def estimate_hessian(dof, eps=1e-4):
"""Estimate the Hessian using the symmetric finite difference approximation.
**Arguments:**
dof
A DOF object
**Optional arguments:**
eps
The magnitude of the displacements
"""
with log.section('HESS'), timer.section('Hessian'):
# Loop over all displacements
if log.do_medium:
log('The following displacements are computed:')
log('DOF Dir Energy')
log.hline()
x1 = dof.x0.copy()
rows = np.zeros((len(x1), len(x1)), float)
for i in xrange(len(x1)):
x1[i] = dof.x0[i] + eps
epot, gradient_p = dof.fun(x1, do_gradient=True)
if log.do_medium:
log('% 7i pos %s' % (i, log.energy(epot)))
x1[i] = dof.x0[i] - eps
epot, gradient_m = dof.fun(x1, do_gradient=True)
if log.do_medium:
log('% 7i neg %s' % (i, log.energy(epot)))
rows[i] = (gradient_p-gradient_m)/(2*eps)
x1[i] = dof.x0[i]
dof.reset()
if log.do_medium:
log.hline()
# Enforce symmetry and return
return 0.5*(rows + rows.T)
def estimate_hessian(dof, eps=1e-4):
"""Estimate the Hessian using the symmetric finite difference approximation.
**Arguments:**
dof
A DOF object
**Optional arguments:**
eps
The magnitude of the displacements
"""
with log.section('HESS'), timer.section('Hessian'):
# Loop over all displacements
if log.do_medium:
log('The following displacements are computed:')
log('DOF Dir Energy')
log.hline()
x1 = dof.x0.copy()
rows = np.zeros((len(x1), len(x1)), float)
for i in xrange(len(x1)):
x1[i] = dof.x0[i] + eps
epot, gradient_p = dof.fun(x1, do_gradient=True)
if log.do_medium:
log('% 7i pos %s' % (i, log.energy(epot)))
x1[i] = dof.x0[i] - eps
epot, gradient_m = dof.fun(x1, do_gradient=True)
if log.do_medium:
log('% 7i neg %s' % (i, log.energy(epot)))
rows[i] = (gradient_p - gradient_m) / (2 * eps)
x1[i] = dof.x0[i]
dof.reset()
if log.do_medium:
log.hline()
# Enforce symmetry and return
return 0.5 * (rows + rows.T)
def __call__(self):
"""Perform a trial move and calculate the associated energy difference,
decide whether it is accepted or not, and update the state of the
MC simulation accordingly
"""
with timer.section("MC %s move" % self.log_name):
e = self.compute()
p = self.probability(e)
if np.random.rand()>p:
accepted = False
self.reject()
else:
accepted = True
self.mc.energy += e
self.accept()
if log.do_debug:
log("MC %s: N = %d energy difference = %s acceptance probability = %6.2f %% accepted = %s"
% (self.__class__.__name__, self.mc.N, log.energy(e), p*100.0, accepted))
return accepted
def __call__(self, iterative):
if log.do_medium:
if self.time0 is None:
self.time0 = time.time()
if log.do_medium:
log.hline()
log('Conv.val. =&the highest ratio of a convergence criterion over its threshold.')
log('N =&the number of convergence criteria that is not met.')
log('Worst =&the name of the convergence criterion that is worst.')
log('counter Conv.val. N Worst Energy Walltime')
log.hline()
log('%7i % 10.3e %2i %15s %s %10.1f' % (
iterative.counter,
iterative.dof.conv_val,
iterative.dof.conv_count,
iterative.dof.conv_worst,
log.energy(iterative.epot),
time.time() - self.time0,
))
def __call__(self, iterative):
if log.do_medium:
if self.time0 is None:
self.time0 = time.time()
if log.do_medium:
log.hline()
log('Conv.val. =&the highest ratio of a convergence criterion over its threshold.')
log('N =&the number of convergence criteria that is not met.')
log('Worst =&the name of the convergence criterion that is worst.')
log('counter Conv.val. N Worst Energy Walltime')
log.hline()
log('%7i % 10.3e %2i %15s %s %10.1f' % (
iterative.counter,
iterative.dof.conv_val,
iterative.dof.conv_count,
iterative.dof.conv_worst,
log.energy(iterative.epot),
time.time() - self.time0,
))
def log(self):
return '%10d %10.6f %s %s' % ( self.N, self.Nmean,
log.energy(self.energy), log.energy(self.emean))
def log(self):
return '%s %s %s %s' % ( log.volume(self.current_configuration.cell.volume),
log.volume(self.Vmean), log.energy(self.energy), log.energy(self.emean))
def log(self):
return '%s %s' % (log.energy(self.energy), log.energy(self.emean))