"""
Module containing tensor related functions
"""
import numpy as np
_paths = dict()
[docs]def rotation_tensor_as_matrix(R, order):
einsum_input = []
for i in range(order):
einsum_input.append(R)
einsum_input.append([i, order + i])
R_tensor = np.einsum(*einsum_input)
R_matrix = R_tensor.reshape((3**order, 3**order))
return R_matrix
[docs]def rotate_tensor_precalc(T, R):
order = len(T.shape)
return np.dot(T.ravel(), R).reshape((3,) * order)
[docs]def rotate_tensor(T, R, path=None):
"""Equivalent to T_abc... = T_ijk... R_ia R_jb R_kc ... """
order = len(T.shape)
if order not in _paths:
path = ['einsum_path', (0, 1)]
for i in range(order - 1, 0, -1):
path.append((0, i))
_paths[order] = path
einsum_input = [T, list(range(order))]
for i in range(order):
einsum_input.append(R)
einsum_input.append([i, order + i])
return np.einsum(*einsum_input, optimize=_paths[order])
[docs]def rotation_to_cart_coord(R, cell):
"""Return the rotation matrix in cart coord given a cell metric """
return np.dot(np.dot(cell.T, R), np.linalg.inv(cell.T))