code: def test_get_model(self) -> None:
      x = torch.rand(2, 2)
      y = torch.rand(2, 1)
      var = torch.rand(2, 1)
      partial_var = torch.tensor([0, float("nan")]).unsqueeze(-1)
      unknown_var = torch.tensor(
          [float("nan"), float("nan")]
      ).unsqueeze(-1)
      model = _get_model(x, y, unknown_var, None)
      self.assertIsInstance(model, SingleTaskGP)
      self.assertIsInstance(model.likelihood, GaussianLikelihood)
  
      model = _get_model(X=x, Y=y, Yvar=var)
      self.assertIsInstance(model, SingleTaskGP)
      self.assertIsInstance(
          model.likelihood, FixedNoiseGaussianLikelihood
      )
      self.assertEqual(
          model.covar_module.base_kernel.lengthscale_prior.concentration,
          3.0,
      )
      self.assertEqual(
          model.covar_module.base_kernel.lengthscale_prior.rate, 6.0
      )
      model = _get_model(X=x, Y=y, Yvar=unknown_var, task_feature=1)
      self.assertIs(
          type(model), MultiTaskGP
      )  # Don't accept subclasses.
      self.assertIsInstance(model.likelihood, GaussianLikelihood)
      model = _get_model(X=x, Y=y, Yvar=var, task_feature=1)
      self.assertIsInstance(model, MultiTaskGP)
      self.assertIsInstance(
          model.likelihood, FixedNoiseGaussianLikelihood
      )
      model = _get_model(
          X=x, Y=y, Yvar=partial_var.clone(), task_feature=1
      )
      self.assertIsInstance(model, MultiTaskGP)
      model = _get_model(
          X=x, Y=y, Yvar=partial_var.clone(), task_feature=1, rank=1
      )
      self.assertEqual(model._rank, 1)
      with self.assertRaises(ValueError):
          model = _get_model(
              X=x, Y=y, Yvar=partial_var, task_feature=None
          )
      model = _get_model(X=x, Y=y, Yvar=var, fidelity_features=[-1])
      self.assertTrue(isinstance(model, SingleTaskMultiFidelityGP))
      with self.assertRaises(NotImplementedError):
          _get_model(
              X=x, Y=y, Yvar=var, task_feature=1, fidelity_features=[-1]
          )
      # test fixed prior
      kwargs = {
          "prior": {
              "type": LKJCovariancePrior,
              "sd_prior": GammaPrior(2.0, 0.44),
              "eta": 0.6,
          }
      }
      # pyre-fixme[6]: For 5th param expected `Optional[List[int]]` but got
      #  `Dict[str, Union[Type[LKJCovariancePrior], float, GammaPrior]]`.
      # pyre-fixme[6]: For 5th param expected `bool` but got `Dict[str,
      #  Union[Type[LKJCovariancePrior], float, GammaPrior]]`.
      model = _get_model(
          X=x, Y=y, Yvar=partial_var.clone(), task_feature=1, **kwargs
      )
      self.assertIsInstance(
          model.task_covar_module.IndexKernelPrior,
          LKJCovariancePrior,
      )
      self.assertEqual(
          model.task_covar_module.IndexKernelPrior.sd_prior.concentration,
          2.0,
      )
      self.assertEqual(
          model.task_covar_module.IndexKernelPrior.sd_prior.rate, 0.44
      )
      self.assertEqual(
          model.task_covar_module.IndexKernelPrior.correlation_prior.eta,
          0.6,
      )
  
      kwargs2 = {"prior": {"type": LKJCovariancePrior}}
      model = _get_model(
          X=x,
          Y=y,
          Yvar=partial_var.clone(),
          task_feature=1,
          # pyre-fixme[6]: For 5th param expected `Optional[List[int]]` but got
          #  `Dict[str, Type[LKJCovariancePrior]]`.
          # pyre-fixme[6]: For 5th param expected `bool` but got `Dict[str,
          #  Type[LKJCovariancePrior]]`.
          **kwargs2,
      )
      self.assertIsInstance(
          model.task_covar_module.IndexKernelPrior,
          LKJCovariancePrior,
      )
      self.assertEqual(
          model.task_covar_module.IndexKernelPrior.sd_prior.concentration,
          1.0,
      )
      self.assertEqual(
          model.task_covar_module.IndexKernelPrior.sd_prior.rate, 0.15
      )
      self.assertEqual(
          model.task_covar_module.IndexKernelPrior.correlation_prior.eta,
          0.5,
      )
      kwargs3 = {
          "prior": {
              "type": LKJCovariancePrior,
              "sd_prior": GammaPrior(2.0, 0.44),
              "eta": "hi",
          }
      }
      with self.assertRaises(ValueError):
          # pyre-fixme[6]: For 5th param expected `Optional[List[int]]` but got
          #  `Dict[str, Union[Type[LKJCovariancePrior], GammaPrior, str]]`.
          # pyre-fixme[6]: For 5th param expected `bool` but got `Dict[str,
          #  Union[Type[LKJCovariancePrior], GammaPrior, str]]`.
          _get_model(
              X=x,
              Y=y,
              Yvar=partial_var.clone(),
              task_feature=1,
              **kwargs3,
          )
  
