def plot_mcmc_results(chain):
# Pull m and b arrays out of the Markov chain.
mm = [m for b,m in chain]
bb = [b for b,m in chain]
# Scatterplot of m,b posterior samples
plt.clf()
plt.contour(bgrid, mgrid, posterior, pdf_contour_levels(posterior))
plt.plot(bb, mm, 'b.', alpha=0.1)
plot_mb_setup()
plt.show()
# Histograms
import triangle
triangle.corner(chain, labels=['b','m'], extents=[0.99]*2)
plt.show()
# Traces
plt.clf()
plt.subplot(2,1,1)
plt.plot(mm, 'k-')
plt.ylim(mlo,mhi)
plt.ylabel('m')
plt.subplot(2,1,2)
plt.plot(bb, 'k-')
plt.ylabel('b')
plt.ylim(blo,bhi)
plt.show()
def triangle_plot_chain(chain, lnprob, prefix):
"""
Make a 7x7 triangle.
"""
nx, nq = chain.shape
maxlnp = np.max(lnprob)
lnpextent = [(maxlnp-14.5, maxlnp+0.5)]
bar = SixPosition(chain[0]) # temporary variable to get names
foo = np.concatenate((chain, lnprob.reshape((nx, 1))), axis=1)
labels = np.append(bar.get_sixpos_names(), [r"$\ln p$"])
extents = bar.get_sixpos_extents() + lnpextent
fig = tri.corner(foo, labels=labels, extents=extents, plot_contours=False)
fn = prefix + "a.png"
print "triangle_plot_chain(): writing " + fn
fig.savefig(fn)
obsfoo = 1. * foo # copy
for i in range(nx):
obsfoo[i,:6] = SixPosition(foo[i,:6]).get_observables_array()
labels = np.append(bar.get_observables_names(), [r"$\ln p$"])
extents = bar.get_observables_extents() + lnpextent
fig = tri.corner(obsfoo, labels=labels, extents=extents, plot_contours=False)
fn = prefix + "b.png"
print "triangle_plot_chain(): writing " + fn
fig.savefig(fn)
intfoo = 1. * foo[:,2:] # copy
for i in range(nx):
intfoo[i,:4] = SixPosition(foo[i,:6]).get_integrals_of_motion()
labels = np.append(bar.get_integrals_of_motion_names(), [r"$\ln p$"])
extents = bar.get_integrals_of_motion_extents() + lnpextent
fig = tri.corner(intfoo, labels=labels, extents=extents, plot_contours=False)
fn = prefix + "c.png"
print "triangle_plot_chain(): writing " + fn
fig.savefig(fn)
return None
def plot(spergel_sampler, series_samplers, args):
p_initial = [args.x0, args.y0, args.HLR, args.flux, args.e1, args.e2]
ndim = spergel_sampler.chain.shape[-1]
# triangle plots
spergel_samples = spergel_sampler.chain[:, args.nburn:, :].reshape(
(-1, ndim))
extents = []
for i in range(ndim):
vals = spergel_samples[:, i]
for jmax in range(args.jmaxmin, args.jmaxmax + 1):
series_samples = series_samplers[jmax].chain[:, args.
nburn:, :].reshape(
(-1, ndim))
vals = np.concatenate([vals, series_samples[:, i]])
extents.append(np.percentile(vals, [0.5, 99.5]))
for jmax in range(args.jmaxmin, args.jmaxmax + 1):
series_samples = series_samplers[jmax].chain[:,
args.nburn:, :].reshape(
(-1, ndim))
labels = ["x0", "y0", "HLR", "flux", "e1", "e2"]
fig = triangle.corner(spergel_samples,
labels=labels,
truths=p_initial,
extents=extents)
fig = triangle.corner(series_samples,
color='red',
extents=extents,
fig=fig)
fig.savefig(args.plot_prefix +
"_jmax_{:02d}_triangle.png".format(jmax))
plt.close(fig)
def plot_corner(logpost, chain, outdir=None):
flatchain = chain.reshape((-1, chain.shape[2]))
tri.corner(flatchain, labels=logpost.pnames, quantiles=[0.05, 0.95])
if outdir is not None:
pp.savefig(op.join(outdir, 'corner.pdf'))
def plot_PDFtriangle(self,parameterset, labels): if parameterset=='10pars': figure = triangle.corner(self.chain.flatchain, labels= labels, plot_contours=True, plot_datapoints = False, show_titles=True, quantiles=[0.16, 0.50, 0.84]) elif parameterset == 'int_lums': figure = triangle.corner(self.int_lums.T, labels= labels, plot_contours=True, plot_datapoints = False, show_titles=True, quantiles=[0.16, 0.50, 0.84]) return figure
def MCParTemp(nwalkers,steps,ntemps=40,burnin=100,threads=1):
t1 = time.time()
# use emcee parallel tempering sampler to find prob. surface
ndim = 4
startpos = [[[0,0,0,0] + 5e-3*np.random.randn(ndim) for i in range(nwalkers)] for i in range(ntemps)]
# time how long it should take
t0 = time.time()
testpos = [[[0,0,0,0] + 5e-3*np.random.randn(4) for i in range(8)] for i in range(8)]
sampler = emcee.PTSampler(8,8, 4, lnlike, xs.lnprior, threads=threads)
for ptest,logprobtest, logliketest in sampler.sample(testpos,iterations=10):
pass
sampler.reset()
tdiff = time.time() - t0
esttime = ntemps/8.*nwalkers/8.*(burnin+steps)/10.*tdiff/60.
print 'Estimated time = {} minutes'.format(esttime)
# burn-in for defined number of steps (default=100)
sampler = emcee.PTSampler(ntemps,nwalkers, ndim, lnlike, xs.lnprior, threads=threads)
for p,logprob, loglike in sampler.sample(startpos,iterations=burnin):
pass
sampler.reset()
# run mcmc
sampler = emcee.PTSampler(ntemps, nwalkers, ndim, lnlike, xs.lnprior, threads=threads)
for p, logprob, loglike in sampler.sample(p, lnprob0=logprob, lnlike0=loglike,iterations=steps):
pass
print 'Time: {} minutes'.format(time.time() - t0)
samples = sampler.chain[:,:,:,:].reshape((-1, ndim))
triangle.corner(samples,labels=[r'$\Delta s$',r'$M_A$',r'$F_1^S$',r'$\mu_S$'],quantiles=[0.05,0.5,0.95])
print sampler.thermodynamic_integration_log_evidence(fburnin=0)
return samples
def triangleMAPs(savefilename,basename):
with open(savefilename,'rb') as savefile:
bf= numpy.array(pickle.load(savefile))
samples= numpy.array(pickle.load(savefile))
bf_g15= numpy.array(pickle.load(savefile))
samples_g15= numpy.array(pickle.load(savefile))
bf_zero= numpy.array(pickle.load(savefile))
samples_zero= numpy.array(pickle.load(savefile))
labels= []
for jj in range(samples.shape[2]):
labels.append(r"$\mathrm{param}\ %i$" % jj)
maps= define_rcsample.MAPs()
for ii, map in enumerate(maps.map()):
if ii >= len(bf): break
tfeh= numpy.nanmedian(map['FE_H'])
tafe= numpy.nanmedian(map[define_rcsample._AFETAG])
for tbf,tsamples,ext in zip([bf,bf_g15,bf_zero],
[samples,samples_g15,samples_zero],
['fid','g15','zero']):
try:
triangle.corner(tsamples[ii,].T,quantiles=[0.16, 0.5, 0.84],
labels=labels,
show_titles=True,title_args={"fontsize": 12},
bins=21)
except ValueError: pass
else:
bovy_plot.bovy_text(r'$[\mathrm{{Fe/H}}] = {feh:.1f},$'\
.format(feh=tfeh)+'\n'
+r'$[\alpha/\mathrm{{Fe}}] = {afe:.2f}$'\
.format(afe=tafe),
top_left=True,size=16.)
