# Source code for GPy.kern.src.sde_static

# -*- coding: utf-8 -*-
# Copyright (c) 2015, Alex Grigorevskiy, Arno Solin
"""
Classes in this module enhance Static covariance functions with the
Stochastic Differential Equation (SDE) functionality.
"""
from .static import White
from .static import Bias

import numpy as np

[docs]class sde_White(White):
"""

Class provide extra functionality to transfer this covariance function into
SDE forrm.

White kernel:

.. math::

k(x,y) = \alpha*\delta(x-y)

"""

"""
Update gradient in the order in which parameters are represented in the
kernel
"""

[docs]    def sde(self):
"""
Return the state space representation of the covariance.
"""

variance = float(self.variance.values)

F = np.array( ((-np.inf,),) )
L = np.array( ((1.0,),)  )
Qc = np.array( ((variance,),)  )
H = np.array( ((1.0,),) )

Pinf   = np.array( ((variance,),)  )
P0 = Pinf.copy()

dF = np.zeros((1,1,1))
dQc = np.zeros((1,1,1))
dQc[:,:,0]    = np.array( ((1.0,),) )

dPinf = np.zeros((1,1,1))
dPinf[:,:,0] = np.array( ((1.0,),) )
dP0 = dPinf.copy()

return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)

[docs]class sde_Bias(Bias):
"""

Class provide extra functionality to transfer this covariance function into
SDE forrm.

Bias kernel:

.. math::

k(x,y) = \alpha

"""
"""
Update gradient in the order in which parameters are represented in the
kernel
"""

[docs]    def sde(self):
"""
Return the state space representation of the covariance.
"""
variance = float(self.variance.values)

F = np.array( ((0.0,),))
L = np.array( ((1.0,),))
Qc = np.zeros((1,1))
H = np.array( ((1.0,),))

Pinf   = np.zeros((1,1))
P0 = np.array( ((variance,),) )

dF = np.zeros((1,1,1))
dQc    = np.zeros((1,1,1))

dPinf = np.zeros((1,1,1))
dP0 = np.zeros((1,1,1))
dP0[:,:,0] = np.array( ((1.0,),) )

return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)