mirror of
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Merge branch 'master' of github.com:SheffieldML/GPy
This commit is contained in:
James Hensman
commit
054faae4af
4 changed files with 202 additions and 3 deletions
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@ -92,6 +92,13 @@ class linear(kernpart):
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self._psi_computations(Z,mu,S)
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self._psi_computations(Z,mu,S)
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target += np.sum(self.variances*self.mu2_S,1)
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target += np.sum(self.variances*self.mu2_S,1)
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def dKdiag_dtheta(self,partial, X, target):
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tmp = partial[:,None]*X**2
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if self.ARD:
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target += tmp.sum(0)
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else:
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target += tmp.sum()
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def dpsi0_dtheta(self,partial,Z,mu,S,target):
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def dpsi0_dtheta(self,partial,Z,mu,S,target):
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self._psi_computations(Z,mu,S)
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self._psi_computations(Z,mu,S)
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tmp = partial[:, None] * self.mu2_S
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tmp = partial[:, None] * self.mu2_S
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@ -171,3 +171,66 @@ class periodic_Matern32(kernpart):
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target[1] += np.sum(dK_dlen*partial)
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target[1] += np.sum(dK_dlen*partial)
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#np.add(target[:,:,2],dK_dper, target[:,:,2])
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#np.add(target[:,:,2],dK_dper, target[:,:,2])
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target[2] += np.sum(dK_dper*partial)
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target[2] += np.sum(dK_dper*partial)
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def dKdiag_dtheta(self,partial,X,target):
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"""derivative of the diagonal covariance matrix with respect to the parameters"""
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FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
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La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega, self.a[2]*self.basis_omega**2))
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Lo = np.column_stack((self.basis_omega,self.basis_omega,self.basis_omega))
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Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2,self.basis_phi+np.pi))
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r,omega,phi = self._cos_factorization(La,Lo,Lp)
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Gint = self._int_computation( r,omega,phi, r,omega,phi)
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Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
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F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
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#dK_dvar
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dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX.T)
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#dK_dlen
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da_dlen = [-6/self.lengthscale**3,-2*np.sqrt(3)/self.lengthscale**2,0.]
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db_dlen = [0.,2*self.lengthscale/3.]
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dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega,da_dlen[2]*self.basis_omega**2))
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r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
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dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
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dGint_dlen = dGint_dlen + dGint_dlen.T
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dG_dlen = self.lengthscale**2/(4*np.sqrt(3))*Gint + self.lengthscale**3/(12*np.sqrt(3))*dGint_dlen + db_dlen[0]*np.dot(Flower,Flower.T) + db_dlen[1]*np.dot(F1lower,F1lower.T)
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dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX.T)
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#dK_dper
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dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
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dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period, -self.a[2]*self.basis_omega**3/self.period))
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dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi,self.basis_phi+np.pi*3/2))
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r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
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IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
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IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
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IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
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IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
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IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
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IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
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IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
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IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
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IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
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IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
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dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period))
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dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi))
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r2,omega2,phi2 = self._cos_factorization(dLa_dper2,Lo[:,0:2],dLp_dper2)
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dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
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dGint_dper = dGint_dper + dGint_dper.T
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dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
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dF1lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower)+self._cos(-self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
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dG_dper = 1./self.variance*(self.lengthscale**3/(12*np.sqrt(3))*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)) + self.b[1]*(np.dot(dF1lower_dper,F1lower.T)+np.dot(F1lower,dF1lower_dper.T)))
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dK_dper = 2* mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
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target[0] += np.sum(np.diag(dK_dvar)*partial)
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target[1] += np.sum(np.diag(dK_dlen)*partial)
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target[2] += np.sum(np.diag(dK_dper)*partial)
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@ -183,3 +183,74 @@ class periodic_Matern52(kernpart):
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target[1] += np.sum(dK_dlen*partial)
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target[1] += np.sum(dK_dlen*partial)
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#np.add(target[:,:,2],dK_dper, target[:,:,2])
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#np.add(target[:,:,2],dK_dper, target[:,:,2])
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target[2] += np.sum(dK_dper*partial)
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target[2] += np.sum(dK_dper*partial)
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def dKdiag_dtheta(self,partial,X,target):
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"""derivative of the diagonal of the covariance matrix with respect to the parameters"""
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FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
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La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)), self.a[1]*self.basis_omega, self.a[2]*self.basis_omega**2, self.a[3]*self.basis_omega**3))
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Lo = np.column_stack((self.basis_omega, self.basis_omega, self.basis_omega, self.basis_omega))
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Lp = np.column_stack((self.basis_phi, self.basis_phi+np.pi/2, self.basis_phi+np.pi, self.basis_phi+np.pi*3/2))
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r,omega,phi = self._cos_factorization(La,Lo,Lp)
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Gint = self._int_computation( r,omega,phi, r,omega,phi)
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Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
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F1lower = np.array(self._cos(self.basis_alpha*self.basis_omega,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
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F2lower = np.array(self._cos(self.basis_alpha*self.basis_omega**2,self.basis_omega,self.basis_phi+np.pi)(self.lower))[:,None]
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#dK_dvar
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dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX2.T)
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#dK_dlen
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da_dlen = [-3*self.a[0]/self.lengthscale, -2*self.a[1]/self.lengthscale, -self.a[2]/self.lengthscale, 0.]
