class MCMC(CovmatSampler):
r"""
Adaptive, speed-hierarchy-aware MCMC sampler (adapted from CosmoMC)
\cite{Lewis:2002ah,Lewis:2013hha}.
"""
_at_resume_prefer_new = CovmatSampler._at_resume_prefer_new + [
"burn_in", "callback_function", "callback_every", "max_tries",
"output_every", "learn_every", "learn_proposal_Rminus1_max",
"learn_proposal_Rminus1_max_early", "learn_proposal_Rminus1_min",
"max_samples", "Rminus1_stop", "Rminus1_cl_stop", "Rminus1_cl_level",
"covmat", "covmat_params"
]
_at_resume_prefer_old = CovmatSampler._at_resume_prefer_new + [
"proposal_scale", "blocking"
]
file_base_name = 'mcmc'
# instance variables from yaml
burn_in: NumberWithUnits
learn_every: NumberWithUnits
output_every: NumberWithUnits
callback_every: NumberWithUnits
max_tries: NumberWithUnits
max_samples: int
drag: bool
callback_function: Optional[Callable]
blocking: Optional[Sequence]
proposal_scale: float
learn_proposal: bool
learn_proposal_Rminus1_max: float
learn_proposal_Rminus1_max_early: float
Rminus1_cl_level: float
Rminus1_stop: float
Rminus1_cl_stop: float
Rminus1_single_split: int
learn_proposal_Rminus1_min: float
measure_speeds: bool
oversample_thin: int
oversample_power: float
def set_instance_defaults(self):
super().set_instance_defaults()
# checkpoint variables
self.converged = False
self.mpi_size = None
self.Rminus1_last = np.inf
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:
raise LoggedError(
self.log, "`oversample` has been deprecated. "
"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:
raise LoggedError(
self.log, "`check_every` has been deprecated. "
"Please use `learn_every` instead.")
# 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) !=
mpi.size()):
raise LoggedError(
self.log,
"Cannot resume a run with a different number of chains: "
"was %d and now is %d.", max(self.mpi_size or 0, 1),
mpi.size())
sync_processes()
# One collection per MPI process: `name` is the MPI rank + 1
name = str(1 + mpi.rank())
self.collection = SampleCollection(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:
self.callback_function_callable = (get_external_function(
self.callback_function))
# Useful for getting last points added inside callback function
self.last_point_callback = 0
self.i_learn = 1
# Monitoring/restore progress
if is_main_process():
cols = [
"N", "timestamp", "acceptance_rate", "Rminus1", "Rminus1_cl"
]
self.progress = DataFrame(columns=cols)
if self.output and not self.output.is_resuming():
header_fmt = {
"N": 6 * " " + "N",
"timestamp": 17 * " " + "timestamp"
}
with open(self.progress_filename(), "w",
encoding="utf-8") as progress_file:
progress_file.write("# " + " ".join([
header_fmt.get(col, ((7 + 8) - len(col)) * " " + col)
for col in 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):
last = len(self.collection) - 1
initial_point = (self.collection[
self.collection.sampled_params].iloc[last]).to_numpy(
dtype=np.float64, copy=True)
results = LogPosterior(
logpost=-self.collection[OutPar.minuslogpost].iloc[last],
logpriors=-(self.collection[
self.collection.minuslogprior_names].iloc[last].to_numpy(
dtype=np.float64, copy=True)),
loglikes=-0.5 *
(self.collection[self.collection.chi2_names].iloc[last].
to_numpy(dtype=np.float64, copy=True)),
derived=(self.collection[
self.collection.derived_params].iloc[last].to_numpy(
dtype=np.float64, copy=True)))
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, results = \
self.model.get_valid_point(max_tries=self.max_tries.value,
random_state=self._rng)
# 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.mpi_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,
random_state=self._rng)
self.set_proposer_blocking()
self.set_proposer_initial_covmat(load=True)
self.current_point.add(initial_point, results)
self.log.info("Initial point: %s", self.current_point)
# Max #(learn+convergence checks) to wait,
# in case one process dies/hangs without raising error
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
self._msg_ready = ("Ready to check convergence" +
(" and learn a new proposal covmat"
if self.learn_proposal else ""))
# Initial dummy checkpoint
# (needed when 1st "learn point" not reached in prev. run)
self.write_checkpoint()
@property
def i_last_slow_block(self):
if self.drag:
return next(i for i, o in enumerate(self.oversampling_factors)
if o != 1) - 1
self.log.warning(
"`i_last_slow_block` is only well defined when dragging.")
return 0
@property
def slow_blocks(self):
return self.blocks[:1 + self.i_last_slow_block]
@property
def slow_params(self):
return list(chain(*self.slow_blocks))
@property
def n_slow(self):
return len(self.slow_params)
@property
def fast_blocks(self):
return self.blocks[self.i_last_slow_block + 1:]
@property
def fast_params(self):
return list(chain(*self.fast_blocks))
@property
def n_fast(self):
return len(self.fast_params)
def get_acceptance_rate(self, first=0, last=None):
return (((last or self.n()) - (first or 0)) /
self.collection[OutPar.weight][first:last].sum())
def set_proposer_blocking(self):
if self.blocking:
# Includes the case in which we are resuming
self.blocks, self.oversampling_factors = \
self.model.check_blocking(self.blocking)
else:
self.blocks, self.oversampling_factors = \
self.model.get_param_blocking_for_sampler(
oversample_power=self.oversample_power, split_fast_slow=self.drag)
# Turn off dragging if one block, or if speed differences < 2x, or no differences
if self.drag:
if len(self.blocks) == 1:
self.drag = False
self.log.warning(
"Dragging disabled: not possible if there is only one block."
