code: def aggregation(
      self, transform_fun: Callable[[torch.Tensor], torch.Tensor]
  ) -> torch.Tensor:
      gradients_measure_list = []
      for j in range(self.num_gp_samples):
          gradients_measure_list.append(
              torch.tensor(
                  [
                      torch.mean(
                          transform_fun(
                              not_none(self.samples_gradients)[j][:, i]
                          )
                      )
                      for i in range(self.dim)
                  ]
              ).unsqueeze(0)
          )
      gradients_measure_list = torch.cat(gradients_measure_list, dim=0)
      if not (self.bootstrap):
          gradients_measure_mean_var = []
          for i in range(self.dim):
              gradients_measure_mean_var.append(
                  torch.tensor(
                      [
                          torch.mean(gradients_measure_list[:, i]),
                          torch.var(gradients_measure_list[:, i]),
                          torch.sqrt(
                              torch.var(gradients_measure_list[:, i])
                              / self.num_gp_samples
                          ),
                      ]
                  ).unsqueeze(0)
              )
          gradients_measure_mean_var = torch.cat(
              gradients_measure_mean_var, dim=0
          )
          return gradients_measure_mean_var
      else:
          gradients_measure_list_btsp = []
          for j in range(self.num_gp_samples):
              gradients_measure_btsp = [
                  gradients_measure_list[j].unsqueeze(0)
              ] + [
                  torch.tensor(
                      [
                          torch.mean(
                              transform_fun(
                                  not_none(self.samples_gradients_btsp)[
                                      j
                                  ][b][:, i]
                              )
                          )
                          for i in range(self.dim)
                      ]
                  ).unsqueeze(0)
                  for b in range(self.num_bootstrap_samples)
              ]
              gradients_measure_list_btsp.append(
                  torch.cat(gradients_measure_btsp, dim=0).unsqueeze(0)
              )
          gradients_measure_list_btsp = torch.cat(
              gradients_measure_list_btsp, dim=0
          )
  
          var_per_bootstrap = torch.var(
              gradients_measure_list_btsp, dim=0
          )
          gp_var = torch.mean(var_per_bootstrap, dim=0)
          gp_se = torch.sqrt(gp_var / self.num_gp_samples)
          var_per_gp_sample = torch.var(
              gradients_measure_list_btsp, dim=1
          )
          mc_var = torch.mean(var_per_gp_sample, dim=0)
          mc_se = torch.sqrt(mc_var / (self.num_bootstrap_samples + 1))
          total_mean = gradients_measure_list_btsp.reshape(
              -1, self.dim
          ).mean(dim=0)
          gradients_measure_mean_vargp_segp_varmc_segp = torch.cat(
              [
                  torch.tensor(
                      [
                          total_mean[i],
                          gp_var[i],
                          gp_se[i],
                          mc_var[i],
                          mc_se[i],
                      ]
                  ).unsqueeze(0)
                  for i in range(self.dim)
              ],
              dim=0,
          )
          return gradients_measure_mean_vargp_segp_varmc_segp
  
imports: from copy import deepcopy
  from typing import Callable, List, Optional, Union
  import torch
  from ax.utils.common.typeutils import checked_cast, not_none
  from ax.utils.sensitivity.derivative_gp import posterior_derivative
  from botorch.models.model import Model
  from botorch.posteriors.gpytorch import GPyTorchPosterior
  from botorch.posteriors.posterior import Posterior
  from botorch.sampling.normal import SobolQMCNormalSampler
  from botorch.utils.sampling import draw_sobol_samples
  from botorch.utils.transforms import unnormalize
  from gpytorch.distributions import MultivariateNormal
label_desc: Use image node_id 3 for calling the GpDGSMGpSampling obj's underlying member method code with example usage: obj.aggregation(transform_fun) and returns: gradients_measure_mean_var, gradients_measure_mean_vargp_segp_varmc_segp