def update_gradients_full(self, dL_dK, X, X2=None):
if X2 is None:<EOL><INDENT>X2 = X<EOL><DEDENT>base = np.pi * (X[:, None, :] - X2[None, :, :]) / self.period<EOL>sin_base = np.sin( base )<EOL>exp_dist = np.exp( -<NUM_LIT:0.5>* np.sum( np.square(  sin_base / self.lengthscale ), axis = -<NUM_LIT:1> ) )<EOL>dwl = self.variance * (<NUM_LIT:1.0>/np.square(self.lengthscale)) * sin_base*np.cos(base) * (base / self.period)<EOL>dl = self.variance * np.square( sin_base) / np.power( self.lengthscale, <NUM_LIT:3>)<EOL>self.variance.gradient = np.sum(exp_dist * dL_dK)<EOL>if self.ARD1: <EOL><INDENT>self.period.gradient = (dwl * exp_dist[:,:,None] * dL_dK[:, :, None]).sum(<NUM_LIT:0>).sum(<NUM_LIT:0>)<EOL><DEDENT>else:  <EOL><INDENT>self.period.gradient = np.sum(dwl.sum(-<NUM_LIT:1>) * exp_dist * dL_dK)<EOL><DEDENT>if self.ARD2: <EOL><INDENT>self.lengthscale.gradient = (dl * exp_dist[:,:,None] * dL_dK[:, :, None]).sum(<NUM_LIT:0>).sum(<NUM_LIT:0>)<EOL><DEDENT>else: <EOL><INDENT>self.lengthscale.gradient = np.sum(dl.sum(-<NUM_LIT:1>) * exp_dist * dL_dK)<EOL><DEDENT>
derivative of the covariance matrix with respect to the parameters.