bovy_plot.bovy_end_print(basename+"_%i_%s.png" % (ii,ext))
return None
def plot_triangle(self, **kwargs):
try:
from triangle import corner
except ImportError:
raise ImportError('Plotting requires trianglepy')
corner(self.posterior_data[self.parameter_names],
labels=self.parameter_names, **kwargs)
def plotCorner(self):
model = self.model
mcmcVParams = self.mcmcRes.vparam_names
nestVParams = self.nestRes.vparam_names
mcmcSamples = self.mcmcRes.samples
nestSamples = self.nestRes.samples
mcmc_ndim, mcmc_nsamples = len(mcmcVParams), len(mcmcSamples)
nest_ndim, nest_nsamples = len(nestVParams), len(nestSamples)
# make figure
figure_mcmc = triangle.corner(mcmcSamples, labels=[mcmcVParams[0], mcmcVParams[1], mcmcVParams[2], mcmcVParams[3]],
truths=[model.get(mcmcVParams[0]), model.get(mcmcVParams[1]),
model.get(mcmcVParams[2]), model.get(mcmcVParams[3])],
range=mcmc_ndim*[0.9999],
show_titles=True, title_args={"fontsize": 12})
figure_mcmc.gca().annotate("mcmc sampling", xy=(0.5, 1.0), xycoords="figure fraction",
xytext=(0, -5), textcoords="offset points",
ha="center", va="top")
figure_nest = triangle.corner(nestSamples, labels=[nestVParams[0], nestVParams[1], nestVParams[2], nestVParams[3]],
truths=[model.get(nestVParams[0]), model.get(nestVParams[1]),
model.get(nestVParams[2]), model.get(nestVParams[3])],
weights=self.nestRes.weights, range=nest_ndim*[0.9999],
show_titles=True, title_args={"fontsize": 12})
figure_nest.gca().annotate("nest sampling", xy=(0.5, 1.0), xycoords="figure fraction",
xytext=(0, -5), textcoords="offset points",
ha="center", va="top")
return figure_mcmc, figure_nest
def plot_mcmc_results(chain,mlimits,blimits):
# Pull m and b arrays out of the Markov chain.
mm = [m for b,m in chain]
bb = [b for b,m in chain]
# Scatterplot of m,b posterior samples
plt.clf()
plt.contour(bgrid, mgrid, posterior, pdf_contour_levels(posterior))
plt.plot(bb, mm, 'b.', alpha=0.1)
plot_mb_setup(mlimits,blimits)
plt.show()
# Histograms
import triangle
triangle.corner(chain, labels=['b','m'], extents=[0.99]*2)
plt.show()
# Traces
plt.clf()
plt.subplot(2,1,1)
plt.plot(mm, 'k-')
plt.ylim(mlimits[0],mlimits[1])
plt.ylabel('m')
plt.subplot(2,1,2)
plt.plot(bb, 'k-')
plt.ylabel('b')
plt.ylim(blimits[0],blimits[1])
plt.show()
def subtriangle(sample_results, outname=None, showpars=None,
start=0, thin=1, truths=None, trim_outliers=None,
extents=None, **kwargs):
"""Make a triangle plot of the (thinned, latter) samples of the posterior
parameter space. Optionally make the plot only for a supplied subset of
the parameters.
:param start:
The iteration number to start with when drawing samples to plot.
:param thin:
The thinning of each chain to perform when drawing samples to plot.
:param showpars:
List of string names of parameters to include in the corner plot.
:param truths:
List of truth values for the chosen parameters
"""
try:
import triangle
except(ImportError):
import corner as triangle
# pull out the parameter names and flatten the thinned chains
try:
parnames = np.array(sample_results['theta_labels'])
except(KeyError):
parnames = np.array(sample_results['model'].theta_labels())
flatchain = sample_results['chain'][:, start::thin, :]
flatchain = flatchain.reshape(flatchain.shape[0] * flatchain.shape[1],
flatchain.shape[2])
# logify mass
if 'mass' in parnames:
midx = [l=='mass' for l in parnames]
flatchain[:,midx] = np.log10(flatchain[:,midx])
parnames[midx] = 'logmass'
# restrict to parameters you want to show
if showpars is not None:
ind_show = np.array([p in showpars for p in parnames], dtype=bool)
flatchain = flatchain[:, ind_show]
#truths = truths[ind_show]
parnames = parnames[ind_show]
if trim_outliers is not None:
trim_outliers = len(parnames) * [trim_outliers]
try:
fig = triangle.corner(flatchain, labels=parnames, truths=truths, verbose=False,
quantiles=[0.16, 0.5, 0.84], range=trim_outliers, **kwargs)
except:
fig = triangle.corner(flatchain, labels=parnames, truths=truths, verbose=False,
quantiles=[0.16, 0.5, 0.84], range=trim_outliers, **kwargs)
if outname is not None:
fig.savefig('{0}.triangle.png'.format(outname))
#pl.close(fig)
else:
return fig
def mcmctriangle(ID):
filename=('tables/ndim_' + str(ndim) + '_walkers_' + str(nwalkers) + '.fits')
data = Table.read(filename)
data_t = np.array([data[key] for key in param_keys]).transpose()
truths = [np.median(data[key]) for key in param_keys]
triangle.corner(data_t,labels=param_labels,quantiles=[0.1587,0.5000,0.8413])
plt.savefig('plots/triangle_ndim_' + str(ndim) + '_walkers_' + str(nwalkers) + '.pdf')
plt.close()
def plot_triangle(self, **kwargs):
try:
from triangle import corner
except ImportError:
raise ImportError('Plotting requires trianglepy')
data_columns = self.posterior_data.columns[2:]
corner(self.posterior_data[data_columns],
weights=self.posterior_data.posterior, **kwargs)
def convergence_plots(sampler):
plt.figure()
plt.plot(sampler.lnprobability.T)
plt.figure()
pu.plot_emcee_chains(sampler.chain)
triangle.corner(sampler.flatchain)
print 'Autocorrelation lengths: ', ac.emcee_chain_autocorrelation_lengths(sampler.chain)
print 'Gelman-Rubin R: ', ac.emcee_gelman_rubin_r(sampler.chain)
def convergence_plots(sampler):
plt.figure()
plt.plot(sampler.lnprobability.T)
plt.figure()
pu.plot_emcee_chains(sampler.chain)
triangle.corner(sampler.flatchain)
print 'Autocorrelation lengths: ', ac.emcee_chain_autocorrelation_lengths(
sampler.chain)
print 'Gelman-Rubin R: ', ac.emcee_gelman_rubin_r(sampler.chain)
def PlotTriangle(fileroot,usetruths=True):
data = np.loadtxt(fileroot+'post_equal_weights.dat', usecols=(0,1,2,3,4,5))
if (usetruths):
truths = np.loadtxt(fileroot+'injected_values.txt')
figure = triangle.corner(data, labels=names, truths=truths, bins=30, quantiles=[0.05, 0.5, 0.95],
show_titles=True, title_args={"fontsize": 12})
else:
figure = triangle.corner(data, labels=names, bins=30, quantiles=[0.05, 0.5, 0.95],
show_titles=True, title_args={"fontsize": 12})
figure.savefig(fileroot+'posterior_plot.png')
def plot_triangle(samples):
import triangle
if samples.shape[1] == 2:
fig = triangle.corner(samples, labels=["$t_0$", "$P$"])
if samples.shape[1] == 6:
fig = triangle.corner(samples, labels=["$t_0$", r"depth", r"duration",
r"$b$", "$q_1$", "$q_2$"])
elif samples.shape[1] == 8:
fig = triangle.corner(samples, labels=["$t_0$", r"depth", r"duration",
r"$b$", "$q_1$", "$q_2$", "$q_3$", "$q_4$"])
plt.show()
def subtriangle(sample_results, outname=None, showpars=None,
start=0, thin=1, truths=None, trim_outliers=None,
extents=None, **kwargs):
"""Make a triangle plot of the (thinned, latter) samples of the posterior
parameter space. Optionally make the plot only for a supplied subset of
the parameters.
