code: def test_constrained_expected_improvement_batch(self):
      for dtype in (torch.float, torch.double):
          mean = torch.tensor(
              [
                  [-0.5, 0.0, 5.0, 0.0],
                  [0.0, 0.0, 5.0, 0.0],
                  [0.5, 0.0, 5.0, 0.0],
              ],
              device=self.device,
              dtype=dtype,
          ).unsqueeze(dim=-2)
          variance = torch.ones(
              3, 4, device=self.device, dtype=dtype
          ).unsqueeze(dim=-2)
          N = torch.distributions.Normal(loc=0.0, scale=1.0)
          a = N.icdf(
              torch.tensor(0.75)
          )  # get a so that P(-a <= N <= a) = 0.5
          mm = MockModel(MockPosterior(mean=mean, variance=variance))
          kwargs = {
              "model": mm,
              "best_f": 0.0,
              "objective_index": 0,
              "constraints": {1: [None, 0], 2: [5.0, None], 3: [-a, a]},
          }
          module = ConstrainedExpectedImprovement(**kwargs)
          log_module = LogConstrainedExpectedImprovement(**kwargs)
          X = torch.empty(
              3, 1, 1, device=self.device, dtype=dtype
          )  # dummy
          ei, log_ei = module(X), log_module(X)
          self.assertTrue(ei.shape == torch.Size([3]))
          self.assertTrue(log_ei.shape == torch.Size([3]))
          ei_expected_unconstrained = torch.tensor(
              [0.19780, 0.39894, 0.69780],
              device=self.device,
              dtype=dtype,
          )
          ei_expected = ei_expected_unconstrained * 0.5 * 0.5 * 0.5
          self.assertAllClose(ei, ei_expected, atol=1e-4)
          self.assertAllClose(log_ei, ei.log(), atol=1e-4)
  
imports: import math
  import torch
  from botorch.acquisition import qAnalyticProbabilityOfImprovement
  from botorch.acquisition.analytic import _compute_log_prob_feas, _ei_helper, _log_ei_helper, AnalyticAcquisitionFunction, ConstrainedExpectedImprovement, ExpectedImprovement, LogConstrainedExpectedImprovement, LogExpectedImprovement, LogNoisyExpectedImprovement, LogProbabilityOfImprovement, NoisyExpectedImprovement, PosteriorMean, PosteriorStandardDeviation, ProbabilityOfImprovement, ScalarizedPosteriorMean, UpperConfidenceBound
  from botorch.acquisition.objective import IdentityMCObjective, ScalarizedPosteriorTransform
  from botorch.exceptions import UnsupportedError
  from botorch.models import SingleTaskGP
  from botorch.posteriors import GPyTorchPosterior
  from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood
label_desc: Use image node_id 2 for calling the TestConstrainedExpectedImprovement obj's underlying member method code with example usage: obj.test_constrained_expected_improvement_batch() without return types