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import warnings
import numpy as np
from numpy.linalg import eigh
from ase.optimize.optimize import Optimizer
class BFGS(Optimizer):
# default parameters
defaults = {**Optimizer.defaults, 'alpha': 70.0}
def __init__(self, atoms, restart=None, logfile='-', trajectory=None,
maxstep=None, master=None, alpha=None):
"""BFGS optimizer.
Parameters:
atoms: Atoms object
The Atoms object to relax.
restart: string
Pickle file used to store hessian matrix. If set, file with
such a name will be searched and hessian matrix stored will
be used, if the file exists.
trajectory: string
Pickle file used to store trajectory of atomic movement.
logfile: file object or str
If *logfile* is a string, a file with that name will be opened.
Use '-' for stdout.
maxstep: float
Used to set the maximum distance an atom can move per
iteration (default value is 0.2 Å).
master: boolean
Defaults to None, which causes only rank 0 to save files. If
set to true, this rank will save files.
alpha: float
Initial guess for the Hessian (curvature of energy surface). A
conservative value of 70.0 is the default, but number of needed
steps to converge might be less if a lower value is used. However,
a lower value also means risk of instability.
"""
if maxstep is None:
self.maxstep = self.defaults['maxstep']
else:
self.maxstep = maxstep
if self.maxstep > 1.0:
warnings.warn('You are using a *very* large value for '
'the maximum step size: %.1f Å' % maxstep)
if alpha is None:
self.alpha = self.defaults['alpha']
else:
self.alpha = alpha
Optimizer.__init__(self, atoms, restart, logfile, trajectory, master)
def todict(self):
d = Optimizer.todict(self)
if hasattr(self, 'maxstep'):
d.update(maxstep=self.maxstep)
return d
def initialize(self):
# initial hessian
self.H0 = np.eye(3 * len(self.atoms)) * self.alpha
self.H = None
self.r0 = None
self.f0 = None
def read(self):
self.H, self.r0, self.f0, self.maxstep = self.load()
def step(self, f=None):
atoms = self.atoms
if f is None:
f = atoms.get_forces()
r = atoms.get_positions()
f = f.reshape(-1)
self.update(r.flat, f, self.r0, self.f0)
omega, V = eigh(self.H)
# FUTURE: Log this properly
# # check for negative eigenvalues of the hessian
# if any(omega < 0):
# n_negative = len(omega[omega < 0])
# msg = '\n** BFGS Hessian has {} negative eigenvalues.'.format(
# n_negative
# )
# print(msg, flush=True)
# if self.logfile is not None:
# self.logfile.write(msg)
# self.logfile.flush()
dr = np.dot(V, np.dot(f, V) / np.fabs(omega)).reshape((-1, 3))
steplengths = (dr**2).sum(1)**0.5
dr = self.determine_step(dr, steplengths)
atoms.set_positions(r + dr)
self.r0 = r.flat.copy()
self.f0 = f.copy()
self.dump((self.H, self.r0, self.f0, self.maxstep))
def determine_step(self, dr, steplengths):
"""Determine step to take according to maxstep
Normalize all steps as the largest step. This way
we still move along the eigendirection.
"""
maxsteplength = np.max(steplengths)
if maxsteplength >= self.maxstep:
scale = self.maxstep / maxsteplength
# FUTURE: Log this properly
# msg = '\n** scale step by {:.3f} to be shorter than {}'.format(
# scale, self.maxstep
# )
# print(msg, flush=True)
dr *= scale
return dr
def update(self, r, f, r0, f0):
if self.H is None:
self.H = self.H0
return
dr = r - r0
if np.abs(dr).max() < 1e-7:
# Same configuration again (maybe a restart):
return
df = f - f0
a = np.dot(dr, df)
dg = np.dot(self.H, dr)
b = np.dot(dr, dg)
self.H -= np.outer(df, df) / a + np.outer(dg, dg) / b
def replay_trajectory(self, traj):
"""Initialize hessian from old trajectory."""
if isinstance(traj, str):
from ase.io.trajectory import Trajectory
traj = Trajectory(traj, 'r')
self.H = None
atoms = traj[0]
r0 = atoms.get_positions().ravel()
f0 = atoms.get_forces().ravel()
for atoms in traj:
r = atoms.get_positions().ravel()
f = atoms.get_forces().ravel()
self.update(r, f, r0, f0)
r0 = r
f0 = f
self.r0 = r0
self.f0 = f0
class oldBFGS(BFGS):
def determine_step(self, dr, steplengths):
"""Old BFGS behaviour for scaling step lengths
This keeps the behaviour of truncating individual steps. Some might
depend of this as some absurd kind of stimulated annealing to find the
global minimum.
"""
dr /= np.maximum(steplengths / self.maxstep, 1.0).reshape(-1, 1)
return dr
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