def _integrate(self, prev, dt, eta0, q, g0=np.eye(4), intermediate=False):
self.xi[0, :] = np.array([0, 0, 0, 0, 0, 1])
self.eta[0, :] = eta0
# integration over the body (don't need the initial point as the initial values are determined already)
# g_half = g0 # known initial condition
g_half = expm(dt / 2 * se(prev.eta[0, :]))
for i in range(self.N - 1):
# averaging over steps to get half step values
xi_half = (self.xi[i, :] + prev.xi[i, :]) / 2
eta_half = (self.eta[i, :] + prev.eta[i, :]) / 2
# implicit midpoint approximation
xi_dot = (self.xi[i, :] - prev.xi[i, :]) / dt
eta_dot = (self.eta[i, :] - prev.eta[i, :]) / dt
# external loads
A_bar = 0
B_bar = 0
# viscosity
B_bar += self.V @ xi_dot
# other loads
for load in self.loads:
A, B = load.dist_load(g_half, xi_half, eta_half, xi_dot,
eta_dot, self, q)
A_bar += A
B_bar += B
if intermediate and i == self.N - 2:
for load in self.loads:
W = load.tip_load(g_half, xi_half, eta_half, xi_dot,
eta_dot, self, q)
B_bar += W
# spatial derivatives
xi_der = np.linalg.inv(self.K - A_bar) @ (
(self.M @ eta_dot) -
(adjoint(eta_half).T @ self.M @ eta_half) +
(adjoint(xi_half).T @ self.K @ (xi_half - self.xi_ref)) +
B_bar)
eta_der = xi_dot - (adjoint(xi_half) @ eta_half)
# explicit Euler step
xi_half_next = xi_half + self.ds * xi_der
eta_half_next = eta_half + self.ds * eta_der
g_half = g_half @ expm(se(self.ds * xi_half))
# determine next step from half step value
self.xi[i + 1, :] = 2 * xi_half_next - prev.xi[i + 1, :]
self.eta[i + 1, :] = 2 * eta_half_next - prev.eta[i + 1, :]
# midpoint RKMK to step the g values
for i in range(self.N):
self.g[i, :] = flatten(
unflatten(prev.g[i, :]) @ expm(
se(dt * (self.eta[i, :] + prev.eta[i, :]) / 2)))
return g_half
def benchmark_method(method="delta"): # or MILC
for org in ["Mycobacterium_smegmatis"]:#problem_species:#validation_orgs:
print org
gbk_filename = get_genome_filename(org,'gbk')
genome = get_genome(org)
cdss = get_cdss(genome)
Method = MILC if method == "MILC" else Delta
method = Method(org)
org_exp_dict = master_exp_dict[org]
scores = []
expss = [] # list of lists; one for each replicates
for i,cds in enumerate(cdss):
if i % 100 == 0:
print i
locus_tag = head(cds.qualifiers['locus_tag'])
try:
gene = head(cds.qualifiers['gene'])
except:
gene = None
if locus_tag in org_exp_dict:
exp_scores = org_exp_dict[locus_tag]
elif gene in org_exp_dict:
exp_scores = org_exp_dict[gene]
try:
seq = str(cds.extract(genome).seq)
method_score = method.score(seq)
expss.append(exp_scores)
scores.append(method_score)
except:
print "tag failed:",locus_tag
print "recovered scores for: ",len(scores),"tags"
print "distinct scores:",len(set(scores))
if method == "MILC":
scores = [-x for x in scores] #flip scores so they correlate
#positively w/ expression
spearmans = [spearmanr(scores,exps)[0] for exps in transpose(expss)]
spearman_mean = mean(spearmans)
spearman_se = se(spearmans)
print "Correlation:",org,spearman_mean,spearman_se#,milc.num_ribosomals
def benchmark_cat():
"""Compute correlation with expression for the CDC method of Zhang
BMC Bioinformatics 2012"""
for org in validation_orgs:
print org
try:
gbk_filename = get_genome_filename(org,'gbk')
genome = get_genome(org)
cdss = get_cdss(genome)
ncid = org2nc_id(org)
cat_filename = os.path.join("index_results",ncid+"_CAT",ncid+".cat")
with open(cat_filename) as f:
lines = [line.split("\t") for line in f.readlines()[1:]]
labels,cdcs = transpose([(fields[0],fields[10]) for fields in lines])
matches = [re.search(r":(c?)(\d+)-(\d+)",label).groups() for label in labels]
locations = [((int(start),int(stop))
if c == ''
else (int(stop) - 1,int(start)))
for (c,start,stop) in matches]
cat_dict = {location:float(cdc) for location,cdc in zip(locations,cdcs)}
org_exp_dict = master_exp_dict[org]
# a dictionary of form {(start,stop):[locus tags]}
location2lt = {(feature.location.start+1,feature.location.end):
feature.qualifiers['locus_tag'][0]
for feature in genome.features
if ('locus_tag' in feature.qualifiers)}
correlates = [(cdc,org_exp_dict[location2lt[location]])
for location,cdc in cat_dict.items()
if location in location2lt
and location2lt[location] in org_exp_dict]
cdcs,exps = transpose(correlates)
rhos = [spearmanr(cdcs,map(lambda xs:xs[i],exps))[0]
for i in range(len(exps[0]))]
print "num correlates:",len(correlates)
print "Correlation:",org,mean(rhos),se(rhos)
except:
print "Failed on:",org
def _initRod(self):
# setup g, xi, and eta for the initial configuration
g = np.zeros((self.N, 12))
xi = np.zeros((self.N, 6))
eta = np.zeros((self.N, 6))
# set xi and eta
for i in range(self.N):
s = self.ds * i
xi[i, :] = self.xi_init(s)
eta[i, :] = self.eta_init(s)
# integrate G
G = np.eye(4)
g[0, :] = flatten(G)
for i in range(1, self.N):
G = G @ expm(se(self.ds * xi[i - 1, :]))
g[i, :] = flatten(G)
# set state
self.g = g
self.xi = xi
self.eta = eta