)
if max(self.oversampling_factors) / min(
self.oversampling_factors) < 2:
self.drag = False
self.log.warning("Dragging disabled: speed ratios < 2.")
if self.drag:
# The definition of oversample_power=1 as spending the same amount of time in
# the slow and fast block would suggest a 1/2 factor here, but this additional
# factor of 2 w.r.t. oversampling should produce an equivalent exploration
# efficiency.
self.drag_interp_steps = int(
np.round(
self.oversampling_factors[self.i_last_slow_block + 1] *
self.n_fast / self.n_slow))
if self.drag_interp_steps < 2:
self.drag = False
self.log.warning(
"Dragging disabled: "
"speed ratio and fast-to-slow ratio not large enough.")
# Define proposer and other blocking-related quantities
if self.drag:
# MARKED FOR DEPRECATION IN v3.0
if getattr(self, "drag_limits", None) is not None:
raise LoggedError(
self.log, "`drag_limits` has been deprecated. "
"Use 'oversample_power' to control the amount"
" of dragging steps.")
# END OF DEPRECATION BLOCK
self.get_new_sample = self.get_new_sample_dragging
self.mpi_info("Dragging with number of interpolating steps:")
max_width = len(str(self.drag_interp_steps))
self.mpi_info("* %" + "%d" % max_width + "d : %r", 1,
self.slow_blocks)
self.mpi_info("* %" + "%d" % max_width + "d : %r",
self.drag_interp_steps, self.fast_blocks)
elif np.any(np.array(self.oversampling_factors) > 1):
self.mpi_info("Oversampling with factors:")
max_width = len(str(max(self.oversampling_factors)))
for f, b in zip(self.oversampling_factors, self.blocks):
self.mpi_info("* %" + "%d" % max_width + "d : %r", f, b)
if self.oversample_thin:
self.current_point.output_thin = int(
np.round(
sum(
len(b) * o for b, o in zip(
self.blocks, self.oversampling_factors)) /
self.model.prior.d()))
# Save blocking in updated info, in case we want to resume
self._updated_info["blocking"] = list(
zip(self.oversampling_factors, self.blocks))
sampled_params_list = list(
self.model.parameterization.sampled_params())
blocks_indices = [[sampled_params_list.index(p) for p in b]
for b in self.blocks]
self.proposer = BlockedProposer(
blocks_indices,
self._rng,
oversampling_factors=self.oversampling_factors,
i_last_slow_block=(self.i_last_slow_block if self.drag else None),
proposal_scale=self.proposal_scale)
# Cycle length, taking into account oversampling/dragging
if self.drag:
self.cycle_length = self.n_slow
else:
self.cycle_length = sum(
len(b) * o
for b, o in zip(blocks_indices, self.oversampling_factors))
self.log.debug("Cycle length in steps: %r", self.cycle_length)
for number in self._quants_d_units:
number.set_scale(self.cycle_length //
self.current_point.output_thin)
def set_proposer_initial_covmat(self, load=False):
if load:
# Build the initial covariance matrix of the proposal, or load from checkpoint
self._initial_covmat, where_nan = self._load_covmat(
prefer_load_old=self.output.is_resuming())
if np.any(where_nan) and self.learn_proposal:
# We want to start learning the covmat earlier.
self.mpi_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 (would be %g if all params loaded).",
self.learn_proposal_Rminus1_max_early,
self.learn_proposal_Rminus1_max)
self.learn_proposal_Rminus1_max = self.learn_proposal_Rminus1_max_early
self.log.debug(
"Sampling with covmat:\n%s",
DataFrame(self._initial_covmat,
columns=self.model.parameterization.sampled_params(),
index=self.model.parameterization.sampled_params()).
to_string(line_width=line_width))
self.proposer.set_covariance(self._initial_covmat)
def _get_last_nondragging_block(self, blocks, speeds):
# blocks and speeds are already sorted
log_differences = np.zeros(len(blocks) - 1)
for i in range(len(blocks) - 1):
log_differences[i] = (np.log(np.min(speeds[:i + 1])) -
np.log(np.min(speeds[i + 1:])))
i_max = np.argmin(log_differences)
return i_max
def run(self):
"""
Runs the sampler.
