class mcmc(Sampler):
def initialize(self):
"""Initializes the sampler:
creates the proposal distribution and draws the initial sample."""
self.log.debug("Initializing")
for p in [
"burn_in", "max_tries", "output_every", "check_every",
"callback_every"
]:
setattr(
self, p,
read_dnumber(getattr(self, p), self.model.prior.d(),
dtype=int))
if self.callback_every is None:
self.callback_every = self.check_every
# Burning-in countdown -- the +1 accounts for the initial point (always accepted)
self.burn_in_left = self.burn_in + 1
# Max # checkpoints to wait, in case one process dies without sending MPI_ABORT
self.been_waiting = 0
self.max_waiting = max(50, self.max_tries / self.model.prior.d())
if self.resuming and (max(self.mpi_size or 0, 1) != max(
get_mpi_size(), 1)):
self.log.error(
"Cannot resume a sample with a different number of chains: "
"was %d and now is %d.", max(self.mpi_size, 1),
max(get_mpi_size(), 1))
raise HandledException
if not self.resuming and self.output:
# Delete previous files (if not "forced", the run would have already failed)
if ((os.path.abspath(self.covmat_filename()) != os.path.abspath(
str(self.covmat)))):
try:
os.remove(self.covmat_filename())
except OSError:
pass
# There may be more that chains than expected,
# if #ranks was bigger in a previous run
i = 0
while True:
i += 1
collection_filename, _ = self.output.prepare_collection(str(i))
try:
os.remove(collection_filename)
except OSError:
break
# 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.resuming)
self.current_point = OnePoint(self.model, OutputDummy({}), name=name)
# Use standard MH steps by default
self.get_new_sample = self.get_new_sample_metropolis
# Prepare oversampling / dragging if applicable
self.effective_max_samples = self.max_samples
if self.oversample and self.drag:
self.log.error("Choose either oversampling or dragging, not both.")
raise HandledException
if self.oversample:
factors, blocks = self.model.likelihood._speeds_of_params(
int_speeds=True)
self.oversampling_factors = factors
self.log.info("Oversampling with factors:\n" + "\n".join([
" %d : %r" % (f, b)
for f, b in zip(self.oversampling_factors, blocks)
]))
self.i_last_slow_block = None
# No way right now to separate slow and fast
slow_params = list(self.model.parameterization.sampled_params())
elif self.drag:
speeds, blocks = self.model.likelihood._speeds_of_params(
fast_slow=True, int_speeds=True)
# For now, no blocking inside either fast or slow: just 2 blocks
self.i_last_slow_block = 0
if np.all(speeds == speeds[0]):
self.log.error(
"All speeds are equal or too similar: cannot drag! "
"Make sure to define accurate likelihoods' speeds.")
raise HandledException
# Make the 1st factor 1:
speeds = [1, speeds[1] / speeds[0]]
# Target: dragging step taking as long as slow step
self.drag_interp_steps = self.drag * speeds[1]
# Per dragging step, the (fast) posterior is evaluated *twice*,
self.drag_interp_steps /= 2
self.drag_interp_steps = int(np.round(self.drag_interp_steps))
fast_params = list(chain(*blocks[1 + self.i_last_slow_block:]))
# Not too much or too little dragging
drag_limits = [(int(l) * len(fast_params) if l is not None else l)
for l in self.drag_limits]
if drag_limits[
0] is not None and self.drag_interp_steps < drag_limits[0]:
self.log.warning(
"Number of dragging steps clipped from below: was not "
"enough to efficiently explore the fast directions -- "
"avoid this limit by decreasing 'drag_limits[0]'.")
self.drag_interp_steps = drag_limits[0]
if drag_limits[
1] is not None and self.drag_interp_steps > drag_limits[1]:
self.log.warning(
"Number of dragging steps clipped from above: "
"excessive, probably inefficient, exploration of the "
"fast directions -- "
"avoid this limit by increasing 'drag_limits[1]'.")
