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import numpy as np
from collections import namedtuple
from ase.geometry import find_mic
def fit_raw(energies, forces, positions, cell=None, pbc=None):
"""Calculates parameters for fitting images to a band, as for
a NEB plot."""
energies = np.array(energies) - energies[0]
n_images = len(energies)
fit_energies = np.empty((n_images - 1) * 20 + 1)
fit_path = np.empty((n_images - 1) * 20 + 1)
path = [0]
for i in range(n_images - 1):
dR = positions[i + 1] - positions[i]
if cell is not None and pbc is not None:
dR, _ = find_mic(dR, cell, pbc)
path.append(path[i] + np.sqrt((dR**2).sum()))
lines = [] # tangent lines
lastslope = None
for i in range(n_images):
if i == 0:
direction = positions[i + 1] - positions[i]
dpath = 0.5 * path[1]
elif i == n_images - 1:
direction = positions[-1] - positions[-2]
dpath = 0.5 * (path[-1] - path[-2])
else:
direction = positions[i + 1] - positions[i - 1]
dpath = 0.25 * (path[i + 1] - path[i - 1])
direction /= np.linalg.norm(direction)
slope = -(forces[i] * direction).sum()
x = np.linspace(path[i] - dpath, path[i] + dpath, 3)
y = energies[i] + slope * (x - path[i])
lines.append((x, y))
if i > 0:
s0 = path[i - 1]
s1 = path[i]
x = np.linspace(s0, s1, 20, endpoint=False)
c = np.linalg.solve(np.array([(1, s0, s0**2, s0**3),
(1, s1, s1**2, s1**3),
(0, 1, 2 * s0, 3 * s0**2),
(0, 1, 2 * s1, 3 * s1**2)]),
np.array([energies[i - 1], energies[i],
lastslope, slope]))
y = c[0] + x * (c[1] + x * (c[2] + x * c[3]))
fit_path[(i - 1) * 20:i * 20] = x
fit_energies[(i - 1) * 20:i * 20] = y
lastslope = slope
fit_path[-1] = path[-1]
fit_energies[-1] = energies[-1]
return ForceFit(path, energies, fit_path, fit_energies, lines)
class ForceFit(namedtuple('ForceFit', ['path', 'energies', 'fit_path',
'fit_energies', 'lines'])):
"""Data container to hold fitting parameters for force curves."""
def plot(self, ax=None):
import matplotlib.pyplot as plt
if ax is None:
ax = plt.gca()
ax.plot(self.path, self.energies, 'o')
for x, y in self.lines:
ax.plot(x, y, '-g')
ax.plot(self.fit_path, self.fit_energies, 'k-')
ax.set_xlabel(r'path [Å]')
ax.set_ylabel('energy [eV]')
Ef = max(self.energies) - self.energies[0]
Er = max(self.energies) - self.energies[-1]
dE = self.energies[-1] - self.energies[0]
ax.set_title(r'$E_\mathrm{{f}} \approx$ {:.3f} eV; '
r'$E_\mathrm{{r}} \approx$ {:.3f} eV; '
r'$\Delta E$ = {:.3f} eV'.format(Ef, Er, dE))
return ax
def fit_images(images):
"""Fits a series of images with a smoothed line for producing a standard
NEB plot. Returns a `ForceFit` data structure; the plot can be produced
by calling the `plot` method of `ForceFit`."""
R = [atoms.positions for atoms in images]
E = [atoms.get_potential_energy() for atoms in images]
F = [atoms.get_forces() for atoms in images] # XXX force consistent???
A = images[0].cell
pbc = images[0].pbc
return fit_raw(E, F, R, A, pbc)
def force_curve(images, ax=None):
"""Plot energies and forces as a function of accumulated displacements.
This is for testing whether a calculator's forces are consistent with
the energies on a set of geometries where energies and forces are
available."""
if ax is None:
import matplotlib.pyplot as plt
ax = plt.gca()
nim = len(images)
accumulated_distances = []
accumulated_distance = 0.0
# XXX force_consistent=True will work with some calculators,
# but won't work if images were loaded from a trajectory.
energies = [atoms.get_potential_energy()
for atoms in images]
for i in range(nim):
atoms = images[i]
f_ac = atoms.get_forces()
if i < nim - 1:
rightpos = images[i + 1].positions
else:
rightpos = atoms.positions
if i > 0:
leftpos = images[i - 1].positions
else:
leftpos = atoms.positions
disp_ac, _ = find_mic(rightpos - leftpos, cell=atoms.cell,
pbc=atoms.pbc)
def total_displacement(disp):
disp_a = (disp**2).sum(axis=1)**.5
return sum(disp_a)
dE_fdotr = -0.5 * np.vdot(f_ac.ravel(), disp_ac.ravel())
linescale = 0.45
disp = 0.5 * total_displacement(disp_ac)
if i == 0 or i == nim - 1:
disp *= 2
dE_fdotr *= 2
x1 = accumulated_distance - disp * linescale
x2 = accumulated_distance + disp * linescale
y1 = energies[i] - dE_fdotr * linescale
y2 = energies[i] + dE_fdotr * linescale
ax.plot([x1, x2], [y1, y2], 'b-')
ax.plot(accumulated_distance, energies[i], 'bo')
ax.set_ylabel('Energy [eV]')
ax.set_xlabel('Accumulative distance [Å]')
accumulated_distances.append(accumulated_distance)
accumulated_distance += total_displacement(rightpos - atoms.positions)
ax.plot(accumulated_distances, energies, ':', zorder=-1, color='k')
return ax
def plotfromfile(*fnames):
from ase.io import read
nplots = len(fnames)
for i, fname in enumerate(fnames):
images = read(fname, ':')
import matplotlib.pyplot as plt
plt.subplot(nplots, 1, 1 + i)
force_curve(images)
plt.show()
if __name__ == '__main__':
import sys
fnames = sys.argv[1:]
plotfromfile(*fnames)
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