def MU(einsumString, Z, factors):
Zhat = hat(self._A, self._H, self._C)
return (
einsum(
einsumString,
self.data * (Zhat ** (self.beta - 2)),
*factors) /
einsum(
einsumString,
Zhat ** (self.beta - 1),
*factors
)
)
def hat(A, H, C, eps=None):
"""Builds common fate model tensor from factors
makes use of numpys einstein summation
Parameters
----------
A : tuple
The shape
H : tuple
The shape
C : tuple
The shape
Returns
-------
np.ndarray, shape=(P.shape + H.shape + C.shape)
tensor with same shape as common fate transform
"""
if eps is None:
eps = np.finfo(float).eps
return eps + einsum('abfj,tj,cj->abftc', A, H, C)
def find_x_bonds(initial_atoms, final_atoms, simulation_params):
slip_system = simulation_params[0]
motif = slip_system['motif']
if motif.ndim == 1:
motif_length = 1
else:
motif_length = len(motif)
size = simulation_params[2]
initial_positions = initial_atoms[:,:3]
final_positions = final_atoms[:,:3]
x_bonds = np.zeros_like(initial_positions, dtype=myfloat)
b = slip_system['latt_params'][0]
rolled_initial = np.roll(initial_positions,
-motif_length,
axis=0)
rolled_final = np.roll(final_positions,
-motif_length,
axis=0)
mask = ((rolled_initial - initial_positions)
- np.array([b, 0, 0]))
mask = einsum('ni,ni->n', mask, mask)
mask = mask < 1e-16
# number of bonds expected to be left hanging
# at the positive x extreme:
if slip_system['motif'].shape == (4,):
motif_length = 1
else:
motif_length = len(slip_system['motif'])
if size[2] == 0:
no_of_missing_bonds = 2 * size[1] * motif_length
else:
no_of_missing_bonds = (2
* size[1]
* 2
* size[2]
* motif_length)
if np.count_nonzero(mask) == (len(mask) - no_of_missing_bonds):
x_bonds[mask] = rolled_final[mask] - final_positions[mask]
else:
# A slow backup if we don't find any
# bonds assume we've messed up,
# should work for an arbitrary ordered array
for i in range(initial_atoms.shape[0]):
rolled_initial = np.roll(initial_positions,
-(i+1),
axis=0)
rolled_final = np.roll(final_positions, -(i+1), axis=0)
mask = ((rolled_initial - initial_positions)
- np.array([b, 0, 0]))
mask = einsum('ni,ni->n', mask, mask)
mask = mask < 1e-16
x_bonds[mask] = (rolled_final[mask]
- final_positions[mask])
return x_bonds
def hat(P, At, Ac, eps=None):
if eps is None:
eps = np.finfo(float).eps
return eps + einsum('abfj,tj,cj->abftc', P, At, Ac)