self.drag_interp_steps = drag_limits[1]
# Re-scale steps between checkpoint and callback to the slow dimensions only
slow_params = list(chain(*blocks[:1 + self.i_last_slow_block]))
self.n_slow = len(slow_params)
for p in ["check_every", "callback_every"]:
setattr(
self, p,
int(getattr(self, p) * self.n_slow / self.model.prior.d()))
self.log.info("Dragging with oversampling per step:\n" +
"\n".join([
" %d : %r" % (f, b)
for f, b in zip([1, self.drag_interp_steps],
[blocks[0], fast_params])
]))
self.get_new_sample = self.get_new_sample_dragging
else:
_, blocks = self.model.likelihood._speeds_of_params()
self.oversampling_factors = [1 for b in blocks]
slow_params = list(self.model.parameterization.sampled_params())
self.n_slow = len(slow_params)
# Turn parameter names into indices
self.blocks = [[
list(self.model.parameterization.sampled_params()).index(p)
for p in b
] for b in blocks]
self.proposer = BlockedProposer(
self.blocks,
oversampling_factors=self.oversampling_factors,
i_last_slow_block=self.i_last_slow_block,
proposal_scale=self.proposal_scale)
# Build the initial covariance matrix of the proposal, or load from checkpoint
if self.resuming:
covmat = np.loadtxt(self.covmat_filename())
self.log.info("Covariance matrix from checkpoint.")
else:
covmat = self.initial_proposal_covmat(slow_params=slow_params)
self.log.info("Initial covariance matrix.")
self.log.debug(
"Sampling with covmat:\n%s",
DataFrame(
covmat,
columns=self.model.parameterization.sampled_params(),
index=self.model.parameterization.sampled_params()).to_string(
line_width=_line_width))
self.proposer.set_covariance(covmat)
# Prepare callback function
if self.callback_function is not None:
self.callback_function_callable = (get_external_function(
self.callback_function))
def initial_proposal_covmat(self, slow_params=None):
"""
Build the initial covariance matrix, using the data provided, in descending order
of priority:
1. "covmat" field in the "mcmc" sampler block.
2. "proposal" field for each parameter.
3. variance of the reference pdf.
4. variance of the prior pdf.
The covariances between parameters when both are present in a covariance matrix
provided through option 1 are preserved. All other covariances are assumed 0.
"""
params_infos = self.model.parameterization.sampled_params_info()
covmat = np.diag([np.nan] * len(params_infos))
# Try to generate it automatically
if isinstance(self.covmat,
six.string_types) and self.covmat.lower() == "auto":
slow_params_info = {
p: info
for p, info in params_infos.items() if p in slow_params
}
auto_covmat = self.model.likelihood._get_auto_covmat(
slow_params_info)
if auto_covmat:
self.covmat = os.path.join(auto_covmat["folder"],
auto_covmat["name"])
self.log.info("Covariance matrix selected automatically: %s",
self.covmat)
else:
self.covmat = None
self.log.info(
"Could not automatically find a good covmat. "
"Will generate from parameter info (proposal and prior).")
# If given, load and test the covariance matrix
if isinstance(self.covmat, six.string_types):
covmat_pre = "{%s}" % _path_install
if self.covmat.startswith(covmat_pre):
self.covmat = self.covmat.format(
**{
_path_install: self.path_install
}).replace("/", os.sep)
try:
with open(self.covmat, "r") as file_covmat:
header = file_covmat.readline()
loaded_covmat = np.loadtxt(self.covmat)
except TypeError:
self.log.error(
"The property 'covmat' must be a file name,"
"but it's '%s'.", str(self.covmat))
raise HandledException
except IOError:
self.log.error("Can't open covmat file '%s'.", self.covmat)
raise HandledException
if header[0] != "#":
self.log.error(
"The first line of the covmat file '%s' "
"must be one list of parameter names separated by spaces "
"and staring with '#', and the rest must be a square matrix, "
"with one row per line.", self.covmat)
raise HandledException
loaded_params = header.strip("#").strip().split()
elif hasattr(self.covmat, "__getitem__"):
if not self.covmat_params:
self.log.error(
"If a covariance matrix is passed as a numpy array, "
"you also need to pass the parameters it corresponds to "
"via 'covmat_params: [name1, name2, ...]'.")
raise HandledException
loaded_params = self.covmat_params
loaded_covmat = self.covmat
if self.covmat is not None:
if len(loaded_params) != len(set(loaded_params)):
self.log.error(
"There are duplicated parameters in the header of the "
"covmat file '%s' ", self.covmat)
raise HandledException
if len(loaded_params) != loaded_covmat.shape[0]:
self.log.error(
"The number of parameters in the header of '%s' and the "
"dimensions of the matrix do not coincide.", self.covmat)
raise HandledException
if not (np.allclose(loaded_covmat.T, loaded_covmat)
and np.all(np.linalg.eigvals(loaded_covmat) > 0)):
self.log.error(
"The covmat loaded from '%s' is not a positive-definite, "
"symmetric square matrix.", self.covmat)
raise HandledException
# Fill with parameters in the loaded covmat
renames = [[p] + np.atleast_1d(v.get(_p_renames, [])).tolist()
for p, v in params_infos.items()]
renames = odict([[a[0], a] for a in renames])
indices_used, indices_sampler = zip(*[[
loaded_params.index(p),
[
list(params_infos).index(q) for q, a in renames.items()
if p in a
]
] for p in loaded_params])
if not any(indices_sampler):
self.log.error(
"A proposal covariance matrix has been loaded, but none of its "
"parameters are actually sampled here. Maybe a mismatch between"
" parameter names in the covariance matrix and the input file?"