      kwargs5 = {
          "prior": {
              "type": Prior,
              "sd_prior": GammaPrior(2.0, 0.44),
              "eta": 0.5,
          }
      }
      with self.assertRaises(NotImplementedError):
          # pyre-fixme[6]: For 5th param expected `Optional[List[int]]` but got
          #  `Dict[str, Union[Type[Prior], float, GammaPrior]]`.
          # pyre-fixme[6]: For 5th param expected `bool` but got `Dict[str,
          #  Union[Type[Prior], float, GammaPrior]]`.
          _get_model(
              X=x,
              Y=y,
              Yvar=partial_var.clone(),
              task_feature=1,
              **kwargs5,
          )
      # test passing customized prior
      kwargs6 = {
          "prior": {
              "covar_module_prior": {
                  "lengthscale_prior": GammaPrior(12.0, 2.0)
              },
              "type": LKJCovariancePrior,
          }
      }
      model = _get_model(
          X=x, Y=y, Yvar=var, **deepcopy(kwargs6)
      )  # pyre-ignore
      self.assertIsInstance(model, SingleTaskGP)
      self.assertEqual(
          model.covar_module.base_kernel.lengthscale_prior.concentration,
          12.0,
      )
      self.assertEqual(
          model.covar_module.base_kernel.lengthscale_prior.rate, 2.0
      )
      model = _get_model(
          X=x,
          Y=y,
          Yvar=unknown_var,
          task_feature=1,
          **deepcopy(kwargs6),  # pyre-ignore
      )
      self.assertIs(type(model), MultiTaskGP)
      self.assertIsInstance(model.likelihood, GaussianLikelihood)
      self.assertEqual(
          model.covar_module.base_kernel.lengthscale_prior.concentration,
          12.0,
      )
      self.assertEqual(
          model.covar_module.base_kernel.lengthscale_prior.rate, 2.0
      )
      self.assertIsInstance(
          model.task_covar_module.IndexKernelPrior,
          LKJCovariancePrior,
      )
      model = _get_model(
          X=x,
          Y=y,
          Yvar=var,
          task_feature=1,
          **deepcopy(kwargs6),  # pyre-ignore
      )
      self.assertIsInstance(model, MultiTaskGP)
      self.assertIsInstance(
          model.likelihood, FixedNoiseGaussianLikelihood
      )
      self.assertEqual(
          model.covar_module.base_kernel.lengthscale_prior.concentration,
          12.0,
      )
      self.assertEqual(
          model.covar_module.base_kernel.lengthscale_prior.rate, 2.0
      )
      self.assertIsInstance(
          model.task_covar_module.IndexKernelPrior, LKJCovariancePrior
      )
      # test passing customized prior
      kwargs7 = {
          "prior": {
              "covar_module_prior": {
                  "lengthscale_prior": GammaPrior(12.0, 2.0)
              },
          }
      }
      covar_module = MaternKernel(
          nu=2.5,
          ard_num_dims=2,
          lengthscale_prior=GammaPrior(6.0, 6.0),
      )
      model = _get_model(
          X=x,
          Y=y,
          Yvar=var,
          covar_module=covar_module,
          **kwargs7,  # pyre-ignore
      )
      self.assertIsInstance(model, SingleTaskGP)
      self.assertIsInstance(
          model.likelihood, FixedNoiseGaussianLikelihood
      )
      self.assertEqual(covar_module, model.covar_module)
  
      # test input warping dimension checks.
      with self.assertRaisesRegex(
          UnsupportedError, "batched multi output models"
      ):
          _get_model(
              X=torch.ones(4, 3, 2),
              Y=torch.ones(4, 3, 2),
              Yvar=torch.zeros(4, 3, 2),
              use_input_warping=True,
          )
  
imports: from copy import deepcopy
  from unittest import mock
  from unittest.mock import Mock
  import torch
  from ax.models.torch.botorch_defaults import _get_acquisition_func, _get_customized_covar_module, _get_model, get_and_fit_model, get_warping_transform, NO_FEASIBLE_POINTS_MESSAGE
  from ax.utils.common.testutils import TestCase
  from ax.utils.common.typeutils import checked_cast, not_none
  from ax.utils.testing.mock import fast_botorch_optimize
  from botorch.acquisition.logei import qLogExpectedImprovement, qLogNoisyExpectedImprovement
  from botorch.acquisition.monte_carlo import qExpectedImprovement, qNoisyExpectedImprovement, qProbabilityOfImprovement, qSimpleRegret
  from botorch.acquisition.objective import ConstrainedMCObjective
  from botorch.acquisition.penalized import L1PenaltyObjective, PenalizedMCObjective
  from botorch.exceptions.errors import UnsupportedError
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.gp_regression_fidelity import SingleTaskMultiFidelityGP
  from botorch.models.multitask import MultiTaskGP
  from botorch.models.transforms.input import Warp
  from botorch.utils.constraints import get_outcome_constraint_transforms
  from gpytorch.kernels import MaternKernel, ScaleKernel
  from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood, GaussianLikelihood
  from gpytorch.module import Module
  from gpytorch.priors import GammaPrior
  from gpytorch.priors.lkj_prior import LKJCovariancePrior
  from gpytorch.priors.prior import Prior
label_desc: Use image node_id 1 for calling the BotorchDefaultsTest obj's underlying member method code with example usage: obj.test_get_model() without return types