import warnings
from typing import IO, Optional, Union
import numpy as np
from numpy.linalg import eigh
from ase import Atoms
from ase.optimize.optimize import Optimizer, UnitCellFilter
[docs]
class BFGS(Optimizer):
# default parameters
defaults = {**Optimizer.defaults, 'alpha': 70.0}
def __init__(
self,
atoms: Atoms,
restart: Optional[str] = None,
logfile: Optional[Union[IO, str]] = '-',
trajectory: Optional[str] = None,
append_trajectory: bool = False,
maxstep: Optional[float] = None,
alpha: Optional[float] = None,
**kwargs,
):
"""BFGS optimizer.
Parameters
----------
atoms: :class:`~ase.Atoms`
The Atoms object to relax.
restart: str
JSON 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: str
Trajectory file used to store optimisation path.
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).
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.
kwargs : dict, optional
Extra arguments passed to
:class:`~ase.optimize.optimize.Optimizer`.
"""
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' % self.maxstep)
self.alpha = alpha
if self.alpha is None:
self.alpha = self.defaults['alpha']
Optimizer.__init__(self, atoms=atoms, restart=restart,
logfile=logfile, trajectory=trajectory,
append_trajectory=append_trajectory,
**kwargs)
def initialize(self):
# initial hessian
self.H0 = np.eye(3 * len(self.optimizable)) * self.alpha
self.H = None
self.pos0 = None
self.forces0 = None
def read(self):
file = self.load()
if len(file) == 5:
(self.H, self.pos0, self.forces0, self.maxstep,
self.atoms.orig_cell) = file
else:
self.H, self.pos0, self.forces0, self.maxstep = file
def step(self, forces=None):
optimizable = self.optimizable
if forces is None:
forces = optimizable.get_forces()
pos = optimizable.get_positions()
dpos, steplengths = self.prepare_step(pos, forces)
dpos = self.determine_step(dpos, steplengths)
optimizable.set_positions(pos + dpos)
if isinstance(self.atoms, UnitCellFilter):
self.dump((self.H, self.pos0, self.forces0, self.maxstep,
self.atoms.orig_cell))
else:
self.dump((self.H, self.pos0, self.forces0, self.maxstep))
def prepare_step(self, pos, forces):
forces = forces.reshape(-1)
self.update(pos.flat, forces, self.pos0, self.forces0)
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()
dpos = np.dot(V, np.dot(forces, V) / np.fabs(omega)).reshape((-1, 3))
steplengths = (dpos**2).sum(1)**0.5
self.pos0 = pos.flat.copy()
self.forces0 = forces.copy()
return dpos, steplengths
def determine_step(self, dpos, steplengths):
"""Determine step to take according to maxstep
Normalize all steps as the largest step. This way
we still move along the direction.
"""
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)
dpos *= scale
return dpos
def update(self, pos, forces, pos0, forces0):
if self.H is None:
self.H = self.H0
return
dpos = pos - pos0
if np.abs(dpos).max() < 1e-7:
# Same configuration again (maybe a restart):
return
dforces = forces - forces0
a = np.dot(dpos, dforces)
dg = np.dot(self.H, dpos)
b = np.dot(dpos, dg)
self.H -= np.outer(dforces, dforces) / 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]
pos0 = atoms.get_positions().ravel()
forces0 = atoms.get_forces().ravel()
for atoms in traj:
pos = atoms.get_positions().ravel()
forces = atoms.get_forces().ravel()
self.update(pos, forces, pos0, forces0)
pos0 = pos
forces0 = forces
self.pos0 = pos0
self.forces0 = forces0
class oldBFGS(BFGS):
def determine_step(self, dpos, 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.
"""
dpos /= np.maximum(steplengths / self.maxstep, 1.0).reshape(-1, 1)
return dpos