def get_harmonically_extended_MDS(self):
Lbb = Ftree.TB_to_L_block(self.T, self.B, self.internal, self.internal)
Lba = Ftree.TB_to_L_block(self.T, self.B, self.internal, self.leaves)
L_schur = Ftree.TB_to_L_schur(self.T, self.B, self.leaves)
W, V = scipy.linalg.eigh(L_schur, eigvals=(1, 2))
V = V * np.reciprocal(np.sqrt(W))
V = self._reflected_to_reference(V)
Y = -np.dot(np.dot(np.linalg.pinv(Lbb), Lba), V)
return np.vstack([V, Y])
def get_response_content(fs):
# read the trees
T_true, B_true, N_true = FtreeIO.newick_to_TBN(fs.true_tree)
T_test, B_test, N_test = FtreeIO.newick_to_TBN(fs.test_tree)
# we are concerned about the names of the leaves of the two trees
true_leaves = Ftree.T_to_leaves(T_true)
test_leaves = Ftree.T_to_leaves(T_test)
true_leaf_to_n = dict((v, N_true[v]) for v in true_leaves)
test_leaf_to_n = dict((v, N_test[v]) for v in test_leaves)
# check that all leaves are named
if len(true_leaves) != len(true_leaf_to_n):
raise ValueError(
'all leaves in the leaf MDS tree should be named')
if len(test_leaves) != len(test_leaf_to_n):
raise ValueError(
'all leaves in the harmonic extension tree should be named')
# check that within each tree all leaves are uniquely named
if len(set(true_leaf_to_n.values())) != len(true_leaves):
raise ValueError(
'all leaf names in the leaf MDS tree should be unique')
if len(set(test_leaf_to_n.values())) != len(test_leaves):
raise ValueError(
'all leaf names in the harmonic extension tree '
'should be unique')
# check that the leaf name sets are the same
if set(true_leaf_to_n.values()) != set(test_leaf_to_n.values()):
raise ValueError(
'the two trees should have corresponding leaf names')
# invert the leaf name maps
true_n_to_leaf = dict((n, v) for v, n in true_leaf_to_n.items())
test_n_to_leaf = dict((n, v) for v, n in test_leaf_to_n.items())
# get correspondingly ordered leaf sequences
leaf_names = true_leaf_to_n.values()
true_leaves_reordered = [true_n_to_leaf[n] for n in leaf_names]
test_leaves_reordered = [test_n_to_leaf[n] for n in leaf_names]
# get the Schur complement matrix for the leaves
L_schur_true = Ftree.TB_to_L_schur(T_true, B_true, true_leaves_reordered)
# get the MDS points
w, V = scipy.linalg.eigh(L_schur_true, eigvals=(1, 2))
X = np.dot(V, np.diag(np.reciprocal(np.sqrt(w))))
# get the linear operator that defines the harmonic extension
test_internal = Ftree.T_to_internal_vertices(T_test)
L22 = Ftree.TB_to_L_block(T_test, B_test,
test_internal, test_internal)
L21 = Ftree.TB_to_L_block(T_test, B_test,
test_internal, test_leaves_reordered)
M = -np.dot(np.linalg.pinv(L22), L21)
# get the harmonic extension
X_extension = np.dot(M, X)
X_extended = np.vstack([X, X_extension])
# draw the image
v_to_index = Ftree.invseq(test_leaves_reordered + test_internal)
physical_size = (640, 480)
ext = Form.g_imageformat_to_ext[fs.imageformat]
return get_animation_frame(ext, physical_size, fs.scale,
v_to_index, T_test, X_extended)
def get_harmonically_extended_MDS(T, B, leaves, internal):
"""
Use harmonically extended 2D MDS.
"""
Lbb = Ftree.TB_to_L_block(T, B, internal, internal)
Lba = Ftree.TB_to_L_block(T, B, internal, leaves)
L_schur = Ftree.TB_to_L_schur(T, B, leaves)
W, V = scipy.linalg.eigh(L_schur, eigvals=(1, 2))
V = V * np.reciprocal(np.sqrt(W))
Y = -np.dot(np.dot(np.linalg.pinv(Lbb), Lba), V)
return np.vstack([V, Y])
def get_v_to_point(self):
"""
This uses the harmonic extension.
Also it uses the reference MDS for reflection.