"""
self.mpi_info("Sampling!" + (
" (NB: no accepted step will be saved until %d burn-in samples " %
self.burn_in.value +
"have been obtained)" if self.burn_in.value else ""))
self.n_steps_raw = 0
last_output: float = 0
last_n = self.n()
state_check_every = 1
with mpi.ProcessState(self) as state:
while last_n < self.max_samples and not self.converged:
self.get_new_sample()
self.n_steps_raw += 1
if self.output_every.unit:
# if output_every in sec, print some info
# and dump at fixed time intervals
now = datetime.datetime.now()
now_sec = now.timestamp()
if now_sec >= last_output + self.output_every.value:
self.do_output(now)
last_output = now_sec
state.check_error()
if self.current_point.weight == 1:
# have added new point
# Callback function
n = self.n()
if n != last_n:
# and actually added
last_n = n
if (self.callback_function
and not (max(n, 1) % self.callback_every.value)
and self.current_point.weight == 1):
self.callback_function_callable(self)
self.last_point_callback = len(self.collection)
if more_than_one_process():
# Checking convergence and (optionally) learning
# the covmat of the proposal
if self.check_ready() and state.set(
mpi.State.READY):
self.log.info(self._msg_ready +
" (waiting for the rest...)")
if state.all_ready():
self.mpi_info("All chains are r%s",
self._msg_ready[1:])
self.check_convergence_and_learn_proposal()
self.i_learn += 1
else:
if self.check_ready():
self.log.debug(self._msg_ready)
self.check_convergence_and_learn_proposal()
self.i_learn += 1
elif self.current_point.weight % state_check_every == 0:
state.check_error()
# more frequent checks near beginning
state_check_every = min(10, state_check_every + 1)
if last_n == self.max_samples:
self.log.info(
"Reached maximum number of accepted steps allowed (%s). "
"Stopping.", self.max_samples)
# Write the last batch of samples ( < output_every (not in sec))
self.collection.out_update()
ns = mpi.gather(self.n())
self.mpi_info("Sampling complete after %d accepted steps.", sum(ns))
def n(self, burn_in=False):
"""
Returns the total number of accepted steps taken, including or not burn-in steps
depending on the value of the `burn_in` keyword.
"""
return len(self.collection) + (
0 if not burn_in else self.burn_in.value -
self.burn_in_left // self.current_point.output_thin + 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 = self.current_point.values.copy()
self.proposer.get_proposal(trial)
trial_results = self.model.logposterior(trial)
accept = self.metropolis_accept(trial_results.logpost,
self.current_point.logpost)
self.process_accept_or_reject(accept, trial, trial_results)
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
current_start_point = self.current_point.values
current_start_logpost = self.current_point.logpost
current_end_point = current_start_point.copy()
self.proposer.get_proposal_slow(current_end_point)
self.log.debug("Proposed slow end-point: %r", current_end_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
current_end = self.model.logposterior(current_end_point)
if current_end.logpost == -np.inf:
self.current_point.weight += 1
return False
# accumulators for the "dragging" probabilities to be metropolis-tested
# at the end of the interpolation
start_drag_logpost_acc = current_start_logpost
end_drag_logpost_acc = current_end.logpost
# don't compute derived during drag, unless must be computed anyway
derived = self.model.requires_derived
# alloc mem
delta_fast = np.empty(len(current_start_point))
# 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[:] = 0.
self.proposer.get_proposal_fast(delta_fast)
self.log.debug("Proposed fast step delta: %r", delta_fast)
proposal_start_point = current_start_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,
return_derived=bool(derived),
_no_check=True).logpost
if proposal_start_logpost != -np.inf:
proposal_end_point = current_end_point + delta_fast
proposal_end = self.model.logposterior(
proposal_end_point,
return_derived=bool(derived),
_no_check=True)
if 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)
if accept_drag:
# If the dragging step was accepted, do the drag
current_start_point = proposal_start_point
current_start_logpost = proposal_start_logpost
current_end_point = proposal_end_point
current_end = proposal_end
else:
accept_drag = False
else:
accept_drag = False
self.log.debug("Dragging step: %s",
("accepted" if accept_drag else "rejected"))
# 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
n_average = 1 + self.drag_interp_steps
accept = self.metropolis_accept(end_drag_logpost_acc / n_average,
start_drag_logpost_acc / n_average)
if accept and not derived:
# recompute with derived parameters (slow parameter ones should be cached)
current_end = self.model.logposterior(current_end_point)
self.process_accept_or_reject(accept, current_end_point, current_end)
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 self._rng.standard_exponential() > (logp_current -
logp_trial)
def process_accept_or_reject(self, accept_state, trial, trial_results):
"""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:
if self.current_point.add_to_collection(self.collection):
self.log.debug("New sample, #%d: \n %s", self.n(),
self.current_point)
# Update chain files, if output_every *not* in sec
if not self.output_every.unit:
if self.n() % self.output_every.value == 0:
self.collection.out_update()
else:
self.burn_in_left -= 1
self.log.debug("Burn-in sample:\n %s", 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.value)
# set the new point as the current one, with weight one
self.current_point.add(trial, trial_results)
else: # not accepted
self.current_point.weight += 1
# Failure criterion: chain stuck! (but be more permissive during burn_in)
max_tries_now = self.max_tries.value * (
1 + (10 - 1) * np.sign(self.burn_in_left))
if self.current_point.weight > max_tries_now:
self.collection.out_update()
raise LoggedError(
self.log,
"The chain has been stuck for %d attempts, stopping sampling. "
"Make sure the reference point is semsible and initial covmat."
