def MCMC(theta, x, y, yerr, P, name):
# Sample the posterior probability for m.
nwalkers, ndim = 64, len(theta)
p0 = [theta+1e-4*np.random.rand(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args = (x, y, yerr, P))
bi, pr = 100, 300
start = time.clock()
print("Burn-in")
p0, lp, state = sampler.run_mcmc(p0, bi)
sampler.reset()
print("Production run")
sampler.run_mcmc(p0, pr)
elapsed = time.clock() - start
print 'time = ', elapsed/60., 'mins'
print("Making triangle plots")
fig_labels = ["$A$", "$l_2$", "$l_1$", "$s$"]
fig = triangle.corner(sampler.flatchain, truths=theta, labels=fig_labels[:len(theta)])
fig.savefig("%striangle.png"%name)
print("Plotting traces")
pl.figure()
for i in range(ndim):
pl.clf()
pl.axhline(theta[i], color = "r", zorder=2)
pl.plot(sampler.chain[:, :, i].T, 'k-', alpha=0.3, zorder=1)
pl.savefig("{0}.png".format(i))
# Flatten chain
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
# Find values
mcmc_result = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
theta = np.array(mcmc_result)[:, 0]
print 'mcmc result (exp) = ', np.exp(theta)
print 'mcmc result (lin) = ', theta
like = lnlike(theta, x, y, yerr, P)
print "Final lnlike = ", like
# plot mcmc result
pl.clf()
pl.errorbar(x, y, yerr=yerr, fmt='k.')
xs = np.arange(min(x), max(x), 0.01)
pl.plot(xs, predict(xs, x, y, yerr, theta, P)[0], 'r-')
pl.xlabel('time (days)')
pl.savefig('%sresult'%name)
savedata = np.empty(len(theta)+1)
savedata[:len(theta)] = theta
savedata[-1] = like
np.savetxt('%sresult.txt'%name, savedata)
return like
def lnprob(theta, x, y, yerr, bm, bp):
lp = lnprior(theta, bm, bp)
if not np.isfinite(lp):
return -np.inf
try:
return lp + lnlike(theta, x, y, yerr)
except:
print theta
raise
def MCMC(theta, x, y, yerr, bm, bp):
# Sample the posterior probability for m.
nwalkers, ndim = 64, len(theta)
p0 = [theta + 1e-4 * np.random.rand(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
lnprob,
args=(x, y, yerr, bm, bp))
bi, pr = 200, 2000
start = time.clock()
print("Burn-in")
p0, lp, state = sampler.run_mcmc(p0, bi)
sampler.reset()
print("Production run")
sampler.run_mcmc(p0, pr)
elapsed = time.clock() - start
print 'time = ', elapsed / 60., 'mins'
print("Making triangle plots")
fig_labels = ["$A$", "$l_2$", "$l_1$", "$s$", "$P$"]
fig = triangle.corner(sampler.flatchain,
truths=theta,
labels=fig_labels[:len(theta)])
fig.savefig("triangle.png")
print("Plotting traces")
pl.figure()
for i in range(ndim):
pl.clf()
pl.axhline(theta[i], color="r", zorder=2)
pl.plot(sampler.chain[:, :, i].T, 'k-', alpha=0.3, zorder=1)
pl.savefig("{0}.png".format(i))
# Flatten chain
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
# Find values
mcmc_result = map(lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
theta = np.array(mcmc_result)[:, 0]
print 'mcmc result = ', theta
like = lnlike(theta, x, y, yerr)
print "Final lnlike = ", like
# plot mcmc result
pl.clf()
pl.errorbar(x, y, yerr=yerr, fmt='k.')
xs = np.arange(min(x), max(x), 0.01)
pl.plot(xs, predict(xs, x, y, yerr, theta, theta[4])[0], 'r-')
pl.xlabel('time (days)')
pl.savefig('result')
def MCMC(theta, x, y, yerr, bm, bp):
# Compute initial likelihood
print 'initial lnlike = ', lnlike(theta, x, y, yerr)
# Sample the posterior probability for m.
nwalkers, ndim = 64, len(theta)
p0 = [theta+1e-4*np.random.rand(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args = (x, y, yerr,
bm, bp))
bi, pr = 200, 2000
print("Burn-in")
p0, lp, state = sampler.run_mcmc(p0, bi)
sampler.reset()
nstep = 2000
nruns = 100.
print("Production run")
for j in range(int(nstep/nruns)):
print 'run', j
p0, lp, state = sampler.run_mcmc(p0, nruns)
print("Plotting traces")
pl.figure()
for i in range(ndim):
pl.clf()
pl.axhline(theta[i], color = "r")
pl.plot(sampler.chain[:, :, i].T, 'k-', alpha=0.3)
pl.savefig("%s.png" %i)
flat = sampler.chain[:, 50:, :].reshape((-1, ndim))
mcmc_result = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),
zip(*np.percentile(flat, [16, 50, 84], axis=0)))
print mcmc_result
mres = np.array(mcmc_result)[:, 0]
print 'mcmc_result = ', mres
print("Making triangle plot")
fig_labels = ["$A$", "$l_2$", "$l_1$", "$s$", "$P$"]
fig = triangle.corner(sampler.flatchain, truths=theta,
labels=fig_labels[:len(theta)])
fig.savefig("triangle.png")
# Flatten chain
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
# Find values
mcmc_result = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
theta = np.array(mcmc_result)[:, 0]
print 'mcmc result = ', theta
like = lnlike(theta, x, y, yerr)
print "Final lnlike = ", like
# plot mcmc result
pl.clf()
pl.errorbar(x, y, yerr=yerr, fmt='k.')
