def check_all_ready(self):
"""
Checks if the chain(s) is(/are) ready to check convergence and, if requested,
learn a new covariance matrix for the proposal distribution.
"""
msg_ready = (
("Ready to" if get_mpi() or self.learn_proposal else "") +
" check convergence" +
(" and" if get_mpi() and self.learn_proposal else "") +
(" learn a new proposal covmat" if self.learn_proposal else ""))
# If *just* (weight==1) got ready to check+learn
if (self.n() > 0 and self.current_point[_weight] == 1
and not (self.n() % self.check_every)):
self.log.info("Checkpoint: %d samples accepted.", self.n())
if get_mpi():
self.been_waiting += 1
if self.been_waiting > self.max_waiting:
self.log.error(
"Waiting for too long for all chains to be ready. "
"Maybe one of them is stuck or died unexpectedly?")
raise HandledException
self.model.dump_timing()
# If not MPI, we are ready
if not get_mpi():
if msg_ready:
self.log.info(msg_ready)
return True
# If MPI, tell the rest that we are ready -- we use a "gather"
# ("reduce" was problematic), but we are in practice just pinging
if not hasattr(self, "req"): # just once!
self.all_ready = np.empty(get_mpi_size())
self.req = get_mpi_comm().Iallgather(np.array([1.]),
self.all_ready)
self.log.info(msg_ready + " (waiting for the rest...)")
# If all processes are ready to learn (= communication finished)
if self.req.Test() if hasattr(self, "req") else False:
# Sanity check: actually all processes have finished
assert np.all(self.all_ready == 1), (
"This should not happen! Notify the developers. (Got %r)",
self.all_ready)
if get_mpi_rank() == 0:
self.log.info("All chains are r" + msg_ready[1:])
delattr(self, "req")
self.been_waiting = 0
# Just in case, a barrier here
get_mpi_comm().barrier()
return True
return False
def format(self, record):
self._fmt = (("[%d]" % get_mpi_rank() if get_mpi() else "") +
"[%(name)s] " + {
logging.ERROR: "*ERROR* ",
logging.WARNING: "*WARNING* "
}.get(record.levelno, "") + "%(message)s")
return logging.Formatter.format(self, record)
def lock_error(self):
if not self.has_lock():
assert self.lock_error_file
try:
# make lock_err so process holding lock can check
# another process had an error
with open(self.lock_error_file, 'wb'):
pass
except OSError:
pass
if mpi.get_mpi():
import mpi4py
else:
mpi4py = None
if mpi.is_main_process() and use_portalocker() is None:
self.log.warning('install "portalocker" for better file lock control.')
raise LoggedError(self.log,
"File %s is locked.\nYou may be running multiple jobs with "
"the same output when you intended to run with MPI. "
"Check that mpi4py is correctly installed and "
"configured (using the same mpi as mpirun/mpiexec); "
"e.g. try the test at\n"
"https://cobaya.readthedocs.io/en/latest/installation."
"html#mpi-parallelization-optional-but-encouraged\n"
+ ("Your current mpi4py config is:"
"\n %s" % mpi4py.get_config()
if mpi4py is not None else
"mpi4py is NOT currently installed."), self.lock_file)
def run(self):
"""
Prepares the posterior function and calls ``PolyChord``'s ``run`` function.
"""
# Prepare the posterior
# Don't forget to multiply by the volume of the physical hypercube,
# since PolyChord divides by it
def logpost(params_values):
logposterior, logpriors, loglikes, derived = (
self.model.logposterior(params_values))
if len(derived) != len(self.model.parameterization.derived_params()):
derived = np.full(
len(self.model.parameterization.derived_params()), np.nan)
if len(loglikes) != len(self.model.likelihood._likelihoods):
loglikes = np.full(
len(self.model.likelihood._likelihoods), np.nan)
derived = list(derived) + list(logpriors) + list(loglikes)
return (
max(logposterior + self.logvolume, 0.99 * self.pc_settings.logzero), derived)
self.log.info("Sampling!")
if get_mpi():
get_mpi_comm().barrier()
self.pc.run_polychord(logpost, self.nDims, self.nDerived,
self.pc_settings, self.pc_prior)
def format(self, record):
self._fmt = ("[" +
("%d : " % get_mpi_rank() if get_mpi() else "") +
"%(name)s" + (" %(asctime)s " if debug else "") +
"] " + {
logging.ERROR: "*ERROR* ",
logging.WARNING: "*WARNING* "
}.get(record.levelno, "") + "%(message)s")
return logging.Formatter.format(self, record)
def check_convergence_and_learn_proposal(self):
"""
Checks the convergence of the sampling process (MPI only), and, if requested,
learns a new covariance matrix for the proposal distribution from the covariance
of the last samples.
