def alignRotation(XA, XB):
"""
Align structure XB with XA
Align structure XB to be as similar as possible to structure XA.
To be precise, rotate XB, so as to minimize the distance |XA - XB|.
Rotations will be done around the origin, not the center of mass
"""
nsites = len(XA) / 3
dist, Q2 = getAlignRotation(XA, XB)
###################################################################
# Q2 contains the quaternion which rotates XB to best align with X1.
# rotate XB according to Q2
###################################################################
rot_mx = rot.q2mx(Q2)
#print rot_mx
for j in range(nsites):
i = 3 * j
XB[i:i + 3] = np.dot(rot_mx, XB[i:i + 3])
dist = np.linalg.norm(XA - XB) #more precise than what it returned
return dist, XB
def alignRotation(XA, XB):
"""
Align structure XB with XA
Align structure XB to be as similar as possible to structure XA.
To be precise, rotate XB, so as to minimize the distance |XA - XB|.
Rotations will be done around the origin, not the center of mass
"""
nsites = len(XA)/3
dist, Q2 = getAlignRotation(XA, XB)
###################################################################
# Q2 contains the quaternion which rotates XB to best align with X1.
# rotate XB according to Q2
###################################################################
rot_mx = rot.q2mx( Q2 )
#print rot_mx
for j in range(nsites):
i = 3*j
XB[i:i+3] = np.dot( rot_mx, XB[i:i+3] )
dist = np.linalg.norm(XA - XB) #more precise than what it returned
return dist, XB
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 _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
# 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
if __name__ == "__main__":
natoms = 35
from pygmin.utils import rotations
for i in xrange(100):
xx1 = np.random.random(3 * natoms) * 5
xx1 = xx1.reshape([-1, 3])
mx = rotations.q2mx(rotations.random_q())
xx2 = np.dot(mx, xx1.transpose()).transpose()
xx2 += 2.0 * (np.random.random(xx2.shape) - 0.5) * 0.003
# xx2 = xx1.copy()
tmp = xx2[1].copy()
xx2[1] = xx2[4]
xx2[4] = tmp
# dist, x1n, x2n = findBestPermutation(xx1.flatten(), xx2.flatten())
# print dist
print i, ExactMatchCluster()(xx1, xx2)
def findrotation_kearsley(coords1, coords2, align_com=True):
"""
Return the quaternion which aligns XB with XA
Return the matrix which
aligns structure XB to be as similar as possible to structure XA.
To be precise, rotate XB, so as to minimize the distance |XA - XB|.
Rotations will be done around the origin, not the center of mass
Rotational alignment follows the prescription of
Kearsley, Acta Cryst. A, 45, 208-210, 1989
http://dx.doi.org/10.1107/S0108767388010128
"""
if(coords1.size != coords2.size):
raise BaseException("dimension of arrays does not match")
# reshape the arrays
x1 = coords1.flatten()
x2 = coords2.flatten()
x1 = x1.reshape([-1,3])
x2 = x2.reshape([-1,3])
#
# # determine number of atoms
natoms = x1.shape[0]
# set both com to zero
if(align_com):
com1 = np.sum(x1,axis=0) / float(natoms)
com2 = np.sum(x2,axis=0) / float(natoms)
x1 = x1.copy() - com1
x2 = x2.copy() - com2
x1 = x1.flatten()
x2 = x2.flatten()
# TODO: this is very dirty!
#########################################
#Create matrix QMAT
#########################################
QMAT = np.zeros([4,4], np.float64)
for J1 in xrange(natoms):
J2 = 3*(J1) -1
XM = x1[J2+1] - x2[J2+1]
YM = x1[J2+2] - x2[J2+2]
ZM = x1[J2+3] - x2[J2+3]
XP = x1[J2+1] + x2[J2+1]
YP = x1[J2+2] + x2[J2+2]
ZP = x1[J2+3] + x2[J2+3]
QMAT[0,0] = QMAT[0,0] + XM**2 + YM**2 + ZM**2
QMAT[0,1] = QMAT[0,1] - YP*ZM + YM*ZP
QMAT[0,2] = QMAT[0,2] - XM*ZP + XP*ZM
QMAT[0,3] = QMAT[0,3] - XP*YM + XM*YP
QMAT[1,1] = QMAT[1,1] + YP**2 + ZP**2 + XM**2
QMAT[1,2] = QMAT[1,2] + XM*YM - XP*YP
QMAT[1,3] = QMAT[1,3] + XM*ZM - XP*ZP
QMAT[2,2] = QMAT[2,2] + XP**2 + ZP**2 + YM**2
QMAT[2,3] = QMAT[2,3] + YM*ZM - YP*ZP
QMAT[3,3] = QMAT[3,3] + XP**2 + YP**2 + ZM**2
QMAT[1,0] = QMAT[0,1]
QMAT[2,0] = QMAT[0,2]
QMAT[2,1] = QMAT[1,2]
QMAT[3,0] = QMAT[0,3]
QMAT[3,1] = QMAT[1,3]
QMAT[3,2] = QMAT[2,3]
###########################################
"""
Find eigenvalues and eigenvectors of QMAT. The eigenvector corresponding
to the smallest eigenvalue is the quaternion which rotates XB into best
alignment with XA. The smallest eigenvalue is the squared distance between
the resulting structures.
