matrices.append(M)
accum += n
# write the report
out = StringIO()
print >> out, 'algebraic connectivity:'
print >> out, get_algebraic_connectivity(T, B, leaves)
print >> out
print >> out
print >> out, 'perron values:'
print >> out
for M, leaf_list in zip(principal_matrices, leaf_lists):
value = scipy.linalg.eigh(M, eigvals_only=True)[0]
name_list = [N[v] for v in leaf_list]
print >> out, name_list
print >> out, value
print >> out
return out.getvalue()
def main(args):
# do some validation
if args.nframes < 2:
raise ValueError('nframes should be at least 2')
# define the requested physical size of the images (in pixels)
physical_size = (args.physical_width, args.physical_height)
# get the directed edges and the branch lengths and vertex names
R, B, N = FtreeIO.newick_to_RBN(args.tree)
# get the requested undirected edge
edge = get_edge(R, N, args.branch_name)
initial_length = B[edge]
# get the undirected tree topology
T = Ftree.R_to_T(R)
# get the leaves and the vertices of articulation
leaves = Ftree.T_to_leaves(T)
internal = Ftree.T_to_internal_vertices(T)
vertices = leaves + internal
nleaves = len(leaves)
v_to_index = Ftree.invseq(vertices)
# get the requested indices
x_index = args.x_axis - 1
y_index = args.y_axis - 1
if x_index >= nleaves - 1 or y_index >= nleaves - 1:
raise ValueError(
'projection indices must be smaller than the number of leaves')
X_prev = None
# create the animation frames and write them as image files
pbar = Progress.Bar(args.nframes)
for frame_index in range(args.nframes):
linear_progress = frame_index / float(args.nframes - 1)
if args.interpolation == 'sigmoid':
t = sigmoid(linear_progress)
else:
t = linear_progress
B[edge] = (1 - t) * initial_length + t * args.final_length
w, v = Ftree.TB_to_harmonic_extension(T, B, leaves, internal)
X_full = np.dot(v, np.diag(np.reciprocal(np.sqrt(w))))
X = np.vstack([X_full[:, x_index], X_full[:, y_index]]).T
if X_prev is not None:
X = reflect_to_match(X, X_prev)
X_prev = X
image_string = get_animation_frame(args.image_format, physical_size,
args.scale, v_to_index, T, X, w)
image_filename = 'frame-%04d.%s' % (frame_index, args.image_format)
image_pathname = os.path.join(args.output_directory, image_filename)
with open(image_pathname, 'wb') as fout:
fout.write(image_string)
pbar.update(frame_index + 1)
pbar.finish()
def test_leaf_distn_schur(self):
# Read the example tree.
example_tree = LeafWeights.g_acl_tree
R, B, N = FtreeIO.newick_to_RBN(example_tree)
T = Ftree.R_to_T(R)
r = Ftree.R_to_root(R)
# Get the leaf distribution associated with the root.
leaf_distn = get_leaf_distn_schur(R, B)
leaves = Ftree.T_to_leaves(T)
observed_name_weight_pairs = [
(N[v], leaf_distn[v]) for v in leaves]
# Do the comparison for testing.
observed_name_to_weight = dict(observed_name_weight_pairs)
for name in LeafWeights.g_acl_ordered_names:
s_expected = LeafWeights.g_acl_expected_weights[name]
s_observed = '%.3f' % observed_name_to_weight[name]
self.assertEqual(s_expected, s_observed)
def get_leaf_distn_schur(R, B):
"""
This is a possibly equivalent formulation.
It is based on removing all internal vertices except the root
by Schur complement.
"""
# Get the vertex order.
# This order is different from the acl order.
T = Ftree.R_to_T(R)
r = Ftree.R_to_root(R)
leaves = Ftree.T_to_leaves(T)
non_r_internal = [v for v in Ftree.T_to_internal_vertices(T) if v != r]
vertices = leaves + [r] + non_r_internal
# Get the combinatorial Laplacian matrix
# and Schur complement out all of the non-root internal vertices.
L_schur = Ftree.TB_to_L_schur(T, B, leaves + [r])