"""
if get_mpi():
# Compute and gather means, covs and CL intervals of last half of chains
mean = self.collection.mean(first=int(self.n() / 2))
cov = self.collection.cov(first=int(self.n() / 2))
mcsamples = self.collection._sampled_to_getdist_mcsamples(
first=int(self.n() / 2))
try:
bound = np.array([[
mcsamples.confidence(i,
limfrac=self.Rminus1_cl_level / 2.,
upper=which)
for i in range(self.model.prior.d())
] for which in [False, True]]).T
success_bounds = True
except:
bound = None
success_bounds = False
Ns, means, covs, bounds = map(
lambda x: np.array(get_mpi_comm().gather(x)),
[self.n(), mean, cov, bound])
else:
# Compute and gather means, covs and CL intervals of last m-1 chain fractions
m = 1 + self.Rminus1_single_split
cut = int(self.collection.n() / m)
if cut <= 1:
self.log.error(
"Not enough points in chain to check convergence. "
"Increase `check_every` or reduce `Rminus1_single_split`.")
raise HandledException
Ns = (m - 1) * [cut]
means = np.array([
self.collection.mean(first=i * cut, last=(i + 1) * cut - 1)
for i in range(1, m)
])
covs = np.array([
self.collection.cov(first=i * cut, last=(i + 1) * cut - 1)
for i in range(1, m)
])
# No logging of warnings temporarily, so getdist won't complain unnecessarily
logging.disable(logging.WARNING)
mcsampleses = [
self.collection._sampled_to_getdist_mcsamples(
first=i * cut, last=(i + 1) * cut - 1)
for i in range(1, m)
]
logging.disable(logging.NOTSET)
try:
bounds = [
np.array([[
mcs.confidence(i,
limfrac=self.Rminus1_cl_level / 2.,
upper=which)
for i in range(self.model.prior.d())
] for which in [False, True]]).T for mcs in mcsampleses
]
success_bounds = True
except:
bounds = None
success_bounds = False
# Compute convergence diagnostics
if not get_mpi_rank():
# "Within" or "W" term -- our "units" for assessing convergence
# and our prospective new covariance matrix
mean_of_covs = np.average(covs, weights=Ns, axis=0)
# "Between" or "B" term
# We don't weight with the number of samples in the chains here:
# shorter chains will likely be outliers, and we want to notice them
cov_of_means = np.atleast_2d(np.cov(means.T)) # , fweights=Ns)
# For numerical stability, we turn mean_of_covs into correlation matrix:
# rho = (diag(Sigma))^(-1/2) * Sigma * (diag(Sigma))^(-1/2)
# and apply the same transformation to the mean of covs (same eigenvals!)
diagSinvsqrt = np.diag(np.power(np.diag(cov_of_means), -0.5))
corr_of_means = diagSinvsqrt.dot(cov_of_means).dot(diagSinvsqrt)
norm_mean_of_covs = diagSinvsqrt.dot(mean_of_covs).dot(
diagSinvsqrt)
# Cholesky of (normalized) mean of covs and eigvals of Linv*cov_of_means*L
try:
L = np.linalg.cholesky(norm_mean_of_covs)
except np.linalg.LinAlgError:
self.log.warning(
"Negative covariance eigenvectors. "
"This may mean that the covariance of the samples does not "
"contain enough information at this point. "
"Skipping this checkpoint")
success = False
else:
Linv = np.linalg.inv(L)
try:
eigvals = np.linalg.eigvalsh(
Linv.dot(corr_of_means).dot(Linv.T))
success = True
except np.linalg.LinAlgError:
self.log.warning("Could not compute eigenvalues. "
"Skipping this checkpoint.")