"For parameters not included in an initial covmat, the 'proposal' "
"width set for each parameter should be of order of the expected "
"conditional posterior width, which may be much smaller than the "
"marginalized posterior width - choose a smaller "
"rather than larger value if in doubt. You can also decrease the "
"'proposal_scale' option for mcmc, though small values will sample "
"less efficiently once things converge.\n"
"Alternatively (though not advisable) make 'max_tries: np.inf' "
"(or 'max_tries: .inf' in yaml).\n"
"Current point: %s", max_tries_now, self.current_point)
# Functions to check convergence and learn the covariance of the proposal distribution
def check_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.
"""
n = len(self.collection)
# If *just* (weight==1) got ready to check+learn
if not (n % self.learn_every.value) and n > 0:
self.log.info("Learn + convergence test @ %d samples accepted.", n)
self.model.dump_timing()
if more_than_one_process():
self.been_waiting += 1
if self.been_waiting > self.max_waiting:
raise LoggedError(
self.log,
"Waiting for too long for all chains to be ready. "
"Maybe one of them is stuck or died unexpectedly?")
return True
return False
# noinspection PyUnboundLocalVariable
@np.errstate(all="ignore")
def check_convergence_and_learn_proposal(self):
"""
Checks the convergence of the sampling process, and, if requested,
learns a new covariance matrix for the proposal distribution from the covariance
of the last samples.
"""
# Compute Rminus1 of means
self.been_waiting = 0
if more_than_one_process():
# Compute and gather means and covs
use_first = int(self.n() / 2)
mean = self.collection.mean(first=use_first)
cov = self.collection.cov(first=use_first)
acceptance_rate = self.get_acceptance_rate(use_first)
Ns, means, covs, acceptance_rates = mpi.array_gather(
[self.n(), mean, cov, acceptance_rate])
else:
# Compute and gather means, covs and CL intervals of last m-1 chain fractions
m = 1 + self.Rminus1_single_split
cut = int(len(self.collection) / m)
try:
acceptance_rate = self.get_acceptance_rate(cut)
Ns = np.ones(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)
])
except always_stop_exceptions:
raise
except Exception:
self.log.info(
"Not enough points in chain to check convergence. "
"Waiting for next checkpoint.")
return
acceptance_rates = None
if is_main_process():
self.progress.at[self.i_learn, "N"] = sum(Ns)
self.progress.at[self.i_learn, "timestamp"] = \
datetime.datetime.now().isoformat()
acceptance_rate = (np.average(acceptance_rates, weights=Ns)
if acceptance_rates is not None else
acceptance_rate)
self.log.info(
" - Acceptance rate: %.3f" +
(" = avg(%r)" % list(acceptance_rates)
if acceptance_rates is not None else ""), acceptance_rate)
self.progress.at[self.i_learn, "acceptance_rate"] = acceptance_rate
# "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!)
d = np.sqrt(np.diag(cov_of_means))
corr_of_means = (cov_of_means / d).T / d
norm_mean_of_covs = (mean_of_covs / d).T / d
success_means = False
converged_means = False
# 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 learning a new covmat for now.")
else:
Linv = np.linalg.inv(L)
try:
eigvals = np.linalg.eigvalsh(
Linv.dot(corr_of_means).dot(Linv.T))
success_means = True
except np.linalg.LinAlgError:
self.log.warning("Could not compute eigenvalues. "
"Skipping learning a new covmat for now.")
else:
Rminus1 = max(np.abs(eigvals))
self.progress.at[self.i_learn, "Rminus1"] = Rminus1
# 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)) +
(" = sum(%r)" %
list(Ns) if more_than_one_process() else ""))
# Have we converged in means?
# (criterion must be fulfilled twice in a row)
converged_means = max(
Rminus1, self.Rminus1_last) < self.Rminus1_stop
else:
mean_of_covs = None
success_means = None
converged_means = False
Rminus1 = None
success_means, converged_means = mpi.share(
(success_means, converged_means))
# 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 converged_means:
if more_than_one_process():
mcsamples = self.collection.sampled_to_getdist_mcsamples(
first=use_first)
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
bounds = np.array(mpi.gather(bound))
else:
try:
mcsamples_list = [
self.collection.sampled_to_getdist_mcsamples(
first=i * cut, last=(i + 1) * cut - 1)
for i in range(1, m)
]
except always_stop_exceptions:
raise
except:
self.log.info(
"Not enough points in chain to check c.l. convergence. "
"Waiting for next checkpoint.")
return
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 mcsamples_list
]
success_bounds = True
except:
bounds = None
success_bounds = False
if is_main_process():
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)
Rminus1_cl = np.max(Rminus1_cl)
self.progress.at[self.i_learn, "Rminus1_cl"] = Rminus1_cl
self.log.info(
" - Convergence of bounds: R-1 = %f after %d " %
(Rminus1_cl,
(sum(Ns) if more_than_one_process() else self.n())) +
"accepted steps" +
(" = sum(%r)" %
list(Ns) if more_than_one_process() else ""))
if 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 converge check.")
