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 get_tikz_lines(newick, eigenvector_index, yaw, pitch):
"""
@param eigenvector_index: 1 is Fiedler
"""
tree = Newick.parse(newick, SpatialTree.SpatialTree)
# change the node names and get the new tree string
for node in tree.preorder():
node.name = 'n' + str(id(node))
newick = NewickIO.get_newick_string(tree)
# do the layout
layout = FastDaylightLayout.StraightBranchLayout()
layout.do_layout(tree)
tree.fit((g_xy_scale, g_xy_scale))
name_to_location = dict(
(x.name, tree._layout_to_display(x.location)) for x in tree.preorder())
T, B, N = FtreeIO.newick_to_TBN(newick)
# get some vertices
leaves = Ftree.T_to_leaves(T)
internal = Ftree.T_to_internal_vertices(T)
vertices = leaves + internal
# get the locations
v_to_location = dict((v, name_to_location[N[v]]) for v in vertices)
# get the valuations
w, V = Ftree.TB_to_harmonic_extension(T, B, leaves, internal)
index_to_val = V[:, eigenvector_index - 1]
v_to_val = dict(
(vertices[i], g_z_scale * val) for i, val in enumerate(index_to_val))
# get the coordinates
v_to_xyz = get_v_to_xyz(yaw, v_to_location, v_to_val)
# add intersection vertices
add_intersection_vertices(T, B, v_to_xyz)
intersection_vertices = sorted(v for v in v_to_xyz if v not in vertices)
# get lines of the tikz file
return xyz_to_tikz_lines(T, B, pitch, v_to_xyz, leaves, internal,
intersection_vertices)
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 valuations with harmonic extensions
w, V = Ftree.TB_to_harmonic_extension(T, B, leaves, internal)
# get the Fiedler valuations with harmonic extensions
h = V[:, 0]
# check for vertices with small valuations
eps = 1e-8
if any(abs(x) < x for x in h):
raise ValueError('the tree has no clear harmonic Fiedler point')
# find the edge contining the harmonic Fiedler point
v_to_val = dict((v, h[i]) for i, v in enumerate(leaves + internal))
d_edges = [(a, b) for a, b in T if v_to_val[a] * v_to_val[b] < 0]
if len(d_edges) != 1:
raise ValueError('expected the point to fall clearly on a single edge')
d_edge = d_edges[0]
a, b = d_edge
# find the proportion along the directed edge
t = v_to_val[a] / (v_to_val[a] - v_to_val[b])
# find the distance from the new root to each endpoint vertices
u_edge = frozenset(d_edge)
d = B[u_edge]
da = t * d
db = (1 - t) * d
# create the new tree
r = max(Ftree.T_to_order(T)) + 1
N[r] = fs.root_name
T.remove(u_edge)
del B[u_edge]
ea = frozenset((r, a))
eb = frozenset((r, b))
T.add(ea)
T.add(eb)
B[ea] = da
B[eb] = db
# add a new leaf with arbitrary branch length
leaf = r + 1
N[leaf] = fs.leaf_name
u_edge = frozenset((r, leaf))
T.add(u_edge)
B[u_edge] = 1.0
# get the best branch length to cause eigenvalue multiplicity
blen = scipy.optimize.golden(get_gap, (T, B, u_edge),
full_output=False,
tol=1e-12)
B[u_edge] = blen
# return the string representation of the new tree
R = Ftree.T_to_R_specific(T, r)
return FtreeIO.RBN_to_newick(R, B, N)
def _get_v_to_point(self):
# Get the leaf vertices and the internal vertices.
leaves = Ftree.T_to_leaves(self.T)
internal = Ftree.T_to_internal_vertices(self.T)
vertices = leaves + internal
# Get the harmonic extensions of eigenvectors of schur complement.
w, v = Ftree.TB_to_harmonic_extension(self.T, self.B, leaves, internal)
x_values = -v.T[0]
y_values = -v.T[1]
z_values = v.T[2]
points = [np.array(xyz) for xyz in zip(x_values, y_values, z_values)]
# get the vertex to point map
return dict(zip(vertices, points))
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 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 valuations with harmonic extensions
w, V = Ftree.TB_to_harmonic_extension(T, B, leaves, internal)
# get the Fiedler valuations with harmonic extensions
h = V[:, 0]
# check for vertices with small valuations
eps = 1e-8
if any(abs(x) < x for x in h):
raise ValueError('the tree has no clear harmonic Fiedler point')
# find the edge contining the harmonic Fiedler point
v_to_val = dict((v, h[i]) for i, v in enumerate(leaves + internal))
d_edges = [(a, b) for a, b in T if v_to_val[a] * v_to_val[b] < 0]
if len(d_edges) != 1:
raise ValueError('expected the point to fall clearly on a single edge')
d_edge = d_edges[0]
a, b = d_edge
# find the proportion along the directed edge
t = v_to_val[a] / (v_to_val[a] - v_to_val[b])
# find the distance from the new root to each endpoint vertices
u_edge = frozenset(d_edge)
d = B[u_edge]
da = t * d
db = (1 - t) * d
# create the new tree
r = max(Ftree.T_to_order(T)) + 1
T.remove(u_edge)
del B[u_edge]
ea = frozenset((r, a))
eb = frozenset((r, b))
T.add(ea)
T.add(eb)
B[ea] = da
B[eb] = db
R = Ftree.T_to_R_specific(T, r)
# return the string representation of the new tree
return FtreeIO.RBN_to_newick(R, B, N)