:param start:
The iteration number to start with when drawing samples to plot.
:param thin:
The thinning of each chain to perform when drawing samples to plot.
:param showpars:
List of string names of parameters to include in the corner plot.
:param truths:
List of truth values for the chosen parameters
"""
try:
import triangle
except(ImportError):
import corner as triangle
# pull out the parameter names and flatten the thinned chains
try:
parnames = np.array(sample_results['theta_labels'])
except(KeyError):
parnames = np.array(sample_results['model'].theta_labels())
flatchain = sample_results['chain'][:, start::thin, :]
flatchain = flatchain.reshape(flatchain.shape[0] * flatchain.shape[1],
flatchain.shape[2])
# restrict to parameters you want to show
if showpars is not None:
ind_show = np.array([p in showpars for p in parnames], dtype=bool)
flatchain = flatchain[:, ind_show]
#truths = truths[ind_show]
parnames = parnames[ind_show]
if trim_outliers is not None:
trim_outliers = len(parnames) * [trim_outliers]
try:
fig = triangle.corner(flatchain, labels=parnames, truths=truths, verbose=False,
quantiles=[0.16, 0.5, 0.84], extents=trim_outliers, **kwargs)
except:
fig = triangle.corner(flatchain, labels=parnames, truths=truths, verbose=False,
quantiles=[0.16, 0.5, 0.84], range=trim_outliers, **kwargs)
if outname is not None:
fig.savefig('{0}.triangle.png'.format(outname))
#pl.close(fig)
else:
return fig
def main():
pot = agama.Potential(type="Dehnen", mass=1, scaleRadius=1.)
actf = agama.ActionFinder(pot)
particles, masses = createHernquistModel(100000)
actions = actf(particles)
# do a parameter search to find best-fit distribution function describing these particles
initparams = numpy.array([2.0, 4.0, 1.0, 1.0, 0.0])
result = minimize(model_search_fnc,
initparams,
args=(actions, ),
method='Nelder-Mead',
options=dict(maxiter=1000, maxfev=1000, disp=True))
# explore the parameter space around the best-fit values using the MCMC chain
import emcee, matplotlib.pyplot as plt, triangle as corner
print 'Starting MCMC'
ndim = len(initparams)
nwalkers = 16 # number of parallel walkers in the chain
nsteps = 300 # number of steps in MCMC chain
nburnin = 100 # number of initial steps to discard
# initial coverage of parameter space - around the best-fit solution with a small dispersion
initwalkers = [
result.x + 0.01 * numpy.random.randn(ndim) for i in range(nwalkers)
]
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
model_search_emcee,
args=(actions, ))
sampler.run_mcmc(initwalkers, nsteps)
# show the time evolution of parameters carried by the ensemble of walkers (time=number of MC steps)
fig, axes = plt.subplots(ndim + 1, 1, sharex=True)
for i in range(ndim):
axes[i].plot(sampler.chain[:, :, i].T, color='k', alpha=0.5)
axes[i].set_ylabel(labels[i])
# last panel shows the evolution of log-likelihood for the ensemble of walkers
axes[-1].plot(sampler.lnprobability.T, color='k', alpha=0.5)
axes[-1].set_ylabel('log(L)')
maxloglike = numpy.max(sampler.lnprobability)
axes[-1].set_ylim(maxloglike - 3 * ndim, maxloglike)
fig.tight_layout(h_pad=0.)
plt.show()
# show the posterior distribution of parameters
samples = sampler.chain[:, nburnin:, :].reshape((-1, ndim))
corner.corner(samples, \
labels=labels, quantiles=[0.16, 0.5, 0.84], truths=result.x)
plt.show()
print "Acceptance fraction: ", numpy.mean(
sampler.acceptance_fraction) # should be in the range 0.2-0.5
print "Autocorrelation time: ", sampler.acor # should be considerably shorter than the total number of steps
def triangle_plot_chain(chain, lnprob, prefix, truth=None, truth_lnprob=0.):
"""
Make a 7x7 triangle.
