Confusion about transformation matrix

[chengyangXu]

Dear Qi,
Your code is quite helpful, yet I have a question about transfomation matrix in the unfold class. You have written B = np.dot(np.linalg.inv(M).T, b) , but I found b=np.dot(M,B) i.e. B = np.dot(np.linalg.inv(M), b) in Phys. Rev. B 85, 085201 (2012), which lead differences of K sampling in supercell brillioun zone between two cases. Could you tell me why you choose transformation matrix M.T?

Thank you sincerely,
Xu

[QijingZheng]

Please refer to the docstring of the unfold class.

        M is the transformation matrix between supercell and primitive cell: 
         
            M = np.dot(A, np.linalg.inv(a))     
         
        In real space, the basis vectors of Supercell (A) and those of the
        primitive cell (a) satisfy:
         
            A = np.dot(M, a);      a = np.dot(np.linalg.inv(M), A)
         
        Whereas in reciprocal space
         
            b = np.dot(M.T, B);    B = np.dot(np.linalg.inv(M).T, b)    

[chengyangXu]

Thank you for your reply!

[Gargee-123]

Dear Prof. Qijing Zheng,

I have calculated the transformation matrix definitions and it matches with your definition that you have mentioned. I have another question,
In those above definitions, A and a matrix is represented as column vectors . Is it correct ?

I mean to say, A = M.a
where,
A =
[Ax Bx Cx,
Ay By Cy,
Az Bz Cz]
and
a =
[ax bx cx,
ay by cy,
az bz cz]

Please let me know whether this is correct.

Best regards
Gargee