def findNextVec(S, parentlatt, which):
''' Applies all symmetry operations, and chooses a new primitive vector that is
most orthogonal to the other(s)'''
eps = 1.0e-6
found = False
newvec = array([0., 0., 0.])
rotvecs = zeros((3, parentlatt.nops), dtype=np_float)
dotvecs = zeros((parentlatt.nops), dtype=np_float)
dotvecs0 = zeros((parentlatt.nops), dtype=np_float)
for iop in range(parentlatt.nops):
rotvecs[:, iop] = transpose(
dot(parentlatt.symops[:, :, iop],
S[:, which - 1])) # all 1-d arrays are horizontal
dotvecs[iop] = cosvecs(rotvecs[:, iop], S[:, which - 1])
if norm(abs(dotvecs) - 1) > eps: # We have at least one independent vector
if which == 1: #Take the one that is most perpendicular to the earlier one
found = True
op2 = argmin(abs(dotvecs))
newvec = rotvecs[:, op2]
elif which == 2: # Third vector needs to be independent of first S vector, too. Use the first vector that is ind. of both
for iop in range(parentlatt.nops):
if isindependent(rotvecs[:, iop], S[:, 0]) and isindependent(
rotvecs[:, iop], S[:, 1]):
found = True
newvec = rotvecs[:, iop]
break
return [found, newvec]
def eigenvecfind(S, parentlatt):
'''Find eigenvectors of symmetry operations (in cartesian basis). A single eigenvector of eigenvalue 1
signifies a rotation operator. This returns a cartesian vector that corresponds to a rotation axis that is not in
the plane of the first two vectors of S'''
# print 'S after array convert'; print S
eps = 1.0e-6
for iop in range(parentlatt.nops): #loop for printing only
evals, evecs = eig(parentlatt.symops[:, :, iop])
for iop in range(parentlatt.nops):
evals, evecs = eig(parentlatt.symops[:, :, iop])
nOne = 0
for i, eval in enumerate(evals):
if abs(eval - 1) < eps:
nOne += 1
indexOne = i
if nOne == 1:
axis = evecs[indexOne]
unitaxis = axis / norm(axis) #unit vector
if abs(cosvecs(cross(S[:, 0], S[:, 1]), axis)) > eps:
#print'found independent third vector'
return unitaxis
def eigenvecfind(S,parentlatt):
'''Find eigenvectors of symmetry operations (in cartesian basis). A single eigenvector of eigenvalue 1
signifies a rotation operator. This returns a cartesian vector that corresponds to a rotation axis that is not in
the plane of the first two vectors of S'''
# print 'S after array convert'; print S
eps = 1.0e-6
for iop in range(parentlatt.nops): #loop for printing only
evals,evecs = eig(parentlatt.symops[:,:,iop])
for iop in range(parentlatt.nops):
evals,evecs = eig(parentlatt.symops[:,:,iop])
nOne = 0
for i, eval in enumerate(evals):
if abs(eval - 1) < eps:
nOne += 1
indexOne = i
if nOne == 1:
axis = evecs[indexOne]
unitaxis = axis/norm(axis) #unit vector
if abs(cosvecs(cross(S[:,0],S[:,1]),axis))>eps:
#print'found independent third vector'
return unitaxis
def eigenvecfind(S,parentlatt):
'''Find eigenvectors of symmetry operations (in cartesian basis). A single eigenvector of eigenvalue 1
signifies a rotation operator. This returns a cartesian vector that corresponds to a rotation axis that is not in
the plane of the first two vectors of S'''
# print 'S after array convert'; print S
eps = 1.0e-6
for iop in range(parentlatt.nops): #loop for printing only
evals,evecs = eig(parentlatt.symops[:,:,iop])
# print; print iop;
# print 'symop R'; print parentlatt.symops[:,:,iop]
# print 'symop m'; print dot(dot(inv(parentlatt.vecs[:,:]),parentlatt.symops[:,:,iop]),parentlatt.vecs[:,:])
# print 'det(m)', det( dot(dot(inv(parentlatt.vecs[:,:]),parentlatt.symops[:,:,iop]),parentlatt.vecs[:,:]) )
# print 'eigenvalues',evals
# print 'eigenvectors'; print evecs #loop for printing only
for iop in range(parentlatt.nops):
evals,evecs = eig(parentlatt.symops[:,:,iop])
nOne = 0