"""
nx, nq = chain.shape
maxlnp = np.max(lnprob)
lnpextent = [(maxlnp-14.5, maxlnp+0.5)]
bar = SixPosition(chain[0]) # temporary variable to get names
foo = np.concatenate((chain, lnprob.reshape((nx, 1))), axis=1)
if truth is None:
truths = None
else:
truths = np.append(truth, [truth_lnprob])
labels = np.append(bar.get_sixpos_names(), [r"$\ln p$"])
extents = bar.get_sixpos_extents() + lnpextent
fig = tri.corner(foo, labels=labels, extents=extents,
truths=truths, plot_contours=False)
fn = prefix + "a.png"
print "triangle_plot_chain(): writing " + fn
fig.savefig(fn)
obsfoo = 1. * foo # copy
for i in range(nx):
obsfoo[i,:6] = SixPosition(foo[i,:6]).get_observables_array()
if truth is None:
trueobs = None
else:
trueobs = 1. * truths # copy
trueobs[:6] = SixPosition(truth).get_observables_array()
labels = np.append(bar.get_observables_names(), [r"$\ln p$"])
extents = bar.get_observables_extents() + lnpextent
fig = tri.corner(obsfoo, labels=labels, extents=extents,
truths=trueobs, plot_contours=False)
fn = prefix + "b.png"
print "triangle_plot_chain(): writing " + fn
fig.savefig(fn)
intfoo = 1. * foo[:,2:] # copy
for i in range(nx):
intfoo[i,:4] = SixPosition(foo[i,:6]).get_integrals_of_motion()
if truth is None:
trueint = None
else:
trueint = 1. * truths[2:] # copy
trueint[:4] = SixPosition(truth).get_integrals_of_motion()
labels = np.append(bar.get_integrals_of_motion_names(), [r"$\ln p$"])
extents = bar.get_integrals_of_motion_extents() + lnpextent
fig = tri.corner(intfoo, labels=labels, extents=extents,
truths=trueint, plot_contours=False)
fn = prefix + "c.png"
print "triangle_plot_chain(): writing " + fn
fig.savefig(fn)
return None
def visModel(self, labels=None, fname=None):
nSamples = 1e6
samples = self.reg.sample(n_samples=nSamples)
#quick fix for better plotting
samples = np.log10(samples)
if self.pred == None:
if hasTriangle:
figure = triangle.corner(samples, labels=labels,
quantiles=[0.16, 0.5, 0.84],
show_titles=True, title_args={"fontsize": 12})
if fname!=None:
plt.savefig('predicted_'+fname)
elif samples.size[1]==2:
f, ax = plt.subplots(1)
ax.hist2d(samples[:,0], samples[:,1])
if fname!=None:
plt.savefig('predicted_'+fname)
else:
raise NotImplementedError("Plotting datasets w/ dim > 2 without Triangle not implemented")
else:
if hasTriangle:
figure = triangle.corner(samples, labels=labels,
quantiles=[0.16, 0.5, 0.84],
show_titles=True, title_args={"fontsize": 12})
if fname!=None:
plt.savefig('predicted_'+fname)
figure = triangle.corner(self.X, labels=labels,
quantiles=[0.16, 0.5, 0.84],
show_titles=True, title_args={"fontsize": 12})
if fname!=None:
plt.savefig('original_'+fname)
elif samples.size[1]==2:
f, ax = plt.subplots(2)
ax[0].hist2d(samples[:,0], samples[:,1])
ax[1].hist2d(self.X[:,0], self.X[:,1])
ax[1].set_xlabel(labels[0])
ax[1].set_ylabel(labels[1])
plt.tight_layout()
if fname!=None:
plt.savefig(fname)
else:
raise NotImplementedError("Plotting datasets w/ dim > 2 without Triangle not implemented")
def trianglePlot(restart, fn, burnIn=0):
shp = np.shape(restart['chain'])
prs = shp[0] * (shp[1] - burnIn) * shp[2]
prior = [sampleFromPrior() for i in range(prs)]
shape = np.shape(restart['chain'])
ndim = shape[2]
trifig = triangle.corner(restart['chain'][:,burnIn:,:].reshape((-1,ndim)), \
labels=[r'$f_{g,0}$',r'$\mu_0$',r'$\alpha_\mu$', r'$r_\mathrm{acc}/r_\mathrm{vir}$', \
r'$\epsilon_0$',r'$\alpha_z$',r'$\alpha_{M_h}$',r'$\epsilon_\mathrm{max}$',r'$f_\mathrm{cool}$'])
trifigPrior = triangle.corner(prior,
color='red',
fig=trifig,
plot_datapoints=False)
trifig.savefig(fn)
def plot_grid_points(db='phoenix2016.db3',saveplot=False):
# plot the grid points
connection = sqlite.connect(db)
sql_query = 'SELECT teff,logg,mh,alpha FROM parameter_sets'
tab = pd.read_sql_query(sql_query,connection)
connection.close()
arr = np.array([np.array(tab['teff']),np.array(tab['logg']),np.array(tab['mh']),tab['alpha']])
corner(tab,plot_contours=False,labels=['Teff','log g', '[M/H]', '[alpha/Fe]'])
if saveplot:
fname = os.path.basename(db)
fname = os.path.splitext(fname)
plt.savefig(fname[0]+'.pdf')
def make_chain_plots(model_filename):
"""
Create analysis plots:
- chain values vs. iteration number
- histogram of chain values
- triangle plot of chains
Args:
model_filename (str): Name of input zipped model pickle file.
"""
try:
p_data = pickle.loads(gzip.open(model_filename).read())
except UnicodeDecodeError:
p_data = pickle.loads(gzip.open(model_filename).read(),
encoding="latin1")
model = p_data["model"]
params = p_data["comp_params"]
# We can do this intelligently based on number of iterations.
samples = model.sampler.chain[:, 50:, :].reshape(
(-1, model.total_parameter_count))
if np.size(samples) == 0:
print("WARNING, size of samples is 0! Exiting analysis code now...")
exit()
fig = triangle.corner(samples, labels=model.model_parameter_names())
figname = "plots/{0}_triangle.png".format(model_filename)
fig.savefig(figname)
print("\tWrote {0}".format(figname))
# First, calculate the median and confidence intervals
# where frac is the fraction of samples within the
# quoted uncertainties. frac = 0.68 is the default.
# Columns are median, -error1, +error2.
print(median_values(samples, frac=0.68))
# Second, calculate the mean and standard deviation.
# Columns are mean, standard deviation.
print(mean_values(samples))
# Third, plot the MCMC chains as a function of iteration.
# You can easily tell if the chains are converged because you can
# no longer tell where the individual particle chains are sliced together.
# For testing, I saved 2000 iterations and ignored the first 1000.
fig = plot_chains(samples, labels=model.model_parameter_names())
figname = "plots/{0}_chain.png".format(model_filename)
fig.savefig(figname)
print("\tWrote {0}".format(figname))
# Fourth, plot the posterior PDFs for each parameter.
# These are histograms of the MCMC chains. We should add
# parameter names to this and the previous plots at some point.
# boxes = 20 is the default.
fig = plot_posteriors(samples,
labels=model.model_parameter_names(),
boxes=20,
params=params)
figname = "plots/{0}_posterior.png".format(model_filename)
fig.savefig(figname)
print("\tWrote {0}".format(figname))
def triangle_plot(self,*args,**kwargs):
if not args:
args=self.keys
assert len(args)>1
labels=[]
idx=[]
for key in args:
if key.startswith('_sigma_'):
name=key.split('_sigma_')[1]
label=r'$\sigma_{%s}$' % name
else:
namestr=key
for g in greek:
if key.startswith(g):
namestr=r'\%s' % key
label='$%s$' % namestr
labels.append(label)
idx.append(self.index[key])
fig = triangle.corner(self.samples[:,idx], labels=labels)
def make_plots(whichx, fname):
x, y, xerr, yerr = load_data(whichx)
with h5py.File("%s_samples_%s.h5" % (whichx, fname)) as f:
samp = f["samples"][...]
m, c, sig = map(lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samp, [16, 50, 84], axis=0)))
pars = [m[0], c[0], sig[0]]
print pars
plt.clf()
plt.errorbar(x, y, xerr=xerr, yerr=yerr, fmt="k.", capsize=0, ecolor=".7")
plt.plot(x, model1(pars, x), "k")
ndraws = 100
p0s = np.random.choice(samp[:, 0], ndraws)
p1s = np.random.choice(samp[:, 1], ndraws)
p2s = np.random.choice(samp[:, 2], ndraws)
for i in range(ndraws):
y = p0s[i] * x + p1s[i]
plt.plot(x, (y + p2s[i]), "k", alpha=.1)
plt.savefig("mcmc_%s_%s" % (whichx, fname))
labels = ["$m$", "$c$", "$\sigma$"]
plt.clf()
fig = triangle.corner(samp, labels=labels)
fig.savefig("triangle_%s_%s" % (whichx, fname))
def results(fn):
model, sampler = pickle.load(open(fn, "rb"))
mu = np.median(model.f)
