[Spglib-users] Clarification of Crystallographic Choice and Rotation

[Daniel M. <dan...@gm...>]

Hi Spg Mailing LIst,

I"m a bit confused with regard to the Transformation Matrix. I"m following
the example given in the documentation:
https://atztogo.github.io/spglib/definition.html#crystallographic-choice-and-rigid-rotation

The original lattice is:

lattice = [[7.17851431, 0, 0],  # a
           [0, 3.99943947, 0],  # b
           [0, 0, 8.57154746]]  # c


The modified lattice is constructed by swapping 'a' and 'b':

lattice = [[8.57154746, 0, 0],  # a
           [0, 3.99943947, 0],  # b
           [0, 0, 7.17851431]]  # c


My confusion is with regards of the 'transformation matrix':

Transformation matrix:
   0  0  1
   0  1  0
  -1  0  0


According to Equation 6
<https://atztogo.github.io/spglib/definition.html#equation-transformation-matrix>
I
should be able to recover the original matrix via:

(a b c) = (as bs cs) P

However, in my case the Transformation Matrix above, does not restore the
original lattice, rather it generates:

matrix([[ 0. , 0. , 8.57154746],
             [ 0. , 3.99943947, 0. ],
             [-7.17851431, 0. , 0. ]])

This is similar, but not the exact same as my original lattice. I'm
guessing the two are equivalent. In my use case I want to recover the exact
original lattice, is this possible, perhaps with a final step that puts the
lattice in a 'standard' form?

Best,

Daniel