Source code for ase.optimize.bfgs

import warnings

import numpy as np
from numpy.linalg import eigh

from ase.optimize.optimize import Optimizer

[docs]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 =,, 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 =, df) dg =, dr) b =, 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 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