def get_reciprocal_metric_tensor(lattice: Lattice) -> np.ndarray:
"""Reciprocal metric tensor as defined in EMsoft.
Parameters
----------
lattice
Crystal structure lattice.
Returns
-------
np.ndarray
"""
a, b, c = lattice.abcABG()[:3]
ca, cb, cg = lattice.ca, lattice.cb, lattice.cg
sa, sb, sg = lattice.sa, lattice.sb, lattice.sg
terms_12_21 = a * b * (c ** 2) * (ca * cb - cg)
terms_13_31 = a * (b ** 2) * c * (cg * ca - cb)
terms_23_32 = (a ** 2) * b * c * (cb * cg - ca)
return np.array(
[
[(b * c * sa) ** 2, terms_12_21, terms_13_31],
[terms_12_21, (a * c * sb) ** 2, terms_23_32],
[terms_13_31, terms_23_32, (a * b * sg) ** 2],
]
) / np.linalg.det(lattice.metrics)
def get_direct_structure_matrix(lattice: Lattice) -> np.ndarray:
"""Direct structure matrix as defined in EMsoft.
Parameters
----------
lattice
Crystal structure lattice.
Returns
-------
"""
a, b, c = lattice.abcABG()[:3]
ca, cb, cg = lattice.ca, lattice.cb, lattice.cg
sa, sb, sg = lattice.sa, lattice.sb, lattice.sg
return np.array([
[a, b * cg, c * cb],
[0, b * sg, -c * (cb * cg - ca) / sg],
[0, 0, lattice.volume / (a * b * sg)],
])