def sample_parallel_tempering(self, n_temps, n_walkers, burn_in, n_samples, quiet=False):
"""
Sample with parallel tempering
:param: n_temps
:param: n_walkers
:param: burn_in
:param: n_samples
:return: MCMC samples
"""
free_parameters = self._likelihood_model.free_parameters
n_dim = len(free_parameters.keys())
sampler = emcee.PTSampler(n_temps, n_walkers, n_dim, self._log_like, self._log_prior)
# Get one starting point for each temperature
p0 = np.empty((n_temps, n_walkers, n_dim))
for i in range(n_temps):
p0[i, :, :] = self._get_starting_points(n_walkers)
print("Running burn-in of %s samples...\n" % burn_in)
p, lnprob, lnlike = sample_with_progress("Burn-in", p0, sampler, burn_in)
# Reset sampler
sampler.reset()
print("\nSampling\n")
_ = sample_with_progress("Sampling", p, sampler, n_samples,
lnprob0=lnprob, lnlike0=lnlike)
self._sampler = sampler
# Now build the _samples dictionary
self._raw_samples = sampler.flatchain.reshape(-1, sampler.flatchain.shape[-1])
self._log_probability_values = None
self._log_like_values = None
self._marginal_likelihood = None
self._build_samples_dictionary()
self._build_results()
# Display results
if not quiet:
self._results.display()
return self.samples
def __init__(self,
likelihood_evaluator,
ntemps,
nwalkers,
pool=None,
burn_in_iterations=None):
try:
import emcee
except ImportError:
raise ImportError("emcee is not installed.")
# construct the sampler: PTSampler needs the likelihood and prior
# functions separately
likelihood_evaluator.set_callfunc('loglikelihood')
ndim = len(likelihood_evaluator.waveform_generator.variable_args)
sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
likelihood_evaluator,
likelihood_evaluator._prior,
pool=pool)
# initialize
super(EmceePTSampler, self).__init__(sampler,
likelihood_evaluator,
min_burn_in=burn_in_iterations)
self._nwalkers = nwalkers
self._ntemps = ntemps
def __init__(self,
likelihood_evaluator,
ntemps,
nwalkers,
pool=None,
likelihood_call=None):
try:
import emcee
except ImportError:
raise ImportError("emcee is not installed.")
if likelihood_call is None:
likelihood_call = likelihood_evaluator
# construct the sampler: PTSampler needs the likelihood and prior
# functions separately
ndim = len(likelihood_evaluator.variable_args)
sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
_callloglikelihood(likelihood_call),
_callprior(likelihood_call),
pool=pool)
# initialize
super(EmceePTSampler, self).__init__(sampler, likelihood_evaluator)
self._nwalkers = nwalkers
self._ntemps = ntemps
def __init__(self, model, ntemps, nwalkers, betas=None,
checkpoint_interval=None, checkpoint_signal=None,
loglikelihood_function=None,
nprocesses=1, use_mpi=False):
self.model = model
# create a wrapper for calling the model
if loglikelihood_function is None:
loglikelihood_function = 'loglikelihood'
# frustratingly, emcee_pt does not support blob data, so we have to
# turn it off
model_call = models.CallModel(model, loglikelihood_function,
return_all_stats=False)
# these are used to help paralleize over multiple cores / MPI
models._global_instance = model_call
model_call = models._call_global_model
prior_call = models._call_global_model_logprior
self.pool = choose_pool(mpi=use_mpi, processes=nprocesses)
# construct the sampler: PTSampler needs the likelihood and prior
# functions separately
ndim = len(model.variable_params)
self._sampler = emcee.PTSampler(ntemps, nwalkers, ndim,
model_call, prior_call, pool=self.pool,
betas=betas)
self.nwalkers = nwalkers
self._ntemps = ntemps
self._checkpoint_interval = checkpoint_interval
self._checkpoint_signal = checkpoint_signal
def calculate_logevidence(cls,
fp,
thin_start=None,
thin_end=None,
thin_interval=None):
"""Calculates the log evidence from the given file using emcee's
thermodynamic integration.
Parameters
----------
fp : InferenceFile
An open file handler to read the stats from.
thin_start : int
Index of the sample to begin returning stats. Default is to read
stats after burn in. To start from the beginning set thin_start
to 0.
thin_interval : int
Interval to accept every i-th sample. Default is to use the
`fp.acl`. If `fp.acl` is not set, then use all stats
(set thin_interval to 1).
thin_end : int
Index of the last sample to read. If not given then
`fp.niterations` is used.
Returns
-------
lnZ : float
The estimate of log of the evidence.
dlnZ : float
The error on the estimate.
"""
try:
import emcee
except ImportError:
raise ImportError("emcee is not installed.")
logstats = cls.read_likelihood_stats(fp,
thin_start=thin_start,
thin_end=thin_end,
thin_interval=thin_interval,
temps='all',
flatten=False)
# get the likelihoods
logls = logstats['loglr'] + fp.lognl
# we need the betas that were used
betas = fp.attrs['betas']
# annoyingly, theromdynaimc integration in PTSampler is an instance
# method, so we'll implement a dummy one
ntemps = fp.ntemps
nwalkers = fp.nwalkers
ndim = len(fp.variable_args)
dummy_sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
None,
None,
betas=betas)
return dummy_sampler.thermodynamic_integration_log_evidence(
logls=logls, fburnin=0.)
