def sp_subvector_error(self, radius, sp_dimensions, sp_subdimensions=1):
"""Estimate of representational error of a subvector of a semantic
pointer (unit vector).
Requires Scipy.
Paramaters
----------
radius : float or ndarray
Radius of the representing ensemble.
sp_dimensions : int
Dimensionality of the complete semantic pointer/unit vector.
sp_subdimensions : int, optional
Dimensionality of the subvector represented by some ensemble.
Returns
-------
Error estimates for representing a subvector with `subdimensions`
dimensions of a `dimensions` dimensional unit vector with an ensemble
initialized with of `radius`.
"""
dist = SubvectorLength(sp_dimensions, sp_subdimensions)
in_range = self._sp_subvector_error_in_range(radius, sp_subdimensions)
out_of_range = self._sp_subvector_error_out_of_range(
radius, sp_dimensions, sp_subdimensions)
return dist.cdf(radius) * in_range + (
1.0 - dist.cdf(radius)) * out_of_range
def _sp_subvector_error_out_of_range(radius, dimensions, subdimensions):
dist = SubvectorLength(dimensions, subdimensions)
sq_r = radius * radius
normalization = 1.0 - dist.cdf(radius)
b = (dimensions - subdimensions) / 2.0
aligned_integral = beta(subdimensions / 2.0 + 1.0, b) * (1.0 - betainc(
subdimensions / 2.0 + 1.0, b, sq_r))
cross_integral = beta((subdimensions + 1) / 2.0, b) * (1.0 - betainc(
(subdimensions + 1) / 2.0, b, sq_r))
numerator = (sq_r * normalization + (
aligned_integral - 2.0 * radius * cross_integral) / beta(
subdimensions / 2.0, b))
with np.errstate(invalid='ignore'):
return np.where(
numerator > np.MachAr().eps,
numerator / normalization, np.zeros_like(normalization))