)
raise HandledException
indices_used, indices_sampler = zip(
*[[i, j] for i, j in zip(indices_used, indices_sampler) if j])
if any(len(j) - 1 for j in indices_sampler):
first = next(j for j in indices_sampler if len(j) > 1)
self.log.error(
"The parameters %s have duplicated aliases. Can't assign them an "
"element of the covariance matrix unambiguously.",
", ".join([list(params_infos)[i] for i in first]))
raise HandledException
indices_sampler = list(chain(*indices_sampler))
covmat[np.ix_(indices_sampler,
indices_sampler)] = (loaded_covmat[np.ix_(
indices_used, indices_used)])
self.log.info("Covariance matrix loaded for params %r",
[list(params_infos)[i] for i in indices_sampler])
missing_params = set(params_infos).difference(
set([list(params_infos)[i] for i in indices_sampler]))
if missing_params:
self.log.info("Missing proposal covariance for params %r", [
p for p in self.model.parameterization.sampled_params()
if p in missing_params
])
else:
self.log.info(
"All parameters' covariance loaded from given covmat.")
# Fill gaps with "proposal" property, if present, otherwise ref (or prior)
where_nan = np.isnan(covmat.diagonal())
if np.any(where_nan):
covmat[where_nan, where_nan] = np.array([
info.get(_p_proposal, np.nan)**2
for info in params_infos.values()
])[where_nan]
# we want to start learning the covmat earlier
self.log.info(
"Covariance matrix " +
("not present" if np.all(where_nan) else "not complete") + ". "
"We will start learning the covariance of the proposal earlier:"
" R-1 = %g (was %g).", self.learn_proposal_Rminus1_max_early,
self.learn_proposal_Rminus1_max)
self.learn_proposal_Rminus1_max = self.learn_proposal_Rminus1_max_early
where_nan = np.isnan(covmat.diagonal())
if np.any(where_nan):
covmat[where_nan, where_nan] = (
self.model.prior.reference_covmat().diagonal()[where_nan])
assert not np.any(np.isnan(covmat))
return covmat
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 n(self, burn_in=False):
"""
Returns the total number of steps taken, including or not burn-in steps depending
on the value of the `burn_in` keyword.
"""
return self.collection.n() + (0 if not burn_in else self.burn_in -
self.burn_in_left + 1)
def get_new_sample_metropolis(self):
"""
Draws a new trial point from the proposal pdf and checks whether it is accepted:
if it is accepted, it saves the old one into the collection and sets the new one
as the current state; if it is rejected increases the weight of the current state
by 1.
Returns:
``True`` for an accepted step, ``False`` for a rejected one.
"""
trial = deepcopy(
self.current_point[self.model.parameterization._sampled])
self.proposer.get_proposal(trial)
logpost_trial, logprior_trial, loglikes_trial, derived = self.model.logposterior(
trial)
accept = self.metropolis_accept(logpost_trial,
-self.current_point["minuslogpost"])
self.process_accept_or_reject(accept, trial, derived, logpost_trial,
logprior_trial, loglikes_trial)
return accept
def get_new_sample_dragging(self):
"""
Draws a new trial point in the slow subspace, and gets the corresponding trial
in the fast subspace by "dragging" the fast parameters.
Finally, checks the acceptance of the total step using the "dragging" pdf:
if it is accepted, it saves the old one into the collection and sets the new one
as the current state; if it is rejected increases the weight of the current state
by 1.
Returns:
``True`` for an accepted step, ``False`` for a rejected one.
