code: def test_evaluate_qMFKG(self):
      for dtype in (torch.float, torch.double):
          tkwargs = {"device": self.device, "dtype": dtype}
          # basic test
          n_f = 4
          current_value = torch.rand(1, **tkwargs)
          cau = GenericCostAwareUtility(mock_util)
          mean = torch.rand(n_f, 1, 1, **tkwargs)
          variance = torch.rand(n_f, 1, 1, **tkwargs)
          mfm = MockModel(MockPosterior(mean=mean, variance=variance))
          with mock.patch.object(
              MockModel, "fantasize", return_value=mfm
          ) as patch_f:
              with mock.patch(
                  NO, new_callable=mock.PropertyMock
              ) as mock_num_outputs:
                  mock_num_outputs.return_value = 1
                  mm = MockModel(None)
                  qMFKG = qMultiFidelityKnowledgeGradient(
                      model=mm,
                      num_fantasies=n_f,
                      current_value=current_value,
                      cost_aware_utility=cau,
                  )
                  X = torch.rand(n_f + 1, 1, **tkwargs)
                  val = qMFKG(X)
                  patch_f.assert_called_once()
                  cargs, ckwargs = patch_f.call_args
                  self.assertEqual(
                      ckwargs["X"].shape, torch.Size([1, 1, 1])
                  )
          val_exp = mock_util(X, mean.squeeze(-1) - current_value).mean(
              dim=0
          )
          self.assertAllClose(val, val_exp, atol=1e-4)
          self.assertTrue(
              torch.equal(qMFKG.extract_candidates(X), X[..., :-n_f, :])
          )
          # batched evaluation
          b = 2
          current_value = torch.rand(b, **tkwargs)
          cau = GenericCostAwareUtility(mock_util)
          mean = torch.rand(n_f, b, 1, **tkwargs)
          variance = torch.rand(n_f, b, 1, **tkwargs)
          mfm = MockModel(MockPosterior(mean=mean, variance=variance))
          X = torch.rand(b, n_f + 1, 1, **tkwargs)
          with mock.patch.object(
              MockModel, "fantasize", return_value=mfm
          ) as patch_f:
              with mock.patch(
                  NO, new_callable=mock.PropertyMock
              ) as mock_num_outputs:
                  mock_num_outputs.return_value = 1
                  mm = MockModel(None)
                  qMFKG = qMultiFidelityKnowledgeGradient(
                      model=mm,
                      num_fantasies=n_f,
                      current_value=current_value,
                      cost_aware_utility=cau,
                  )
                  val = qMFKG(X)
                  patch_f.assert_called_once()
                  cargs, ckwargs = patch_f.call_args
                  self.assertEqual(
                      ckwargs["X"].shape, torch.Size([b, 1, 1])
                  )
          val_exp = mock_util(X, mean.squeeze(-1) - current_value).mean(
              dim=0
          )
          self.assertAllClose(val, val_exp, atol=1e-4)
          self.assertTrue(
              torch.equal(qMFKG.extract_candidates(X), X[..., :-n_f, :])
          )
          # pending points and current value
          mean = torch.rand(n_f, 1, 1, **tkwargs)
          variance = torch.rand(n_f, 1, 1, **tkwargs)
          X_pending = torch.rand(2, 1, **tkwargs)
          mfm = MockModel(MockPosterior(mean=mean, variance=variance))
          current_value = torch.rand(1, **tkwargs)
          X = torch.rand(n_f + 1, 1, **tkwargs)
          with mock.patch.object(
              MockModel, "fantasize", return_value=mfm
          ) as patch_f:
              with mock.patch(
                  NO, new_callable=mock.PropertyMock
              ) as mock_num_outputs:
                  mock_num_outputs.return_value = 1
                  mm = MockModel(None)
                  qMFKG = qMultiFidelityKnowledgeGradient(
                      model=mm,
                      num_fantasies=n_f,
                      X_pending=X_pending,
                      current_value=current_value,
                      cost_aware_utility=cau,
                  )
                  val = qMFKG(X)
                  patch_f.assert_called_once()
                  cargs, ckwargs = patch_f.call_args
                  self.assertEqual(
                      ckwargs["X"].shape, torch.Size([1, 3, 1])
                  )
          val_exp = mock_util(X, mean.squeeze(-1) - current_value).mean(
              dim=0
          )
          self.assertAllClose(val, val_exp, atol=1e-4)
