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GPy/kern/_src/ODE_UYC.py
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GPy/kern/_src/ODE_UYC.py
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# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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from kern import Kern
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from ...core.parameterization import Param
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from ...core.parameterization.transformations import Logexp
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import numpy as np
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from independent_outputs import index_to_slices
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class ODE_UYC(Kern):
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def __init__(self, input_dim, variance_U=3., variance_Y=1., lengthscale_U=1., lengthscale_Y=1., ubias =1. ,active_dims=None, name='ode_uyc'):
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assert input_dim ==2, "only defined for 2 input dims"
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super(ODE_UYC, self).__init__(input_dim, active_dims, name)
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self.variance_Y = Param('variance_Y', variance_Y, Logexp())
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self.variance_U = Param('variance_U', variance_U, Logexp())
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self.lengthscale_Y = Param('lengthscale_Y', lengthscale_Y, Logexp())
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self.lengthscale_U = Param('lengthscale_U', lengthscale_U, Logexp())
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self.ubias = Param('ubias', ubias, Logexp())
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self.add_parameters(self.variance_Y, self.variance_U, self.lengthscale_Y, self.lengthscale_U, self.ubias)
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def K(self, X, X2=None):
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# model : a * dy/dt + b * y = U
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#lu=sqrt(3)/theta1 ly=1/theta2 theta2= a/b :thetay sigma2=1/(2ab) :sigmay
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X,slices = X[:,:-1],index_to_slices(X[:,-1])
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if X2 is None:
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X2,slices2 = X,slices
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K = np.zeros((X.shape[0], X.shape[0]))
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else:
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X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1])
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K = np.zeros((X.shape[0], X2.shape[0]))
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#stop
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#rdist = X[:,0][:,None] - X2[:,0][:,None].T
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rdist = X - X2.T
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ly=1/self.lengthscale_Y
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lu=np.sqrt(3)/self.lengthscale_U
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#iu=self.input_lengthU #dimention of U
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Vu=self.variance_U
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Vy=self.variance_Y
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#Vy=ly/2
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#stop
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# kernel for kuu matern3/2
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kuu = lambda dist:Vu * (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist)) +self.ubias
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# kernel for kyy
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k1 = lambda dist:np.exp(-ly*np.abs(dist))*(2*lu+ly)/(lu+ly)**2
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k2 = lambda dist:(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 = lambda dist:np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 )
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kyy = lambda dist:Vu*Vy*(k1(dist) + k2(dist) + k3(dist))
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# cross covariance function
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kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly)))
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#kyu3 = lambda dist: 0
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k1cros = lambda dist:np.exp(ly*dist)/(lu-ly) * ( 1- np.exp( (lu-ly)*dist) + lu* ( dist*np.exp( (lu-ly)*dist ) + (1- np.exp( (lu-ly)*dist ) ) /(lu-ly) ) )
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#k1cros = lambda dist:0
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k2cros = lambda dist:np.exp(ly*dist)*( 1/(lu+ly) + lu/(lu+ly)**2 )
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#k2cros = lambda dist:0
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Vyu=np.sqrt(Vy*ly*2)
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# cross covariance kuy
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kuyp = lambda dist:Vu*Vyu*(kyu3(dist)) #t>0 kuy
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kuyn = lambda dist:Vu*Vyu*(k1cros(dist)+k2cros(dist)) #t<0 kuy
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# cross covariance kyu
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kyup = lambda dist:Vu*Vyu*(k1cros(-dist)+k2cros(-dist)) #t>0 kyu
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kyun = lambda dist:Vu*Vyu*(kyu3(-dist)) #t<0 kyu
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for i, s1 in enumerate(slices):
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for j, s2 in enumerate(slices2):
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for ss1 in s1:
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for ss2 in s2:
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if i==0 and j==0:
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K[ss1,ss2] = kuu(np.abs(rdist[ss1,ss2]))
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elif i==0 and j==1:
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#K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[ss1,ss2]) ) )
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K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(rdist[ss1,ss2]), kuyn(rdist[ss1,ss2] ) )
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elif i==1 and j==1:
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K[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2]))
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else:
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#K[ss1,ss2]= 0
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#K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[ss1,ss2]) ) )
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K[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(rdist[ss1,ss2]), kyun(rdist[ss1,ss2] ) )
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return K
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def Kdiag(self, X):
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"""Compute the diagonal of the covariance matrix associated to X."""
