# Source code for gpytorch.kernels.polynomial_kernel

#!/usr/bin/env python3

from typing import Optional

import torch

from ..constraints import Interval, Positive
from ..priors import Prior
from .kernel import Kernel

[docs]class PolynomialKernel(Kernel):
r"""
Computes a covariance matrix based on the Polynomial kernel
between inputs :math:\mathbf{x_1} and :math:\mathbf{x_2}:

.. math::
\begin{equation*}
k_\text{Poly}(\mathbf{x_1}, \mathbf{x_2}) = (\mathbf{x_1}^\top
\mathbf{x_2} + c)^{d}.
\end{equation*}

where

* :math:c is an offset parameter.

Args:
offset_prior (:class:gpytorch.priors.Prior):
Prior over the offset parameter (default None).
offset_constraint (Constraint, optional):
Constraint to place on offset parameter. Default: Positive.
active_dims (list):
List of data dimensions to operate on.
len(active_dims) should equal num_dimensions.
"""

def __init__(
self,
power: int,
offset_prior: Optional[Prior] = None,
offset_constraint: Optional[Interval] = None,
**kwargs,
):
super().__init__(**kwargs)
if offset_constraint is None:
offset_constraint = Positive()

self.register_parameter(name="raw_offset", parameter=torch.nn.Parameter(torch.zeros(*self.batch_shape, 1)))

# We want the power to be a float so we dont have to worry about its device / dtype.
if torch.is_tensor(power):
if power.numel() > 1:
raise RuntimeError("Cant create a Polynomial kernel with more than one power")
else:
power = power.item()

self.power = power

if offset_prior is not None:
if not isinstance(offset_prior, Prior):
raise TypeError("Expected gpytorch.priors.Prior but got " + type(offset_prior).__name__)
self.register_prior("offset_prior", offset_prior, lambda m: m.offset, lambda m, v: m._set_offset(v))

self.register_constraint("raw_offset", offset_constraint)

@property
def offset(self) -> torch.Tensor:
return self.raw_offset_constraint.transform(self.raw_offset)

@offset.setter
def offset(self, value: torch.Tensor) -> None:
self._set_offset(value)

def _set_offset(self, value: torch.Tensor) -> None:
if not torch.is_tensor(value):
value = torch.as_tensor(value).to(self.raw_offset)
self.initialize(raw_offset=self.raw_offset_constraint.inverse_transform(value))

def forward(
self,
x1: torch.Tensor,
x2: torch.Tensor,
diag: Optional[bool] = False,
last_dim_is_batch: Optional[bool] = False,
**params,
) -> torch.Tensor:
offset = self.offset.view(*self.batch_shape, 1, 1)

if last_dim_is_batch:
x1 = x1.transpose(-1, -2).unsqueeze(-1)
x2 = x2.transpose(-1, -2).unsqueeze(-1)

if diag:
return ((x1 * x2).sum(dim=-1) + self.offset).pow(self.power)

if (x1.dim() == 2 and x2.dim() == 2) and offset.dim() == 2: