UBI_to_mt

anri.crystal.UBI_to_mt(UBI)

Convert from (U.B)^-1 matrix to metric tensor.

Parameters:

UBI (Array) – [3,3] (U.B)^-1 matrix

Returns:

jax.Array – [3,3] Metric tensor

Notes

\[\begin{split} \begin{aligned} \tens{G_{ij}} &= \left(\matr{UB}\right)^{-1} \cdot \left(\left(\matr{UB}\right)^{-1}\right)^T \\ \tens{G_{ij}} &= \matr{B}^{-1}\matr{U}^{-1} \cdot \left(\matr{B}^{-1}\matr{U}^{-1}\right)^T \\ \tens{G_{ij}} &= \matr{B}^{-1}\matr{U}^{-1} \cdot \left(\matr{U}^{-1}\right)^T \left(\matr{B}^{-1}\right)^T \\ \tens{G_{ij}} &= \matr{B}^{-1}\matr{U}^{-1} \cdot \matr{U} \left(\matr{B}^{-1}\right)^T \\ \tens{G_{ij}} &= \matr{B}^{-1} \cdot \left(\matr{B}^{-1}\right)^T \\ \tens{G_{ij}} &= \matr{B}^{-1} \cdot \left(\matr{B}^T\right)^{-1} \\ \tens{G_{ij}} &= \left(\matr{B}^T \cdot \matr{B}\right)^{-1} \\ \tens{G_{ij}} &= \left(\tens{G^{ij}}\right)^{-1} \\ \end{aligned} \end{split}\]