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Kdiag = np.zeros(X.shape[0])
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ly=1/self.lengthscale_Y
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lu=np.sqrt(3)/self.lengthscale_U
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Vu = self.variance_U
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Vy=self.variance_Y
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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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slices = index_to_slices(X[:,-1])
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for i, ss1 in enumerate(slices):
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for s1 in ss1:
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if i==0:
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Kdiag[s1]+= self.variance_U + self.ubias
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elif i==1:
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Kdiag[s1]+= Vu*Vy*(k1+k2+k3)
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else:
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raise ValueError, "invalid input/output index"
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#Kdiag[slices[0][0]]+= self.variance_U #matern32 diag
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#Kdiag[slices[1][0]]+= self.variance_U*self.variance_Y*(k1+k2+k3) # diag
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return Kdiag
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def update_gradients_full(self, dL_dK, X, X2=None):
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"""derivative of the covariance matrix with respect to the parameters."""
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X,slices = X[:,:-1],index_to_slices(X[:,-1])
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if X2 is None:
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X2,slices2 = X,slices
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else:
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X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1])
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#rdist = X[:,0][:,None] - X2[:,0][:,None].T
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rdist = X - X2.T
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ly=1/self.lengthscale_Y
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lu=np.sqrt(3)/self.lengthscale_U
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Vu=self.variance_U
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Vy=self.variance_Y
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Vyu = np.sqrt(Vy*ly*2)
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dVdly = 0.5/np.sqrt(ly)*np.sqrt(2*Vy)
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dVdVy = 0.5/np.sqrt(Vy)*np.sqrt(2*ly)
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rd=rdist.shape[0]
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dktheta1 = np.zeros([rd,rd])
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dktheta2 = np.zeros([rd,rd])
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dkUdvar = np.zeros([rd,rd])
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dkYdvar = np.zeros([rd,rd])
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dkdubias = np.zeros([rd,rd])
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# dk dtheta for UU
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UUdtheta1 = lambda dist: np.exp(-lu* dist)*dist + (-dist)*np.exp(-lu* dist)*(1+lu*dist)
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UUdtheta2 = lambda dist: 0
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#UUdvar = lambda dist: (1 + lu*dist)*np.exp(-lu*dist)
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UUdvar = lambda dist: (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist))
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# dk dtheta for YY
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dk1theta1 = lambda dist: np.exp(-ly*dist)*2*(-lu)/(lu+ly)**3
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dk2theta1 = lambda dist: (1.0)*(
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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 = lambda dist: 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 = lambda dist: self.variance_U*self.variance_Y*(dk1theta1+dk2theta1+dk3theta1)
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dk1theta2 = lambda dist: np.exp(-ly*dist) * ((lu+ly)**(-2)) * ( (-dist)*(2*lu+ly) + 1 + (-2)*(2*lu+ly)/(lu+ly) )
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dk2theta2 =lambda dist: 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 = lambda dist: np.exp(-dist*lu) * (-3*lu-ly-dist*lu**2-lu*ly*dist)/(lu+ly)**3
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#dktheta2 = lambda dist: self.variance_U*self.variance_Y*(dk1theta2 + dk2theta2 +dk3theta2)
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# kyy kernel
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k1 = lambda dist: np.exp(-ly*dist)*(2*lu+ly)/(lu+ly)**2
