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57 lines
1.5 KiB
Python
57 lines
1.5 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Classes in this module enhance Brownian motion covariance function with the
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Stochastic Differential Equation (SDE) functionality.
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"""
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from .brownian import Brownian
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import numpy as np
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class sde_Brownian(Brownian):
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"""
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Class provide extra functionality to transfer this covariance function into
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SDE form.
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Linear kernel:
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.. math::
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k(x,y) = \sigma^2 min(x,y)
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"""
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def sde_update_gradient_full(self, gradients):
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"""
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Update gradient in the order in which parameters are represented in the
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kernel
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"""
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self.variance.gradient = gradients[0]
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def sde(self):
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"""
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Return the state space representation of the covariance.
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"""
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variance = float(self.variance.values) # this is initial variancve in Bayesian linear regression
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F = np.array( ((0,1.0),(0,0) ))
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L = np.array( ((1.0,),(0,)) )
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Qc = np.array( ((variance,),) )
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H = np.array( ((1.0,0),) )
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Pinf = np.array( ( (0, -0.5*variance ), (-0.5*variance, 0) ) )
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#P0 = Pinf.copy()
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P0 = np.zeros((2,2))
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#Pinf = np.array( ( (t0, 1.0), (1.0, 1.0/t0) ) ) * variance
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dF = np.zeros((2,2,1))
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dQc = np.ones( (1,1,1) )
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dPinf = np.zeros((2,2,1))
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dPinf[:,:,0] = np.array( ( (0, -0.5), (-0.5, 0) ) )
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#dP0 = dPinf.copy()
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dP0 = np.zeros((2,2,1))
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return (F, L, Qc, H, Pinf, P0, dF, dQc, dPinf, dP0)
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