def to_dict(self):
        """
        Convert the object into a json serializable dictionary.

        Note: It uses the private method _save_to_input_dict of the parent.

        :return dict: json serializable dictionary containing the needed information to instantiate the object
        """

        #TODO: Implement a more memory efficient variant
        if self.L is None:
            return { "mu": self.mu.tolist(), "Sigma": self.Sigma.tolist()}
        else:
            return { "mu": self.mu.tolist(), "Sigma": self.Sigma.tolist(), "L": self.L.tolist()}