def test_simulation(n=1e2, tau=0.995):
T = pth.GaussianKernel(tau)
X = [np.random.random(int(n)) * 100]
for i in xrange(1000):
X.append(T(X[-1]))
X = np.array(X)
## plot convergence to stationary distribution
fig, ax = plt.subplots(1, 2, figsize=(8, 4))
fig.suptitle(r'$\tau={0:.3e}$'.format(tau), y=1.)
[ax[0].plot(x, lw=2, color='k', alpha=0.1) for x in X.T]
ax[0].plot(X.mean(1), lw=3, color='r')
ax[0].axhline(T.stationary.mu, ls='--', lw=3, label=r'$\mu$', color='k')
ax[0].set_xlabel('iteration')
ax[0].set_ylabel('mean')
ax[0].legend()
ax[1].plot(X.std(1), color='r')
ax[1].axhline(T.stationary.sigma,
ls='--',
lw=3,
label=r'$\sigma$',
color='k')
ax[1].set_xlabel('iteration')
ax[1].set_ylabel('standard deviation')
ax[1].legend()
fig.tight_layout()
def test_composition():
T = pth.GaussianKernel(0.9,
np.random.standard_normal() * 10,
np.random.gamma(1))
print T
print T.compose(T.compose(T.compose(T)))
print T.power(4)
print T.stationary
import numpy as np
import paths as pth
import matplotlib.pylab as plt
start = pth.GaussianKernel(0.9, 20., 10.)
end = pth.GaussianKernel(0.995, 0., 1.)
log_Z = end.stationary.log_Z - start.stationary.log_Z
scheduler = pth.Scheduler(start, end, pth.Bridge)
schedule = scheduler.find_schedule(10)
scheduler = pth.Scheduler(start, end, pth.GeometricBridge)
schedule2 = scheduler.find_schedule(10)
bridge = pth.make_bridge(start, end, schedule, constructor=pth.Bridge)
bridge2 = pth.make_bridge(start,
end,
schedule2,
constructor=pth.GeometricBridge)
prob = [T.stationary for T in bridge]
prob2 = [T.stationary for T in bridge2]
kl = [q.kl(p) for p, q in zip(prob[1:], prob)]
kl2 = [q.kl(p) for p, q in zip(prob2[1:], prob2)]
print 'first bridge', np.mean(kl), np.std(kl)
print 'second bridge', np.mean(kl2), np.std(kl)
colors = ('b', 'g')