@return: a map from vertex to point
"""
Lbb = Ftree.TB_to_L_block(self.T, self.B, self.internal, self.internal)
Lba = Ftree.TB_to_L_block(self.T, self.B, self.internal, self.leaves)
L_schur = Ftree.TB_to_L_schur(self.T, self.B, self.leaves)
W, V = scipy.linalg.eigh(L_schur, eigvals=(1, 2))
V = V * np.reciprocal(np.sqrt(W))
V = self._reflected_to_reference(V)
Y = -np.dot(np.dot(np.linalg.pinv(Lbb), Lba), V)
MDS = np.vstack([V, Y])
vertices = self.leaves + self.internal
return dict((vertices[i], tuple(pt)) for i, pt in enumerate(MDS))
def get_response_content(fs):
# read the ordered leaf names for the distance matrix
D_names = Util.get_stripped_lines(fs.names.splitlines())
# read the tree
T_test, B_test, N_test = FtreeIO.newick_to_TBN(fs.test_tree)
# we are concerned about the names of the leaves of the two trees
test_leaves = Ftree.T_to_leaves(T_test)
test_leaf_to_n = dict((v, N_test[v]) for v in test_leaves)
# check that all leaves are named
if len(D_names) != len(fs.D):
raise HandlingError('the number of ordered leaf names '
'should be the same as the number of rows '
'in the distance matrix')
if len(test_leaves) != len(test_leaf_to_n):
raise ValueError('all leaves in the harmonic extension tree '
'should be named')
# check that leaves are uniquely named
if len(set(D_names)) != len(D_names):
raise ValueError('all ordered leaf names in the distance matrix '
'should be unique')
# check that the leaf name sets are the same
if set(D_names) != set(test_leaf_to_n.values()):
raise ValueError('the set of leaf names on the tree '
'should be the same as '
'the set of leaf names for the distance matrix')
# invert the leaf name map
test_n_to_leaf = dict((n, v) for v, n in test_leaf_to_n.items())
# get correspondingly ordered leaf sequences
test_leaves_reordered = [test_n_to_leaf[n] for n in D_names]
# get the MDS points
X = MDS_v4(fs.D)
# get the linear operator that defines the harmonic extension
test_internal = Ftree.T_to_internal_vertices(T_test)
L22 = Ftree.TB_to_L_block(T_test, B_test, test_internal, test_internal)
L21 = Ftree.TB_to_L_block(T_test, B_test, test_internal,
test_leaves_reordered)
M = -np.dot(np.linalg.pinv(L22), L21)
# get the harmonic extension
X_extension = np.dot(M, X)
X_extended = np.vstack([X, X_extension])
# draw the image
v_to_index = Ftree.invseq(test_leaves_reordered + test_internal)
physical_size = (640, 480)
ext = Form.g_imageformat_to_ext[fs.imageformat]
return get_animation_frame(ext, physical_size, fs.scale, v_to_index,
T_test, X_extended)
def TB_to_harmonic_valuations(T, B):
"""
@param T: topology
@param B: branch lengths
@return: a number of dictionaries equal to the number of leaves
"""
leaves = Ftree.T_to_leaves(T)
internal = Ftree.T_to_internal_vertices(T)
vertices = leaves + internal
nleaves = len(leaves)
Lbb = Ftree.TB_to_L_block(T, B, internal, internal)
Lba = Ftree.TB_to_L_block(T, B, internal, leaves)
L_schur = Ftree.TB_to_L_schur(T, B, leaves)
w, v1 = scipy.linalg.eigh(L_schur)
v2 = -np.dot(np.dot(np.linalg.pinv(Lbb), Lba), v1)
V = np.vstack([v1, v2])
vs = []
for col in range(nleaves):
d = dict((v, V[row, col]) for row, v in enumerate(vertices))
vs.append(d)
return vs
def harmonically_interpolate(T, B, v_to_value):
"""
Use the harmonic extension to augment the v_to_value map.
The T and B data is not modified.
"""
vertices = Ftree.T_to_order(T)
# Define the lists of vertices for which the values are known and unknown.
known = sorted(v_to_value)
unknown = sorted(set(vertices) - set(v_to_value))
# If everything is known then we do not need to interpolate.
if not unknown:
return
# Get pieces of the Laplacian matrix.
Lbb = Ftree.TB_to_L_block(T, B, unknown, unknown)
Lba = Ftree.TB_to_L_block(T, B, unknown, known)
# Get the numpy array of known values.
v_known = np.array([v_to_value[v] for v in known])
# Get the numpy array of harmonic extensions to previously unknown values.
v_unknown = -np.dot(np.dot(np.linalg.pinv(Lbb), Lba), v_known)
# Put the interpolated values into the dictionary.
for vertex, value in zip(unknown, v_unknown):
v_to_value[vertex] = value
def get_internal_vertex_to_leaf_distn(T, B):
"""
Return a map from an internal vertex to a leaf distribution.
@return: a dictionary that maps an internal vertex to a leaf distribution
"""
leaves = Ftree.T_to_leaves(T)
internal = Ftree.T_to_internal_vertices(T)
vertices = leaves + internal
# Get pieces of the Laplacian matrix.
Lbb = Ftree.TB_to_L_block(T, B, internal, internal)
Lba = Ftree.TB_to_L_block(T, B, internal, leaves)
# Get the numpy array of harmonic extensions to previously unknown values.
interpolator = -np.dot(np.linalg.pinv(Lbb), Lba)
#print 'L interpolator:'
#print interpolator.shape
#print interpolator
d = {}
for i, v in enumerate(internal):
distn = {}
for j, leaf in enumerate(leaves):
distn[leaf] = interpolator[i, j]
d[v] = distn
return d
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()
