get_distance_matrix#

Orientation.get_distance_matrix(lazy: bool = False, chunk_size: int = 20, progressbar: bool = True, degrees: bool = False) → ndarray[source]#

Return the symmetry reduced smallest angle of rotation transforming all these orientations to all the other orientations [Johnstone et al., 2020].

Parameters:

lazy: Whether to perform the computation lazily with Dask. Default is False.
chunk_size: Number of orientations per axis to include in each iteration of the computation. Default is 20. Only applies when lazy=True. Increasing this might reduce the computation time at the cost of increased memory use.
progressbar: Whether to show a progressbar during computation if lazy=True. Default is True.
degrees: If True, the angles are returned in degrees. Default is False.

Returns:

angles: Symmetry reduced angles in radians (degrees=False) or degrees (degrees=True).

Notes

Given two orientations \(g_i\) and \(g_j\), the smallest angle is considered as the geodesic distance

\[d(O_i, O_j) = \arccos(2(O_i \cdot O_j)^2 - 1),\]

where \((O_i \cdot O_j)\) is the highest dot product between symmetrically equivalent orientations to \(O_{i,j}\).