ODE_UY

GPy/kern/parts/ODE_UY.py

@@ -0,0 +1,253 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+
+from kernpart import Kernpart
+import numpy as np
+
+def index_to_slices(index):
+    """
+    take a numpy array of integers (index) and return a  nested list of slices such that the slices describe the start, stop points for each integer in the index. 
+
+    e.g.
+    >>> index = np.asarray([0,0,0,1,1,1,2,2,2])
+    returns
+    >>> [[slice(0,3,None)],[slice(3,6,None)],[slice(6,9,None)]]
+
+    or, a more complicated example
+    >>> index = np.asarray([0,0,1,1,0,2,2,2,1,1])
+    returns
+    >>> [[slice(0,2,None),slice(4,5,None)],[slice(2,4,None),slice(8,10,None)],[slice(5,8,None)]]
+    """
+
+    #contruct the return structure
+    ind = np.asarray(index,dtype=np.int64)
+    ret = [[] for i in range(ind.max()+1)]
+
+    #find the switchpoints
+    ind_ = np.hstack((ind,ind[0]+ind[-1]+1))
+    switchpoints = np.nonzero(ind_ - np.roll(ind_,+1))[0]
+
+    [ret[ind_i].append(slice(*indexes_i)) for ind_i,indexes_i in zip(ind[switchpoints[:-1]],zip(switchpoints,switchpoints[1:]))]
+    return ret
+
+class ODE_UY(Kernpart):
+    """
+    kernel resultiong from a first order ODE with OU driving GP
+
+    :param input_dim: the number of input dimension, has to be equal to one
+    :type input_dim: int
+    :param input_lengthU: the number of input U length
+    :type input_dim: int   
+    :param varianceU: variance of the driving GP
+    :type varianceU: float
+    :param lengthscaleU: lengthscale of the driving GP  (sqrt(3)/lengthscaleU)
+    :type lengthscaleU: float
+    :param varianceY: 'variance' of the transfer function
+    :type varianceY: float
+    :param lengthscaleY: 'lengthscale' of the transfer function (1/lengthscaleY)
+    :type lengthscaleY: float
+    :rtype: kernel object
+
+    """
+
+
+
+
+    def __init__(self, input_dim=2,varianceU=1., varianceY=1., lengthscaleU=None, lengthscaleY=None):
+        assert input_dim==2, "Only defined for input_dim = 1"
+        self.input_dim = input_dim
+        self.num_params = 4
+        self.name = 'ODE_UY'
+
+
+        if lengthscaleU is not None:
+            lengthscaleU = np.asarray(lengthscaleU)
+            assert lengthscaleU.size == 1, "lengthscaleU should be one dimensional"
+        else:
+            lengthscaleU = np.ones(1)
+        if lengthscaleY is not None:
+            lengthscaleY = np.asarray(lengthscaleY)
+            assert lengthscaleY.size == 1, "lengthscaleY should be one dimensional"
+        else:
+            lengthscaleY = np.ones(1)
+            #lengthscaleY = 0.5
+        self._set_params(np.hstack((varianceU, varianceY, lengthscaleU,lengthscaleY)))
+
+    def _get_params(self):
+        """return the value of the parameters."""
+        return np.hstack((self.varianceU,self.varianceY, self.lengthscaleU,self.lengthscaleY))
+
+    def _set_params(self, x):
+        """set the value of the parameters."""
+        assert x.size == self.num_params
+
+        self.varianceU = x[0]
+        self.varianceY = x[1]
+        self.lengthscaleU = x[2]
+        self.lengthscaleY = x[3]
+
+
+    def _get_param_names(self):
+        """return parameter names."""
+        return ['varianceU','varianceY', 'lengthscaleU', 'lengthscaleY']
+
+
+    def K(self, X, X2, target):
+        """Compute the covariance matrix between X and X2."""
+
+        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.lengthscaleY
+        lu=np.sqrt(3)/self.lengthscaleU
+        #iu=self.input_lengthU  #dimention of U
+        
+        Vu=self.varianceU
+        Vy=self.varianceY
+
+        kuu = lambda dist:Vu * (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist))
+
+        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))
+
+        kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(1+lu*(dist+1/(lu+ly)))
+        kyup = lambda dist:Vu*Vy*(k1(dist)+k2(dist))    #t>0 kyu
+        kyun = lambda dist:Vu*Vy*(kyu3(dist))       #t<0 kyu