success = False
if success:
Rminus1 = max(np.abs(eigvals))
# For real square matrices, a possible def of the cond number is:
condition_number = Rminus1 / min(np.abs(eigvals))
self.log.debug("Condition number = %g", condition_number)
self.log.debug("Eigenvalues = %r", eigvals)
self.log.info(
"Convergence of means: R-1 = %f after %d accepted steps"
% (Rminus1, (sum(Ns) if get_mpi() else self.n())) +
(" = sum(%r)" % list(Ns) if get_mpi() else ""))
# Have we converged in means?
# (criterion must be fulfilled twice in a row)
if max(Rminus1, self.Rminus1_last) < self.Rminus1_stop:
# Check the convergence of the bounds of the confidence intervals
# Same as R-1, but with the rms deviation from the mean bound
# in units of the mean standard deviation of the chains
if success_bounds:
Rminus1_cl = (np.std(bounds, axis=0).T /
np.sqrt(np.diag(mean_of_covs)))
self.log.debug("normalized std's of bounds = %r",
Rminus1_cl)
self.log.info(
"Convergence of bounds: R-1 = %f after %d " %
(np.max(Rminus1_cl),
(sum(Ns) if get_mpi() else self.n())) +
"accepted steps" +
(" = sum(%r)" % list(Ns) if get_mpi() else ""))
if np.max(Rminus1_cl) < self.Rminus1_cl_stop:
self.converged = True
self.log.info("The run has converged!")
self._Ns = Ns
else:
self.log.info(
"Computation of the bounds was not possible. "
"Waiting until the next checkpoint")
if get_mpi():
# Broadcast and save the convergence status and the last R-1 of means
success = get_mpi_comm().bcast(
(success if not get_mpi_rank() else None), root=0)
if success:
self.Rminus1_last = get_mpi_comm().bcast(
(Rminus1 if not get_mpi_rank() else None), root=0)
self.converged = get_mpi_comm().bcast(
(self.converged if not get_mpi_rank() else None), root=0)
else:
if success:
self.Rminus1_last = Rminus1
# Do we want to learn a better proposal pdf?
if self.learn_proposal and not self.converged and success:
good_Rminus1 = (self.learn_proposal_Rminus1_max > self.Rminus1_last
> self.learn_proposal_Rminus1_min)
if not good_Rminus1:
if not get_mpi_rank():
self.log.info("Bad convergence statistics: "
"waiting until the next checkpoint.")
return
if get_mpi():
if get_mpi_rank():
mean_of_covs = np.empty(
(self.model.prior.d(), self.model.prior.d()))
get_mpi_comm().Bcast(mean_of_covs, root=0)
elif not get_mpi():
mean_of_covs = covs[0]
try:
self.proposer.set_covariance(mean_of_covs)
except:
self.log.debug(
"Updating covariance matrix failed unexpectedly. "
"waiting until next checkpoint.")
if not get_mpi_rank():
self.log.info("Updated covariance matrix of proposal pdf.")
self.log.debug("%r", mean_of_covs)
# Save checkpoint info
self.write_checkpoint()
def run(self):
"""
Runs the sampler.
"""
# Get first point, to be discarded -- not possible to determine its weight
# Still, we need to compute derived parameters, since, as the proposal "blocked",
# we may be saving the initial state of some block.
# NB: if resuming but nothing was written (burn-in not finished): re-start
self.log.info("Initial point:")
if self.resuming and self.collection.n():
initial_point = (self.collection[
self.collection.sampled_params].ix[self.collection.n() -
1]).values.copy()
logpost = -(self.collection[_minuslogpost].ix[self.collection.n() -
1].copy())
logpriors = -(self.collection[self.collection.prior_names].ix[
self.collection.n() - 1].copy())
loglikes = -0.5 * (self.collection[self.collection.chi2_names].ix[
self.collection.n() - 1].copy())
derived = (self.collection[self.collection.derived_params].ix[
self.collection.n() - 1].values.copy())
else:
initial_point = self.model.prior.reference(
max_tries=self.max_tries)
logpost, logpriors, loglikes, derived = self.model.logposterior(
initial_point)
self.current_point.add(initial_point,
derived=derived,
logpost=logpost,
logpriors=logpriors,
loglikes=loglikes)
self.log.info(
"\n%s",
self.current_point.data.to_string(index=False,
line_width=_line_width))
# Initial dummy checkpoint (needed when 1st checkpoint not reached in prev. run)
self.write_checkpoint()
