code: def fantasy_covar_cache(self):
      train_train_covar = self.train_prior_dist.lazy_covariance_matrix
      inducing_covar = train_train_covar.base_linear_op
  
      # we need to enforce a cholesky here for numerical stability
      interp_inner_prod_root = (
          self.interp_inner_prod.root_decomposition(
              method="cholesky"
          ).root
      )
      inducing_compression_matrix = inducing_covar.matmul(
          interp_inner_prod_root
      )
  
      current_qmatrix = (
          interp_inner_prod_root.transpose(-1, -2)
          .matmul(inducing_compression_matrix)
          .add_jitter(1.0)
      )
  
      if settings.fast_pred_var.on():
          qmat_inv_root = current_qmatrix.root_inv_decomposition()
          # to to_linear_operator you have to evaluate the inverse root which is slow
          # otherwise, you can't backprop your way through it
          inner_cache = RootLinearOperator(
              inducing_compression_matrix.matmul(
                  qmat_inv_root.root.to_dense()
              )
          )
      else:
          inner_cache = inducing_compression_matrix.matmul(
              current_qmatrix.solve(
                  inducing_compression_matrix.transpose(-1, -2)
              )
          )
  
      # Precomputed factor
      if settings.fast_pred_samples.on():
          predictive_covar_cache = inducing_covar - inner_cache
          inside_root = predictive_covar_cache.root_decomposition(
              method="cholesky"
          ).root
          # Prevent backprop through this variable
          if settings.detach_test_caches.on():
              inside_root = inside_root.detach()
          covar_cache = inside_root, None
      else:
          root = inner_cache.root_decomposition(method="cholesky").root
  
          # Prevent backprop through this variable
          if settings.detach_test_caches.on():
              root = root.detach()
          covar_cache = None, root
  
      return covar_cache
  
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 10 for calling the InterpolatedPredictionStrategy obj's underlying member method code with example usage: obj.fantasy_covar_cache() and returns: covar_cache