# -*- coding: utf-8 -*-
# Copyright (c) 2015, Alex Grigorevskiy, Arno Solin
# Licensed under the BSD 3-clause license (see LICENSE.txt)
"""
Classes in this module enhance Linear covariance function with the
Stochastic Differential Equation (SDE) functionality.
"""
from .linear import Linear
import numpy as np
[docs]class sde_Linear(Linear):
"""
Class provide extra functionality to transfer this covariance function into
SDE form.
Linear kernel:
.. math::
k(x,y) = \sum_{i=1}^{input dim} \sigma^2_i x_iy_i
"""
def __init__(self, input_dim, X, variances=None, ARD=False, active_dims=None, name='linear'):
"""
Modify the init method, because one extra parameter is required. X - points
on the X axis.
"""
super(sde_Linear, self).__init__(input_dim, variances, ARD, active_dims, name)
self.t0 = np.min(X)
[docs] def sde_update_gradient_full(self, gradients):
"""
Update gradient in the order in which parameters are represented in the
kernel
"""
self.variances.gradient = gradients[0]
[docs] def sde(self):
"""
Return the state space representation of the covariance.
"""
variance = float(self.variances.values) # this is initial variancve in Bayesian linear regression
t0 = float(self.t0)
F = np.array( ((0,1.0),(0,0) ))
L = np.array( ((0,),(1.0,)) )
Qc = np.zeros((1,1))
H = np.array( ((1.0,0),) )
Pinf = np.zeros((2,2))
P0 = np.array( ( (t0**2, t0), (t0, 1) ) ) * variance
dF = np.zeros((2,2,1))
dQc = np.zeros( (1,1,1) )
dPinf = np.zeros((2,2,1))
dP0 = np.zeros((2,2,1))
dP0[:,:,0] = P0 / variance
return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)