# Main loop!
self.log.info("Sampling!" + (
" (NB: nothing will be printed until %d burn-in samples " %
self.burn_in + "have been obtained)" if self.burn_in else ""))
while self.n() < self.effective_max_samples and not self.converged:
self.get_new_sample()
# Callback function
if (hasattr(self, "callback_function_callable")
and not (max(self.n(), 1) % self.callback_every)
and self.current_point[_weight] == 1):
self.callback_function_callable(self)
# Checking convergence and (optionally) learning the covmat of the proposal
if self.check_all_ready():
self.check_convergence_and_learn_proposal()
if self.n() == self.effective_max_samples:
self.log.info(
"Reached maximum number of accepted steps allowed. "
"Stopping.")
# Make sure the last batch of samples ( < output_every ) are written
self.collection._out_update()
if get_mpi():
Ns = (lambda x: np.array(get_mpi_comm().gather(x)))(self.n())
else:
Ns = [self.n()]
if not get_mpi_rank():
self.log.info("Sampling complete after %d accepted steps.",
sum(Ns))
def initialize(self):
"""Initializes the sampler:
creates the proposal distribution and draws the initial sample."""
if not self.model.prior.d():
raise LoggedError(self.log,
"No parameters being varied for sampler")
self.log.debug("Initializing")
# MARKED FOR DEPRECATION IN v3.0
if getattr(self, "oversample", None) is not None:
self.log.warning(
"*DEPRECATION*: `oversample` will be deprecated in the "
"next version. Oversampling is now requested by setting "
"`oversample_power` > 0.")
# END OF DEPRECATION BLOCK
# MARKED FOR DEPRECATION IN v3.0
if getattr(self, "check_every", None) is not None:
self.log.warning(
"*DEPRECATION*: `check_every` will be deprecated in the "
"next version. Please use `learn_every` instead.")
# BEHAVIOUR TO BE REPLACED BY ERROR:
self.learn_every = getattr(self, "check_every")
# END OF DEPRECATION BLOCK
if self.callback_every is None:
self.callback_every = self.learn_every
self._quants_d_units = []
for q in ["max_tries", "learn_every", "callback_every", "burn_in"]:
number = NumberWithUnits(getattr(self, q), "d", dtype=int)
self._quants_d_units.append(number)
setattr(self, q, number)
self.output_every = NumberWithUnits(self.output_every, "s", dtype=int)
if is_main_process():
if self.output.is_resuming() and (max(self.mpi_size or 0, 1) !=
max(get_mpi_size(), 1)):
raise LoggedError(
self.log,
"Cannot resume a run with a different number of chains: "
"was %d and now is %d.", max(self.mpi_size, 1),
max(get_mpi_size(), 1))
if more_than_one_process():
if get_mpi().Get_version()[0] < 3:
raise LoggedError(
self.log, "MPI use requires MPI version 3.0 or "
"higher to support IALLGATHER.")
sync_processes()
# One collection per MPI process: `name` is the MPI rank + 1
name = str(1 + (lambda r: r if r is not None else 0)(get_mpi_rank()))
self.collection = Collection(self.model,
self.output,
name=name,
resuming=self.output.is_resuming())
self.current_point = OneSamplePoint(self.model)
# Use standard MH steps by default
self.get_new_sample = self.get_new_sample_metropolis
# Prepare callback function
if self.callback_function is not None:
self.callback_function_callable = (get_external_function(
self.callback_function))
# Useful for getting last points added inside callback function
self.last_point_callback = 0
# Monitoring/restore progress
if is_main_process():
cols = [
"N", "timestamp", "acceptance_rate", "Rminus1", "Rminus1_cl"
]
self.progress = DataFrame(columns=cols)
self.i_learn = 1
if self.output and not self.output.is_resuming():
with open(self.progress_filename(), "w",
encoding="utf-8") as progress_file:
progress_file.write("# " +
" ".join(self.progress.columns) + "\n")
# Get first point, to be discarded -- not possible to determine its weight
# Still, we need to compute derived parameters, since, as the proposal "blocked",
# we may be saving the initial state of some block.
# NB: if resuming but nothing was written (burn-in not finished): re-start
if self.output.is_resuming() and len(self.collection):
initial_point = (self.collection[
self.collection.sampled_params].iloc[len(self.collection) -
1]).values.copy()
logpost = -(self.collection[_minuslogpost].iloc[
len(self.collection) - 1].copy())
logpriors = -(self.collection[self.collection.minuslogprior_names].