+
+        kuyp = lambda dist:Vu*Vy*(kyu3(dist))       #t>0 kuy
+        kuyn = lambda dist:Vu*Vy*(k1(dist)+k2(dist))      #t<0 kuy
+        
+        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]))
+                        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]]) )   )
+                        elif i==1 and j==1:
+                            target[ss1,ss2] = kyy(np.abs(rdist[ss1,ss2]))
+                        else:
+                            target[ss1,ss2] = np.where(  rdist[ss1,ss2]>0 , kyup(np.abs(rdist[ss1,ss2])), kyun(np.abs(rdist[s1[0],s2[0]]) )   )
+
+
+        #KUU = kuu(np.abs(rdist[:iu,:iu]))
+
+        #KYY = kyy(np.abs(rdist[iu:,iu:]))
+
+        #KYU = np.where(rdist[iu:,:iu]>0,kyup(np.abs(rdist[iu:,:iu])),kyun(np.abs(rdist[iu:,:iu]) ))
+
+        #KUY = np.where(rdist[:iu,iu:]>0,kuyp(np.abs(rdist[:iu,iu:])),kuyn(np.abs(rdist[:iu,iu:]) ))
+
+        #ker=np.vstack((np.hstack([KUU,KUY]),np.hstack([KYU,KYY])))
+
+        #np.add(ker, target, target)
+
+    def Kdiag(self, X, target):
+        """Compute the diagonal of the covariance matrix associated to X."""
+        ly=1/self.lengthscaleY
+        lu=np.sqrt(3)/self.lengthscaleU
+        #ly=self.lengthscaleY
+        #lu=self.lengthscaleU
+        
+        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:
+                    target[s1]+= self.varianceU 
+                elif i==1:
+                    target[s1]+= self.varianceU*self.varianceY*(k1+k2+k3)
+                else:
+                    raise ValueError, "invalid input/output index"
+        
+        #target[slices[0][0]]+= self.varianceU   #matern32 diag
+        #target[slices[1][0]]+= self.varianceU*self.varianceY*(k1+k2+k3)  #  diag
+
+
+
+
+
+
+    def dK_dtheta(self, dL_dK, X, X2, target):
+        """derivative of the covariance matrix with respect to the parameters."""
+        if X2 is None: X2 = X
+        dist = np.abs(X - X2.T)
+
+        ly=1/self.lengthscaleY
+        lu=np.sqrt(3)/self.lengthscaleU
+        #ly=self.lengthscaleY
+        #lu=self.lengthscaleU
+
+        dk1theta1 = lambda dist: np.exp(-ly*dist)*2*(-lu)/(lu+ly)**3
+        #c=np.sqrt(3)
+        #t1=c/lu
+        #t2=1/ly
+        #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   )
+
+        dk2theta1 = lambda dist: 1*( 
+            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.varianceU*self.varianceY*(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.varianceU*self.varianceY*(dk1theta2 + dk2theta2 +dk3theta2)
+
+
+
+        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
+
+        target[0] += np.sum(self.varianceY*dkdvar * dL_dK)
+        target[1] += np.sum(self.varianceU*dkdvar * dL_dK)
+        target[2] += np.sum(dktheta1*(-np.sqrt(3)*self.lengthscaleU**(-2)) * dL_dK)
+        target[3] += np.sum(dktheta2*(-self.lengthscaleY**(-2)) * dL_dK)
+
+
+    # def dKdiag_dtheta(self, dL_dKdiag, X, target):
+    #     """derivative of the diagonal of the covariance matrix with respect to the parameters."""
+    #     # NB: derivative of diagonal elements wrt lengthscale is 0
+    #     target[0] += np.sum(dL_dKdiag)
+
+    # def dK_dX(self, dL_dK, X, X2, target):
+    #     """derivative of the covariance matrix with respect to X."""
+    #     if X2 is None: X2 = X
+    #     dist = np.sqrt(np.sum(np.square((X[:, None, :] - X2[None, :, :]) / self.lengthscale), -1))[:, :, None]
+    #     ddist_dX = (X[:, None, :] - X2[None, :, :]) / self.lengthscale ** 2 / np.where(dist != 0., dist, np.inf)
+    #     dK_dX = -np.transpose(self.variance * np.exp(-dist) * ddist_dX, (1, 0, 2))
+    #     target += np.sum(dK_dX * dL_dK.T[:, :, None], 0)
+
+    # def dKdiag_dX(self, dL_dKdiag, X, target):
+    #     pass

GPy/kern/parts/__init__.py

@@ -14,7 +14,7 @@ import Matern32
 import Matern52
 import mlp
 import ODE_1
-#import ODE_UY
+import ODE_UY
 import periodic_exponential
 import periodic_Matern32
 import periodic_Matern52