code: def test_LCEAGP(self):
      for dtype, infer_noise in (
          (torch.float, False),
          (torch.double, True),
      ):
          tkwargs = {"device": self.device, "dtype": dtype}
          datasets, (train_X, train_Y, train_Yvar) = _gen_datasets(
              infer_noise, **tkwargs
          )
          # Test setting attributes
          decomposition = {"1": [0, 1], "2": [2, 3]}
          # test instantiate model
          model = LCEAGP(
              train_X=train_X,
              train_Y=train_Y,
              train_Yvar=train_Yvar,
              decomposition=decomposition,
          )
          mll = ExactMarginalLogLikelihood(model.likelihood, model)
          fit_gpytorch_mll(
              mll, optimizer_kwargs={"options": {"maxiter": 1}}
          )
  
          self.assertIsInstance(model, LCEAGP)
          self.assertIsInstance(model.covar_module, LCEAKernel)
          self.assertDictEqual(model.decomposition, decomposition)
          self.assertIsInstance(
              model.likelihood,
              GaussianLikelihood
              if infer_noise
              else FixedNoiseGaussianLikelihood,
          )
  
          test_x = torch.rand(5, 4, device=self.device, dtype=dtype)
          posterior = model(test_x)
          self.assertIsInstance(posterior, MultivariateNormal)
  
imports: from typing import Dict, Tuple
  import torch
  from botorch.fit import fit_gpytorch_mll
  from botorch.models.contextual import LCEAGP, SACGP
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.kernels.contextual_lcea import LCEAKernel
  from botorch.models.kernels.contextual_sac import SACKernel
  from botorch.utils.datasets import SupervisedDataset
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.distributions.multivariate_normal import MultivariateNormal
  from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood, GaussianLikelihood
  from gpytorch.means import ConstantMean
  from gpytorch.mlls.exact_marginal_log_likelihood import ExactMarginalLogLikelihood
  from torch import Tensor
label_desc: Use image node_id 3 for calling the TestContextualGP obj's underlying member method code with example usage: obj.test_LCEAGP() without return types