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k2 = lambda dist: (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 = lambda dist: 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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# cross covariance function
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kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly)))
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k1cros = lambda dist:np.exp(ly*dist)/(lu-ly) * ( 1- np.exp( (lu-ly)*dist) + lu* ( dist*np.exp( (lu-ly)*dist ) + (1- np.exp( (lu-ly)*dist ) ) /(lu-ly) ) )
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k2cros = lambda dist:np.exp(ly*dist)*( 1/(lu+ly) + lu/(lu+ly)**2 )
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# cross covariance kuy
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kuyp = lambda dist:(kyu3(dist)) #t>0 kuy
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kuyn = lambda dist:(k1cros(dist)+k2cros(dist)) #t<0 kuy
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# cross covariance kyu
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kyup = lambda dist:(k1cros(-dist)+k2cros(-dist)) #t>0 kyu
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kyun = lambda dist:(kyu3(-dist)) #t<0 kyu
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# dk dtheta for UY
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dkyu3dtheta2 = lambda dist: np.exp(-lu*dist) * ( (-1)*(lu+ly)**(-2)*(1+lu*dist+lu*(lu+ly)**(-1)) + (lu+ly)**(-1)*(-lu)*(lu+ly)**(-2) )
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dkyu3dtheta1 = lambda dist: np.exp(-lu*dist)*(lu+ly)**(-1)* ( (-dist)*(1+dist*lu+lu*(lu+ly)**(-1)) -\
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(lu+ly)**(-1)*(1+dist*lu+lu*(lu+ly)**(-1)) +dist+(lu+ly)**(-1)-lu*(lu+ly)**(-2) )
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dkcros2dtheta1 = lambda dist: np.exp(ly*dist)* ( -(ly+lu)**(-2) + (ly+lu)**(-2) + (-2)*lu*(lu+ly)**(-3) )
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dkcros2dtheta2 = lambda dist: np.exp(ly*dist)*dist* ( (ly+lu)**(-1) + lu*(lu+ly)**(-2) ) + \
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np.exp(ly*dist)*( -(lu+ly)**(-2) + lu*(-2)*(lu+ly)**(-3) )
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dkcros1dtheta1 = lambda dist: np.exp(ly*dist)*( -(lu-ly)**(-2)*( 1-np.exp((lu-ly)*dist) + lu*dist*np.exp((lu-ly)*dist)+ \
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lu*(1-np.exp((lu-ly)*dist))/(lu-ly) ) + (lu-ly)**(-1)*( -np.exp( (lu-ly)*dist )*dist + dist*np.exp( (lu-ly)*dist)+\
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lu*dist**2*np.exp((lu-ly)*dist)+(1-np.exp((lu-ly)*dist))/(lu-ly) - lu*np.exp((lu-ly)*dist)*dist/(lu-ly) -\
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lu*(1-np.exp((lu-ly)*dist))/(lu-ly)**2 ) )
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dkcros1dtheta2 = lambda t: np.exp(ly*t)*t/(lu-ly)*( 1-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)+\
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lu*(1-np.exp((lu-ly)*t))/(lu-ly) )+\
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np.exp(ly*t)/(lu-ly)**2* ( 1-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t) + lu*( 1-np.exp((lu-ly)*t) )/(lu-ly) )+\
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np.exp(ly*t)/(lu-ly)*( np.exp((lu-ly)*t)*t -lu*t*t*np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)/(lu-ly)+\
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lu*( 1-np.exp((lu-ly)*t) )/(lu-ly)**2 )
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dkuypdtheta1 = lambda dist:(dkyu3dtheta1(dist)) #t>0 kuy
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dkuyndtheta1 = lambda dist:(dkcros1dtheta1(dist)+dkcros2dtheta1(dist)) #t<0 kuy
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# cross covariance kyu
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dkyupdtheta1 = lambda dist:(dkcros1dtheta1(-dist)+dkcros2dtheta1(-dist)) #t>0 kyu
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dkyundtheta1 = lambda dist:(dkyu3dtheta1(-dist)) #t<0 kyu
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dkuypdtheta2 = lambda dist:(dkyu3dtheta2(dist)) #t>0 kuy
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dkuyndtheta2 = lambda dist:(dkcros1dtheta2(dist)+dkcros2dtheta2(dist)) #t<0 kuy
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# cross covariance kyu
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dkyupdtheta2 = lambda dist:(dkcros1dtheta2(-dist)+dkcros2dtheta2(-dist)) #t>0 kyu
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dkyundtheta2 = lambda dist:(dkyu3dtheta2(-dist)) #t<0 kyu
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for i, s1 in enumerate(slices):
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for j, s2 in enumerate(slices2):
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for ss1 in s1:
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for ss2 in s2:
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if i==0 and j==0:
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#target[ss1,ss2] = kuu(np.abs(rdist[ss1,ss2]))
