Linear¶
-
class
probnum.kernels.
Linear
(input_dim, constant=0.0)¶ Bases:
probnum.kernels._kernel.Kernel
[numpy.ndarray
]Linear kernel.
Linear covariance function defined by \(k(x_0, x_1) = x_0^\top x_1 + c\).
- Parameters
See also
Polynomial
Polynomial covariance function.
Examples
>>> import numpy as np >>> from probnum.kernels import Linear >>> K = Linear(input_dim=2) >>> K(np.array([[1, 2], [2, 3]])) array([[ 5., 8.], [ 8., 13.]])
Attributes Summary
Dimension of arguments of the covariance function.
Dimension of the evaluated covariance function.
Methods Summary
__call__
(x0[, x1])Evaluate the kernel.
Attributes Documentation
-
input_dim
¶ Dimension of arguments of the covariance function.
The dimension of inputs to the covariance function \(k : \mathbb{R}^{ d_{in}} \times \mathbb{R}^{d_{in}} \rightarrow \mathbb{R}^{d_{out} \times d_{out}}\).
- Return type
-
output_dim
¶ Dimension of the evaluated covariance function.
The resulting evaluated kernel \(k(x_0, x_1) \in \mathbb{R}^{d_{out} \times d_{out}}\) has shape=(output_dim, output_dim).
- Return type
Methods Documentation
-
__call__
(x0, x1=None)[source]¶ Evaluate the kernel.
Computes the covariance function at
x0
andx1
. If the inputs have more than one dimension the covariance function is evaluated pairwise for all observations determined by the first dimension ofx0
andx1
. If onlyx0
is given the kernel matrix \(K=k(X_0, X_0)\) is computed.- Parameters
- Returns
shape=(), (output_dim, output_dim) or (n0, n1) or (n0, n1, output_dim, output_dim) – Kernel evaluated at
x0
andx1
or kernel matrix containing pairwise evaluations for all observations inx0
(andx1
).- Return type
cov