code: def _log_cell_lengths(
      self,
      log_improvement_i: Tensor,
      view_shape: Union[Tuple, torch.Size],
  ) -> Tensor:
      cell_upper_bounds = self.cell_upper_bounds.clamp_max(
          1e10 if log_improvement_i.dtype == torch.double else 1e8
      )  # num_cells x num_objectives
      # add batch-dim to compute area for each segment (pseudo-pareto-vertex)
      log_cell_lengths = (
          (cell_upper_bounds - self.cell_lower_bounds)
          .log()
          .view(view_shape)
      )  # (mc_samples = 1) x (batch_shape = 1) x n_cells x (q_choose_i = 1) x m
      # mc_samples x batch_shape x num_cells x q_choose_i x m
      return self._smooth_minimum(
          log_improvement_i,
          log_cell_lengths,
      )
  
imports: from __future__ import annotations
  from typing import Callable, List, Optional, Tuple, Union
  import torch
  from botorch.acquisition.logei import TAU_MAX, TAU_RELU
  from botorch.acquisition.multi_objective import MultiObjectiveMCAcquisitionFunction
  from botorch.acquisition.multi_objective.objective import MCMultiOutputObjective
  from botorch.models.model import Model
  from botorch.sampling.base import MCSampler
  from botorch.utils.multi_objective.box_decompositions.non_dominated import NondominatedPartitioning
  from botorch.utils.multi_objective.hypervolume import NoisyExpectedHypervolumeMixin, SubsetIndexCachingMixin
  from botorch.utils.objective import compute_smoothed_feasibility_indicator
  from botorch.utils.safe_math import fatmin, log_fatplus, log_softplus, logdiffexp, logmeanexp, logplusexp, logsumexp, smooth_amin
  from botorch.utils.transforms import concatenate_pending_points, is_ensemble, match_batch_shape, t_batch_mode_transform
  from torch import Tensor
label_desc: Use image node_id 4 for calling the qLogExpectedHypervolumeImprovement obj's underlying member method code with example usage: obj._log_cell_lengths(log_improvement_i, view_shape) and returns: self