"""
###########################################
(eigs, vecs) = np.linalg.eig(QMAT)
#print "eigenvalues", eigs
imin = np.argmin(eigs)
eigmin = eigs[imin] #the minimum eigenvector
Q2 = vecs[:,imin] #the eigenvector corresponding to the minimum eigenvalue
if eigmin < 0.:
if abs(eigmin) < 1e-6:
eigmin = 0.
else:
print 'minDist> WARNING minimum eigenvalue is ',eigmin,' change to absolute value'
eigmin = -eigmin
dist = np.sqrt(eigmin) #this is the minimized distance between the two structures
#print "dist from eigenvalue", dist
#print "Q2", Q2, "norm", np.linalg.norm(Q2)
#aa = rot.q2aa( Q2)
#print "aa ", aa, "norm", np.linalg.norm(aa)
return dist, rotations.q2mx(Q2)
def findrotation_kearsley(coords1, coords2, align_com=True):
"""
Return the quaternion which aligns XB with XA
Return the matrix which
aligns structure XB to be as similar as possible to structure XA.
To be precise, rotate XB, so as to minimize the distance |XA - XB|.
Rotations will be done around the origin, not the center of mass
Rotational alignment follows the prescription of
Kearsley, Acta Cryst. A, 45, 208-210, 1989
http://dx.doi.org/10.1107/S0108767388010128
"""
if (coords1.size != coords2.size):
raise BaseException("dimension of arrays does not match")
# reshape the arrays
x1 = coords1.flatten()
x2 = coords2.flatten()
x1 = x1.reshape([-1, 3])
x2 = x2.reshape([-1, 3])
#
# # determine number of atoms
natoms = x1.shape[0]
# set both com to zero
if (align_com):
com1 = np.sum(x1, axis=0) / float(natoms)
com2 = np.sum(x2, axis=0) / float(natoms)
x1 = x1.copy() - com1
x2 = x2.copy() - com2
x1 = x1.flatten()
x2 = x2.flatten()
# TODO: this is very dirty!
#########################################
#Create matrix QMAT
#########################################
QMAT = np.zeros([4, 4], np.float64)
for J1 in xrange(natoms):
J2 = 3 * (J1) - 1
XM = x1[J2 + 1] - x2[J2 + 1]
YM = x1[J2 + 2] - x2[J2 + 2]
ZM = x1[J2 + 3] - x2[J2 + 3]
XP = x1[J2 + 1] + x2[J2 + 1]
YP = x1[J2 + 2] + x2[J2 + 2]
ZP = x1[J2 + 3] + x2[J2 + 3]
QMAT[0, 0] = QMAT[0, 0] + XM**2 + YM**2 + ZM**2
QMAT[0, 1] = QMAT[0, 1] - YP * ZM + YM * ZP
QMAT[0, 2] = QMAT[0, 2] - XM * ZP + XP * ZM
QMAT[0, 3] = QMAT[0, 3] - XP * YM + XM * YP
QMAT[1, 1] = QMAT[1, 1] + YP**2 + ZP**2 + XM**2
QMAT[1, 2] = QMAT[1, 2] + XM * YM - XP * YP
QMAT[1, 3] = QMAT[1, 3] + XM * ZM - XP * ZP
QMAT[2, 2] = QMAT[2, 2] + XP**2 + ZP**2 + YM**2
QMAT[2, 3] = QMAT[2, 3] + YM * ZM - YP * ZP
QMAT[3, 3] = QMAT[3, 3] + XP**2 + YP**2 + ZM**2
QMAT[1, 0] = QMAT[0, 1]
QMAT[2, 0] = QMAT[0, 2]
QMAT[2, 1] = QMAT[1, 2]
QMAT[3, 0] = QMAT[0, 3]
QMAT[3, 1] = QMAT[1, 3]
QMAT[3, 2] = QMAT[2, 3]
###########################################
"""
Find eigenvalues and eigenvectors of QMAT. The eigenvector corresponding
to the smallest eigenvalue is the quaternion which rotates XB into best
alignment with XA. The smallest eigenvalue is the squared distance between
the resulting structures.
"""
###########################################
(eigs, vecs) = np.linalg.eig(QMAT)
#print "eigenvalues", eigs
imin = np.argmin(eigs)
eigmin = eigs[imin] #the minimum eigenvector
Q2 = vecs[:,
imin] #the eigenvector corresponding to the minimum eigenvalue
if eigmin < 0.:
if abs(eigmin) < 1e-6:
eigmin = 0.
else:
print 'minDist> WARNING minimum eigenvalue is ', eigmin, ' change to absolute value'
eigmin = -eigmin
dist = np.sqrt(
eigmin) #this is the minimized distance between the two structures
#print "dist from eigenvalue", dist
#print "Q2", Q2, "norm", np.linalg.norm(Q2)
#aa = rot.q2aa( Q2)
#print "aa ", aa, "norm", np.linalg.norm(aa)
return dist, rotations.q2mx(Q2)
imin = np.argmin(eigs)
eigmin = eigs[imin] #the minimum eigenvector
Q2 = vecs[:,
imin] #the eigenvector corresponding to the minimum eigenvalue
if eigmin < 0.:
if abs(eigmin) < 1e-6:
eigmin = 0.
else:
print 'minDist> WARNING minimum eigenvalue is ', eigmin, ' change to absolute value'
eigmin = -eigmin
dist = np.sqrt(
eigmin) #this is the minimized distance between the two structures
#print "dist from eigenvalue", dist
#print "Q2", Q2, "norm", np.linalg.norm(Q2)
#aa = rot.q2aa( Q2)
#print "aa ", aa, "norm", np.linalg.norm(aa)
return dist, rotations.q2mx(Q2)
findrotation = findrotation_kearsley
if __name__ == "__main__":
from pygmin.utils import rotations
x1 = np.random.random(24)
mx = rotations.q2mx(rotations.random_q())
x2 = np.dot(mx, x1.reshape(-1, 3).transpose()).transpose().reshape(-1)
print x2 - x1
print mx - findrotation_kabsch(x1, x2)