def run_chain(self,
n_walkers,
n_steps,
ntemps,
reset=False,
name='mcmc',
filename='MCMC.h5'):
ndim = 3
theta_initial = [0, 0.58, -0.014] #gamma11, M11, N11
if self.prior_type == 'flat':
cov = np.diagflat([
self.sub(self.priors['gamma11']),
self.sub(self.priors['M11']),
self.sub(self.priors['N11'])
])
elif self.prior_type == 'gaussian':
cov = np.diagflat([
self.priors['gamma11'][1], self.priors['M11'][1],
self.priors['N11'][1]
])
walkers_positions = np.zeros((ntemps, n_walkers, ndim))
lnikely = np.zeros((ntemps, n_walkers, n_steps))
i = 0
j = 0
while (i < ntemps):
while (j < n_walkers):
ran = np.random.multivariate_normal(theta_initial, cov)
if self.prior_type == 'flat':
if self.lnprior(ran) == 0.0:
walkers_positions[i][j] = ran
elif self.prior_type == 'gaussian':
walkers_positions[i][j] = ran
j += 1
i += 1
j = 0
with Pool() as pool:
Sampler = emcee.PTSampler(nwalkers=n_walkers,
dim=ndim,
ntemps=ntemps,
logl=self.lnlike,
logp=self.lnprob,
pool=pool)
start = time.time()
Sampler.run_mcmc(
walkers_positions, N=n_steps, storechain=True
) #,progress=True)#,skip_initial_state_check=True)
end = time.time()
multi_time = end - start
print("Multiprocessing took {0:.1f} seconds".format(multi_time))
chain = np.save('MCMC_PT', Sampler.chain)
chi2 = np.save('chi2', Sampler.lnprobability)
return Sampler
def __init__(self,
pars,
cov,
regconsts,
nwalkers=None,
nthreads=1,
ntemps=5):
self.t0 = time.time()
global hackpars, hackcosts, nregs
self.pars = []
self.costs = []
self.deterministics = []
self.regs = regconsts
self.nregs = len(self.regs)
self.ntemps = ntemps
self.nthreads = nthreads
for par in pars:
try:
if par.observed == True:
self.costs.append(par)
else:
self.pars.append(par)
except:
self.deterministics.append(par)
#now append the regconsts to the pars, and give them a dummy covariance
#for reg in self.regs:
# #break
# self.pars.append(reg)
# if type(cov)==list:
# self.cov.append(reg.value/100.)
# else:
# cov=numpy.append(cov,reg.value/100.)
self.nvars = len(self.pars)
self.ndim = self.nvars
self.cov = cov
if nwalkers == None:
self.nwalkers = self.ndim * 8
else:
self.nwalkers = nwalkers
hackpars = self.pars
hackcosts = self.costs
nregs = self.nregs
print emcee.__file__
try:
self.sampler = emcee.PTSampler(self.ntemps,
self.nwalkers,
self.ndim,
optFunc,
logp,
threads=nthreads)
except AttributeError:
"There is no Parallel Tempered Emcee sampler installed, try the untempered option?"
def run(self):
print("enabling ParallelTempering sampler.")
pos0 = [[self.para_guess + 1.0e-8*np.random.randn(self.ndim) for j in range(self.nwalkers)] for k in range(self.ntemps)]
sampler = emcee.PTSampler(self.ntemps, self.nwalkers, self.ndim, self.LikelihoodsObj.lnlikelihood, self.PriorsObj.lnprior)
# burn-in
print("start burning in. nburn:", self.nburn)
for j, result in enumerate(sampler.sample(pos0, iterations=self.nburn, thin=10)):
self._display_bar(j, self.nburn)
sys.stdout.write("\n")
pos, lnpost, lnlike = result
sampler.reset()
# actual iteration
print("start iterating. nsteps:", self.nsteps)
for j, result in enumerate(sampler.sample(pos, iterations=self.nsteps)):#, lnprob0=lnpost, lnlike0=lnlike
self._display_bar(j, self.nsteps)
sys.stdout.write("\n")
# modify samples
samples = sampler.chain[0,:,:,:].reshape((-1,self.ndim))
# fold the parameter space of i
if self.FitParametersObj.ifFreeInclination:
idx = samples[:,-1]<0.
samples[idx,-1]=-samples[idx,-1]
idx = samples[:,-1]>np.pi/2.
samples[idx,-1]=np.pi-samples[idx,-1]
self.samples = samples
# save evidence
self.evidence = sampler.thermodynamic_integration_log_evidence()
print("Bayesian evidence lnZ: {:0.5f}".format(self.evidence[0]))
print("Bayesian evidence error dlnZ: {:0.5f}".format(self.evidence[1]))
# save estimation result
# 16, 50, 84 quantiles
result = np.array(list(map(lambda v: (v[1], v[2]-v[1], v[1]-v[0]),
zip(*np.percentile(samples, [16, 50, 84],axis=0)))))
self.para_fit = result[:,0]
# maximum
para_fitmax = np.zeros(self.ndim)
for ipara in range(self.ndim):
n, bins, _ = plt.hist(samples[:,ipara], bins=80)
idx = np.where(n == n.max())[0][0]
para_fitmax[ipara] = bins[idx:idx+1].mean()
self.para_fitmax = para_fitmax
self.result = np.concatenate([result, para_fitmax.reshape(self.ndim,1)], axis=1)
# save acceptance fraction
self.acceptance_fraction = np.array([np.mean(sampler.acceptance_fraction)])
print("Mean acceptance fraction: {:0.3f}".format(self.acceptance_fraction[0]))
return
def walkers_parallel_tempered_decay(mN1_data,
guesses,
time_min,
time_max,
fromcsv,
dataN,
runN,
gaus_var,
nwalkers,
nsteps,
prior,
scale_factor=100 * 100,
withlaserskew=False):
"""
This function samples the posterior using MCMC. It is recommended to use 1e-4 for gaus_var when withlaserskew=False,
and 1e-3 for gaus_var when withlaserskew=True.
