code: def test_pivot_(self):
      piv_chol = deepcopy(self.piv_chol)
      self.assertEqual(
          piv_chol.perm.tolist(), [[0, 2, 1, 3, 4], [0, 3, 2, 1, 4]]
      )
  
      piv_chol.pivot_(torch.tensor([2, 3]))
      self.assertEqual(
          piv_chol.perm.tolist(), [[0, 2, 1, 3, 4], [0, 3, 1, 2, 4]]
      )
      self.assertTrue(piv_chol.tril[0].equal(self.piv_chol.tril[0]))
  
      error_msg = "Argument `pivot` does to match with batch shape`."
      with self.assertRaisesRegex(ValueError, error_msg):
          piv_chol.pivot_(torch.tensor([1, 2, 3]))
  
      A = self.piv_chol.tril[1]
      B = piv_chol.tril[1]
      self.assertTrue(A[2:4, :2].equal(B[2:4, :2].roll(1, 0)))
      self.assertTrue(A[4:, 2:4].equal(B[4:, 2:4].roll(1, 1)))
  
file_path: botorch/test/utils/probability/test_linalg.py
imports: from __future__ import annotations
  from copy import deepcopy
  import torch
  from botorch.utils.probability.linalg import augment_cholesky, PivotedCholesky
  from botorch.utils.testing import BotorchTestCase
label_desc: Use image node_id 3 for calling the TestPivotedCholesky obj's underlying member method code with example usage: obj.test_pivot_() without return types