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dktheta1[ss1,ss2] = Vu*UUdtheta1(np.abs(rdist[ss1,ss2]))
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dktheta2[ss1,ss2] = 0
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dkUdvar[ss1,ss2] = UUdvar(np.abs(rdist[ss1,ss2]))
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dkYdvar[ss1,ss2] = 0
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dkdubias[ss1,ss2] = 1
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elif i==0 and j==1:
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########target[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[s1[0],s2[0]]) ) )
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#np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[s1[0],s2[0]]) ) )
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#dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , self.variance_U*self.variance_Y*dkcrtheta1(np.abs(rdist[ss1,ss2])) ,self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))) )
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#dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , self.variance_U*self.variance_Y*dkcrtheta2(np.abs(rdist[ss1,ss2])) ,self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2]))+dk2theta2(np.abs(rdist[ss1,ss2]))) )
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dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkuypdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta1(rdist[ss1,ss2]) )
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dkUdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vyu*kuyp(rdist[ss1,ss2]), Vyu* kuyn(rdist[ss1,ss2]) )
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dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkuypdtheta2(rdist[ss1,ss2])+Vu*dVdly*kuyp(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta2(rdist[ss1,ss2])+Vu*dVdly*kuyn(rdist[ss1,ss2]) )
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dkYdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*dVdVy*kuyp(rdist[ss1,ss2]), Vu*dVdVy* kuyn(rdist[ss1,ss2]) )
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dkdubias[ss1,ss2] = 0
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elif i==1 and j==1:
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#target[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2]))
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dktheta1[ss1,ss2] = self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))+dk3theta1(np.abs(rdist[ss1,ss2])))
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dktheta2[ss1,ss2] = self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2])) + dk2theta2(np.abs(rdist[ss1,ss2])) +dk3theta2(np.abs(rdist[ss1,ss2])))
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dkUdvar[ss1,ss2] = self.variance_Y*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) )
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dkYdvar[ss1,ss2] = self.variance_U*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) )
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dkdubias[ss1,ss2] = 0
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else:
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#######target[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[s1[0],s2[0]]) ) )
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#dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 ,self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))) , self.variance_U*self.variance_Y*dkcrtheta1(np.abs(rdist[ss1,ss2])) )
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#dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 ,self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2]))+dk2theta2(np.abs(rdist[ss1,ss2]))) , self.variance_U*self.variance_Y*dkcrtheta2(np.abs(rdist[ss1,ss2])) )
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dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkyupdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta1(rdist[ss1,ss2]) )
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dkUdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vyu*kyup(rdist[ss1,ss2]),Vyu*kyun(rdist[ss1,ss2]))
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dktheta2[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkyupdtheta2(rdist[ss1,ss2])+Vu*dVdly*kyup(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta2(rdist[ss1,ss2])+Vu*dVdly*kyun(rdist[ss1,ss2]) )
|
||||
dkYdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*dVdVy*kyup(rdist[ss1,ss2]), Vu*dVdVy*kyun(rdist[ss1,ss2]))
|
||||
dkdubias[ss1,ss2] = 0
|
||||
#stop
|
||||
self.variance_U.gradient = np.sum(dkUdvar * dL_dK) # Vu
|
||||
|
||||
self.variance_Y.gradient = np.sum(dkYdvar * dL_dK) # Vy
|
||||
|
||||
self.lengthscale_U.gradient = np.sum(dktheta1*(-np.sqrt(3)*self.lengthscale_U**(-2))* dL_dK) #lu
|
||||
|
||||
self.lengthscale_Y.gradient = np.sum(dktheta2*(-self.lengthscale_Y**(-2)) * dL_dK) #ly
|
||||
|
||||
self.ubias.gradient = np.sum(dkdubias * dL_dK)
|
||||
|
||||
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Reference in a new issue