# Broadcast and save the convergence status and the last R-1 of means
if success_means:
self.Rminus1_last, self.converged = mpi.share((
Rminus1, self.converged) if is_main_process() else None)
# Do we want to learn a better proposal pdf?
if self.learn_proposal and not self.converged:
good_Rminus1 = (self.learn_proposal_Rminus1_max >
self.Rminus1_last >
self.learn_proposal_Rminus1_min)
if not good_Rminus1:
self.mpi_info(
"Convergence less than requested for updates: "
"waiting until the next convergence check.")
return
mean_of_covs = mpi.share(mean_of_covs)
try:
self.proposer.set_covariance(mean_of_covs)
self.mpi_info(
" - Updated covariance matrix of proposal pdf.")
self.mpi_debug("%r", mean_of_covs)
except:
self.mpi_debug(
"Updating covariance matrix failed unexpectedly. "
"waiting until next covmat learning attempt.")
# Save checkpoint info
self.write_checkpoint()
def do_output(self, date_time):
self.collection.out_update()
msg = "Progress @ %s : " % date_time.strftime("%Y-%m-%d %H:%M:%S")
msg += "%d steps taken" % self.n_steps_raw
if self.burn_in_left and self.burn_in: # NB: burn_in_left = 1 even if no burn_in
msg += " -- still burning in, %d accepted steps left." % self.burn_in_left
else:
msg += ", and %d accepted." % self.n()
self.log.info(msg)
def write_checkpoint(self):
if is_main_process() and self.output:
checkpoint_filename = self.checkpoint_filename()
self.dump_covmat(self.proposer.get_covariance())
checkpoint_info = {
"sampler": {
self.get_name():
dict([
("converged", self.converged),
("Rminus1_last", self.Rminus1_last),
(
"burn_in",
(
self.burn_in.
value # initial: repeat burn-in if not finished
if not self.n() and self.burn_in_left else 0)
), # to avoid overweighting last point of prev. run
("mpi_size", get_mpi_size())
])
}
}
yaml_dump_file(checkpoint_filename,
checkpoint_info,
error_if_exists=False)
if not self.progress.empty:
with open(self.progress_filename(), "a",
encoding="utf-8") as progress_file:
fmts = {"N": lambda x: "{:9d}".format(x)}
# TODO: next one is ignored when added to the dict
# "acceptance_rate": lambda x: "{:15.8g}".format(x)}
progress_file.write(
self.progress.tail(1).to_string(
header=False, index=False, formatters=fmts) + "\n")
self.log.debug(
"Dumped checkpoint and progress info, and current covmat.")
def converge_info_changed(self, old_info, new_info):
converge_params = [
'Rminus1_stop', "Rminus1_cl_stop", "Rminus1_cl_level",
"max_samples"
]
return any(old_info.get(p) != new_info.get(p) for p in converge_params)
# Finally: returning the computed products ###########################################
def products(self):
"""
Auxiliary function to define what should be returned in a scripted call.
Returns:
The sample ``SampleCollection`` containing the accepted steps.
"""
products = {"sample": self.collection}
if is_main_process():
products["progress"] = self.progress
return products
# Class methods
@classmethod
def output_files_regexps(cls, output, info=None, minimal=False):
regexps = [output.collection_regexp(name=None)]
if minimal:
return [(r, None) for r in regexps]
regexps += [
re.compile(output.prefix_regexp_str + re.escape(ext.lstrip(".")) +
"$") for ext in
[Extension.checkpoint, Extension.progress, Extension.covmat]
]
return [(r, None) for r in regexps]
@classmethod
def get_version(cls):
return get_version()
@classmethod
def _get_desc(cls, info=None):
drag_string = r" using the fast-dragging procedure described in \cite{Neal:2005}"
if info is None:
# Unknown case (no info passed)
string = " [(if drag: True)%s]" % drag_string
else:
string = drag_string if info.get(
"drag",
cls.get_defaults()["drag"]) else ""
return (
"Adaptive, speed-hierarchy-aware MCMC sampler (adapted from CosmoMC) "
r"\cite{Lewis:2002ah,Lewis:2013hha}" + string + ".")
class mcmc(CovmatSampler):
_at_resume_prefer_new = CovmatSampler._at_resume_prefer_new + [
"burn_in", "callback_function", "callback_every", "max_tries",
"output_every", "learn_every", "learn_proposal_Rminus1_max",
"learn_proposal_Rminus1_max_early", "learn_proposal_Rminus1_min",
"max_samples", "Rminus1_stop", "Rminus1_cl_stop", "Rminus1_cl_level",
"covmat", "covmat_params"
]
_at_resume_prefer_old = CovmatSampler._at_resume_prefer_new + [
"proposal_scale", "blocking"
]
# instance variables from yaml
burn_in: NumberWithUnits
learn_every: NumberWithUnits
output_every: NumberWithUnits
callback_every: NumberWithUnits
max_tries: NumberWithUnits
max_samples: int
drag: bool
callback_function: Optional[callable]
blocking: Optional[Sequence]
proposal_scale: float
learn_proposal: bool
learn_proposal_Rminus1_max_early: float
Rminus1_cl_level: float
Rminus1_stop: float
Rminus1_cl_stop: float
Rminus1_single_split: int
learn_proposal_Rminus1_min: float
measure_speeds: bool
oversample_thin: int
oversample_power: float
def set_instance_defaults(self):
super().set_instance_defaults()
# checkpoint variables
self.converged = None
self.mpi_size = None
self.Rminus1_last = np.inf
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()
@property
def i_last_slow_block(self):
if self.drag:
return next(i for i, o in enumerate(self.oversampling_factors)
if o != 1) - 1
self.log.warning(
"`i_last_slow_block` is only well defined when dragging.")