"""
# Prepare starting and ending points *in the SLOW subspace*
# "start_" and "end_" mean here the extremes in the SLOW subspace
start_slow_point = self.current_point[
self.model.parameterization._sampled]
start_slow_logpost = -self.current_point["minuslogpost"]
end_slow_point = deepcopy(start_slow_point)
self.proposer.get_proposal_slow(end_slow_point)
self.log.debug("Proposed slow end-point: %r", end_slow_point)
# Save derived parameters of delta_slow jump, in case I reject all the dragging
# steps but accept the move in the slow direction only
end_slow_logpost, end_slow_logprior, end_slow_loglikes, derived = (
self.model.logposterior(end_slow_point))
if end_slow_logpost == -np.inf:
self.current_point.increase_weight(1)
return False
# trackers of the dragging
current_start_point = start_slow_point
current_end_point = end_slow_point
current_start_logpost = start_slow_logpost
current_end_logpost = end_slow_logpost
current_end_logprior = end_slow_logprior
current_end_loglikes = end_slow_loglikes
# accumulators for the "dragging" probabilities to be metropolist-tested
# at the end of the interpolation
start_drag_logpost_acc = start_slow_logpost
end_drag_logpost_acc = end_slow_logpost
# start dragging
for i_step in range(1, 1 + self.drag_interp_steps):
self.log.debug("Dragging step: %d", i_step)
# take a step in the fast direction in both slow extremes
delta_fast = np.zeros(len(current_start_point))
self.proposer.get_proposal_fast(delta_fast)
self.log.debug("Proposed fast step delta: %r", delta_fast)
proposal_start_point = deepcopy(current_start_point)
proposal_start_point += delta_fast
proposal_end_point = deepcopy(current_end_point)
proposal_end_point += delta_fast
# get the new extremes for the interpolated probability
# (reject if any of them = -inf; avoid evaluating both if just one fails)
# Force the computation of the (slow blocks) derived params at the starting
# point, but discard them, since they contain the starting point's fast ones,
# not used later -- save the end point's ones.
proposal_start_logpost = self.model.logposterior(
proposal_start_point)[0]
proposal_end_logpost, proposal_end_logprior, \
proposal_end_loglikes, derived_proposal_end = (
self.model.logposterior(proposal_end_point)
if proposal_start_logpost > -np.inf
else (-np.inf, None, [], []))
if proposal_start_logpost > -np.inf and proposal_end_logpost > -np.inf:
# create the interpolated probability and do a Metropolis test
frac = i_step / (1 + self.drag_interp_steps)
proposal_interp_logpost = (
(1 - frac) * proposal_start_logpost +
frac * proposal_end_logpost)
current_interp_logpost = ((1 - frac) * current_start_logpost +
frac * current_end_logpost)
accept_drag = self.metropolis_accept(proposal_interp_logpost,
current_interp_logpost)
else:
accept_drag = False
self.log.debug("Dragging step: %s",
("accepted" if accept_drag else "rejected"))
# If the dragging step was accepted, do the drag
if accept_drag:
current_start_point = proposal_start_point
current_start_logpost = proposal_start_logpost
current_end_point = proposal_end_point
current_end_logpost = proposal_end_logpost
current_end_logprior = proposal_end_logprior
current_end_loglikes = proposal_end_loglikes
derived = derived_proposal_end
# In any case, update the dragging probability for the final metropolis test
start_drag_logpost_acc += current_start_logpost
end_drag_logpost_acc += current_end_logpost
# Test for the TOTAL step
accept = self.metropolis_accept(
end_drag_logpost_acc / self.drag_interp_steps,
start_drag_logpost_acc / self.drag_interp_steps)
self.process_accept_or_reject(accept, current_end_point, derived,
current_end_logpost,
current_end_logprior,
current_end_loglikes)
self.log.debug("TOTAL step: %s",
("accepted" if accept else "rejected"))
return accept
def metropolis_accept(self, logp_trial, logp_current):
"""
Symmetric-proposal Metropolis-Hastings test.
Returns:
``True`` or ``False``.
"""
if logp_trial == -np.inf:
return False
elif logp_trial > logp_current:
return True
else:
return np.random.exponential() > (logp_current - logp_trial)
def process_accept_or_reject(self,
accept_state,
trial=None,
derived=None,
logpost_trial=None,
logprior_trial=None,
loglikes_trial=None):
"""Processes the acceptance/rejection of the new point."""
