def find_mean_field_approximation(ks,q,ps=None):
eps = eps_from_ks(ks)
if ps is None:
ps = occupancies_ref(ks,q)
mu_min = -10
mu_max = 10
mu_steps = 1000
mus = interpolate(mu_min,mu_max,mu_steps)
coeffs = map(lambda mu:polyfit(ps,probs(eps,mu),1)[0],
mus)
max_coeff_idx = argmax(coeffs)
# find mu corresponding to best fit. Cutoff at peak, since curve
# has two intersections with y = 1.
mu_idx = argmin(map(lambda coeff:(1-coeff)**2,coeffs[:max_coeff_idx]))
best_mu = mus[mu_idx]
qs = probs(eps,best_mu)
print "best_mu:",best_mu
print "mean copy number: %s (sd: %s) vs. sum(ps) %s" %(mean_occ(eps,best_mu),sd_occ(eps,best_mu),sum(ps))
print "pearson correlation:",pearsonr(ps,qs)
print "best linear fit: p = %s*q + %s" % tuple(polyfit(qs,ps,1))
return best_mu
def free_energy(eps,q,mu,samples=1000,use_annealed_approx=False):
"""Compute free energy for true distribution given best approximation. Return beta*free_energy,actually"""
# def Q(xs):
# return product(fd(ep,mu) if x else 1 - fd(ep,mu) for x,ep in zip(xs,eps))
Sq = -sum((p*log(p)+(1-p)*log(1-p) for p in probs(eps,mu)))
def E(xs):
"""Compute energy function for P,unnormalized"""
ff = falling_fac(q,sum(xs))
if ff == 0:
return 1000
else:
return log(ff) + sum(ep*x for (x,ep) in zip(xs,eps))
if use_annealed_approx: # to get around impossible states where E=\infty
mean_E = log(mean(exp(E(rstate(eps,mu))) for i in range(samples))) # take <E(xs)>_Q
else:
mean_E = mean(E(rstate(eps,mu)) for i in range(samples)) # take <E(xs)>_Q
return beta*mean_E - Sq