return 0
@property
def slow_blocks(self):
return self.blocks[:1 + self.i_last_slow_block]
@property
def slow_params(self):
return list(chain(*self.slow_blocks))
@property
def n_slow(self):
return len(self.slow_params)
@property
def fast_blocks(self):
return self.blocks[self.i_last_slow_block + 1:]
@property
def fast_params(self):
return list(chain(*self.fast_blocks))
@property
def n_fast(self):
return len(self.fast_params)
@property
def acceptance_rate(self):
return self.n() / self.collection[_weight].sum()
def set_proposer_blocking(self):
if self.blocking:
# Includes the case in which we are resuming
self.blocks, self.oversampling_factors = \
self.model.check_blocking(self.blocking)
else:
self.blocks, self.oversampling_factors = \
self.model.get_param_blocking_for_sampler(
oversample_power=self.oversample_power, split_fast_slow=self.drag)
# Turn off dragging if one block, or if speed differences < 2x, or no differences
if self.drag:
if len(self.blocks) == 1:
self.drag = False
self.log.warning(
"Dragging disabled: not possible if there is only one block."
)
if max(self.oversampling_factors) / min(
self.oversampling_factors) < 2:
self.drag = False
self.log.warning("Dragging disabled: speed ratios < 2.")
if self.drag:
# The definition of oversample_power=1 as spending the same amount of time in
# the slow and fast block would suggest a 1/2 factor here, but this additional
# factor of 2 w.r.t. oversampling should produce an equivalent exploration
# efficiency.
self.drag_interp_steps = int(
np.round(
self.oversampling_factors[self.i_last_slow_block + 1] *
self.n_fast / self.n_slow))
if self.drag_interp_steps < 2:
self.drag = False
self.log.warning(
"Dragging disabled: "
"speed ratio and fast-to-slow ratio not large enough.")
# Define proposer and other blocking-related quantities
if self.drag:
# MARKED FOR DEPRECATION IN v3.0
if getattr(self, "drag_limits", None) is not None:
self.log.warning(
"*DEPRECATION*: 'drag_limits' has been deprecated. "
"Use 'oversample_power' to control the amount of "
"dragging steps.")
# END OF DEPRECATION BLOCK
self.get_new_sample = self.get_new_sample_dragging
self.mpi_info("Dragging with number of interpolating steps:")
max_width = len(str(self.drag_interp_steps))
self.mpi_info("* %" + "%d" % max_width + "d : %r", 1,
self.slow_blocks)
self.mpi_info("* %" + "%d" % max_width + "d : %r",
self.drag_interp_steps, self.fast_blocks)
elif np.any(np.array(self.oversampling_factors) > 1):
self.mpi_info("Oversampling with factors:")
max_width = len(str(max(self.oversampling_factors)))
for f, b in zip(self.oversampling_factors, self.blocks):
self.mpi_info("* %" + "%d" % max_width + "d : %r", f, b)
if self.oversample_thin:
self.current_point.output_thin = int(
np.round(
sum(
len(b) * o for b, o in zip(
self.blocks, self.oversampling_factors)) /
self.model.prior.d()))
# Save blocking in updated info, in case we want to resume
self._updated_info["blocking"] = list(
zip(self.oversampling_factors, self.blocks))
sampled_params_list = list(
self.model.parameterization.sampled_params())
blocks_indices = [[sampled_params_list.index(p) for p in b]
for b in self.blocks]
self.proposer = BlockedProposer(
blocks_indices,
oversampling_factors=self.oversampling_factors,
i_last_slow_block=(self.i_last_slow_block if self.drag else None),
proposal_scale=self.proposal_scale)
# Cycle length, taking into account oversampling/dragging
if self.drag:
self.cycle_length = self.n_slow
else:
self.cycle_length = sum(
len(b) * o
for b, o in zip(blocks_indices, self.oversampling_factors))
self.log.debug("Cycle length in steps: %r", self.cycle_length)
for number in self._quants_d_units:
number.set_scale(self.cycle_length //
self.current_point.output_thin)
def set_proposer_covmat(self, load=False):
if load:
# Build the initial covariance matrix of the proposal, or load from checkpoint
self._covmat, where_nan = self._load_covmat(
self.output.is_resuming())
if np.any(where_nan) and self.learn_proposal:
# We want to start learning the covmat earlier.
self.mpi_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 (would be %g if all params loaded).",
self.learn_proposal_Rminus1_max_early,
self.learn_proposal_Rminus1_max)
self.learn_proposal_Rminus1_max = self.learn_proposal_Rminus1_max_early
self.log.debug(
"Sampling with covmat:\n%s",
DataFrame(self._covmat,
columns=self.model.parameterization.sampled_params(),
index=self.model.parameterization.sampled_params()).
to_string(line_width=_line_width))
self.proposer.set_covariance(self._covmat)
def _get_last_nondragging_block(self, blocks, speeds):
# blocks and speeds are already sorted
log_differences = np.zeros(len(blocks) - 1)
for i in range(len(blocks) - 1):
log_differences[i] = (np.log(np.min(speeds[:i + 1])) -
np.log(np.min(speeds[i + 1:])))
i_max = np.argmin(log_differences)
return i_max
def _run(self):
"""
Runs the sampler.