# Get the vector of negative weights between the root and the leaves.
w_unnormalized = L_schur[-1, :-1]
# Get the normalized weight vector
w = w_unnormalized / w_unnormalized.sum()
return dict((v, w[i]) for i, v in enumerate(leaves))
def get_response_content(fs):
# read the tree
R, B, N = FtreeIO.newick_to_RBN(fs.tree)
r = Ftree.R_to_root(R)
T = Ftree.R_to_T(R)
leaves = Ftree.T_to_leaves(T)
internal_not_r = [v for v in Ftree.T_to_internal_vertices(T) if v is not r]
# define the lists of leaves induced by the root
vertex_partition = sorted(Ftree.R_to_vertex_partition(R))
vertex_lists = [sorted(p) for p in vertex_partition]
leaf_set = set(leaves)
leaf_lists = [sorted(s & leaf_set) for s in vertex_partition]
# order the list of leaves in a nice block form
leaves = [v for lst in leaf_lists for v in lst]
# remove internal vertices by Schur complementation
L_schur_rooted = Ftree.TB_to_L_schur(T, B, leaves + [r])
L_schur_full = Ftree.TB_to_L_schur(T, B, leaves)
# show the matrix
np.set_printoptions(linewidth=132)
out = StringIO()
# show the rooted schur complement
w, v = scipy.linalg.eigh(L_schur_rooted)
print >> out, 'rooted Schur complement:'
print >> out, L_schur_rooted
print >> out, 'Felsenstein weights at the root:'
print >> out, -L_schur_rooted[-1][:-1] / L_schur_rooted[-1, -1]
print >> out, 'rooted Schur complement eigendecomposition:'
print >> out, w
print >> out, v
print >> out
# show the full schur complement
w, v = scipy.linalg.eigh(L_schur_full)
print >> out, 'full Schur complement:'
print >> out, L_schur_full
print >> out, 'full Schur complement eigendecomposition:'
print >> out, w
print >> out, v
print >> out
# analyze perron components
print >> out, 'perron components:'
print >> out
start = 0
for lst in leaf_lists:
n = len(lst)
C = L_schur_rooted[start:start + n, start:start + n]
print >> out, 'C:'
print >> out, C
w_eff = np.sum(C)
b_eff = 1 / w_eff
print >> out, 'effective conductance:'
print >> out, w_eff
print >> out, 'effective branch length (or resistance or variance):'
print >> out, b_eff
S = np.linalg.pinv(C)
print >> out, 'C^-1 (rooted covariance-like):'
print >> out, S
w, v = scipy.linalg.eigh(S)
print >> out, 'rooted covariance-like eigendecomposition:'
print >> out, w
print >> out, v
print >> out, 'perron value:'
print >> out, w[-1]
print >> out, 'reciprocal of perron value:'
print >> out, 1 / w[-1]
print >> out
start += n
print >> out
# analyze subtrees
print >> out, 'subtree Laplacian analysis:'
print >> out
start = 0
for lst in vertex_lists:
n = len(lst)
C = Ftree.TB_to_L_schur(T, B, lst + [r])
w, v = scipy.linalg.eigh(C)
print >> out, 'subtree Laplacian:'
print >> out, C
print >> out, 'eigendecomposition:'
print >> out, w
print >> out, v
print >> out
start += n
# analyze subtrees
print >> out, 'full Schur complement subtree analysis:'
print >> out
start = 0
for lst in leaf_lists:
n = len(lst)
C = Ftree.TB_to_L_schur(T, B, lst + [r])
w, v = scipy.linalg.eigh(C)
print >> out, 'full Schur complement in subtree:'
print >> out, C
print >> out, 'eigendecomposition:'
print >> out, w
print >> out, v
print >> out
start += n
return out.getvalue()
def set_root(self, v):
"""
This is slow, probably as a result of the design.
"""
self.R = Ftree.T_to_R_specific(Ftree.R_to_T(self.R), v)
self.v_to_source = Ftree.R_to_v_to_source(self.R)
def get_response_content(fs):
nseconds_limit = 5.0
R_true, B_true = FtreeIO.newick_to_RB(fs.true_tree, int)
R_test = FtreeIO.newick_to_R(fs.test_tree, int)
# get the unrooted tree topology
T_true = Ftree.R_to_T(R_true)
T_test = Ftree.R_to_T(R_test)
# check the trees for vertex compatibility
if set(Ftree.T_to_order(T_true)) != set(Ftree.T_to_order(T_test)):
raise ValueError('vertex sets are not equal')
if set(Ftree.T_to_leaves(T_true)) != set(Ftree.T_to_leaves(T_test)):
raise ValueError('leaf vertex sets are not equal')
if set(Ftree.T_to_internal_vertices(T_true)) != set(
Ftree.T_to_internal_vertices(T_test)):
raise ValueError('internal vertex sets are not equal')
# get the 2D MDS for the true tree
leaves = Ftree.T_to_leaves(T_true)
internal = Ftree.T_to_internal_vertices(T_true)
vertices = leaves + internal
L_schur = Ftree.TB_to_L_schur(T_true, B_true, leaves)
w_all, Vp_all = scipy.linalg.eigh(L_schur)
w, Vp = w_all[1:3], Vp_all[:, 1:3]
# make the constant matrix for Frobenius norm comparison
C = np.zeros((len(vertices), 2))
C[:len(leaves)] = w * Vp
# keep doing iterations until we run out of time
mymax = 256
t_initial = time.time()
while time.time() - t_initial < nseconds_limit / 2:
mymax *= 2
f = Functor(T_test.copy(), Vp.copy(), C.copy(), w.copy())
initial_guess = np.ones(len(T_test) + 2 * len(internal))
results = scipy.optimize.fmin(f,
initial_guess,
ftol=1e-8,
xtol=1e-8,
full_output=True,
maxfun=mymax,
maxiter=mymax)
xopt, fopt, itr, funcalls, warnflag = results
# look at the values from the longest running iteration
B, Vr = f.X_to_B_Vr(xopt)
L, V = f.X_to_L_V(xopt)
Lrr = Ftree.TB_to_L_block(T_test, B, internal, internal)
Lrp = Ftree.TB_to_L_block(T_test, B, internal, leaves)
H_ext = -np.dot(np.linalg.pinv(Lrr), Lrp)
N = dict((v, str(v)) for v in vertices)
# start writing the response
out = StringIO()
print >> out, 'xopt:', xopt
print >> out, 'fopt:', fopt
print >> out, 'number of iterations:', itr
print >> out, 'number of function calls:', funcalls
print >> out, 'warning flags:', warnflag
print >> out, 'first four eigenvalues:', w_all[:4]
print >> out, 'Vr:'
print >> out, Vr
print >> out, '-Lrr^-1 Lrp Vp:'
print >> out, np.dot(H_ext, Vp)
print >> out, C
print >> out, np.dot(L, V)
print >> out, FtreeIO.RBN_to_newick(R_test, B, N)
return out.getvalue()
