def _dK_computations(self, dL_dK):
        """Pre-computations for the gradients of the covaraince function. Here the gradient of the covariance with respect to all the individual lengthscales is computed.
        :param dL_dK: the gradient of the objective with respect to the covariance function.
        :type dL_dK: ndarray"""
        
        self._dL_dl = (dL_dK*self.variance*self._K_dvar*(self.input_dim/2.*(self._lengthscales_two.T**4 - self._lengthscales**4) + 2*self._lengthscales2*self._K_dist2)/(self._w2*self._w2*self._lengthscales)).sum(1)
        if self._lengthscales_two is self._lengthscales:
            self._dL_dl_two = None
        else:
            self._dL_dl_two = (dL_dK*self.variance*self._K_dvar*(self.input_dim/2.*(self._lengthscales**4 - self._lengthscales_two.T**4 ) + 2*self._lengthscales_two2.T*self._K_dist2)/(self._w2*self._w2*self._lengthscales_two.T)).sum(0)
Pre-computations for the gradients of the covaraince function. Here the gradient of the covariance with respect to all the individual lengthscales is computed.
        :param dL_dK: the gradient of the objective with respect to the covariance function.
        :type dL_dK: ndarray