"""
self.log.info("Sampling!" + (
" (NB: no accepted step will be saved until %d burn-in samples " %
self.burn_in.value +
"have been obtained)" if self.burn_in.value else ""))
self.n_steps_raw = 0
last_output = 0
last_n = self.n()
while last_n < self.max_samples and not self.converged:
self.get_new_sample()
self.n_steps_raw += 1
if self.output_every.unit:
# if output_every in sec, print some info and dump at fixed time intervals
now = datetime.datetime.now()
now_sec = now.timestamp()
if now_sec >= last_output + self.output_every.value:
self.do_output(now)
last_output = now_sec
if self.current_point.weight == 1:
# have added new point
# Callback function
n = self.n()
if n != last_n:
# and actually added
last_n = n
if (hasattr(self, "callback_function_callable")
and not (max(n, 1) % self.callback_every.value)
and self.current_point.weight == 1):
self.callback_function_callable(self)
self.last_point_callback = len(self.collection)
# Checking convergence and (optionally) learning
# the covmat of the proposal
if self.check_all_ready():
self.check_convergence_and_learn_proposal()
if is_main_process():
self.i_learn += 1
if last_n == self.max_samples:
self.log.info("Reached maximum number of accepted steps allowed. "
"Stopping.")
# Make sure the last batch of samples ( < output_every (not in sec)) are written
self.collection.out_update()
if more_than_one_process():
Ns = (lambda x: np.array(get_mpi_comm().gather(x)))(self.n())
if not is_main_process():
Ns = []
else:
Ns = [self.n()]
self.mpi_info("Sampling complete after %d accepted steps.", sum(Ns))
def n(self, burn_in=False):
"""
Returns the total number of accepted steps taken, including or not burn-in steps
depending on the value of the `burn_in` keyword.
"""
return len(self.collection) + (
0 if not burn_in else self.burn_in.value -
self.burn_in_left // self.current_point.output_thin + 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 = self.current_point.values.copy()
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.logpost)
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.values.copy()
start_slow_logpost = self.current_point.logpost
end_slow_point = start_slow_point.copy()
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.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 metropolis-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 = current_start_point + delta_fast
proposal_end_point = current_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:
if self.current_point.add_to_collection(self.collection):
self.log.debug("New sample, #%d: \n %s", self.n(),
self.current_point)
# Update chain files, if output_every *not* in sec
if not self.output_every.unit:
if self.n() % self.output_every.value == 0:
self.collection.out_update()
else:
self.burn_in_left -= 1
self.log.debug("Burn-in sample:\n %s", 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.value)
# set the new point as the current one, with weight one
self.current_point.add(trial,
derived=derived,
logpost=logpost_trial,
logpriors=logprior_trial,
loglikes=loglikes_trial)
else: # not accepted
self.current_point.weight += 1
# Failure criterion: chain stuck! (but be more permissive during burn_in)
max_tries_now = self.max_tries.value * \
(1 + (10 - 1) * np.sign(self.burn_in_left))
if self.current_point.weight > max_tries_now:
self.collection.out_update()
raise LoggedError(
self.log,
"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).\n"
"Current point: %s", max_tries_now, self.current_point)
# 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 check convergence" +
(" and learn a new proposal covmat"
if self.learn_proposal else ""))
n = len(self.collection)
# If *just* (weight==1) got ready to check+learn
if not (n % self.learn_every.value) and n > 0:
self.log.info("Learn + convergence test @ %d samples accepted.", n)
if more_than_one_process():
self.been_waiting += 1
if self.been_waiting > self.max_waiting:
raise LoggedError(
self.log,
"Waiting for too long for all chains to be ready. "
"Maybe one of them is stuck or died unexpectedly?")
self.model.dump_timing()
# If not MPI size > 1, we are ready
if not more_than_one_process():
self.log.debug(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 more_than_one_process() and is_main_process():
self.log.info("All chains are r" + msg_ready[1:])
delattr(self, "req")
self.been_waiting = 0
# Just in case, a barrier here
sync_processes()
return True
return False
def check_convergence_and_learn_proposal(self):
"""
Checks the convergence of the sampling process, and, if requested,
learns a new covariance matrix for the proposal distribution from the covariance
of the last samples.
