code: def test_fantasize(self):
      for batch_shape, m, dtype, use_octf in itertools.product(
          (torch.Size(), torch.Size([2])),
          (1, 2),
          (torch.float, torch.double),
          (False, True),
      ):
          tkwargs = {"device": self.device, "dtype": dtype}
          octf = (
              Standardize(m=m, batch_shape=batch_shape)
              if use_octf
              else None
          )
          model, _ = self._get_model_and_data(
              batch_shape=batch_shape,
              m=m,
              outcome_transform=octf,
              **tkwargs,
          )
          # fantasize
          X_f = torch.rand(
              torch.Size(batch_shape + torch.Size([4, 1])), **tkwargs
          )
          sampler = SobolQMCNormalSampler(sample_shape=torch.Size([3]))
          fm = model.fantasize(X=X_f, sampler=sampler)
          self.assertIsInstance(fm, model.__class__)
  
      # check that input transforms are applied to X.
      tkwargs = {"device": self.device, "dtype": torch.float}
      intf = Normalize(d=1, bounds=torch.tensor([[0], [10]], **tkwargs))
      model, _ = self._get_model_and_data(
          batch_shape=torch.Size(),
          m=1,
          input_transform=intf,
          **tkwargs,
      )
      X_f = torch.rand(4, 1, **tkwargs)
      fm = model.fantasize(
          X_f,
          sampler=SobolQMCNormalSampler(sample_shape=torch.Size([3])),
      )
      self.assertTrue(
          torch.allclose(
              fm.train_inputs[0][:, -4:], intf(X_f).expand(3, -1, -1)
          )
      )
  
imports: import itertools
  import warnings
  import torch
  from botorch.exceptions.warnings import OptimizationWarning
  from botorch.fit import fit_gpytorch_mll
  from botorch.models.gp_regression import FixedNoiseGP, HeteroskedasticSingleTaskGP, SingleTaskGP
  from botorch.models.transforms import Normalize, Standardize
  from botorch.models.transforms.input import InputStandardize
  from botorch.posteriors import GPyTorchPosterior
  from botorch.sampling import SobolQMCNormalSampler
  from botorch.utils.datasets import SupervisedDataset
  from botorch.utils.sampling import manual_seed
  from botorch.utils.test_helpers import get_pvar_expected
  from botorch.utils.testing import _get_random_data, BotorchTestCase
  from gpytorch.kernels import MaternKernel, RBFKernel, ScaleKernel
  from gpytorch.likelihoods import _GaussianLikelihoodBase, FixedNoiseGaussianLikelihood, GaussianLikelihood, HeteroskedasticNoise
  from gpytorch.means import ConstantMean, ZeroMean
  from gpytorch.mlls.exact_marginal_log_likelihood import ExactMarginalLogLikelihood
  from gpytorch.mlls.noise_model_added_loss_term import NoiseModelAddedLossTerm
  from gpytorch.priors import GammaPrior
label_desc: Use image node_id 6 for calling the TestSingleTaskGP obj's underlying member method code with example usage: obj.test_fantasize() without return types