code: def test_get_f_X_samples(self):
      tkwargs = {"device": self.device}
      constructors = [
          DeprecatedCachedCholeskyAcqf,
          DummyCachedCholeskyAcqf,
      ]
      for constructor in constructors:
          for dtype in (torch.float, torch.double):
              tkwargs["dtype"] = dtype
              mean = torch.zeros(5, 1, **tkwargs)
              variance = torch.ones(5, 1, **tkwargs)
              mm = MockModel(
                  MockPosterior(
                      mean=mean,
                      variance=variance,
                      samples=torch.rand(5, 1, **tkwargs),
                  )
              )
              # basic test
              sampler = IIDNormalSampler(sample_shape=torch.Size([1]))
  
              with self.assertWarnsRegex(RuntimeWarning, "cache_root"):
                  acqf = constructor(
                      model=mm, sampler=sampler, cache_root=True
                  )
              self.assertFalse(acqf._cache_root)
              acqf._cache_root = True
              q = 3
              baseline_L = torch.eye(5 - q, **tkwargs)
              acqf._baseline_L = baseline_L
              posterior = mm.posterior(torch.rand(5, 1, **tkwargs))
              # basic test
              rv = torch.rand(1, 5, 1, **tkwargs)
              with mock.patch(
                  "botorch.acquisition.cached_cholesky.sample_cached_cholesky",
                  return_value=rv,
              ) as mock_sample_cached_cholesky:
                  samples = acqf._get_f_X_samples(
                      posterior=posterior, q_in=q
                  )
                  mock_sample_cached_cholesky.assert_called_once_with(
                      posterior=posterior,
                      baseline_L=acqf._baseline_L,
                      q=q,
                      base_samples=acqf.sampler.base_samples,
                      sample_shape=acqf.sampler.sample_shape,
                  )
              self.assertTrue(torch.equal(rv, samples))
  
              # test fall back when sampling from cached cholesky fails
              for error_cls in (NanError, NotPSDError):
                  base_samples = torch.rand(1, 5, 1, **tkwargs)
                  acqf.sampler.base_samples = base_samples
                  acqf._baseline_L = baseline_L
                  with mock.patch(
                      "botorch.acquisition.cached_cholesky.sample_cached_cholesky",
                      side_effect=error_cls,
                  ) as mock_sample_cached_cholesky:
                      with warnings.catch_warnings(
                          record=True
                      ) as ws, settings.debug(True):
                          samples = acqf._get_f_X_samples(
                              posterior=posterior, q_in=q
                          )
                          mock_sample_cached_cholesky.assert_called_once_with(
                              posterior=posterior,
                              baseline_L=acqf._baseline_L,
                              q=q,
                              base_samples=base_samples,
                              sample_shape=acqf.sampler.sample_shape,
                          )
                          self.assertTrue(
                              issubclass(ws[0].category, BotorchWarning)
                          )
                          self.assertTrue(
                              samples.shape, torch.Size([1, q, 1])
                          )
              # test HOGP
              hogp = HigherOrderGP(
                  torch.zeros(2, 1), torch.zeros(2, 1, 1)
              ).eval()
              acqf = constructor(
                  model=hogp, sampler=sampler, cache_root=True
              )
              mock_samples = torch.rand(5, 1, 1, **tkwargs)
              posterior = MockPosterior(
                  mean=mean, variance=variance, samples=mock_samples
              )
              samples = acqf._get_f_X_samples(
                  posterior=posterior, q_in=q
              )
              self.assertTrue(
                  torch.equal(samples, mock_samples[2:].unsqueeze(0))
              )
  
imports: import warnings
  from typing import Optional
  from unittest import mock
  import torch
  from botorch import settings
  from botorch.acquisition.cached_cholesky import CachedCholeskyMCAcquisitionFunction, CachedCholeskyMCSamplerMixin
  from botorch.acquisition.monte_carlo import MCAcquisitionFunction
  from botorch.acquisition.objective import GenericMCObjective, MCAcquisitionObjective
  from botorch.exceptions.warnings import BotorchWarning
  from botorch.models import SingleTaskGP
  from botorch.models.deterministic import GenericDeterministicModel
  from botorch.models.higher_order_gp import HigherOrderGP
  from botorch.models.model import Model, ModelList
  from botorch.models.transforms.outcome import Log
  from botorch.sampling.normal import IIDNormalSampler, MCSampler
  from botorch.utils.low_rank import extract_batch_covar
  from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
  from linear_operator.utils.errors import NanError, NotPSDError
label_desc: Use image node_id 3 for calling the TestCachedCholeskyMCSamplerMixin obj's underlying member method code with example usage: obj.test_get_f_X_samples() without return types