code: def root_inv_decomposition(
      input: Anysor,
      initial_vectors: Optional[Tensor] = None,
      test_vectors: Optional[Tensor] = None,
      method: Optional[str] = None,
  ) -> LinearOperator:
      r"""
      Returns a (usually low-rank) inverse root decomposition linear operator
      of the PSD LinearOperator :math:`\mathbf A`.
      This can be used for sampling from a Gaussian distribution, or for obtaining a
      low-rank version of a matrix.
  
      The root_inv_decomposition is performed using a partial Lanczos tridiagonalization.
  
      :param input: The matrix (or batch of matrices) :math:`\mathbf A` (... x N x N).
      :param initial_vectors: Vectors used to initialize the Lanczos decomposition.
          The best initialization vector (determined by :attr:`test_vectors`) will be chosen.
      :param test_vectors: Vectors used to test the accuracy of the decomposition.
      :param method: Root decomposition method to use (symeig, diagonalization, lanczos, or cholesky).
      :return: A tensor :math:`\mathbf R` such that :math:`\mathbf R \mathbf R^\top \approx \mathbf A^{-1}`.
      """
      return linear_operator.root_inv_decomposition(
          input=input,
          initial_vectors=initial_vectors,
          test_vectors=test_vectors,
          method=method,
      )
  
imports: from typing import Optional, Tuple, Union
  import linear_operator
  import torch
  from linear_operator import LinearOperator
  from torch import Tensor
  from .None import beta_features, distributions, kernels, lazy, likelihoods, means, metrics, mlls, models, optim, priors, settings, utils, variational
  from .functions import inv_matmul, log_normal_cdf, logdet, matmul
  from .lazy import cat, delazify, lazify
  from .mlls import ExactMarginalLogLikelihood
  from .module import Module
label_desc: Use image node_id 9 for calling a global function with example usage: root_inv_decomposition(input, initial_vectors, test_vectors, method) and returns: linear_operator