code: def test_expand(self):
      other = self.piv_chol.expand(3, 2)
      for key in ("tril", "perm", "diag"):
          a = getattr(self.piv_chol, key)
          b = getattr(other, key)
          self.assertEqual(b.shape[: -a.ndim], (3,))
          self.assertTrue(b._base is a)
  
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 7 for calling the TestPivotedCholesky obj's underlying member method code with example usage: obj.test_expand() without return types