orix.measure.pole_density_function(*args: Union[ndarray, Vector3d], resolution: float = 1, sigma: float = 5, weights: Optional[ndarray] = None, hemisphere: str = 'upper', symmetry: Optional[Symmetry] = None, log: bool = False, mrd: bool = True) Tuple[MaskedArray, Tuple[ndarray, ndarray]][source]#

Compute the Pole Density Function (PDF) of vectors in the stereographic projection. See [Rohrer et al., 2004].

If symmetry is defined then the PDF is folded back into the point group fundamental sector and accumulated.


Vector(s), or azimuth and polar angles of the vectors, the latter passed as two separate arguments.


The angular resolution of the sampling grid in degrees. Default value is 1.


The angular resolution of the applied broadening in degrees. Default value is 5.


The weights for the individual vectors. Default is None, in which case the weight of each vector is 1.


Which hemisphere(s) to plot the vectors on, options are "upper" and "lower". Default is "upper".


If provided the PDF is calculated within the fundamental sector of the point group symmetry, otherwise the PDF is calculated on hemisphere. Default is None.


If True the log(PDF) is calculated. Default is True.


If True the returned PDF is in units of Multiples of Random Distribution (MRD), otherwise the units are bin counts. Default is True.


The computed histogram, shape is (N, M).

x, y

Tuple of coordinate grids for the bin edges of hist. The units of x and y are cartesian coordinates on the stereographic projection plane and the shape of both x and y is (N + 1, M + 1).