def __call__(self, X_logs):
"""
The vth entry of X corresponds to the log rate of the branch above v.
Return the quantity to be minimized (the neg log likelihood).
@param X: vector of branch rate logs
@return: negative log likelihood
"""
X = [math.exp(x) for x in X_logs]
B_subs = {}
for v_parent, v_child in self.R:
edge = frozenset([v_parent, v_child])
r = X[v_child]
t = self.B[edge]
B_subs[edge] = r * t
newick_string = FtreeIO.RBN_to_newick(self.R, B_subs, self.N_leaves)
tree = Newick.parse(newick_string, Newick.NewickTree)
# define the rate matrix object; horrible
dictionary_rate_matrix = RateMatrix.get_jukes_cantor_rate_matrix()
ordered_states = list('ACGT')
row_major_rate_matrix = MatrixUtil.dict_to_row_major(
dictionary_rate_matrix, ordered_states, ordered_states)
rate_matrix_object = RateMatrix.RateMatrix(
row_major_rate_matrix, ordered_states)
# get the log likelihood
ll = PhyLikelihood.get_log_likelihood(
tree, self.alignment, rate_matrix_object)
return -ll
def get_starting_tree_defn(R, B, N_leaves):
"""
"""
out = StringIO()
N_aug = dict((v, 'taxon_' + name) for v, name in N_leaves.items())
print >> out, '<newick id="startingTree">'
print >> out, FtreeIO.RBN_to_newick(R, B, N_aug)
print >> out, '</newick>'
return out.getvalue().rstrip()
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_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)
def get_response_content(fs):
# init the response and get the user variables
out = StringIO()
nleaves = fs.nleaves
nvertices = nleaves * 2 - 1
nbranches = nvertices - 1
nsites = fs.nsites
# sample the coalescent tree with timelike branch lengths
R, B = kingman.sample(fs.nleaves)
r = Ftree.R_to_root(R)
# get the leaf vertex names
N = dict(zip(range(nleaves), string.uppercase[:nleaves]))
N_leaves = dict(N)
# get the internal vertex names
v_to_leaves = R_to_v_to_leaves(R)
for v, leaves in sorted(v_to_leaves.items()):
if len(leaves) > 1:
N[v] = ''.join(sorted(N[leaf] for leaf in leaves))
# get vertex ages
v_to_age = kingman.RB_to_v_to_age(R, B)
# sample the rates on the branches
b_to_rate = sample_b_to_rate(R)
xycorr = get_correlation(R, b_to_rate)
# define B_subs in terms of substitutions instead of time
B_subs = dict((p, t * b_to_rate[p]) for p, t in B.items())
# sample the alignment
v_to_seq = sample_v_to_seq(R, B_subs, nsites)
# get the log likelihood; this is kind of horrible
pairs = [(N[v], ''.join(v_to_seq[v])) for v in range(nleaves)]
headers, sequences = zip(*pairs)
alignment = Fasta.create_alignment(headers, sequences)
newick_string = FtreeIO.RBN_to_newick(R, B_subs, N_leaves)
tree = Newick.parse(newick_string, Newick.NewickTree)
dictionary_rate_matrix = RateMatrix.get_jukes_cantor_rate_matrix()
ordered_states = list('ACGT')
row_major_rate_matrix = MatrixUtil.dict_to_row_major(
dictionary_rate_matrix, ordered_states, ordered_states)
rate_matrix_object = RateMatrix.RateMatrix(
row_major_rate_matrix, ordered_states)
ll = PhyLikelihood.get_log_likelihood(
tree, alignment, rate_matrix_object)
# get ll when rates are all 1.0
newick_string = FtreeIO.RBN_to_newick(R, B, N_leaves)
tree = Newick.parse(newick_string, Newick.NewickTree)
ll_unity = PhyLikelihood.get_log_likelihood(
tree, alignment, rate_matrix_object)
# get ll when rates are numerically optimized
# TODO incorporate the result into the xml file
# TODO speed up the likelihood evaluation (beagle? C module?)
#f = Opt(R, B, N_leaves, alignment)
#X_logs = [0.0] * nbranches
#result = scipy.optimize.fmin(f, X_logs, full_output=True)
#print result
#
print >> out, '<?xml version="1.0"?>'
print >> out, '<beast>'
print >> out
print >> out, '<!-- actual rate autocorrelation', xycorr, '-->'
print >> out, '<!-- actual root height', v_to_age[r], '-->'
print >> out, '<!-- actual log likelihood', ll, '-->'
print >> out, '<!-- ll if rates were unity', ll_unity, '-->'
print >> out
print >> out, '<!--'
print >> out, 'predefine the taxa as in'
print >> out, 'http://beast.bio.ed.ac.uk/Introduction_to_XML_format'
print >> out, '-->'
print >> out, get_leaf_taxon_defn(list(string.uppercase[:nleaves]))
print >> out
print >> out, '<!--'
print >> out, 'define the alignment as in'
print >> out, 'http://beast.bio.ed.ac.uk/Introduction_to_XML_format'
print >> out, '-->'
print >> out, get_alignment_defn(leaves, N, v_to_seq)
print >> out
print >> out, '<!--'
print >> out, 'specify the starting tree as in'
print >> out, 'http://beast.bio.ed.ac.uk/Tutorial_4'
print >> out, '-->'
print >> out, get_starting_tree_defn(R, B, N_leaves)
print >> out
print >> out, '<!--'
print >> out, 'connect the tree model as in'
print >> out, 'http://beast.bio.ed.ac.uk/Tutorial_4'
print >> out, '-->'
print >> out, g_tree_model_defn
print >> out
print >> out, g_uncorrelated_relaxed_clock_info
print >> out
"""
print >> out, '<!--'
print >> out, 'create a list of taxa for which to constrain the mrca as in'
print >> out, 'http://beast.bio.ed.ac.uk/Tutorial_3.1'
print >> out, '-->'
for v, leaves in sorted(v_to_leaves.items()):
if len(leaves) > 1:
print >> out, get_mrca_subset_defn(N, v, leaves)
print >> out
print >> out, '<!--'
print >> out, 'create a tmrcaStatistic that will record the height as in'
print >> out, 'http://beast.bio.ed.ac.uk/Tutorial_3.1'
print >> out, '-->'
for v, leaves in sorted(v_to_leaves.items()):
if len(leaves) > 1:
print >> out, get_mrca_stat_defn(N[v])
"""
print >> out
print >> out, g_likelihood_info
print >> out
print >> out, '<!--'
print >> out, 'run the mcmc'
print >> out, 'http://beast.bio.ed.ac.uk/Tutorial_3.1'
print >> out, '-->'
print >> out, get_mcmc_defn(v_to_leaves, v_to_age, N)
print >> out
print >> out, '</beast>'
# return the response
return out.getvalue()
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()
