def test_dsygv_dgelsd(self):
a = Diamond('C', size=[4,4,4])
b = a.copy()
b.positions += (np.random.random(b.positions.shape)-0.5)*0.1
i, j = neighbour_list("ij", b, 1.85)
dr_now = mic(b.positions[i] - b.positions[j], b.cell)
dr_old = mic(a.positions[i] - a.positions[j], a.cell)
dgrad1 = get_delta_plus_epsilon_dgesv(len(b), i, dr_now, dr_old)
dgrad2 = get_delta_plus_epsilon(len(b), i, dr_now, dr_old)
self.assertArrayAlmostEqual(dgrad1, dgrad2)
def get_D_square_min(atoms_now,
atoms_old,
i_now,
j_now,
delta_plus_epsilon=None):
"""
Calculate the D^2_min norm of Falk and Langer
"""
nat = len(atoms_now)
assert len(atoms_now) == len(atoms_old)
pos_now = atoms_now.positions
pos_old = atoms_old.positions
# Compute current and old distance vectors. Note that current distance
# vectors cannot be taken from the neighbor calculation, because neighbors
# are calculated from the sheared cell while these distance need to come
# from the unsheared cell. Taking the distance from the unsheared cell
# make periodic boundary conditions (and flipping of cell) a lot easier.
dr_now = mic(pos_now[i_now] - pos_now[j_now], atoms_now.cell)
dr_old = mic(pos_old[i_now] - pos_old[j_now], atoms_old.cell)
# Sanity check: Shape needs to be identical!
assert dr_now.shape == dr_old.shape
if delta_plus_epsilon is None:
# Get minimum strain tensor
delta_plus_epsilon = get_delta_plus_epsilon(nat, i_now, dr_now, dr_old)
# Spread epsilon out for each neighbor index
delta_plus_epsilon_n = delta_plus_epsilon[i_now]
# Compute D^2_min (residual of the least squares fit)
residual_n = np.sum((dr_now - np.sum(
delta_plus_epsilon_n.reshape(-1, 3, 3) * dr_old.reshape(-1, 1, 3),
axis=2))**2,
axis=1)
# For each atom, sum over all neighbors
residual = np.bincount(i_now, weights=residual_n)
return delta_plus_epsilon, residual
def _fill_shifts_upto(self, i):
# Iterate up to frame i the full trajectory first and generate a list
# of displacement vectors.
while len(self.shifts) <= i:
j = len(self.shifts)
a0 = self.traj[j - 1]
a1 = self.traj[j]
s0 = a0.get_scaled_positions() % 1.0
s1 = a1.get_scaled_positions() % 1.0
sdisps = mic(s1 - s0, np.eye(3), pbc=a0.pbc)
self.shifts += [self.shifts[-1] + sdisps.mean(axis=0)]
def _fill_shifts_upto(self, i):
# Iterate up to frame i the full trajectory first and generate a list
# of displacement vectors.
while len(self.shifts) <= i:
j = len(self.shifts)
a0 = self.traj[j-1]
a1 = self.traj[j]
s0 = a0.get_scaled_positions()%1.0
s1 = a1.get_scaled_positions()%1.0
sdisps = mic(s1-s0, np.eye(3), pbc=a0.pbc)
self.shifts += [self.shifts[-1]+sdisps.mean(axis=0)]
def get_D_square_min(atoms_now, atoms_old, i_now, j_now, delta_plus_epsilon=None):
"""
Calculate the D^2_min norm of Falk and Langer
"""
nat = len(atoms_now)
assert len(atoms_now) == len(atoms_old)