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db_dlen = [0., 4*self.b[1]/self.lengthscale, 2*self.b[2]/self.lengthscale, 2*self.b[3]/self.lengthscale, 2*self.b[4]/self.lengthscale]
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dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)), da_dlen[1]*self.basis_omega, da_dlen[2]*self.basis_omega**2, da_dlen[3]*self.basis_omega**3))
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r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
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dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
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dGint_dlen = dGint_dlen + dGint_dlen.T
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dlower_terms_dlen = db_dlen[0]*np.dot(Flower,Flower.T) + db_dlen[1]*np.dot(F2lower,F2lower.T) + db_dlen[2]*np.dot(F1lower,F1lower.T) + db_dlen[3]*np.dot(F2lower,Flower.T) + db_dlen[4]*np.dot(Flower,F2lower.T)
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dG_dlen = 15*self.lengthscale**4/(400*np.sqrt(5))*Gint + 3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dlen + dlower_terms_dlen
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dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX.T)
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#dK_dper
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dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
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dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period, -self.a[2]*self.basis_omega**3/self.period, -self.a[3]*self.basis_omega**4/self.period))
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dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi,self.basis_phi+np.pi*3/2,self.basis_phi))
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r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
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IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
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IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
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IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
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IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
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IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
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IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
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IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
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IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + .5*self.upper**2*np.cos(phi-phi1.T)
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IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + .5*self.lower**2*np.cos(phi-phi1.T)
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IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
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dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period, -2*self.a[2]*self.basis_omega**2/self.period, -3*self.a[3]*self.basis_omega**3/self.period))
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dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2, self.basis_phi+np.pi, self.basis_phi+np.pi*3/2))
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r2,omega2,phi2 = self._cos_factorization(dLa_dper2,Lo[:,0:2],dLp_dper2)
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dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
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dGint_dper = dGint_dper + dGint_dper.T
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dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
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dF1lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower)+self._cos(-self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
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dF2lower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega**3/self.period,self.basis_omega,self.basis_phi+np.pi*3/2)(self.lower) + self._cos(-2*self.basis_alpha*self.basis_omega**2/self.period,self.basis_omega,self.basis_phi+np.pi)(self.lower))[:,None]
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dlower_terms_dper = self.b[0] * (np.dot(dFlower_dper,Flower.T) + np.dot(Flower.T,dFlower_dper))
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dlower_terms_dper += self.b[1] * (np.dot(dF2lower_dper,F2lower.T) + np.dot(F2lower,dF2lower_dper.T)) - 4*self.b[1]/self.period*np.dot(F2lower,F2lower.T)
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dlower_terms_dper += self.b[2] * (np.dot(dF1lower_dper,F1lower.T) + np.dot(F1lower,dF1lower_dper.T)) - 2*self.b[2]/self.period*np.dot(F1lower,F1lower.T)
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dlower_terms_dper += self.b[3] * (np.dot(dF2lower_dper,Flower.T) + np.dot(F2lower,dFlower_dper.T)) - 2*self.b[3]/self.period*np.dot(F2lower,Flower.T)
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dlower_terms_dper += self.b[4] * (np.dot(dFlower_dper,F2lower.T) + np.dot(Flower,dF2lower_dper.T)) - 2*self.b[4]/self.period*np.dot(Flower,F2lower.T)
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dG_dper = 1./self.variance*(3*self.lengthscale**5/(400*np.sqrt(5))*dGint_dper + 0.5*dlower_terms_dper)
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dK_dper = 2*mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
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target[0] += np.sum(np.diag(dK_dvar)*partial)
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target[1] += np.sum(np.diag(dK_dlen)*partial)
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target[2] += np.sum(np.diag(dK_dper)*partial)
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@ -162,9 +162,67 @@ class periodic_exponential(kernpart):
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dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
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dK_dper = mdot(dFX_dper,self.Gi,FX2.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX2.T) + mdot(FX,self.Gi,dFX2_dper.T)
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# np.add(target[:,:,0],dK_dvar, target[:,:,0])
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target[0] += np.sum(dK_dvar*partial)
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target[0] += np.sum(dK_dvar*partial)
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#np.add(target[:,:,1],dK_dlen, target[:,:,1])
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target[1] += np.sum(dK_dlen*partial)
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target[1] += np.sum(dK_dlen*partial)
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#np.add(target[:,:,2],dK_dper, target[:,:,2])
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target[2] += np.sum(dK_dper*partial)
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target[2] += np.sum(dK_dper*partial)
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def dKdiag_dtheta(self,partial,X,target):
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"""derivative of the diagonal of the covariance matrix with respect to the parameters"""
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FX = self._cos(self.basis_alpha[None,:],self.basis_omega[None,:],self.basis_phi[None,:])(X)
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La = np.column_stack((self.a[0]*np.ones((self.n_basis,1)),self.a[1]*self.basis_omega))
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Lo = np.column_stack((self.basis_omega,self.basis_omega))
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Lp = np.column_stack((self.basis_phi,self.basis_phi+np.pi/2))
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r,omega,phi = self._cos_factorization(La,Lo,Lp)
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Gint = self._int_computation( r,omega,phi, r,omega,phi)
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Flower = np.array(self._cos(self.basis_alpha,self.basis_omega,self.basis_phi)(self.lower))[:,None]
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#dK_dvar
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dK_dvar = 1./self.variance*mdot(FX,self.Gi,FX.T)
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#dK_dlen
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da_dlen = [-1./self.lengthscale**2,0.]