iloc[len(self.collection) - 1].copy())
loglikes = -0.5 * (self.collection[self.collection.chi2_names].
iloc[len(self.collection) - 1].copy())
derived = (self.collection[self.collection.derived_params].iloc[
len(self.collection) - 1].values.copy())
else:
# NB: max_tries adjusted to dim instead of #cycles (blocking not computed yet)
self.max_tries.set_scale(self.model.prior.d())
self.log.info(
"Getting initial point... (this may take a few seconds)")
initial_point, logpost, logpriors, loglikes, derived = \
self.model.get_valid_point(max_tries=self.max_tries.value)
# If resuming but no existing chain, assume failed run and ignore blocking
# if speeds measurement requested
if self.output.is_resuming() and not len(self.collection) \
and self.measure_speeds:
self.blocking = None
if self.measure_speeds and self.blocking:
self.log.warning(
"Parameter blocking manually fixed: speeds will not be measured."
)
elif self.measure_speeds:
n = None if self.measure_speeds is True else int(
self.measure_speeds)
self.model.measure_and_set_speeds(n=n, discard=0)
self.set_proposer_blocking()
self.set_proposer_covmat(load=True)
self.current_point.add(initial_point,
derived=derived,
logpost=logpost,
logpriors=logpriors,
loglikes=loglikes)
self.log.info("Initial point: %s", self.current_point)
# Max #(learn+convergence checks) to wait,
# in case one process dies without sending MPI_ABORT
self.been_waiting = 0
self.max_waiting = max(50, self.max_tries.unit_value)
# Burning-in countdown -- the +1 accounts for the initial point (always accepted)
self.burn_in_left = self.burn_in.value * self.current_point.output_thin + 1
# Initial dummy checkpoint
# (needed when 1st "learn point" not reached in prev. run)
self.write_checkpoint()
def initialize(self):
"""Imports the PolyChord sampler and prepares its arguments."""
if not get_mpi_rank(): # rank = 0 (MPI master) or None (no MPI)
self.log.info("Initializing")
# If path not given, try using general path to modules
if not self.path and self.path_install:
self.path = get_path(self.path_install)
if self.path:
if not get_mpi_rank():
self.log.info("Importing *local* PolyChord from " + self.path)
if not os.path.exists(os.path.realpath(self.path)):
self.log.error("The given path does not exist.")
raise HandledException
pc_build_path = get_build_path(self.path)
if not pc_build_path:
self.log.error("Either PolyChord is not in the given folder, "
"'%s', or you have not compiled it.", self.path)
raise HandledException
# Inserting the previously found path into the list of import folders
sys.path.insert(0, pc_build_path)
else:
self.log.info("Importing *global* PolyChord.")
try:
import pypolychord
from pypolychord.settings import PolyChordSettings
self.pc = pypolychord
except ImportError:
self.log.error(
"Couldn't find the PolyChord python interface. "
"Make sure that you have compiled it, and that you either\n"
" (a) specify a path (you didn't) or\n"
" (b) install the Python interface globally with\n"
" '/path/to/PolyChord/python setup.py install --user'")
raise HandledException
# Prepare arguments and settings
self.nDims = self.model.prior.d()
self.nDerived = (len(self.model.parameterization.derived_params()) +
len(self.model.prior) + len(self.model.likelihood._likelihoods))
if self.logzero is None:
self.logzero = np.nan_to_num(-np.inf)
if self.max_ndead == np.inf:
self.max_ndead = -1
for p in ["nlive", "num_repeats", "nprior", "max_ndead"]:
setattr(self, p, read_dnumber(getattr(self, p), self.nDims, dtype=int))
# Fill the automatic ones
if getattr(self, "feedback", None) is None:
values = {logging.CRITICAL: 0, logging.ERROR: 0, logging.WARNING: 0,
logging.INFO: 1, logging.DEBUG: 2}
self.feedback = values[self.log.getEffectiveLevel()]
try:
output_folder = getattr(self.output, "folder")
output_prefix = getattr(self.output, "prefix") or ""
self.read_resume = self.resuming
except AttributeError:
