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161 lines
6.2 KiB
Python
161 lines
6.2 KiB
Python
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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from kernpart import Kernpart
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import numpy as np
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class ODE_1(Kernpart):
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"""
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kernel resultiong from a first order ODE with OU driving GP
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:param input_dim: the number of input dimension, has to be equal to one
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:type input_dim: int
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:param varianceU: variance of the driving GP
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:type varianceU: float
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:param lengthscaleU: lengthscale of the driving GP (sqrt(3)/lengthscaleU)
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:type lengthscaleU: float
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:param varianceY: 'variance' of the transfer function
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:type varianceY: float
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:param lengthscaleY: 'lengthscale' of the transfer function (1/lengthscaleY)
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:type lengthscaleY: float
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:rtype: kernel object
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"""
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def __init__(self, input_dim=1, varianceU=1., varianceY=1., lengthscaleU=None, lengthscaleY=None):
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assert input_dim==1, "Only defined for input_dim = 1"
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self.input_dim = input_dim
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self.num_params = 4
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self.name = 'ODE_1'
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if lengthscaleU is not None:
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lengthscaleU = np.asarray(lengthscaleU)
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assert lengthscaleU.size == 1, "lengthscaleU should be one dimensional"
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else:
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lengthscaleU = np.ones(1)
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if lengthscaleY is not None:
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lengthscaleY = np.asarray(lengthscaleY)
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assert lengthscaleY.size == 1, "lengthscaleY should be one dimensional"
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else:
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lengthscaleY = np.ones(1)
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#lengthscaleY = 0.5
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self._set_params(np.hstack((varianceU, varianceY, lengthscaleU,lengthscaleY)))
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def _get_params(self):
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"""return the value of the parameters."""
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return np.hstack((self.varianceU,self.varianceY, self.lengthscaleU,self.lengthscaleY))
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def _set_params(self, x):
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"""set the value of the parameters."""
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assert x.size == self.num_params
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self.varianceU = x[0]
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self.varianceY = x[1]
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self.lengthscaleU = x[2]
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self.lengthscaleY = x[3]
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def _get_param_names(self):
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"""return parameter names."""
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return ['varianceU','varianceY', 'lengthscaleU', 'lengthscaleY']
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def K(self, X, X2, target):
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"""Compute the covariance matrix between X and X2."""
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if X2 is None: X2 = X
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# i1 = X[:,1]
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# i2 = X2[:,1]
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# X = X[:,0].reshape(-1,1)
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# X2 = X2[:,0].reshape(-1,1)
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dist = np.abs(X - X2.T)
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ly=1/self.lengthscaleY
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lu=np.sqrt(3)/self.lengthscaleU
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#ly=self.lengthscaleY
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#lu=self.lengthscaleU
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k1 = np.exp(-ly*dist)*(2*lu+ly)/(lu+ly)**2
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k2 = (np.exp(-lu*dist)*(ly-2*lu+lu*ly*dist-lu**2*dist) + np.exp(-ly*dist)*(2*lu-ly) ) / (ly-lu)**2
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k3 = np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 )
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np.add(self.varianceU*self.varianceY*(k1+k2+k3), target, target)
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def Kdiag(self, X, target):
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"""Compute the diagonal of the covariance matrix associated to X."""
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ly=1/self.lengthscaleY
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lu=np.sqrt(3)/self.lengthscaleU
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#ly=self.lengthscaleY
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#lu=self.lengthscaleU
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k1 = (2*lu+ly)/(lu+ly)**2
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k2 = (ly-2*lu + 2*lu-ly ) / (ly-lu)**2
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k3 = 1/(lu+ly) + (lu)/(lu+ly)**2
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np.add(self.varianceU*self.varianceY*(k1+k2+k3), target, target)
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def _param_grad_helper(self, dL_dK, X, X2, target):
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"""derivative of the covariance matrix with respect to the parameters."""
