def uniform_motif(N,
L,
desired_ic,
epsilon=0.1,
beta=None,
ps=None,
count_sampler=None,
verbose=False):
if verbose: print "uniform motif accept reject:", N, L, desired_ic, beta
correction_per_col = 3 / (2 * log(2) * N)
desired_ic_for_beta = desired_ic + L * correction_per_col
if desired_ic_for_beta == 2 * L: # if we reach the upper limit, things break down
cols = [sample_col_from_count((0, 0, 0, N)) for _ in range(L)]
motif_p = map(lambda site: "".join(site), transpose(cols))
return motif_p
if beta is None:
beta = find_beta_for_mean_motif_ic(N, L, desired_ic_for_beta)
if verbose:
print "beta:", beta
if ps is None:
ps = count_ps_from_beta(N, beta)
if count_sampler is None:
count_sampler = inverse_cdf_sampler(enumerate_counts(N), ps)
def rQ_raw():
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
motif_p = map(lambda site: "".join(site), transpose(cols))
return motif_p
def rQ():
return sample_until(lambda M: inrange(M, desired_ic, epsilon),
rQ_raw,
1,
progress_bar=False)[0]
def dQhat(motif):
return exp(beta * motif_ic(motif))
Imin = desired_ic - epsilon
Imax = desired_ic + epsilon
log_M = -beta * Imin
if verbose: print "Imin, Imax, log_M:", Imin, Imax, log_M
def dQ(motif):
return exp(beta * motif_ic(motif) + log_M)
def AR(motif):
return 1.0 / dQ(motif)
#M = exp(-beta*(desired_ic - epsilon)) # which ic? +/- correction
trials = 0
while True:
trials += 1
motif = rQ()
r = random.random()
if r < AR(motif):
return motif
if verbose and trials % 100 == 0:
print trials, AR(motif)
def uniform_motifs(N,
L,
desired_ic,
num_motifs,
epsilon=0.1,
beta=None,
verbose=False):
if beta is None:
correction_per_col = 3 / (2 * log(2) * N)
desired_ic_for_beta = desired_ic + L * correction_per_col
beta = find_beta_for_mean_motif_ic(N,
L,
desired_ic_for_beta,
verbose=verbose)
ps = count_ps_from_beta(N, beta)
count_sampler = inverse_cdf_sampler(enumerate_counts(N), ps)
return [
uniform_motif(N,
L,
desired_ic,
epsilon=epsilon,
beta=beta,
ps=ps,
count_sampler=count_sampler,
verbose=verbose) for i in trange(num_motifs)
]
def maxent_motif(N,
L,
desired_ic,
tolerance=10**-10,
beta=None,
verbose=False,
A=4):
"""sample motif from max ent distribution with mean desired_ic"""
# first we adjust the desired ic upwards so that when motif_ic is
# called with 1st order correction, we get the desired ic.
if beta is None:
if verbose:
print "finding beta"
correction_per_col = (A - 1) / (2 * log(2) * N)
desired_ic += L * correction_per_col
beta = find_beta_for_mean_motif_ic(N,
L,
desired_ic,
tolerance=tolerance,
verbose=verbose,
A=A)
ps = count_ps_from_beta(N, beta, A=A)
count_sampler = inverse_cdf_sampler(enumerate_counts(N, A), ps)
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count, A=A) for count in counts]
return map(lambda site: "".join(site), transpose(cols))
def maxent_motifs(N, L, desired_ic, num_motifs, tolerance=10**-10, A=4, beta=None, countses=None,
entropies=None, log_cols=None, verbose=False):
### computational
if countses is None:
logger("countses", verbose)
countses = enumerate_counts(N, A, verbose=verbose)
if entropies is None:
logger("entropies", verbose)
entropies = np.array(map(entropy_from_counts, tqdm(countses)))
if log_cols is None:
iterator = tqdm(countses) if verbose else countses
logger("log_cols", verbose)
log_cols = np.array([log_counts_to_cols(counts, A=A) for counts in iterator])
if beta is None:
correction_per_col = (A-1)/(2*log(2)*N)
desired_ic += L * correction_per_col
beta = find_beta_for_mean_motif_ic(N,L,desired_ic,tolerance=tolerance,verbose=verbose, A=A,
countses=countses, entropies=entropies, log_cols=log_cols)
logger("beta: %s" % beta, verbose)
logger("computing count ps from beta", verbose)
ps = count_ps_from_beta(N,beta, A=A, verbose=verbose,
log_cols=log_cols, entropies=entropies)
count_sampler = inverse_cdf_sampler(countses, ps)
def sample():
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count, A=A) for count in counts]
return map(lambda site:"".join(site),transpose(cols))
iterator = trange if verbose else xrange
if verbose:
print "sampling"
return [sample() for _ in iterator(num_motifs)]