Parameters:
mN1_data: fluoresence data for each time step (RRDataContainer)
guesses: the initial guesses for the parameters of the model (array of floats)
time_min: minimum Raman-Rabi pulse time (float)
time_max: maximum Raman-Rabi pulse time (float)
fromcsv: marks whether these data were read from a CSV file (bool)
dataN: number of experiment repititions summed (int)
runN: number of runs over which the experiment was done (int)
gaus_var: variance of the gaussian that defines the starting positions (float)
nwalkers: the number of walkers with which to sample (int)
nsteps: the number of steps each walker should take (int)
withlaserskew (optional): marks whether to use laserskew functions or not (bool)
priors (optional): an array specifying the priors to use in log_prior
Returns:
sampler: the sampler object which now contains the samples taken by nwalkers
walkers over nsteps steps
"""
ndim = len(guesses)
# use temperature ladder specified in Gregory (see p. 330)
betas = np.array([1.0, 0.7525, 0.505, 0.2575, 0.01])
ntemps = len(betas)
sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
decay_loglikelihood,
log_prior,
betas=betas,
loglargs=[
mN1_data, time_min, time_max, fromcsv, dataN,
runN, scale_factor
],
loglkwargs={'withlaserskew': withlaserskew},
logpkwargs={'priors': prior})
starting_positions = np.tile(guesses, (
ntemps, nwalkers, 1)) + 1e-4 * np.random.randn(ntemps, nwalkers, ndim)
sampler.run_mcmc(starting_positions, nsteps)
return sampler
def calculate_logevidence(cls,
filename,
thin_start=None,
thin_end=None,
thin_interval=None):
"""Calculates the log evidence from the given file using ``emcee_pt``'s
thermodynamic integration.
Parameters
----------
filename : str
Name of the file to read the samples from. Should be an
``EmceePTFile``.
thin_start : int
Index of the sample to begin returning stats. Default is to read
stats after burn in. To start from the beginning set thin_start
to 0.
thin_interval : int
Interval to accept every i-th sample. Default is to use the
`fp.acl`. If `fp.acl` is not set, then use all stats
(set thin_interval to 1).
thin_end : int
Index of the last sample to read. If not given then
`fp.niterations` is used.
Returns
-------
lnZ : float
The estimate of log of the evidence.
dlnZ : float
The error on the estimate.
"""
with cls._io(filename, 'r') as fp:
logls = fp.read_raw_samples(['loglikelihood'],
thin_start=thin_start,
thin_interval=thin_interval,
thin_end=thin_end,
temps='all',
flatten=False)
logls = logls['loglikelihood']
# we need the betas that were used
betas = fp.betas
# annoyingly, theromdynaimc integration in PTSampler is an instance
# method, so we'll implement a dummy one
ntemps = fp.ntemps
nwalkers = fp.nwalkers
ndim = len(fp.variable_params)
dummy_sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
None,
None,
betas=betas)
return dummy_sampler.thermodynamic_integration_log_evidence(
logls=logls, fburnin=0.)
def run_one_model(model, data, prior_vals, ns, pool=None):
# Vector of estimated parameters
pe = [p for p in model.parameters if p.name.startswith('k')]
# Generate model equations
generate_equations(model)
Solver._use_inline = True
sol = Solver(model, numpy.linspace(0, 10, 10))
sol.run()
# Number of temperatures, dimensions and walkers
ntemps = 20
ndim = len(pe)
blocksize = 48
nwalkers = get_num_walkers(ndim, blocksize)
print 'Running %d walkers at %d temperatures for %d steps.' %\
(nwalkers, ntemps, ns)
sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
likelihood,
prior,
threads=1,
pool=pool,
betas=None,
a=2.0,
Tmax=None,
loglargs=[model, data],
logpargs=[model, prior_vals],
loglkwargs={},
logpkwargs={})
# Random initial parameters for walkers
p0 = numpy.ones((ntemps, nwalkers, ndim))
for i in range(ntemps):
for j in range(nwalkers):
for k, pp in enumerate(pe):
p0[i, j, k] = prior_vals.vals[j][pp.name]
print p0
# Run sampler
fname = scratch_path + 'chain_%s.dat' % model.name
step = 0
for result in sampler.sample(p0, iterations=ns, storechain=True):
print '---'
position = result[0]
with open(fname, 'a') as fh:
for w in range(nwalkers):
for t in range(ntemps):
pos_str = '\t'.join(['%f' % p for p in position[t][w]])
fh.write('%d\t%d\t%d\t%s\n' % (step, w, t, pos_str))
step += 1
return sampler
def PTSampler(self, ntemps, nwalkers, **kwargs):
self.ntemps = ntemps
self.nwalkers = nwalkers
self.__sampler = "PTSampler"
if self.lnlikeType == "gcs":
loglargs = (self.x, self.y, self.xerr, self.yerr, self.flag)
else:
loglargs = (self.x, self.y, self.xerr, self.yerr)
self.sampler = emcee.PTSampler(ntemps, nwalkers, self.ndim,
logl=self.lnlike, logp=lnprior,
loglargs=loglargs, logpargs=[self.pRanges], **kwargs)
print("[linfit]: Use the PTSampler.")
