def update_gradients_full(self, dL_dK, X, X2=None):
X,slices = X[:,:-<NUM_LIT:1>],index_to_slices(X[:,-<NUM_LIT:1>])<EOL>if X2 is None:<EOL><INDENT>X2,slices2 = X,slices<EOL><DEDENT>else:<EOL><INDENT>X2,slices2 = X2[:,:-<NUM_LIT:1>],index_to_slices(X2[:,-<NUM_LIT:1>])<EOL><DEDENT>rdist = X - X2.T<EOL>ly=<NUM_LIT:1>/self.lengthscale_Y<EOL>lu=np.sqrt(<NUM_LIT:3>)/self.lengthscale_U<EOL>Vu=self.variance_U<EOL>Vy=self.variance_Y<EOL>Vyu = np.sqrt(Vy*ly*<NUM_LIT:2>)<EOL>dVdly = <NUM_LIT:0.5>/np.sqrt(ly)*np.sqrt(<NUM_LIT:2>*Vy)<EOL>dVdVy = <NUM_LIT:0.5>/np.sqrt(Vy)*np.sqrt(<NUM_LIT:2>*ly)<EOL>rd=rdist.shape[<NUM_LIT:0>]<EOL>dktheta1 = np.zeros([rd,rd])<EOL>dktheta2 = np.zeros([rd,rd])<EOL>dkUdvar = np.zeros([rd,rd])<EOL>dkYdvar = np.zeros([rd,rd])<EOL>dkdubias = np.zeros([rd,rd])<EOL>UUdtheta1 = lambda dist: np.exp(-lu* dist)*dist + (-dist)*np.exp(-lu* dist)*(<NUM_LIT:1>+lu*dist)<EOL>UUdtheta2 = lambda dist: <NUM_LIT:0><EOL>UUdvar = lambda dist: (<NUM_LIT:1> + lu* np.abs(dist)) * np.exp(-lu * np.abs(dist))<EOL>dk1theta1 = lambda dist: np.exp(-ly*dist)*<NUM_LIT:2>*(-lu)/(lu+ly)**<NUM_LIT:3><EOL>dk2theta1 = lambda dist: (<NUM_LIT:1.0>)*(<EOL>np.exp(-lu*dist)*dist*(-ly+<NUM_LIT:2>*lu-lu*ly*dist+dist*lu**<NUM_LIT:2>)*(ly-lu)**(-<NUM_LIT:2>) + np.exp(-lu*dist)*(-<NUM_LIT:2>+ly*dist-<NUM_LIT:2>*dist*lu)*(ly-lu)**(-<NUM_LIT:2>)<EOL>+np.exp(-dist*lu)*(ly-<NUM_LIT:2>*lu+ly*lu*dist-dist*lu**<NUM_LIT:2>)*<NUM_LIT:2>*(ly-lu)**(-<NUM_LIT:3>)<EOL>+np.exp(-dist*ly)*<NUM_LIT:2>*(ly-lu)**(-<NUM_LIT:2>)<EOL>+np.exp(-dist*ly)*<NUM_LIT:2>*(<NUM_LIT:2>*lu-ly)*(ly-lu)**(-<NUM_LIT:3>)<EOL>)<EOL>dk3theta1 = lambda dist: np.exp(-dist*lu)*(lu+ly)**(-<NUM_LIT:2>)*((<NUM_LIT:2>*lu+ly+dist*lu**<NUM_LIT:2>+lu*ly*dist)*(-dist-<NUM_LIT:2>/(lu+ly))+<NUM_LIT:2>+<NUM_LIT:2>*lu*dist+ly*dist)<EOL>dk1theta2 = lambda dist: np.exp(-ly*dist) * ((lu+ly)**(-<NUM_LIT:2>)) * (  (-dist)*(<NUM_LIT:2>*lu+ly)  +  <NUM_LIT:1>  +  (-<NUM_LIT:2>)*(<NUM_LIT:2>*lu+ly)/(lu+ly)  )<EOL>dk2theta2 =lambda dist:  <NUM_LIT:1>*(<EOL>np.exp(-dist*lu)*(ly-lu)**(-<NUM_LIT:2>) * ( <NUM_LIT:1>+lu*dist+(-<NUM_LIT:2>)*(ly-<NUM_LIT:2>*lu+lu*ly*dist-dist*lu**<NUM_LIT:2>)*(ly-lu)**(-<NUM_LIT:1>) )<EOL>+np.exp(-dist*ly)*(ly-lu)**(-<NUM_LIT:2>) * ( (-dist)*(<NUM_LIT:2>*lu-ly) -<NUM_LIT:1>+(<NUM_LIT:2>*lu-ly)*(-<NUM_LIT:2>)*(ly-lu)**(-<NUM_LIT:1>) )<EOL>)<EOL>dk3theta2 = lambda dist: np.exp(-dist*lu) * (-<NUM_LIT:3>*lu-ly-dist*lu**<NUM_LIT:2>-lu*ly*dist)/(lu+ly)**<NUM_LIT:3><EOL>k1 = lambda dist: np.exp(-ly*dist)*(<NUM_LIT:2>*lu+ly)/(lu+ly)**<NUM_LIT:2><EOL>k2 = lambda dist: (np.exp(-lu*dist)*(ly-<NUM_LIT:2>*lu+lu*ly*dist-lu**<NUM_LIT:2>*dist) + np.exp(-ly*dist)*(<NUM_LIT:2>*lu-ly) ) / (ly-lu)**<NUM_LIT:2><EOL>k3 = lambda dist: np.exp(-lu*dist) * ( (<NUM_LIT:1>+lu*dist)/(lu+ly) + (lu)/(lu+ly)**<NUM_LIT:2> )<EOL>kyu3 = lambda dist:np.exp(-lu*dist)/(lu+ly)*(<NUM_LIT:1>+lu*(dist+<NUM_LIT:1>/(lu+ly)))<EOL>k1cros = lambda dist:np.exp(ly*dist)/(lu-ly) * ( <NUM_LIT:1>- np.exp( (lu-ly)*dist) + lu* ( dist*np.exp( (lu-ly)*dist ) + (<NUM_LIT:1>- np.exp( (lu-ly)*dist ) ) /(lu-ly)   )    )<EOL>k2cros = lambda dist:np.exp(ly*dist)*( <NUM_LIT:1>/(lu+ly) + lu/(lu+ly)**<NUM_LIT:2> )<EOL>kuyp = lambda dist:(kyu3(dist))       <EOL>kuyn = lambda dist:(k1cros(dist)+k2cros(dist))      <EOL>kyup = lambda dist:(k1cros(-dist)+k2cros(-dist))    <EOL>kyun = lambda dist:(kyu3(-dist))       <EOL>dkyu3dtheta2 = lambda dist: np.exp(-lu*dist) * ( (-<NUM_LIT:1>)*(lu+ly)**(-<NUM_LIT:2>)*(<NUM_LIT:1>+lu*dist+lu*(lu+ly)**(-<NUM_LIT:1>)) + (lu+ly)**(-<NUM_LIT:1>)*(-lu)*(lu+ly)**(-<NUM_LIT:2>) )<EOL>dkyu3dtheta1 = lambda dist: np.exp(-lu*dist)*(lu+ly)**(-<NUM_LIT:1>)* ( (-dist)*(<NUM_LIT:1>+dist*lu+lu*(lu+ly)**(-<NUM_LIT:1>)) -(lu+ly)**(-<NUM_LIT:1>)*(<NUM_LIT:1>+dist*lu+lu*(lu+ly)**(-<NUM_LIT:1>)) +dist+(lu+ly)**(-<NUM_LIT:1>)-lu*(lu+ly)**(-<NUM_LIT:2>) )<EOL>dkcros2dtheta1 = lambda dist: np.exp(ly*dist)* ( -(ly+lu)**(-<NUM_LIT:2>) + (ly+lu)**(-<NUM_LIT:2>) + (-<NUM_LIT:2>)*lu*(lu+ly)**(-<NUM_LIT:3>)  )<EOL>dkcros2dtheta2 = lambda dist: np.exp(ly*dist)*dist* ( (ly+lu)**(-<NUM_LIT:1>) + lu*(lu+ly)**(-<NUM_LIT:2>) ) +np.exp(ly*dist)*( -(lu+ly)**(-<NUM_LIT:2>) + lu*(-<NUM_LIT:2>)*(lu+ly)**(-<NUM_LIT:3>)  )<EOL>dkcros1dtheta1 = lambda dist: np.exp(ly*dist)*(     -(lu-ly)**(-<NUM_LIT:2>)*(  <NUM_LIT:1>-np.exp((lu-ly)*dist) + lu*dist*np.exp((lu-ly)*dist)+lu*(<NUM_LIT:1>-np.exp((lu-ly)*dist))/(lu-ly)  )  +  (lu-ly)**(-<NUM_LIT:1>)*(  -np.exp( (lu-ly)*dist )*dist + dist*np.exp( (lu-ly)*dist)+lu*dist**<NUM_LIT:2>*np.exp((lu-ly)*dist)+(<NUM_LIT:1>-np.exp((lu-ly)*dist))/(lu-ly) - lu*np.exp((lu-ly)*dist)*dist/(lu-ly) -lu*(<NUM_LIT:1>-np.exp((lu-ly)*dist))/(lu-ly)**<NUM_LIT:2>  )   )<EOL>dkcros1dtheta2 = lambda t: np.exp(ly*t)*t/(lu-ly)*( <NUM_LIT:1>-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)+lu*(<NUM_LIT:1>-np.exp((lu-ly)*t))/(lu-ly)  )+np.exp(ly*t)/(lu-ly)**<NUM_LIT:2>* ( <NUM_LIT:1>-np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t) + lu*( <NUM_LIT:1>-np.exp((lu-ly)*t) )/(lu-ly)  )+np.exp(ly*t)/(lu-ly)*( np.exp((lu-ly)*t)*t -lu*t*t*np.exp((lu-ly)*t) +lu*t*np.exp((lu-ly)*t)/(lu-ly)+lu*( <NUM_LIT:1>-np.exp((lu-ly)*t) )/(lu-ly)**<NUM_LIT:2> )<EOL>dkuypdtheta1 = lambda dist:(dkyu3dtheta1(dist))       <EOL>dkuyndtheta1 = lambda dist:(dkcros1dtheta1(dist)+dkcros2dtheta1(dist))      <EOL>dkyupdtheta1 = lambda dist:(dkcros1dtheta1(-dist)+dkcros2dtheta1(-dist))    <EOL>dkyundtheta1 = lambda dist:(dkyu3dtheta1(-dist))       <EOL>dkuypdtheta2 = lambda dist:(dkyu3dtheta2(dist))       <EOL>dkuyndtheta2 = lambda dist:(dkcros1dtheta2(dist)+dkcros2dtheta2(dist))      <EOL>dkyupdtheta2 = lambda dist:(dkcros1dtheta2(-dist)+dkcros2dtheta2(-dist))    <EOL>dkyundtheta2 = lambda dist:(dkyu3dtheta2(-dist))       <EOL>for i, s1 in enumerate(slices):<EOL><INDENT>for j, s2 in enumerate(slices2):<EOL><INDENT>for ss1 in s1:<EOL><INDENT>for ss2 in s2:<EOL><INDENT>if i==<NUM_LIT:0> and j==<NUM_LIT:0>:<EOL><INDENT>dktheta1[ss1,ss2] = Vu*UUdtheta1(np.abs(rdist[ss1,ss2]))<EOL>dktheta2[ss1,ss2] = <NUM_LIT:0><EOL>dkUdvar[ss1,ss2] = UUdvar(np.abs(rdist[ss1,ss2]))<EOL>dkYdvar[ss1,ss2] = <NUM_LIT:0><EOL>dkdubias[ss1,ss2] = <NUM_LIT:1><EOL><DEDENT>elif i==<NUM_LIT:0> and j==<NUM_LIT:1>:<EOL><INDENT>dktheta1[ss1,ss2] = np.where(  rdist[ss1,ss2]><NUM_LIT:0> , Vu*Vyu*dkuypdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta1(rdist[ss1,ss2]) )<EOL>dkUdvar[ss1,ss2] = np.where(  rdist[ss1,ss2]><NUM_LIT:0> , Vyu*kuyp(rdist[ss1,ss2]), Vyu* kuyn(rdist[ss1,ss2])  )<EOL>dktheta2[ss1,ss2] = np.where(  