code: def _inducing_inv_root(self):
      if not self.training and hasattr(self, "_cached_kernel_inv_root"):
          return self._cached_kernel_inv_root
      else:
          chol = psd_safe_cholesky(self._inducing_mat, upper=True)
          eye = torch.eye(
              chol.size(-1), device=chol.device, dtype=chol.dtype
          )
          inv_root = torch.linalg.solve_triangular(
              chol, eye, upper=True
          )
  
          res = inv_root
          if not self.training:
              self._cached_kernel_inv_root = res
          return res
  
imports: import copy
  import math
  from typing import Optional, Tuple
  import torch
  from linear_operator import to_dense
  from linear_operator.operators import DiagLinearOperator, LowRankRootAddedDiagLinearOperator, LowRankRootLinearOperator, MatmulLinearOperator
  from linear_operator.utils.cholesky import psd_safe_cholesky
  from torch import Tensor
  from ..None import settings
  from ..distributions import MultivariateNormal
  from ..likelihoods import Likelihood
  from ..mlls import InducingPointKernelAddedLossTerm
  from ..models import exact_prediction_strategies
  from .kernel import Kernel
label_desc: Use image node_id 4 for calling the InducingPointKernel obj's underlying member method code with example usage: obj._inducing_inv_root() and returns: self, res