ppm = lambda f: (f / mu - 1) * 1e6
# Plot the data.
fig = pl.figure(figsize=(6, 6))
ax = fig.add_subplot(111)
ax.plot(model.t, ppm(model.f), ".k")
ax.set_xlim(np.min(model.t), np.max(model.t))
ax.set_xlabel("time since transit [days]")
ax.set_ylabel("relative flux [ppm]")
fig.subplots_adjust(left=0.2, bottom=0.2, top=0.9, right=0.9)
# Plot the predictions.
samples = sampler.flatchain
t = np.linspace(model.t.min(), model.t.max(), 1000)
for i in np.random.randint(len(samples), size=10):
model.vector = samples[i]
ax.plot(t, ppm(model.predict(t)), color="#4682b4", alpha=0.5)
fig.savefig(os.path.splitext(fn)[0] + "-results.pdf")
# Plot the corner plot.
fig = triangle.corner(samples, labels=model.labels,
truths=model.true_vector)
fig.savefig(os.path.splitext(fn)[0] + "-triangle.png")
def plot(flatchain,
base=args.outdir,
triangle_plot=args.triangle,
chain_plot=args.chain,
lnprob=args.lnprob,
clip_stellar='all',
format=".pdf"):
'''
Make a bunch of plots to diagnose how the run went.
'''
import matplotlib
matplotlib.rc("font", size=16)
#Navigate the flatchain tree, and each time we encounter a flatchain, plot it.
if flatchain.id == "stellar" and clip_stellar != "all":
flatchain.clip_param(clip_stellar)
params = flatchain.param_tuple
samples = flatchain.samples
labels = [label_dict.get(key, "unknown") for key in params]
figure = triangle.corner(samples,
labels=labels,
quantiles=[0.16, 0.5, 0.84],
show_titles=True,
title_args={"fontsize": 16},
plot_contours=True,
plot_datapoints=False)
figure.savefig(base + flatchain.id + format)
def animate_triangle(pos_T, labels=None, truths=None, samps_per_frame=10, fps=30, rough_length=10.0, outname='triangle.mp4'):
from matplotlib import animation
import triangle
nframes, nwalkers, ndim = pos_T.shape
final_bins = 50 #number of bins covering final posterior
# Use last time step to get y-limits of histograms
bins = []
ymaxs = []
for x in range(ndim):
dx = (pos_T[-1,:,x].max() - pos_T[-1,:,x].min())/final_bins
nbins = int((pos_T[0,:,x].max() - pos_T[0,:,x].min())/dx)
bins.append(np.linspace(pos_T[0,:,x].min(), pos_T[0,:,x].max(), nbins+1)[:-1])
hist, _ = np.histogram(pos_T[-1,:,x], bins=bins[-1], normed=True)
ymaxs.append(1.1*max(hist))
# Use the first time sample as the initial frame
fig = triangle.corner(pos_T[0], labels=labels, plot_contours=False, truths=truths)
axes = np.array(fig.axes).reshape((ndim, ndim))
for x in range(ndim):
axes[x,x].set_ylim(top=ymaxs[x])
# Determine number of frames
thin_factor = int(nframes/rough_length)/fps
if thin_factor > 1:
pos_T = pos_T[::thin_factor]
samps_per_frame *= thin_factor
samps_per_sec = fps * samps_per_frame
# Make the movie
anim = animation.FuncAnimation(fig, update_triangle, frames=xrange(len(pos_T)), blit=True,
fargs=(pos_T, fig, bins, truths))
return anim
def triangle_plot(fname, mcmc_result, flatchain, fig_labels):
print 'yes'
mres = np.array(mcmc_result)[:, 0]
print 'mcmc_result = ', mres
print len(mres), len(fig_labels)
fig = triangle.corner(flatchain, truths=mres, labels=fig_labels)
fig.savefig("triangle_%s.png" % fname)
def corner_plot(results, showpars=None, start=0, thin=1):
#just wrap subtriangle
"""
Make a triangle plot of the (thinned, latter) samples of the posterior
parameter space. Optionally make the plot only for a supplied subset
of the parameters.
"""
# pull out the parameter names and flatten the thinned chains
parnames = np.array(results['model'].theta_labels())
flatchain = results['chain'][:,start::thin,:]
flatchain = flatchain.reshape(flatchain.shape[0] * flatchain.shape[1],
flatchain.shape[2])
truths = results['initial_center']
# restrict to parameters you want to show
if showpars is not None:
ind_show = np.array([p in showpars for p in parnames], dtype= bool)
flatchain = flatchain[:,ind_show]
truths = truths[ind_show]
parnames= parnames[ind_show]
parlabels = [pardict[p] for p in parnames]
fig = triangle.corner(flatchain, labels = parlabels,
quantiles=[0.16, 0.5, 0.84], verbose=False,
truths = truths)
return fig
def plotTriangle(new_flatchain, field, objid, dataIDX, save_opt=None, copy_opt=None):
import triangle
import matplotlib.pylab as plt
vNames = ['tau (dust2)','delta (dust_index)', 'Eb (uvb)', 'log10(age)',
'log10(M_star)']
triangle_figure = triangle.corner(new_flatchain, labels=vNames,
quantiles=[0.16, 0.5, 0.84],
show_titles=True, title_args={"fontsize": 12},
plot_contours=True,
plot_datapoints=False,
verbose=False
)
triangle_figure.gca().annotate(field+'-'+objid+', hunters index: '+str(dataIDX)+', after trimming',
xy=(0.5, 1.0), xycoords="figure fraction",
xytext=(0, -5), textcoords="offset points",
ha="center", va="top")
if save_opt != None:
triangle_figure.savefig(save_opt+'triangle.png')
plt.close('all')
if copy_opt != None:
shutil.copyfile(save_opt+'triangle.png', copy_opt+'triangle-'+str(field)+'-'+str(objid)+'.png')
else:
triangle_figure.show()
def make_plots(whichx, fname):
x, y, xerr, yerr = load_data(whichx)
with h5py.File("%s_samples.h5" % whichx) as f:
samp = f["samples"][...]
