diff --git a/GPy/kern/_src/ODE_UYC.py b/GPy/kern/_src/ODE_UYC.py new file mode 100644 index 00000000..1722d2e1 --- /dev/null +++ b/GPy/kern/_src/ODE_UYC.py @@ -0,0 +1,290 @@ +# Copyright (c) 2013, GPy authors (see AUTHORS.txt). +# Licensed under the BSD 3-clause license (see LICENSE.txt) + +from kern import Kern +from ...core.parameterization import Param +from ...core.parameterization.transformations import Logexp +import numpy as np +from independent_outputs import index_to_slices + +class ODE_UYC(Kern): + 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'): + assert input_dim ==2, "only defined for 2 input dims" + super(ODE_UYC, self).__init__(input_dim, active_dims, name) + + self.variance_Y = Param('variance_Y', variance_Y, Logexp()) + self.variance_U = Param('variance_U', variance_U, Logexp()) + self.lengthscale_Y = Param('lengthscale_Y', lengthscale_Y, Logexp()) + self.lengthscale_U = Param('lengthscale_U', lengthscale_U, Logexp()) + self.ubias = Param('ubias', ubias, Logexp()) + + self.add_parameters(self.variance_Y, self.variance_U, self.lengthscale_Y, self.lengthscale_U, self.ubias) + + def K(self, X, X2=None): + # model : a * dy/dt + b * y = U + #lu=sqrt(3)/theta1 ly=1/theta2 theta2= a/b :thetay sigma2=1/(2ab) :sigmay + + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + K = np.zeros((X.shape[0], X.shape[0])) + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + K = np.zeros((X.shape[0], X2.shape[0])) + + #stop + #rdist = X[:,0][:,None] - X2[:,0][:,None].T + rdist = X - X2.T + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + #iu=self.input_lengthU #dimention of U + Vu=self.variance_U + Vy=self.variance_Y + #Vy=ly/2 + #stop + + + # kernel for kuu matern3/2 + kuu = lambda dist:Vu * (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist)) +self.ubias + + # kernel for kyy + k1 = lambda dist:np.exp(-ly*np.abs(dist))*(2*lu+ly)/(lu+ly)**2 + 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 + k3 = lambda dist:np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 ) + kyy = lambda dist:Vu*Vy*(k1(dist) + k2(dist) + k3(dist)) + + + # cross covariance function + kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly))) + #kyu3 = lambda dist: 0 + + 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) ) ) + #k1cros = lambda dist:0 + + k2cros = lambda dist:np.exp(ly*dist)*( 1/(lu+ly) + lu/(lu+ly)**2 ) + #k2cros = lambda dist:0 + + Vyu=np.sqrt(Vy*ly*2) + + # cross covariance kuy + kuyp = lambda dist:Vu*Vyu*(kyu3(dist)) #t>0 kuy + kuyn = lambda dist:Vu*Vyu*(k1cros(dist)+k2cros(dist)) #t<0 kuy + # cross covariance kyu + kyup = lambda dist:Vu*Vyu*(k1cros(-dist)+k2cros(-dist)) #t>0 kyu + kyun = lambda dist:Vu*Vyu*(kyu3(-dist)) #t<0 kyu + + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + K[ss1,ss2] = kuu(np.abs(rdist[ss1,ss2])) + elif i==0 and j==1: + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[ss1,ss2]) ) ) + K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kuyp(rdist[ss1,ss2]), kuyn(rdist[ss1,ss2] ) ) + elif i==1 and j==1: + K[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2])) + else: + #K[ss1,ss2]= 0 + #K[ss1,ss2]= np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[ss1,ss2]) ) ) + K[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(rdist[ss1,ss2]), kyun(rdist[ss1,ss2] ) ) + return K + + + + def Kdiag(self, X): + """Compute the diagonal of the covariance matrix associated to X.""" + Kdiag = np.zeros(X.shape[0]) + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + + Vu = self.variance_U + Vy=self.variance_Y + + k1 = (2*lu+ly)/(lu+ly)**2 + k2 = (ly-2*lu + 2*lu-ly ) / (ly-lu)**2 + k3 = 1/(lu+ly) + (lu)/(lu+ly)**2 + + slices = index_to_slices(X[:,-1]) + + for i, ss1 in enumerate(slices): + for s1 in ss1: + if i==0: + Kdiag[s1]+= self.variance_U + self.ubias + elif i==1: + Kdiag[s1]+= Vu*Vy*(k1+k2+k3) + else: + raise ValueError, "invalid input/output index" + #Kdiag[slices[0][0]]+= self.variance_U #matern32 diag + #Kdiag[slices[1][0]]+= self.variance_U*self.variance_Y*(k1+k2+k3) # diag + return Kdiag + + + def update_gradients_full(self, dL_dK, X, X2=None): + """derivative of the covariance matrix with respect to the parameters.""" + X,slices = X[:,:-1],index_to_slices(X[:,-1]) + if X2 is None: + X2,slices2 = X,slices + else: + X2,slices2 = X2[:,:-1],index_to_slices(X2[:,-1]) + #rdist = X[:,0][:,None] - X2[:,0][:,None].T + + rdist = X - X2.T + ly=1/self.lengthscale_Y + lu=np.sqrt(3)/self.lengthscale_U + + Vu=self.variance_U + Vy=self.variance_Y + Vyu = np.sqrt(Vy*ly*2) + dVdly = 0.5/np.sqrt(ly)*np.sqrt(2*Vy) + dVdVy = 0.5/np.sqrt(Vy)*np.sqrt(2*ly) + + rd=rdist.shape[0] + dktheta1 = np.zeros([rd,rd]) + dktheta2 = np.zeros([rd,rd]) + dkUdvar = np.zeros([rd,rd]) + dkYdvar = np.zeros([rd,rd]) + + dkdubias = np.zeros([rd,rd]) + + # dk dtheta for UU + UUdtheta1 = lambda dist: np.exp(-lu* dist)*dist + (-dist)*np.exp(-lu* dist)*(1+lu*dist) + UUdtheta2 = lambda dist: 0 + #UUdvar = lambda dist: (1 + lu*dist)*np.exp(-lu*dist) + UUdvar = lambda dist: (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist)) + + # dk dtheta for YY + + dk1theta1 = lambda dist: np.exp(-ly*dist)*2*(-lu)/(lu+ly)**3 + + dk2theta1 = lambda dist: (1.0)*( + 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) + +np.exp(-dist*lu)*(ly-2*lu+ly*lu*dist-dist*lu**2)*2*(ly-lu)**(-3) + +np.exp(-dist*ly)*2*(ly-lu)**(-2) + +np.exp(-dist*ly)*2*(2*lu-ly)*(ly-lu)**(-3) + ) + + 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) + + #dktheta1 = lambda dist: self.variance_U*self.variance_Y*(dk1theta1+dk2theta1+dk3theta1) + + + + + dk1theta2 = lambda dist: np.exp(-ly*dist) * ((lu+ly)**(-2)) * ( (-dist)*(2*lu+ly) + 1 + (-2)*(2*lu+ly)/(lu+ly) ) + + dk2theta2 =lambda dist: 1*( + np.exp(-dist*lu)*(ly-lu)**(-2) * ( 1+lu*dist+(-2)*(ly-2*lu+lu*ly*dist-dist*lu**2)*(ly-lu)**(-1) ) + +np.exp(-dist*ly)*(ly-lu)**(-2) * ( (-dist)*(2*lu-ly) -1+(2*lu-ly)*(-2)*(ly-lu)**(-1) ) + ) + + dk3theta2 = lambda dist: np.exp(-dist*lu) * (-3*lu-ly-dist*lu**2-lu*ly*dist)/(lu+ly)**3 + + #dktheta2 = lambda dist: self.variance_U*self.variance_Y*(dk1theta2 + dk2theta2 +dk3theta2) + + # kyy kernel + + k1 = lambda dist: np.exp(-ly*dist)*(2*lu+ly)/(lu+ly)**2 + 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 + k3 = lambda dist: np.exp(-lu*dist) * ( (1+lu*dist)/(lu+ly) + (lu)/(lu+ly)**2 ) + #dkdvar = k1+k2+k3 + + + + # cross covariance function + kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly))) + + 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) ) ) + + k2cros = lambda dist:np.exp(ly*dist)*( 1/(lu+ly) + lu/(lu+ly)**2 ) + # cross covariance kuy + kuyp = lambda dist:(kyu3(dist)) #t>0 kuy + kuyn = lambda dist:(k1cros(dist)+k2cros(dist)) #t<0 kuy + # cross covariance kyu + kyup = lambda dist:(k1cros(-dist)+k2cros(-dist)) #t>0 kyu + kyun = lambda dist:(kyu3(-dist)) #t<0 kyu + + # dk dtheta for UY + + + 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) ) + dkyu3dtheta1 = lambda dist: np.exp(-lu*dist)*(lu+ly)**(-1)* ( (-dist)*(1+dist*lu+lu*(lu+ly)**(-1)) -\ + (lu+ly)**(-1)*(1+dist*lu+lu*(lu+ly)**(-1)) +dist+(lu+ly)**(-1)-lu*(lu+ly)**(-2) ) + + dkcros2dtheta1 = lambda dist: np.exp(ly*dist)* ( -(ly+lu)**(-2) + (ly+lu)**(-2) + (-2)*lu*(lu+ly)**(-3) ) + dkcros2dtheta2 = lambda dist: np.exp(ly*dist)*dist* ( (ly+lu)**(-1) + lu*(lu+ly)**(-2) ) + \ + np.exp(ly*dist)*( -(lu+ly)**(-2) + lu*(-2)*(lu+ly)**(-3) ) + + dkcros1dtheta1 = lambda dist: np.exp(ly*dist)*( -(lu-ly)**(-2)*( 1-np.exp((lu-ly)*dist) + lu*dist*np.exp((lu-ly)*dist)+ \ + lu*(1-np.exp((lu-ly)*dist))/(lu-ly) ) + (lu-ly)**(-1)*( -np.exp( (lu-ly)*dist )*dist + dist*np.exp( (lu-ly)*dist)+\ + 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) -\ + lu*(1-np.exp((lu-ly)*dist))/(lu-ly)**2 ) ) + + dkcros1dtheta2 = lambda t: np.exp(ly*t)*t/(lu-ly)*( 1-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)+\ + lu*(1-np.exp((lu-ly)*t))/(lu-ly) )+\ + 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) )+\ + 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)+\ + lu*( 1-np.exp((lu-ly)*t) )/(lu-ly)**2 ) + + dkuypdtheta1 = lambda dist:(dkyu3dtheta1(dist)) #t>0 kuy + dkuyndtheta1 = lambda dist:(dkcros1dtheta1(dist)+dkcros2dtheta1(dist)) #t<0 kuy + # cross covariance kyu + dkyupdtheta1 = lambda dist:(dkcros1dtheta1(-dist)+dkcros2dtheta1(-dist)) #t>0 kyu + dkyundtheta1 = lambda dist:(dkyu3dtheta1(-dist)) #t<0 kyu + + dkuypdtheta2 = lambda dist:(dkyu3dtheta2(dist)) #t>0 kuy + dkuyndtheta2 = lambda dist:(dkcros1dtheta2(dist)+dkcros2dtheta2(dist)) #t<0 kuy + # cross covariance kyu + dkyupdtheta2 = lambda dist:(dkcros1dtheta2(-dist)+dkcros2dtheta2(-dist)) #t>0 kyu + dkyundtheta2 = lambda dist:(dkyu3dtheta2(-dist)) #t<0 kyu + + + for i, s1 in enumerate(slices): + for j, s2 in enumerate(slices2): + for ss1 in s1: + for ss2 in s2: + if i==0 and j==0: + #target[ss1,ss2] = kuu(np.abs(rdist[ss1,ss2])) + dktheta1[ss1,ss2] = Vu*UUdtheta1(np.abs(rdist[ss1,ss2])) + dktheta2[ss1,ss2] = 0 + dkUdvar[ss1,ss2] = UUdvar(np.abs(rdist[ss1,ss2])) + dkYdvar[ss1,ss2] = 0 + dkdubias[ss1,ss2] = 1 + elif i==0 and j==1: + ########target[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[s1[0],s2[0]]) ) ) + #np.where( rdist[ss1,ss2]>0 , kuyp(np.abs(rdist[ss1,ss2])), kuyn(np.abs(rdist[s1[0],s2[0]]) ) ) + #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]))) ) + #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]))) ) + dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkuypdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta1(rdist[ss1,ss2]) ) + dkUdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vyu*kuyp(rdist[ss1,ss2]), Vyu* kuyn(rdist[ss1,ss2]) ) + 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]) ) + dkYdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*dVdVy*kuyp(rdist[ss1,ss2]), Vu*dVdVy* kuyn(rdist[ss1,ss2]) ) + dkdubias[ss1,ss2] = 0 + elif i==1 and j==1: + #target[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2])) + 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]))) + 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]))) + dkUdvar[ss1,ss2] = self.variance_Y*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) ) + dkYdvar[ss1,ss2] = self.variance_U*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) ) + dkdubias[ss1,ss2] = 0 + else: + #######target[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[s1[0],s2[0]]) ) ) + #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])) ) + #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])) ) + dktheta1[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vu*Vyu*dkyupdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta1(rdist[ss1,ss2]) ) + dkUdvar[ss1,ss2] = np.where( rdist[ss1,ss2]>0 , Vyu*kyup(rdist[ss1,ss2]),Vyu*kyun(rdist[ss1,ss2])) + 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) +