return self.sampler
def PTSampler(self, ntemps, nwalkers, **kwargs):
if self.__modelunct:
self.__lnlike = lnlike_gp
else:
self.__lnlike = lnlike
self.sampler = emcee.PTSampler(ntemps, nwalkers, self.__dim,
logl=self.__lnlike, logp=lnprior,
loglargs=[self.__data, self.__model],
logpargs=[self.__data, self.__model,
self.__modelunct, self.__unctDict],
**kwargs)
self.__ntemps = ntemps
self.__nwalkers = nwalkers
self.__sampler = "PTSampler"
return self.sampler
def get_sampler(self, **kwargs):
if not self.pt:
return emcee.EnsembleSampler(self.nwalkers,
self.ndim,
self.lnprob,
args=self.lnlike_args,
**kwargs
)
else:
return emcee.PTSampler(self.ntemps,
self.nwalkers,
self.ndim,
logl=self.lnlike,
logp=self.lnprior,
loglargs=self.lnlike_args,
**kwargs
)
def emcee_init(self,
nwalkers,
ndim,
lnprob,
ntemps=None,
lnprob_kwargs={},
sampler_kwargs={},
PT=False):
"""
Initialize an ensemble sampler
nwalkers : int
number of walkers
ndim : int
number of parameter dimensions
lnprob : method
posterior function call
lnprob_kwargs : dict
keyword arguments for lnprob function call
sampler_kwargs : dict
keyword arguments for emcee EnsembleSampler instatiation
"""
self.nwalkers = nwalkers
self.ndim = ndim
self.lnprob = lnprob
self.ntemps = ntemps
self.PT = PT
if PT == True:
self.sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
self.lnlike,
self.lnprior,
loglkwargs=lnprob_kwargs,
**sampler_kwargs)
else:
self.sampler = emcee.EnsembleSampler(self.nwalkers,
self.ndim,
self.lnprob,
kwargs=lnprob_kwargs,
**sampler_kwargs)
def run(self):
'''Main body of the EMCEE run
'''
self.sampler = emcee.PTSampler(self.ntemps, self.nwalkers, \
self.ndims, \
self.like, self.prior, \
threads = 1)
p0 = np.zeros([self.ntemps, self.nwalkers, self.ndims])
if self.start_kdes == 'none':
for i in range(self.ntemps):
for j in range(self.nwalkers):
p0[i,j,:] = self.start_params * \
(1.0 + np.random.randn(self.ndims) * 0.0001)
#If KDEs exist, distribute walkers from those distributions
else:
for i in range(self.ntemps):
for j in range(self.ndims):
xs, ys = self.start_kdes[j]
cdf = integrate.cumtrapz(ys, xs, initial=0)
inv_cdf = interpolate.interp1d(cdf, xs)
p0[i, :, j] = inv_cdf(np.random.rand(self.nwalkers))
if self.start_kdes == 'none': print('\nBurning in...')
for p1, lnpp, lnlp in tqdm(
self.sampler.sample(p0, iterations=self.niter)):
pass
self.sampler.reset()
if self.start_kdes == 'none': print('\nRunning again...')
for i in range(self.max_conv):
for pp, lnpp, lnlp in tqdm(
self.sampler.sample(p1, iterations=self.niter / 2)):
pass
#Convergence check: Standard deviation as 2% of the median value
med = np.median(self.sampler.chain[0, :, -self.niter:-1, :],
axis=0)
conv = np.std(med, axis=0) / np.median(med, axis=0)
if np.all(conv < self.conv_accept):
break
samples = self.sampler.chain[0, :, :, :].reshape((-1, self.ndims))
return np.array(samples)
def do_fit_PT(fit_dir, db_path):
'''Fits data using emcee.PTtempering'''
comm = mpi.COMM_WORLD
pool = emcee_lik.MPIPool_stay_alive(loadbalance=True)
files = glob(path.join(fit_dir, '*.pik'))
# start fits
for gal in files:
comm.barrier()
data = {}
temp = pik.load(open(gal))
data[gal] = temp[-1]
data = comm.bcast(data, root=0)
posterior = emcee_lik.LRG_emcee_PT(data, db_path, have_dust=False,
have_losvd=False)
posterior.init()
nwalkers = 2 * posterior.ndim()
#ntemps = 20
Tmax = 1.7*10**12
if pool.is_master():
# need to make pos0 (ntemps, nwalkers, dim)
pos0 = posterior.inital_pos(nwalkers, ntemps)
sampler = emcee.PTSampler(None, nwalkers, posterior.ndim() ,
posterior, dummy_prior,Tmax=Tmax,
pool=pool)
burnin = 2000
iterations = 10 * 10**3
#pos, prob = [], []
i = 0
#burn in
pos, prob, state = sampler.run_mcmc(pos0, burnin)
sampler.reset()
#mcmc
for tpos, tprob, _ in sampler.sample(pos, iterations=iterations
, rstate0=state):
acept = sampler.acceptance_fraction.mean()
print '%i out of %i, accept=%2.1f'%(i, iterations, acept)
if i % 100:
pik.dump((temp,sampler), open(gal + '.pt.incomplte', 'w'), 2)
i+=1
pik.dump((temp,sampler), open(gal + '.pt', 'w'), 2)
pool.close()
else:
pool.wait(posterior)
def run_PTmcmc(ntemps,
lnlike,
priors,
position,
ndim=3,
nwalkers=100,
logargs=[]):
# Run MCMC sampler
sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
lnlike,
priors.lnprior,
loglargs=logargs)
sams = sampler.run_mcmc(position, 1000)
return sampler, sams
def GetSampler(self, SamplerType, NTemps, NWalkers, Threads):
'''
Set up sampler and position.
