class_docstr: Test on the problem (with the simplying assumption on general position)
  from Table 1 in:
  https://www.sciencedirect.com/science/article/pii/S0305054816301538
class_docstr_tok: ["Test","on","the","problem","(","with","the","simplying","assumption","on","general","position",")","from","Table","1","in",":","https",":","\/\/www.sciencedirect.com\/science\/article\/pii\/S0305054816301538"]
code: def setUp(self):
      super().setUp()
      self.ref_point = -torch.tensor(
          [10.0, 10.0, 10.0], device=self.device
      )
      self.U = -self.ref_point.clone().view(1, -1)
      self.Z = torch.empty(1, 3, 3, device=self.device)
      ideal_value = 0.0
      for j in range(self.U.shape[-1]):
          self.Z[0, j] = torch.full(
              (1, self.U.shape[-1]),
              ideal_value,
              dtype=self.Z.dtype,
              device=self.device,
          )
          self.Z[0, j, j] = self.U[0][j]
      self.pareto_Y = -torch.tensor(
          [
              [3.0, 5.0, 7.0],
              [6.0, 2.0, 4.0],
              [4.0, 7.0, 3.0],
          ],
          device=self.device,
      )
      self.expected_U_after_update = torch.tensor(
          [
              [3.0, 10.0, 10.0],
              [6.0, 5.0, 10.0],
              [10.0, 2.0, 10.0],
              [4.0, 10.0, 7.0],
              [6.0, 7.0, 7.0],
              [10.0, 7.0, 4.0],
              [10.0, 10.0, 3.0],
          ],
          device=self.device,
      )
      self.expected_Z_after_update = torch.tensor(
          [
              [[3.0, 5.0, 7.0], [0.0, 10.0, 0.0], [0.0, 0.0, 10.0]],
              [[6.0, 2.0, 4.0], [3.0, 5.0, 7.0], [0.0, 0.0, 10.0]],
              [[10.0, 0.0, 0.0], [6.0, 2.0, 4.0], [0.0, 0.0, 10.0]],
              [[4.0, 7.0, 3.0], [0.0, 10.0, 0.0], [3.0, 5.0, 7.0]],
              [[6.0, 2.0, 4.0], [4.0, 7.0, 3.0], [3.0, 5.0, 7.0]],
              [[10.0, 0.0, 0.0], [4.0, 7.0, 3.0], [6.0, 2.0, 4.0]],
              [[10.0, 0.0, 0.0], [0.0, 10.0, 0.0], [4.0, 7.0, 3.0]],
          ],
          device=self.device,
      )
  
file_path: botorch/test/utils/multi_objective/box_decompositions/test_utils.py
imports: from __future__ import annotations
  import torch
  from botorch.exceptions.errors import BotorchTensorDimensionError, UnsupportedError
  from botorch.utils.multi_objective.box_decompositions.utils import _expand_ref_point, _pad_batch_pareto_frontier, compute_dominated_hypercell_bounds_2d, compute_local_upper_bounds, compute_non_dominated_hypercell_bounds_2d, get_partition_bounds, update_local_upper_bounds_incremental
  from botorch.utils.testing import BotorchTestCase
label_desc: Use image node_id 1 for calling the TestFastPartitioningUtils obj's underlying member method code with example usage: obj.setUp() without return types