def __call__(self, x1, x2):
if self.align_com:
x1 = CoMToOrigin(x1).reshape([-1, 3])
x2 = CoMToOrigin(x2).reshape([-1, 3])
# calculate distance of all atoms
R1 = np.sqrt(np.sum(x1 * x1, axis=1))
R2 = np.sqrt(np.sum(x2 * x2, axis=1))
# at least 2 atoms are needed
# get atom most outer atom
# get 1. reference atom in configuration 1
# use the atom with biggest distance to com
idx_sorted = R1.argsort()
idx1_1 = idx_sorted[-1]
# find second atom which is not in a line
for idx1_2 in reversed(idx_sorted[0:-1]):
# stop if angle is larger than threshold
cos_theta1 = np.dot(x1[idx1_1], x1[idx1_2]) / (np.linalg.norm(x1[idx1_1]) * np.linalg.norm(x1[idx1_2]))
if cos_theta1 < 0.9:
break
# do a very quick check if most distant atom from
# center are within accuracy
if np.abs(R1[idx1_1] - R2.max()) > self.accuracy:
return False
# get indices of atoms in shell of thickness 2*accuracy
candidates1 = np.arange(len(R2))[(R2 > R1[idx1_1] - self.accuracy) * (R2 < R1[idx1_1] + self.accuracy)]
candidates2 = np.arange(len(R2))[(R2 > R1[idx1_2] - self.accuracy) * (R2 < R1[idx1_2] + self.accuracy)]
# now loop over all combinations
for idx2_1 in candidates1:
for idx2_2 in candidates2:
if idx2_1 == idx2_2:
continue
# we can immediately trash the match if angle does not match
cos_theta2 = np.dot(x2[idx2_1], x2[idx2_2]) / (np.linalg.norm(x2[idx2_1]) * np.linalg.norm(x2[idx2_2]))
if np.abs(cos_theta2 - cos_theta2) > 0.5:
continue
# get rotation for current atom match candidates
rot = rmsfit.findrotation_kabsch(x1[[idx1_1, idx1_2]], x2[[idx2_1, idx2_2]], False)
# pass on the match for a closer check
if self.check_match(x1, x2, rot, 1.0):
return True
if self.check_inversion:
# get rotation for current atom match candidates
rot = rmsfit.findrotation_kabsch(x1[[idx1_1, idx1_2]], -x2[[idx2_1, idx2_2]], False)
# pass on the match for a closer check
if self.check_match(x1, -x2, rot, -1.0):
return True
return False
def check_match(self, x1, x2, rot, inverse):
""" Make a more detailed comparison if the 2 structures match
Parameters
----------
x1: np.array
coordinates of structure 1
x2: np.array
coordinates of structure 2
rot: np.array, 3x3
guessed rotation based on reference atoms
inverse: double
-1.0 if do match for inverted coordinates, 1.0 otherwise
returns: boolean
True or False for match
"""
# apply the rotation
x1_trial = np.dot(rot, x1.transpose()).transpose()
# make a copy since findBestPermutation will mess up order
x2_trial = x2.copy()
# get the best permutation
dist, x1n, x2n = findBestPermutation(x1_trial.flatten(), x2_trial.flatten())
x1n = x1n.reshape([-1, 3])
x2n = x2n.reshape([-1, 3])
# x1n = x1_trial
# x2n = x2_trial
# now find best rotational alignment, this is more reliable than just
# aligning the 2 reference atoms
rot2 = rmsfit.findrotation_kabsch(x1n, x2n)
x1n = np.dot(rot2, x1n.transpose()).transpose()
# use the maximum distance, not rms as cutoff criterion
max_dist = np.sqrt(np.sum((x1n - x2n) * (x1n - x2n), axis=1)).max()
if max_dist < self.accuracy:
self.best_rotation = np.dot(rot2, rot)
return True
return False