Args:
SamplerType (str): 'Ensemble' or 'PT'
NTemps (int): only valid for Parallel-Tempering. set the # of temperature
NWalkers (int): # of walkers
Threads (int): # of threads
'''
self._SamplerType = SamplerType
if SamplerType == "Ensemble":
self._Sampler = em.EnsembleSampler(NWalkers,
self._FitDim,
LogPosterior,
threads=Threads,
args=[
self._FitBound, self._Info,
self._P, self.FluxGenerator,
self.Times, self.Freqs,
self.Fluxes, self.FluxErrs
])
self._Position0 = self._InitialBound[:, 0] + (
self._InitialBound[:, 1] - self._InitialBound[:, 0]
) * np.random.rand(NWalkers, self._FitDim)
else:
self._Sampler = em.PTSampler(NTemps,
NWalkers,
self._FitDim,
LogLike,
LogPrior,
threads=Threads,
loglargs=[
self._Info, self._P,
self.FluxGenerator, self.Times,
self.Freqs, self.Fluxes,
self.FluxErrs
],
logpargs=[self._FitBound, self._Info])
self._Position0 = self._InitialBound[:, 0] + (
self._InitialBound[:, 1] - self._InitialBound[:, 0]
) * np.random.rand(NTemps, NWalkers, self._FitDim)
def run_emcee(nllf, p0, bounds, burn, nsamples, nwalkers, temperatures):
if np.isscalar(temperatures):
ntemps, betas = temperatures, None
else:
ntemps, betas = len(temperatures), 1 / temperatures
log_prior = lambda p: 0 if (
(p >= bounds[0]) & (p <= bounds[1])).all() else -inf
log_likelihood = lambda p: -nllf(p)
sampler = emcee.PTSampler(
ntemps=ntemps,
nwalkers=nwalkers,
dim=len(p0),
logl=log_likelihood,
logp=log_prior,
betas=betas,
)
nthin = 1
steps = nsamples // (nwalkers * nthin)
monitor = Monitor(burn + steps)
# Burn-in
pop = eps_init(nwalkers * ntemps, p0, bounds).reshape(ntemps, nwalkers, -1)
for p, lnprob, lnlike in sampler.sample(pop, iterations=burn):
monitor(p, lnlike)
sampler.reset()
print("== after burn ==", monitor.index, monitor.best)
# Collect
for p, lnprob, lnlike in sampler.sample(p,
lnprob0=lnprob,
lnlike0=lnlike,
iterations=nthin * steps,
thin=nthin):
monitor(p, lnlike)
print("== after sample ==", monitor.index, monitor.best)
assert sampler.chain.shape == (ntemps, nwalkers, steps, len(p0))
#import pprint; pprint.pprint(sampler.__dict__)
#[print(k, v.shape) for k, v in sampler.__dict__.items() if isinstance(v, np.ndarray)]
return sampler
def run_one_model(model, model_number, data, ns, pool=None):
# Vector of nominal parameters
p = numpy.log10(numpy.array([pp.value for pp in model.parameters
if pp.name[0]=='k']))
print posterior(p, model, data)
# Number of temperatures, dimensions and walkers
ntemps = 20
ndim = len(p)
blocksize = 4
nblocks = int(numpy.ceil((2*ndim+1)/(1.0*blocksize)))
nwalkers = blocksize * nblocks
print 'Running %d walkers at %d temperatures for %d steps.' %\
(nwalkers, ntemps, ns)
sampler = emcee.PTSampler(ntemps, nwalkers, ndim, likelihood, prior,
threads=1, pool=pool, betas=None, a=2.0, Tmax=None,
loglargs=[model, data], logpargs=[model],
loglkwargs={}, logpkwargs={})
# Random initial parameters for walkers
p0 = numpy.ones((ntemps, nwalkers, ndim))
for i in range(ntemps):
for j in range(nwalkers):
p0[i, j, :] = p + 1.0*(numpy.random.rand(ndim)-0.5)
# Run sampler
fname = folder_path + 'chain_%d.dat' % model_number
step = 0
for result in sampler.sample(p0, iterations=ns, storechain=True):
print '---'
position = result[0]
with open(fname, 'a') as fh:
for w in range(nwalkers):
for t in range(ntemps):
pos_str = '\t'.join(['%f' % p for p in position[t][w]])
fh.write('%d\t%d\t%d\t%s\n' % (step, w, t, pos_str))
step += 1
return sampler
def ptmcmc(self, p0s):
"""Runs Parallel Tempering Monte Carlo Markov Chain algorithm to determine multi-modal uncertainties
"""
def logl(theta):
return -self.chi(theta)
sampler = emcee.PTSampler(self.n_temps, self.n_walkers, self.n_dim,
logl, self.lnprior)
if self.savefile is not None:
f = open(self.savefile, "w")
f.close()
for result in tqdm(sampler.sample(p0s,
iterations=self.n_steps,
thin=self.thin),
total=self.n_steps):
if self.savefile is not None:
position = result[0]
f = open(self.savefile, "a")
for k in range(position.shape[0]):
f.write("{0:4d} {1:s}\n".format(
k, " ".join([str(pos) for pos in position[k]])))
f.close()
return sampler
def __init__(self, model, ntemps, nwalkers, pool=None, model_call=None):
try:
import emcee
except ImportError:
raise ImportError("emcee is not installed.")
if model_call is None:
model_call = model
# construct the sampler: PTSampler needs the likelihood and prior
# functions separately
ndim = len(model.variable_params)
sampler = emcee.PTSampler(ntemps,
nwalkers,
ndim,
_callloglikelihood(model_call),
_callprior(model_call),
pool=pool)
# initialize
super(EmceePTSampler, self).__init__(sampler, model)
self._nwalkers = nwalkers
self._ntemps = ntemps
def prep_pt_sampler(init_params,
lnprior,
lnlikelihood,
lnlikeargs,
nwalkers,
# nthreads,
# a=2,
ntemps=10,
ballsize=1e-4,
**kwargs):
ndim = len(init_params) # number of parameters in the model
sampler = emcee.PTSampler(ntemps, nwalkers, ndim,
logp=lnprior,
logl=lnlikelihood,
loglargs=lnlikeargs,
**kwargs)
gaussian_ball = np.random.randn(ndim * nwalkers * ntemps).reshape(
ntemps, nwalkers, ndim)
initpar_ball = ( init_params + ballsize * gaussian_ball)
return sampler, initpar_ball
def run_mcmc_sample(
Nsamples,
mag_band,
maglimits,
# Isochrone set -- currently probably only Padova will work in all cases
which_iso='Padova',
# Extra magnitudes to calculate
extra_mags=None,
# Introduce a colour cut
color=None,
colorlimits=None,
# Coordinate cuts (in radians) -- remove everything |b|<modbcut
# If deccut>0 cut all dec<deccut-pi/2
# If deccut<0 cut all dec>deccut+pi/2
modbcut=0.,
deccut=2. * np.pi,
# Spectroscopic parameter cut -- log10Teff
logglimits=None,
Tefflimits=None,
fehlimits=None,
# Flags for different options
extinct=True,
with_halo=True,
interp=False,
dered=False,
# Debugging and outputting
output_file=None,
messages=True,
extra_magnitudes=None,
# Sampler parameters
nwalkers=1000,
Nburn=None,
threads=1,
thin=20,
pt=False,
ntemp=1,
asampler=2.,
# Adjust magnitude selection with a taper (1-break_grad(mag-break_pos))
#break_pos=1000.,break_grad=1000.,
# If cutting on error-convolved teff, logg and color -- currently won't do anything
tgcolor_errs=np.array([0., 0., 0.])):
'''
Draws a Monte Carlo sample from an EDF model
Draws Nsamples across the sky between magnitudes maglimits for band mag_band
'''
nsamples = int(Nsamples / nwalkers) + 1
# Turn on/off halo
if (with_halo):
edf_sampling.turn_on_halo()
else:
edf_sampling.turn_off_halo()
# -- Set arguments
check = lambda x: np.array([-10000., 10000.]) if x is None else x
checkcolor = lambda x: np.array(['J', 'K']
) if x is None else color # as a default
args = [
which_iso, mag_band, maglimits, extinct, interp, modbcut, deccut,
check(color),
check(colorlimits),
check(Tefflimits),
check(logglimits),
check(fehlimits)
]
# -- Set sampler
ndim, nwalker = 9, nwalkers
sampler = emcee.EnsembleSampler(nwalker,
ndim,
LogL_Zsample,
threads=threads,
args=args)
if (pt):
# Parallel tempering
sampler = emcee.PTSampler(ntemp,
nwalker,
ndim,
los_magbox_LogL_sample_py,
logp,
loglargs=llos_args,
threads=threads)
# Initialize walkers
# Sample uniform in age, mass
# Sample gaussian in Z and velocities
# Sample exp in (unextincted) magnitude
lomag, himag = maglimits[0], maglimits[1]
Zlim = [-3., 1.]