m, c, sig = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),
zip(*np.percentile(samp, [16, 50, 84], axis=0)))
pars = [m[0], c[0], sig[0]]
print pars
plt.clf()
plt.errorbar(x, y, xerr=xerr, yerr=yerr, fmt="k.", capsize=0, ecolor=".7")
plt.plot(x, model1(pars, x), "k")
ndraws = 100
p0s = np.random.choice(samp[:, 0], ndraws)
p1s = np.random.choice(samp[:, 1], ndraws)
p2s = np.random.choice(samp[:, 2], ndraws)
for i in range(ndraws):
y = p0s[i] * x + p1s[i]
plt.plot(x, (y + p2s[i]), "k", alpha=.1)
plt.savefig("mcmc_%s_%s" % (whichx, fname))
labels = ["$m$", "$c$", "$\sigma$"]
plt.clf()
fig = triangle.corner(samp, labels=labels)
fig.savefig("triangle_%s_%s" % (whichx, fname))
def plot_corner(posterior, percentiles, parvals=None):
"""
Local version of a corner plot to allow bespoke truth values
posterior: posterior object
percentiles: percentiles to draw on 1D histograms
parvals: dictionary of parameters with true values. These parameters are
used to select which params in posterior to use for the triangle plot, as
well as to draw the target values
"""
if parvals == None:
print >> sys.stderr, "need param names and values"
parnames = parvals.keys()
parnames = filter(lambda x: x in posterior.names, parnames)
truths = [parvals[p] for p in parnames]
data = np.hstack([posterior[p].samples for p in parnames])
extents = [get_extent(posterior, name, parvals) for name in parnames]
trifig = triangle.corner(data,
labels=parnames,
truths=truths,
quantiles=percentiles,
truth_color='r',
extents=extents)
return trifig
def MCMC(theta, x, y, yerr, M1, ecc, fname, n, sub, plot=False):
nwalkers, ndim = 32, 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, M1, ecc))
p0, lp, state = sampler.run_mcmc(p0, 500)
sampler.reset()
p0, lp, state = sampler.run_mcmc(p0, 5000)
if plot == True:
fig_labels = ['P', 'M2', 'T0', 'V0', 'omega']
flatchain = sampler.chain[:, 50:, :].reshape((-1, ndim))
fig = triangle.corner(flatchain, truths=theta, labels=fig_labels)
plt.savefig("%s_triangle" % fname)
print "saving samples"
f = h5py.File("%s/results/%s_%s_%s_samples" % (DIR, n, fname, sub), "w")
data = f.create_dataset("samples", np.shape(sampler.chain))
data[:, :] = np.array(sampler.chain)
f.close()
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)))
np.savetxt("%s/results/%s_%s_%s_results.txt" % (DIR, n, fname, sub),
mcmc_result)
return mcmc_result
def run_EMCEE(initial_position, dimensions, walkers, step_number, burn):
ndim, nwalkers = dimensions, walkers
pos = [initial_position + 1e-2*np.random.randn(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(x, y, yerr))
# Clear and run the production chain.
print("Running MCMC...")
sampler.run_mcmc(pos, step_number, rstate0=np.random.get_state())
print("Done.")
plt.clf()
fig, axes = plt.subplots(4, 1, sharex=True, figsize=(8, 9))
axes[0].plot(sampler.chain[:, :, 0].T, color="k", alpha=0.4)
axes[0].yaxis.set_major_locator(MaxNLocator(5))
axes[0].axhline(T1_ml, color="#888888", lw=2)
axes[0].set_ylabel("$T1$")
axes[1].plot(sampler.chain[:, :, 1].T, color="k", alpha=0.4)
axes[1].yaxis.set_major_locator(MaxNLocator(5))
axes[1].axhline(P2_ml, color="#888888", lw=2)
axes[1].set_ylabel("$P2$")
axes[2].plot(sampler.chain[:, :, 2].T, color="k", alpha=0.4)
axes[2].yaxis.set_major_locator(MaxNLocator(5))
axes[2].axhline(T2_ml, color="#888888", lw=2)
axes[2].set_ylabel("$T2$")
axes[3].plot(sampler.chain[:, :, 3].T, color="k", alpha=0.4)
axes[3].yaxis.set_major_locator(MaxNLocator(5))
axes[3].axhline(P3_ml, color="#888888", lw=2)
axes[3].set_ylabel("$P3$")
fig.tight_layout(h_pad=0.0)
fig.savefig("line-time_4_variables_"+str(counter)+".png")
# Make the triangle plot.
burnin = burn
samples = sampler.chain[:, burnin:, :].reshape((-1, ndim))
fig = triangle.corner(samples, labels=["$T1$","$P2$", "$T2$","$P3$"], truths=[T1_ml, P2_ml, T2_ml, P3_ml])
fig.savefig("line-triangle_4_variables_"+str(counter)+".png")
def triangle_gen():
plt.clf()
plot_chi()
burnIn = input('Burn off how many steps? ')
samples = chainDat[:,burnIn:,:].reshape((-1,ndim))
triangle.corner(samples, labels=['$R_{In}$ [AU]','$\Delta$R [AU]','log($M_{D}$ [$M_{Earth}$])','i [degrees]','PA [degrees]'], truths=[best_disk[0],best_disk[1],best_disk[2],best_disk[3],best_disk[4]], truth_color='g', quantiles=[0.16,.5,.84], show_titles=True, plot_contours=True)
plt.savefig('MCMCRUNS/'+append+'/'+whatbywhat+'/'+disk_name+'_'+whatbywhat+'_'+append+'_Triangle.png')
plt.show()
values = np.zeros((ndim,3))
for i in range(ndim):
chainSqueeze=chainDat[:,burnIn:,i].reshape(-1)
quantiles = mstats.mquantiles(chainSqueeze,prob=[.16,.5,.84],axis=None)
values[i,0] = quantiles[1] #median
values[i,1] = quantiles[2]-quantiles[1] #plus one sigma
values[i,2] = quantiles[0]-quantiles[1] #minus one sigma
def triangle_plot(self, labels=None, truths=None):
samples = self.model.get_burned_in_samples()
if labels is None:
labels = greek_label_mapping(self.model.all_param_names)
fig = triangle.corner(samples,
labels=labels,
truths=truths)
def sample(ndim, nwalkers, nsteps, start, w, ur, sigma_ur, nuvu, sigma_nuvu, age, pd, ps):
if len(age) != len(ur):
raise SystemExit("Number of ages does not coincide with number of galaxies...")
p0 = [start + 1e-4 * N.random.randn(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(w, ur, sigma_ur, nuvu, sigma_nuvu, age, pd, ps))
# burn in
pos, prob, state = sampler.run_mcmc(p0, 50)
# reset and run with last positions of burn in run
sampler.reset()
print "RESET", pos
sampler.run_mcmc(pos, nsteps)
samples = sampler.chain[:, :, :].reshape((-1, ndim))
samples_save = (
"/Users/becky/Projects/Green-Valley-Project/bayesian/find_t_tau/gv/not_clean/samples_gv_not_clean_"
+ str(len(samples))
+ "_"
+ str(len(age))
+ "_"
+ str(time.strftime("%H_%M_%d_%m_%y"))
+ ".npy"
)
N.save(samples_save, samples)
fig = triangle.corner(samples, labels=[r"$ t_{smooth} $", r"$ \tau_{smooth} $", r"$ t_{disc} $", r"$ \tau_{disc}$"])
fig.savefig(
"triangle_t_tau_gv_not_clean_"
+ str(len(samples))
+ "_"
+ str(len(age))
+ "_"
+ str(time.strftime("%H_%M_%d_%m_%y"))
+ ".pdf"
)
return samples, fig
def results(fn):
model, sampler = pickle.load(open(fn, "rb"))
mu = np.median(model.f)
ppm = lambda f: (f / mu - 1) * 1e6
# Plot the data.
fig = pl.figure(figsize=(6, 6))
ax = fig.add_subplot(111)
ax.plot(model.t, ppm(model.f), ".k")
ax.set_xlim(np.min(model.t), np.max(model.t))
ax.set_xlabel("time since transit [days]")
ax.set_ylabel("relative flux [ppm]")
fig.subplots_adjust(left=0.2, bottom=0.2, top=0.9, right=0.9)
# Plot the predictions.
samples = sampler.flatchain
t = np.linspace(model.t.min(), model.t.max(), 1000)
for i in np.random.randint(len(samples), size=10):
model.vector = samples[i]
ax.plot(t, ppm(model.predict(t)), color="#4682b4", alpha=0.5)
fig.savefig(os.path.splitext(fn)[0] + "-results.pdf")
