code: def test_condition_on_observations(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, model_kwargs = self._get_model_and_data(
              batch_shape=batch_shape,
              m=m,
              outcome_transform=octf,
              **tkwargs,
          )
          # evaluate model
          model.posterior(torch.rand(torch.Size([4, 1]), **tkwargs))
          # test condition_on_observations
          fant_shape = torch.Size([2])
          # fantasize at different input points
          X_fant, Y_fant = _get_random_data(
              batch_shape=fant_shape + batch_shape, m=m, n=3, **tkwargs
          )
          c_kwargs = (
              {"noise": torch.full_like(Y_fant, 0.01)}
              if isinstance(
                  model.likelihood, FixedNoiseGaussianLikelihood
              )
              else {}
          )
          cm = model.condition_on_observations(
              X_fant, Y_fant, **c_kwargs
          )
          # fantasize at same input points (check proper broadcasting)
          c_kwargs_same_inputs = (
              {"noise": torch.full_like(Y_fant[0], 0.01)}
              if isinstance(
                  model.likelihood, FixedNoiseGaussianLikelihood
              )
              else {}
          )
          cm_same_inputs = model.condition_on_observations(
              X_fant[0], Y_fant, **c_kwargs_same_inputs
          )
  
          test_Xs = [
              # test broadcasting single input across fantasy and model batches
              torch.rand(4, 1, **tkwargs),
              # separate input for each model batch and broadcast across
              # fantasy batches
              torch.rand(batch_shape + torch.Size([4, 1]), **tkwargs),
              # separate input for each model and fantasy batch
              torch.rand(
                  fant_shape + batch_shape + torch.Size([4, 1]),
                  **tkwargs,
              ),
          ]
          for test_X in test_Xs:
              posterior = cm.posterior(test_X)
              self.assertEqual(
                  posterior.mean.shape,
                  fant_shape + batch_shape + torch.Size([4, m]),
              )
              posterior_same_inputs = cm_same_inputs.posterior(test_X)
              self.assertEqual(
                  posterior_same_inputs.mean.shape,
                  fant_shape + batch_shape + torch.Size([4, m]),
              )
  
              # check that fantasies of batched model are correct
              if len(batch_shape) > 0 and test_X.dim() == 2:
                  state_dict_non_batch = {
                      key: (val[0] if val.numel() > 1 else val)
                      for key, val in model.state_dict().items()
                  }
                  model_kwargs_non_batch = {
                      "train_X": model_kwargs["train_X"][0],
                      "train_Y": model_kwargs["train_Y"][0],
                  }
                  if "train_Yvar" in model_kwargs:
                      model_kwargs_non_batch[
                          "train_Yvar"
                      ] = model_kwargs["train_Yvar"][0]
                  if model_kwargs["outcome_transform"] is not None:
                      model_kwargs_non_batch[
                          "outcome_transform"
                      ] = Standardize(m=m)
                  model_non_batch = type(model)(
                      **model_kwargs_non_batch
                  )
                  model_non_batch.load_state_dict(state_dict_non_batch)
                  model_non_batch.eval()
                  model_non_batch.likelihood.eval()
                  model_non_batch.posterior(
                      torch.rand(torch.Size([4, 1]), **tkwargs)
                  )
                  c_kwargs = (
                      {"noise": torch.full_like(Y_fant[0, 0, :], 0.01)}
                      if isinstance(
                          model.likelihood, FixedNoiseGaussianLikelihood
                      )
                      else {}
                  )
                  cm_non_batch = (
                      model_non_batch.condition_on_observations(
                          X_fant[0][0], Y_fant[:, 0, :], **c_kwargs
                      )
                  )
                  non_batch_posterior = cm_non_batch.posterior(test_X)
                  self.assertTrue(
                      torch.allclose(
                          posterior_same_inputs.mean[:, 0, ...],
                          non_batch_posterior.mean,
                          atol=1e-3,
                      )
                  )
                  self.assertTrue(
                      torch.allclose(
                          posterior_same_inputs.distribution.covariance_matrix[
                              :, 0, :, :
                          ],
                          non_batch_posterior.distribution.covariance_matrix,
                          atol=1e-3,
                      )
                  )
  
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 5 for calling the TestSingleTaskGP obj's underlying member method code with example usage: obj.test_condition_on_observations() without return types