pos_now = atoms_now.positions
pos_old = atoms_old.positions
# Compute current and old distance vectors. Note that current distance
# vectors cannot be taken from the neighbor calculation, because neighbors
# are calculated from the sheared cell while these distance need to come
# from the unsheared cell. Taking the distance from the unsheared cell
# make periodic boundary conditions (and flipping of cell) a lot easier.
dr_now = mic(pos_now[i_now] - pos_now[j_now], atoms_now.cell)
dr_old = mic(pos_old[i_now] - pos_old[j_now], atoms_old.cell)
# Sanity check: Shape needs to be identical!
assert dr_now.shape == dr_old.shape
if delta_plus_epsilon is None:
# Get minimum strain tensor
delta_plus_epsilon = get_delta_plus_epsilon(nat, i_now, dr_now, dr_old)
# Spread epsilon out for each neighbor index
delta_plus_epsilon_n = delta_plus_epsilon[i_now]
# Compute D^2_min (residual of the least squares fit)
residual_n = np.sum(
(
dr_now-
np.sum(delta_plus_epsilon_n.reshape(-1,3,3)*dr_old.reshape(-1,1,3),
axis=2)
)**2,
axis=1)
# For each atom, sum over all neighbors
residual = np.bincount(i_now, weights=residual_n)
return delta_plus_epsilon, residual
def test_neighbour_list(self):
a = io.read('aC.cfg')
j, dr, i, abs_dr = neighbour_list("jDid", a, 1.85)
self.assertTrue((np.bincount(i) == np.bincount(j)).all())
r = a.get_positions()
dr_direct = mic(r[j] - r[i], a.cell)
abs_dr_from_dr = np.sqrt(np.sum(dr * dr, axis=1))
abs_dr_direct = np.sqrt(np.sum(dr_direct * dr_direct, axis=1))
self.assertTrue(np.all(np.abs(abs_dr - abs_dr_from_dr) < 1e-12))
self.assertTrue(np.all(np.abs(abs_dr - abs_dr_direct) < 1e-12))
self.assertTrue(np.all(np.abs(dr - dr_direct) < 1e-12))
def test_neighbour_list(self):
a = io.read('aC.cfg')
j, dr, i, abs_dr = neighbour_list("jDid", a, 1.85)
self.assertTrue((np.bincount(i) == np.bincount(j)).all())
r = a.get_positions()
dr_direct = mic(r[j]-r[i], a.cell)
abs_dr_from_dr = np.sqrt(np.sum(dr*dr, axis=1))
abs_dr_direct = np.sqrt(np.sum(dr_direct*dr_direct, axis=1))
self.assertTrue(np.all(np.abs(abs_dr-abs_dr_from_dr) < 1e-12))
self.assertTrue(np.all(np.abs(abs_dr-abs_dr_direct) < 1e-12))
self.assertTrue(np.all(np.abs(dr-dr_direct) < 1e-12))
def test_neighbour_list(self):
for pbc in [True, False, [True, False, True]]:
a = io.read('aC.cfg')
a.set_pbc(pbc)
j, dr, i, abs_dr, shift = neighbour_list("jDidS", a, 1.85)
self.assertTrue((np.bincount(i) == np.bincount(j)).all())
r = a.get_positions()
dr_direct = mic(r[j]-r[i], a.cell)
self.assertArrayAlmostEqual(r[j]-r[i]+shift.dot(a.cell), dr_direct)
abs_dr_from_dr = np.sqrt(np.sum(dr*dr, axis=1))
abs_dr_direct = np.sqrt(np.sum(dr_direct*dr_direct, axis=1))
self.assertTrue(np.all(np.abs(abs_dr-abs_dr_from_dr) < 1e-12))
self.assertTrue(np.all(np.abs(abs_dr-abs_dr_direct) < 1e-12))
self.assertTrue(np.all(np.abs(dr-dr_direct) < 1e-12))
def test_neighbour_list(self):
for pbc in [True, False, [True, False, True]]:
a = io.read('aC.cfg')
a.set_pbc(pbc)
j, dr, i, abs_dr, shift = neighbour_list("jDidS", a, 1.85)
self.assertTrue((np.bincount(i) == np.bincount(j)).all())
r = a.get_positions()
dr_direct = mic(r[j]-r[i], a.cell)
self.assertArrayAlmostEqual(r[j]-r[i]+shift.dot(a.cell), dr_direct)
abs_dr_from_dr = np.sqrt(np.sum(dr*dr, axis=1))
abs_dr_direct = np.sqrt(np.sum(dr_direct*dr_direct, axis=1))
self.assertTrue(np.all(np.abs(abs_dr-abs_dr_from_dr) < 1e-12))
self.assertTrue(np.all(np.abs(abs_dr-abs_dr_direct) < 1e-12))
self.assertTrue(np.all(np.abs(dr-dr_direct) < 1e-12))
def compare_configurations(dislo, bulk, dislo_ref, bulk_ref,
alat, cylinder_r=None, print_info=True):
"""Compares two dislocation configurations based on the gradient of
the displacements along the bonds.
