code: def test_gp(self, double_only: bool = False):
      bounds = torch.tensor([[-1.0], [1.0]])
      for (
          batch_shape,
          m,
          dtype,
          use_octf,
          use_intf,
      ) in itertools.product(
          (torch.Size(), torch.Size([2])),
          (1, 2),
          (torch.double,)
          if double_only
          else (torch.float, torch.double),
          (False, True),
          (False, True),
      ):
          tkwargs = {"device": self.device, "dtype": dtype}
          octf = (
              Standardize(m=m, batch_shape=batch_shape)
              if use_octf
              else None
          )
          intf = (
              Normalize(
                  d=1,
                  bounds=bounds.to(**tkwargs),
                  transform_on_train=True,
              )
              if use_intf
              else None
          )
          model, model_kwargs = self._get_model_and_data(
              batch_shape=batch_shape,
              m=m,
              outcome_transform=octf,
              input_transform=intf,
              **tkwargs,
          )
          mll = ExactMarginalLogLikelihood(model.likelihood, model).to(
              **tkwargs
          )
          with warnings.catch_warnings():
              warnings.filterwarnings(
                  "ignore", category=OptimizationWarning
              )
              fit_gpytorch_mll(
                  mll,
                  optimizer_kwargs={"options": {"maxiter": 1}},
                  max_attempts=1,
              )
  
          # test init
          self.assertIsInstance(model.mean_module, ConstantMean)
          self.assertIsInstance(model.covar_module, ScaleKernel)
          matern_kernel = model.covar_module.base_kernel
          self.assertIsInstance(matern_kernel, MaternKernel)
          self.assertIsInstance(
              matern_kernel.lengthscale_prior, GammaPrior
          )
          if use_octf:
              self.assertIsInstance(
                  model.outcome_transform, Standardize
              )
          if use_intf:
              self.assertIsInstance(model.input_transform, Normalize)
              # permute output dim
              train_X, train_Y, _ = model._transform_tensor_args(
                  X=model_kwargs["train_X"], Y=model_kwargs["train_Y"]
              )
              # check that the train inputs have been transformed and set on the model
              self.assertTrue(
                  torch.equal(model.train_inputs[0], intf(train_X))
              )
  
          # test param sizes
          params = dict(model.named_parameters())
          for p in params:
              self.assertEqual(
                  params[p].numel(),
                  m * torch.tensor(batch_shape).prod().item(),
              )
  
          # test posterior
          # test non batch evaluation
          X = torch.rand(batch_shape + torch.Size([3, 1]), **tkwargs)
          expected_shape = batch_shape + torch.Size([3, m])
          posterior = model.posterior(X)
          self.assertIsInstance(posterior, GPyTorchPosterior)
          self.assertEqual(posterior.mean.shape, expected_shape)
          self.assertEqual(posterior.variance.shape, expected_shape)
  
          # test adding observation noise
          posterior_pred = model.posterior(X, observation_noise=True)
          self.assertIsInstance(posterior_pred, GPyTorchPosterior)
          self.assertEqual(posterior_pred.mean.shape, expected_shape)
          self.assertEqual(
              posterior_pred.variance.shape, expected_shape
          )
          if use_octf:
              # ensure un-transformation is applied
              tmp_tf = model.outcome_transform
              del model.outcome_transform
              pp_tf = model.posterior(X, observation_noise=True)
              model.outcome_transform = tmp_tf
              expected_var = tmp_tf.untransform_posterior(
                  pp_tf
              ).variance
              self.assertAllClose(posterior_pred.variance, expected_var)
          else:
              pvar = posterior_pred.variance
              pvar_exp = get_pvar_expected(posterior, model, X, m)
              self.assertAllClose(pvar, pvar_exp, rtol=1e-4, atol=1e-5)
  
          # Tensor valued observation noise.
          obs_noise = torch.rand(X.shape, **tkwargs)
          posterior_pred = model.posterior(
              X, observation_noise=obs_noise
          )
          self.assertIsInstance(posterior_pred, GPyTorchPosterior)
          self.assertEqual(posterior_pred.mean.shape, expected_shape)
          self.assertEqual(
              posterior_pred.variance.shape, expected_shape
          )
          if use_octf:
              _, obs_noise = model.outcome_transform.untransform(
                  obs_noise, obs_noise
              )
          self.assertAllClose(
              posterior_pred.variance, posterior.variance + obs_noise
          )
  
          # test batch evaluation
          X = torch.rand(2, *batch_shape, 3, 1, **tkwargs)
          expected_shape = (
              torch.Size([2]) + batch_shape + torch.Size([3, m])
          )
  
          posterior = model.posterior(X)
          self.assertIsInstance(posterior, GPyTorchPosterior)
          self.assertEqual(posterior.mean.shape, expected_shape)
          # test adding observation noise in batch mode
          posterior_pred = model.posterior(X, observation_noise=True)
          self.assertIsInstance(posterior_pred, GPyTorchPosterior)
          self.assertEqual(posterior_pred.mean.shape, expected_shape)
          if use_octf:
              # ensure un-transformation is applied
              tmp_tf = model.outcome_transform
              del model.outcome_transform
              pp_tf = model.posterior(X, observation_noise=True)
              model.outcome_transform = tmp_tf
              expected_var = tmp_tf.untransform_posterior(
                  pp_tf
              ).variance
              self.assertAllClose(posterior_pred.variance, expected_var)
          else:
              pvar = posterior_pred.variance
              pvar_exp = get_pvar_expected(posterior, model, X, m)
              self.assertAllClose(pvar, pvar_exp, rtol=1e-4, atol=1e-5)
  
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 3 for calling the TestSingleTaskGP obj's underlying member method code with example usage: obj.test_gp(double_only) without return types