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Bug in ODE_UY fix
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Alan Saul
parent
990dab77ff
commit
997b5d596d
1 changed files with 20 additions and 16 deletions
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@ -7,7 +7,7 @@ import numpy as np
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def index_to_slices(index):
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"""
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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.
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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.
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e.g.
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>>> index = np.asarray([0,0,0,1,1,1,2,2,2])
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@ -38,7 +38,7 @@ class ODE_UY(Kernpart):
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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 input_lengthU: the number of input U length
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:type input_dim: int
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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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@ -96,7 +96,7 @@ class ODE_UY(Kernpart):
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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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# 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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#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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@ -110,14 +110,14 @@ class ODE_UY(Kernpart):
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ly=1/self.lengthscaleY
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lu=np.sqrt(3)/self.lengthscaleU
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#iu=self.input_lengthU #dimention of U
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Vu=self.varianceU
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Vy=self.varianceY
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kuu = lambda dist:Vu * (1 + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist))
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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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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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@ -127,7 +127,7 @@ class ODE_UY(Kernpart):
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kuyp = lambda dist:Vu*Vy*(kyu3(dist)) #t>0 kuy
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kuyn = lambda dist:Vu*Vy*(k1(dist)+k2(dist)) #t<0 kuy
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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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@ -160,22 +160,22 @@ class ODE_UY(Kernpart):
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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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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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target[s1]+= self.varianceU
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target[s1]+= self.varianceU
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elif i==1:
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target[s1]+= self.varianceU*self.varianceY*(k1+k2+k3)
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else:
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raise ValueError, "invalid input/output index"
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#target[slices[0][0]]+= self.varianceU #matern32 diag
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#target[slices[1][0]]+= self.varianceU*self.varianceY*(k1+k2+k3) # diag
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@ -207,13 +207,13 @@ class ODE_UY(Kernpart):
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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 = lambda dist: 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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dk2theta1 = lambda dist: 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 = 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.varianceU*self.varianceY*(dk1theta1+dk2theta1+dk3theta1)
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@ -235,7 +235,7 @@ class ODE_UY(Kernpart):
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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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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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@ -246,12 +246,16 @@ class ODE_UY(Kernpart):
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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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pass
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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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pass
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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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pass
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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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pass
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