Re: [Spglib-users] symmetrizing positions/cell vectors without altering cell?

[Noam B. <noa...@nr...>]

> On Dec 16, 2017, at 2:08 AM, Atsushi Togo <atz...@gm...> wrote:
> 
> You can obtain more information by spg_get_dataset:
> https://atztogo.github.io/spglib/api.html#spg-get-dataset-and-spg-get-dataset-with-hall-number
> 

Thanks - I now see transformation matrix, which is very helpful.  I’m slightly confused by the output I get, however.  

I tried a simple example, identifying a rotated FCC lattice.  Lattice vectors start out as (1,1,0) etc, and are rotate by 45 deg around \hat{z}.
import ase, ase.io, sys, spglib, numpy as np

at = ase.Atoms(cell=[[0,1.41421356237309504880,0],
     [.70710678118654752440,.70710678118654752440,1],
     [-.70710678118654752440,.70710678118654752440,1]], numbers=[32])
ase.io.write(sys.stdout, at, format="extxyz")

symprec=0.1
dataset = spglib.get_symmetry_dataset((at.get_cell(), at.get_positions(), at.get_atomic_numbers()), symprec=symprec)
sys.stderr.write("loose initial symmetry group number {}, international (Hermann-Mauguin) {} Hall {} prec {}\n".format(dataset["number"],dataset["international"],dataset["hall"],symprec))
print "std lattice\n", dataset['std_lattice']
print "orig cell\n", at.get_cell()
print "supposed to be orig cell\n", np.dot(dataset['std_lattice'].T, dataset['transformation_matrix']).T
print "supposed to be standardized cell\n", np.dot(at.get_cell().T, np.linalg.inv(dataset['transformation_matrix'])).T

I expected the second to last line to print out something identical to the original cell, according to the documentation at
	https://atztogo.github.io/spglib/api.html#api-origin-shift-and-transformation <https://atztogo.github.io/spglib/api.html#api-origin-shift-and-transformation>
which says that "(a b c) = (as bs cs) P” (I’m using 1.9.9).  However, the output is actually
1
Lattice="0.0 1.41421356237 0.0 0.707106781187 0.707106781187 1.0 -0.707106781187 0.707106781187 1.0" Properties=species:S:1:pos:R:3:Z:I:1 pbc="F F F"
Ge       0.00000000       0.00000000       0.00000000       32
loose initial symmetry group number 225, international (Hermann-Mauguin) Fm-3m Hall -F 4 2 3 prec 0.1
std lattice
[[ 2.  0.  0.]
 [ 0.  2.  0.]
 [ 0.  0.  2.]]
orig cell
[[ 0.          1.41421356  0.        ]
 [ 0.70710678  0.70710678  1.        ]
 [-0.70710678  0.70710678  1.        ]]
supposed to be orig cell
[[  0.00000000e+00   1.00000000e+00  -1.00000000e+00]
 [ -1.00000000e+00   1.00000000e+00   3.92523115e-17]
 [ -1.00000000e+00  -1.50274614e-16  -1.00000000e+00]]
supposed to be standardized cell
[[  0.00000000e+00  -2.22044605e-16  -2.00000000e+00]
 [  1.41421356e+00   1.41421356e+00   0.00000000e+00]
 [  1.41421356e+00  -1.41421356e+00   0.00000000e+00]]
so the “supposed to be orig cell” line prints out something that is a _rotated_ version of the original cell.  That’s actually fine in practice, but it’s not what I was expecting.  Am I just misunderstanding the documentation, or am I actually doing something wrong?

								thanks,
								Noam