# dummy output -- no resume!
self.read_resume = False
from tempfile import gettempdir
output_folder = gettempdir()
if not get_mpi_rank():
from random import random
output_prefix = hex(int(random() * 16 ** 6))[2:]
else:
output_prefix = None
if get_mpi():
output_prefix = get_mpi_comm().bcast(output_prefix, root=0)
self.base_dir = os.path.join(output_folder, self.base_dir)
self.file_root = output_prefix
if not get_mpi_rank():
# Creating output folder, if it does not exist (just one process)
if not os.path.exists(self.base_dir):
os.makedirs(self.base_dir)
# Idem, a clusters folder if needed -- notice that PolyChord's default
# is "True", here "None", hence the funny condition below
if self.do_clustering is not False: # None here means "default"
try:
os.makedirs(os.path.join(self.base_dir, clusters))
except OSError: # exists!
pass
self.log.info("Storing raw PolyChord output in '%s'.",
self.base_dir)
# Exploiting the speed hierarchy
speeds, blocks = self.model.likelihood._speeds_of_params(int_speeds=True)
blocks_flat = list(chain(*blocks))
self.ordering = [
blocks_flat.index(p) for p in self.model.parameterization.sampled_params()]
self.grade_dims = [len(block) for block in blocks]
# self.grade_frac = np.array(
# [i*j for i,j in zip(self.grade_dims, speeds)])
# self.grade_frac = (
# self.grade_frac/sum(self.grade_frac))
# Disabled for now. We need a way to override the "time" part of the meaning of grade_frac
self.grade_frac = [1 / len(self.grade_dims) for _ in self.grade_dims]
# Assign settings
pc_args = ["nlive", "num_repeats", "nprior", "do_clustering",
"precision_criterion", "max_ndead", "boost_posterior", "feedback",
"logzero", "update_files", "posteriors", "equals",
"cluster_posteriors", "write_resume", "read_resume", "write_stats",
"write_live", "write_dead", "base_dir", "grade_frac", "grade_dims",
"feedback", "read_resume", "base_dir", "file_root", "grade_frac",
"grade_dims"]
self.pc_settings = PolyChordSettings(
self.nDims, self.nDerived, seed=(self.seed if self.seed is not None else -1),
**{p: getattr(self, p) for p in pc_args if getattr(self, p) is not None})
# prior conversion from the hypercube
bounds = self.model.prior.bounds(
confidence_for_unbounded=self.confidence_for_unbounded)
# Check if priors are bounded (nan's to inf)
inf = np.where(np.isinf(bounds))
if len(inf[0]):
params_names = self.model.parameterization.sampled_params()
params = [params_names[i] for i in sorted(list(set(inf[0])))]
self.log.error("PolyChord needs bounded priors, but the parameter(s) '"
"', '".join(params) + "' is(are) unbounded.")
raise HandledException
locs = bounds[:, 0]
scales = bounds[:, 1] - bounds[:, 0]
# This function re-scales the parameters AND puts them in the right order
self.pc_prior = lambda x: (locs + np.array(x)[self.ordering] * scales).tolist()
# We will need the volume of the prior domain, since PolyChord divides by it
self.logvolume = np.log(np.prod(scales))
# Done!
if not get_mpi_rank():
self.log.info("Calling PolyChord with arguments:")
for p, v in inspect.getmembers(self.pc_settings, lambda a: not (callable(a))):
if not p.startswith("_"):
self.log.info(" %s: %s", p, v)
def check_convergence_and_learn_proposal(self):
"""
Checks the convergence of the sampling process (MPI only), and, if requested,
learns a new covariance matrix for the proposal distribution from the covariance
of the last samples.