xs = np.arange(min(x), max(x), 0.01)
pl.plot(xs, predict(xs, x, y, yerr, theta, theta[4])[0], 'r-')
pl.xlabel('time (days)')
pl.savefig('result')
y = np.random.multivariate_normal(np.zeros(len(x)), K)
# plot data
pl.clf()
pl.errorbar(x, y, yerr=yerr, fmt='k.', capsize=0, ecolor='0.5', zorder=2)
xs = np.linspace(min(x), max(x), 1000)
pl.plot(xs, predict(xs, x, y, yerr, theta, P)[0], color='#339999', linestyle = '-',\
zorder=1, linewidth='2')
pl.xlabel('$\mathrm{Time~(days)}$')
pl.ylabel('$\mathrm{Normalised~Flux}$')
pl.gca().yaxis.set_major_locator(MaxNLocator(prune='lower'))
pl.savefig('data')
print "Initial parameters = (exp)", theta
start = time.clock()
print "Initial lnlike = ", lnlike(theta, x, y, yerr, P), "\n"
elapsed = (time.clock() - start)
print 'time =', elapsed
# Grid over periods
Periods = np.arange(0.2, 5, 0.2)
L = np.zeros_like(Periods)
for i, P in enumerate(Periods):
L[i] = MCMC(theta, x, y, yerr, P, i)
pl.clf()
pl.plot(Periods, L, 'k-')
pl.xlabel('Period')
pl.ylabel('Likelihood')
pl.savefig('update')
# subsample and truncate
x_sub, y_sub, yerr_sub = subs(x, y, yerr, 1., 500, 100)
# A, l2, l1, s
P = np.log(.7)
theta = [-2., -2., -1.2, 1., P]
# plot data and prediction
pl.clf()
pl.errorbar(x_sub, y_sub, yerr=yerr_sub, fmt='k.', capsize=0)
xs = np.linspace(min(x_sub), max(x_sub), 100)
pl.plot(xs, predict(xs, x_sub, y_sub, yerr_sub, theta, P)[0], color='.7')
pl.savefig('single_binary_data')
# Compute initial likelihood
print 'initial lnlike = ', lnlike(theta, x, y, yerr)
# bm, bp = minimum and maximum periods
bm, bp = np.log(.2), np.log(2)
# Sample the posterior probability for m.
nwalkers, ndim = 64, len(theta)
p0 = [theta+1e-4*np.random.rand(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args = (x, y, yerr, bm, bp))
# print("Burn-in")
# p0, lp, state = sampler.run_mcmc(p0, 200)
# sampler.reset()
nstep = 2000
nruns = 100.
np.savetxt("mcmc_result%s.txt"%fname, mcmc_result)
mres = np.array(mcmc_result)[:, 0]
print 'mcmc_result = ', mres
print("Making triangle plot")
fig_labels = ["$A_1$", "$l2_1$", "$l1_1$", "$s$", "$P_1$", "$A_2$", "$l2_2$", \
"$l1_2$", "$P_2$", "$a$"]
fig = triangle.corner(sampler.flatchain, truths=theta, labels=fig_labels[:len(theta)])
fig.savefig("triangle_%s.png" %fname)
# Flatten chain
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
# Find values
mcmc_result = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
theta = np.array(mcmc_result)[:, 0]
print 'mcmc result = ', theta
like = lnlike(theta, x, y, yerr)
print "Final lnlike = ", like
# plot mcmc result
pl.clf()
pl.errorbar(x, y, yerr=yerr, fmt='k.')
xs = np.arange(min(x), max(x), 0.01)
pl.plot(xs, predict(xs, x, y, yerr, theta, theta[4])[0], 'r-')
pl.xlabel('time (days)')
pl.savefig('result%s'%fname)
y = np.random.multivariate_normal(np.zeros(len(x)), K)
# plot data
pl.clf()
pl.errorbar(x, y, yerr=yerr, fmt='k.', capsize=0, ecolor='0.5', zorder=2)
xs = np.linspace(min(x), max(x), 1000)
pl.plot(xs, predict(xs, x, y, yerr, theta, P)[0], color='#339999', linestyle = '-',\
zorder=1, linewidth='2')
pl.xlabel('$\mathrm{Time~(days)}$')
pl.ylabel('$\mathrm{Normalised~Flux}$')
pl.gca().yaxis.set_major_locator(MaxNLocator(prune='lower'))
pl.savefig('data')
print "Initial parameters = (exp)", theta
start = time.clock()
print "Initial lnlike = ", lnlike(theta, x, y, yerr, P),"\n"
elapsed = (time.clock() - start)
print 'time =', elapsed
# Grid over periods
Periods = np.arange(0.2, 5, 0.2)
L = np.zeros_like(Periods)
for i, P in enumerate(Periods):
L[i] = MCMC(theta, x, y, yerr, P, i)
pl.clf()
pl.plot(Periods, L, 'k-')
pl.xlabel('Period')
pl.ylabel('Likelihood')
pl.savefig('update')