"""White noise kernel."""
from typing import Optional
import numpy as np
import probnum.utils as _utils
from probnum.type import IntArgType, ScalarArgType
from ._kernel import Kernel
_InputType = np.ndarray
class WhiteNoise(Kernel[_InputType]):
"""White noise kernel.
Kernel representing independent and identically distributed white noise :math:`k(
x_0, x_1) = \\sigma^2 \\delta(x_0, x_1)`.
Parameters
----------
input_dim :
Input dimension of the kernel.
sigma :
Noise level.
"""
def __init__(self, input_dim: IntArgType, sigma: ScalarArgType = 1.0):
self.sigma = _utils.as_numpy_scalar(sigma)
super().__init__(input_dim=input_dim, output_dim=1)
[docs] def __call__(self, x0: _InputType, x1: Optional[_InputType] = None) -> np.ndarray:
x0, x1, kernshape = self._check_and_reshape_inputs(x0, x1)
# Compute kernel matrix
if x1 is None:
kernmat = self.sigma ** 2 * np.eye(x0.shape[0])
else:
kernmat = self.sigma ** 2 * np.equal(x0, x1[:, np.newaxis, :]).all(
axis=2
).T.astype(float)
return Kernel._reshape_kernelmatrix(kernmat, newshape=kernshape)