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dLa_dlen = np.column_stack((da_dlen[0]*np.ones((self.n_basis,1)),da_dlen[1]*self.basis_omega))
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r1,omega1,phi1 = self._cos_factorization(dLa_dlen,Lo,Lp)
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dGint_dlen = self._int_computation(r1,omega1,phi1, r,omega,phi)
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dGint_dlen = dGint_dlen + dGint_dlen.T
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dG_dlen = 1./2*Gint + self.lengthscale/2*dGint_dlen
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dK_dlen = -mdot(FX,self.Gi,dG_dlen/self.variance,self.Gi,FX.T)
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||||||
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#dK_dper
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dFX_dper = self._cos(-self.basis_alpha[None,:]*self.basis_omega[None,:]/self.period*X ,self.basis_omega[None,:],self.basis_phi[None,:]+np.pi/2)(X)
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||||||
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||||||
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dLa_dper = np.column_stack((-self.a[0]*self.basis_omega/self.period, -self.a[1]*self.basis_omega**2/self.period))
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||||||
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dLp_dper = np.column_stack((self.basis_phi+np.pi/2,self.basis_phi+np.pi))
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r1,omega1,phi1 = self._cos_factorization(dLa_dper,Lo,dLp_dper)
|
||||||
|
|
||||||
|
IPPprim1 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi/2))
|
||||||
|
IPPprim1 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + 1./(omega-omega1.T)*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi/2))
|
||||||
|
IPPprim2 = self.upper*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi/2) + self.upper*np.cos(phi-phi1.T))
|
||||||
|
IPPprim2 -= self.lower*(1./(omega+omega1.T)*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi/2) + self.lower*np.cos(phi-phi1.T))
|
||||||
|
IPPprim = np.where(np.isnan(IPPprim1),IPPprim2,IPPprim1)
|
||||||
|
|
||||||
|
IPPint1 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.upper+phi-phi1.T-np.pi)
|
||||||
|
IPPint1 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./(omega-omega1.T)**2*np.cos((omega-omega1.T)*self.lower+phi-phi1.T-np.pi)
|
||||||
|
IPPint2 = 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.upper+phi+phi1.T-np.pi) + 1./2*self.upper**2*np.cos(phi-phi1.T)
|
||||||
|
IPPint2 -= 1./(omega+omega1.T)**2*np.cos((omega+omega1.T)*self.lower+phi+phi1.T-np.pi) + 1./2*self.lower**2*np.cos(phi-phi1.T)
|
||||||
|
IPPint = np.where(np.isnan(IPPint1),IPPint2,IPPint1)
|
||||||
|
|
||||||
|
dLa_dper2 = np.column_stack((-self.a[1]*self.basis_omega/self.period))
|
||||||
|
dLp_dper2 = np.column_stack((self.basis_phi+np.pi/2))
|
||||||
|
r2,omega2,phi2 = dLa_dper2.T,Lo[:,0:1],dLp_dper2.T
|
||||||
|
|
||||||
|
dGint_dper = np.dot(r,r1.T)/2 * (IPPprim - IPPint) + self._int_computation(r2,omega2,phi2, r,omega,phi)
|
||||||
|
dGint_dper = dGint_dper + dGint_dper.T
|
||||||
|
|
||||||
|
dFlower_dper = np.array(self._cos(-self.lower*self.basis_alpha*self.basis_omega/self.period,self.basis_omega,self.basis_phi+np.pi/2)(self.lower))[:,None]
|
||||||
|
|
||||||
|
dG_dper = 1./self.variance*(self.lengthscale/2*dGint_dper + self.b[0]*(np.dot(dFlower_dper,Flower.T)+np.dot(Flower,dFlower_dper.T)))
|
||||||
|
|
||||||
|
dK_dper = 2*mdot(dFX_dper,self.Gi,FX.T) - mdot(FX,self.Gi,dG_dper,self.Gi,FX.T)
|
||||||
|
|
||||||
|
target[0] += np.sum(np.diag(dK_dvar)*partial)
|
||||||
|
target[1] += np.sum(np.diag(dK_dlen)*partial)
|
||||||
|
target[2] += np.sum(np.diag(dK_dper)*partial)
|
||||||
|
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue