import torch
from torch import Tensor
from ..distance.select_distance import SelectDistance
from ...utils import extend_docstring
[docs]
@extend_docstring(SelectDistance)
class Triweight(SelectDistance):
r"""
Triweight kernel.
.. math::
k(x,y) = %
\begin{cases}
\left(1 - \left(\frac{d(x,y)}{\sigma}\right)^2\right)^3 & \text{for } \frac{d(x,y)}{\sigma} \leq 1, \\
0 & \text{otherwise}.
\end{cases}
"""
def __init__(self, *args, **kwargs):
super(Triweight, self).__init__(*args, **kwargs)
def __str__(self):
return 'triweight kernel'
@property
def _naturally_normalized(self) -> bool:
# Triweight kernels are always naturally normalized
return True
@property
def hparams_fixed(self) -> dict:
return {'Kernel': 'Triweight',
**super(Triweight, self).hparams_variable}
def _implicit(self, x, y) -> Tensor:
d = self._dist_sigma(x, y)
return (d <= 1) * (1 - d ** 2) ** 3