"""
if more_than_one_process():
# Compute and gather means, covs and CL intervals of last half of chains
use_first = int(self.n() / 2)
mean = self.collection.mean(first=use_first)
cov = self.collection.cov(first=use_first)
mcsamples = self.collection._sampled_to_getdist_mcsamples(
first=use_first)
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, acceptance_rates = map(
lambda x: np.array(get_mpi_comm().gather(x)),
[self.n(), mean, cov, bound, self.acceptance_rate])
else:
# Compute and gather means, covs and CL intervals of last m-1 chain fractions
m = 1 + self.Rminus1_single_split
cut = int(len(self.collection) / m)
try:
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)
])
mcsamples_list = [
self.collection._sampled_to_getdist_mcsamples(
first=i * cut, last=(i + 1) * cut - 1)
for i in range(1, m)
]
except:
self.log.info(
"Not enough points in chain to check convergence. "
"Waiting for next checkpoint.")
return
acceptance_rates = self.acceptance_rate
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 mcsamples_list
]
success_bounds = True
except:
bounds = None
success_bounds = False
# Compute convergence diagnostics
if is_main_process():
self.progress.at[self.i_learn,
"N"] = (sum(Ns)
if more_than_one_process() else self.n())
self.progress.at[self.i_learn, "timestamp"] = \
datetime.datetime.now().isoformat()
acceptance_rate = (np.average(acceptance_rates, weights=Ns) if
more_than_one_process() else acceptance_rates)
self.log.info(
" - Acceptance rate: %.3f" +
(" = avg(%r)" %
list(acceptance_rates) if more_than_one_process() else ""),
acceptance_rate)
self.progress.at[self.i_learn, "acceptance_rate"] = acceptance_rate
# "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)
success = False
# 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 learning a new covmat for now.")
else:
Linv = np.linalg.inv(L)
# Suppress numpy warnings (restored later in this function)
error_handling = deepcopy(np.geterr())
np.seterr(all="ignore")
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 learning a new covmat for now.")
else:
Rminus1 = max(np.abs(eigvals))
self.progress.at[self.i_learn, "Rminus1"] = Rminus1
# 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 more_than_one_process() else self.n())) +
(" = sum(%r)" %
list(Ns) if more_than_one_process() 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)
Rminus1_cl = np.max(Rminus1_cl)
self.progress.at[self.i_learn,
"Rminus1_cl"] = Rminus1_cl
self.log.info(
" - Convergence of bounds: R-1 = %f after %d "
% (Rminus1_cl,
(sum(Ns) if more_than_one_process(
) else self.n())) + "accepted steps" +
(" = sum(%r)" %
list(Ns) if more_than_one_process() else ""))
if 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 converge check.")
np.seterr(**error_handling)
else:
mean_of_covs = np.empty(
(self.model.prior.d(), self.model.prior.d()))
success = None
Rminus1 = None
# Broadcast and save the convergence status and the last R-1 of means
success = share_mpi(success)
if success:
self.Rminus1_last, self.converged = share_mpi((
Rminus1, self.converged) if is_main_process() else None)
# Do we want to learn a better proposal pdf?
if self.learn_proposal and not self.converged:
good_Rminus1 = (self.learn_proposal_Rminus1_max >
self.Rminus1_last >
self.learn_proposal_Rminus1_min)
if not good_Rminus1:
self.mpi_info(
"Convergence less than requested for updates: "
"waiting until the next convergence check.")
return
if more_than_one_process():
get_mpi_comm().Bcast(mean_of_covs, root=0)
else:
mean_of_covs = covs[0]
try:
self.proposer.set_covariance(mean_of_covs)
if is_main_process():
self.log.info(
" - Updated covariance matrix of proposal pdf.")
self.log.debug("%r", mean_of_covs)
except:
if is_main_process():
self.log.debug(
"Updating covariance matrix failed unexpectedly. "
"waiting until next covmat learning attempt.")
# Save checkpoint info
self.write_checkpoint()
def do_output(self, date_time):
self.collection.out_update()
msg = "Progress @ %s : " % date_time.strftime("%Y-%m-%d %H:%M:%S")
msg += "%d steps taken" % self.n_steps_raw
if self.burn_in_left and self.burn_in: # NB: burn_in_left = 1 even if no burn_in
msg += " -- still burning in, %d accepted steps left." % self.burn_in_left
else:
msg += ", and %d accepted." % self.n()
self.log.info(msg)
def write_checkpoint(self):
if is_main_process() 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 = {
kinds.sampler: {
self.get_name():
dict([
("converged", bool(self.converged)),
("Rminus1_last", self.Rminus1_last),
(
"burn_in",
(
self.burn_in.
value # initial: repeat burn-in if not finished
if not self.n() and self.burn_in_left else 0)
), # to avoid overweighting last point of prev. run
("mpi_size", get_mpi_size())
])
}
}
yaml_dump_file(checkpoint_filename,
checkpoint_info,
error_if_exists=False)
if not self.progress.empty:
with open(self.progress_filename(), "a",
encoding="utf-8") as progress_file:
progress_file.write(
self.progress.tail(1).to_string(header=False,
index=False) + "\n")
self.log.debug(
"Dumped checkpoint and progress 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.
"""
products = {"sample": self.collection}
if is_main_process():
products["progress"] = self.progress
return products
# Class methods
@classmethod
def output_files_regexps(cls, output, info=None, minimal=False):
regexps = [output.collection_regexp(name=None)]
if minimal:
return [(r, None) for r in regexps]
regexps += [
re.compile(output.prefix_regexp_str + re.escape(ext.lstrip(".")) +
"$") for ext in
[_checkpoint_extension, _progress_extension, _covmat_extension]
]
return [(r, None) for r in regexps]
@classmethod
def get_version(cls):
return __version__
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}