code: def test_subset_model(self):
      for batch_shape, dtype, use_octf in itertools.product(
          (torch.Size(), torch.Size([2])),
          (torch.float, torch.double),
          (True, False),
      ):
          tkwargs = {"device": self.device, "dtype": dtype}
          octf = (
              Standardize(m=2, batch_shape=batch_shape)
              if use_octf
              else None
          )
          model, model_kwargs = self._get_model_and_data(
              batch_shape=batch_shape,
              m=2,
              outcome_transform=octf,
              **tkwargs,
          )
          subset_model = model.subset_output([0])
          X = torch.rand(
              torch.Size(batch_shape + torch.Size([3, 1])), **tkwargs
          )
          p = model.posterior(X)
          p_sub = subset_model.posterior(X)
          self.assertTrue(
              torch.allclose(
                  p_sub.mean, p.mean[..., [0]], atol=1e-4, rtol=1e-4
              )
          )
          self.assertTrue(
              torch.allclose(
                  p_sub.variance,
                  p.variance[..., [0]],
                  atol=1e-4,
                  rtol=1e-4,
              )
          )
          # test subsetting each of the outputs (follows a different code branch)
          subset_all_model = model.subset_output([0, 1])
          p_sub_all = subset_all_model.posterior(X)
          self.assertAllClose(p_sub_all.mean, p.mean)
          # subsetting should still return a copy
          self.assertNotEqual(model, subset_all_model)
  
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 7 for calling the TestSingleTaskGP obj's underlying member method code with example usage: obj.test_subset_model() without return types