def minDist(X1, X2):
"""
Minimize the distance between two clusters. The following symmetries
will be accounted for.
Translational symmetry
Global rotational symmetry
"""
#alignCoM(X1, X2)
X1 = CoMToOrigin(X1)
X2 = CoMToOrigin(X2)
#align rotation degrees of freedom
dist, X2 = alignRotation(X1, X2)
return dist, X1, X2
def minPermDistStochastic(X1, X2, niter=100, permlist=None, verbose=False, accuracy=0.01,
check_inversion=True, use_quench=False):
"""
Minimize the distance between two clusters.
Parameters
----------
X1, X2 :
the structures to align. X2 will be aligned with X1, both
the center of masses will be shifted to the origin
niter : int
the number of basinhopping iterations to perform
permlist : a list of lists of atoms
A list of lists of atoms which are interchangable.
e.g. if all the atoms are interchangable
permlist = [range(natoms)]
For a 50/50 binary mixture,
permlist = [range(1,natoms/2), range(natoms/2,natoms)]
verbose :
whether to print status information
accuracy :
accuracy for determining if the structures are identical
check_inversion :
if true, account for point inversion symmetry
use_quench :
for each step of the iteration, minimize a permutationally invariant
distance metric. This slows the algorithm, but can potentially make
it more accurate.
Notes
-----
The following symmetries will be accounted for::
1. Translational symmetry
#. Global rotational symmetry
#. Permutational symmetry
#. Point inversion symmetry
The algorithm here to find the best distance is
for i in range(niter):
random_rotation(coords)
findBestPermutation(coords)
alignRotation(coords)
"""
natoms = len(X1) / 3
if permlist is None:
permlist = [range(natoms)]
X1init = X1
X2init = X2
X1 = np.copy(X1)
X2 = np.copy(X2)
#first check for exact match
exactmatch = ExactMatchCluster(accuracy=accuracy, permlist=permlist)
if exactmatch(X1, X2):
#this is kind of cheating, I would prefer to return
#X2 in best alignment and the actual (small) distance
return 0.0, X1, X1.copy()
#bring center of mass of x1 and x2 to the origin
#save the center of mass of X1 for later
X1com = X1.reshape([-1,3]).sum(0) / natoms
X1 = CoMToOrigin(X1)
X2 = CoMToOrigin(X2)
#print "X2.shape", X2.shape
#find the best rotation stochastically
X20 = X2.copy()
distbest, mxbest = _optimizePermRot(X1, X2, niter, permlist, verbose=verbose, use_quench=use_quench)
use_inversion = False
if check_inversion:
X20i = -X20.copy()
X2 = X20i.copy()
distbest1, mxbest1 = _optimizePermRot(X1, X2, niter, permlist, verbose=verbose, use_quench=use_quench)
if distbest1 < distbest:
if verbose:
print "using inversion in minpermdist"
use_inversion = True
distbest = distbest1
mxbest = mxbest1
#now we know the best rotation
if use_inversion: X20 = X20i
X2 = applyRotation(mxbest, X20)
dist, X1, X2 = findBestPermutation(X1, X2, permlist)
dist, X2 = alignRotation(X1, X2)
if dist > distbest+0.001:
print "ERROR: minPermDistRanRot: dist is different from distbest %f %f" % (dist, distbest)
if verbose:
print "finaldist", dist, "distmin", distbest
#add back in the center of mass of X1
X1 = X1.reshape([-1,3])
X2 = X2.reshape([-1,3])
X1 += X1com
X2 += X1com
X1 = X1.reshape(-1)
X2 = X2.reshape(-1)
return dist, X1, X2