if fehlimits is not None:
Zlim = fehcut
if not with_halo:
Zlim[0] = edf_sampling.minZ()
Zlim[1] = edf_sampling.maxZ()
p0 = np.random.uniform(
low=[0.2, Zlim[0], 0.5, -150., 50., -100., lomag, 0., modbcut],
high=[
12., Zlim[1], 3.5, 150., 350., 100., himag, 2. * np.pi, np.pi / 2.
],
size=(nwalker, ndim))
p0[:, -1] *= (1. - 2. *
(np.random.uniform(low=0, high=1, size=nwalker) > 0.5))
if fehlimits is not None:
meanZ, sigZ = 0., .4
p0.T[1] = np.random.normal(size=nwalker) * sigZ + meanZ
meanV, sigV = 0., 50.
for i in range(3, 6):
p0.T[i] = np.random.normal(size=nwalker) * sigV + meanV
p0.T[4] += 200.
p0.T[6] = trunc_exp_rv(lomag, himag, 1., size=len(p0))
# -- Only choose physically allowed masses for selected age, Z
for i in np.arange(len(p0)):
maxmass, minmass = 0., 0.
maxmass = edf_sampling.check_highmass_Z(p0[i][0], p0[i][1], which_iso)
minmass = edf_sampling.check_lowmass_Z(p0[i][0], p0[i][1], which_iso)
while (maxmass < 0. or minmass < 0.
or edf_sampling.check_radius_positive(p0[i][0], p0[i][1]) == 0
or deccut_fn(p0[i][-2], p0[i][-1], deccut)):
p0[i][-3] = np.random.uniform(low=lomag, high=himag)
p0[i][1] = np.random.uniform(low=Zlim[0], high=Zlim[1])
p0[i][0] = np.random.uniform(low=0., high=12.)
maxmass = edf_sampling.check_highmass_Z(p0[i][0], p0[i][1],
which_iso)
minmass = edf_sampling.check_lowmass_Z(p0[i][0], p0[i][1],
which_iso)
MAXMASS = 3.
if (maxmass > MAXMASS):
maxmass = MAXMASS
p0[i][2] = np.random.uniform(low=minmass, high=maxmass)
# Check other cuts satisfied
if (check(colorlimits)[0] > -10. or check(logglimits)[0] > -10.
or check(Tefflimits)[0] > -10.):
while (edf_sampling.check_color_logg_cut(p0[i][0], p0[i][1],
p0[i][2], 0., 180.,
checkcolor(color),
check(colorlimits),
check(logglimits),
check(Tefflimits),
which_iso, False) == 0):
p0[i][2] = np.random.uniform(low=minmass, high=maxmass)
# Now wiggle the walkers a bit
err = [0.5, 0.1, 0.1, 10., 10., 10., 0.1, 0.01, 0.01]
for i in np.arange(len(p0)):
extinctMag = edf_sampling.get_extinct(p0[i][-2], p0[i][-1], 3.,
mag_band)
if (extinctMag > err[-3]):
err[-3] = extinctMag
pp = edf_sampling.LogL_sample(p0[i], *args)
n = 0
while (np.isinf(pp) and n < 10000):
p0[i] = p0[np.random.randint(
len(p0))] + np.random.normal(size=ndim) * err
pp = edf_sampling.LogL_sample(p0[i], *args)
n += 1
if (n == 10000):
print "Can't find start point:", p0[i], deccut_fn(
p0[i][-2], p0[i][-1], deccut)
if (messages): print 'Initial points sampled'
if (pt):
p0 = np.reshape(p0, (ntemp, nwalker, ndim))
if (Nburn == None):
Nburn = 2 * thin * nsamples
# -- Run a burn-in
pos, prob, state = sampler.run_mcmc(p0, Nburn, storechain=False)
if messages:
print 'Number of logl=-inf = ' + str(len(prob[np.isinf(prob)]))
if messages: print("Burnt")
sampler.reset()
# -- Sample with thinning and calculating dependent variables
pos, prob, state = sampler.run_mcmc(pos, nsamples * thin, thin=thin)
if messages: print("Sampled")
flatchain = sampler.flatchain
lnprob = sampler.lnprobability
if (pt):
flatchain = flatchain[0]
lnprob = lnprob[0]
extras = np.array(
map(
lambda i: edf_sampling.get_extra_data(i, mag_band, which_iso,
False, extinct, interp),
sampler.flatchain))
actions = np.array([
edf_sampling.get_actions(np.concatenate((b[4:7], a[3:6])))
for a, b in izip(flatchain, extras)
])
nameslist = np.copy(names)
nameslist[1] = "Z"
nameslist[10] = "RcP"
nameslist[23] = mag_band
nameslist[6] = mag_band + "0"
if messages:
print("Mean acceptance fraction:",
np.mean(sampler.acceptance_fraction))
everything = np.vstack(
(flatchain.T, extras.T, actions.T, lnprob.flatten())).T
if color is not None:
if extra_magnitudes is not None:
extra_magnitudes = np.unique(
np.concatenate(
(color, extra_magnitudes, np.array([mag_band]))))
else:
extra_magnitudes = np.unique(
np.concatenate((color, np.array([mag_band]))))
extra_magnitudes = extra_magnitudes[extra_magnitudes != mag_band]
if extra_magnitudes is not None:
extra_mags = np.array(
map(
lambda i: edf_sampling.get_extra_magnitudes(
i, mag_band, extra_magnitudes, which_iso, False, extinct,
interp), flatchain))
nameslist = np.concatenate((nameslist, extra_magnitudes))
print extra_magnitudes
nameslist = np.concatenate(
(nameslist, np.array([e + '0' for e in list(extra_magnitudes)])))
everything = np.vstack((everything.T, extra_mags.T)).T
df = pd.DataFrame(everything, columns=nameslist)
df = df.sample(Nsamples, replace=False).reset_index(drop=True)
if (output_file):
df.to_csv(output_file)
return df
def run():
"""
Initialize and run the MCMC sampler.