if accept_state:
# add the old point to the collection (if not burning or initial point)
if self.burn_in_left <= 0:
self.current_point.add_to_collection(self.collection)
self.log.debug("New sample, #%d: \n %r", self.n(),
self.current_point)
if self.n() % self.output_every == 0:
self.collection._out_update()
else:
self.burn_in_left -= 1
self.log.debug("Burn-in sample:\n %r", self.current_point)
if self.burn_in_left == 0 and self.burn_in:
self.log.info(
"Finished burn-in phase: discarded %d accepted steps.",
self.burn_in)
# set the new point as the current one, with weight one
self.current_point.add(trial,
derived=derived,
weight=1,
logpost=logpost_trial,
logpriors=logprior_trial,
loglikes=loglikes_trial)
else: # not accepted
self.current_point.increase_weight(1)
# Failure criterion: chain stuck! (but be more permissive during burn_in)
max_tries_now = self.max_tries * (
1 + (10 - 1) * np.sign(self.burn_in_left))
if self.current_point[_weight] > max_tries_now:
self.collection._out_update()
self.log.error(
"The chain has been stuck for %d attempts. Stopping sampling. "
"If this has happened often, try improving your "
"reference point/distribution. Alternatively (though not advisable) "
"make 'max_tries: np.inf' (or 'max_tries: .inf' in yaml)",
max_tries_now)
raise HandledException
# Functions to check convergence and learn the covariance of the proposal distribution
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 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 write_checkpoint(self):
if not get_mpi_rank() and self.output:
checkpoint_filename = self.checkpoint_filename()
covmat_filename = self.covmat_filename()
np.savetxt(covmat_filename,
self.proposer.get_covariance(),
header=" ".join(
list(self.model.parameterization.sampled_params())))
checkpoint_info = {
_sampler: {
self.name:
odict([
["converged", bool(self.converged)],
["Rminus1_last", self.Rminus1_last],
["proposal_scale",
self.proposer.get_scale()],
["blocks", self.blocks],
["oversampling_factors", self.oversampling_factors],
["i_last_slow_block", self.i_last_slow_block],
[
"burn_in",
(
self.
burn_in # initial: repeat burn-in if not finished
if not self.n() and self.burn_in_left else "d")
], # to avoid overweighting last point of prev. run
["mpi_size", get_mpi_size()]
])
}
}
yaml_dump_file(checkpoint_filename,
checkpoint_info,
error_if_exists=False)
self.log.debug("Dumped checkpoint info and current covmat.")
# Finally: returning the computed products ###########################################
def products(self):
"""
Auxiliary function to define what should be returned in a scripted call.
Returns:
The sample ``Collection`` containing the accepted steps.
"""
return {"sample": self.collection}
class mcmc(Sampler):
def initialise(self):
"""Initialises the sampler:
creates the proposal distribution and draws the initial sample."""
self.log.info("Initializing")
# Burning-in countdown -- the +1 accounts for the initial point (always accepted)
self.burn_in_left = self.burn_in + 1
# 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.parametrization,
self.likelihood,
self.output,
name=name)
self.current_point = OnePoint(self.parametrization,
self.likelihood,
self.output,
name=name)
# Use the standard steps by default
self.get_new_sample = self.get_new_sample_metropolis
# Prepare oversampling / fast-dragging if applicable
self.effective_max_samples = self.max_samples
if self.oversample and self.drag:
self.log.error(
"Choose either oversampling or fast-dragging, not both.")
raise HandledException
# if (self.oversample or self.drag) and len(set(factors)) == 1:
# self.log.error("All block speeds are similar: "
# "no dragging or oversampling possible.")
# raise HandledException
if self.oversample:
factors, blocks = self.likelihood.speeds_of_params(
oversampling_factors=True)
self.oversampling_factors = factors
# WIP: actually, we would have to re-normalise to the dimension of the blocks.
self.log.info("Oversampling with factors:\n" + "\n".join([
" %d : %r" % (f, b)
for f, b in zip(self.oversampling_factors, blocks)
]))
# WIP: useless until likelihoods have STATES!
self.log.error("Sorry, oversampling is WIP")
raise HandledException
elif self.drag:
# WIP: for now, can only separate between theory and likelihoods
# until likelihoods have states
if not self.likelihood.theory:
self.log.error(
"WIP: dragging disabled for now when no theory code present."
)
raise HandledException
# if self.max_speed_slow < min(speeds) or self.max_speed_slow >= max(speeds):
# self.log.error("The maximum speed considered slow, `max_speed_slow`, must be "
# "%g <= `max_speed_slow < %g, and is %g",
# min(speeds), max(speeds), self.max_speed_slow)
# raise HandledException
speeds, blocks = self.likelihood.speeds_of_params(int_speeds=True,
fast_slow=True)
if np.all(speeds == speeds[0]):
self.log.error(
"All speeds are equal: cannot drag! Make sure to define, "
"especially, the speed of the fastest likelihoods.")
