code: def test_scalarized_posterior_transform(self):
      for batch_shape, m, dtype in itertools.product(
          ([], [3]), (1, 2), (torch.float, torch.double)
      ):
          offset = torch.rand(1).item()
          weights = torch.randn(m, device=self.device, dtype=dtype)
          obj = ScalarizedPosteriorTransform(
              weights=weights, offset=offset
          )
          posterior = _get_test_posterior(
              batch_shape, m=m, device=self.device, dtype=dtype
          )
          mean, covar = (
              posterior.distribution.mean,
              posterior.distribution.covariance_matrix,
          )
          new_posterior = obj(posterior)
          exp_size = torch.Size(batch_shape + [1, 1])
          self.assertEqual(new_posterior.mean.shape, exp_size)
          new_mean_exp = offset + mean @ weights
          self.assertAllClose(new_posterior.mean[..., -1], new_mean_exp)
          self.assertEqual(new_posterior.variance.shape, exp_size)
          new_covar_exp = ((covar @ weights) @ weights).unsqueeze(-1)
          self.assertTrue(
              torch.allclose(
                  new_posterior.variance[..., -1], new_covar_exp
              )
          )
          # test error
          with self.assertRaises(ValueError):
              ScalarizedPosteriorTransform(weights=torch.rand(2, m))
          # test evaluate
          Y = torch.rand(2, m, device=self.device, dtype=dtype)
          val = obj.evaluate(Y)
          val_expected = offset + Y @ weights
          self.assertTrue(torch.equal(val, val_expected))
  
imports: import itertools
  import warnings
  from typing import Optional
  import torch
  from botorch import settings
  from botorch.acquisition import LearnedObjective
  from botorch.acquisition.objective import ConstrainedMCObjective, DEFAULT_NUM_PREF_SAMPLES, ExpectationPosteriorTransform, GenericMCObjective, IdentityMCObjective, LEARNED_OBJECTIVE_PREF_MODEL_MIXED_DTYPE_WARN, LinearMCObjective, MCAcquisitionObjective, PosteriorTransform, ScalarizedPosteriorTransform
  from botorch.exceptions.errors import UnsupportedError
  from botorch.exceptions.warnings import _get_single_precision_warning, InputDataWarning
  from botorch.models.deterministic import PosteriorMeanModel
  from botorch.models.pairwise_gp import PairwiseGP
  from botorch.models.transforms.input import Normalize
  from botorch.posteriors import GPyTorchPosterior
  from botorch.utils import apply_constraints
  from botorch.utils.testing import _get_test_posterior, BotorchTestCase
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from linear_operator.operators.dense_linear_operator import to_linear_operator
  from torch import Tensor
label_desc: Use image node_id 1 for calling the TestScalarizedPosteriorTransform obj's underlying member method code with example usage: obj.test_scalarized_posterior_transform() without return types