"""
global _loglkwargs
start_time = time.time()
args = parse_args()
config = ConfigParser()
config.read(args.config_file)
# set the mcmc parameters
nwalkers = config.getint('mcmc_settings', 'nwalkers')
ntemps = config.getint('mcmc_settings', 'ntemps')
nplanets = config.getint('mcmc_settings', 'nplanets')
nstep = config.getint('mcmc_settings', 'nstep')
nthreads = config.getint('mcmc_settings', 'nthreads')
use_epoch_astrometry = config.getboolean('mcmc_settings',
'use_epoch_astrometry',
fallback=False)
HipID = config.getint('data_paths', 'HipID', fallback=0)
start_file = config.get('data_paths', 'start_file', fallback='none')
# set initial conditions
par0 = set_initial_parameters(start_file, ntemps, nplanets, nwalkers)
ndim = par0[0, 0, :].size
data, H1f, H2f, Gf = initialize_data(config)
# set arguments for emcee PTSampler and the log-likelyhood (lnprob)
samplekwargs = {'thin': 50}
loglkwargs = {
'returninfo': False,
'use_epoch_astrometry': use_epoch_astrometry,
'data': data,
'nplanets': nplanets,
'H1f': H1f,
'H2f': H2f,
'Gf': Gf
}
_loglkwargs = loglkwargs
# run sampler without feeding it loglkwargs directly, since loglkwargs contains non-picklable C objects.
print('Running MCMC.')
sample0 = emcee.PTSampler(ntemps,
nwalkers,
ndim,
avoid_pickle_lnprob,
return_one,
threads=nthreads)
sample0.run_mcmc(par0, nstep, **samplekwargs)
print('Total Time: %.2f' % (time.time() - start_time))
print("Mean acceptance fraction (cold chain): {0:.6f}".format(
np.mean(sample0.acceptance_fraction[0, :])))
# save data
shape = sample0.lnprobability[0].shape
parfit = np.zeros((shape[0], shape[1], 8))
loglkwargs['returninfo'] = True
for i in range(shape[0]):
for j in range(shape[1]):
res = lnprob(sample0.chain[0][i, j], **loglkwargs)
parfit[i, j] = [
res.plx_best, res.pmra_best, res.pmdec_best, res.chisq_sep,
res.chisq_PA, res.chisq_H, res.chisq_HG, res.chisq_G
]
out = fits.HDUList(fits.PrimaryHDU(sample0.chain[0].astype(np.float32)))
out.append(fits.PrimaryHDU(sample0.lnprobability[0].astype(np.float32)))
out.append(fits.PrimaryHDU(parfit.astype(np.float32)))
for i in range(1000):
filename = os.path.join(args.output_dir,
'HIP%d_chain%03d.fits' % (HipID, i))
if not os.path.isfile(filename):
print('Writing output to {0}'.format(filename))
out.writeto(filename, overwrite=False)
break
if p0.shape[-1] != len(F.parameters):
raise ValueError("Parameter mismatch between "
"walker (%dd) and Fitter (%dd)" %
(p0.shape[-1], len(F.parameters)))
if len(p0.shape) == 2:
logger.info("using EnsembleSampler (warning: untested)")
sampler = emcee.EnsembleSampler(p0.shape[0],
p0.shape[1],
lnprob_internal,
pool=pool) # FIXME: untested
else:
logger.info("using PTSampler (warning: can't handle blobs)")
sampler = emcee.PTSampler(ntemps=p0.shape[0],
nwalkers=p0.shape[1],
dim=p0.shape[2],
logl=lnprob,
logp=lnprior,
pool=pool)
def save():
subprocess.check_call([
'rsync', '-rt', '--append-verify', local_dbdir + "/",
"nimrod:" + dbdir + "/"
])
if not trust_nfs:
# Run saving in the background so it doesn't interfere with computation
done = False
def save_loop():
logger.debug("starting saving loop")
#rvsys, K, w, ecc, T0, period
labels=['rvsys', 'K', 'w', 'ecc', 'T0', 'period','sig2']
initial=[0,40,90,0.01,15,6.25,20]
#VALUES
print(np.c_[labels,initial])
plt.errorbar(time,rv,erv,fmt='.')
plt.plot(mod_time,rv_pl(mod_time,initial[:-1]))
plt.show()
# Set up the sampler.
ntemps, nwalkers, niter, ndim = 2, 500, 2500, len(labels)
sampler = emcee.PTSampler(ntemps, nwalkers, ndim, lnlike, lnprior, loglargs=(time, rv, erv))
p0 = np.zeros([ntemps, nwalkers, ndim])
for i in range(ntemps):
for j in range(nwalkers):
p0[i,j,:] = initial + 1e-2*np.random.randn(ndim)
print('... burning in ...')
