code: def test_initializations(self):
      train_X = torch.rand(15, 1, device=self.device)
      train_Y = torch.rand(15, 1, device=self.device)
  
      stacked_train_X = torch.cat((train_X, train_X), dim=0)
      for X, num_ind in [
          [train_X, 5],
          [stacked_train_X, 20],
          [stacked_train_X, 5],
      ]:
          model = SingleTaskVariationalGP(
              train_X=X, inducing_points=num_ind
          )
          if num_ind == 5:
              self.assertLessEqual(
                  model.model.variational_strategy.inducing_points.shape,
                  torch.Size((5, 1)),
              )
          else:
              # should not have 20 inducing points when 15 singular dimensions
              # are passed
              self.assertLess(
                  model.model.variational_strategy.inducing_points.shape[
                      -2
                  ],
                  num_ind,
              )
  
      test_X = torch.rand(5, 1, device=self.device)
  
      # test transforms
      for inp_trans, out_trans in itertools.product(
          [None, Normalize(d=1)], [None, Log()]
      ):
          model = SingleTaskVariationalGP(
              train_X=train_X,
              train_Y=train_Y,
              outcome_transform=out_trans,
              input_transform=inp_trans,
          )
  
          if inp_trans is not None:
              self.assertIsInstance(model.input_transform, Normalize)
          else:
              self.assertFalse(hasattr(model, "input_transform"))
          if out_trans is not None:
              self.assertIsInstance(model.outcome_transform, Log)
  
              posterior = model.posterior(test_X)
              self.assertIsInstance(posterior, TransformedPosterior)
          else:
              self.assertFalse(hasattr(model, "outcome_transform"))
  
      # test default inducing point allocator
      self.assertIsInstance(
          model._inducing_point_allocator, GreedyVarianceReduction
      )
  
      # test that can specify an inducing point allocator
      for ipa in [
          GreedyVarianceReduction(),
          GreedyImprovementReduction(model, maximize=True),
      ]:
          model = SingleTaskVariationalGP(
              train_X, inducing_point_allocator=ipa
          )
          self.assertTrue(
              type(model._inducing_point_allocator), type(ipa)
          )
  
      # test warning when learning on and custom IPA provided
      with self.assertWarnsRegex(
          UserWarning, r"set `learn_inducing_points` to False"
      ):
          SingleTaskVariationalGP(
              train_X,
              learn_inducing_points=True,
              inducing_point_allocator=GreedyVarianceReduction(),
          )
  
imports: import itertools
  import warnings
  import torch
  from botorch.fit import fit_gpytorch_mll
  from botorch.models.approximate_gp import _SingleTaskVariationalGP, ApproximateGPyTorchModel, SingleTaskVariationalGP
  from botorch.models.transforms.input import Normalize
  from botorch.models.transforms.outcome import Log
  from botorch.models.utils.inducing_point_allocators import GreedyImprovementReduction, GreedyVarianceReduction
  from botorch.posteriors import GPyTorchPosterior, TransformedPosterior
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.likelihoods import GaussianLikelihood, MultitaskGaussianLikelihood
  from gpytorch.mlls import VariationalELBO
  from gpytorch.variational import IndependentMultitaskVariationalStrategy, VariationalStrategy
label_desc: Use image node_id 5 for calling the TestSingleTaskVariationalGP obj's underlying member method code with example usage: obj.test_initializations() without return types