# Plot the corner plot.
fig = triangle.corner(samples,
labels=model.labels,
truths=model.true_vector)
fig.savefig(os.path.splitext(fn)[0] + "-triangle.png")
def bayesian_fitting(x, y, y_error, distance, nwalkers, ndim, cores, nburn,
nsteps, galaxy_name):
np.random.seed(0)
print('Number of free parameters in our model =', ndim)
starting_guesses = np.random.rand(nwalkers, ndim)
starting_guesses[:, 0] *= 5
starting_guesses[:, 1] *= 25
starting_guesses[:, 2] *= 2.5
pool = Pool(cores)
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
log_post_one_with_beta,
args=[x, y, y_error, distance],
pool=pool)
sampler.run_mcmc(starting_guesses, nsteps)
sample = sampler.chain # shape = (nwalkers, nsteps, ndim)
sample = sampler.chain[:, nburn:, :].reshape(-1, ndim)
logposteriors = sampler.lnprobability[:, nburn:].reshape(-1)
answers = np.mean(sample[np.where(logposteriors == np.max(logposteriors))],
0).reshape(ndim)
figure = triangle.corner(sample,
labels=['Log(Dust Mass)', 'Temp', 'Beta'],
truths=answers)
figure.savefig("triangle_three_dims_" + galaxy_name + ".png", format='png')
sampler.pool.terminate()
plt.clf()
plt.close()
return answers
def _run_corner(nm, pandas=False, N=10000, seed=1234, ndim=3, ret=False,
factor=None, **kwargs):
print(" .. {0}".format(nm))
if not os.path.exists(FIGURE_PATH):
os.makedirs(FIGURE_PATH)
np.random.seed(seed)
data1 = np.random.randn(ndim*4*N/5.).reshape([4*N/5., ndim])
data2 = (5 * np.random.rand(ndim)[None, :]
+ np.random.randn(ndim*N/5.).reshape([N/5., ndim]))
data = np.vstack([data1, data2])
if factor is not None:
data[:, 0] *= factor
data[:, 1] /= factor
if pandas:
data = pd.DataFrame.from_items(zip(map("d{0}".format, range(ndim)),
data.T))
fig = triangle.corner(data, **kwargs)
fig.savefig(os.path.join(FIGURE_PATH, "triangle_{0}.png".format(nm)))
if ret:
return fig
else:
pl.close(fig)
def triangle_plot(fname, mcmc_result, flatchain, fig_labels):
print 'yes'
mres = np.array(mcmc_result)[:, 0]
print 'mcmc_result = ', mres
print len(mres), len(fig_labels)
fig = triangle.corner(flatchain, truths=mres, labels=fig_labels)
fig.savefig("triangle_%s.png" % fname)
def sample_lnprob(weight_index):
import emcee
ndim = 4
nwalkers = 8 * ndim
print("using {} walkers".format(nwalkers))
p0 = np.vstack((np.random.uniform(-0.5, 2, size=(1, nwalkers)),
np.random.uniform(50, 300, size=(1, nwalkers)),
np.random.uniform(0.2, 1.5, size=(1, nwalkers)),
np.random.uniform(0.2, 1.5, size=(1, nwalkers)))).T
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=(weight_index,), threads=cfg['threads'])
print("Running Sampler")
pos, prob, state = sampler.run_mcmc(p0, cfg['burn_in'])
print("Burn-in complete")
sampler.reset()
sampler.run_mcmc(pos, cfg['samples'])
samples = sampler.flatchain
np.save(cfg['outdir'] + "samples_w{}.npy".format(weight_index), samples)
import triangle
fig = triangle.corner(samples)
fig.savefig(cfg['outdir'] + "triangle_w{}.png".format(weight_index))
def plot_PDFtriangle(self, parameterset, labels):
if parameterset == '10pars':
figure = triangle.corner(self.chain.flatchain,
labels=labels,
plot_contours=True,
plot_datapoints=False,
show_titles=True,
quantiles=[0.16, 0.50, 0.84])
elif parameterset == 'int_lums':
figure = triangle.corner(self.int_lums.T,
labels=labels,
plot_contours=True,
plot_datapoints=False,
show_titles=True,
quantiles=[0.16, 0.50, 0.84])
return figure
def weights_triangle_plot(self, labels=None, thin=1):
samples = self.model.get_burned_in_samples()
if labels is None:
labels = ["w%d" % idx for idx in range(len(self.model.fit_models))]
#labels = greek_label_mapping(labels)
print(labels)
fig = triangle.corner(samples[::thin,
-len(self.model.fit_models):]) #,
def thumbPlot(chain, labels, **kwargs):
seaborn.set(style='ticks')
seaborn.set_style({"xtick.direction": "in", "ytick.direction": "in"})
fig = triangle.corner(chain,
labels=labels,
bins=50,
label_kwargs=dict(fontsize=18),
**kwargs)
return fig
def triangle_plot(self):
samples = self.model.get_burned_in_samples()
labels = [
"$%s$" % param_name for model in self.model.fit_models
for param_name in model.all_param_names
]
labels.extend(["$%s$" for model in self.model.fit_models])
fig = triangle.corner(samples, labels=labels)
def MCMC(theta, x, y, yerr, fname, burn_in, nsteps, nruns):
# calculate initial likelihood and plot initial hparams
xs = np.linspace(min(x), max(x), 1000)
k = theta[0] * ExpSquaredKernel(theta[1]) * ExpSine2Kernel(theta[2], theta[4])
k += WhiteKernel(theta[3])
gp = george.GP(k)
print 'initial lnlike = ', lnlike(theta, x, y, yerr)
mu, cov = predict(theta, xs, x, y, yerr)
plt.clf()
plt.errorbar(x, y, yerr=yerr, fmt='k.', capsize=0)
plt.plot(xs, mu, 'r')
std = np.sqrt(np.diag(cov))
# plt.fill_between(mu-std, mu+std, color='r', alpha='.5')
plt.savefig('%s_init' % fname)
# setup sampler
nwalkers, ndim = 32, len(theta)
p0 = [theta+1e-4*np.random.rand(ndim) for i in range(nwalkers)]
args = [x, y, yerr]
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=args)
print("Burning in...")