self.i_last_slow_block = 0 # just theory can be slow for now
fast_params = list(chain(*blocks[1 + self.i_last_slow_block:]))
self.n_slow = sum(
len(blocks[i]) for i in range(1 + self.i_last_slow_block))
self.drag_interp_steps = int(self.drag *
np.round(min(speeds[1:]) / speeds[0]))
self.log.info("Dragging with oversampling per step:\n" +
"\n".join([
" %d : %r" % (f, b)
for f, b in zip([1, self.drag_interp_steps],
[blocks[0], fast_params])
]))
self.get_new_sample = self.get_new_sample_dragging
else:
_, blocks = self.likelihood.speeds_of_params()
self.oversampling_factors = [1 for b in blocks]
self.n_slow = len(self.parametrization.sampled_params())
# Turn parameter names into indices
blocks = [[
list(self.parametrization.sampled_params().keys()).index(p)
for p in b
] for b in blocks]
self.proposer = BlockedProposer(
blocks,
oversampling_factors=getattr(self, "oversampling_factors", None),
i_last_slow_block=getattr(self, "i_last_slow_block", None),
propose_scale=self.propose_scale)
# Build the initial covariance matrix of the proposal
covmat = self.initial_proposal_covmat()
self.log.info("Sampling with covariance matrix:")
self.log.info("%r", covmat)
self.proposer.set_covariance(covmat)
# Prepare callback function
if self.callback_function is not None:
self.callback_function_callable = (get_external_function(
self.callback_function))
def initial_proposal_covmat(self):
"""
Build the initial covariance matrix, using the data provided, in descending order
of priority:
1. "covmat" field in the "mcmc" sampler block.
2. "proposal" field for each parameter.
3. variance of the reference pdf.
4. variance of the prior pdf.
The covariances between parameters when both are present in a covariance matrix
provided through option 1 are preserved. All other covariances are assumed 0.
"""
params, params_infos = zip(
*self.parametrization.sampled_params().items())
covmat = np.diag([np.nan] * len(params))
# If given, load and test the covariance matrix
if isinstance(self.covmat, six.string_types):
covmat_pre = "MODULES:"
if self.covmat.startswith(covmat_pre):
self.covmat = os.path.join(get_path_to_installation(),
self.covmat[len(covmat_pre):])
try:
with open(self.covmat, "r") as file_covmat:
header = file_covmat.readline()
loaded_covmat = np.loadtxt(self.covmat)
except TypeError:
self.log.error(
"The property 'covmat' must be a file name,"
"but it's '%s'.", str(self.covmat))
raise HandledException
except IOError:
self.log.error("Can't open covmat file '%s'.", self.covmat)
raise HandledException
if header[0] != "#":
self.log.error(
"The first line of the covmat file '%s' "
"must be one list of parameter names separated by spaces "
"and staring with '#', and the rest must be a square matrix, "
"with one row per line.", self.covmat)
raise HandledException
loaded_params = header.strip("#").strip().split()
elif hasattr(self.covmat, "__getitem__"):
if not self.covmat_params:
self.log.error(
"If a covariance matrix is passed as a numpy array, "
"you also need to pass the parameters it corresponds to "
"via 'covmat_params: [name1, name2, ...]'.")
raise HandledException
loaded_params = self.covmat_params
loaded_covmat = self.covmat
if self.covmat is not None:
if len(loaded_params) != len(set(loaded_params)):
self.log.error(
"There are duplicated parameters in the header of the "
"covmat file '%s' ", self.covmat)
raise HandledException
if len(loaded_params) != loaded_covmat.shape[0]:
self.log.error(
"The number of parameters in the header of '%s' and the "
"dimensions of the matrix do not coincide.", self.covmat)
raise HandledException
if not (np.allclose(loaded_covmat.T, loaded_covmat)
and np.all(np.linalg.eigvals(loaded_covmat) > 0)):
self.log.error(
"The covmat loaded from '%s' is not a positive-definite, "
"symmetric square matrix.", self.covmat)
raise HandledException
# Fill with parameters in the loaded covmat
aliases = [[p] + np.atleast_1d(v.get(_p_alias, [])).tolist()
for p, v in zip(params, params_infos)]
aliases = odict([[a[0], a] for a in aliases])
indices_used, indices_sampler = zip(*[[
loaded_params.index(p),
[params.index(q) for q, a in aliases.items() if p in a]
] for p in loaded_params])
indices_used, indices_sampler = zip(
*[[i, j] for i, j in zip(indices_used, indices_sampler) if j])
if any(len(j) - 1 for j in indices_sampler):
first = next(j for j in indices_sampler if len(j) > 1)
self.log.error(
"The parameters %s have duplicated aliases. Can't assign them an "
"element of the covariance matrix unambiguously.",
", ".join([params[i] for i in first]))
raise HandledException
indices_sampler = list(chain(*indices_sampler))
if not indices_used:
self.log.error(
"A proposal covariance matrix has been loaded, but none of its "
"parameters are actually sampled here. Maybe a mismatch between"
" parameter names in the covariance matrix and the input file?"
