def _optimizePermRot(X1, X2, niter, permlist, verbose=False, use_quench=True):
if use_quench:
pot = MinPermDistPotential(X1, X2.copy(), permlist=permlist)
distbest = getDistxyz(X1, X2)
mxbest = np.identity(3)
X20 = X2.copy()
for i in range(niter):
#get and apply a random rotation
aa = random_aa()
if not use_quench:
mx = aa2mx(aa)
mxtot = mx
#print "X2.shape", X2.shape
else:
#optimize the rotation using a permutationally invariand distance metric
ret = defaults.quenchRoutine(aa, pot.getEnergyGradient, tol=0.01)
aa1 = ret[0]
mx1 = aa2mx(aa1)
mxtot = mx1
X2 = applyRotation(mxtot, X20)
#optimize the permutations
dist, X1, X2 = findBestPermutation(X1, X2, permlist)
if verbose:
print "dist", dist, "distbest", distbest
#print "X2.shape", X2.shape
#optimize the rotation
dist, Q2 = getAlignRotation(X1, X2)
# print "dist", dist, "Q2", Q2
mx2 = q2mx(Q2)
mxtot = np.dot(mx2, mxtot)
if dist < distbest:
distbest = dist
mxbest = mxtot
return distbest, mxbest
def minPermDistLong(X1, X2, max_permutations = 10000):
"""
Minimize the distance between two clusters. The following symmetries will be accounted for
Translational symmetry
Global rotational symmetry
Permutational symmetry
This routine is deterministic, but ludicrously slow. Use the minPermDistStochastic instead
"""
print "This routine is deterministic, but ludicrously slow. Use the minPermDistStochastic instead"
X2in = np.copy(X2)
X2min = np.copy(X2)
dmin = np.linalg.norm( X2-X1 )
nsites = len(X1) / 3
#this is a really dumb way to do this
nperm = math.factorial(nsites)
print nperm, "permutations in total. Stopping at ", max_permutations
count = 0
for perm in itertools.permutations(range(nsites)):
#print perm
X2 = permuteArray( X2in, perm)
dist, X1, X2 = minDist(X1, X2)
if dist < dmin:
dmin = dist
X2min = np.copy(X2)
#print dist, np.linalg.norm(X1-X2)
if dmin < 1e-6:
print "found exact match (to accuracy 1e-6)"
break
count += 1
if count % 1000 == 0:
print "finished", count, "permutations out of", min(nperm, max_permutations), " mindist is", dmin, "last try was", dist
if count == max_permutations:
print "reached maximum number of perterbations (", max_permutations, ")."
use_hungarian = True
if use_hungarian:
print "will now fix alignment and calculate the best permutation using the Hungarian algorithm"
#print "dist before hungarian algorithm", dmin
ret = findBestPermutation( X1, X2min )
if ret != None:
dmin, X1, X2min = findBestPermutation( X1, X2min )
#print "dist after hungarian algorithm", dmin
break
return dmin, X1, X2min
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