          self.assertTrue(
              torch.equal(qMFKG.extract_candidates(X), X[..., :-n_f, :])
          )
          # test objective (inner MC sampling)
          objective = GenericMCObjective(
              objective=lambda Y, X: Y.norm(dim=-1)
          )
          samples = torch.randn(3, 1, 1, **tkwargs)
          mfm = MockModel(MockPosterior(samples=samples))
          X = torch.rand(n_f + 1, 1, **tkwargs)
          with mock.patch.object(
              MockModel, "fantasize", return_value=mfm
          ) as patch_f:
              with mock.patch(
                  NO, new_callable=mock.PropertyMock
              ) as mock_num_outputs:
                  mock_num_outputs.return_value = 1
                  mm = MockModel(None)
                  qMFKG = qMultiFidelityKnowledgeGradient(
                      model=mm,
                      num_fantasies=n_f,
                      objective=objective,
                      current_value=current_value,
                      cost_aware_utility=cau,
                  )
                  val = qMFKG(X)
                  patch_f.assert_called_once()
                  cargs, ckwargs = patch_f.call_args
                  self.assertEqual(
                      ckwargs["X"].shape, torch.Size([1, 1, 1])
                  )
          val_exp = mock_util(
              X, objective(samples) - current_value
          ).mean(dim=0)
          self.assertAllClose(val, val_exp, atol=1e-4)
          self.assertTrue(
              torch.equal(qMFKG.extract_candidates(X), X[..., :-n_f, :])
          )
          # test valfunc_cls and valfunc_argfac
          d, p, d_prime = 4, 3, 2
          samples = torch.ones(3, 1, 1, **tkwargs)
          mean = torch.tensor(
              [[0.25], [0.5], [0.75]], **tkwargs
          ).expand(n_f, 1, -1, -1)
          weights = torch.tensor([0.5, 1.0, 1.0], **tkwargs)
          mfm = MockModel(MockPosterior(mean=mean, samples=samples))
          X = torch.rand(n_f * d + d, d, **tkwargs)
          sample_points = torch.rand(p, d_prime, **tkwargs)
          with mock.patch.object(
              MockModel, "fantasize", return_value=mfm
          ) as patch_f:
              with mock.patch(
                  NO, new_callable=mock.PropertyMock
              ) as mock_num_outputs:
                  mock_num_outputs.return_value = 1
                  mm = MockModel(None)
                  qMFKG = qMultiFidelityKnowledgeGradient(
                      model=mm,
                      num_fantasies=n_f,
                      project=lambda X: project_to_sample_points(
                          X, sample_points
                      ),
                      valfunc_cls=ScalarizedPosteriorMean,
                      valfunc_argfac=lambda model: {"weights": weights},
                  )
                  val = qMFKG(X)
                  patch_f.assert_called_once()
                  cargs, ckwargs = patch_f.call_args
                  self.assertEqual(
                      ckwargs["X"].shape, torch.Size([1, 16, 4])
                  )
                  val_exp = torch.tensor([1.375], **tkwargs)
                  self.assertAllClose(val, val_exp, atol=1e-4)
  
                  patch_f.reset_mock()
                  # Make posterior sample shape agree with X
                  mfm._posterior._samples = torch.ones(
                      1, 3, 1, **tkwargs
                  )
                  qMFKG = qMultiFidelityKnowledgeGradient(
                      model=mm,
                      num_fantasies=n_f,
                      project=lambda X: project_to_sample_points(
                          X, sample_points
                      ),
                      valfunc_cls=qExpectedImprovement,
                      valfunc_argfac=lambda model: {"best_f": 0.0},
                  )
                  val = qMFKG(X)
                  patch_f.assert_called_once()
                  cargs, ckwargs = patch_f.call_args
                  self.assertEqual(
                      ckwargs["X"].shape, torch.Size([1, 16, 4])
                  )
                  val_exp = torch.tensor(
                      1.0, device=self.device, dtype=dtype
                  )
                  self.assertAllClose(val, val_exp, atol=1e-4)
  
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 2 for calling the TestQMultiFidelityKnowledgeGradient obj's underlying member method code with example usage: obj.test_evaluate_qMFKG() without return types