)
raise HandledException
covmat[np.ix_(indices_sampler,
indices_sampler)] = (loaded_covmat[np.ix_(
indices_used, indices_used)])
self.log.info("Covariance matrix loaded for params %r",
[params[i] for i in indices_sampler])
missing_params = set(params).difference(
set([params[i] for i in indices_sampler]))
if missing_params:
self.log.info("Missing proposal covarince for params %r", [
p for p in self.parametrization.sampled_params()
if p in missing_params
])
else:
self.log.info(
"All parameters' covariance loaded from given covmat.")
# Fill gaps with "proposal" property, if present, otherwise ref (or prior)
where_nan = np.isnan(covmat.diagonal())
if np.any(where_nan):
covmat[where_nan, where_nan] = np.array([
info.get(_p_proposal, np.nan)**2 for info in params_infos
])[where_nan]
# we want to start learning the covmat earlier
self.log.info(
"Covariance matrix " +
("not present" if np.all(where_nan) else "not complete") + ". "
"We will start learning the covariance of the proposal earlier: "
"R-1 = %g (was %g).", self.learn_proposal_Rminus1_max_early,
self.learn_proposal_Rminus1_max)
self.learn_proposal_Rminus1_max = self.learn_proposal_Rminus1_max_early
where_nan = np.isnan(covmat.diagonal())
if np.any(where_nan):
covmat[where_nan, where_nan] = (
self.prior.reference_covmat().diagonal()[where_nan])
assert not np.any(np.isnan(covmat))
return covmat
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.
initial_point = self.prior.reference(max_tries=self.max_tries)
logpost, _, _, derived = self.logposterior(initial_point)
self.current_point.add(initial_point, derived=derived, logpost=logpost)
self.log.info("Initial point:\n %r ", self.current_point)
# Main loop!
self.converged = False
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()
# Make sure the last batch of samples ( < output_every ) are written
self.collection.out_update()
if not get_mpi_rank():
self.log.info("Sampling complete after %d accepted steps.",
self.n())
def n(self, burn_in=False):
"""
Returns the total number of steps taken, including or not burn-in steps depending
on the value of the `burn_in` keyword.
"""
return self.collection.n() + (0 if not burn_in else self.burn_in -
self.burn_in_left + 1)
def get_new_sample_metropolis(self):
"""
Draws a new trial point from the proposal pdf and checks whether it is accepted:
if it is accepted, it saves the old one into the collection and sets the new one
as the current state; if it is rejected increases the weight of the current state
by 1.
Returns:
``True`` for an accepted step, ``False`` for a rejected one.
"""
trial = deepcopy(
self.current_point[self.parametrization.sampled_params()])
self.proposer.get_proposal(trial)
logpost_trial, logprior_trial, logliks_trial, derived = self.logposterior(
trial)
accept = self.metropolis_accept(logpost_trial,
-self.current_point["minuslogpost"])
self.process_accept_or_reject(accept, trial, derived, logpost_trial,
logprior_trial, logliks_trial)
return accept
def get_new_sample_dragging(self):
"""
Draws a new trial point in the slow subspace, and gets the corresponding trial
in the fast subspace by "dragging" the fast parameters.
Finally, checks the acceptance of the total step using the "dragging" pdf:
if it is accepted, it saves the old one into the collection and sets the new one
as the current state; if it is rejected increases the weight of the current state
by 1.
Returns:
``True`` for an accepted step, ``False`` for a rejected one.
"""
# Prepare starting and ending points *in the SLOW subspace*
# "start_" and "end_" mean here the extremes in the SLOW subspace
start_slow_point = self.current_point[
self.parametrization.sampled_params()]
start_slow_logpost = -self.current_point["minuslogpost"]
end_slow_point = deepcopy(start_slow_point)
self.proposer.get_proposal_slow(end_slow_point)
self.log.debug("Proposed slow end-point: %r", end_slow_point)
# Save derived paramters of delta_slow jump, in case I reject all the dragging
# steps but accept the move in the slow direction only
end_slow_logpost, end_slow_logprior, end_slow_logliks, derived = (
self.logposterior(end_slow_point))
if end_slow_logpost == -np.inf:
self.current_point.increase_weight(1)
return False
# trackers of the dragging
current_start_point = start_slow_point
current_end_point = end_slow_point
current_start_logpost = start_slow_logpost
current_end_logpost = end_slow_logpost
current_end_logprior = end_slow_logprior
current_end_logliks = end_slow_logliks
# accumulators for the "dragging" probabilities to be metropolist-tested
# at the end of the interpolation
start_drag_logpost_acc = start_slow_logpost
end_drag_logpost_acc = end_slow_logpost
# start dragging
for i_step in range(1, 1 + self.drag_interp_steps):
self.log.debug("Dragging step: %d", i_step)
# take a step in the fast direction in both slow extremes
delta_fast = np.zeros(len(current_start_point))
self.proposer.get_proposal_fast(delta_fast)
self.log.debug("Proposed fast step delta: %r", delta_fast)
proposal_start_point = deepcopy(current_start_point)
proposal_start_point += delta_fast
proposal_end_point = deepcopy(current_end_point)
