def _hamiltonian_step(self, start, p0, step_size):
n_steps = max(1, int(self.path_length / step_size))
n_steps = min(self.max_steps, n_steps)
energy_change = -np.inf
state = start
last = state
div_info = None
try:
for _ in range(n_steps):
last = state
state = self.integrator.step(step_size, state)
except IntegrationError as e:
div_info = DivergenceInfo("Integration failed.", e, last, None)
else:
if not np.isfinite(state.energy):
div_info = DivergenceInfo(
"Divergence encountered, bad energy.", None, last, state)
energy_change = start.energy - state.energy
if np.isnan(energy_change):
energy_change = -np.inf
if np.abs(energy_change) > self.Emax:
div_info = DivergenceInfo(
"Divergence encountered, large integration error.", None,
last, state)
accept_stat = min(1, np.exp(energy_change))
if div_info is not None or np.random.rand() >= accept_stat:
end = start
accepted = False
else:
end = state
accepted = True
stats = {
"path_length": self.path_length,
"n_steps": n_steps,
"accept": accept_stat,
"energy_error": energy_change,
"energy": state.energy,
"accepted": accepted,
"model_logp": state.model_logp,
}
return HMCStepData(end, accept_stat, div_info, stats)
def _hamiltonian_step(self, start, p0, step_size):
n_steps = max(1, int(self.path_length / step_size))
n_steps = min(self.max_steps, n_steps)
energy_change = -np.inf
state = start
div_info = None
try:
for _ in range(n_steps):
state = self.integrator.step(step_size, state)
except IntegrationError as e:
div_info = DivergenceInfo('Divergence encountered.', e, state)
else:
if not np.isfinite(state.energy):
div_info = DivergenceInfo(
'Divergence encountered, bad energy.', None, state)
energy_change = start.energy - state.energy
if np.isnan(energy_change):
energy_change = -np.inf
if np.abs(energy_change) > self.Emax:
div_info = DivergenceInfo(
'Divergence encountered, large integration error.', None,
state)
accept_stat = min(1, np.exp(energy_change))
if div_info is not None or np.random.rand() >= accept_stat:
end = start
accepted = False
else:
end = state
accepted = True
stats = {
'path_length': self.path_length,
'n_steps': n_steps,
'accept': accept_stat,
'energy_error': energy_change,
'energy': state.energy,
'accepted': accepted,
'model_logp': state.model_logp,
}
return HMCStepData(end, accept_stat, div_info, stats)
def _hamiltonian_step(self, start, p0, step_size):
path_length = np.random.rand() * self.path_length
n_steps = max(1, int(path_length / step_size))
energy_change = -np.inf
state = start
div_info = None
try:
for _ in range(n_steps):
state = self.integrator.step(step_size, state)
except IntegrationError as e:
div_info = DivergenceInfo('Divergence encountered.', e, state)
else:
if not np.isfinite(state.energy):
div_info = DivergenceInfo('Divergence encountered, bad energy.', None, state)
energy_change = start.energy - state.energy
if np.abs(energy_change) > self.Emax:
div_info = DivergenceInfo('Divergence encountered, large integration error.',
None, state)
accept_stat = min(1, np.exp(energy_change + state.log_jac))
if div_info is not None or np.random.rand() >= accept_stat:
end = start
accepted = False
else:
end = state
accepted = True
stats = {
'path_length': path_length,
'n_steps': n_steps,
'accept': accept_stat,
'energy_error': energy_change,
'energy': state.energy,
'accepted': accepted,
# 'log_jacobian': state.log_jac, # TODO: backends/ndarray.py to allow this
}
return HMCStepData(end, accept_stat, div_info, stats)
def _single_step(self, left, epsilon):
"""Perform a leapfrog step and handle error cases."""
try:
# `State` type
right = self.integrator.step(epsilon, left)
except IntegrationError as err:
error_msg = str(err)
error = err
right = None
else:
# h - H0
energy_change = right.energy - self.start_energy
if np.isnan(energy_change):
energy_change = np.inf
if np.abs(energy_change) > np.abs(self.max_energy_change):
self.max_energy_change = energy_change
if np.abs(energy_change) < self.Emax:
# Acceptance statistic
# e^{H(q_0, p_0) - H(q_n, p_n)} max(1, e^{H(q_0, p_0) - H(q_n, p_n)})
# Saturated Metropolis accept probability with Boltzmann weight
# if h - H0 < 0
log_p_accept_weighted = -energy_change + min(
0.0, -energy_change)
log_size = -energy_change
proposal = Proposal(
right.q.data,
right.q_grad.data,
right.energy,
log_p_accept_weighted,
right.model_logp,
)
tree = Subtree(right, right, right.p.data, proposal, log_size,
log_p_accept_weighted, 1)
return tree, None, False
else:
error_msg = "Energy change in leapfrog step is too large: %s." % energy_change
error = None
tree = Subtree(None, None, None, None, -np.inf, -np.inf, 1)
divergance_info = DivergenceInfo(error_msg, error, left, right)
return tree, divergance_info, False