code: def test_initialize_q_knowledge_gradient(self):
      for dtype in (torch.float, torch.double):
          mean = torch.zeros(1, 1, device=self.device, dtype=dtype)
          mm = MockModel(MockPosterior(mean=mean))
          # test error when neither specifying neither sampler nor num_fantasies
          with self.assertRaises(ValueError):
              qKnowledgeGradient(model=mm, num_fantasies=None)
          # test error when sampler and num_fantasies arg are inconsistent
          sampler = IIDNormalSampler(sample_shape=torch.Size([16]))
          with self.assertRaises(ValueError):
              qKnowledgeGradient(
                  model=mm, num_fantasies=32, sampler=sampler
              )
          # test default construction
          qKG = qKnowledgeGradient(model=mm, num_fantasies=32)
          self.assertEqual(qKG.num_fantasies, 32)
          self.assertIsInstance(qKG.sampler, SobolQMCNormalSampler)
          self.assertEqual(qKG.sampler.sample_shape, torch.Size([32]))
          self.assertIsNone(qKG.objective)
          self.assertIsNone(qKG.inner_sampler)
          self.assertIsNone(qKG.X_pending)
          self.assertIsNone(qKG.current_value)
          self.assertEqual(qKG.get_augmented_q_batch_size(q=3), 32 + 3)
          # test custom construction
          obj = GenericMCObjective(lambda Y, X: Y.mean(dim=-1))
          sampler = IIDNormalSampler(sample_shape=torch.Size([16]))
          X_pending = torch.zeros(2, 2, device=self.device, dtype=dtype)
          qKG = qKnowledgeGradient(
              model=mm,
              num_fantasies=16,
              sampler=sampler,
              objective=obj,
              X_pending=X_pending,
          )
          self.assertEqual(qKG.num_fantasies, 16)
          self.assertEqual(qKG.sampler, sampler)
          self.assertEqual(qKG.sampler.sample_shape, torch.Size([16]))
          self.assertEqual(qKG.objective, obj)
          self.assertIsInstance(
              qKG.inner_sampler, SobolQMCNormalSampler
          )
          self.assertEqual(
              qKG.inner_sampler.sample_shape, torch.Size([128])
          )
          self.assertTrue(torch.equal(qKG.X_pending, X_pending))
          self.assertIsNone(qKG.current_value)
          self.assertEqual(qKG.get_augmented_q_batch_size(q=3), 16 + 3)
          # test assignment of num_fantasies from sampler if not provided
          qKG = qKnowledgeGradient(
              model=mm, num_fantasies=None, sampler=sampler
          )
          self.assertEqual(qKG.sampler.sample_shape, torch.Size([16]))
          # test custom construction with inner sampler and current value
          inner_sampler = SobolQMCNormalSampler(
              sample_shape=torch.Size([256])
          )
          current_value = torch.zeros(
              1, device=self.device, dtype=dtype
          )
          qKG = qKnowledgeGradient(
              model=mm,
              num_fantasies=8,
              objective=obj,
              inner_sampler=inner_sampler,
              current_value=current_value,
          )
          self.assertEqual(qKG.num_fantasies, 8)
          self.assertEqual(qKG.sampler.sample_shape, torch.Size([8]))
          self.assertEqual(qKG.objective, obj)
          self.assertIsInstance(
              qKG.inner_sampler, SobolQMCNormalSampler
          )
          self.assertEqual(qKG.inner_sampler, inner_sampler)
          self.assertIsNone(qKG.X_pending)
          self.assertTrue(torch.equal(qKG.current_value, current_value))
          self.assertEqual(qKG.get_augmented_q_batch_size(q=3), 8 + 3)
          # test construction with posterior_transform
          qKG_s = qKnowledgeGradient(
              model=mm,
              num_fantasies=16,
              sampler=sampler,
              posterior_transform=ScalarizedPosteriorTransform(
                  weights=torch.rand(2)
              ),
          )
          self.assertIsNone(qKG_s.inner_sampler)
          self.assertIsInstance(
              qKG_s.posterior_transform, ScalarizedPosteriorTransform
          )
          # test error if multi-output model and no objective or posterior transform
          mean2 = torch.zeros(1, 2, device=self.device, dtype=dtype)
          mm2 = MockModel(MockPosterior(mean=mean2))
          with self.assertRaises(UnsupportedError):
              qKnowledgeGradient(model=mm2)
          # test error if multi-output model and no objective and posterior transform
          # does not scalarize
          with self.assertRaises(UnsupportedError):
              qKnowledgeGradient(
                  model=mm2,
                  posterior_transform=DummyNonScalarizingPosteriorTransform(),
              )
  
          with self.assertRaisesRegex(
              UnsupportedError,
              "Objectives that are not an `MCAcquisitionObjective` are not "
              "supported.",
          ):
              qKnowledgeGradient(model=mm, objective="car")
  
imports: from contextlib import ExitStack
  from unittest import mock
  import torch
  from botorch.acquisition.analytic import PosteriorMean, ScalarizedPosteriorMean
  from botorch.acquisition.cost_aware import GenericCostAwareUtility
  from botorch.acquisition.knowledge_gradient import _get_value_function, _split_fantasy_points, ProjectedAcquisitionFunction, qKnowledgeGradient, qMultiFidelityKnowledgeGradient
  from botorch.acquisition.monte_carlo import qExpectedImprovement, qSimpleRegret
  from botorch.acquisition.objective import GenericMCObjective, ScalarizedPosteriorTransform
  from botorch.acquisition.utils import project_to_sample_points
  from botorch.exceptions.errors import UnsupportedError
  from botorch.generation.gen import gen_candidates_scipy
  from botorch.models import SingleTaskGP
  from botorch.optim.optimize import optimize_acqf
  from botorch.optim.utils import _filter_kwargs
  from botorch.posteriors.gpytorch import GPyTorchPosterior
  from botorch.sampling.normal import IIDNormalSampler, SobolQMCNormalSampler
  from botorch.utils.test_helpers import DummyNonScalarizingPosteriorTransform
  from botorch.utils.testing import BotorchTestCase, MockModel, MockPosterior
  from gpytorch.distributions import MultitaskMultivariateNormal
label_desc: Use image node_id 1 for calling the TestQKnowledgeGradient obj's underlying member method code with example usage: obj.test_initialize_q_knowledge_gradient() without return types