def uniform_motifs(N,L,desired_ic,num_motifs,epsilon=0.1,beta=None,verbose=False):
if beta is None:
correction_per_col = 3/(2*log(2)*N)
desired_ic_for_beta = desired_ic + L * correction_per_col
beta = find_beta_for_mean_motif_ic(N,L,desired_ic_for_beta,verbose=verbose)
ps = count_ps_from_beta(N,beta)
count_sampler = inverse_cdf_sampler(enumerate_counts(N),ps)
return [uniform_motif(N,L,desired_ic,epsilon=epsilon,beta=beta,
ps=ps,count_sampler=count_sampler,verbose=verbose)
for i in trange(num_motifs)]
def maxent_motifs(N,
L,
desired_ic,
num_motifs,
tolerance=10**-10,
A=4,
beta=None,
countses=None,
entropies=None,
log_cols=None,
verbose=False):
### computational
if countses is None:
logger("countses", verbose)
countses = enumerate_counts(N, A, verbose=verbose)
if entropies is None:
logger("entropies", verbose)
entropies = np.array(map(entropy_from_counts, tqdm(countses)))
if log_cols is None:
iterator = tqdm(countses) if verbose else countses
logger("log_cols", verbose)
log_cols = np.array(
[log_counts_to_cols(counts, A=A) for counts in iterator])
if beta is None:
correction_per_col = (A - 1) / (2 * log(2) * N)
desired_ic += L * correction_per_col
beta = find_beta_for_mean_motif_ic(N,
L,
desired_ic,
tolerance=tolerance,
verbose=verbose,
A=A,
countses=countses,
entropies=entropies,
log_cols=log_cols)
logger("beta: %s" % beta, verbose)
logger("computing count ps from beta", verbose)
ps = count_ps_from_beta(N,
beta,
A=A,
verbose=verbose,
log_cols=log_cols,
entropies=entropies)
count_sampler = inverse_cdf_sampler(countses, ps)
def sample():
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count, A=A) for count in counts]
return map(lambda site: "".join(site), transpose(cols))
iterator = trange if verbose else xrange
if verbose:
print "sampling"
return [sample() for _ in iterator(num_motifs)]
def maxent_motif(N,L,desired_ic,tolerance=10**-10,beta=None,verbose=False, A=4):
"""sample motif from max ent distribution with mean desired_ic"""
# first we adjust the desired ic upwards so that when motif_ic is
# called with 1st order correction, we get the desired ic.
if beta is None:
if verbose:
print "finding beta"
correction_per_col = (A-1)/(2*log(2)*N)
desired_ic += L * correction_per_col
beta = find_beta_for_mean_motif_ic(N,L,desired_ic,tolerance=tolerance,verbose=verbose, A=A)
ps = count_ps_from_beta(N, beta, A=A)
count_sampler = inverse_cdf_sampler(enumerate_counts(N, A), ps)
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count, A=A) for count in counts]
return map(lambda site:"".join(site),transpose(cols))
def uniform_motif(N,L,desired_ic,epsilon=0.1,beta=None,ps=None,count_sampler=None,verbose=False):
if verbose: print "uniform motif accept reject:",N,L,desired_ic,beta
correction_per_col = 3/(2*log(2)*N)
desired_ic_for_beta = desired_ic + L * correction_per_col
if desired_ic_for_beta == 2*L: # if we reach the upper limit, things break down
cols = [sample_col_from_count((0,0,0,N)) for _ in range(L)]
motif_p = map(lambda site:"".join(site),transpose(cols))
return motif_p
if beta is None:
beta = find_beta_for_mean_motif_ic(N,L,desired_ic_for_beta)
if verbose:
print "beta:",beta
if ps is None:
ps = count_ps_from_beta(N,beta)
if count_sampler is None:
count_sampler = inverse_cdf_sampler(enumerate_counts(N),ps)
def rQ_raw():
counts = [count_sampler() for i in range(L)]
cols = [sample_col_from_count(count) for count in counts]
motif_p = map(lambda site:"".join(site),transpose(cols))
return motif_p
def rQ():
return sample_until(lambda M:inrange(M,desired_ic,epsilon),rQ_raw,1,progress_bar=False)[0]
def dQhat(motif):
return exp(beta*motif_ic(motif))
Imin = desired_ic - epsilon
Imax = desired_ic + epsilon
log_M = -beta*Imin
if verbose: print "Imin, Imax, log_M:",Imin, Imax, log_M
def dQ(motif):
return exp(beta*motif_ic(motif) + log_M)
def AR(motif):
return 1.0/dQ(motif)
#M = exp(-beta*(desired_ic - epsilon)) # which ic? +/- correction
trials = 0
while True:
trials +=1
motif = rQ()
r = random.random()
if r < AR(motif):
return motif
if verbose and trials % 100 == 0:
print trials, AR(motif)