code: def test_MultitaskGPPosterior(self):
      sample_shaping = torch.Size([5, 3])
  
      for post_collection in self.post_list:
          model, test_x, posterior = post_collection
  
          self.assertIsInstance(posterior, MultitaskGPPosterior)
  
          batch_shape = test_x.shape[:-2]
          expected_extended_shape = batch_shape + sample_shaping
  
          self.assertEqual(
              posterior._extended_shape(), expected_extended_shape
          )
  
          # test providing no base samples
          samples_0 = posterior.rsample()
          self.assertEqual(
              samples_0.shape, torch.Size((1, *expected_extended_shape))
          )
  
          # test that providing all base samples produces non-torch.random results
          scale = 2 if posterior.observation_noise else 1
          base_sample_shaping = torch.Size(
              [
                  2 * model.train_targets.numel()
                  + scale * sample_shaping[0] * sample_shaping[1]
              ]
          )
  
          expected_base_sample_shape = batch_shape + base_sample_shaping
          self.assertEqual(
              posterior.base_sample_shape,
              expected_base_sample_shape,
          )
          base_samples = torch.randn(
              8, *expected_base_sample_shape, device=self.device
          )
  
          samples_1 = posterior.rsample_from_base_samples(
              base_samples=base_samples, sample_shape=torch.Size((8,))
          )
          samples_2 = posterior.rsample_from_base_samples(
              base_samples=base_samples, sample_shape=torch.Size((8,))
          )
          self.assertTrue(torch.allclose(samples_1, samples_2))
  
          # test that botorch.sampler picks up the correct shapes
          sampler = IIDNormalSampler(sample_shape=torch.Size([5]))
          samples_det_shape = sampler(posterior).shape
          self.assertEqual(
              samples_det_shape,
              torch.Size([5, *expected_extended_shape]),
          )
  
          # test that providing only some base samples is okay
          base_samples = torch.randn(
              8, np.prod(expected_extended_shape), device=self.device
          )
          samples_3 = posterior.rsample_from_base_samples(
              base_samples=base_samples, sample_shape=torch.Size((8,))
          )
          self.assertEqual(
              samples_3.shape, torch.Size([8, *expected_extended_shape])
          )
  
          # test that providing the wrong number base samples errors out
          base_samples = torch.randn(8, 50 * 2 * 3, device=self.device)
          with self.assertRaises(BotorchTensorDimensionError):
              posterior.rsample_from_base_samples(
                  base_samples=base_samples,
                  sample_shape=torch.Size((8,)),
              )
  
          # test that providing the wrong shapes of base samples fails
          base_samples = torch.randn(8, 5 * 2 * 3, device=self.device)
          with self.assertRaises(RuntimeError):
              posterior.rsample_from_base_samples(
                  base_samples=base_samples,
                  sample_shape=torch.Size((4,)),
              )
  
          # finally we check the quality of the variances and the samples
          # test that the posterior variances are the same as the evaluation variance
          posterior_variance = posterior.variance
          posterior_mean = posterior.mean.view(-1)
  
          model.eval()
          if not posterior.observation_noise:
              eval_mode_variance = model(test_x).variance
          else:
              eval_mode_variance = model.likelihood(
                  model(test_x)
              ).variance
          eval_mode_variance = eval_mode_variance.reshape_as(
              posterior_variance
          )
  
          self.assertLess(
              (posterior_variance - eval_mode_variance).norm()
              / eval_mode_variance.norm(),
              4e-2,
          )
  
          # and finally test that sampling with no base samples is okay
          samples_3 = posterior.rsample(
              sample_shape=torch.Size((10000,))
          )
          sampled_variance = samples_3.var(dim=0).view(-1)
          sampled_mean = samples_3.mean(dim=0).view(-1)
  
          posterior_variance = posterior_variance.view(-1)
  
          # slightly higher tolerance here because of the potential for low norms
          self.assertLess(
              (posterior_mean - sampled_mean).norm()
              / posterior_mean.norm(),
              0.12,
          )
          self.assertLess(
              (posterior_variance - sampled_variance).norm()
              / posterior_variance.norm(),
              5e-2,
          )
  
file_path: botorch/test/posteriors/test_multitask.py
imports: import numpy
  import torch
  from botorch.exceptions.errors import BotorchTensorDimensionError
  from botorch.models.multitask import KroneckerMultiTaskGP
  from botorch.posteriors.multitask import MultitaskGPPosterior
  from botorch.sampling.normal import IIDNormalSampler
  from botorch.utils.testing import BotorchTestCase
label_desc: Use image node_id 2 for calling the TestMultitaskGPPosterior obj's underlying member method code with example usage: obj.test_MultitaskGPPosterior() without return types