# Source code for GPy.kern.src.spline

# Copyright (c) 2015, Thomas Hornung

import numpy as np
from .kern import Kern
from ...core.parameterization import Param
from paramz.transformations import Logexp

[docs]class Spline(Kern):
"""
Linear spline kernel. You need to specify 2 parameters: the variance and c.
The variance is defined in powers of 10. Thus specifying -2 means 10^-2.
The parameter c allows to define the stiffness of the spline fit. A very stiff
spline equals linear regression.
See https://www.youtube.com/watch?v=50Vgw11qn0o starting at minute 1:17:28
Lit: Wahba, 1990
"""

def __init__(self, input_dim, variance=1., c=1., active_dims=None, name='spline'):
super(Spline, self).__init__(input_dim, active_dims, name)
self.variance = Param('variance', variance, Logexp())
self.c = Param('c', c)

[docs]    def K(self, X, X2=None):
if X2 is None: X2=X
term1 = (X+8.)*(X2.T+8.)/16.
term2 = abs((X-X2.T)/16.)**3
term3 = ((X+8.)/16.)**3 + ((X2.T+8.)/16.)**3
return (self.variance**2 * (1. + (1.+self.c) * term1 + self.c/3. * (term2 - term3)))

[docs]    def Kdiag(self, X):
term1 = np.square(X+8.,X+8.)/16.
term3 = 2. * ((X+8.)/16.)**3
return (self.variance**2 * (1. + (1.+self.c) * term1 - self.c/3. * term3))[:,0]

[docs]    def update_gradients_full(self, dL_dK, X, X2=None):
if X2 is None: X2=X
term1 = (X+8.)*(X2.T+8.)/16.
term2 = abs((X-X2.T)/16.)**3
term3 = ((X+8.)/16.)**3 + ((X2.T+8.)/16.)**3
self.variance.gradient = np.sum(dL_dK * (2*self.variance * (1. + (1.+self.c) * term1 + self.c/3. * ( term2 - term3))))
self.c.gradient = np.sum(dL_dK * (self.variance**2* (term1 + 1./3.*(term2 - term3))))