code: def test_q_log_expected_improvement_batch(self):
      for dtype in (torch.float, torch.double):
          # the event shape is `b x q x t` = 2 x 2 x 1
          samples = torch.zeros(
              2, 2, 1, device=self.device, dtype=dtype
          )
          samples[0, 0, 0] = 1.0
          mm = MockModel(MockPosterior(samples=samples))
  
          # X is a dummy and unused b/c of mocking
          X = torch.zeros(2, 2, 1, device=self.device, dtype=dtype)
  
          # test batch mode
          sampler = IIDNormalSampler(sample_shape=torch.Size([2]))
          acqf = qLogExpectedImprovement(
              model=mm, best_f=0, sampler=sampler
          )
          exp_log_res = acqf(X).exp()
          # with no approximations (qEI): self.assertEqual(res[0].item(), 1.0)
          self.assertEqual(exp_log_res.dtype, dtype)
          self.assertEqual(exp_log_res.device.type, self.device.type)
          self.assertTrue(1.0 <= exp_log_res[0].item())
          self.assertTrue(exp_log_res[0].item() <= 1.0 + acqf.tau_relu)
  
          # with no approximations (qEI): self.assertEqual(res[1].item(), 0.0)
          self.assertTrue(0 < exp_log_res[1].item())
          self.assertTrue(exp_log_res[1].item() <= acqf.tau_relu)
  
          # test batch model, batched best_f values
          sampler = IIDNormalSampler(sample_shape=torch.Size([3]))
          acqf = qLogExpectedImprovement(
              model=mm, best_f=torch.Tensor([0, 0]), sampler=sampler
          )
          exp_log_res = acqf(X).exp()
          # with no approximations (qEI): self.assertEqual(res[0].item(), 1.0)
          self.assertTrue(1.0 <= exp_log_res[0].item())
          self.assertTrue(exp_log_res[0].item() <= 1.0 + acqf.tau_relu)
          # with no approximations (qEI): self.assertEqual(res[1].item(), 0.0)
          self.assertTrue(0 < exp_log_res[1].item())
          self.assertTrue(exp_log_res[1].item() <= acqf.tau_relu)
  
          # test shifting best_f value
          acqf = qLogExpectedImprovement(
              model=mm, best_f=-1, sampler=sampler
          )
          exp_log_res = acqf(X).exp()
          # with no approximations (qEI): self.assertEqual(res[0].item(), 2.0)
          # TODO: figure out numerically stable tests and principled tolerances
          # With q > 1, maximum value can get moved down due to L_q-norm approximation
          # of the maximum over the q-batch.
          safe_upper_lower_bound = 1.999
          self.assertTrue(
              safe_upper_lower_bound <= exp_log_res[0].item()
          )
          self.assertTrue(
              exp_log_res[0].item()
              <= 2.0 + acqf.tau_relu + acqf.tau_max
          )
          # with no approximations (qEI): self.assertEqual(res[1].item(), 1.0)
          self.assertTrue(1.0 <= exp_log_res[1].item())
          # ocurring ~tau_max error when all candidates in a q-batch have the
          # acquisition value
          self.assertTrue(
              exp_log_res[1].item()
              <= 1.0 + acqf.tau_relu + acqf.tau_max
          )
  
          # test batch mode
          sampler = IIDNormalSampler(
              sample_shape=torch.Size([2]), seed=12345
          )
          acqf = qLogExpectedImprovement(
              model=mm, best_f=0, sampler=sampler
          )
          # res = acqf(X)  # 1-dim batch
          exp_log_res = acqf(X).exp()  # 1-dim batch
          # with no approximations (qEI): self.assertEqual(res[0].item(), 1.0)
          safe_upper_lower_bound = 0.999
          self.assertTrue(
              safe_upper_lower_bound <= exp_log_res[0].item()
          )
          self.assertTrue(exp_log_res[0].item() <= 1.0 + acqf.tau_relu)
          # with no approximations (qEI): self.assertEqual(res[1].item(), 0.0)
          self.assertTrue(0.0 <= exp_log_res[1].item())
          self.assertTrue(exp_log_res[1].item() <= 0.0 + acqf.tau_relu)
          self.assertEqual(
              acqf.sampler.base_samples.shape, torch.Size([2, 1, 2, 1])
          )
          bs = acqf.sampler.base_samples.clone()
          acqf(X)
          self.assertTrue(torch.equal(acqf.sampler.base_samples, bs))
          exp_log_res = acqf(X.expand(2, 2, 1)).exp()  # 2-dim batch
          # self.assertEqual(res[0].item(), 1.0)
          safe_upper_lower_bound = 0.999
          self.assertTrue(
              safe_upper_lower_bound <= exp_log_res[0].item()
          )
          self.assertTrue(exp_log_res[0].item() <= 1.0 + acqf.tau_relu)
          # self.assertEqual(res[1].item(), 0.0)
          self.assertTrue(0.0 <= exp_log_res[1].item())
          self.assertTrue(exp_log_res[1].item() <= 0.0 + acqf.tau_relu)
          # the base samples should have the batch dim collapsed
          self.assertEqual(
              acqf.sampler.base_samples.shape, torch.Size([2, 1, 2, 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 = qLogExpectedImprovement(
              model=mm, best_f=0, sampler=sampler
          )
          exp_log_res = acqf(X).exp()
          # self.assertEqual(res[0].item(), 1.0)
          safe_upper_lower_bound = 0.999
          self.assertTrue(
              safe_upper_lower_bound <= exp_log_res[0].item()
          )
          self.assertTrue(exp_log_res[0].item() <= 1.0 + acqf.tau_relu)
          # self.assertEqual(res[1].item(), 0.0)
          self.assertTrue(0.0 <= exp_log_res[1].item())
          self.assertTrue(exp_log_res[1].item() <= 0.0 + acqf.tau_relu)
          self.assertEqual(
              acqf.sampler.base_samples.shape, torch.Size([2, 1, 2, 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 itertools import product
  from math import pi
  from unittest import mock
  import torch
  from botorch import settings
  from botorch.acquisition import AcquisitionFunction, LogImprovementMCAcquisitionFunction, qLogExpectedImprovement, qLogNoisyExpectedImprovement
  from botorch.acquisition.analytic import ExpectedImprovement, LogExpectedImprovement, LogNoisyExpectedImprovement, NoisyExpectedImprovement
  from botorch.acquisition.input_constructors import ACQF_INPUT_CONSTRUCTOR_REGISTRY
  from botorch.acquisition.monte_carlo import qExpectedImprovement, qNoisyExpectedImprovement
  from botorch.acquisition.multi_objective.logei import qLogNoisyExpectedHypervolumeImprovement
  from botorch.acquisition.objective import ConstrainedMCObjective, GenericMCObjective, IdentityMCObjective, PosteriorTransform, ScalarizedPosteriorTransform
  from botorch.acquisition.utils import prune_inferior_points
  from botorch.exceptions import BotorchWarning, UnsupportedError
  from botorch.exceptions.errors import BotorchError
  from botorch.models import ModelListGP, SingleTaskGP
  from botorch.models.gp_regression import FixedNoiseGP
  from botorch.sampling.normal import IIDNormalSampler, SobolQMCNormalSampler
  from botorch.utils.low_rank import sample_cached_cholesky
  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 TestQLogExpectedImprovement obj's underlying member method code with example usage: obj.test_q_log_expected_improvement_batch() without return types