code: def test_ModelListGP_multi_task(self):
      tkwargs = {"device": self.device, "dtype": torch.float}
      train_x_raw, train_y = _get_random_data(
          batch_shape=torch.Size(), m=1, n=10, **tkwargs
      )
      task_idx = torch.cat(
          [torch.ones(5, 1, **tkwargs), torch.zeros(5, 1, **tkwargs)],
          dim=0,
      )
      train_x = torch.cat([train_x_raw, task_idx], dim=-1)
      model = MultiTaskGP(
          train_X=train_x,
          train_Y=train_y,
          task_feature=-1,
          output_tasks=[0],
      )
      # Wrap a single single-output MTGP.
      model_list_gp = ModelListGP(model)
      self.assertEqual(model_list_gp.num_outputs, 1)
      with torch.no_grad():
          model_mean = model.posterior(train_x_raw).mean
          model_list_gp_mean = model_list_gp.posterior(train_x_raw).mean
      self.assertAllClose(model_mean, model_list_gp_mean)
      # Wrap two single-output MTGPs.
      model_list_gp = ModelListGP(model, model)
      self.assertEqual(model_list_gp.num_outputs, 2)
      with torch.no_grad():
          model_list_gp_mean = model_list_gp.posterior(train_x_raw).mean
      expected_mean = torch.cat([model_mean, model_mean], dim=-1)
      self.assertAllClose(expected_mean, model_list_gp_mean)
      # Wrap a multi-output MTGP.
      model2 = MultiTaskGP(
          train_X=train_x,
          train_Y=train_y,
          task_feature=-1,
      )
      model_list_gp = ModelListGP(model2)
      self.assertEqual(model_list_gp.num_outputs, 2)
      with torch.no_grad():
          model2_mean = model2.posterior(train_x_raw).mean
          model_list_gp_mean = model_list_gp.posterior(train_x_raw).mean
      self.assertAllClose(model2_mean, model_list_gp_mean)
      # Mix of multi-output and single-output MTGPs.
      model_list_gp = ModelListGP(model, model2, deepcopy(model))
      self.assertEqual(model_list_gp.num_outputs, 4)
      with torch.no_grad():
          posterior = model_list_gp.posterior(train_x_raw)
      expected_mean = torch.cat(
          [model_mean, model2_mean, model_mean], dim=-1
      )
      self.assertAllClose(expected_mean, posterior.mean)
      C1 = model.posterior(train_x_raw).covariance_matrix
      C2 = model2.posterior(train_x_raw).covariance_matrix[:10, :10]
      C3 = model2.posterior(train_x_raw).covariance_matrix[-10:, -10:]
      expected_covariance = torch.block_diag(C1, C2, C3, C1)
      self.assertTrue(
          torch.allclose(
              expected_covariance,
              posterior.covariance_matrix,
              atol=1e-5,
          )
      )
      # test subset outputs
      subset_model = model_list_gp.subset_output([1])
      self.assertEqual(subset_model.num_outputs, 2)
      subset_model = model_list_gp.subset_output([0, 1])
      self.assertEqual(subset_model.num_outputs, 3)
      self.assertEqual(len(subset_model.models), 2)
      # Test condition on observations
      model_s1 = SingleTaskGP(
          train_X=train_x_raw,
          train_Y=train_y,
      )
      model_list_gp = ModelListGP(model_s1, model2, deepcopy(model_s1))
      model_list_gp.posterior(train_x_raw)
      f_x = [torch.rand(5, 1, **tkwargs) for _ in range(2)]
      C1 = torch.cat((f_x[0], torch.zeros(5, 1, **tkwargs)), dim=-1)
      C2 = torch.cat((f_x[1], torch.ones(5, 1, **tkwargs)), dim=-1)
      f_x2 = [f_x[0], C1, C2, f_x[1]]
      f_y = torch.rand(5, 4, **tkwargs)
      cm = model_list_gp.condition_on_observations(f_x2, f_y)
      self.assertIsInstance(cm, ModelListGP)
      self.assertEqual(cm.num_outputs, 4)
      self.assertEqual(len(cm.models), 3)
      for i in [0, 2]:
          self.assertIsInstance(cm.models[i], SingleTaskGP)
          self.assertEqual(
              cm.models[i].train_inputs[0].shape, torch.Size([15, 1])
          )
      self.assertIsInstance(cm.models[1], MultiTaskGP)
      self.assertEqual(
          cm.models[1].train_inputs[0].shape, torch.Size([20, 2])
      )
  
imports: import itertools
  import warnings
  from copy import deepcopy
  from typing import Optional
  import torch
  from botorch.acquisition.objective import ScalarizedPosteriorTransform
  from botorch.exceptions.errors import BotorchTensorDimensionError
  from botorch.exceptions.warnings import OptimizationWarning
  from botorch.fit import fit_gpytorch_mll
  from botorch.models.gp_regression import SingleTaskGP
  from botorch.models.model_list_gp_regression import ModelListGP
  from botorch.models.multitask import MultiTaskGP
  from botorch.models.transforms.input import Normalize
  from botorch.models.transforms.outcome import ChainedOutcomeTransform, Log, Standardize
  from botorch.posteriors import GPyTorchPosterior, PosteriorList, TransformedPosterior
  from botorch.sampling.base import MCSampler
  from botorch.sampling.list_sampler import ListSampler
  from botorch.sampling.normal import IIDNormalSampler
  from botorch.utils.testing import _get_random_data, BotorchTestCase
  from gpytorch.distributions import MultitaskMultivariateNormal, MultivariateNormal
  from gpytorch.kernels import MaternKernel, ScaleKernel
  from gpytorch.likelihoods import LikelihoodList
  from gpytorch.likelihoods.gaussian_likelihood import FixedNoiseGaussianLikelihood, GaussianLikelihood
  from gpytorch.means import ConstantMean
  from gpytorch.mlls import SumMarginalLogLikelihood
  from gpytorch.mlls.exact_marginal_log_likelihood import ExactMarginalLogLikelihood
  from gpytorch.priors import GammaPrior
  from torch import Tensor
label_desc: Use image node_id 5 for calling the TestModelListGP obj's underlying member method code with example usage: obj.test_ModelListGP_multi_task() without return types