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GPy: Some rewriting for the exponential and Matern kernels. They now pass the unit test.

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Nicolas 2012-12-03 10:26:28 +00:00
parent d71ad99db9
commit 3edd867ece
3 changed files with 63 additions and 49 deletions
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51
GPy/kern/Matern32.py
View file

@ -39,11 +39,13 @@ class Matern32(kernpart):
def get_param(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscales))
def set_param(self,x):
"""set the value of the parameters."""
assert x.size==(self.D+1)
self.variance = x[0]
self.lengthscales = x[1:]
def get_param_names(self):
"""return parameter names."""
if self.D==1:
@ -56,10 +58,37 @@ class Matern32(kernpart):
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
np.add(self.variance*(1+np.sqrt(3.)*dist)*np.exp(-np.sqrt(3.)*dist), target,target)
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
np.add(target,self.variance,target)
def dK_dtheta(self,partial,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
dvar = (1+np.sqrt(3.)*dist)*np.exp(-np.sqrt(3.)*dist)
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
target[0] += np.sum(dvar*partial)
target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
def dKdiag_dtheta(self,partial,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
target[0] += np.sum(partial)
def dK_dX(self,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.lengthscales),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
dK_dX += - np.transpose(3*self.variance*dist*np.exp(-np.sqrt(3)*dist)*ddist_dX,(1,0,2))
target += np.sum(dK_dX*partial.T[:,:,None],0)
def dKdiag_dX(self,X,target):
pass
def Gram_matrix(self,F,F1,F2,lower,upper):
"""
Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to D=1.
@ -87,25 +116,3 @@ class Matern32(kernpart):
#return(G)
return(self.lengthscales**3/(12.*np.sqrt(3)*self.variance) * G + 1./self.variance*np.dot(Flower,Flower.T) + self.lengthscales**2/(3.*self.variance)*np.dot(F1lower,F1lower.T))
def dK_dtheta(self,X,X2,target):
"""derivative of the cross-covariance matrix with respect to the parameters (shape is NxMxNparam)"""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
dvar = (1+np.sqrt(3.)*dist)*np.exp(-np.sqrt(3.)*dist)
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
dl = (self.variance* 3 * dist * np.exp(-np.sqrt(3.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
np.add(target[:,:,0],dvar, target[:,:,0])
np.add(target[:,:,1:],dl, target[:,:,1:])
def dKdiag_dtheta(self,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters (shape is NxNparam)"""
np.add(target[:,0],1.,target[:,0])
def dK_dX(self,X,X2,target):
"""derivative of the covariance matrix with respect to X (*! shape is NxMxD !*)."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
target += - np.transpose(3*self.variance*dist*np.exp(-np.sqrt(3)*dist)*ddist_dX,(1,0,2))
def dKdiag_dX(self,X,target):
pass

55
GPy/kern/Matern52.py
View file

@ -33,33 +33,61 @@ class Matern52(kernpart):
self.Nparam = self.D + 1
self.name = 'Mat52'
self.set_param(np.hstack((variance,lengthscales)))
self._Z, self._mu, self._S = np.empty(shape=(3,1)) # cached versions of Z,mu,S
def get_param(self):
"""return the value of the parameters."""
return np.hstack((self.variance,self.lengthscales))
def set_param(self,x):
"""set the value of the parameters."""
assert x.size==(self.D+1)
self.variance = x[0]
self.lengthscales = x[1:]
self.lengthscales2 = np.square(self.lengthscales)
self._Z, self._mu, self._S = np.empty(shape=(3,1)) # cached versions of Z,mu,S
def get_param_names(self):
"""return parameter names."""
if self.D==1:
return ['variance','lengthscale']
else:
return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscales.size)]
def K(self,X,X2,target):
"""Compute the covariance matrix between X and X2."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
np.add(self.variance*(1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist), target,target)
def Kdiag(self,X,target):
"""Compute the diagonal of the covariance matrix associated to X."""
np.add(target,self.variance,target)
def dK_dtheta(self,partial,X,X2,target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
dvar = (1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist)
dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
target[0] += np.sum(dvar*partial)
target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
def dKdiag_dtheta(self,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters."""
target[0] += np.sum(partial)
def dK_dX(self,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.lengthscales),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
dK_dX += - np.transpose(self.variance*5./3*dist*(1+np.sqrt(5)*dist)*np.exp(-np.sqrt(5)*dist)*ddist_dX,(1,0,2))
target += np.sum(dK_dX*partial.T[:,:,None],0)
def dKdiag_dX(self,X,target):
pass
def Gram_matrix(self,F,F1,F2,F3,lower,upper):
"""
Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to D=1.
@ -91,26 +119,5 @@ class Matern52(kernpart):
orig2 = 3./5*self.lengthscales**2 * ( np.dot(F1lower,F1lower.T) + 1./8*np.dot(Flower,F2lower.T) + 1./8*np.dot(F2lower,Flower.T))
return(1./self.variance* (G_coef*G + orig + orig2))
def dK_dtheta(self,X,X2,target):
"""derivative of the cross-covariance matrix with respect to the parameters (shape is NxMxNparam)"""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
invdist = 1./np.where(dist!=0.,dist,np.inf)
dist2M = np.square(X[:,None,:]-X2[None,:,:])/self.lengthscales**3
dvar = (1+np.sqrt(5.)*dist+5./3*dist**2)*np.exp(-np.sqrt(5.)*dist)
dl = (self.variance * 5./3 * dist * (1 + np.sqrt(5.)*dist ) * np.exp(-np.sqrt(5.)*dist))[:,:,np.newaxis] * dist2M*invdist[:,:,np.newaxis]
np.add(target[:,:,0],dvar, target[:,:,0])
np.add(target[:,:,1:],dl, target[:,:,1:])
def dKdiag_dtheta(self,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters (shape is NxNparam)"""
np.add(target[:,0],1.,target[:,0])
def dK_dX(self,X,X2,target):
"""derivative of the covariance matrix with respect to X (*! shape is NxMxD !*)."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)
target += - np.transpose(self.variance*5./3*dist*(1+np.sqrt(5)*dist)*np.exp(-np.sqrt(5)*dist)*ddist_dX,(1,0,2))
def dKdiag_dX(self,X,target):
pass

6
GPy/kern/exponential.py
View file

@ -62,7 +62,7 @@ class exponential(kernpart):
np.add(target,self.variance,target)
def dK_dtheta(self,partial,X,X2,target):
"""derivative of the cross-covariance matrix with respect to the parameters (shape is NxMxNparam)"""
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.sqrt(np.sum(np.square((X[:,None,:]-X2[None,:,:])/self.lengthscales),-1))
invdist = 1./np.where(dist!=0.,dist,np.inf)
@ -73,12 +73,12 @@ class exponential(kernpart):
target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
def dKdiag_dtheta(self,partial,X,target):
"""derivative of the diagonal of the covariance matrix with respect to the parameters (shape is NxNparam)"""
"""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(partial)
def dK_dX(self,X,X2,target):
"""derivative of the covariance matrix with respect to X (*! shape is NxMxD !*)."""
"""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.lengthscales),-1))[:,:,None]
ddist_dX = (X[:,None,:]-X2[None,:,:])/self.lengthscales**2/np.where(dist!=0.,dist,np.inf)