proposal_end_point += delta_fast
# get the new extremes for the interpolated probability
# (reject if any of them = -inf; avoid evaluating both if just one fails)
# Force the computation of the (slow blocks) derived params at the starting
# point, but discard them, since they contain the starting point's fast ones,
# not used later -- save the end point's ones.
proposal_start_logpost = self.logposterior(proposal_start_point)[0]
proposal_end_logpost, proposal_end_logprior, \
proposal_end_logliks, derived_proposal_end = (
self.logposterior(proposal_end_point)
if proposal_start_logpost > -np.inf
else (-np.inf, None, [], []))
if proposal_start_logpost > -np.inf and proposal_end_logpost > -np.inf:
# create the interpolated probability and do a Metropolis test
frac = i_step / (1 + self.drag_interp_steps)
proposal_interp_logpost = (
(1 - frac) * proposal_start_logpost +
frac * proposal_end_logpost)
current_interp_logpost = ((1 - frac) * current_start_logpost +
frac * current_end_logpost)
accept_drag = self.metropolis_accept(proposal_interp_logpost,
current_interp_logpost)
else:
accept_drag = False
self.log.debug("Dragging step: %s",
("accepted" if accept_drag else "rejected"))
# If the dragging step was accepted, do the drag
if accept_drag:
current_start_point = proposal_start_point
current_start_logpost = proposal_start_logpost
current_end_point = proposal_end_point
current_end_logpost = proposal_end_logpost
current_end_logprior = proposal_end_logprior
current_end_logliks = proposal_end_logliks
derived = derived_proposal_end
# In any case, update the dragging probability for the final metropolis test
start_drag_logpost_acc += current_start_logpost
end_drag_logpost_acc += current_end_logpost
# Test for the TOTAL step
accept = self.metropolis_accept(
end_drag_logpost_acc / self.drag_interp_steps,
start_drag_logpost_acc / self.drag_interp_steps)
self.process_accept_or_reject(accept, current_end_point, derived,
current_end_logpost,
current_end_logprior,
current_end_logliks)
self.log.debug("TOTAL step: %s",
("accepted" if accept else "rejected"))
return accept
def metropolis_accept(self, logp_trial, logp_current):
"""
Symmetric-proposal Metropolis-Hastings test.
Returns:
``True`` or ``False``.
"""
if logp_trial == -np.inf:
return False
elif logp_trial > logp_current:
return True
else:
return np.random.exponential() > (logp_current - logp_trial)
def process_accept_or_reject(self,
accept_state,
trial=None,
derived=None,
logpost_trial=None,
logprior_trial=None,
logliks_trial=None):
"""Processes the acceptance/rejection of the new point."""
if accept_state:
# add the old point to the collection (if not burning or initial point)
if self.burn_in_left <= 0:
self.current_point.add_to_collection(self.collection)
self.log.debug("New sample, #%d: \n %r", self.n(),
self.current_point)
if self.n() % self.output_every == 0:
self.collection.out_update()
else:
self.burn_in_left -= 1
self.log.debug("Burn-in sample:\n %r", self.current_point)
if self.burn_in_left == 0:
self.log.info(
"Finished burn-in phase: discarded %d accepted steps.",
self.burn_in)
# set the new point as the current one, with weight one
self.current_point.add(trial,
derived=derived,
weight=1,
logpost=logpost_trial,
logprior=logprior_trial,
logliks=logliks_trial)
else: # not accepted
self.current_point.increase_weight(1)
# Failure criterion: chain stuck!
if self.current_point[_weight] > self.max_tries:
self.collection.out_update()
self.log.error(
"The chain has been stuck for %d attempts. "
"Stopping sampling. If this has happened often, try improving your"
" reference point/distribution.", self.max_tries)
raise HandledException
# Functions to check convergence and learn the covariance of the proposal distribution
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" if get_mpi() else "") +
(" 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_dimension_times * self.n_slow))):
self.log.info("Checkpoint: %d samples accepted.", self.n())
# 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")
# Just in case, a barrier here
get_mpi_comm().barrier()
return True
return False
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)
# Finally: returning the computed products ###########################################
def products(self):
"""
Auxiliary function to define what should be returned in a scripted call.
Returns:
The sample ``Collection`` containing the accepted steps.
"""
return {"sample": self.collection}