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if X2 is None: X2 = X
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dist = np.abs(X - X2.T)
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ly=1/self.lengthscaleY
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lu=np.sqrt(3)/self.lengthscaleU
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#ly=self.lengthscaleY
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#lu=self.lengthscaleU
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dk1theta1 = np.exp(-ly*dist)*2*(-lu)/(lu+ly)**3
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#c=np.sqrt(3)
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#t1=c/lu
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#t2=1/ly
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#dk1theta1=np.exp(-dist*ly)*t2*( (2*c*t2+2*t1)/(c*t2+t1)**2 -2*(2*c*t2*t1+t1**2)/(c*t2+t1)**3 )
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dk2theta1 = 1*(
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np.exp(-lu*dist)*dist*(-ly+2*lu-lu*ly*dist+dist*lu**2)*(ly-lu)**(-2) + np.exp(-lu*dist)*(-2+ly*dist-2*dist*lu)*(ly-lu)**(-2)
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+np.exp(-dist*lu)*(ly-2*lu+ly*lu*dist-dist*lu**2)*2*(ly-lu)**(-3)
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+np.exp(-dist*ly)*2*(ly-lu)**(-2)
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+np.exp(-dist*ly)*2*(2*lu-ly)*(ly-lu)**(-3)
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)
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dk3theta1 = np.exp(-dist*lu)*(lu+ly)**(-2)*((2*lu+ly+dist*lu**2+lu*ly*dist)*(-dist-2/(lu+ly))+2+2*lu*dist+ly*dist)
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dktheta1 = self.varianceU*self.varianceY*(dk1theta1+dk2theta1+dk3theta1)
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dk1theta2 = np.exp(-ly*dist) * ((lu+ly)**(-2)) * ( (-dist)*(2*lu+ly) + 1 + (-2)*(2*lu+ly)/(lu+ly) )
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dk2theta2 = 1*(
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np.exp(-dist*lu)*(ly-lu)**(-2) * ( 1+lu*dist+(-2)*(ly-2*lu+lu*ly*dist-dist*lu**2)*(ly-lu)**(-1) )
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+np.exp(-dist*ly)*(ly-lu)**(-2) * ( (-dist)*(2*lu-ly) -1+(2*lu-ly)*(-2)*(ly-lu)**(-1) )
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)
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dk3theta2 = np.exp(-dist*lu) * (-3*lu-ly-dist*lu**2-lu*ly*dist)/(lu+ly)**3
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dktheta2 = self.varianceU*self.varianceY*(dk1theta2 + dk2theta2 +dk3theta2)
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k1 = np.exp(-ly*dist)*(2*lu+ly)/(lu+ly)**2
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k2 = (np.exp(-lu*dist)*(ly-2*lu+lu*ly*dist-lu**2*dist) + np.exp(-ly*dist)*(2*lu-ly) ) / (ly-lu)**2
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k3 = np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 )
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dkdvar = k1+k2+k3
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target[0] += np.sum(self.varianceY*dkdvar * dL_dK)
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target[1] += np.sum(self.varianceU*dkdvar * dL_dK)
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target[2] += np.sum(dktheta1*(-np.sqrt(3)*self.lengthscaleU**(-2)) * dL_dK)
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target[3] += np.sum(dktheta2*(-self.lengthscaleY**(-2)) * dL_dK)
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# def dKdiag_dtheta(self, dL_dKdiag, X, target):
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# """derivative of the diagonal of the covariance matrix with respect to the parameters."""
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# # NB: derivative of diagonal elements wrt lengthscale is 0
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# target[0] += np.sum(dL_dKdiag)
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# def dK_dX(self, dL_dK, X, X2, target):
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# """derivative of the covariance matrix with respect to X."""
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# if X2 is None: X2 = X
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# dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))[:, :, None]
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# ddist_dX = (X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf)
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# dK_dX = -np.transpose(self.variance * np.exp(-dist) * ddist_dX, (1, 0, 2))
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# target += np.sum(dK_dX * dL_dK.T[:, :, None], 0)
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# def dKdiag_dX(self, dL_dKdiag, X, target):
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# pass
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