Parameters
----------
dislo : ase.Atoms
Dislocation configuration.
bulk : ase.Atoms
Corresponding bulk configuration for calculation of displacements.
dislo_ref : ase.Atoms
Reference dislocation configuration.
bulk_ref : ase.Atoms
Corresponding reference bulk configuration
for calculation of displacements.
alat : float
Lattice parameter for calculation of neghbour list cutoff.
cylinder_r : float or None
Radius of region of comparison around the dislocation coreself.
If None makes global comparison based on the radius of
`dislo` configuration, else compares the regions with `cylinder_r`
around the dislocation core position.
print_info : bool
Flag to switch print statement about the type of the comparison
Returns
-------
float
The Du norm of the differences per atom.
"""
if cylinder_r is None:
x, y, __ = bulk.positions.T
radius = np.sqrt(x**2 + y**2)
cutoff_radius = radius.max() - 10.
if print_info:
print("Making a global comparison with radius %.2f" % cutoff_radius)
else:
cutoff_radius = cylinder_r
if print_info:
print("Making a local comparison with radius %.2f" % cutoff_radius)
x, y, __ = bulk_ref.positions.T
radius = np.sqrt(x**2 + y**2)
cutoff_mask = (radius < cutoff_radius)
second_NN_distance = alat
bulk_i, bulk_j = neighbour_list('ij', bulk_ref, second_NN_distance)
I_core, J_core = np.array([(i, j) for i, j in zip(bulk_i, bulk_j) if cutoff_mask[i]]).T
mapping = {}
for i in range(len(bulk)):
mapping[i] = np.linalg.norm(bulk_ref.positions -
bulk.positions[i], axis=1).argmin()
u_ref = dislo_ref.positions - bulk_ref.positions
u = dislo.positions - bulk.positions
u_extended = np.zeros(u_ref.shape)
u_extended[mapping.values(), :] = u
du = u_extended - u_ref
Du = np.linalg.norm(np.linalg.norm(mic(du[J_core, :] - du[I_core, :],
bulk.cell), axis=1))
return Du
ref_frame = traj[0]
individual_elements = set(ref_frame.numbers)
s = '#{:>9s}'.format('frame')
if 'time' in ref_frame.info:
s = '{} {:>10s}'.format(s, 'time')
s = '{} {:>10s}'.format(s, 'tot. rms')
for element in individual_elements:
s = '{} {:>10s}'.format(s, 'rms ({})'.format(chemical_symbols[element]))
print(s)
last_frame = traj[0]
displacements = np.zeros_like(ref_frame.positions)
for i, frame in enumerate(traj[1:]):
last_frame.set_cell(frame.cell, scale_atoms=True)
cur_displacements = frame.positions - last_frame.positions
cur_displacements = mic(cur_displacements, frame.cell, frame.pbc)
displacements += cur_displacements
s = '{:10}'.format(i+1)
if 'time' in frame.info:
s = '{} {:10.6}'.format(s, frame.info['time'])
s = '{} {:10.6}'.format(s, np.sqrt((displacements**2).mean()))
for element in individual_elements:
s = '{} {:10.6}'.format(s, np.sqrt(
(displacements[frame.numbers == element]**2).mean()))
print(s)
last_frame = frame