rdist[ss1,ss2]><NUM_LIT:0> , Vu*Vyu*dkuypdtheta2(rdist[ss1,ss2])+Vu*dVdly*kuyp(rdist[ss1,ss2]),Vu*Vyu*dkuyndtheta2(rdist[ss1,ss2])+Vu*dVdly*kuyn(rdist[ss1,ss2]) )<EOL>dkYdvar[ss1,ss2] = np.where(  rdist[ss1,ss2]><NUM_LIT:0> , Vu*dVdVy*kuyp(rdist[ss1,ss2]), Vu*dVdVy* kuyn(rdist[ss1,ss2])  )<EOL>dkdubias[ss1,ss2] = <NUM_LIT:0><EOL><DEDENT>elif i==<NUM_LIT:1> and j==<NUM_LIT:1>:<EOL><INDENT>dktheta1[ss1,ss2] = self.variance_U*self.variance_Y*(dk1theta1(np.abs(rdist[ss1,ss2]))+dk2theta1(np.abs(rdist[ss1,ss2]))+dk3theta1(np.abs(rdist[ss1,ss2])))<EOL>dktheta2[ss1,ss2] = self.variance_U*self.variance_Y*(dk1theta2(np.abs(rdist[ss1,ss2])) + dk2theta2(np.abs(rdist[ss1,ss2])) +dk3theta2(np.abs(rdist[ss1,ss2])))<EOL>dkUdvar[ss1,ss2] = self.variance_Y*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) )<EOL>dkYdvar[ss1,ss2] = self.variance_U*(k1(np.abs(rdist[ss1,ss2]))+k2(np.abs(rdist[ss1,ss2]))+k3(np.abs(rdist[ss1,ss2])) )<EOL>dkdubias[ss1,ss2] = <NUM_LIT:0><EOL><DEDENT>else:<EOL><INDENT>dktheta1[ss1,ss2] = np.where(  rdist[ss1,ss2]><NUM_LIT:0> , Vu*Vyu*dkyupdtheta1(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta1(rdist[ss1,ss2])  )<EOL>dkUdvar[ss1,ss2] = np.where(  rdist[ss1,ss2]><NUM_LIT:0> , Vyu*kyup(rdist[ss1,ss2]),Vyu*kyun(rdist[ss1,ss2]))<EOL>dktheta2[ss1,ss2] = np.where(  rdist[ss1,ss2]><NUM_LIT:0> , Vu*Vyu*dkyupdtheta2(rdist[ss1,ss2])+Vu*dVdly*kyup(rdist[ss1,ss2]),Vu*Vyu*dkyundtheta2(rdist[ss1,ss2])+Vu*dVdly*kyun(rdist[ss1,ss2])  )<EOL>dkYdvar[ss1,ss2] = np.where(  rdist[ss1,ss2]><NUM_LIT:0> , Vu*dVdVy*kyup(rdist[ss1,ss2]), Vu*dVdVy*kyun(rdist[ss1,ss2]))<EOL>dkdubias[ss1,ss2] = <NUM_LIT:0><EOL><DEDENT><DEDENT><DEDENT><DEDENT><DEDENT>self.variance_U.gradient = np.sum(dkUdvar * dL_dK)     <EOL>self.variance_Y.gradient = np.sum(dkYdvar * dL_dK)     <EOL>self.lengthscale_U.gradient = np.sum(dktheta1*(-np.sqrt(<NUM_LIT:3>)*self.lengthscale_U**(-<NUM_LIT:2>))* dL_dK)     <EOL>self.lengthscale_Y.gradient = np.sum(dktheta2*(-self.lengthscale_Y**(-<NUM_LIT:2>)) * dL_dK)              <EOL>self.ubias.gradient = np.sum(dkdubias * dL_dK)<EOL>
derivative of the covariance matrix with respect to the parameters.