# Source code for ase.geometry.distance

import numpy as np

[docs]def distance(s1, s2, permute=True):
"""Get the distance between two structures s1 and s2.

The distance is defined by the Frobenius norm of
the spatial distance between all coordinates (see
numpy.linalg.norm for the definition).

permute: minimise the distance by 'permuting' same elements
"""

s1 = s1.copy()
s2 = s2.copy()
for s in [s1, s2]:
s.translate(-s.get_center_of_mass())
s2pos = 1. * s2.get_positions()

def align(struct, xaxis='x', yaxis='y'):
"""Align moments of inertia with the coordinate system."""
Is, Vs = struct.get_moments_of_inertia(True)
IV = list(zip(Is, Vs))
IV.sort(key=lambda x: x[0])
struct.rotate(IV[0][1], xaxis)

Is, Vs = struct.get_moments_of_inertia(True)
IV = list(zip(Is, Vs))
IV.sort(key=lambda x: x[0])
struct.rotate(IV[1][1], yaxis)

align(s1)

def dd(s1, s2, permute):
if permute:
s2 = s2.copy()
dist = 0
for a in s1:
imin = None
dmin = np.Inf
for i, b in enumerate(s2):
if a.symbol == b.symbol:
d = np.sum((a.position - b.position)**2)
if d < dmin:
dmin = d
imin = i
dist += dmin
s2.pop(imin)
return np.sqrt(dist)
else:
return np.linalg.norm(s1.get_positions() - s2.get_positions())

dists = []
# principles
for x, y in zip(['x', '-x', 'x', '-x'], ['y', 'y', '-y', '-y']):
s2.set_positions(s2pos)
align(s2, x, y)
dists.append(dd(s1, s2, permute))

return min(dists)