for i, eval in enumerate(evals):
if abs(eval - 1) < eps:
nOne += 1
indexOne = i
# print 'indexOne',indexOne
if nOne == 1:
# print; print iop;print 'eigenvalues',evals
# print 'eigenvectors'; print evecs
axis = evecs[indexOne]
unitaxis = axis/norm(axis) #unit vector
#print "S";print S
#print 'axis', axis
#test to see if it's independent of the first two axes
#print 'cos angle between (cross(S[:,0],S[:,1]) and axis)', cosvecs(cross(S[:,0],S[:,1]),axis)
# print 'cross(S[:,0],S[:,1]),axis', cross(S[:,0],S[:,1]),axis
if abs(cosvecs(cross(S[:,0],S[:,1]),axis))>eps:
#print'found independent third vector'
return unitaxis
def eigenvecfind(S, parentlatt):
'''Find eigenvectors of symmetry operations (in cartesian basis). A single eigenvector of eigenvalue 1
signifies a rotation operator. This returns a cartesian vector that corresponds to a rotation axis that is not in
the plane of the first two vectors of S'''
# print 'S after array convert'; print S
eps = 1.0e-6
for iop in range(parentlatt.nops): #loop for printing only
evals, evecs = eig(parentlatt.symops[:, :, iop])
# print; print iop;
# print 'symop R'; print parentlatt.symops[:,:,iop]
# print 'symop m'; print dot(dot(inv(parentlatt.vecs[:,:]),parentlatt.symops[:,:,iop]),parentlatt.vecs[:,:])
# print 'det(m)', det( dot(dot(inv(parentlatt.vecs[:,:]),parentlatt.symops[:,:,iop]),parentlatt.vecs[:,:]) )
# print 'eigenvalues',evals
# print 'eigenvectors'; print evecs #loop for printing only
for iop in range(parentlatt.nops):
evals, evecs = eig(parentlatt.symops[:, :, iop])
nOne = 0
for i, eval in enumerate(evals):
if abs(eval - 1) < eps:
nOne += 1
indexOne = i
# print 'indexOne',indexOne
if nOne == 1:
# print; print iop;print 'eigenvalues',evals
# print 'eigenvectors'; print evecs
axis = evecs[indexOne]
unitaxis = axis / norm(axis) #unit vector
#print "S";print S
#print 'axis', axis
#test to see if it's independent of the first two axes
#print 'cos angle between (cross(S[:,0],S[:,1]) and axis)', cosvecs(cross(S[:,0],S[:,1]),axis)
# print 'cross(S[:,0],S[:,1]),axis', cross(S[:,0],S[:,1]),axis
if abs(cosvecs(cross(S[:, 0], S[:, 1]), axis)) > eps:
#print'found independent third vector'
return unitaxis
def findNextVec(S,parentlatt,which):
''' Applies all symmetry operations, and chooses a new primitive vector that is
most orthogonal to the other(s)'''
eps = 1.0e-6
found = False
newvec = array([0.,0.,0.])
rotvecs = zeros((3,parentlatt.nops),dtype=np_float)
dotvecs = zeros((parentlatt.nops),dtype=np_float)
dotvecs0 = zeros((parentlatt.nops),dtype=np_float)
for iop in range(parentlatt.nops):
rotvecs[:,iop] = transpose(dot(parentlatt.symops[:,:,iop],S[:,which-1])) # all 1-d arrays are horizontal
dotvecs[iop] = cosvecs(rotvecs[:,iop],S[:,which-1])
if norm(abs(dotvecs)-1)>eps:# We have at least one independent vector
if which == 1: #Take the one that is most perpendicular to the earlier one
found = True
op2 = argmin(abs(dotvecs))
newvec = rotvecs[:,op2]
elif which == 2: # Third vector needs to be independent of first S vector, too. Use the first vector that is ind. of both
for iop in range(parentlatt.nops):
if isindependent(rotvecs[:,iop],S[:,0]) and isindependent(rotvecs[:,iop],S[:,1]):
found = True
newvec = rotvecs[:,iop]
break
return [found, newvec]
def matchDirection(vec,list):
'''if vec parallel or antiparallel to any vector in the list, don't include it'''
for vec2 in list:
if areEqual(abs(cosvecs(vec,vec2)),1.0):
return True
return False
def matchDirection(vec, list):
'''if vec parallel or antiparallel to any vector in the list, don't include it'''
for vec2 in list:
if areEqual(abs(cosvecs(vec, vec2)), 1.0):
return True
return False