code: def test_fantasize(self):
      for fixed_noise in (False, True):
          x1 = torch.rand(5, 2)
          y1 = torch.rand(5, 1)
          x2 = torch.rand(5, 2)
          y2 = torch.rand(5, 1)
          yvar1 = torch.full_like(y1, 0.1) if fixed_noise else None
          yvar2 = torch.full_like(y2, 0.2) if fixed_noise else None
          m1 = SingleTaskGP(x1, y1, yvar1).eval()
          m2 = SingleTaskGP(x2, y2, yvar2).eval()
          modellist = ModelListGP(m1, m2)
          fm = modellist.fantasize(
              torch.rand(3, 2),
              sampler=IIDNormalSampler(sample_shape=torch.Size([2])),
          )
          self.assertIsInstance(fm, ModelListGP)
          for i in range(2):
              fm_i = fm.models[i]
              self.assertIsInstance(fm_i, SingleTaskGP)
              self.assertIsInstance(
                  fm_i.likelihood,
                  FixedNoiseGaussianLikelihood
                  if fixed_noise
                  else GaussianLikelihood,
              )
              self.assertEqual(
                  fm_i.train_inputs[0].shape, torch.Size([2, 8, 2])
              )
              self.assertEqual(
                  fm_i.train_targets.shape, torch.Size([2, 8])
              )
  
          # test decoupled
          sampler1 = IIDNormalSampler(sample_shape=torch.Size([2]))
          sampler2 = IIDNormalSampler(sample_shape=torch.Size([2]))
          eval_mask = torch.tensor(
              [[1, 0], [0, 1], [1, 0]],
              dtype=torch.bool,
          )
          num_designs_per_output = eval_mask.sum(dim=0)
          fm = modellist.fantasize(
              torch.rand(3, 2),
              sampler=ListSampler(sampler1, sampler2),
              evaluation_mask=eval_mask,
          )
          self.assertIsInstance(fm, ModelListGP)
          for i in range(2):
              fm_i = fm.models[i]
              self.assertIsInstance(fm_i, SingleTaskGP)
              self.assertIsInstance(
                  fm_i.likelihood,
                  FixedNoiseGaussianLikelihood
                  if fixed_noise
                  else GaussianLikelihood,
              )
              num_points = 7 - i
              self.assertEqual(
                  fm_i.train_inputs[0].shape,
                  torch.Size([2, num_points, 2]),
              )
              self.assertEqual(
                  fm_i.train_targets.shape, torch.Size([2, num_points])
              )
          # test decoupled with observation_noise
          if fixed_noise:
              # already transformed
              observation_noise = torch.full(
                  (3, 2), 0.3, dtype=x1.dtype, device=x1.device
              )
              observation_noise[:, 1] = 0.4
              for obs_noise in (None, observation_noise):
                  fm = modellist.fantasize(
                      torch.rand(3, 2),
                      sampler=ListSampler(sampler1, sampler2),
                      evaluation_mask=eval_mask,
                      observation_noise=obs_noise,
                  )
                  self.assertIsInstance(fm, ModelListGP)
                  for i in range(2):
                      fm_i = fm.models[i]
                      self.assertIsInstance(fm_i, SingleTaskGP)
                      self.assertIsInstance(
                          fm_i.likelihood, FixedNoiseGaussianLikelihood
                      )
                      num_points = 7 - i
                      self.assertEqual(
                          fm_i.train_inputs[0].shape,
                          torch.Size([2, num_points, 2]),
                      )
                      self.assertEqual(
                          fm_i.train_targets.shape,
                          torch.Size([2, num_points]),
                      )
                      # check observation_noise
                      if obs_noise is not None:
                          self.assertTrue(
                              torch.equal(
                                  fm_i.likelihood.noise[
                                      ..., -num_designs_per_output[i] :
                                  ],
                                  observation_noise[
                                      -num_designs_per_output[i] :, i
                                  ],
                              )
                          )
                      else:
                          self.assertTrue(
                              torch.allclose(
                                  fm_i.likelihood.noise[
                                      ..., -num_designs_per_output[i] :
                                  ],
                                  modellist.models[i]
                                  .likelihood.noise[
                                      ..., -num_designs_per_output[i] :
                                  ]
                                  .mean(),
                              )
                          )
  
imports: import itertools
  import warnings
  from copy import deepcopy
  from typing import Optional
  import torch
  from botorch.acquisition.objective import ScalarizedPosteriorTransform
  from botorch.exceptions.errors import BotorchTensorDimensionError
  from botorch.exceptions.warnings import OptimizationWarning
  from botorch.fit import fit_gpytorch_mll
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.models.multitask import MultiTaskGP
  from botorch.models.transforms.input import Normalize
  from botorch.models.transforms.outcome import ChainedOutcomeTransform, Log, Standardize
  from botorch.posteriors import GPyTorchPosterior, PosteriorList, TransformedPosterior
  from botorch.sampling.base import MCSampler
  from botorch.sampling.list_sampler import ListSampler
  from botorch.sampling.normal import IIDNormalSampler
  from botorch.utils.testing import _get_random_data, BotorchTestCase
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from gpytorch.kernels import MaternKernel, ScaleKernel
  from gpytorch.likelihoods import LikelihoodList
  from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood, GaussianLikelihood
  from gpytorch.means import ConstantMean
  from gpytorch.mlls import SumMarginalLogLikelihood
  from gpytorch.mlls.exact_marginal_log_likelihood import ExactMarginalLogLikelihood
  from gpytorch.priors import GammaPrior
  from torch import Tensor
label_desc: Use image node_id 7 for calling the TestModelListGP obj's underlying member method code with example usage: obj.test_fantasize() without return types