code: def test_q_noisy_expected_improvement_batch(self):
      for dtype in (torch.float, torch.double):
          # the event shape is `b x q x t` = 2 x 3 x 1
          samples_noisy = torch.zeros(
              2, 3, 1, device=self.device, dtype=dtype
          )
          samples_noisy[0, -1, 0] = 1.0
          mm_noisy = MockModel(MockPosterior(samples=samples_noisy))
          # X is `q x d` = 1 x 1
          X = torch.zeros(2, 2, 1, device=self.device, dtype=dtype)
          X_baseline = torch.zeros(
              1, 1, device=self.device, dtype=dtype
          )
  
          # test batch mode
          sampler = IIDNormalSampler(sample_shape=torch.Size([2]))
          acqf = qNoisyExpectedImprovement(
              model=mm_noisy,
              X_baseline=X_baseline,
              sampler=sampler,
              prune_baseline=False,
              cache_root=False,
          )
          res = acqf(X)
          self.assertEqual(res[0].item(), 1.0)
          self.assertEqual(res[1].item(), 0.0)
  
          # test batch mode
          sampler = IIDNormalSampler(
              sample_shape=torch.Size([2]), seed=12345
          )
          acqf = qNoisyExpectedImprovement(
              model=mm_noisy,
              X_baseline=X_baseline,
              sampler=sampler,
              prune_baseline=False,
              cache_root=False,
          )
          res = acqf(X)  # 1-dim batch
          self.assertEqual(res[0].item(), 1.0)
          self.assertEqual(res[1].item(), 0.0)
          self.assertEqual(
              acqf.sampler.base_samples.shape, torch.Size([2, 1, 3, 1])
          )
          bs = acqf.sampler.base_samples.clone()
          acqf(X)
          self.assertTrue(torch.equal(acqf.sampler.base_samples, bs))
          res = acqf(X.expand(2, 2, 1))  # 2-dim batch
          self.assertEqual(res[0].item(), 1.0)
          self.assertEqual(res[1].item(), 0.0)
          # the base samples should have the batch dim collapsed
          self.assertEqual(
              acqf.sampler.base_samples.shape, torch.Size([2, 1, 3, 1])
          )
          bs = acqf.sampler.base_samples.clone()
          acqf(X.expand(2, 2, 1))
          self.assertTrue(torch.equal(acqf.sampler.base_samples, bs))
  
          # test batch mode, qmc
          sampler = SobolQMCNormalSampler(sample_shape=torch.Size([2]))
          acqf = qNoisyExpectedImprovement(
              model=mm_noisy,
              X_baseline=X_baseline,
              sampler=sampler,
              prune_baseline=False,
              cache_root=False,
          )
          res = acqf(X)
          self.assertEqual(res[0].item(), 1.0)
          self.assertEqual(res[1].item(), 0.0)
          self.assertEqual(
              acqf.sampler.base_samples.shape, torch.Size([2, 1, 3, 1])
          )
          bs = acqf.sampler.base_samples.clone()
          acqf(X)
          self.assertTrue(torch.equal(acqf.sampler.base_samples, bs))
  
imports: import warnings
  from copy import deepcopy
  from functools import partial
  from itertools import product
  from math import pi
  from unittest import mock
  import torch
  from botorch import settings
  from botorch.acquisition.monte_carlo import MCAcquisitionFunction, qExpectedImprovement, qNoisyExpectedImprovement, qProbabilityOfImprovement, qSimpleRegret, qUpperConfidenceBound, SampleReducingMCAcquisitionFunction
  from botorch.acquisition.objective import ConstrainedMCObjective, GenericMCObjective, IdentityMCObjective, ScalarizedPosteriorTransform
  from botorch.acquisition.utils import prune_inferior_points
  from botorch.exceptions import BotorchWarning, UnsupportedError
  from botorch.models import SingleTaskGP
  from botorch.sampling.normal import IIDNormalSampler, SobolQMCNormalSampler
  from botorch.utils.low_rank import sample_cached_cholesky
  from botorch.utils.test_helpers import DummyNonScalarizingPosteriorTransform
  from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
  from botorch.utils.transforms import standardize
  from torch import Tensor
label_desc: Use image node_id 2 for calling the TestQNoisyExpectedImprovement obj's underlying member method code with example usage: obj.test_q_noisy_expected_improvement_batch() without return types