def minkowski_reduce(self):
"""Minkowski-reduce this cell, returning new cell and mapping.
See also :func:`ase.geometry.minkowski_reduction.minkowski_reduce`."""
from ase.geometry.minkowski_reduction import minkowski_reduce
rcell, op = minkowski_reduce(self)
return Cell(rcell), op
def find_mic(v, cell, pbc=True):
"""Finds the minimum-image representation of vector(s) v"""
pbc = cell.any(1) & pbc2pbc(pbc)
v = np.array(v)
single = len(v.shape) == 1
v = np.atleast_2d(v)
if np.sum(pbc) > 0:
cell = complete_cell(cell)
rcell, _ = minkowski_reduce(cell, pbc=pbc)
# in a Minkowski-reduced cell we only need to test nearest neighbors
cs = [np.arange(-1 * p, p + 1) for p in pbc]
neighbor_cells = list(itertools.product(*cs))
positions = wrap_positions(v, rcell, pbc=pbc, eps=0)
vmin = positions.copy()
vlen = np.linalg.norm(positions, axis=1)
for nbr in neighbor_cells:
trial = positions + np.dot(rcell.T, nbr)
trial_len = np.linalg.norm(trial, axis=1)
indices = np.where(trial_len < vlen)
vmin[indices] = trial[indices]
vlen[indices] = trial_len[indices]
else:
vmin = v.copy()
vlen = np.linalg.norm(vmin, axis=1)
if single:
return vmin[0], vlen[0]
else:
return vmin, vlen
def general_find_mic(v, cell, pbc=True):
"""Finds the minimum-image representation of vector(s) v. Using the
Minkowski reduction the algorithm is relatively slow but safe for any cell.
"""
cell = complete_cell(cell)
rcell, _ = minkowski_reduce(cell, pbc=pbc)
positions = wrap_positions(v, rcell, pbc=pbc, eps=0)
# In a Minkowski-reduced cell we only need to test nearest neighbors,
# or "Voronoi-relevant" vectors. These are a subset of combinations of
# [-1, 0, 1] of the reduced cell vectors.
# Define ranges [-1, 0, 1] for periodic directions and [0] for aperiodic
# directions.
ranges = [np.arange(-1 * p, p + 1) for p in pbc]
# Get Voronoi-relevant vectors.
# Pre-pend (0, 0, 0) to resolve issue #772
hkls = np.array([(0, 0, 0)] + list(itertools.product(*ranges)))
vrvecs = hkls @ rcell
# Map positions into neighbouring cells.
x = positions + vrvecs[:, None]
# Find minimum images
lengths = np.linalg.norm(x, axis=2)
indices = np.argmin(lengths, axis=0)
vmin = x[indices, np.arange(len(positions)), :]
vlen = lengths[indices, np.arange(len(positions))]
return vmin, vlen
def minkowski_reduce(self):
"""Minkowski-reduce this cell, returning new cell and mapping.
See also :func:`ase.geometry.minkowski_reduction.minkowski_reduce`."""
from ase.geometry.minkowski_reduction import minkowski_reduce
cell, op = minkowski_reduce(self, self.any(1))
result = Cell(cell)
return result, op