"""
# Compute and gather means, covs and CL intervals of last half of chains
mean = self.collection.mean(first=int(self.n() / 2))
cov = self.collection.cov(first=int(self.n() / 2))
# No logging of warnings temporarily, so getdist won't complain innecessarily
logging.disable(logging.WARNING)
mcsamples = self.collection.sampled_to_getdist_mcsamples(
first=int(self.n() / 2))
logging.disable(logging.NOTSET)
bound = np.array([[
mcsamples.confidence(i,
limfrac=self.Rminus1_cl_level / 2.,
upper=which) for i in range(self.prior.d())
] for which in [False, True]]).T
Ns, means, covs, bounds = map(
lambda x: np.array((get_mpi_comm().gather(x)
if get_mpi() else [x])),
[self.n(), mean, cov, bound])
# Compute convergence diagnostics
if get_mpi():
if get_mpi_rank() == 0:
# "Within" or "W" term -- our "units" for assessing convergence
# and our prospective new covariance matrix
mean_of_covs = np.average(covs, weights=Ns, axis=0)
# "Between" or "B" term
# We don't weight with the number of samples in the chains here:
# shorter chains will likely be outliers, and we want to notice them
cov_of_means = np.cov(means.T) # , fweights=Ns)
# For numerical stability, we turn mean_of_covs into correlation matrix:
# rho = (diag(Sigma))^(-1/2) * Sigma * (diag(Sigma))^(-1/2)
# and apply the same transformation to the mean of covs (same eigenvals!)
diagSinvsqrt = np.diag(np.power(np.diag(cov_of_means), -0.5))
corr_of_means = diagSinvsqrt.dot(cov_of_means).dot(
diagSinvsqrt)
norm_mean_of_covs = diagSinvsqrt.dot(mean_of_covs).dot(
diagSinvsqrt)
# Cholesky of (normalized) mean of covs and eigvals of Linv*cov_of_means*L
try:
L = np.linalg.cholesky(norm_mean_of_covs)
except np.linalg.LinAlgError:
self.log.warning(
"Negative covariance eigenvectors. "
"This may mean that the covariance of the samples does not "
"contain enough information at this point. "
"Skipping this checkpoint")
success = False
else:
Linv = np.linalg.inv(L)
eigvals = np.linalg.eigvalsh(
Linv.dot(corr_of_means).dot(Linv.T))
Rminus1 = max(np.abs(eigvals))
# For real square matrices, a possible def of the cond number is:
condition_number = Rminus1 / min(np.abs(eigvals))
self.log.debug("Condition number = %g", condition_number)
self.log.debug("Eigenvalues = %r", eigvals)
self.log.info(
"Convergence of means: R-1 = %f after %d samples",
Rminus1, self.n())
success = True
# Have we converged in means?
# (criterion must be fulfilled twice in a row)
if (max(Rminus1, getattr(self, "Rminus1_last", np.inf)) <
self.Rminus1_stop):
# Check the convergence of the bounds of the confidence intervals
# Same as R-1, but with the rms deviation from the mean bound
# in units of the mean standard deviation of the chains
Rminus1_cl = (np.std(bounds, axis=0).T /
np.sqrt(np.diag(mean_of_covs)))
self.log.debug("normalized std's of bounds = %r",
Rminus1_cl)
self.log.info(
"Convergence of bounds: R-1 = %f after %d samples",
np.max(Rminus1_cl), self.n())
if np.max(Rminus1_cl) < self.Rminus1_cl_stop:
self.converged = True
self.log.info("The run has converged!")
# Broadcast and save the convergence status and the last R-1 of means
success = get_mpi_comm().bcast(
(success if not get_mpi_rank() else None), root=0)
if success:
self.Rminus1_last = get_mpi_comm().bcast(
(Rminus1 if not get_mpi_rank() else None), root=0)
self.converged = get_mpi_comm().bcast(
(self.converged if not get_mpi_rank() else None), root=0)
else: # No MPI
pass
# Do we want to learn a better proposal pdf?
if self.learn_proposal and not self.converged:
# update iff (not MPI, or MPI and "good" Rminus1)
if get_mpi():
good_Rminus1 = (self.learn_proposal_Rminus1_max >
self.Rminus1_last >
self.learn_proposal_Rminus1_min)
if not good_Rminus1:
if not get_mpi_rank():
self.log.info("Bad convergence statistics: "
"waiting until the next checkpoint.")
return
if get_mpi():
if get_mpi_rank():
mean_of_covs = np.empty((self.prior.d(), self.prior.d()))
get_mpi_comm().Bcast(mean_of_covs, root=0)
elif not get_mpi():
mean_of_covs = covs[0]
self.proposer.set_covariance(mean_of_covs)
if not get_mpi_rank():
self.log.info("Updated covariance matrix of proposal pdf.")
self.log.debug("%r", mean_of_covs)
