def tensor_constraint(dim, rank, rots, mappings=None, other_constraits=None):
"""
rank: of tensor
rots: list of rotation matrix (Cartesian)
mappings: mapping function (0..N-1 to 0..N-1 one-to-one)
"""
if rank <= 0:
null = scipy.sparse.identity(1)
else:
dimtensor = dim**rank
pi = [list(range(rank))] * len(rots) if mappings is None else mappings
assert len(pi) == len(rots), ValueError(
'Number of matrices and mappings %d != %d' % (len(rots), len(pi)))
Bmats = [
fct_trans_c(rank, dim, rots[i], pi[i]) -
scipy.sparse.identity(dimtensor) for i in range(len(rots))
]
if other_constraits is not None:
Bmats.extend([m for m in other_constraits if m.shape[0] > 0])
if len(Bmats) > 0:
Bmat = scipy.sparse.vstack(Bmats)
null = mychop(get_nullspace(Bmat), 1e-12)
else:
null = scipy.sparse.identity(dimtensor)
return null
def symmetrize_site_tensors(self, tlist):
"""
symmetrize tensors on atoms, one orbit at a time
:param tlist:
:return:
"""
tensors=np.array(tlist)
rank = np.array(tensors[0]).ndim
dim = tensors[0].shape[0]
tensors_s = np.zeros_like(tensors)
for i,orb in enumerate(self.orbits):
cmat= tensor_constraint(3, rank, [self.spacegroup[ig].rot for ig,pi in orb.isotropy if ig>0])
# print('debug sublatice', i , orb.pointgroup_symbol[0], self.name_orb[i], 'shape', cmat.shape)
# print('debug sublat', i, 'cmat', cmat, 'orbit', orb, 'isotropy', orb.isotropy)
tr_mat = scipy.sparse.vstack([fct_trans_c(rank, dim, self.spacegroup[orb.clusters_ig[ic]].rot,
np.arange(rank, dtype=int)).dot(cmat.T) for ic in range(self.orbits[i].multiplicity)])
t_s = get_symmetrized_lsq(tr_mat, tensors[self.l_list_of_orb[i]].reshape((-1)))
tensors_s[self.l_list_of_orb[i]] = t_s.reshape(tensors[self.l_list_of_orb[i]].shape)
return tensors_s