def mixing_times(H, trials=10):
"""runs the two samplers with the given energy a bunch of times
reports back their average mixing times
"""
order = len(H) * 2
c_tm = np.zeros(trials)
d_tm = np.zeros(trials)
for i in xrange(trials):
# todo: add reset methods
print "trial: {}".format(i)
hmc = AlgebraicDiscrete(order, energies=H)
chmc = AlgebraicContinuous(order, energies=H)
d_tm[i] = hmc.calculate_mixing_time()
c_tm[i] = chmc.calculate_mixing_time()
print "Average mixing time for discrete sampler: {}".format(np.mean(d_tm))
print "Average mixing time for continuous sampler: {}".format(np.mean(c_tm))
def calc_spectral_gaps(order, trials=1, n_sample_step=1000):
"""Approximates the spectral gap for each sampler at a certain order
returns avg_discrete_sg, discrete_sg_var, avg_continuous_sg, continuous_sg_var
"""
assert order % 2 == 0
# normally distributed?
H = np.random.randn(order / 2)
c_sg = np.zeros(trials)
h_sg = np.zeros(trials)
print "Order: {}".format(order)
for i in xrange(trials):
hmc = AlgebraicDiscrete(order, energies=H)
chmc = AlgebraicContinuous(order, energies=H)
# runs until close to equilibrium distribution
n_hmc = hmc.calculate_mixing_time()
n_chmc = chmc.calculate_mixing_time()
h_sg[i] = sg(hmc)
c_sg[i] = sg(chmc)
print "{} samplings steps for hmc to approach equilibirium".format(n_hmc)
print "{} samplings steps for chmc to approach equilibirium".format(n_chmc)
return np.mean(h_sg), np.std(h_sg), np.mean(c_sg), np.std(c_sg)