p0, lp, state = sampler.run_mcmc(p0, burn_in)
sampler.reset()
for i in range(nruns):
print 'Running... ', i
p0, lp, state = sampler.run_mcmc(p0, nsteps)
# results
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
mcmc_result = map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
mres = np.array(mcmc_result)[:, 0]
print 'mcmc_result = ', np.exp(mres)
np.savetxt("parameters_%s.txt" % fname, np.array(mcmc_result))
print "saving samples"
f = h5py.File("samples%s" % fname, "w")
data = f.create_dataset("samples", np.shape(sampler.chain))
data[:,:] = np.array(sampler.chain)
f.close()
# make triangle plot
fig_labels = ["$A$", "$l1$", "$l2$", "$wn$", "$P$"]
fig = triangle.corner(samples, truths=mres, labels=fig_labels)
fig.savefig("triangle_%s.png" % fname)
# plot result
mu, cov = predict(mres, xs, x, y, yerr)
plt.clf()
plt.errorbar(x, y, yerr=yerr, fmt='k.', capsize=0)
plt.plot(xs, mu, 'r')
plt.savefig('%s_final' % fname)
def make_plot(sampler,
x,
y,
yerr,
ID,
DIR,
traces=False,
tri=False,
prediction=True):
nwalkers, nsteps, ndims = np.shape(sampler)
flat = np.reshape(sampler, (nwalkers * nsteps, ndims))
mcmc_result = map(lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(flat, [16, 50, 84], axis=0)))
mcmc_result = np.array([i[0] for i in mcmc_result])
print("\n", np.exp(np.array(mcmc_result[-1])), "period (days)", "\n")
print(mcmc_result)
np.savetxt("%s/%s_result.txt" % (DIR, ID), mcmc_result)
fig_labels = ["A", "l", "G", "s", "P"]
if traces:
print("Plotting traces")
for i in range(ndims):
plt.clf()
plt.plot(sampler[:, :, i].T, 'k-', alpha=0.3)
plt.ylabel(fig_labels[i])
plt.savefig("%s/%s_%s.png" % (DIR, ID, fig_labels[i]))
if tri:
print("Making triangle plot")
flat[:, -1] = np.exp(flat[:, -1])
try:
fig = corner.corner(flat, labels=fig_labels)
except:
fig = triangle.corner(flat, labels=fig_labels)
fig.savefig("%s/%s_triangle" % (DIR, ID))
print("%s/%s_triangle.png" % (DIR, ID))
if prediction:
print("plotting prediction")
theta = np.exp(np.array(mcmc_result))
k = theta[0] * ExpSquaredKernel(theta[1]) \
* ExpSine2Kernel(theta[2], theta[4])
gp = george.GP(k, solver=george.HODLRSolver)
gp.compute(x, yerr)
xs = np.linspace(x[0], x[-1], 1000)
mu, cov = gp.predict(y, xs)
plt.clf()
plt.errorbar(x - x[0], y, yerr=yerr, **reb)
plt.xlabel("$\mathrm{Time~(days)}$")
plt.ylabel("$\mathrm{Normalised~Flux}$")
plt.plot(xs, mu, color=cols.lightblue)
plt.xlim(min(x), max(x))
plt.savefig("%s/%s_prediction" % (DIR, ID))
print("%s/%s_prediction.png" % (DIR, ID))
def plot_global(nsne, under_model):
samples = np.load("samples_%s/globalsamples_%s.npy"%(under_model.name(nsne),under_model.name(nsne)))
labels = under_model.labels
truths = under_model.initial
fig = triangle.corner(samples, labels=labels, bins=15,
truths=truths)
plt.savefig('globalsamples_%s.png'%(under_model.name(nsne)))
return
def plot_triangle(model, quantiles=[0.16, 0.5, 0.84]):
import triangle
seaborn.set_style('ticks')
fixed = np.array([model.fixed[n] for n in model.param_names])
labels = [tex_names[n] for n in np.array(model.param_names)[~fixed]]
fig = triangle.corner(model.chain_nb, quantiles=quantiles,
labels=labels, verbose=False, plot_contours=False)
seaborn.despine()
return fig
def MCMC(theta, x, y, yerr, bm, bp):
# Sample the posterior probability for m.
nwalkers, ndim = 64, len(theta)
p0 = [theta + 1e-4 * np.random.rand(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers,
ndim,
lnprob,
args=(x, y, yerr, bm, bp))
bi, pr = 200, 2000
start = time.clock()
print("Burn-in")
p0, lp, state = sampler.run_mcmc(p0, bi)
sampler.reset()
print("Production run")
sampler.run_mcmc(p0, pr)
elapsed = time.clock() - start
print 'time = ', elapsed / 60., 'mins'
print("Making triangle plots")
fig_labels = ["$A$", "$l_2$", "$l_1$", "$s$", "$P$"]
fig = triangle.corner(sampler.flatchain,
truths=theta,
labels=fig_labels[:len(theta)])
fig.savefig("triangle.png")
print("Plotting traces")
pl.figure()
for i in range(ndim):
pl.clf()
pl.axhline(theta[i], color="r", zorder=2)
pl.plot(sampler.chain[:, :, i].T, 'k-', alpha=0.3, zorder=1)
pl.savefig("{0}.png".format(i))
# Flatten chain
samples = sampler.chain[:, 50:, :].reshape((-1, ndim))
# Find values
mcmc_result = map(lambda v: (v[1], v[2] - v[1], v[1] - v[0]),
zip(*np.percentile(samples, [16, 50, 84], axis=0)))
theta = np.array(mcmc_result)[:, 0]
print 'mcmc result = ', theta
like = lnlike(theta, x, y, yerr)
print "Final lnlike = ", like
# plot mcmc result
pl.clf()
pl.errorbar(x, y, yerr=yerr, fmt='k.')
xs = np.arange(min(x), max(x), 0.01)
pl.plot(xs, predict(xs, x, y, yerr, theta, theta[4])[0], 'r-')
pl.xlabel('time (days)')
pl.savefig('result')
def triangle_plot(self, labels=None):
samples = self.model.get_burned_in_samples()
if labels is None:
labels = [
"$%s$" % (param_name) for model in self.model.fit_models
for param_name in model.function_params
]
labels.append("$sigma$")
labels.extend(
["$w%d$" % idx for idx in range(len(self.model.fit_models))])
labels = greek_label_mapping(labels)
fig = triangle.corner(samples, labels=labels)
def vis2hammer(cpo,ivar=[1., 0.5],ndim=2,nwalcps=50,plot=False,nsteps=1000,burnin=100,paramlimits=[0.5,5.,0.,1.],muprior=[0.64,0.03]): '''Default implementation of emcee, the MCMC Hammer, for closure phase fitting. Requires a closure phase object cpo, and is best called with ivar chosen to be near the peak - it can fail to converge otherwise.''' def lnprior(params): if paramlimits[0] < params[0] < paramlimits[1] and paramlimits[2] < params[1] < paramlimits[3]: return -0.5*((params[1]-muprior[0])/muprior[1])**2. #0.0 return -np.inf def lnprob(params,u,v,wavels,visdata,viserr): return lnprior(params) + vis_loglikelihood(params,u,v,wavels,visdata,viserr) ivar = np.array(ivar) # initial parameters for model-fit p0 = [ivar + 0.1*ivar*np.random.rand(ndim) for i in range(nwalcps)] # initialise walcps in a ball print 'Running emcee now!' t0 = time.time() sampler = emcee.EnsembleSampler(nwalcps, ndim, lnprob, args=[cpo.u,cpo.v,cpo.wavels,cpo.vis2,cpo.vis2err]) # burn in pos,prob,state = sampler.run_mcmc(p0, burnin) print 'Burnt in' sampler.reset() # restart sampler.run_mcmc(pos,nsteps) tf = time.time() print 'Time elapsed =', tf-t0,'s' ds = sampler.flatchain[:,0] mus = sampler.flatchain[:,1] meand = np.mean(ds) derr = np.std(ds) meanmu = np.mean(mus) dmu = np.std(mus) print 'Diameter',meand,'pm',derr,'mas' print 'Limb-Darkening',meanmu,'pm',dmu if plot==True: fig = triangle.corner(sampler.flatchain, labels=["$d$ (mas)", "$\mu$"]) plt.show() return sampler.flatchain