docstr: Computes a cache for K_X*X (K_XX + sigma^2 I)^-1 K_X*X if possible. By default, this does no work and returns
  the first argument.
  
  Args:
      train_train_covar_inv_root (:obj:`torch.tensor`): a root of (K_XX + sigma^2 I)^-1
      test_train_covar (:obj:`torch.tensor`): the observed noise (from the likelihood)
  
  Returns
      A precomputed cache
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code: def _exact_predictive_covar_inv_quad_form_cache(
      self, train_train_covar_inv_root, test_train_covar
  ):
      """
      Computes a cache for K_X*X (K_XX + sigma^2 I)^-1 K_X*X if possible. By default, this does no work and returns
      the first argument.
  
      Args:
          train_train_covar_inv_root (:obj:`torch.tensor`): a root of (K_XX + sigma^2 I)^-1
          test_train_covar (:obj:`torch.tensor`): the observed noise (from the likelihood)
  
      Returns
          A precomputed cache
      """
      res = train_train_covar_inv_root
      if settings.detach_test_caches.on():
          res = res.detach()
  
      if res.grad_fn is not None:
          wrapper = functools.partial(clear_cache_hook, self)
          functools.update_wrapper(wrapper, clear_cache_hook)
          res.grad_fn.register_hook(wrapper)
  
      return res
  
imports: import functools
  import string
  import warnings
  import torch
  from linear_operator import to_dense, to_linear_operator
  from linear_operator.operators import AddedDiagLinearOperator, BatchRepeatLinearOperator, ConstantMulLinearOperator, DenseLinearOperator, InterpolatedLinearOperator, LinearOperator, LowRankRootAddedDiagLinearOperator, MaskedLinearOperator, MatmulLinearOperator, RootLinearOperator, ZeroLinearOperator
  from linear_operator.utils.cholesky import psd_safe_cholesky
  from linear_operator.utils.interpolation import left_interp, left_t_interp
  from torch import Tensor
  from ..None import settings
  from ..distributions import MultitaskMultivariateNormal
  from ..lazy import LazyEvaluatedKernelTensor
  from ..utils.memoize import add_to_cache, cached, clear_cache_hook, pop_from_cache
label_desc: Use image node_id 3 for calling the DefaultPredictionStrategy obj's underlying member method code with example usage: obj._exact_predictive_covar_inv_quad_form_cache(train_train_covar_inv_root, test_train_covar) and returns: res