for p, lnprob, lnlike in tqdm(sampler.sample(p0, iterations=niter),total=niter):
sleep(0.001)
#print(np.shape(p0))
#print(np.shape(p))
# Clear and run the production chain.
sampler.reset()
print('... running sampler ...')
print('Name: '+str(NAME_OF_CHAIN))
print(str(socket.gethostname())+': Starting calculation at: '+time.ctime())
print('Testing proposal is: '+str(allparameters_proposal))
time_start_single=time.time()
print('Likelihood for the testing proposal is: '+str(multi_model(allparameters_proposal)))
time_end_single=time.time()
print('Time for single calculation is '+str(time_end_single-time_start_single))
#####################################################################################################################
# First emcee
sampler = emcee.PTSampler(parInitnT.shape[0],parInitnT.shape[1], parInitnT.shape[2], multi_model,modelP,
pool=pool)
sampler.run_mcmc(parInitnT, nsteps)
#Export this file
np.save(RESULT_FOLDER+NAME_OF_CHAIN+'Emcee1',sampler.chain)
np.save(RESULT_FOLDER+NAME_OF_LIKELIHOOD_CHAIN+'Emcee1',sampler.lnlikelihood)
# Create minchain and save it
likechain0=sampler.lnlikelihood[0]
chain0=sampler.chain[0]
minchain=chain0[np.abs(likechain0)==np.min(np.abs(likechain0))][0]
np.save(RESULT_FOLDER+NAME_OF_CHAIN+'minchain',minchain)
print('Time when first emcee run finished was: '+time.ctime())
def mcmcSample(self, theta_ml, emcee_threads, nsteps=1000, PT=True, ntemps=20, Tmax=None, betas=None, thin=1, burn=1000):
''' Helper function to do MCMC sampling. This uses the emcee implementations of Ensemble
Sampling MCMC or Parallel-Tempering MCMC (PT-MCMC). In the latter case, a number of
``temperatures'' must be defined. These are used to modify the likelihood in a way that
makes exploration of multimodal distributions easier. PT-MCMC also allows an estimation of
the model log-evidence, although to lower accuracy than nested sampling.
theta_ml : array
Initial parameters to start MCMC exploration from.
nsteps : int, optional
Number of steps required from MCMC. Default is 1000. The number of steps is rounded to a multiple
of the ``thin'' factor.
PT : bool, optional
Boolean used to activate Parallel Tempering. With this option, an evaluation of log-evidence
is possible, but is expected to be less accurate than in nested sampling.
emcee_threads : int, optional
Number of threads used within emcee. Parallelization is possible only within a single machine/node.
ntemps : int, optional
Number of temperatures used in PT-MCMC. This is a rather arbitrary number. Note that in emcee
the temperature ladder is implemented such that each temperature is larger by a factor of \sqrt{2}.
Tmax : float, optional
Maximum temperature allowed for emcee PTSampler. If ``ntemps`` is not given, this argument
controls the number of temperatures. Temperatures are chosen according to the spacing criteria until
the maximum temperature exceeds ``Tmax`. Default is to set ``ntemps`` and leave Tmax=None.
betas : array, optional
Array giving the inverse temperatures, :math:`\\beta=1/T`, used in the ladder. The default is chosen
so that a Gaussian posterior in the given number of dimensions will have a 0.25 tswap acceptance rate.
thin: int, optional
thinning factor (choose 1 to avoid thinning)
burn : int, optional
Burn-in of chains. Default is 1000
'''
# round number of steps to multiple of thinning factor:
nsteps = nsteps - nsteps%thin
if PT: print("Using PT-MCMC!")
ndim, nwalkers = len(theta_ml), len(theta_ml)*4
if PT == False:
# pos has shape (nwalkers, ndim)
pos = [theta_ml + 1e-4 * np.random.randn(ndim) for i in np.arange(nwalkers)]
# use affine-invariant Ensemble Sampling
sampler = emcee.EnsembleSampler(nwalkers, ndim, _LnPost_Wrapper(self), threads=emcee_threads) # self.lineModel.lnprob
# get MCMC samples, adding 'burn' steps which will be burnt later
sampler.run_mcmc(pos, nsteps+burn)
# flatten chain (but keep ndim)
samples = sampler.chain[:,burn::thin, :].reshape((-1, ndim))
else:
# testing purposes ONLY
#betas=np.asarray([1.0,0.9,0.8,0.7,0.6, 0.5])
# use PT-MCMC
sampler = emcee.PTSampler(ntemps, nwalkers, ndim, _LnLike_Wrapper(self), _LnPrior_Wrapper(self),
threads=emcee_threads, Tmax=Tmax, betas=betas)
# if Tmax is not None, ntemps was set internally in PTSampler
ntemps = sampler.ntemps
# pos has shape (ntemps, nwalkers, ndim)
pos = [[theta_ml + 1e-4 * np.random.randn(ndim) for i in np.arange(nwalkers)] for t in np.arange(ntemps)]
# burn-in 'burn' iterations
for p, lnprob, lnlike in sampler.sample(pos, iterations=burn):
pass
sampler.reset()
# now sample (and thin by a factor of `thin`):
for p, lnprob, lnlike in sampler.sample(p, lnprob0=lnprob, lnlike0=lnlike, iterations=nsteps, thin=thin):
pass
# Keep only samples corresponding to T=0 chains
samples = sampler.chain[0,:,:,:].reshape((-1, ndim))
# sanity check
if PT==True:
assert sampler.chain.shape == (ntemps, nwalkers, nsteps//thin, ndim)
assert samples.shape == ( nwalkers * nsteps//thin, ndim)
else:
assert sampler.chain.shape == (nwalkers, burn+nsteps, ndim)
assert samples.shape == (nwalkers * nsteps//thin, ndim)
return samples, sampler