diff --git a/GPy/kern/Matern32.py b/GPy/kern/Matern32.py index c37bd5c0..8223b37a 100644 --- a/GPy/kern/Matern32.py +++ b/GPy/kern/Matern32.py @@ -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 - diff --git a/GPy/kern/Matern52.py b/GPy/kern/Matern52.py index 4af65a89..65059a5b 100644 --- a/GPy/kern/Matern52.py +++ b/GPy/kern/Matern52.py @@ -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 diff --git a/GPy/kern/exponential.py b/GPy/kern/exponential.py index 402ebd82..ba97881e 100644 --- a/GPy/kern/exponential.py +++ b/GPy/kern/exponential.py @@ -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)