code: def exact_predictive_covar(self, test_test_covar, test_train_covar):
      covar_cache = self.covar_cache
      # covar_cache = K_{UU}^{-1/2} K_{UX}( K_{XX} + \sigma^2 I )^{-1} K_{XU} K_{UU}^{-1/2}
  
      # Decompose test_train_covar = l, r
      # Main case: test_x and train_x are different - test_train_covar is a MatmulLinearOperator
      if isinstance(test_train_covar, MatmulLinearOperator):
          L = test_train_covar.left_linear_op.to_dense()
      # Edge case: test_x and train_x are the same - test_train_covar is a LowRankRootAddedDiagLinearOperator
      elif isinstance(
          test_train_covar, LowRankRootAddedDiagLinearOperator
      ):
          L = test_train_covar._linear_op.root.to_dense()
      else:
          # We should not hit this point of the code - this is to catch potential bugs in GPyTorch
          raise ValueError(
              "Expected SGPR output to be a MatmulLinearOperator or AddedDiagLinearOperator. "
              f"Got {test_train_covar.__class__.__name__} instead. "
              "This is likely a bug in GPyTorch."
          )
  
      res = test_test_covar - (L @ (covar_cache @ L.transpose(-1, -2)))
      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 4 for calling the SGPRPredictionStrategy obj's underlying member method code with example usage: obj.exact_predictive_covar(test_test_covar, test_train_covar) and returns: res