def METHOD_NAME(
    self: Float[LinearOperator, "*batch N N"],
    inv_quad_rhs: Optional[Union[Float[Tensor, "*batch N M"], Float[Tensor, "*batch N"]]] = None,
    logdet: Optional[bool] = False,
    reduce_inv_quad: Optional[bool] = True,
) -> Tuple[
    Optional[Union[Float[Tensor, "*batch M"], Float[Tensor, " *batch"], Float[Tensor, " 0"]]],
    Optional[Float[Tensor, "..."]],