# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
# Copyright (c) 2015, James Hensman
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
from ..core.mapping import Mapping
from ..core import Param
[docs]class Kernel(Mapping):
"""
Mapping based on a kernel/covariance function.
.. math::
f(\mathbf{x}) = \sum_i \alpha_i k(\mathbf{z}_i, \mathbf{x})
or for multple outputs
.. math::
f_i(\mathbf{x}) = \sum_j \alpha_{i,j} k(\mathbf{z}_i, \mathbf{x})
:param input_dim: dimension of input.
:type input_dim: int
:param output_dim: dimension of output.
:type output_dim: int
:param Z: input observations containing :math:`\mathbf{Z}`
:type Z: ndarray
:param kernel: a GPy kernel, defaults to GPy.kern.RBF
:type kernel: GPy.kern.kern
"""
def __init__(self, input_dim, output_dim, Z, kernel, name='kernmap'):
super(Kernel, self).__init__(input_dim=input_dim, output_dim=output_dim, name=name)
self.kern = kernel
self.Z = Z
self.num_bases, Zdim = Z.shape
assert Zdim == self.input_dim
self.A = Param('A', np.random.randn(self.num_bases, self.output_dim))
self.link_parameter(self.A)
[docs] def f(self, X):
return np.dot(self.kern.K(X, self.Z), self.A)
[docs] def update_gradients(self, dL_dF, X):
self.kern.update_gradients_full(np.dot(dL_dF, self.A.T), X, self.Z)
self.A.gradient = np.dot( self.kern.K(self.Z, X), dL_dF)
[docs] def gradients_X(self, dL_dF, X):
return self.kern.gradients_X(np.dot(dL_dF, self.A.T), X, self.Z)