code: def test_num_output_dims(self):
      for dtype in [torch.float, torch.double]:
          train_x = torch.rand(
              2, 10, 1, device=self.device, dtype=dtype
          )
          train_y = torch.randn(
              2, 10, 3, 5, device=self.device, dtype=dtype
          )
          model = HigherOrderGP(train_x, train_y)
  
          # check that it correctly inferred that this is a batched model
          self.assertEqual(model._num_outputs, 2)
  
          train_x = torch.rand(10, 1, device=self.device, dtype=dtype)
          train_y = torch.randn(
              10, 3, 5, 2, device=self.device, dtype=dtype
          )
          model = HigherOrderGP(train_x, train_y)
  
          # non-batched case
          self.assertEqual(model._num_outputs, 1)
  
          train_x = torch.rand(
              3, 2, 10, 1, device=self.device, dtype=dtype
          )
          train_y = torch.randn(
              3, 2, 10, 3, 5, device=self.device, dtype=dtype
          )
  
          # check the error when using multi-dim batch_shape
          with self.assertRaises(NotImplementedError):
              model = HigherOrderGP(train_x, train_y)
  
imports: import itertools
  from unittest import mock
  import torch
  from botorch.acquisition.objective import PosteriorTransform
  from botorch.models import HigherOrderGP
  from botorch.models.higher_order_gp import FlattenedStandardize
  from botorch.models.transforms.input import Normalize
  from botorch.models.transforms.outcome import Standardize
  from botorch.optim.fit import fit_gpytorch_mll_torch
  from botorch.posteriors import GPyTorchPosterior, TransformedPosterior
  from botorch.sampling import IIDNormalSampler
  from botorch.utils.testing import BotorchTestCase
  from gpytorch.kernels import RBFKernel
  from gpytorch.likelihoods import GaussianLikelihood
  from gpytorch.mlls import ExactMarginalLogLikelihood
  from gpytorch.settings import max_cholesky_size, skip_posterior_variances
label_desc: Use image node_id 2 for calling the TestHigherOrderGP obj's underlying member method code with example usage: obj.test_num_output_dims() without return types