#!/usr/bin/env python
import numpy as np
import supervillain.action
from supervillain.generator import Generator
from supervillain.h5 import ReadWriteable
from supervillain.lattice import d
import logging
logger = logging.getLogger(__name__)
[docs]class SiteUpdate(ReadWriteable, Generator):
r'''
This performs the same update to $\phi$ as :class:`NeighborhoodUpdate <supervillain.generator.villain.NeighborhoodUpdate>` but leaves $n$ untouched.
Proposals are drawn according to
.. math ::
\Delta \phi_x \sim \text{uniform}(-\texttt{interval\_phi}, +\texttt{interval\_phi})
'''
def __init__(self, action, interval_phi = np.pi):
if not isinstance(action, supervillain.action.Villain):
raise ValueError('Need a Villain action')
self.Action = action
self.Lattice = action.Lattice
self.kappa = action.kappa
self.interval_phi = interval_phi
self.rng = np.random.default_rng()
self.accepted = 0
self.proposed = 0
self.acceptance = 0.
self.sweeps = 0
def __str__(self):
return 'SiteUpdate'
[docs] def step(self, cfg):
r'''
Make volume's worth of random single-site updates to $\phi$.
Parameters
----------
cfg: dict
A dictionary with phi and n as Forms.
Returns
-------
dict
Updated configuration.
'''
S = self.Action
L = S.Lattice
phi = cfg['phi'].copy()
n = cfg['n']
self.sweeps += 1
total_accepted = 0
total_acceptance = 0
metropolis = self.rng.uniform(0, 1, (L.N,) * L.D)
# The idea is to make the same sort of update to phi as the Neighborhood update gives.
# However, rather than a python-level for loop over space, we can accomplish a lot more at the numpy level,
# as in the villain.LinkUpdate.
# However, in the LinkUpdate we change n, and each n contributes to an independent term in the action.
# In contrast, what enters the action (per link) is dphi, which knows about phi on two sites.
#
# That poses a small problem because if we change the action by changing dphi, we want to be able to track
# that change in dphi back to a change in phi on ONE particular site.
# Therefore, we use checkerboarding.
# Precompute dphi once; we update it incrementally as accepted changes accumulate.
dphi = d(phi)
for color in L.checkerboarding:
# We only offer changes to phi on a single color at once. The benefit is that the surrounding sites
# do not have updates. So we know where any change in the action on any link came from: it came from
# the site in the partition (color) we are updating.
change_phi = L.zeros(0)
change_phi[0, *color] = self.rng.uniform(-self.interval_phi, +self.interval_phi, len(color[0]))
# Expanding S.local(phi+Δφ, n) − S.local(phi, n) algebraically avoids two full d(phi) calls and additional arithmetic operations:
# κ/2 · (dφ + dΔφ − 2πn)² − κ/2 · (dφ − 2πn)² = κ/2 · dΔφ · (2(dφ−2πn) + dΔφ)
change_dphi = d(change_phi)
dS_link = (S.kappa / 2) * change_dphi * (2 * (dphi - 2 * np.pi * n) + change_dphi)
# The change in action originating from the change in phi on the color under consideration
# is just the sum of all the changes from the adjacent links. face_sum collects them.
dS = dS_link.face_sum()
# dS is not 0 on the off-color sites---those sites still have links that land on the current color.
# We only want to accept/reject updates on the current color.
acceptance = np.clip(np.exp(-dS[0, *color]), a_min=0, a_max=1)
accepted = metropolis[color] < acceptance
total_accepted += accepted.sum()
total_acceptance += acceptance.sum()
# Update phi and dphi where the change is accepted.
change_phi[0, *color] *= accepted
phi = phi + change_phi
dphi = dphi + d(change_phi)
sites = self.Lattice.cells_of_degree[0]
self.proposed += sites
self.acceptance += total_acceptance / sites
self.accepted += total_accepted
logger.debug(f'Average proposal acceptance {total_acceptance / sites:.6f}; Actually accepted {total_accepted} / {sites} = {total_accepted / sites}')
return cfg | {'phi': phi}
[docs] def inline_observables(self, steps):
return {}
[docs] def report(self):
return (
f'There were {self.accepted} single-phi proposals accepted of {self.proposed} proposed updates.'
+'\n'+
f' {self.accepted/self.proposed:.6f} acceptance rate'
+'\n'+
f' {self.acceptance / self.sweeps:.6f} average Metropolis acceptance probability.'
)