This is a (P)ure python implementation of algorithm to determin Niggli cell. The library supports both 2D and 3D niggli transformations.
Rows of list or rows of numpy.ndarray correspond basis vectors, a, b, c or a, b They are input to niggli_reduce as a row with three colum matrices, same as most DFT softwares' lattice inputs.
In the implementation details, since the lattice is represented by a row vector, the transformation operation on the lattice is left-multiplied, such as:
import numpy as np
# TMatrix is the transform matrix
new_Lattice = np.matmul(TMatrix, old_Lattice)For details of the algorithm, see [[Niggli for 2d and 3d]](http://)
$ pip install pnigglifrom pniggli import niggli_reduce, niggli_check
lattice_3D = [4.912, 0.000, 0.000,
-2.456, 4.254, 0.000,
0.000, 0.000, 0.000]
niggli_lattice = niggli_reduce(lattice_3D)
print(niggli_lattice)
# Out:
# array([[ 4.912, 0. , 0. ],
# [-2.456, 4.254, 0. ],
# [ 0. , 0. , 16. ]])
print(niggli_check(niggli_lattice)) # True
lattice_2D = [2.4560000896, 0.0000000000,
11.0520002567, 2.1269502021]
niggli_lattice = niggli_reduce(lattice_2D)
print(niggli_lattice)
# Out[6]:
# array([[-1.2279999 , -2.1269502 ],
# [-1.22800019, 2.1269502 ]])The 2D example is a triangle motif.
- 2D and 3D niggli reduce support
- niggli_check for 3D lattice
- 3D niggli reduce support
- niggli_check for 3D lattice